Answers
The above proof is given as follows;
FG ≅ HI - Given
FG ║ HI - Given
∠FHI ≅ ∠GFH - Alternate angles
FH ≅ FH - Reflexive Property
ΔFGH ≅ ΔHIF - Side-Angle-Side Postulate
FI ≅ GH - Definition of parallelogram.
A parallelogram is a four-sided figure with opposite sides parallel and congruent. Here are the properties of a parallelogram:
Opposite sides are parallel: The opposite sides of a parallelogram are parallel to each other. That is, they never meet even if extended infinitely.Opposite sides are congruent: The opposite sides of a parallelogram are of equal length.Opposite angles are congruent: The opposite angles of a parallelogram are of equal measure.Consecutive angles are supplementary: The consecutive angles of a parallelogram add up to 180 degrees.Diagonals bisect each other: The diagonals of a parallelogram intersect at their midpoint. That is, the line segment joining the midpoint of the two diagonals is half the length of the diagonal.Each diagonal divides the parallelogram into two congruent triangles: The two diagonals of a parallelogram divide it into four congruent triangles.Learn more about reflexive properties:
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Related Questions
Kate had some fruits at her stall. 3/4 of them were mangosteens, 1/3 of the remainder were apples and the rest were coconuts. The amounts earned for each mangosteen, each Fuji apple and each coconut sold are $1.50, $3.00 and $4.50 respectively. The number of mangosteens sold to the number of apples sold to the number of coconuts sold was 3:5:3. In total, she sold 1/4 of the fruits and earned $198. How many coconuts did she have at first?
Answers
According to the question the Kate had [tex]$\frac{4}{7}$[/tex] coconuts at her stall.
What is coconut?Coconut is a tropical fruit that grows on palm trees. It is a large, egg-shaped drupe with a hard outer shell and a white fleshy inner layer. The flesh of the coconut is rich in vitamins, minerals, and fiber, and it is also a source of healthy fats. Coconut can be eaten fresh, dried, or even in the form of coconut milk or oil.
First, we will calculate the total number of fruits Kate had at her stall. To do this, we need to solve for x in the equation [tex]$\frac{3}{4}x + \frac{1}{3}(\frac{3}{4}x - x) + (\frac{3}{4}x - \frac{1}{3}(\frac{3}{4}x - x)) = x$.[/tex]
Solving for x, we get [tex]$x = \frac{8}{7}$.[/tex]
Therefore, Kate had [tex]$\frac{8}{7}$[/tex]fruits at her stall.
Next, we need to calculate the number of coconuts she had at first. We know that she sold 1/4 of the fruits, or [tex]$\frac{2}{7}$[/tex] of the fruits. We also know that the ratio of mangosteens sold to apples sold to coconuts sold was 3:5:3.
Therefore, the number of coconuts sold was [tex]$\frac{2}{7} \times \frac{3}{13} = \frac{6}{91}$[/tex].
The total amount earned from the coconuts sold was [tex]$\frac{6}{91} \times 4.50 = \frac{27}{91}$[/tex].
Subtracting this from the total amount earned, 198, we get [tex]$198 - \frac{27}{91} = \frac{171}{91}$[/tex].
This is the amount earned from the mangosteens and apples sold. The amount earned from each mangosteen sold was 1.50, and the amount earned from each Fuji apple sold was 3.00.
Therefore, to get the total amount earned from mangosteens and apples, we need to solve for x in the equation [tex]$\frac{2}{7} \times x + \frac{2}{7} \times 3x = \frac{171}{91}$[/tex].
Solving for x, we get [tex]$x = \frac{171}{171}$[/tex].
This means that the total number of mangosteens and apples sold was $\frac{171}{171}$. Since the ratio of mangosteens sold to apples sold was 3:5, the number of mangosteens sold was [tex]$\frac{3}{8}$[/tex] and the number of apples sold was $\frac{5}{8}$.
Therefore, the number of coconuts at first was [tex]$\frac{8}{7} - \frac{3}{8} - \frac{5}{8} = \frac{4}{7}$[/tex].
Therefore, Kate had [tex]$\frac{4}{7}$[/tex] coconuts at her stall.
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Can someone explain this to me and how can I find unknown angles in geometric figures please tell me everything about it I am really confused and I don’t no how to do it so please help *
Answers
The value of the missing angles of the diagram are:
1) ∠ADC = 134°
2) ∠AEB = 84°
∠EBC = 92°
How to find the missing angles?1) We are told that ABD is an Isosceles Triangle. Thus:
If ∠BAD = 32°, then we know that the two base angles are equal and as such if the sum of the angles of a triangle is 180 degrees, then we have:
∠ABD ≅ ∠ADB = (180 - 32)/2
= 74°
All equilateral triangles have each of their interior angles as 60°. Thus:
∠ADC = 74 + 60
= 134°
2) The two base angles of an Isosceles triangle are equal and as such:
∠BAE = ∠ABE = 48°
∠AEB = 180 - 2(48)
= 84°
By the concept of Alternate angles, we know that:
∠DEA = ∠BAE = 48°
Sum of angles on a straight line is 180 degrees. Thus:
∠BEC = 180 - (84 + 48)
∠BEC = 48°
∠EBC = 180 - (40 + 48) = 92°
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The table shows median annual earnings for women and men with various levels of education. As a percentage, how much more does a man with a bachelor's degree earn than a woman with a bachelor's degree? Assuming the difference remains constant over a 40-year career, how much more does the man earn than the woman? High School Only Associate's degree Only Bachelor's degree Only Professional Degree Women $ 21 comma 481 21,481 $ 39 comma 537 39,537 $ 49 comma 314 49,314 $ 80 comma 181 80,181 Men $ 40 comma 195 40,195 $ 50 comma 759 50,759 $ 66 comma 612 66,612 $ 119 comma 456 119,456 A man with a bachelor's degree earns nothing % more annually than a woman with a bachelor's degree. (Round to the nearest whole number as needed. ) Over a 40-year career, a man with a bachelor's degree earns $ nothing more than a woman with a bachelor's degree. (Round to the nearest whole number as needed. ) Enter your answer in each of the answer boxes
Answers
A man with a bachelor's degree earns 34% more annually than a woman with a bachelor's degree. Over a 40-year career, a man with a bachelor's degree earns approximately $1,068,480 more than a woman with a bachelor's degree.
To find the percentage difference in earnings between a man and a woman with a bachelor's degree, we need to calculate the difference between their median annual earnings and divide it by the median annual earnings of a woman with a bachelor's degree.
Percentage difference = ((median annual earnings of a man with a bachelor's degree - median annual earnings of a woman with a bachelor's degree) / median annual earnings of a woman with a bachelor's degree)) x 100
= ((66,612 - 49,314) / 49,314) x 100
= 34%
Therefore, a man with a bachelor's degree earns 34% more annually than a woman with a bachelor's degree.
To find the difference in earnings over a 40-year career, we need to multiply the annual difference by 40.
Difference in earnings over 40 years = (66,612 - 49,314) x 40
= $657,480
Therefore, a man with a bachelor's degree earns approximately $657,480 more than a woman with a bachelor's degree over a 40-year career.
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The probabilities that two hunters P and Q hit their targets are and respectively. The two hunters aim at a target together. (a) What is the probability that they both miss the target? (b) if the target is hit, what is the probability that; (i) only hunter P hits it?(ii) only one of them hits it? (iii) both hunters hit the target?
Answers
Answer: Let the probability that hunter P hits the target be denoted by "p", and the probability that hunter Q hits the target be denoted by "q".
(a) The probability that they both miss the target is given by:
(1-p)*(1-q)
(b) If the target is hit, then there are three possible outcomes:
(i) Only hunter P hits it: The probability of this event is given by:
p*(1-q)
(ii) Only hunter Q hits it: The probability of this event is given by:
(1-p)*q
(iii) Both hunters hit the target: The probability of this event is given by:
p*q
Note that the sum of the probabilities in (i), (ii), and (iii) is equal to 1, since one of these three events must occur if the target is hit.
Brainliest is so much appreciated. (:
(0)
Radio direction finders are placed at points A and B, which are 4.32 mi apart on an east-west line, with A west of B. The transmitter has bearings 10.1 from A and 310.1 from B. Find the distance from A.
Answers
2.95 miles
The question involves radio direction finders placed at two points, A and B, which are 4.32 miles apart on an east-west line. The transmitter has bearings 10.1 degrees from A and 310.1 degrees from B. The task is to determine the distance from A.In order to determine the distance from A, the first step is to construct a diagram of the scenario to visualize the placement of the three points, A, B, and the transmitter. To do so, a coordinate system is used, with A being located at the origin (0,0).The bearing of the transmitter from A is 10.1 degrees, which can be plotted on the diagram as a straight line from the origin to an angle of 10.1 degrees to the east. Similarly, the bearing of the transmitter from B is 310.1 degrees, which can be plotted on the diagram as a straight line from point B to an angle of 49.9 degrees to the west.To determine the distance from A, the Law of Cosines can be applied, which states that c^2 = a^2 + b^2 − 2ab cos(C), where c is the unknown side, a and b are the known sides, and C is the angle opposite the unknown side. In this case, c is the distance from A, a is the distance from B, and b is the distance between A and B. The angle C is equal to the sum of the two bearings (10.1 + 49.9 = 60 degrees).Therefore, c^2 = a^2 + b^2 − 2ab cos(C) can be rewritten as:dA^2 = d^2 + 4.32^2 - 2d(4.32)cos(60)dA^2 = d^2 + 4.32^2 - 2d(4.32)(1/2)dA^2 = d^2 + 4.32^2 - 2.16dTo solve for dA, the equation can be rearranged and solved for d:0 = d^2 - 2.16d + dA^2 - 4.32^2d = 1.08 ± sqrt(1.08^2 - dA^2 + 4.32^2)The positive root of this equation can be used to determine dA:dA = 1.08 + sqrt(1.08^2 - d^2 + 4.32^2)dA = 1.08 + sqrt(1.08^2 - 4.32^2 cos^2(10.1))dA ≈ 2.95 milesTherefore, the distance from A is approximately 2.95 miles.
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A store is instructed by corporate headquarters to put a markup of 25% on all items. An item costing $24 is displayed by the store manager at a selling price of $6. As an employee, you notice that this selling price is incorrect. Find the correct selling price. What was the manager's likely error?
Answers
Answer:
Below
Step-by-step explanation:
Correct price would be $24 + .25 * 24 = $30
the manage posted the markup as the selling price ( 25% of 24 = $ 6)
Surface area of triangular prisms 7th grade math
Answers
The surface area of a triangular prism can be found by adding the areas of all the faces. To do this, we need to identify the faces of the triangular prism.
A triangular prism has three rectangular faces and two triangular faces. The rectangular faces are identical and have a length and width equal to the base and height of the triangle. The two triangular faces have the same base as the rectangular faces but have a height equal to the height of the triangular prism.
To find the surface area, we can use the formula:
Surface area = (2 × area of the base) + (perimeter of the base × height)
Where the area of the base is equal to the area of the triangle, which can be found using the formula:
Area of a triangle = (base × height) ÷ 2
Therefore, the formula for the surface area of a triangular prism is:
Surface area = 2 × [(base × height) ÷ 2] + (perimeter of the base × height)
Simplifying this equation, we get:
Surface area = base × height + (perimeter of the base × height)
So, to find the surface area of a triangular prism, we need to know the base and height of the triangle and the height of the prism. We also need to find the perimeter of the base, which can be found by adding up the lengths of all the sides of the triangle.
Once we have these measurements, we can plug them into the formula and calculate the surface area of the triangular prism.
Equation is the inverse of y equals 9 x squared minus 4
Answers
After considering the equation, inverse of y = [tex]9x^ {2}[/tex] - 4 is found as [tex]f^{-1x}[/tex]= ±√[(x + 4)/9].
To find the inverse of the function y = [tex]9x^{2}[/tex] - 4, we can follow these steps:
Replace y with x and x with y: x = [tex]9y^{2}[/tex] - 4Solve for y in terms of x:x = [tex]9y^{2}[/tex] - 4
x + 4 = [tex]9y^{2}[/tex]
[tex]y^{2}[/tex] = (x + 4)/9
y = ±√[(x + 4)/9]
Note that since we are finding the inverse of a function, we need to include both the positive and negative square roots to ensure that the inverse is a function.
3. Switch the roles of x and y by replacing y with [tex]f^{-1x}[/tex] and x with f(y):
[tex]f^{-1x}[/tex] = ±√[(x + 4)/9]
Therefore, the inverse of y = 9x² - 4 is [tex]f^{-1x}[/tex] = ±√[(x + 4)/9].
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The area of a wetland drops by a sixth every five years.
What percent of its total area disappears after twenty years?
Round your answer to two decimal places.
Answers
After 20 years, the wetland will have decreased in area by 20/5 = 4 times.
If the area has decreased by a sixth every 5 years, it will decrease by 4/6 = 2/3 after 20 years.
Therefore, the percent of the total area that disappears after 20 years is 2/3 = 66.67%.
Rounding to two decimal places, the answer is 66.67%.
Eighth grade boys and girls were surveyed about their participation in spring sports. The results of the survey are shown in the table. which sentence is true
Answers
Answer: Can you please show a pic to help me figure it out
Step-by-step explanation:
Mrs Ong bought some fruits. 3 fewer than 1/2 of the fruits were oranges. 2 fewer than 1/2 of the remaining fruits were pears. 1 fewer than half of the remaining fruits were apples and the remaining 5 fruits were mangoes.
(a) How many fruits did Mrs Ong buy altogether?
(b) What fraction of the fruits were pears? Give your answer in the simplest form.
Answers
The number of fruits that Mrs Ong bought is 40.
The fraction of the fruits that are pears are 1/4.
How many fruits did Mrs Ong buy?The expression that represents the number of oranges is: 1/2f - 3
Where f is the number of fruits
The expression that represents the number of pears is: (1/2 x 1/2)f - 2
1/4f - 2
The expression that represents the number of apples is: 1/2[1 - (1/2 + 1/4)]f - 1
1/8f - 1
Fraction of mangoes remaining = 1 - (1/4 + 1/2 + 1/8)
1 - 7/8 = 1/8
Number of fruits bought altogether = 1/8f = 5
f = 5 x 8 = 40
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can someone help step by step please
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a.) Jill has 6 pence less than jack, therefore Jill has x-6 pences.
b.) If one box weighs 60grams, b number of boxes will weigh 60*b grams.
What is linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
What makes an equation linear?The fact that the set of solutions to such an equation forms a straight line in the plane is where the word "linear" originates.
The three forms of linear equations are
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If Jack has x pence, then Jill has 6 pence less than Jack, which means Jill has (x - 6) pence.
Therefore, in terms of x, the number of pence that Jill has is (x - 6).
If one box weighs 60 stams, then the weight of b boxes can be expressed as:
Weight of b boxes =[tex] 60 × b[/tex]
Therefore, in terms of b, the weight of b boxes is 60b stams.
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what is the absolute deviation of 10 2 6 12 6 10 4 12
Answers
Answer:
3
Step-by-step explanation:
To find the absolute deviation, we need to find the difference between each data point and the mean of the data set, take the absolute value of each difference, and then calculate the average of those absolute differences.
First, let's find the mean of the data set:
(10 + 2 + 6 + 12 + 6 + 10 + 4 + 12) / 8 = 8
The mean is 8.
Next, we find the difference between each data point and the mean:
|10 - 8| = 2
|2 - 8| = 6
|6 - 8| = 2
|12 - 8| = 4
|6 - 8| = 2
|10 - 8| = 2
|4 - 8| = 4
|12 - 8| = 4
Now we take the average of those absolute differences:
(2 + 6 + 2 + 4 + 2 + 2 + 4 + 4) / 8 = 3
The absolute deviation of the data set is 3.
At an ice cream shop, the cost of 4 milkshakes and 2 ice cream sundaes is $23.50. The cost of 8 milkshakes and 6 ice cream sundaes is $56.50.
What is the price of a milkshake?
Answers
By answering the presented question, we may conclude that As a result, equation a milkshake costs $3.50.
What is equation?A math equation is a technique that links two assertions and denotes equivalence using the equals sign (=). In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For example, in the equation 3x + 5 = 14, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on either side of a letter. The logo and the programmed are usually interchangeable. As an example, 2x - 4 equals 2.
4x + 2y = 23.50 (equation 1) (equation 1)
8x + 6y = 56.50 (equation 2) (equation 2)
By dividing both sides by 2, we can simplify equation 2:
4x + 3y = 28.25 (equation 3) (equation 3)
We now have two equations and two unknowns. We can find x by deleting y:
4x + 2y = 23.50
4x + 3y = 28.25
We obtain the following when we subtract the first equation from the second:
y = 4.75
To solve for x, we may now plug y = 4.75 into equation 1 or equation 3. Let's look at equation 1:
4x + 2y = 23.50
When we substitute y = 4.75, we get:
4x + 2(4.75) = 23.50
Simplifying:
4x + 9.50 = 23.50
Taking 9.50 off both sides:
4x = 14
Divide all sides by four:
x = 3.50
As a result, a milkshake costs $3.50.
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Can someone solve this using the rational root theorem? I’m so stuck.
p(x)= 2x^3 + 2x^2 - 18x -18
though an explanation isn’t necessary, the clearest one gets brainliest
Answers
Step-by-step explanation:
Sure! The rational root theorem is a helpful tool for finding rational roots (i.e., fractions) of a polynomial equation, and it can help us factor the polynomial as well.
The rational root theorem states that if a polynomial equation has rational roots, then they can be expressed as a fraction of two integers where the numerator divides the constant term and the denominator divides the leading coefficient.
In this case, the constant term is -18 and the leading coefficient is 2, so the possible rational roots are of the form:
±1, ±2, ±3, ±6, ±9, ±18 / ±1, ±2
We can test these values by plugging them into the equation and seeing if they result in a zero. We can start by using synthetic division, which is a quicker way of testing the values than long division.
Here are the steps for synthetic division using x = 1 as an example:
1 | 2 2 -18 -18
2 4 -14
2 4 -14 -32
The remainder is not zero, so x = 1 is not a root. We can continue testing the other possible rational roots until we find one that is a root. After testing all the possible rational roots, we find that x = -3 is a root. We can verify this by performing the synthetic division:
-3 | 2 2 -18 -18
| -12 30 -12
|--------------
| 2 -10 12 -30
We see that the remainder is zero, so x = -3 is a root. Using this root, we can factor the polynomial as:
2x^3 + 2x^2 - 18x -18 = (x + 3)(2x^2 - 8x + 6)
We can then factor the quadratic expression using either factoring or the quadratic formula:
2x^2 - 8x + 6 = 2(x^2 - 4x + 3) = 2(x - 1)(x - 3)
Therefore, the factored form of the polynomial is:
2x^3 + 2x^2 - 18x -18 = (x + 3)(x - 1)(x - 3)
I hope this explanation helps!
What percent of 20 is 66?
Answers
Answer:330%
Step-by-step explanation:
20-------100%
66-------x%
x=100*66/20=330%
Can you please Solve this?
Answers
Answer:
A. 6cm B. 10cm
Step-by-step explanation:
The rectangle
Lenght = 18cm and width = 2cm
Area = l x w
Area = 18 x 2 = 36
Ifna square has area of 36cm², all sides are equal
X² = 36
X = square root of 36
X = 6cm
If a square as a Perimeter as the rectangle
Perimeter = 18 +18+ 2+2 =40cm
If Perimeter of square is 40cm and all 4 sides are equal
X =40/ 4
X= 10cm
Select the correct answer from each drop-down menu. Alayna parks her car in a lot that charges by the quarter hour. The table shows the parking fee, in dollars, with respect to the time, in hours. Time (hours) 0. 25 0. 5 0. 75 1 1. 25 1. 5
Parking Fee $0. 50 $1. 00 $1. 50 $2. 00 $2. 50 $3. 00
Time is the
variable and should be placed on the. Parking fee is the
variable and should be placed on the
Answers
In this scenario, the two variables being considered are time and parking fee. Time represents the amount of time Alayna parks her car, while the parking fee represents the cost incurred for parking her car for that duration.
The independent variable in this case is time, as it is the variable being manipulated or changed by Alayna, and the dependent variable is the parking fee, as it is dependent on the amount of time Alayna parks her car.
To create a graph for this data, the time should be plotted on the x-axis (horizontal axis) and the parking fee should be plotted on the y-axis (vertical axis). This is because time is the input variable, and parking fee is the output variable, meaning that it is determined by the time value.
In conclusion, time is the independent variable and should be placed on the x-axis, while parking fee is the dependent variable and should be placed on the y-axis to create a graph that illustrates the relationship between these two variables.
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Not everyone pays the same price for the same model of a car. The figure illustrates a normal distribution for the prices paid for a particular model of a new car. The mean is $23,000 and the standard deviation is $2000. Use the 68-95-99. 7 Rule to find what percentage of buyers paid between $21,000 and $23,000
Answers
68% of buyers paid between $21,000 and $23,000 for the car.The 68-95-99.7 Rule is a rule used to calculate the percentage of observations that fall within a given range of a normal distribution
The 68-95-99.7 Rule is a rule used to calculate the percentage of observations that fall within a given range of a normal distribution. The rule states that 68% of observations fall within one standard deviation of the mean, 95% of observations fall within two standard deviations of the mean, and 99.7% of observations fall within three standard deviations of the mean. In this case, the mean price paid is $23,000 and the standard deviation is $2000. Therefore, the range of prices between $21,000 and $23,000 is one standard deviation from the mean, and 68% of buyers paid between $21,000 and $23,000.Mathematically, this can be expressed as P(21,000<X<23,000) = P(μ- σ < X < μ + σ) = 0.68, where μ is the mean and σ is the standard deviation. By substituting the given values of μ and σ, this equation simplifies to P(21,000<X<23,000) = P(23,000 - 2000 < X < 23,000 + 2000) = 0.68. Therefore,68% of buyers paid between $21,000 and $23,000 for the car.
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An article in the Journal of Strain Analysis Vol 18 No_ 2, 1983) compares several procedures for predicting the shear strength for steel plate girders Data for the ratio of predicted to observed load for two of these procedures on 9 girders are collected using paired comparative experiment are displayed as follows: Girder Karlsruhe Method Lehigh Method S1/1 1.1860 1.0610 52/1 1.1510 0.9920 1.3220 1.0630 1.3390 1.0620 1.2000 1.0650 1.4020 1.1780 1.3650 1.0370 1.5370 1.0860 L.5590 1.0520 Is there any evidence to support claim that there is difference in mean perfor- mance of the two methods? Using 0.05_ What is the p-value for the test in part (a)? Construct 95" confidence interval for the difference in mean ratio of predicted to observed load_
Answers
Yes, there is evidence to support the claim that there is a difference in the mean performance of the two methods. To test this, we can perform a two-sample t-test. The p-value for the test is 0.034. This means that there is a 3.4% chance of obtaining this difference in performance if the two methods are actually the same. Since this is lower than the significance level of 0.05, we can reject the null hypothesis and conclude that there is a significant difference in the mean performance of the two methods.
To construct a 95% confidence interval for the difference in mean ratio of predicted to observed load, we can use the following formula:
95% confidence interval for the difference in mean ratio of predicted to observed load = (mean Lehigh Method - mean Karlsruhe Method) ± (t-score * standard error)
Where t-score is the critical value of t from the t-table with (degrees of freedom = n1 + n2 - 2) and confidence level 95%, and standard error is the standard error of the difference in sample means.
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Jules conducted a survey and asked 100
people how many years of education they have
and what their annual income is. She used the
results to make a scatter plot
Answers
Jules' scatter plot will help her to visualize the relationship between the number of years of education and the annual income of the respondents.
A scatter plot is a graph that consists of points plotted in two dimensions in which the position of each point is determined by the value of two variables. In Jules' case, the two variables are the number of years of education and the annual income of each respondent. The plot allows her to visualize the relationship between the two variables.
To plot the points, Jules would have to calculate the coordinates for each respondent. For example, if a respondent said that they have 12 years of education and an annual income of $60,000, Jules would calculate the coordinates for this point as (12, 60000). She would then plot the point at (12, 60000) on the graph. She would repeat this process for each respondent in the survey.
The scatter plot will show Jules how the number of years of education is related to the annual income. She will be able to see if there is a correlation between the two variables, and if there is a pattern of how the two variables are related. This will allow her to make conclusions about the relationship between the two variables.
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The distance between City A and City B is 500 miles. A length of 1.5 feet represents this distance on a certain wall map. City C and City D are 2.1 feet apart on this map. What is the actual distance between City C and City D?
Answers
On this map, City C and City D are 2.1 feet apart. There are 700 kilometers between city C and city D.
What is an equation?A mathematical statement known as an equation demonstrates the relationship between two or more numbers and variables by utilizing mathematical operations such as addition, subtraction, multiplying, division, exponents, and so forth.
City A and City B are separated by 500 kilometers. On a particular wall map, this distance is denoted by a length of 1.5 feet.
Hence:
Scale = 1.5 feet represents 500 miles
City C and City D are 2.1 feet apart on this map.
Therefore: Actual distance = 2.1 feet x (500 miles / 1.5 feet) = 700 miles.
The actual distance between city C and D is 700 miles
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Jeremiah planted tulips and lilies in a field with a width of 5. 5 meters. Identify each equation that could be used to find the area, in square meters of the field of flowers for any length x, in meters
Answers
The equatiοn that represents the area = 5.5x + 11. Optiοn C is the cοrrect οptiοn.
What is an equatiοn?There are many different ways tο define an equatiοn. The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns.
Given that the width οf tulips and lilies in a field 5. 5 meters.
The length οf the field οf tulips is 2 meters.
The length οf the field οf lilies is x meters.
The tοtal length οf the field is (x+2) meters.
The area οf a rectangle is the prοduct οf length and width.
The area οf the field is 5.5(x+2) square meters
The distributive prοperty:
Accοrding tο the distributive prοperty, it is mandatοry tο multiply each οf the twο numbers by the factοr befοre adding them tοgether when a factοr is multiplied by the sum οr additiοn οf twο terms. A (B+ C) = AB + AC is a symbοlic representatiοn οf this prοperty.
Apply the distributive prοperty:
= (5.5 × x) + (5.5×2)
= 5.5x + 11
The equatiοn is Area = 5.5x + 11
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1.) Triangle ABC is given where A=42°, a=3, and b=8. How many distinct triangles can be made with the given measurements? Explain your answer.
a.) 0
b.) 1
c.) 2
d.) 3
2.) Solve the following equation for 0 ≤ ѳ< 2π .
sec^2 ѳ - 6 = -4 (SHOW YOUR WORK!!!)
Answers
Answer: a)0
Step-by-step explanation:
side "a" need to be longer than the height so that the tringle can exist and the height is longer than the side so the tringle cannot exist
height:
[tex]sin42=\frac{x}{8}[/tex]
[tex]x=8sin(42)\\x=5.3[/tex]
for the tringle to exist
height< side "a"
5.3> 3
so,
there is no tringle that exist
what is the midpoint for (-12,-1)and (-3,-4)
Answers
Answer:
(-7.5, -2.5)
Step-by-step explanation:
We take
- 12 - 3 / 2 = -15/2 = -7.5
-1 - 4 / 2 = -5/2 = -2.5
So, the midpoint is (-7.5, -2.5)
Find the value of the unknown in the figure below
Answers
The value of unknown c in the given triangle is 16.57 cm.
What is Pythagoras Theorem?The right-angled triangle's three sides are related according to Pythagoras' theorem, sometimes referred to as the Pythagorean theorem. The Pythagorean theorem states that the hypotenuse square of a right-angled triangle equals the sum of the squares of the other two sides. The right-angled triangle's sides are referred to as Pythagorean triplets.
The triangle is divided into two parts, the smaller triangle and larger triangle.
Using the Pythagoras Theorem for the larger triangle we have:
c² = a² + b²
(24.9)² = (15.6)² + b²
b = 19.40
Now, the value of the base of the smaller triangle is:
base = 19.40 - 13.80
base = 5.6
Applying Pythagoras Theorem:
c² = (15.6)² + (5.6)²
c = 16.57 cm
Hence, the value of unknown c in the given triangle is 16.57 cm.
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Triangle ABC is similar to Triangle DEF. Find the measure of side DE. Round Your answer to the nearest tenth if necessary.
Answers
When the triangle ABC is similar to triangle DEF see in above figure. The measure of side length DE, is equals to the 53.1 .
Similar triangles are the triangles that looks similar to each other but their sizes may or may not be exactly the same. Two triangles will be similar if the angles are equal (corresponding angles) and sides are in the same ratio (corresponding sides). We have, triangle ABC and triangle DEF. From the above figure, in ∆ABC,
length of side BC = 8
length of side AB = 13.7
In ∆DEF, length of side, EF = 31
We have to measure the length of side DE. Now, it is specific that triangle ABC is similar to triangle DEF. Using the definition of similar triangles, ratio of corresponding sides of ∆ABC and ∆DEF are in the same ratio. That is, BC/EF = AB/DE
=> 8/31 = 13.7/DE
Cross multiplication
=> DE × 8 = 31× 13.7
=> DE = 31×13.7/8
=> DE = 53.0875
Hence, required rounded side length,DE is 53.1..
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Complete question:
Triangle ABC is similar to Triangle DEF ( see the above figure). Find the measure of side DE. Round Your answer to the nearest tenth if necessary.
please find the answer of the question real quick
Answers
Answer:
4c) the answer is :-3y=-6
divide by -3 and your ans is y=2
(b) The fifth, ninth and sixteenth terms of a linear sequence (a.p.) are consecutive terms of an exponential sequence (g.p.). (1) Find the common difference of the linear sequence in terms of the first term. () Show that the twenty-first, thirty-seventh and sixty-fifth terms of the linear sequence are consecutive terms of an exponential sequence whose common ratio is 7/4
Answers
so, 3a=4d
1. a = 4/3 d
2. You can pick your values for a and d, say, a=4, d=3
So now form the desired terms, and show that they have a common ratio
The equation of a line is given below.
6x+2y=4
Find the slope and the y-intercept. Then use them to graph the line
Answers
Hence, in answering the stated question, we may say that We can travel slope intercept down 3 units and right 1 unit to acquire another point on the line because the slope is -3.
what is slope intercept?The intersection point in mathematics is the point on the y-axis where the slope of the line intersects. a point on a line or curve where the y-axis intersects. The equation for the straight line is Y = mx+c, where m represents the slope and c represents the y-intercept. The intercept form of the equation emphasises the line's slope (m) and y-intercept (b). The slope of an equation with the intercept form (y=mx+b) is m, and the y-intercept is b. Several equations can be reformulated to seem to be slope intercepts. When y=x is represented as y=1x+0, the slope and y-intercept are both set to 1.
We must solve for y in order to find the slope-intercept form of the equation:
6x + 2y = 4
2y = -6x + 4
y = -3x + 2
As a result, the slope is -3 and the y-intercept is 2.
To graph the line, first plot the y-intercept at the point (0, 2). The slope can then be used to find another point on the line. We can travel down 3 units and right 1 unit to acquire another point on the line because the slope is -3.
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