Answer:
If the roots of a quadratic equation are given as x = -1 ± 2i, then the equation can be written in the form:
(x - (-1 + 2i))(x - (-1 - 2i)) = 0
Simplifying this expression, we get:
(x + 1 - 2i)(x + 1 + 2i) = 0
Expanding the left side of this equation, we get:
x^2 + x(2 - 2i + 2 + 2i) + (1 - 2i)(1 + 2i) = 0
Simplifying this expression, we get:
x^2 + 2x + 5 = 0
Therefore, the quadratic equation with roots of x = -1 ± 2i is:
x^2 + 2x + 5 = 0
The cylindrical tank is lying horizontally on the ground.
Diameter - 20ft
Length - 22ft
The depth of water in the tank is 6ft.
1 gallon = 231 cubic inches.
A). How many gallons of water are in the tank?
B). How many more gallons of water will it take to fill the tank?
Blake Shelton donated a large part of his land to the city to use as a conservation area. The area is in a shape of a rectangle with 2314 square miles. One side of the rectangle is 26 miles, what is the other side?
Answer: To find the length of the other side of the rectangle, we can use the formula for the area of a rectangle, which is:
area = length x width
We know that the area is 2314 square miles and one side is 26 miles. Let's plug these values into the formula and solve for the other side:
2314 = 26 x width
Divide both sides by 26:
width = 2314/26
Simplify:
width = 89
Therefore, the other side of the rectangle is 89 miles.
Step-by-step explanation:
Log n 2=1/3
Find the unknown base
Answer:
0.3333333333 is right answer
find the value of X on the lines are parallel
Step-by-step explanation:
60-3x+8x=180
5x=180-60
5x/5=120/5
X=24
An experiment is performed to determine whether the average nicotine content of one kind of cigarette exceeds that of another kind by 0.20 milligram. If n1 = 50 cigarettes of the first kind had an average nicotine content of 2.61 milligrams with a standard deviation of 0.12 milligram, whereas n2 = 40 cigarettes of the other kind had an average nicotine content of 2.38 milligrams with a standard deviation of 0.14 milligram, test the null hypothesis μ1-μ2 = 0.20 against the alternative hypothesis μ1-μ2≠0.20 at the 0.05 level of significance.
the average nicotine content of one kind of cigarette exceeds that of another kind by 0.20 milligram at the 0.05 level of significance.
To test the hypothesis that the average nicotine content of one kind of cigarette exceeds that of another kind by 0.20 milligram, we need to compare the means of two independent samples. We can use a two-sample t-test for this purpose. The null hypothesis is that the difference between the means is equal to 0.20 milligram, and the alternative hypothesis is that it is not equal to 0.20 milligram.
The test statistic is given by:
t = ([tex]x_{1}[/tex] - [tex]x_{2}[/tex] - d) / [tex]\sqrt{s_{1}^{2}/n_{1}+s_{2}^{2}/n_{2} }[/tex]
where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, and d is the hypothesized difference in means (0.20 milligram in this case).
Substituting the given values, we have:
x1 = 2.61 milligrams
[tex]x_{1}[/tex] = 2.38 milligrams
[tex]s_{1}[/tex] = 0.12 milligram
[tex]s_{2}[/tex] = 0.14 milligram
n1 = 50 cigarettes
n2 = 40 cigarettes
d = 0.20 milligram
t = (2.61 - 2.38 - 0.20) / [tex]\sqrt{0.12^{2}/50+0.14^{2}/40 }[/tex]= 4.57
The degrees of freedom for the test are given by:
[tex]df= (s_{1}^{2} /n_{1} +s_{2}^{2}/n_{2})^{2}/(s_{1}^{2} /s_{1})^{2}/_{1}-1 +(s_{2}^{2}/n_{2}^{2} /n_{2}-1[/tex])
Substituting the given values, we have:
df = [tex]( 0.12^{2}/50+0.14^{2}/40)^{2}/((0.12^{2}/50)^{2}/49+(0.14^{2}/40)^{2}/39= 86.36[/tex](rounded to two decimal places)
Using a t-distribution table or a calculator, we can find the critical values for a two-tailed test at the 0.05 level of significance with 86 degrees of freedom. For a two-tailed test, the critical values are ±1.987.
Since the calculated t-value of 4.57 is greater than the critical value of 1.987, we reject the null hypothesis.
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Fractions:
Solve nine-twelfths minus eleven-eighteenths equals blank.
two-twelfths
five thirty-sixths
thirty-nine two hundred sixteenths
nineteen-eighteenths
Answer:
5/36 is the simplest answer
Step-by-step explanation:
i did the math and searched it up i hope this helps
A lawn care company calculates the cost to mow a yard based on the number of square yards
that needs to be mowed. Approximately how many square yards will the company need to mow
for the yard shape below? The company rounds to the nearest whole square yard when
calculating the cost. Do not include units in your answer.
Answer:There’s no equation or numbers in your word problem
Step-by-step explanation:
The square yards the company needs to mow for the yard shape below is 58.88 square yards.
What is a square?A square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is given as side²
We have,
From the figure,
The yard shape has two shapes.
Triangle and a square.
Now,
Area of the triangle shape.
= 1/2 x 6.4 x 5.6
= 17.92 square yards
Area of the square shape.
= 6.4²
= 40.96 square yards
Now,
The square yards the company needs to mow for the yard shape below.
= 17.92 + 40.96
= 58.88 square yards.
Thus,
The square yards the company needs to mow for the yard shape below is 58.88 square yards.
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Please help me put thanks
Hence, x=-2 and y=4 are the answers to the system of equations.
Why do people utilise coordinate geometry?For the purpose of connecting algebra and geometry with the aid of line and curve graphs, coordinate geometry is necessary. Finding points on a plane is a crucial component of mathematics. It also has a number of uses in other scientific fields such dimensional geometry, calculus, and trigonometry. Use y=-2x in place of x in the first equation:
5x - 9(-2x) = -46
Simplify and find x's value:
5x + 18x = -46
23x = -46
x = -2
We can use the second equation to get y now that we know the value of x:
y = -2x = -2(-2) = 4
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Prove or disprove the statement: The point (2, √5) lies on the circle centered at the origin with radius 3. The radius of the circle is The exact distance from the center (0, 0) to the point (2, √5) is (2. √5) lie on the circle. units.
Answer:
The statement is correct
Step-by-step explanation:
Use the equation of a circle:
x² + y² = r²
x² + y² = 3²
then enter the coordinates of the point (2; √5):
2² + (√5)² = 9
4 + 5 = 9 (that is correct)
The point (2, √5) lies on the circle centered at the origin with radius 3 is True statement.
What is Equation of Circle?The standard equation of a circle is given by:
(x-h)² + (y-k)² = r²
Where (h,k) is the coordinates of center of the circle and r is the radius.
We have,
The point (2, √5) lies on the circle centered at the origin with radius 3.
We know the equation of circle at origin is
x² + y² = r², where r is the radius of circle
So, x² + y² = 3²
Now. to check the point put x= 2 and y= √5 as
x² + y²
= 2² + √5²
= 4 +5
= 9
Thus, the given statement is Correct.
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Calculate the radius of the following circle. Round to two decimal places when necessary.
(x+3)² + (y +7)² =121
Answer:
The equation of the given circle is:
(x + 3)² + (y + 7)² = 121
This equation is in standard form, which is:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is its radius.
Comparing the given equation with the standard form, we can see that:
The center of the circle is (-3, -7) (note the signs of h and k).
The radius of the circle is √121 = 11 (since r² = 121, then r = √121 = 11).
Therefore, the radius of the given circle is 11 units.
Step-by-step explanation:
The angle measures of $\triangle ABC$ are $A=54\degree$ , $B=38\degree$ , and $C=88\degree$ . List the sides of the triangle in order from shortest to longest.
The sides of the triangle in order from shortest to longest are b < a < c
How to determine the sides of the triangle in order from shortest to longest.In triangle ABC, the side opposite angle A is denoted by a,
The side opposite angle B is denoted by bThe side opposite angle C is denoted by c.To determine the order of the sides from shortest to longest, we need to use the triangle inequality theorem which implies that
The side opposite the largest angle is the largest side and vice versa
So, we have
b from B = 38 degrees
a from A = 54 degrees
c from C = 88 degrees
Therefore, the order of the sides from shortest to longest is: b < a < c
In other words, the side opposite angle B is the shortest, followed by the side opposite angle A, and the side opposite angle C is the longest.
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Refer to the pie graph that shows the world’s languages and the percentages of the population that speak them.
What percentage of the world’s population does not speak either French or German?
By answering the above question, we may state that Hence, neither expressions French nor German are spoken by nearly 97.7% of the world's population.
what is expression ?In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.
In the image you included, a pie chart illustrating the distribution of the global languages spoken by the entire population can be seen.
We need to figure out what portion of the world's population does not speak either French or German in order to respond to your query.
Around 1.2% of the world's population speaks French, according to the pie chart, and 1.1% speaks German, according to the same data.
Hence, it is possible to determine the proportion of people on Earth who do not speak either French or German as follows:
German: 1.1%; French: 1.2%; 100% = 97.7%
Hence, neither French nor German are spoken by nearly 97.7% of the world's population.
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Finn read an article claiming that 50% of Americans have brown hair,
20% have black hair, 20% have blonde hair, and
10% have red hair. He wondered if the hair colors of students at his school followed this distribution, so he took a random sample of
50 students and recorded their hair colors. Here are his results:
Color Brown Black Blonde Red
Students
17 14 14 5
He wants to use these results to carry out a
�
2
χ
2
\chi, squared goodness-of-fit test to determine if the distribution of hair colors at his school disagrees with the claimed percentages.
Choose 1 answer:
(Choice A)
�
2
=
5.76
;
0.10
<
P-value
<
0.15
χ
2
=5.76;
0.10
A
�
2
=
5.76
;
0.10
<
P-value
<
0.15
χ
2
=5.76;
0.10
(Choice B)
�
2
=
5.76
;
0.20
<
P-value
<
0.25
χ
2
=5.76;
0.20
B
�
2
=
5.76
;
0.20
<
P-value
<
0.25
χ
2
=5.76;
0.20
(Choice C)
�
2
=
6.05
;
0.10
<
P-value
<
0.15
χ
2
=6.05;
0.10
C
�
2
=
6.05
;
0.10
<
P-value
<
0.15
χ
2
=6.05;
0.10
(Choice D)
�
2
=
6.05
;
0.15
<
P-value
<
0.20
χ
2
=6.05;
0.15
D
�
2
=
6.05
;
0.15
<
P-value
<
0.20
χ
2
=6.05;
0.15
Answer: Choice A
χ 2 =5.76;
0.10<P-value<0.15
Step-by-step explanation:
If θ = 31π/4 , the reference angle is
[tex]\cfrac{31\pi }{4}\implies \cfrac{8\pi +8\pi +8\pi +4\pi +3\pi }{4}\implies 2\pi +2\pi +2\pi +\pi +\cfrac{3\pi }{4}[/tex]
so the angle θ is really 3 revolutions plus π and then a little bit more, Check the picture below for the red reference angle.
Please give me some help I don’t get it. U have to complete the the diagram
The probabilities are given as follows:
a = 0.4.b = 0.9.c = 0.5.d = 0.5.How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
For a probability tree, the sum of the nodes at each level must be of 1.
Then the value of a is obtained as follows:
0.6 + a = 1
a = 1 - 0.6
a = 0.4.
The value of b is obtained as follows:
0.9 + b = 1
b = 0.1.
The values of c and d are free, as long as the sum of these two values is of 1, hence we can attribute:
c = 0.5, d = 0.5.
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I WILL GIVE 70 POINTS AND THE BRAINIEST!!!!!
For the equation: 2(x - 7) = 3 - 7x + 5 + 8 + 7x + 11, the right side of the equation can be simplified by combining like terms.
Simplify the right side of the equation: ___________
The left side of the equation can be simplified using the Distributive Property.
Simplify the left side of the equation: ____________
Answer:
Blank 1: incorrectly
Blank 2: no
Step-by-step explanation:
Blank 1:
The student did not properly distribute:
4( x + 4 ) = 4x + 16, NOT 4x + 4
4x + 4 = 4x + 16 [subtract 4x from each side]
4 = 16
An incorrect statement means that there are no solutions
pa help plssss
Identify the solid figure that is represented by each real object below. Write the name of the solid figure on the blank before each number. 1. an ice cream cone 2. an orange 3. a shoe box 4. a coin 5. a soccer ball 6. a die
The name of the solid figure on the below object is indicated in front as follows:
Ice cream cone - ConeOrange - SphereShoe box - Rectangular PrismCoin - CylinderSoccer ball - SphereDie - CubeWhat does solid figure means?Solid figures refers to three-dimensional objects with dimensions of length, width, and height. They have depth and take up space in our universe because they have three dimensions. The features that distinguish each type of solid are used to identify them.
In real life, solid figures include boxes, dice, tubes, traffic cones, balls, and tents. However, Ppisms, cubes, cones, spheres, pyramids, and cylinders are the most basic solid figures. A composite figure is formed by combining multiple solid figures.
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How to find slope of line line from given table with answer and instructions please
Answer:
The slope of the line is 60.
Step-by-step explanation:
We are given a table of values, and h and c are substitutes from x and y. Judging by this, if we know the formula [tex]\frac{y2-y1}{x2-x1}[/tex] then we can evaluate the slope, we just have to take two of the coordinate points from the table.
Lets take (3,205) and (6,385) and plug it into the formula
[tex]\frac{385-205}{6-3}[/tex]
Evaluate
[tex]\frac{180}{3}[/tex]
Simplify the fraction
[tex]\frac{60}{1}=60[/tex]
The slope of the line is 60.
Question A) Work out the distance travelled on a cycle in the first 14 seconds. Q B) Work out thr acceleration speed in the first 4 seconds.
The distance travelled in the first 14 seconds would then be 3.57 x 14 = 49.98 metres.the acceleration would be 7.14 - 3.57 = 3.57 metres per second squared.
What is distance?Distance is the numerical measurement of how far apart two objects are. It is measured in units such as kilometers, meters, miles, feet, inches, and more. Distance can be calculated in one, two, or three dimensions. Distance is a key factor in many real-world applications, such as navigation, transport, and communication. Distance can also be used to describe relationships, such as the connection between two people.
A)To work out the distance travelled on a cycle in the first 14 seconds, we must first determine the velocity of the cycle. This can be done by dividing the distance travelled by the time taken. For example, if the cycle travelled 50 metres in 14 seconds, the velocity would be 50 / 14 = 3.57 metres per second. The distance travelled in the first 14 seconds would then be 3.57 x 14 = 49.98 metres.
B) To work out the acceleration speed in the first 4 seconds, we must first determine the change in velocity over the period of time. We can do this by subtracting the initial velocity from the final velocity. For example, if the cycle started at a velocity of 3.57 metres per second, and increased to 7.14 metres per second after 4 seconds, the acceleration would be 7.14 - 3.57 = 3.57 metres per second squared.
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complete question with diagram is
Question A) Work out the distance travelled on a cycle in the first 14 seconds. Q B) Work out thr acceleration speed in the first 4 seconds.
diagram shows trapezium in graph with velocity at y axiz and time at x axis
Bob and Kevin bought a lottery ticket and won $100 000. Since they paid different amounts for the winning ticket, Bob received $10 000 more than two times what Kevin received. How much did each person receive?
answer: Kevin received $30,000, and Bob received $70,000.
According to the problem, Bob received $10,000 more than two times what Kevin received. So, Bob received:
2X + $10,000
We also know that the total amount won is $100,000. Therefore, we can write the equation:
X + (2X + $10,000) = $100,000
Simplifying the equation, we get:
3X + $10,000 = $100,000
3X = $90,000
X = $30,000
Therefore, Kevin received $30,000, and Bob received:
2X + $10,000 = 2($30,000) + $10,000 = $70,000
So Bob received $70,000.
Solve for the base. Round to the nearest cent. Part: $7421.00 Rate of decrease: 30%
Answer:
≈ $5194,7
Step-by-step explanation:
First, find out how much did the price decrease:
[tex] \frac{7421 \times 30\%}{100\%} = 2226.3[/tex]
Now, subtract this number from the previous one (the price before):
$7421,00 - $2226,30 = $5194,70 ≈ $5194,7
We can describe 3x - 2 as an expression. How can we describe the parts of the expression that the arrows point to? 3x - 2
We can say that the arrοws pοint tο the variable term (3x) and the cοnstant term (-2) οf the expressiοn 3x - 2.
What is Linear Expressiοn?A linear expressiοn is a mathematical expressiοn in οne variable that can be written in the fοrm ax + b, where a and b are cοnstants and x is the variable. It represents a straight line when graphed.
The expressiοn 3x - 2 can be described as a sum οr difference οf twο terms: 3x and -2.
The cοefficient 3 is the numerical factοr οf the term 3x, which represents the prοduct οf 3 and x, a variable οr unknοwn quantity. The term 3x is called the variable term οr the first term οf the expressiοn.
The cοnstant term -2 is a term that dοes nοt invοlve any variables. It is the secοnd term οf the expressiοn and is alsο knοwn as the cοnstant term οr the cοefficient οf the cοnstant term, since it is multiplied by the cοefficient 1 (which is nοt written) in this case.
In οther wοrds, we can say that the arrοws pοint tο the variable term (3x) and the cοnstant term (-2) οf the expressiοn 3x - 2.
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Right triangle ABC is on a coordinate plane. Segment AB is on the like y=2 and is 6 units long. Point C is on the line x=-3. What is the y-value of Point C if the area of ABC is 9 units squared
The y-coordinate value of Point C if the area of ABC is 9 units squared is: 5 or -1
How to find the coordinate of the segment?Point A is at (x, 2) and B is at (x + 6, 2). Since AB must lie on the line y=2 and be 6 units long. Point C is on the line x = -3 . So let C be at (-3, y).
Since ΔABC is a right angle, then point C must have the same x-coordinate as point A. Therefore, A(-3, 2) and B(2, 2).
The area of ΔABC is 9. So,
9 = 1/2 (b)(h)
where b is the base and h is the height.
so b = 6 and h = AC
Solving this for AC gives
9 = 1/2 (6)(AC)
18/6 = AC
3 = AC
Point C must lie 3 units above point A or 3 units below the point A. If it lies 3 units above, then it has a y-coordinate of 2 + 3 = 5.
If it lies 3 units below, it has a y-coordinate 2 - 3 = -1.
Therefore, y-coordinate is 5 or -1.
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What is the next term in the following sequence?
54, -18, 6, ...
2
-3
3
-2
The next term of the sequence is -2
How to determine the next term of the sequenceFrom the question, we have the following parameters that can be used in our computation:
54, -18, 6, ...
The above definitions imply that we simply multiply -1/3 to the previous term to get the current term
Using the above as a guide,
so, we have the following representation
Next term = -1/3 * Current term
Substitute the known values in the above equation, so, we have the following representation
Next term = -1/3 * 6
Evaluate
Next term = -2
Hence, the next term is -2
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Linda needs to have her car towed. Little Town Auto charges a flat fee of $75 plus $2 per miletowed. Write a function expressing Linda's towing cost, C, in terms of miles towed, x. Find thecost of having a car towed 14 miles.
The cost of having a car towed 14 miles is $103.
What is function ?
In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output. Functions are often represented by a formula or rule that describes how to compute the output value from the input value.
The towing cost, C, can be expressed as a function of miles towed, x, using the given information as follows:
C(x) = 75 + 2x
where x is the number of miles towed.
To find the cost of towing a car 14 miles, we can substitute x = 14 into the function:
C(14) = 75 + 2(14)
= 75 + 28
= $103
Therefore, the cost of having a car towed 14 miles is $103.
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Darlena has started taking photos at amateur dog racing events, later offering the photos for sale to the dog owners by email. The prices she has charged per photo at each of her first three events, and the corresponding number of photos sold and total revenue raised, appear in the table below.
Price per Photo Number of Photos Sold Revenue
$45
3
$135
$39
5
$195
$24
10
$240
Treating revenue as a function of the number of photos sold, a graph of the three data points is also shown. If she uses quadratic regression to fit a curve to the data, what number of photos sold and what price per photo will maximize her revenue?
The cost per photo at which revenue is maximized is about $127.95.
We must first calculate the relevant y-value for the quadratic function at
x = 6.5 in order to get the pricing per photo that optimizes revenue (i.e., the revenue). When we enter x = 6.5, we obtain:
[tex]R(6.5) = 0.3(6.5)^2 + 3.9(6.5) + 97.5 =[/tex]$127.95
What is revenue?Before any costs or expenses are subtracted, revenue is the income derived from the sale of goods or services, or from any other use of capital or assets, related to an organization's primary operations. Also, it is known as sales or turnover.
from the question:
We can apply quadratic regression to identify the quadratic function that represents the revenue as a function of how many images are sold. This will provide us with the form's function:
[tex]R(x) = ax^2 + bx + c[/tex]
When x is the number of sold images, R(x), a, b, and c are coefficients we need to discover, and R(x) is the revenue.
We may construct an equation system to find the coefficients using the provided data:
(1) [tex]a(3)^2 + b(3) + c = 135[/tex]
(2)[tex]a(5)^2 + b(5) + c = 195[/tex]
(3) [tex]a(10)^2 + b(10) + c = 240[/tex]
When we simplify each equation, we obtain:
(1) 9a + 3b + c = 135
(2) 25a + 5b + c = 195
(3) 100a + 10b + c = 240
Any approach will work to solve this system of equations. We'll apply the substitution technique in this case.
Equation (1) gives us:
c = 135 - 9a - 3b
When we enter this into equation (2), we obtain:
25a + 5b + (135 - 9a - 3b) = 195
Simplifying, we get:
16a + 2b = 12
From equation (3), we get:
c = 240 - 100a - 10b
Substituting this into equation (1), we get:
9a + 3b + (240 - 100a - 10b) = 135
Simplifying, we get:
-91a - 7b = -105
Solving the system of equations 16a + 2b = 12 and -91a - 7b = -105, we get:
a = 0.3
b = 3.9
c = 97.5
Therefore, the quadratic function that models the revenue as a function of the number of photos sold is:
[tex]R(x) = 0.3x^2 + 3.9x + 97.5[/tex]
We must determine the x-value that corresponds to the parabola's vertex in order to determine the number of images that must be sold in order to maximize revenue. The vertex's x-value is determined by:
x = -b / 2a
Plugging in the values for a and b, we get:
x = -3.9 / 2(0.3) = -6.5
This indicates that the vertex of the parabola lies at x = 6.5 because the number of images sold cannot be negative. Darlena should therefore sell 6.5 photographs in order to increase her money.
We must first calculate the relevant y-value for the quadratic function at x = 6.5 in order to get the pricing per photo that optimizes revenue (i.e., the revenue). When we enter x = 6.5, we obtain:
[tex]R(6.5) = 0.3(6.5)^2 + 3.9(6.5) + 97.5 ≈ $127.95[/tex]
As a result, $127.95 per photo is the price that maximizes sales.
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the price p of a certain computer system decreases immediately after its introduction and then increases. if the price P is estimated by the formula P= 170t^2- 1700t + 6400, where t is the time in months from its introduction, find the time until the minimum price is reached
The time until the minimum price is reached is 5 months. After this time, the price will start to increase again.
Define the term price?Price is the amount of money that must be paid to acquire a product or service, usually expressed in currency units such as dollars or euros.
The price of the computer system is given by the formula:
P = 170t² - 1700t + 6400
To find the time until the minimum price is reached, we need to find the value of t that corresponds to the vertex of the parabola described by this formula. The vertex is the point at which the price reaches its minimum value.
The formula for the x-coordinate of the vertex of a parabola in standard form (ax² + bx + c) is:
x = -b/2a
In this case, the formula for the price of the computer system is:
P = 170t² - 1700t + 6400
So we can see that a = 170, b = -1700, and c = 6400. Substituting these values into the formula for the x-coordinate of the vertex, we get:
t = -b/2a = -(-1700)/(2×170) = 5
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f(x) = 2x^(2)-3x+6 find the value of f(0)
Answer:
f(x) = 2x^(2) - 3x + 6
f(0) = 2(0)^(2) - 3(0) + 6
f(0) = 0 - 0 + 6
f(0) = 6
Therefore, the value of f(0) is 6.
Step-by-step explanation:
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If the triangle above is translated two units to the right, what is the correct coordinate for A'?
A) A'(5, 5)
B) A'(5, 0)
C) A'(0, 5)
D) A'(0, 0)
Question #2
If the triangle above is reflected over the y-axis, what is the correct coordinate for A'?
A) A'(0, 5)
B) A'(2, 5)
C) A'(5, 2)
D) A'(-5, -2)
Answer:
1. C
2. B
Step-by-step explanation:
A. A(-2,5) => A' (-2 + 2, 5) or A' (0,5)
B. A(-2,5) => A' (- -2, 5) or A' (2,5)
NO LINKS!!! URGENT HELP PLEASE!!!
Please help with the Special triangles #19, 21, and 23
[tex]\begin{array}{llll} 19. & \text{x}= \frac{9\sqrt{6}}{2}, & \text{y}= \frac{9\sqrt{6}}{2}, & \text{z}= 18\\\\21. & \text{x}= 6, & \text{y}= 6\sqrt{3}, & \text{z}= 6\sqrt{6}\\\\23. & \text{x}= 10\sqrt{3}, & \text{y}= 5\sqrt{3}, & \text{z}= 15\\\\\end{array}[/tex]
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Work Shown:
Problem 19
The triangle up top is a 30-60-90 triangle. The short leg is opposite the smallest angle 30 degrees. Double the short leg to get the hypotenuse.
z = 2*9 = 18.
The long leg is found like so
[tex]\text{long leg} = (\text{short leg})*\sqrt{3}\\\\\text{long leg} = 9\sqrt{3}\\\\[/tex]
These two formulas apply to 30-60-90 triangles only.
The long leg of the 30-60-90 triangle up top is the hypotenuse of the 45-45-90 triangle at the bottom.
For 45-45-90 triangles, we can say:
[tex]\text{hypotenuse} = (\text{leg})*\sqrt{2}\\\\\text{leg} = \frac{\text{hypotenuse}}{\sqrt{2}}\\\\\text{leg} = \frac{\text{hypotenuse}*\sqrt{2}}{2}\\\\\text{leg} = \frac{9\sqrt{3}*\sqrt{2}}{2}\\\\\text{leg} = \frac{9\sqrt{3*2}}{2}\\\\\text{leg} = \frac{9\sqrt{6}}{2}\\\\[/tex]
This represents the lengths of x and y. For any 45-45-90 triangle, the two legs are the same length (the right triangle is isosceles).
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Problem 21
Focus on the 30-60-90 triangle up top.
The hypotenuse of 12 divides in half to get x = 12/2 = 6 as the short leg.
The long leg is [tex]6\sqrt{3}[/tex]
This is also the leg of the 45-45-90 triangle down below. Therefore, we have [tex]y = 6\sqrt{3}[/tex]
Multiply the leg by sqrt(2) to find the hypotenuse.
[tex]\text{hypotenuse} = \text{leg}*\sqrt{2}\\\\\text{z} = 6\sqrt{3}*\sqrt{2}\\\\\text{z} = 6\sqrt{3*2}\\\\\text{z} = 6\sqrt{6}\\\\[/tex]
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Problem 23
Focus on the triangle on the right. This is a 45-45-90 triangle.
The hypotenuse is 15sqrt(2), which must mean each leg is 15 units long. Therefore, z = 15. The unmarked vertical leg is also 15 units long.
This vertical side is the leg of the 30-60-90 triangle on the left. It's the long leg.
[tex]\text{long leg} = (\text{short leg})*\sqrt{3}\\\\\text{short leg} = \frac{\text{long leg}}{\sqrt{3}}\\\\\text{short leg} = \frac{(\text{long leg})*\sqrt{3}}{3}\\\\\text{y} = \frac{15\sqrt{3}}{3}\\\\\text{y} = 5\sqrt{3}\\\\[/tex]
Double this short leg to get the hypotenuse of the 30-60-90 triangle.
[tex]x = 2y\\\\x = 2*5\sqrt{3}\\\\x = 10\sqrt{3}\\\\[/tex]
Answer:
Question 19:
x = (9√6)/2 unitsy = (9√6)/2 unitsz = 18 unitsQuestion 21:
x = 6 unitsy = 6√3 unitsz = 6√6 unitsQuestion 23:
x = 10√3 unitsy = 5√3 unitsz = 15 unitsStep-by-step explanation:
45-45-90 triangleA 45-45-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : 1 : √2. Therefore, the formula for the ratio of the sides is b : b : b√2 where:
b is each side opposite the 45 degree angles (legs).b√2 is the side opposite the right angle (hypotenuse).30-60-90 triangleA 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : √3 : 2. Therefore, the formula for the ratio of the sides is c: c√3 : 2c where:
c is the shortest side opposite the 30° angle.c√3 is the side opposite the 60° angle.2c is the longest side (hypotenuse) opposite the right angle.Question 19Side z is the hypotenuse of a 30-60-90 triangle where the leg opposite the 30° angle measures 9 units. Therefore, c = 9.
[tex]\implies z=2c =2 \cdot 9=18\; \sf units[/tex]
Therefore, the other leg of the same triangle (opposite the 60° angle) measures c√3 = 9√3 units.
Sides x and y are the congruent legs of a 45-45-90 triangle with hypotenuse measuring 9√3 units. Therefore b√2 = 9√3, so b = (9√6)/2.
[tex]\implies x=\dfrac{9 \sqrt{6}}{2}\; \sf units[/tex]
[tex]\implies y=\dfrac{9 \sqrt{6}}{2}\; \sf units[/tex]
Question 21Side x is the side opposite the 30° angle in a 30-60-90 triangle with a hypotenuse of 12 units. Therefore, 2c = 12 so c = 6.
[tex]\implies x=6\; \sf units[/tex]
Therefore, the other leg of the same triangle (opposite the 60° angle) measures c√3 = 6√3 units.
Side y is one of the congruent legs of a 45-45-90 triangle where the other congruent leg measures 6√3 units.
[tex]\implies y=6\sqrt{3}\; \sf units[/tex]
Side z is the hypotenuse of a 45-45-90 triangle where the congruent legs measure 6√3 units. Therefore b = 6√3.
[tex]\implies z=b\sqrt{2} = 6 \sqrt{3} \sqrt{2}=6\sqrt{6}\; \sf units[/tex]
Question 23Side z is one of the congruent legs of a 45-45-90 triangle where the hypotenuse measures 15√2 units. Therefore, b√2 = 15√2, so b = 15.
[tex]\implies z=b=15\; \sf units[/tex]
Side x is the hypotenuse of a 30-60-90 triangle where the leg opposite the 60° measures 15 units. Therefore, c√3 = 15, so c = 5√3.
[tex]\implies x=2c=2 \cdot 5\sqrt{3}=10\sqrt{3}\; \sf units[/tex]
Side y is the side opposite the 30° angle in a 30-60-90 triangle where the hypotenuse measures 10√3 units. Therefore, 2c = 10√3, so c = 5√3.
[tex]\implies y=c=5\sqrt{3}\; \sf units[/tex]