Answer: -8 ≥ x
Step-by-step explanation:
Let x be the number, we set up an inequality:
-183 ≥ 9 + 24x [we use ≥ to present "at least"]
-192 ≥ 24x
-8 ≥ x
Dylan's mom told him that she would replace each one of his dimes with a quarter. If he uses all of his coins, determine if Dylan would then have enough money to buy a game priced at $20.98 if he must also pay an 8% sales tax.
A tour group has $83 to buy train tickets. Each ticket costs $18. How many train tickets can
the group buy?
PLEASE HELPPPPPPP NEED NOW
Answer:
BC = 24 units
Step-by-step explanation:
This is an isosceles triangle which always has:
two legs that are congruent to each other (i.e., equal),and two angles that are congruent to each other.In this triangle, the legs CA and BA are congruent so CA = BA and the angles C and B are congruent to each other so angle C = angle B.
Thus, we can find x by setting CA and BA equal to each other:
(3x - 15 = x + 33) + 15
(3x = x + 48) - x
(2x = 48) / x
x = 24
Thus, x = 24
Since the length of BC is x and x = 24, BC is 24 units long.
Similar Triangles
Determine whether the triangles are similar. If so, write a similarity statement. If not, what would be sufficient to
prove the triangles similar? Explain your reasoning.
I need help on number 1 and 2
The equivalent ratio of the corresponding sides and the triangle proportionality theorem indicates that the similar triangles are;
1. ΔAJK ~ ΔSWY according to the SAS similarity postulate
2. ΔLMN ~ ΔLPQ according to the AA similarity postulate
3. ΔPQN ~ ΔLMN
LM = 12, QP = 8
4. ΔLMK~ΔLNJ
NL = 21, ML = 14
What are similar triangles?
Similar triangles are triangles that have the same shape but may have different sizes.
1. The ratio of corresponding sides between the two triangles circumscribing the congruent included angle are;
24/16 = 3/2
18/12 = 3/2
The ratio of each of the two sides in the triangle ΔAJK to the corresponding sides in the triangle ΔSWY are equivalent and the included angle, therefore, the triangles ΔAJK and ΔSWY are similar according to the SAS similarity rule.
2. The ratio of the corresponding sides in each of the triangles are;
MN/LN = 8/10 = 4/5
PQ/LQ = 12/(10 + 5) = 12/15 = 4/5
The triangle proportionality theorem indicates that the side MN and PQ are parallel, therefore, the angles ∠LMN ≅ ∠LPQ and ∠LNM ≅ ∠LQP, which indicates that the triangles ΔLMN and ΔLPQ are similar according to the Angle-Angle AA similarity rule
3. The alternate interior angles theorem indicates;
Angles ∠PQN ≅ ∠LMN and ∠MLN ≅ ∠NPQ, therefore;
ΔPQN ~ ΔLMN by the AA similarity postulate
LM/QP = (x + 3)/(x - 1) = 18/12
12·x + 36 = 18·x - 18
18·x - 12·x = 36 + 18 = 54
6·x = 54
x = 54/6 = 9
LM = 9 + 3 = 12
QP = x - 1
QP = 9 - 1 = 8
4. The similar triangles are; ΔLMK and ΔLNJ
ΔLMK ~ ΔLNJ by AA similarity postulate
ML/NL = (6·x + 2)/(6·x + 2 + (x + 5)) = (6·x + 2)/((7·x + 7)
ML/NL = LK/LJ = (24 - 8)/24
(24 - 8)/24 = (6·x + 2)/((7·x + 7)
16/24 = (6·x + 2)/(7·x + 7)
16 × (7·x + 7) = 24 × (6·x + 2)
112·x + 112 = 144·x + 48
144·x - 112·x = 32·x = 112 - 48 = 64
x = 64/32 = 2
ML = 6 × 2 + 2 = 14
NL = 7 × 2 + 7 = 21
MN = 2 + 5 = 7
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Given ABCD, what is the measure of
145
A. 90°
B. 35°
C. 10°
D. 145°
E. 55°
F. 235°
Answer: D. 145°
Step-by-step explanation:
Since it is a parallelogram given by the symbol, then angle B is equal to angle D which is 145°.
NEED NOW PLEASE HELP OUT
Answer:
x=50
Step-by-step explanation:
Make this equal to 180.
x+3x-35+x-35 = 180
5x = 180 + 70
5x=250
x=50
5. A person observes that from point A, the angle of elevation to the top of a cliff at D is 30°. Another person at point B, notes that the angle of elevation to the top of the
cliff is 45°. If the height of the cliff is 80.0 m, find the distance between A and B. Show the steps of your solution.
Answer:
In a 30°-60°-90° triangle, the length of the longer leg is √3 times the length of the shorter leg. So AC = 80√3.
In a 45°-45°-90° triangle, both legs are congruent. So BC = 80.
AB = AC - BC = (80√3 - 80) meters
= 80(√3 - 1) meters
= about 58.56 meters
The distance between points A and B is approximately 138.6 meters.
To find the distance between points A and B, we can use the concept of trigonometry and the given information.
Let's denote the distance between points A and B as x.
From point A, the angle of elevation to the top of the cliff at point D is 30°. This means that in the right triangle formed by points A, D, and the top of the cliff, the opposite side is the height of the cliff (80.0 m) and the adjacent side is x. We can use the tangent function to calculate the length of the adjacent side:
tan(30°) = opposite/adjacent
tan(30°) = 80.0/x
Simplifying the equation, we have:
x = 80.0 / tan(30°)
Using a calculator, we can find the value of tan(30°) ≈ 0.5774.
Substituting the value, we get:
x = 80.0 / 0.5774
Calculating the value, we find:
x ≈ 138.6 meters
In light of this, the separation between positions A and B is roughly 138.6 metres.
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Assume that each circle shown below represents one unit.express the shaded amount as a single fraction and as a mixed number
One fraction :
Mixed number:
The shape is represented as below
As one fraction = 9/4As a mixed number = 2 1/4How to represent the figure as a fractionThe figure is of three shapes, the firs two are whole numbers then the last is a fraction.
Adding them results to
shape 1 + shape 2 + shape 3
1 + 1 + 1/4
As one fraction
= 9/4
as a mixed number
= 2 1/4
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Graph the function f(x)= 3+2 in x and its inverse from model 1.
The graph of the function and its inverse is added as an attachment
Sketching the graph of the function and its inverseFrom the question, we have the following parameters that can be used in our computation:
f(x) = 3 + 2ln(x)
Express as an equation
So, we have
y = 3 + 2ln(x)
Swap x and y in the above equation
x = 3 + 2ln(y)
Next, we have
2ln(y) = x - 3
Divide by 2
ln(y) = (x - 3)/2
Take the exponent of both sides
[tex]y = e^{\frac{x - 3}{2}}[/tex]
Next, we plot the graphs
The graph of the functions is added as an attachment
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What else would need to be congruent to show that ABC=AXYZ by SAS?
A
B
OA. ZB=LY
B. BC = YZ
OC. C= LZ
OD. AC = XZ
с
X
Z
Given:
AB XY
BC=YZ
What is needed to be congruent to show that ABC=AXYZ is AC ≅ XZ. option D
How to determine the statementGiven that in ΔABC and ΔXYZ, ∠X ≅ ∠A and ∠Z ≅ ∠C.
We are to select the correct condition that we will need to show that the triangles ABC and XYZ are congruent to each other by ASA rule..
ASA Congruence Theorem: Two triangles are said to be congruent if two angles and the side lying between them of one triangle are congruent to the corresponding two angles and the side between them of the second triangle.
In ΔABC, side between ∠A and ∠C is AC,
in ΔXYZ, side between ∠X and ∠Z is XZ.
Therefore, for the triangles to be congruent by ASA rule, we must have AC ≅ XZ.
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Find the limit (if the limit exists). Solve in two different ways.
The limit of the trigonometric expression is equal to 0.
How to determine the limit of a trigonometric expression
In this problem we find the case of a trigonometric expression, whose limit must be found. This can be done by means of algebra properties, trigonometric formula and known limits. First, write the entire expression below:
[tex]\lim_{\Delta x \to 0} \frac{\cos (\pi + \Delta x) + 1}{\Delta x}[/tex]
Second, use the trigonometric formula cos (π + Δx) = - cos Δx to simplify the resulting formula:
[tex]\lim_{\Delta x \to 0} \frac{1 - \cos \Delta x}{\Delta x}[/tex]
Third, use known limits to determine the result:
0
The limit of the trigonometric function [cos (π + Δx) + 1] / Δx evaluated at Δx → 0 is equal to 0.
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PLEASE HELP
Suppose that the functions fand g are defined for all real numbers x as follows.
f(x) = 5x
g(x)=4x-4
Write the expressions for (g.f)(x) and (g-f)(x) and evaluate (g+f)(2).
(g•f)(x) =
(g-f)(x) =
(g+r) (2)=
what is (0.3)0 in binominal distribution
Answer:
When p, the probability of success, is zero in a binomial distribution, the probability of getting exactly k successes in n trials is also zero for all values of k except when k is zero (i.e., when there are no successes).
So, in the case of (0.3)^0, the result would be 1, because any number raised to the power of 0 is equal to 1. Therefore, the probability of getting zero successes in a binomial distribution when the probability of success is 0.3 is 1.
Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. common ratio; growth multiplier) was around 1.9. In 1983, about 1600 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2003?
Complete the following number sequence. 2, 4, 7, __, 16, __, 29, __
The completed sequence would then be: 2, 4, 7, 9, 16, 19, 29.
To complete the given number sequence, let's analyze the pattern and identify the missing terms.
Looking at the given sequence 2, 4, 7, __, 16, __, 29, __, we can observe the following pattern:
The difference between consecutive terms in the sequence is increasing by 1. In other words, the sequence is formed by adding 2 to the previous term, then adding 3, then adding 4, and so on.
Using this pattern, we can determine the missing terms as follows:
To obtain the third term, we add 2 to the second term:
7 + 2 = 9
To find the fifth term, we add 3 to the fourth term:
16 + 3 = 19
To determine the seventh term, we add 4 to the sixth term:
__ + 4 = 23
Therefore, the missing terms in the sequence are 9, 19, and 23.
By identifying the pattern of increasing differences, we can extend the sequence and fill in the missing terms accordingly.
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GEOMETRY 100POINTSSS
Find x
Answer:
5.9
Step-by-step explanation:
sin Θ = opp/hyp
sin 36° = x/10
x = 10 × sin 36°
x = 5.88
Answer: 5.9
Solve the missing element . use 3.14 for pi and Area = pi r2 ; C= pi D
We can solve for the missing elements as follows:
1. Radius - 10 inches
Diameter - 20
Circumference - 62.8
Area - 314
2. Radius - 6ft
Diameter - 12
Circumference - 37.68
Area - 113.04
3. Radius - 18
Diameter - 36 yards
Circumference - 113.04
Area - 1017.36
4. Radius 15
Diameter - 30 cm
Circumference 94.2
Area - 706.5
5. Radius - 5 mm
Diameter 10
Circumference 31.4
Area -78.5
6. Radius 20
Diameter - 40 inches
Circumference 125.6
Area -1256
How to solve for the valuesTo solve for the given values, we will use the formulas for area, circumference. Also, we can obtain the radius by dividing the diameter by 2 and the diameter is 2r. So we will solve for the values this way:
1. radius = 10 inches
diameter = 20
circumference = 2pie*r 2 *3.14*10 = 62.8
Area = 314
2. radius = 6ft
diameter = 12
circumference = 37.68
Area = 113.04
3. radius = 18
diameter = 36 yards
circumference = 113.04
Area = 1017.36
4. radius = 15
diameter = 30 cm
circumference = 94.2
Area = 706.5
5. radius = 5 mm
diameter = 10
circumference = 31.4
Area = 78.5
6. radius = 20 inches
diameter = 40 inches
circumference = 125.6
area = 1256
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What is the solution, if any, to the inequality |3x|\ge0? all real numbers no solution x\ge0 x\le0
Answer:
all real numbers
Step-by-step explanation:
Try a negative number, a positive number and zero for x.
All of them work.
Answer: all real numbers
The length of a rectangle is 4 ft longer than its width. If the perimeter of the rectangle is 32 ft, find its area.
To find the area of a rectangle, we need to know its length and width. Let's solve the problem step by step:
Let's assume that the width of the rectangle is represented by "w" (in feet).
According to the given information, the length of the rectangle is 4 feet longer than its width, which means the length can be represented as "w + 4" (in feet).
The perimeter of a rectangle is calculated by adding up all the sides. In this case, the perimeter is given as 32 feet.
Since a rectangle has two pairs of equal sides (length and width), we can express the perimeter equation as the following:
2(length + width) = perimeter
Substituting the values into the equation, we get:
2(w + (w + 4)) = 32
Simplifying the equation, we have:
2(2w + 4) = 32
4w + 8 = 32
4w = 24
w = 6
Now we know that the width of the rectangle is 6 feet. To find the length, we can substitute this value back into the equation for the length:
Length = w + 4 = 6 + 4 = 10 feet
The width is 6 feet, and the length is 10 feet. Now we can calculate the area of the rectangle:
Area = Length × Width = 10 × 6 = 60 square feet
Answer: The area of the rectangle is 60 square feet.
.
At a meat packing plant in Green Bay, the owners want to begin a continuing education program so their 186 employees can get a college education online if they desire. The following table represents an incomplete picture of the results. Use the following two-way frequency table for the questions below:
Men Women Total
No College Credit 28 A B
Some College C D 81
College Graduate 15 22 E
Total 79 F 186
a. Fill in the missing data in the table for values A through F. Explain the strategies you used to get each answer.
b. Describe a few pieces of data in terms of joint relative frequency. Explain why these data are both joint and relative.
c. Explain a few ways we can summarize pieces of this table using conditional relative and marginal relative frequency.
d. Are the data independent or dependent? Why?
Answer:
a. To fill in the missing data in the table, we can use the information given in the table along with the fact that the total number of employees is 186.
For value A: Since the total number of employees with no college credit is 28, and the total number of men is 79, we can subtract the number of men with some college (C) and college graduates (15) from the total number of men to find the missing value A. So A = 79 - C - 15.
For value B: Since the total number of women is 186, we can subtract the number of women with some college (D) and college graduates (22) from the total number of women to find the missing value B. So B = 186 - D - 22.
For value C: Since the total number of employees with some college is 81, and we have already determined the values A and D, we can subtract A and D from the total number of employees with some college to find the missing value C. So C = 81 - A - D.
For value D: Similarly, we can subtract B and E from the total number of women to find the missing value D. So D = 186 - B - E.
For value E: Since the total number of college graduates is 37 (15 men + 22 women), we can subtract the number of college graduates among men (15) from the total to find the missing value E. So E = 37 - 15.
For value F: Since the total number of employees is 186, we can subtract the total number of men (79) from the total to find the missing value F. So F = 186 - 79.
b. Joint relative frequency refers to the proportion of individuals that fall into a particular combination of categories. For example, the joint relative frequency of men with no college credit is the number of men with no college credit divided by the total number of employees (28/186). These data are joint and relative because they represent the proportion of individuals in a specific category combination relative to the total population.
c. To summarize the data using conditional relative frequency, we can calculate the proportion of individuals in each category given a specific condition. For example, we can calculate the conditional relative frequency of women who are college graduates by dividing the number of women who are college graduates (22) by the total number of women (186). Similarly, we can calculate the conditional relative frequency of men with some college by dividing the number of men with some college (C) by the total number of men (79).
To summarize the data using marginal relative frequency, we can calculate the proportion of individuals in each category by dividing the number of individuals in that category by the total number of individuals. For example, we can calculate the marginal relative frequency of men by dividing the total number of men (79) by the total number of employees (186). Similarly, we can calculate the marginal relative frequency of college graduates by dividing the total number of college graduates (37) by the total number of employees (186).
d. The data in the table can be analyzed to determine if there is an association or relationship between the variables. If the values in the table change depending on the categories of the other variable, then the variables are dependent. In this case, the data is dependent because the number of individuals with certain educational levels (no college credit, some college, college graduate) varies based on their gender. For example, there are different proportions of men and women in each educational category, indicating a relationship between gender and education level.
Step-by-step explanation:
The missing values in the two-way frequency table are filled based on the given values and the composition of the table. The table represents joint relative frequency, which is the proportion of specific groups in the total population. We can summarize the data using marginal and conditional relative frequencies, and the data are considered dependent because an employee's education level depends on their gender.
Explanation:To fill in the missing values of the two-way frequency table, we need to use the given numbers and the rules of the two-way frequency table. Here are the strategies used for filling in the values for A through F:
A = Total number of women - Total number of women with some college and college graduate education (in this case A = F - D - 22, because we know the number of total women F and the number of women college graduates 22, but D is still unknown).B = Total number of employees - Total number of men - Total number of women (B = 186 - 79 - F).C = Total number of some college - Number of women with some college (C = 81 - D)D = Total number of some college - Number of men with some college (D = 81 - C).E = Total number of employees - Total of men and women with and without college (E = 186 - B - 81 - 37F = Total number of employees - Total number of men (F = 186 - 79).The table will also represent joint relative frequency because each cell represents the joint occurrence of two categories (gender and education level). For example, the number of male employees with no college credit (28) divided by the total number of employees (186) is a joint relative frequency.
We may summarize the table data using conditional relative frequency and marginal relative frequency. The marginal relative frequency is the total of each row or column divided by the grand total. The conditional relative frequency would be, for example, the proportion of women among those with no college credit.
The data are dependent because the education level depends on whether the employee is a man or a woman.
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the population of a certain state can be estimated by the equation p=80.7t+18,312.3, where p represents the population of the state in thousands of people t years since 2010
The estimated population of the state in the year 2022 is 19,280,700 people.
The given equation represents the population of a certain state as a function of time, where p is the population in thousands of people and t is the number of years since 2010.
The equation is given as p = 80.7t + 18,312.3.
To estimate the population of the state, we substitute the value of t into the equation. For example, if we want to estimate the population in the year 2022 (12 years since 2010), we substitute t = 12 into the equation:
p = 80.7(12) + 18,312.3
= 968.4 + 18,312.3
= 19,280.7.
The estimated population of the state in the year 2022 is 19,280,700 people.
We can estimate the population for any given year by substituting the corresponding value of t into the equation.
It's important to note that the population is given in thousands of people, so we multiply the final result by 1,000 to obtain the population in actual numbers.
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Dewan’s bank account balance is -$16.75. He deposits checks totaling $23.59. What is his new balance? -$1.08
Answer:
$6.84
Step-by-step explanation:
This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.
Original balance: -$16.75Deposit: $23.59New balance: -$16.75 + $23.59 = $6.84PLEASE HELP! EXPLAIN THOROUGHLY EACH QUESTION SHOULD BE ANSWERED IN A 2 SENTENCE EXPLINATION AND I WILL MARK IT BRAINLIEST!
7.
This figure shows a quadrilateral made of triangle ABF
and triangle DEC
.
a. What does it mean for triangles to be congruent?
b. Jane is told that angle A
is congruent to angle D
and angle B
is congruent to angle E
She concludes that the triangles are congruent because of AAA. Explain why she thinks this, and whether or not you think she is right.
c. George is told the same thing as Jane, but he concludes that the triangles are congruent because of ASA. Explain why he thinks this, and whether or not you think he is right.
d. Are there any other ways the two triangles could be congruent with the information Jane and George have been given? Explain why you think this.
The required answers of the given questions are answered below.
a), b), c), d)
What is quadrilateral?A quadrilateral is geometric structure enclosed in 4 sides.
A) Because,
1) the angle A = Angle D
2) its has a common side
3) the angle D = Angle B
∵ ΔEAB ≅ EDC
Thus, Both the triangle is congruent by ASA.
B.)
Jane conclusion is also write for AAA
because by angle E is congruent to angle B, implies angle F is congruent to angle C.
So that is why Jane conclude AAA.
C.) George conclusion is also perfect
George thinks the following conditions-
1) the angle A = Angle D
2) its has a common side
3) the angle D = Angle B
∵ ΔEAB ≅ EDC
Thus, Both the triangle is congruent.
Hence, Both the triangles are congruent by SSS.
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1cm on a picture of a swimming pool represents 1200cm of the actual swimming pool. The length of the pictured swimming pool is 4.5cm and the width is 3cm. What is the perimeter of the actual swimming pool? Express your answer in meters.
Answer:
180 meters
Step-by-step explanation:
To find the perimeter of the actual swimming pool, you need to first find the length and width of the actual swimming pool by multiplying the length and width of the pictured swimming pool by the scale factor of 1200 cm.
Length of actual swimming pool = 4.5 cm × 1200 cm = 5400 cmWidth of actual swimming pool = 3 cm × 1200 cm = 3600 cmPerimeter of actual swimming pool = (5400 cm + 3600 cm) × 2 = 18000 cm.Now that we know that the perimeter of the actual pool is 18000 centimeters, we need to convert that to meters! Keep in mind that:
100cm = 1mNow we can divide 18000 by 100:
18000 cm ÷ 100 = 180 m
Therefore, the perimeter of the actual swimming pool is 180 m.
The base of a triangle is 3 inches more than two times the height. If the area of the triangle is 7 in.² find the base and height.
Answer:
Let's denote the height of the triangle as "h" inches.
According to the given information, the base of the triangle is 3 inches more than two times the height. Therefore, the base can be expressed as (2h + 3) inches.
The formula to calculate the area of a triangle is:
Area = (1/2) * base * height
Substituting the given values, we have:
7 = (1/2) * (2h + 3) * h
To simplify the equation, let's remove the fraction by multiplying both sides by 2:
14 = (2h + 3) * h
Expanding the right side of the equation:
14 = 2h^2 + 3h
Rearranging the equation to bring all terms to one side:
2h^2 + 3h - 14 = 0
Now, we can solve this quadratic equation. We can either factor it or use the quadratic formula. In this case, let's use the quadratic formula:
h = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, the values are:
a = 2
b = 3
c = -14
Substituting these values into the quadratic formula:
h = (-3 ± √(3^2 - 4 * 2 * -14)) / (2 * 2)
Simplifying:
h = (-3 ± √(9 + 112)) / 4
h = (-3 ± √121) / 4
Taking the square root:
h = (-3 ± 11) / 4
This gives us two possible solutions for the height: h = 2 or h = -14/4 = -3.5.
Since a negative height doesn't make sense in this context, we discard the negative solution.
Therefore, the height of the triangle is h = 2 inches.
To find the base, we substitute this value back into the expression for the base:
base = 2h + 3
base = 2(2) + 3
base = 4 + 3
base = 7 inches
Hence, the base of the triangle is 7 inches and the height is 2 inches.
Step-by-step explanation:
-The answer for the height is 5.5 units.
-The base of the triangle is aproximately 2.5454 units.
To answer this problem, you have to set an equation with the information you're given. If you do it correctly, it should look like this:
7=1/2(3+2h)
-Now, you have to solve for h:
7=1.5+h
7-1.5=h
5.5=h
-Now that you have the height, you plug it in into the triangle area formula to solve for the base:
7=1/2(b)5.5
7=2.75b
7/2.75=b
b≈2.5454
-To make sure that the corresponding values for the base and height are correct, we plug the values in and this time we are going to solve for a(AREA):
A(triangle)=1/2(2.5454)(5.5)
A=1/2(13.9997)
A=6.99985 square units
-We round the result to the nearest whole number and we get our 7, which is the given value they gave us.
How would you describe the difference between the graphs of f (x) = 3x²
and g(x) = -2² ?
OA. g(x) is a reflection of f(x) over the line y = x.
B. g(x) is a reflection of f(x) over the line y = -1.
C. g(x) is a reflection of f(x) over the x-axis.
D. g(x) is a reflection of f(x) over the y-axis.
Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C).
The given functions are f(x) = 3x² and g(x) = -2².
To understand the difference between their graphs, let's examine the characteristics of each function individually:
Function f(x) = 3x²:
The coefficient of x² is positive (3), indicating an upward-opening parabola.
The graph of f(x) will be symmetric with respect to the y-axis, as any change in x will result in the same y-value due to the squaring of x.
The vertex of the parabola will be at the origin (0, 0) since there are no additional terms affecting the position of the graph.
Function g(x) = -2²:
The coefficient of x² is negative (-2), indicating a downward-opening parabola.
The negative sign will reflect the graph of f(x) across the x-axis, resulting in a vertical flip.
The vertex of the parabola will also be at the origin (0, 0) due to the absence of additional terms.
Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C). This means that g(x) is obtained by taking the graph of f(x) and flipping it vertically. The reflection occurs over the x-axis, causing the parabola to open downward instead of upward.
Therefore, the correct answer is option C: g(x) is a reflection of f(x) over the x-axis.
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Find the sum of the first 33 terms of the following series, to the nearest
integer.
2, 11, 20,...
Step-by-step explanation:
Common difference , d, is 9
Sn = n/2 ( a1 + a33) a33 = a1 + 32d = 2 + 32(9) = 290
S33 = 33/2 ( 2+290) = 4818
You read online that a 15 ft by 20 ft brick patio would cost about $2,275 to have professionally installed. Estimate the cost of having a 25 by 26 ft brick patio installed.
Answer:
$4929
Step-by-step explanation:
I assume the cost is proportional to the area.
15 ft × 20 ft = 300 ft²
25 ft × 26 ft = 650 ft²
650/300 = x/$2275
300x = 650 × $2275
x = $4929
Answer: $4929
which of the following are like radicals? Check all
of the boxes that apply.
3x√√xy
-12x√√xy
-2x√√xj
x-√4x2²
-x√x²y
2√xy
Answer:
the first 2
Step-by-step explanation:
let me know if it is wrong
Find the net area of the following curve on the interval [0, 2].
(SHOW WORK)
f(x) = ex - e
The net area of the curve represented by f(x) = ex - e on the interval [0, 2] is e2 - 1.
To find the net area of the curve represented by the function f(x) = ex - e on the interval [0, 2], we need to calculate the definite integral of the function over that interval. The net area can be determined by taking the absolute value of the integral.
The integral of f(x) = ex - e with respect to x can be computed as follows:
∫[0, 2] (ex - e) dx
Using the power rule of integration, the antiderivative of ex is ex, and the antiderivative of e is ex. Thus, the integral becomes:
∫[0, 2] (ex - e) dx = ∫[0, 2] ex dx - ∫[0, 2] e dx
Integrating each term separately:
= [ex] evaluated from 0 to 2 - [ex] evaluated from 0 to 2
= (e2 - e0) - (e0 - e0)
= e2 - 1
The net area of the curve represented by f(x) = ex - e on the interval [0, 2] is e2 - 1.
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