For this problem we were given the distance to the moon and the width of a quarter in meters. We need to determine how many quarters we would need to stack in order to reach the moon.
In order to solve this problem, we need to divide the distance from the surface of the Earth to the moon by the width of each quarter. Notice that both numbers are presented in scientific notations, therefore we need to divide the coefficients and subtract the exponents. This is done below:
[tex]\begin{gathered} n=\frac{3.85\cdot10^8}{1.75\cdot10^{-3}} \\ n=2.2\cdot10^{8-(-3)} \\ n=2.2\cdot10^{8+3} \\ b=2.2\cdot10^{11} \end{gathered}[/tex]If Fin's claim were true, he'd need to stack a total of 2.2*10^11 quarters.
Complete both transformations below.
Then enter the final coordinates of the figure.
(1,-3)
A
C (2,-5)
B
(5,-1)
A" ([?], [])
B" ([ ], [])
C" ([],[])
1) Reflect across y - axis
2) <4.5>
Answer:
A''(3, 2), B''(-1, 4), C''(2, 0)
Explanation:
For the first step, negate the y coordinate.
For the second step, add 4 to the x coordinate and 5 to the y coordinate.
[tex]A(1,-3) \longrightarrow A'(-1, -3) \longrightarrow A''(3, 2) \\ \\ B(5,-1) \longrightarrow B'(-5,-1) \longrightarrow B''(-1, 4) \\ \\ C(2, -5) \longrightarrow C'(-2, -5) \longrightarrow C''(2, 0)[/tex]
A pair of dice is rolled 3 times. What is the probability that a sum of 9 on the 2 dice will occur at least once?
The probability that a sum of 9 on the 2 die will occur at least once is 217/729.
Sum of 9 in a pair of dice can occur in the following 4 ways.
3 + 6
4 + 5
5 + 4
6 + 3
Also, total number of ways = 6*6 = 36
Hence, probability of getting a sum of 9 = 4/36 = 1/9.
We know that,
Probability of getting a sum of 9 + Probability of not getting a sum of 9 = 1
Hence, we can write,
1/9 + Probability of not getting a sum of 9 = 1
Probability of not getting a sum of 9 = 8/9
Also,
Probability of getting the sum of 9 atleast 1 + probability of getting the sum 9 none of the times = 1
Hence, we can write,
Probability of getting the sum of 9 atleast once = 1 - probability of getting the sum 9 none of the times/
Probability of getting the sum of 9 atleast 1 = 1 - (8/9)*(8/9)*(8/9) = 1 - 512/729 = 217/729.
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I need help with this question but no one is helping me! Can someone please help me
Answer:
13 + 13 = 26
13/26 * 12/25 = 6/25 = 0.24
Select all equations that are equivalent to x² + 6x = 16
Answer
Options C and F are correct.
x² + 6x + 9 = 25
(x + 3)² = 25
are both equivalent to
x² + 6x = 16
Explanation
The equations that are equivalent to x² + 6x = 16 will all have to reduce to this exact equation on simplification.
x² + 6x + 9 = 0
Option A is not correct as this equation isn't equal to the equation given in the question.
x² + 6x + 9 = 16
x² + 6x = 16 - 9
x² + 6x = 7
Option B is not correct as this equation isn't equal to the equation given in the question.
x² + 6x + 9 = 25
x² + 6x = 25 - 9
x² + 6x = 16
This option C is corect as it matches the equation given in the quesion.
(x + 3)² = 0
x² + 6x + 9 = 0
Option D is not correct as this equation isn't equal to the equation given in the question.
(x + 3)² = 16
x² + 6x + 9 = 16
x² + 6x = 16 - 9
x² + 6x = 7
Option E is not correct as this equation isn't equal to the equation given in the question.
(x + 3)² = 25
x² + 6x + 9 = 25
x² + 6x = 25 - 9
x² + 6x = 16
This option F is corect as it matches the equation given in the quesion.
Hope this Helps!!!
Please help with both ?s I’ll mark you brainly
Answer:
1) CW 270° or CCW 90°
Step-by-step explanation:
In each case, you want to identify two transformations that will map the preimage to the image.
1)We note the transformation maps ...
A(-7, 0) ⇒ A'(0, -7) . . . . . . CCW 90° or CW 270°
B(-4, -1) ⇒ B'(1, -4)
C(-7, 3) ⇒ C'(-3, -7)
These can be described by ...
(x, y) ⇒ (-y, x)
This transformation is equivalent to either of the two transformations ...
rotation CW 270° about the originrotation CCW 90° about the origin2)As above, rotation about the origin by 90° in one direction is the same as rotation 270° about the origin in the other direction. The attached graph shows the result either way. The two equivalent transformations are ...
rotation CW 90° about the originrotation CCW 270° about the originThe coordinate transformation is ...
(x, y) ⇒ (y, -x)
what percent of 29 is 13?
Answer:
45%
Step-by-step explanation:
x * 29 = 13
x = 13/29
x = 0.448
45%
Find missing side length
Answer:
7
Step-by-step explanation:
42 divided by 3 = 14 = total of triangle XYZ
14 divided by 2 = 7
line X/Y = 7
5 In an experiment, the probability that event B occurs is -, and the probability that event A occurs given 8 5 that event B occurs is – 8 What is the probability that events A and B both occur? Simplify any fractions.
We have
probability of B occurs is 5/8
probability that event A occurs given B occurs is 5/8
We have the next formula, that is the conditional probability formula
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]where
P(A|B)= probability of A given B
P(B)= probability of B
P(A∩B)=probability of A and B
so we need to isolate the P(A∩B) in order to obtain the probability that events A and B both occur
[tex]P\mleft(A\cap B\mright)=P(A|B)\cdot P(B)=\frac{5}{8}\cdot\frac{5}{8}=\frac{25}{64}[/tex]There are 15 members in a bicycle club this fall by next summer Bing home saying number of members will be 140% of this number what is the main goal for the number of members next summer 
The main goal is 140 percent i.e., 21 members.
What is meant by percentage?
In mathematics, a percentage (from Latin: percentage , "by a hundred") may be a number or ratio expressed as a fraction of 100. it's often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" also are used. A percentage may be a dimensionless number (pure number); it has no unit of measurement. The term "percent" springs from the Latin per centum, meaning "hundred" or "by the hundred". The Italian word per cento, which means "for a hundred," gradually shrank to become the symbol for "percent." The "per" was often abbreviated as "p."—eventually disappeared entirely. The "cento" was contracted to 2 circles separated by a horizontal line, from which the fashionable "%" symbol is derived.
140 percent of 15 = 15x140/100 = 21 members
Hence, the main goal is 21 members.
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Hey bb I know that it was ur b day and u said u were gonna come out to ur parents as bi. Did u do it and if u did how did it go. Just checking in, ofc u don’t know me so u don’t even have to tell me anything if you want.
An event can be said to be a set of possible outcomes which results from an experiment.
An individual can be said to create a theory after he observes events.
A theory is said to be a set of ideas that explains the results from an experiment.
Therefore, an individual creates a theory after he observes an event.
ANSWER:
Theory
The common factors of 36, 240, and 504
Answer: 1, 2, 3, 4,6 12
Step-by-step explanation:
every single number can be divided by the answer numbes
Though 70% of women with children younger than 18 years participate in the labor force, society still upholds the stay-at-home mother as the traditional model. Some believe that employment distracts mothers from their parenting role, affecting the well-being of children. In the GSS 2014, respondents were asked to indicate their level of agreement to the statement, “A working mother hurts children.” Of the 435 male respondents who answered the question, 18% strongly agreed that a working mother does not hurt children.
Using the z-distribution, the 95% confidence interval for the proportion of male respondents that agree that a working mother does not hurt children is:
(0.1439, 0.2161).
What is a confidence interval of proportions?The bounds of a confidence interval of proportions is given according to the following rule:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the parameters are described as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The values of the other parameters are given as follows:
[tex]\pi = 0.18, n = 435[/tex]
Hence the lower end of the interval is calculated as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.18 - 1.96\sqrt{\frac{0.18(0.82)}{435}} = 0.1439[/tex]
The upper end of the interval is calculated as follows:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.18 + 1.96\sqrt{\frac{0.18(0.82)}{435}} = 0.2161[/tex]
Missing informationThe problem asks for the 95% confidence interval for the proportion of male respondents that agree that a working mother does not hurt children is:
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Find the savings plan balance after 15 months with an APR of 6% and monthly payments of $200.
The savings plan balance after 15 months with an APR of 6% and monthly payments of $200 is $3,123.
Saving plan balanceGiven data :
The APR = 6% coincides with a .06/12 = .005 monthly interest rate
Now let determine or find the total after 15 months
Total after 15 month :
Total after 15 month = 200 [ (1 +.005^ 16) - (1 + .005] /(.005)
Total after 15 month = 200 [( 1.005 ^ 16 - 1.005] /(.005)
Total after 15 month = 200 (15.614)
Total after 15 month = $3,122.8
Total after 15 month = $3,123 (Approximately)
Therefore we can conclude that the total sum is the amount of $3,123.
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Which set of ordered pairs represents y as a function of x? А A {(2,-1),(4,-2),(6,-3),(8,-4)} B {(0,0),(1,1),(1,0),(2, 1)} © {(3,3), (3,4),(4,3),(4,4)} {(1,-5),(1,5),(2,-10),(2, -15)}
Function:
A function is a relation in which every input x has a different output value y.
If there is more than 1 outputs for the same input then it doesn't represent a function.
Let us analyze each of the given options.
Option A:
{(2, -1), (4, -2), (6, -3), (8, -4)}
As you can see, each input x has a different output value y.
Therefore, it is a function
Option B:
{(0, 0), (1, 1), (1, 0), (2, 1)}
As you can see, the input (1) has two different outputs (1 and 0)
Therefore, it is not a function.
Option C:
{(3, 3), (3,4),(4,3),(4,4)}
Trish's resting heart rate is 50 beats per minute. For every
minute she exercises, her heart rate increases 5 beats per
minute. How long will it take her to reach a heart rate of
120 beats per minute?
A 5 minutes
B 14 minutes
C 34 minutes
D 70 minutes
Answer:
B
Step-by-step explanation:
(120 - 50 b/m) / 5 b / m^2 = 14 minutes
The new strain of covid is spreading at the rate of 12% a week. Currently, there are 100,000 people infected with the virus. How long will it take before the virus has infected 800,000 people?
The covid strain will take 17.33 weeks to infect 800,000 people.
To solve the given problem, we only need to utilize the exponential function formula, which is stated as
[tex]A = Pe^{rt}[/tex]
Where A is the final value,
P denotes the starting value
The rate is r and time is given by t.
Given:
The rate of spread of the new strain of covid = 12% a week
Currently the number of people infected with the virus = 100,000
To determine how long will it take before the virus has infected 800,000 people, substitute the values in the formula
[tex]A = Pe^{rt}[/tex]
[tex]800000 = 100000e^{0.12*t}[/tex]
[tex]8 = e^{0.12*t}[/tex]
[tex]ln 8 = {0.12*t}[/tex]
[tex]t = ln 8/0.12[/tex]
[tex]t = 17.33 weeks[/tex]
Therefore, the covid strain will take 17.33 weeks to infect 800,000 people.
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14. Use Structure Consider the rational
number.
a. What are the values of a and b in a)b wher
you use division to find the decimal form?
b. What is the decimal form for?3/11
The decimal form of this rational number is 0.27, where 27 in decimal is recurring.
What are the steps to solve a rational number?
The steps to solve a rational number problem are:
(a) Let 'a/b' be a rational number. From the sentence, we deduce that denotes the denominator of a rational integer, while represents the numerator. Consequently, is 3 and is 11.
(b) The decimal form is achieved by dividing by, and we described the procedure required to do so:
(i) Ten times the numerator:
Dividend is 30, and the result is known to be zero. Remainder: N/A
ii) Dividend less the dividend multiplied by the divisor by two:
Known outcome: 0.2; residuals: 8
iii) 10 times the residue:
Known outcome: 0.2; residuals: 80
iv) Divide the residue by the divisor and multiply it by 7:
0.27 as known result; 3 as residue
v) Ten times the residue:
0.27 as known result; 30 as residue
vi) Divide the divisor by two and deduct the result from the sum:
Results known: 0.272/Residue: 8
vii) 10 times the residue:
The known outcome is 0.272/Residue: 80.
viii) Divide the divisor by 7 and deduct the result from the sum:
A known outcome is 0.2727/Residue: 3.
Therefore, we can see that is a periodic decimal number in its decimal form.
As a result, we deduce that the decimal representation of this rational number is 0.27, where 27 is a regular integer.
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Sean is hiking the Appalachian Trail from Georgia to Maine. The distance of his hike is 2200 miles. It
took Sean 134 days to complete the hike. The data below represent the distance, D, he had hiked t
days after the start of his trip.
t
D(0)
0
0
19
308
In
34
578
67
1070
1. Determine the linear regression equation for this data.
Linear Regression Equation: D =
Round to the nearest tenth as needed.
2. Interpret the meaning of the slope of this regression model.
Sean hiked at a rate of approximately
91
1715
miles.
112
1902
Select an answer
3. Use your linear regression equation to estimate the total number of miles Sean had hiked in 52
days. Round your answer to the nearest mile.
In 52 days, Sean had hiked
4. Use your linear regression equation to estimate the total number of days it took for Sean to hike
377 miles. Round your answer to the nearest day.
days, Sean had hiked 377 miles.
134
2200
From the given table, it is found that:
1. The linear regression equation is: y = 16.96x + 3.
2. The meaning of the slope is that he hiked an average of 16.96 miles a day.
3. In 52 days, Sean had hiked 885 miles.
4. In 22 days, Sean had hiked 377 miles.
How to find the equation of linear regression?To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.
In the context of this problem, the points are given as follows:
(0,0), (19,308), (34, 578), (67, 1070), (91, 1715), (112, 1902), (134, 2200).
Using a calculator, the equation is given as follows:
y = 16.96x + 3.
The input of the function and the output of the function are given as follows:
Input: number of days.Output: number of miles hiked.The slope is the rate of change, that is, change in the output divided by change in the input. Hence the slope of 16.96 means that he hiked an average of 16.96 miles a day.
In 52 days, the number of miles hiked is:
y = 16.96(52) + 3 = 885 miles.
The number of days is took to hike 377 miles is found as follows:
377 = 16.96x + 3
x = 374/16.96
x = 22 days.
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Question 12 of 47Solve kx - 2 = 7 for x.
ANSWER:
D. x = 9/k
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]kx-2=7[/tex]We solving for x:
[tex]\begin{gathered} kx=7+2 \\ \\ x=\frac{9}{k} \end{gathered}[/tex]The correct answer is D. x = 9/k
please help im stuck on this
04) The complementary angles are the angles whose sum is 90° thus { 26°,54°,48°,29°,22°} will be the corresponding angles.05)The supplementary angles are the angles whose sum is 180° thus {54°,48°,12°,135°,91°} will be the corresponding angles.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
If m∠A + m∠B = 90° then A and B will be the complimentary angle.
The complementary of 64° = 90° - 64° = 26°
The complementary angle of 36° = 90° - 36° = 54°
The complementary angle of 42°= 90° - 42° = 48°
The complementary angle of 51°= 90° - 51° = 29°
The complementary angle of 68°= 90° - 68° = 22°
If m∠A + m∠B = 180° then A and B will be the supplementary angle.
The supplementary of = 180° - 126° = 54°
The supplementary of = 180° - 132° = 48°
The supplementary of = 180° - 178° = 12°
The supplementary of = 180° - 45° = 135°
The supplementary of = 180° - 89° = 91°
Hence " { 26°,54°,48°,29°,22°} will be the corresponding complementary angle and {54°,48°,12°,135°,91°} will be the corresponding supplementary angles".
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You deposit $300 each month into an account earning 6% interest compounded monthly. a) How much will you have in the account in 30 years? $ b) How much total money will you put into the account? $ c) How much total interest will you earn?
Using the future value formula, it is found that:
a) You will have $301,355 in the account after 30 years.
b) You will have put $108,000 in the account.
c) You will have earned $193,355 in interest.
What is the future value formula?The future value formula is given by:
[tex]V(n) = P\left[\frac{(1 + r)^n - 1}{r}\right][/tex]
In which the parameters are described as follows:
P is the payment.n is the number of payments.r is the interest rate.Considering the $300 deposits, the interest rate of 6% and the monthly compoundings for 30 years, the values of the parameters are given as follows:
P = 300, r = 0.06/12 = 0.005, n = 12 x 30 = 360.
Hence the balance of the account after 30 years will be given by:
[tex]V(30) = 300\left[\frac{(1.005)^{360} - 1}{0.005}\right][/tex]
V(30) = $301,355.
The amount placed into the account is given by:
360 x 300 = $108,000.
The remaining amount is earned in interest, hence:
301355 - 108000 = $193,355.
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Solve for x. Enter the solutions from least to greatest.2x^2 - 24x + 54 = 0lesser x =greater x =
To solve the equation
[tex]2x^2-24x+54=0[/tex]we are going to use the general formula for quadratic equations:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In our case a=2, b=-24 and c=54. Then
[tex]\begin{gathered} x=\frac{-(-24)\pm\sqrt[]{(-24)^2-4(2)(54)}}{2(2)} \\ =\frac{24\pm\sqrt[]{576-432}}{4} \\ =\frac{24\pm\sqrt[]{144}}{4} \\ =\frac{24\pm12}{4} \end{gathered}[/tex]Then x is:
[tex]\begin{gathered} x=\frac{24-12}{4}=\frac{12}{4}=3 \\ or \\ x=\frac{24+12}{4}=\frac{36}{4}=9 \end{gathered}[/tex]Mr. Jones and Mr. Evansbee both have gardens shaped as squares. The length of each side of Mr. Jones’ garden is 6 yd. The length of each side of Mr. Evansbee’s garden is 10 yd.
(a) Write an expression with exponents for the area of Mr. Jones’ garden. Then, find the area of the garden.
(b) Write an expression with exponents for the area of Mr. Evansbee’s garden. Then, find the area of the garden. Each plant takes up 2 yd(squared) of space in both gardens.
(c) How many plants can Mr. Jones place in his garden? How many plants can Mr. Evansbee place in his garden? Explain your reasoning.
(d) For each garden, the cost per plant is $4.99. Using your answers from part (c), how much will each gentleman spend on plants for his garden?
Answers need to be step-by-step please
Answer:
(a) expression: (6 yd)²; area: 36 yd²
(b) expression: (10 yd)²; area: 100 yd²
(c) Jones: 18; Evansbee: 50
(d) Jones: $89.82; Evansbee: $249.50
Step-by-step explanation:
You want the area, number of plants that can be placed, and the cost of plantings for gardens that are 6 yards square and 10 yards square. Each plant takes 2 square yards and costs $4.99.
Area of a squareThe formula for the area of a square of side length s is ...
A = s²
(a) Jones' gardenThe area of a square garden with a side length of 6 yards is ...
A = (6 yd)² . . . . . expression for the area
A = 36 yd² . . . . . the area of the garden
(b) Evansbee's gardenThe area of a square garden with a side length of 10 yards is ...
A = (10 yd)² . . . . . expression for the area
A = 100 yd² . . . . . the area of the garden
(c) Number of plants
The area used by the plants is the product of their number and the area taken by each.
For Jones' garden, the number of plants that can be placed is ...
n(2 yd²/plant) = 36 yd²
n = (36 yd²)/(2 yd²/plant) = 18 plants
Mr. Jones can place 18 plants in his garden.
For Evansbee's garden, the number of plants that can be placed is ...
n(2 yd²/plant) = 100 yd²
n = (100 yd²)/(2 yd²/plant) = 50 plants
Mr. Evansbee can place 50 plants in his garden.
(d) Cost of plantsAt $4.99 each, the cost of plantings will be $4.99 times the number of plants.
Plants for Jones' garden cost 18($4.99) = $89.82.
Pants for Evansbee's garden cost 50($4.99) = $249.50.
Select the correct answer.
What is the sum of this expression?
The mixed fraction 4 3/8 + 7 3/4 is equivalent to the fraction to 12 1/8
How to solve an equation?An equation shows the relationship between two or more numbers and variables.
The mixed fraction 4 3/8 is equivalent to the fraction (4 * 8 + 3)/8 = 35/8
The mixed fraction 7 3/4 is equivalent to the fraction (4 * 7 + 3)/4 = 31/4
Hence:
4 3/8 + 7 3/4
Substituting:
= 35/8 + 31/4
Simplifying:
= 97/8 = 12 1/8
4 3/8 + 7 3/4 is equal to 12 1/8
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On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction.
The number b varies directly with the number a. Forexample b = 22 when a = -23. Which equation represents this
direct variation between a and b?
O b=-a
O-b=-a
Ob-a=0
Ob(-a)=0
The equation b=-a is the correct equation.
What is an equation?
An equation is a statement in maths that demonstrates the equivalence of two factors by linking them with the equivalent symbol =. Equations are used to define geometric patterns in Euclidean geometry. Because the equations beneath consideration, such as implicitly equations or descriptive equations, contain an unlimited variety of solutions, the goal has started to shift: instead of directly stating the alternatives or collecting them, which again is unattainable, one utilizes equations to analyze the features of figures. This is the fundamental concept of elementary algebra, a significant mathematics discipline. Differential equations is equations in which 1 or more polynomials and its implications are involved. They are addressed by locating a functional expression that doesn't employ derivatives. Differential equations are utilized to analyze rate-related phenomena.
The equation b=-a is the correct equation.
Hence, option (a) b=-a is correct.
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A camera has a listed price of $788.99 before tax. If the sales tax rate is 7.75%, find the total cost of the camera with sales tax included. Round your answer to the nearest cent, as necessary.
Answer:
$850.14
Step-by-step explanation:
7.75% as decimal: 0.0775
788.99 x 0.0775 = 61.146725
788.99 + 61.146725 = 850.136725
850.136725 rounded to nearest cent is 850.14
So the total price of the camera with sales tax included is $850.14
Describe how to determine the average rate of change between x=3 and x=5 for the function f(x)3x^3+2. Include the average rate of change in your answer.
Given the function:
[tex]f\mleft(x\mright)=3x^3+2[/tex]» Solve the equation 2y+6=y-7
Answer:
y = -13
Step-by-step explanation:
a) Subtract y from both sides.
2y + 6 − y = y − 7 − y
y + 6 = −7
b) Subtract 6 from both sides.
y + 6 − 6 = −7 − 6
y = -13
Match the area formula with the correct polygon. A = 1/2bh parallelogram A = bh triangle A = 1/2 (b1 + b ) + trapezoid
The area of a parallelogram can be determined by multiplying its base and height, the formula is
[tex]A=bh[/tex]The area of a triangle is equal to half the product between the base and the height, following the formula:
[tex]A=\frac{1}{2}(bh)[/tex]The area of a trapezoid is equal to the product of half the sum of its bases and its height following the formula:
[tex]A=\frac{1}{2}(b_1+b_2)h[/tex]Solve the equations justify your response by showing mathematical steps
Given:-
[tex]undefined[/tex]