Complete the parts in each step to find the area of each trapezoid?
Press on the picture to see it
Answers
The area of the trapezoid is 20 in².
Solution:
Given data:
Length of the bottom base = 7 in
Length of the top base = 3 in
Height of the trapezoid = 4 in
Step 1: Area of the trapezoid formula,
[tex]$A=\frac{b_{1}+b_{2}}{2} \times h[/tex]
Step 2: Substitute the given values in the formula.
[tex]$A=\frac{7+3}{2} \times 4[/tex]
Step 3: Add 7 and 3.
[tex]$A=\frac{10}{2} \times 4[/tex]
Step 4: Divide 10 by 2, we get
[tex]A=5 \times 4[/tex]
Step 5: Multiply 5 by 4, we get
A = 20 in²
The area given in the picture is wrong.
The area of the trapezoid is 20 in².
Related Questions
Which is true regarding Adi's use of algebra tiles?
Adi used algebra tiles to represent the product
(-2x-2)(2x-1).
A. She used the algebra tiles correctly.
B. She did not represent the two original factors correctly
on the headers.
C. The signs on some of the products are incorrect.
D. Some of the products do not show the correct powers
of x.
Answers
Answer:
A. True
B. False
C. False
D. False
Step-by-step explanation:
Hence she used it correctly by making parts of it.
Answer: Its A my boy
Step-by-step explanation:
Use synthetic substitution to find f(2) and f(3).
1.f(x) = 3x^4 - 12x^3 - 12x^2 + 30x
2. Write the polynomial equation of degree 4 with leading coefficient 1 that has roots at -2, -1, 3, and 4.
Answers
Answer:
see explanation
Step-by-step explanation:
(1)
To obtain f(2) and f(3) substitute x = 2, x = 3 into f(x)
f(2) = 3([tex]2^{4}[/tex] ) - 12(2³) - 12(2²) + 30(2)
= 48 - 96 - 48 + 60 = - 36
f(3) = 3([tex]3^{4}[/tex] ) - 12(3³) - 12(3²) + 30(3)
= 243 - 324 - 108 + 90 = - 99
(2)
Given a polynomial with roots x = a, x = b, then
(x - a), (x - b) are the factors
and the polynomial is the product of the factors
Here the roots are x = - 2, x = - 1, x = 3 and x = 4, thus the factors are
(x + 2), (x + 1), (x - 3) and (x - 4)
The polynomial is the product of the factors, thus
f(x) = (x + 2)(x + 1)(x - 3)(x - 4) ← expand in pairs using FOIL
= (x² + 3x + 2)(x² - 7x + 12) ← distribute
= [tex]x^{4}[/tex] - 7x³ + 12x² + 3x³ - 21x² + 36x + 2x² - 14x + 24 ← collect like terms
= [tex]x^{4}[/tex] - 4x³ - 7x² + 22x + 24
Factor the expression: 8t-32u
Answers
Answer:
Step-by-step explanation:
8t - 32u = 8*t - 8*4*u
= 8*(t - 4u) = 8(t -4u)
Emily has a coupon for 20% off of her purchase at the store. she finds a backpack that she likes on the discount rack. it’s original price is $60 but everything on the rack comes with the 30% discount. Emily says 30% and 20% make 50% so I will cost $30 is Emily correct explain what price will Emily pay for the backpack
Answers
Answer:
$38.40 new price. Usual coupons give 20% only off the sale price if this is the case for the backpack you would need to show both answers one of 50% if both coupons allowed. Second workings would be your answer 30% of $60 = $18 and 20% further =$3.60 $18+$3.60= $21.60 full 20% discount on store 30% discount.
Therefore you can see $60-21.60 = $38.40 new price.
This is $21.60 discount and appears to be 36.8%
Step-by-step explanation:
What is the answer for this equation?
7(8h+2)=
Answers
Answer:
56h+18
Distribute the 7 inside the paranthesis
it take 96 pounds or seed to completely plant a 10-acre field. how many pounds of seed are needed per acre?
Answers
Answer:
9.6 lb/acre
Step-by-step explanation:
This is a unit rate problem. You want to know the number of pounds used for one acre.
You divide 96 pounds by 10 acres to find the number of pounds per 1 acre.
(96 lb)/(10 acres) = 9.6 lb/acre
Answer: 9.6 lb/acre
To find how many pounds of seed are needed per acre, divide the total amount of seed used, which is 96 pounds, by the total area, 10 acres. The answer is 9.6 pounds per acre.
Explanation:This problem is a simple division problem in Mathematics. We start by taking the total amount of seed that was used, which is 96 pounds. Then, we divide this by the total area, which in this case is 10 acres.
When we perform the calculation: 96 pounds ÷ 10 acres, the solution we get is 9.6 pounds per acre.
So, it requires 9.6 pounds of seed to plant one acre of the field. Remember, this is an average estimation. Actual seed requirement may vary depending on the type of seed and other factors such as soil and weather conditions.
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A chemist needs 500mL of 20% acid and 80% water mix for an experiment. He adds x mL of a 10% acid and 90% water and y mal of a 30% acid and 70% water mix to the 20% acid and 80% water mix. Find the amounts x and y
Answers
Answer:
x = y = 250 mL
Step-by-step explanation:
The desired concentration of acid (20%) is exactly halfway between the concentrations of the available supplies (10%, 30%). So, the mix will be equal parts of each of those. x and y are both half the total quantity required:
x = y = (500 mL)/2 = 250 mL
_____
If you need an equation to solve this, you can let x = 500 -y and write the equation for the acid volume in the final mix:
10%(500 -y) +30%(y) = 20%(500)
50 -0.1y +0.3y = 100 . . . . . eliminate parentheses
0.2y = 50 . . . . . . . . . . . . . . subtract 50, collect terms
y = 250 . . . . . . . . . . . . . . . multiply by 5 (equivalently, divide by 0.2)
x = 500 -250 = 250
Cyclone filled 250 bottles of water to give people in the park. He handed out 40 bottles each hour. He had 10 bottles left.How many hours has Cyclone been at the park?
Answers
Answer:
it took Cyclone 6 hours in handing the bottles
Step-by-step explanation:
If cyclone had 10 bottles left after handing 40 bottles per hour = 250 - 10 = 240bottles
which means cyclone handed 240 bottles.
Therefore, if he handed 40bottle each hour and 240 bottles were handed all through. So the amount of hours cyclone used in handing the bottles will be 240 / 40 = 6 hours
can someone plz help me find the riddle.
Why would a prism beat a sphere in a competition??
Answers
A prism would beat a sphere in a competition because a prism has more sides and angles to outmaneuver the sphere, which is a single-sided shape with no angles.
To understand the riddle, one must consider the properties of both a prism and a sphere. A prism is a polyhedron with two congruent and parallel faces (called bases), and its sides are parallelograms.
The number of sides a prism has depends on the shape of its base. For example, a triangular prism has five faces (two triangular bases and three rectangular sides), while a hexagonal prism has eight faces (two hexagonal bases and six rectangular sides).
On the other hand, a sphere is a perfectly round geometrical object in three-dimensional space that is the surface of a ball (viz., the geometric object consisting of all points in three-dimensional space at a distance r from a central point). Unlike a prism, a sphere has no edges or vertices, and it has only one surface with no sides.
In a competition where maneuverability and the ability to approach from different angles are advantageous, a prism would have more options to outmaneuver a sphere. A prism can present multiple faces to the sphere, potentially confusing or disorienting it, while the sphere, being uniform in all directions, has no such advantage. The prism's angles and edges could also be used strategically to deflect or redirect the sphere, giving the prism a competitive edge.
Therefore, the riddle plays on the geometric properties of the two shapes to suggest that in a hypothetical competition, the prism's multiple faces and angles would allow it to outperform the sphere, which has a single continuous surface and no angles to leverage.
The circle is inscribed in triangle PRT. A circle is inscribed in triangle P R T. Points Q, S, and U of the circle are on the sides of the triangle. Point Q is on side P R, point S is on side R T, and point U is on side P T. The length of R S is 5, the length of P U is 8, and the length of U T is 6. Which statements about the figure are true? Select two options. The perimeter of the triangle is 19 units. TU ≅ TS PU ≅ TU The length of line segment PR is 13 units. The length of line segment TR is 10 units.
Answers
Option B: [tex]TU $\cong$ TS PU $\cong$ TU[/tex]
Option C: The length of line segment PR is 13 units.
Explanation:
Given that the circle is inscribed in triangle PRT. Points Q, S, and U of the circle are on the sides of the triangle. Point Q is on side P R, point S is on side R T, and point U is on side P T.
The length of RS is 5, the length of PU is 8 and the length of UT is 6.
Option A: The perimeter of the triangle is 19 units.
The perimeter of the triangle is given by
Perimeter of ΔPRT = PU + UT + TS + SR + RQ + QP
Since, P, T and R are tangents to the circle and we know that "Tangents to a circle drawn to a point outside the circle are equal in length".
Thus, we have,
RS = RQ = 5
PU = PQ = 8 and
UT = TS = 6
Substituting the values in the perimeter of ΔPRT, we get,
Perimeter of ΔPRT = 8 + 6 + 6 + 5 + 5 + 8 =38 units
Thus, the perimeter of the triangle is 38 units.
Hence, Option A is not the correct answer.
Option B : [tex]TU $\cong$ TS PU $\cong$ TU[/tex]
Since, P, T and R are tangents to the circle and we know that "Tangents to a circle drawn to a point outside the circle are equal in length".
Then [tex]TU $\cong$ TS PU $\cong$ TU[/tex]
Hence, Option B is the correct answer.
Option C: The length of line segment PR is 13 units.
The length of PR is given by
PR = PQ + QR
Substituting the values RQ = 5 and PQ = 8, we get,
PR = 5 + 8 = 13 units
Thus, the length of line segment PR is 13 units.
Hence, Option C is the correct answer.
Option D: The length of line segment TR is 10 units.
The length of TR is given by
TR = TS + SR
Substituting the values TS = 6 and SR = 5, we get,
TR = 6 + 5 = 11 units
Thus, the length of line segment TR is 11 units
Hence, Option D is not the correct answer.
Answer: b and e
Step-by-step explanation:
Please answer and explain (surface area)
Answers
Answer:
475 cm^2
Step-by-step explanation:
Base: 6 × 17 = 102
Left-most face: 6 × 11 = 66
Top face: 6 × 20 = 120
Front/Back faces: 11 × 17 = 187
Add: 102 + 66 + 120 + 187 = 475
A rectangle has a width of 28
centimeters and a length of
45 centimeters. What is the
length, in centimeters, of its
diagonal?
Answers
Answer:
diagonal = 53 cm
Step-by-step explanation:
(diagonal)² = (length)²+ (width)²
= (45)² + 28²
= 2025 + 784 =2809
diagonal = √2809 =√53*53 = 53 cm
Answer:53
Step-by-step explanation:
suppose you connect the points on the graph in the example, what would the graph look like?
Answers
Answer:
Your graph would look like lines going up and up and up
Step-by-step explanation:
Why you ask? Well, because the graph shown here is going by the factors of 6. And the factors of 6 are pretty high, which means it would be going up like a twisted line going right ot left depending which way you look at it. It would be going up and up because like 18 times 6 is 108 and 20 times 6 is 120.
something + something = 48
something * something = -40
Answers
Answer:
Hello there!
So, your question is
"something + something = 48"
and
"something * something = -40"
Since you didn't really give that much specific details, and you could correct me on this later, I'd say for the first one it's
47 + 1 = 48
As for the second one, it could be
-5 * 8 = - 40
OR
5 * -8 = -40
both ways are correct.
Step-by-step explanation:
Hope this helps! If you have more instructions on this question, please let me know! Instructions are very important for MATH, cause even I mess up if the instructions are not clear. :)
- immaback2x
Answer:
Hi
Step-by-step explanation:
2. Henri and Talia are mixing paint for an art project. They mixed p liters of red paint,
0.6 liters of blue paint, and p-0.4 liters of white paint. They then divided the mixture
evenly into 2 jars. If each jar contains 2.4 liters of paint, how many liters of red paint did
they use? Type your numeric answer below.
Answers
Answer:
They used 2.3 liters of red paint
Step-by-step explanation:
Henri and Talia are mixing paint for an art project.
They mixed amount of red paint = p liters
They mixed amount of blue paint = 0.6 liters
They mixed amount of white paint = p-0.4 liters
Total amount of paint = p +0.6 +p - 0.4 = 2p+0.2
They then divided the mixture evenly into 2 jars.
Amount of paint in 1 jar = [tex]\frac{2p+0.2}{2}[/tex]
We are given that Each jar contains 2.4 liters of paint
So, [tex]\frac{2p+0.2}{2}=2.4[/tex]
[tex]2p+0.2=2.4 \times 2[/tex]
[tex]2p+0.2=4.8[/tex]
[tex]2p=4.8-0.2[/tex]
2p=4.6
[tex]p=\frac{4.6}{2}[/tex]
p=2.3
Hence They used 2.3 liters of red paint
The correct statement is the red paint they use is 2.3 liters.
What is the linear system?It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
Given
They mixed p liters of red paint, 0.6 liters of blue paint, and a p-0.4 liter of white paint.
They then divided the mixture evenly into 2 jars. If each jar contains 2.4 liters of paint.
How to find the red color in it?They mixed p liters of red paint, 0.6 liters of blue paint, and a p-0.4 liter of white paint. According to this, the total paint will be
The total paint in liters = p + 0.6 + p - 0.4
The total paint in liters = 2p + 0.2
They then divided the mixture evenly into 2 jars. If each jar contains 2.4 liters of paint. According to this,
[tex]\rm \dfrac{2p+0.2}{2} = 2.4[/tex]
On solving the equation, then p will be
[tex]\begin{aligned} \rm \dfrac{2p+0.2}{2} &= 2.4\\\rm 2p + 0.2 &= 4.8\\\rm 2p &= 4.6\\\rm p &= 2.3\end{aligned}[/tex]
Thus, 2.3 liters of red paint did they use.
More about the linear system link is given below.
What is 0.25% as a fraction or mixed number in simplest form.
Answers
Answer:
The answer is one fourth
Answer:
1/4
Step-by-step explanation:
0.25 is the same as 25/100 in simplest form that is 1/4 because you can divide both the numerator and denomenator by 25
The sum of four times a first number and a second number is 68. If the first number is decreased by twice the second number the result is -1. Find the numbers.
Answers
The first number is 15 and the second number is 8.
Step-by-step explanation:
Let us assume,
First number be 'x'.Second number be 'y'.Given :
Sum of four times a first number and a second number is 68.
⇒ 4x + y = 68
⇒ y = 68-4x
If the first number is decreased by twice the second number the result is -1.
⇒ x - 2y = -1
Substitute y = 68-4x in the above equation.
⇒ x - 2(68-4x) = -1
⇒ x-136+8x = -1
⇒ 9x - 136 = -1
⇒ 9x = -1+136
⇒ x = 135/9
⇒ x = 15
The first number is 15.
The second number is y = 68-4x.
⇒ y = 68 - 4(15)
⇒ y = 68-60
⇒ y = 8
The second number is 8.
flagpole casts a shadow that is 50 feet long. At the same time, a woman who is five feet four inches tall casts a shadow 40 inches long. How tall is the flagpole
Answers
Answer:
960 in (or 80 ft)
Step-by-step explanation:
First, we should convert all of the feet measurements to inches so we have equal units of measurements:
50 ft = 600 in
5 ft 4 in = 64 in
40 in = 40 in
Now we can solve this problem with a simple proportion:
h / 600 = 64 / 40
600 * 64 = 40h
38400 = 40h
960 in = h
***also h = 80 ft
By setting up a proportion of corresponding sides from similar triangles, we find that the flagpole's height is roughly 80 feet.
Explanation:This is a problem of similar triangles. The flagpole and its shadow form one triangle, and the woman and her shadow form a smaller, similar triangle. Since the triangles are similar, the ratio of corresponding sides should be equal. In this case, we have:
height of the flagpole / shadow of the flagpole = height of the woman / shadow of the woman
We can plug the provided values into this equation:
height of the flagpole / 50 feet = 5.33 feet / 3.33 feet
To solve for the height of the flagpole, we cross-multiply and divide, giving us:
height of the flagpole = (5.33 feet / 3.33 feet) * 50 feet
Following that logic, the height of the flagpole is approximately 80 feet tall.
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Which is the best step to do next to solve the equation by
completing the square?
The first few steps in solving the quadratic equation 5x2 +
27x = 14 - 13x by completing the square are shown.
5x2 + 27x = 14 - 13x
5x2 + 40x = 14
5(x2 + 8x) = 14
5(x2 + 8x + 16) = 30
5(x2 + 8x + 16) = 94
5(x2 + 8x + 4) = 18
5(x2 + 8x + 4) = 34
Answers
Answer:The correct answer among the choices given is option 2.
Completing the square is done as follows:
1. Write the equation in a way that the constants are in the right side while the terms with x are on the left.
5x^2 + 27x + 13x = 14
5x^2 + 40x = 14
2. Make sure that the coefficient of the x^2 term is 1.
5(x^2 + 8x) = 14
3. Adding a term to both sides that will complete the square in the left side. This is done by dividing the coefficient of the x term by 2 and squaring it. Note: The same amount should be added to the right side to balance the equation.
5(x^2 + 8x + 16) = 14 + 80
5(x+4)^2=94
Step-by-step explanation:
The correct step is 5x2 + 40x = 14.
What is Completing the square method?Completing the square is a method that is used for converting a quadratic expression of the form ax^2 + bx + c to the vertex form a(x - h)2 + k.
The most common application of completing the square is in solving a quadratic equation. This can be done by rearranging the expression obtained after completing the square: a(x + m)^2 + n, such that the left side is a perfect square trinomial. Completing the square method is useful in:
Converting a quadratic expression into vertex form.Analyzing at which point the quadratic expression has minimum/maximum value.Graphing a quadratic function.Solving a quadratic equation.Deriving the quadratic formula.Given:
5x^2 + 27x = 14 - 13x
5x^2 + 27x + 13x = 14
5x^2 + 40x = 14
5(x^2 + 8x) = 14
Now,
Adding a term to both sides that will complete the square in the left side.
by dividing the coefficient of the x term by 2 and squaring it.
5(x^2 + 8x + 16) = 14 + 80
5(x+4)^2=94
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Write an equation of the line that passes through a pair of points (5, -2) , (4,5)
Answers
Answer:
y = -7x + 33
Step-by-step explanation:
Use the Point Slope Form: (y - y1) = m(x - x1)
Step 1: Find the Slope
Slope = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
Slope = [tex]\frac{5 - (-2)}{4 - 5}[/tex]
Slope = [tex]\frac{5 + 2}{-1}[/tex]
Slope = [tex]\frac{7}{-1}[/tex]
Slope = -7
Step 2: Plug into the point slope form
(y - 5) = -7(x - 4)
y - 5 + 5 = -7x + 28 + 5
y = -7x + 33
Answer: y = -7x + 33
Ava washes 12 % windows in /hour. At this rate, how many windows can
she wash in one hour?
Answers
Answer:
She will wash 24% windows in one hour
Step-by-step explanation:
If Ava washes 12% windows in half hour
Since 2 half hours makes one hour
Therefore, 2 × 12% will be washed in one hour
That is, Ava will wash 24% windows in one hour
Select the expression that represents the following statement: 52 minus 4 times the difference of 13 and 7.
Answers
Answer:
(52 - 4) * (13 - 7)
Step-by-step explanation:
Step 1: Convert words into an expression
52 minus 4 times the difference of 13 and 7.
(52 - 4) * (13 - 7)
Answer: (52 - 4) * (13 - 7)
If needed simplify
(52 - 4) * (13 - 7)
48 * 6
288
Which shows all the values of x that make the rational expression undefined? x = 6 x = 7 x = –6 or x = 6 x = –7 or x = 7
Answers
The rational expression is given by:
[tex]E=\frac{2x^2-72}{5x^2-245} \\ \\ Factor \ out: \\ \\ E=\frac{2(x^2-36)}{5(x^2-49)} \\ \\ E=\frac{2(x-6)(x+36)}{5(x-7)(x+7)} : \ \ \ \ a^2-b^2=(a-b)(a+b)[/tex]
The denominator can't be zero, therefore:
[tex](x-7)(x+7)\neq 0 \\ \\ \\ Thus: \\ \\ \boxed{x\neq 7 \ and x \neq -7}[/tex]
Finally, the values of x that make the rational expression undefined are
x = 7 and x = -7
Answer:
x = 7 and x = -7
Step-by-step explanation:
Got it right on edge 2021
I got a 100.
Need the response for this please help
Answers
Answer: it is important to keep both side of the equation balance while solving because, an equality sign is used which means, the right hand side is equal to the left hand side, and if the equation isn't balance we won't be able to get the correct answer for the missing variable.
We use greater than (>), less than (<) and greater than and equal to=> and less than and equal to <=
Step-by-step explanation:
Two functions are combined resulting in the function j(x) = -3x^2+5.
Which operations applied to the specified functions could result in j(x)? Select three options.
-two linear functions by addition
-two quadratic functions by addition
-a linear function and a quadratic function by addition
-two linear functions by multiplication
-two quadratic functions by multiplication
Answers
To obtain j(x) = -3x²+5, we need to combine a linear function and a quadratic function. Three possible options are provided in the response.
Explanation:The function j(x) = -3x²+5 is a quadratic function. To obtain this function by combining two other functions, we can use a linear function and a quadratic function added together. This means that one of the functions will have a degree of 1 and the other will have a degree of 2. Here are three options that could result in j(x):
Quadratic function: 2x²-7x+5
Linear function: -5x
Combining the linear function -5x and the quadratic function 2x²-7x+5 will result in j(x).Quadratic function: -x²+10x-5
Linear function: -4x+5
Combining the linear function -4x+5 and the quadratic function -x²+10x-5 will result in j(x).Quadratic function: 5x²-12x+10
Linear function: -3x+5
Combining the linear function -3x+5 and the quadratic function 5x²-12x+10 will result in j(x).Learn more about linear function and a quadratic function here:
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HELP! PLEASE! Jackson is building a small rectangular basketball section in his backyard. The length of the section will be 1.25 times the width of the section.
Part A
Create an equation to represent the area of the basketball section, A, in terms of the width, w.
Part B
Jackson decides to make the area of the basketball section 245 square feet. What are the dimensions, in feet, of the basketball section?
SHOW ALL WORK PLEASE
Answers
Answer:
Part A) [tex]A=1.25W^2[/tex]
Part B) Length: 17.5 feet and Width: 14 feet
Step-by-step explanation:
Part A) Create an equation to represent the area of the basketball section A, in terms of the width W.
Let
L ----> the length of the rectangular basketball section
W ---> the width of the rectangular basketball section
we know that
The area of the rectangular basketball section is equal to
[tex]A=LW[/tex] ----> equation A
The length of the section will be 1.25 times the width of the section
so
[tex]L=1.25W[/tex] ----> equation B
substitute equation B in equation A
[tex]A=(1.25W)W\\A=1.25W^2[/tex]
Part B) Jackson decides to make the area of the basketball section 245 square feet. What are the dimensions, in feet, of the basketball section?
we have
[tex]A=1.25W^2\\A=245\ ft^2[/tex]
so
[tex]245=1.25W^2[/tex]
solve for W
[tex]W^2=245/1.25\\W^2=196\\W=14\ ft[/tex]
Find the value of L
substitute the value of W in the equation B
[tex]L=1.25(14)=17.5\ ft[/tex]
therefore
The dimensions are :
Length: 17.5 feet
Width: 14 feet
The area equation for the basketball section is A = 1.25w². For an area of 245 square feet, the width, w, is approximately 14 feet, and the length, l, is approximately 17.5 feet.
Explanation:Part A: Equation of the Area
To create an equation that represents the area, A, of the basketball section in terms of the width, w, we start with the fact that the length is 1.25 times the width. So, if l represents the length, then l = 1.25w. The area of a rectangle is found by multiplying the length by the width, hence the area A = l × w. Substituting l = 1.25w gives us the equation A = (1.25w) × w = 1.25w².
Part B: Dimensions of the Basketball Section
Given the area of the basketball section is 245 square feet, we can use the equation found in Part A to determine the width and subsequently the length. The equation A = 1.25w² becomes 245 = 1.25w². Solving for w, we take the square root of both sides after dividing by 1.25, which gives w = √(245/1.25) ≈ 14 feet. To find the length, l, we multiply the width by 1.25, resulting in l = 1.25 × 14 ≈ 17.5 feet. Therefore, the dimensions are approximately 14 feet in width and 17.5 feet in length.
Please answer ASAP! Thank you in advance and make sure to use antibacterial soap and wash your hands for 1 minute.
Answers
Answer:
[tex]12.5 \ ft^2[/tex]
Step-by-step explanation:
Given that height is a quarter the sum of bases and that the height is 2.5ft.
The sum of bases is calculated as:
[tex]h=\frac{1}{4}\sum{b_i}=2.5\\\\\sum{b_i}=2.5\times 4\\\\\sum{b_i}=b_1+b_2=10\ ft[/tex]
#Having that (b1+b2=10 ft), we can now calculate the area using the given formula using the given figures:
[tex]A=\frac{1}{2}\times 2.5\times (b_1+b_2), b_1+b_2=10\\\\=\frac{1}{2}\times 2.5\times10\\\\=12.5[/tex]
Hence, the area of the trapezoid is 12.5 sq ft
*Using the h=2.5ft and the [tex]A=\frac{1}{2}h(b_1+b_2)[/tex]
Triangle A B C is shown. Angle A C B is a right angle. The length of hypotenuse A B is 12 centimeters, the length of C B is 9.8 centimeters, and the length of A C is 6.9 centimeters.
Which expressions can be used to find m∠BAC? Select three options.
Answers
To find the measure of angle BAC in the given right triangle ABC, we can use the trigonometric function sine.
To find the measure of angle BAC in the given right triangle ABC, we can use the trigonometric function sine. The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, we know that the length of the side opposite angle BAC is 6.9 centimeters and the length of the hypotenuse is 12 centimeters. Therefore, we can use the equation sin(BAC) = opposite/hypotenuse to find the measure of angle BAC.
sin(BAC) = 6.9/12
BAC ≈ sin-1(6.9/12)
Using a calculator, we can find that BAC ≈ 33.24°.
Learn more about trigonometry here:https://brainly.com/question/11016599
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What does the value of x have to be so that
(x,-7) and (-1,4) have a slope of 11/4 between them?
Answers
Answer:
x=-5
Step-by-step explanation:
slope=m=11/4
(x, - 7) x1 =x, y1 =-7
(-1,4) x2=-1, y2 =4
m=(y2-y1) /(x2-x1)
m=(4-(-7))/(-1-x)
11/4=(4+7)/(-1-x)
11/4=11/(-1-x)
then 4=-1-x,
-x=4+1
-x=5
x=-5
A small island has a roughly rectangular shape. It is 18.2 kilometers wide and 28.5 kilometers long. Rising water levels are reducing the width by 1.2% each year and the length by 0.8% each year.
Use the drop-down menus to choose or create functions to model:
A. The width of the island over time, w(t)
B. The length of the island over time, l(t)
C. The area of the island over time, a(t)
Answers
Answer:
Part A) [tex]W(t)=18.2(1.012)^t[/tex]
Part B) [tex]L(t)=28.5(1.008)^t[/tex]
Part C) [tex]A(t)=518.7(1.020096)^t[/tex]
Step-by-step explanation:
we know that
The equation of a exponential growth function is equal to
[tex]y=a(1+r)^x[/tex]
where
a is the initial value
r is the rate of change
Part A) Create functions to model :
The width of the island over time, w(t)
we have
[tex]W(t)=a(1+r)^t\\[/tex]
where
[tex]a=18.2\ km\\r=1.2\%=1.2/100=0.012[/tex]
substitute
[tex]W(t)=18.2(1+0.012)^t[/tex]
[tex]W(t)=18.2(1.012)^t[/tex]
Part B) Create functions to model :
The length of the island over time, l(t)
we have
[tex]L(t)=a(1+r)^t\\[/tex]
where
[tex]a=28.5\ km\\r=0.8\%=0.8/100=0.008[/tex]
substitute
[tex]L(t)=28.5(1+0.008)^t[/tex]
[tex]L(t)=28.5(1.008)^t[/tex]
Part C) Create functions to model :
The area of the island over time, a(t)
we have
[tex]W(t)=18.2(1.012)^t[/tex]
[tex]L(t)=28.5(1.008)^t[/tex]
Remember that the area of a rectangle is given by
[tex]A=LW[/tex]
substitute the given values
[tex]A(t)=(28.5(1.008)^t)(18.2(1.012)^t)[/tex]
[tex]A(t)=(28.5*18.2)(1.008*1.012)^t)[/tex]
[tex]A(t)=518.7(1.020096)^t[/tex]
Answer:
Here's the answer ;)