A triangle has a base that is 4cm longer than its height.
a. Write a polynomial that represents the area of the triangle.
b. Find the area when the height is 8cm

Answers

Answer 1

Answer:

a) A =( x^2 -4x)/2

b) 16 cm^2

Step-by-step explanation:

Let the base of the triangle be x cm

since it is longer, then the height would be (x-4) cm

Mathematically, the area of a triangle is the product of the base and the height divided by 2

So, we have this as;

A = 1/2(x-4)x

A = x(x-4)/2

A = (x^2 - 4x)/2

A =( x^2 -4x)/2

To find the area, we only need to substitute 8 cm for x

we have this as;

A = (8^2 -4(8))/2

A = (64-32)/2 = 32/2 = 16 cm^2

Answer 2

We will begin by converting the word problem to relatable mathematical expression in the first part, in the second part, we will substitute for x and find the area which is 48cm^2

Given data

Let the height be x cm

and let the base be y cm

Going by the word problem statement "base that is 4cm longer than its height."

y = x+4

a. the polynomial expression for the area of the triangle is

We know that the area of triangle is given as

Area = 1/2*Base*Height

Area = 1/2*(x+4)*x

Area = 1/2*x^2+4x

Simplify

Area = x^2/2 + 2x

b. The Area when the height is 8cm

We will substitute x= 8cm

Area = (8)^2/2 + 2(8)

Area = 64/2 +  16

Area = 32+16

Area = 48 cm^2

Learn more about Triangle here:

https://brainly.com/question/17335144


Related Questions

the age of 5 men are 48,y, 52,50 and (2y-5).if the average is 47 years find the age of the oldest man​

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The oldest man is 55 years old.

The claim that 20% of Americans know their credit score is tested. Suppose that the sample evidence causes us to fail to reject the null hypothesis claim that 20% of Americans know their credit score. State the final conclusion in simple, nontechnical terms.
A. There is sufficient evidence to support the claim that the percentage of Americans who know their credit score is equal to 20%.
B. There is not sufficient evidence to reject the claim that the percentage of Americans who know their credit score is equal to 20%.
C. There is not sufficient evidence to support the claim that the percentage of Americans who know their credit score is not equal to 20%.
D. There is not sufficient evidence to support the claim.

Answers

B) when you fail to reject you aren’t supporting the null hypothesis, you just didn’t find evidence to prove it as false. So you would not have sufficient evidence to reject the null

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Answer:

The answer is -7, because -15-9=-7

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it sold 300 newspapers because you needed to multiply 25x 12

Step-by-step explanation:

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12 m
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Which rule can be used to find the output numbers in this table?

Answers

Answer:

D

Step-by-step explanation:

22/11 = 2

77/11 = 7

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How do we define transformation?

Answers

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A Dramatic change in appearance or form

Step-by-step explanation:

Answer:

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system. Mathematical transformations describe how two-dimensional figures move around a plane or coordinate system. A preimage or inverse image is the two-dimensional shape before any transformation.

What is the Ka of a solution of 0.025M formic acid, if the pH 10 points
is 2.60? Answers
Ka = 0.025
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Ka = 2.8x10^-4
Ka = 2.8x10^-2

Answers

the answer would be a

Answer:

ka=2.8×10>4

Step-by-step explanation:

.$%_&<</___/%$

which graph correctly represents
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A graph A
B. graph B
с graphic
D graph D

Answers

Answer:

The correct graph should have an x-intercept of 24, a y-intercept of 72, connected by a dashed line, with shading to the right

Step-by-step explanation:

y > -3x + 7

The correct graph should have an x-intercept of 7/3, a y-intercept of 7, connected by a dashed line, with shading to the right

Help meeeeee, i don’t understand

Answers

Answer:

To graph the equation, you need to find the slope and y-intercept.

y = mx + b

[slope-intercept formula; m is the slope, and b is the y-intercept]

y = 4x + −1

[given equation before being simplified]

y = 4x − 1

[given equation]

m = 4

b = (0, −1)

Proof:

m = [tex]\frac{rise}{run}[/tex] = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

x₁ = 0

x₂ = 1

y₁ = −1

y₂ = 3

m = [tex]\frac{3 - -1}{1 - 0}[/tex]

m = 4

b = (0, −1)

[the value for x₁ and y₁ equals the y-intercept: (0, 1)]

Graph:

GIVING BRAINLIEST PLZ HELP

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Answer:

Sebastian

Step-by-step explanation:

What is the distance from the origin to point P graphed on the complex plane below?
A) sqrt 7
B) sqrt 29
C) 7
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Answers

Answer:

Sqrt 29

Step-by-step explanation:

The answer is:

A) sqrt 7

Hope this helped!

Gerald wants to buy a pack of pencils for $1.77. He has 5 quarters, 3 dimes and 4 pennies. How much more money does he need?

Answers

Answer:

18 cents

Step-by-step explanation:

25 times 5 plus 30 plus 4

Answer:

$0.18

Step-by-step explanation:

Can someone help me with this question

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Step-by-step explanation:

Im confused can someone please tell me if this is able to answer?

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Answer:

He has 1/6 of his book left to read.

Step-by-step explanation:

1/2 + 1/3 = 3/6 + 2/6 = 5/6

And 6/6 - 5/6 = 1/6

write 0.0401907 to 3 decimal places.​

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Answer:

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Step-by-step explanation:

Distribute 2 (9x^2 + 3).

Answers

Answer:

18x^2+6

Step-by-step explanation:

2(9x^2+3)

multiply each term in parentheses by 2

2 x 9x^2+2 x 3

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18x^2+2 x 3

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2.5x10^3 times what number is equal to 5x10^6?

Answers

Answer:

2000

Step-by-step explanation:

5 × [tex]10^{6}[/tex] ÷ 2.5 × 10³

5000000 ÷ 2500

2000

Shane is standing near a cell tower. The angle of elevation from him to the top of the tower is 73°. Cara is standing 10 feet behind Shane (further away from the cell tower). From her, the angle of elevation to the top of the tower is 65°. What is the height of the tower, rounded to the nearest tenth of a foot?

Answers

Answer:

75ft

Step-by-step explanation: angles

HELP ASAP IXL PLZ HELP

Answers

Answer:

see explanation

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

R (- 3, 3 ) → R' (3, 3 )

S (- 3, 8 ) → S' (3, 8 )

T (- 2, 7 ) → T' (2, 7 )

Select the equation of the line parallel to y= -3x -5 the equation and that passes through the point (1,2)

Answers

Answer:

[tex]y=-3x+5[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (b)Parallel lines always have the slope slopes and different y-intercepts

1) Determine the slope (m)

[tex]y= -3x -5[/tex]

With the given line, we can identify clearly that -3 is in the place of m, making it the slope. Because parallel lines have the same slopes, the slope of the line we're currently solving for would also be -3. Plug this into [tex]y=mx+b[/tex]:

[tex]y=-3x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=-3x+b[/tex]

Plug in the given point (1,2) and isolate b

[tex]2=-3(1)+b\\2=-3+b[/tex]

Add 3 to both sides

[tex]2+3=-3+b+3\\5=b[/tex]

Therefore, the y-intercept of the line is 5. Plug this back into [tex]y=-3x+b[/tex]:

[tex]y=-3x+5[/tex]

I hope this helps!

These box plots show the number of electoral votes won by Democratic and


Republican presidential candidates for the elections from 1984 through 2012


Republican


159


170


525


Democratic


299


3675


0


50


100


150


400


450


500


550


200 250 300 350


Electoral votes


Which statement best compares the spreads of the data sets?

Answers

Answer:

(a) is true

Step-by-step explanation:

Given

See attachment for box plots

Required

Which of the options is true?

Option A compares the IQR of both plots.

IQR is calculated using:

[tex]IQR = Q_3 - Q_1[/tex]

Where

[tex]Q_1 \to[/tex] Lower quartile

[tex]Q_2 \to[/tex] Upper quartile

From the attached plots, we have:

Republican

[tex]Q_1 = 170.5[/tex]

[tex]Q_3 = 356[/tex]

So:

[tex]IQR = 356 - 170.5[/tex]

[tex]IQR = 185.5[/tex]

Democratic

[tex]Q_1 = 181[/tex]

[tex]Q_3 = 367.5[/tex]

So:

[tex]IQR = 367.5 - 181[/tex]

[tex]IQR = 186.5[/tex]

We have:

[tex]IQR = 185.5[/tex] --- Republican

[tex]IQR = 186.5[/tex] --- Democratic

Hence, (a) is true

If the if a cylinder is 7 in tall and has a volume of 63 Pi inches what is the area of the cross section it goes right down the middle

Answers

Answer: [tex]9\pi \ in.^2[/tex]

Step-by-step explanation:

Given

The height of the cylinder is [tex]h=7\ in.[/tex]

The volume of the cylinder is [tex]V=63\pi \ in.^3[/tex]

The volume of the cylinder is the product of area and height

[tex]\Rightarrow V=\pi r^2h\\[/tex]

Insert the values

[tex]\Rightarrow 63\pi =A\times 7\\\\\Rightarrow A=\dfrac{63\pi}{7}\\\\\Rightarrow A=9\pi\ in.^2[/tex]

Thus, the area of the cross-section is [tex]9\pi \ in.^2[/tex]

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Answers

The measure of AFB is 44 degrees

MAth problem
Help ASAP please

Answers

Answer: 6

Step-by-step explanation:

ab:pq = 5:35, and ac:pr=x:42

because ab:pq=5:35, then it becomes 1:7, as you can divide by 5 on both sides. Ac:pr=x:42, and 42=7x. When you solve that x=6.

hope that makes sense!

CAN SOEMBODYY JUST PLSS IM BEGGIN HEL PMEEEEEEEEEEEEEEEEEEEEEEEE

Answers

Testing testing testing testing testing

Answer:

Hi, there

Question 1: B. 6x^3(x-6)

Question 2: A. (8x+3)^2

Question 3: A. (5x+9y)(5x-9y)

Question 4: D.(x-2)(x-3)

Step-by-step explanation:

Hope this helps :)

25. Kendra owns a toy store. She charges $5.00 for two cars and one piece of candy. She charges \$3.2 for one car and one piece of candy. How much does Kendra charge per car?

Answers

1.56 or 1.5625 if u need the full answer

Kendra's charge per car in the toy store is $1.8.

What is the system of equations?

"Systems of equations, sometimes called simultaneous equations, are a group of relationships between various unknown variables that can be expressed in terms of algebraic expressions".

For the given situation,

Let the number of cars be 'x' and

The number of candy be 'y'

$5.00 for two cars and one piece of candy

$3.2 for one car and one piece of candy

System of the equation for the above case

Equation 1:

[tex]2x + y = 5[/tex]

Equation 2:

[tex]x + y = 3.2[/tex]

Subtract equation 2 from equation 1,

⇒ [tex]x=1.8[/tex]

On substituting x in equation 2, we get

⇒ [tex]y=3.2-1.8[/tex]

⇒ [tex]y=1.4[/tex]

Hence we can conclude that Kendra's charge per car is $1.8.

Learn more about the system of equations here

https://brainly.com/question/9351049

#SPJ2

No links need help ASAP

Answers

Answer:

≈10502.7

Step-by-step explanation:

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

160π cubic units.

»»————- ★ ————-««  

Here’s why:

The formula for volume of a cylinder is:

[tex]V=\pi r^2h[/tex]

[tex]\boxed\text{Key:}\\\\[/tex][tex]\boxed{\text{Key:}}\\\\\text{R - Radius}\\\\\text{H - Height}[/tex]

⸻⸻⸻⸻

We are given:

The height of 10 units.The radius of 4 units.

⸻⸻⸻⸻

We will replace the 'r' with '4' and we will replace the 'h' with '10'.

⸻⸻⸻⸻

There are two ways to express the answer, either an exact answer in terms of pi or an approximation using 3.14 for pi.

For this answer, I will use the exact terms.

⸻⸻⸻⸻

[tex]\boxed{\text{Finding the Volume of the Cylinder:}}\\\\V=\pi 4^210\\\\-------\\\rightarrow V=4^2*10*\pi \\\\\rightarrow V=16*10*\pi\\\\\boxed{V=160\pi}[/tex]

The answer should be [tex]\boxed{160\pi\text{ units} ^3.}[/tex]

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

If I lie about what I say then is the truth a lie or am I telling the truth whilst lie-ing (゚∩゚) ?

Answers

+Answer:

You are lying more then telling the truth.

Step-by-step explanation:

At first, it was a lie but a coincidence happened, so it is more lying in my opinion.

70.5 is what percent of 94

Answers

Answer:

75%

hope this helps

have a good day :)

Step-by-step explanation:

Answer: 75%

Step-by-step explanation:

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