Triangles A and B have vertical heights x cm and (x+3) cm respectively. The areas of Triangles A and B are 30cm² and 32cm² respectively. (a) Find, in terms of x, an expression for the base of: (i) Triangle A (ii) Triangle B (b) Given that the base of Triangle B is 4 cm less than the base of Triangle A, form an equation and show that it reduces to x² + 4x - 25 = 0 (c) Solve the equation and hence, find the height of Triangle B.​

Answers

Answer 1

Answer:

Hi,

Step-by-step explanation:

Let say a the base of the triangle A and b the base of the triangle B.

[tex]a)\\\left\{\begin{array}{ccc}\dfrac{a*x}{2}&=&30\\\dfrac{b*(x+3)}{2}&=&32\\b=a-4\\\end{arraqy}\right.\\\\(i): a=\dfrac{60}{x}\\\\(ii): b=\dfrac{64}{x+3}\\\\b)\\\dfrac{64}{x+3}=\dfrac{60}{x}-4\\\\64x=(60-4x)*(x+3)\\\\4x^2+16x-180=0\\\\x^2+4x-45=0\\\\\Delta=16+4*45=196=14^2\\x=\dfrac{-4+14}{2}=5\ or\ x=\dfrac{-4-14}{2}=-9\ (impossible)\\So\ x=5,\ a=\dfrac{60}{5}=12, b=\dfrac{64}{5+3}=8\\\\Area\ of\ A=12*5/2=30\\Area\ of\ B=8*8/2=32\\\\Height\ of\ triangle\ B=x+3=5+3=8.\\[/tex]

Answer 2
It should equal to eight.

Related Questions

Pls help this is due tomorrow morning and it's 1 am I'll mark brainliest 15 points each

Answers

Answer:

263.76

Step-by-step explanation:

2×3.14×3² + 2×3.14×2×11 = 263.76

I think the answer is 263.76

HELP MEEEEEEEE!!!!!!11 Thirteen babies were born in a hospital on the same day. The weights of the babies (in pounds) were 5.5, 6.4, 5.8, 8.1, 9, 7.6, 8.2, 7.2, 8.8, 6.6, 5.4, 7.7, and 6.9. 30 Select the correct answer. Which measure will help you calculate how much the babies' weights vary, on average, from their mean weight? A. mode B. interquartile range C. range D. mean absolute deviation E. quartile

Answers

Answer:

B interquartile range

Step-by-step explanation:

hope this helps:)

Answer:

B. interquartile range

Hope this helps! Please give brainlist!!

Please help me solve this.It’s really really important

Answers

What are the teaching y’all
What class is this ?

A linear function contains the following points.

What are the slope and y-intercept of this function?

Answers

Answer:

(+6x,+5y)

Step-by-step explanation:

To me its simple math by dividing these 2 numbers you get the slope

sorry i cant help much but this is what i can do also be sure to use rise over run before dividing

have a nice day

The answer is c
The slop is change in y/ change in x… rise over run so it is 5/6. The y intercept is when x is 0 what is y.
In this case, (0, -3)

HELP PLEASEEEEE THank you fractions & ratios fill in space:

Answers

Answer:

2334546

Step-by-step explanation:

the answers is 2/3 /4/2 and 5/6

Diddjdjdjdjcjrnhhdiridjdjsieudhdjswdicnsjsifjw

what would the slop be of the coordinates -6,6 and 6,6

Answers

0 since the two points share the same x coordinates

I think
I have calculated every possible answer and it’s 0

help!! I can't figure this out!!!

Answers

Answer:

I am pretty sure it is 7 leagues.

Step-by-step explanation: Count six squares or leagues from the right to the left and one up.

I think its 7 leagues
Six squares to the left as then one up

Help. Getting kind of fed up with homeschooling and just need to get it done.

Answers

The dot above the 4 is solid so 4 is part of the solution.

Answer: X ≥ 4

the answer to this question is x>4

WILL GIVE BRAILIEST: 8th grade: equations and geometry


help please!!!! also please explain how to solve equations with different variables in it (like 2k+3x= 30)

Answers

That’s should he right but also it could of been 54

Answer:

C. j=2 and h=4

Step-by-step explanation:

Step 1: Create a system of equations for your problem based off what we know.

- we should know that the equation to find the perimeter of something is

[tex]P= 2l+2w[/tex] where P is the perimeter, l is the length, and w is the width.

- we know that the perimeter of Rectangle P is 20 inches and that the perimeter of Rectangle Q is 30

- we know the length and width of both rectangles

Using this information, lets set up our system.:

[tex]\left \{ {{20=2(j+4)+2h} \atop {30=2(3h)+2(j+1)}} \right.[/tex]

Step 2: Using the top equation we're going to try to solve for one of the variables. I chose to solve for variable j.

[tex]20=2(j+4)+2h[/tex]

Start by distributing 2 into j + 4.

[tex]20=2j+8+2h[/tex]

Now subtract 8 from both sides of the equation.

[tex]12=2j+2h[/tex]

Now isolate variable j by subtracting 2h from both sides of the equation.

[tex]12-2h=2j[/tex]

Now condense the equation into simple terms by dividing both sides by its GCF 2 then reorder to get j on the left.

[tex]j=6-h[/tex]

Step 3: Now that we solved for variable j we can now substitute j into one of our equations from the original system. I chose to use the bottom equation and chose to distribute it before substituting.

[tex]30=6h+2j+2[/tex]

Subtract two from both sides to isolate the variables

[tex]28=6h+2j[/tex]

Now we can plug j into our equation

[tex]28=6h+2(6-h)[/tex]

Step 4: Distribute 2 into 6-h

[tex]28=6h+12-2h[/tex]

Step 5: Combine like terms

[tex]28=4h+12[/tex]

Step 6: Subtract 12 from both sides of the equation

[tex]16=4h[/tex]

Step 7: Divide both sides by 4

[tex]4=h[/tex]

Now that we know that h=4 we can plug 4 into one of our earlier equations. I used j=6-h

[tex]j=6-4\\j=2[/tex]

Plug answers into either one of the original equations to check answer

Eric surveyed different people with cell phones.

Ages in years = a
Texts they send per day = t

He drew a best-fit line and determined its equation.

Evaluate how old a person who sends about 70 texts a day is.

Answers

Answer: B = 10.4

A person who sends about 70 texts a day is around 10 years old.

Answer:

B = 10.4

TTETEEETETTET

Help ASAP its due today!

Answers

Answer:

The answer is D) 60

Step-by-step explanation:

The answer is the fourth question, 60.

Divide
(i) 448 ÷ (-7)




I need it now
please someone

Answers

=448/(_7
=-64
Therefore the correct answer is-64

Answer:

-64 is the answer

12. Convierte estas fracciones impropias en números mixtos:
A. 15/7=
B. 16/6=
C. 12/5=
D. 48/7
Por favor.

Answers

Answer:

15/7 = 2 1/7

16/6 = 2 4/6

12/5 = 2 2/5

48/7 = 6 6/7

Step-by-step explanation:

C is 2 2/5 I don’t know the others.

What is the area of this figure? Enter your answer in the box.

Answers

Answer:

33 or 900

Step-by-step explanation:

10+18+5= 33

10x18x5=900

Answer: 70

Step-by-step explanation: math

A gift box has the shape of a rectangular prism. How much wrapping paper do you need to cover the box?

Answers

Answer:

54

2(lb+bh+lh).

Use this formula ^

The answer is 644!!!!!!

someone answer this ASAP!!!!!

Answers

Answer:

The Quotient is 136 and the Remainder is 0

Step-by-step explanation

( I hope it helps ^^)

The quotient is 136 and the remainder is 0

Find the surface area of the rectangular prism

Answers

Answer:

158 in

Step-by-step explanation:

front/back faces: 8 * 3 = 24in

side faces: 8 * 5 = 40in

top/bottom faces: 3 * 5 = 15in

2 * (24 + 40 + 15) = 158in

The answer is 158 the length times width times height

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.
Represent the measurement of angle B in the figure.



In the figure, angle A and angle D are complementary. The measurement of angle D is 45°. Complete the equation to solve for b, the measurement of angle B.

180 =
+ (90 –
) + b

Answers

Answer:

angle b is 45° as it is alternative angle of d so equal to d.

Step-by-step explanation

now....

180 = 90+(90-45)+b

90+45+45

90+90

=180

Answer:

angle b is 45° as it is alternative angle of d so equal to d.

Step-by-step explanation

now....

180 = 90+(90-45)+b

90+45+45

90+90

Match each expression on the left with an equivalent expression on the right. Some answer choices on the right will not be used.

Answers

Answer:

B (second equation down on left) is equal to B (equation 2 down on right)

C=F

D=A

A=C

1. BB
2. CF
3. DA
4. AC

Hope this helps you!

This figure was created by joining two right rectangular prisms.
Enter the volume, in cubic meters, of the figure.

Answers

Answer:

the answer is 30!

Rewrite as a simplified fraction.
\large{3.\overline{1} = {?}}3.
1
=?

Answers

This is incomprehensible, but I would be happy to help if you perhaps re-typed it :D

It may helps if you take a picture or rewriting it

What is the surface area of this figure in square centimeters?
a rectangular prism with dimensions, right triangle base 3 cm by 4 cm, the height of the prism is 7 cm

Answer Choices:
75
60
96
84

Answers

Answer:

96cm

Step-by-step explanation:

front/back triangles: (4 * 3) / 2 = 6cm

bottom rectangle: 4 * 7 = 28cm

side rectangle (left): 3 * 7 = 21cm

slanted rectangle: pythagoras - 3^2 + 4^2 = x^2

9 + 16 = x^2

25 = x^2

square root of 25 = 5

x = 5

7 * 5 = 35cm

6 * 2 + 28 + 21 + 35 = 96cm

96 is the answer to your question

“There are 814 students going non a field trip, and they have 31 buses. How many students should go on each bus if they split up evenly on the buses? Solve the problem. Show your work”

Answers

Answer: 27

Step-by-step explanation: You have to divide. 814 divided by 31 is 26.2580645161, but you can round it to 27 so everyone can be on the bus, but with extra spaces

Answer:

27

Step-by-step explanation:

can someone define the word of an pre-image in math

Answers

Answer:

The image before a transformation is performed.

Step-by-step explanation:

Hope it helps!

This means the image that was there before a translation, reflection, rotation, or dilation was performed.

The image before a transformation is
performed.

This means the image that was there before a
translation, reflection, rotation, or dilation was
performed.

What is the value of x in the figure?

Enter your answer in the box.

x = [__]

Answers

That is a 90 degree angle so:
90-22=68
So X=68

Answer:

x by the box

D+22-x

Step-by-step explanation:

hurry ill give brainly

Answers

Answer: The answer is health

The answer is health.

Hope this helps

(Will give 25 points!) Solve the system of linear equations by substitution. 1/2x + 1/4y = 2 x + y = 1

Answers

El ànswer si si si in what way
X=0.8
Y=0.6
These should be the answers

Which equation can be used to calculate the area of the shaded triangle in the figure below?


A rectangle with length of 12 feet and width 4 feet. A diagonal cuts the rectangle into two halves. One of the triangular halves is shaded.


2(12 + 4) = 32

fraction 1 over 2(12 + 4) = 8

2(12 × 4) = 96

fraction 1 over 2(12 × 4) = 24

I'll mark as brainliest

Answers

Answer:

It is [tex]\frac{1}{2}[/tex] (12 × 4) = 24

Step-by-step explanation:

[tex]\frac{1}{2}[/tex] (base × height) = area of triangle

[tex]\frac{1}{2}[/tex] (12 × 4) = area

area = 24

Use repeated addition to find the solution to each
multiplication problem. Change any improper fractions to mixed numbers

Answers

Answer:

2. 1 1/4

3. 2 1/3

4. 1 2/3

5. 1 3/7

6. 2 2/5

7. 1/2

8. 1 1/2

9. 2 1/4

10. 3 8/9

11. 2

12. 2 2/3

13. 2 1/2

14. 4 2/7

Step-by-step explanation:

2. 5/4 = 1 1/4

3. 3/1 * 7/9 = 7/3 = 2 1/3

4. 2/1 * 5/6 = 5/3 = 1 2/3

5. 10/7 = 1 3/7

6. 12/5 = 2 2/5

7. 3/6 = 1/2

8. 2/1 * 3/4 = 3/2 = 1 1/2

9. 6/1 * 3/8 = 3/1 * 3/4 = 9/4 = 2 1/4

10. 35 / 9 = 3 8/9

11. 8/1 * 1/4 = 2 * 1 = 2

12. 8/3 = 2 2/3

13. 5/2 = 2 1/2

14. 30/7 = 4 2/7

2. 1 (1/4)
3. 2 (1/3)
4. 1 (2/3)
5. 1 (3/7)

The spinner has 3 options: Red, Blue, or Yellow. Jacob says
because there are three colors there is a 1/3 chance of each color
being picked. Brittany says, just because there are three colors
doesn't mean there is always an equal chance of each
og ha
happening. Who do you agree with? How do you know?
SELECT the best answer

Answers

i agree with Jacob, if there are 3 colors there’s a 1/3 chance it can land on any of the colors equally unless one color is bigger than the rest
Jacob is correct as there is 1/3 so it’s equal unlike if there was a 2/3 chance
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