the base of a triangle is five less than twice it’s height, if the area of the triangle is 6 cm^2, find the length of the base

Answers

Answer 1

Answer:

Base = 3 cm

Step-by-step explanation:

Area of a triangle =  [tex]\frac{1}{2} bh[/tex]

Let h = height

base =  2 times the height - 5; b = 2h-5

Area = 6 cm²

 A = [tex]\frac{1}{2}bh[/tex]

[tex]6 =\frac{1}{2}(2h - 5)(h)[/tex]             Multiply 2h(h) -5(h)

[tex]6 (2) = 2(\frac{1}{2})(2h^{2} - 5h[/tex]      Multiply both sides by 2 to remove the fraction

 12 = 2h²- 5h

2h ² -  5h  - 12 = 0                Set the equation = 0 and factor  

(2h + 3)(h - 4) = 0

2h + 3 = 0    or h - 4 = 0

2h = -3               h = 4

h = -3/2        or   h = 4        Answer can not be negative so h = 4cm

The base is 2(4) - 5; The base = 8 - 5; base = 3 cm


Related Questions

what is the prime factorization of 252

1. 2^2x7x9
2. 2x7x27
3.2^2×3^2×7
4.2^3×3×7​

Answers

Answer:

Prime factorization: 2x2x3x3x7

Exponential form: = 2^2 x 3^2 x 7

Step-by-step explanation:

Pls hurry on a test

Answers

Answer:

B

Step-by-step explanation:

Meet at the middle of the two lines

Answer:

pretty sure it's c

Step-by-step explanation:

when we learned that, we're always supposed to start with x which in this occasion is 4 and y is 2

How would 1.047 be written as a percentage form?

Answers

Answer:

104.7%

Step-by-step explanation:

When changing a decimal to a percentage, simply move the decimal point to the right two place values to obtain your percentage:

1.047 = 104.7%

And vice versa, when changing a percentage to a decimal, move the decimal point to the left two place values to obtain your decimal.

~

Carl was given 15% of his paycheck before Christmas if his paycheck was $545.19 how much did he receive before Christmas

Answers

Answer:81.79$

Step-by-step explanation:

Total Value/ Percentage

So in this case it would be 545.19 divided by 25

and you would then get your answer, 81.79$

Express the following ratio as a fraction then reduce the fraction to the lowest terms

4:6

Answers

Step-by-step explanation:

4:6 as a fraction is 4/6

4/6 in its lowest terms is 2/3

hope this helps

if a diagram shows a square with perimeter 40cm whats the percentage of the area inside the square that is shaded

Answers

Answer:

5

Step-by-step explanation:

Eacl side of the square has a length of 5 cm.

Answer:

55%

Step-by-step explanation:

i assume your question is from mathswatch

And this is the answer for it!

The results of a survey about favorite lunch choices are shown.
Which lunch was chosen most often? : Please help!! here’s the chart btw —>

Answers

Answer:

Grilled cheese 1/10

Step-by-step explanation:

If you divide the rest of the fractions you get decimals and since 1/10 is still 10 grilled cheese is the favour lunch

Find the common denominator for all three of them and find the largest one. You do the rest yourself

Match each linear equation to its slope and y-intercept.
slope:2, y-intercept:
-3+5y = 4
slope:2, y-intercept: 2
5y-1 =15
slope:$, y-intercept:
2y-3.1 = 7
slope:6, y-intercept: 3
2y=5T+7
slope:-5, y-intercept: 5

Answers

Answer:

-x + 5y = 4

5y = x + 4

y = x/5 + 4/5

Slope: 1/5

Y-intercept: 4/5

5y - x = 15

5y = x + 15

y = x/5 + 3

Slope: 1/5

Y-intercept: 3

2y - 3x = 7

2y = 3x + 7

y = 3/2x + 7/2

Slope: 3/2

Y-intercept: 7/2

2y = 5x + 7

y = 5/2x + 7/2

Slope: 5/2

Y-intercept: 7/2

help me please (show work)

Answers

Answer: A, B, C, and D have the same volumes:  100 units^3

Step-by-step explanation:

The details are attached.  Use the volume formula for the respective shapes.  Bear in mind that B is he area of the base (I assume).  It is the

[tex]\pi[/tex][tex]r^{2}[/tex] in the formulas that have a round base, and the width x length for bases that are rectangular (or square).

Find the area of the surface generated by revolving x = t y = t^2 1 ≤ t ≤ 2 around the y-axis

Answers

Answer:

4^22x

Step-by-step explanation:

answer is 4^22x (sorry it’s late)

common factor of 24 plz

Answers

Hey there!

Factors of 24 are 1, 2, 3, 4, 6, 8 & 12.

24 = 1 × 2 × 2 × 2 × 3

24 = 2³ × 3 × 1

1 × 24 = 24

2 × 12 = 24

3 × 8 = 24

4 × 6 = 24

Hope it helps ya!

Which of the following statements is NOT true?

Answers

it wont let me loo at it sorry but it seems easy.

The bottom one. The slope of AB is different than the slope of BC.

A worker pushes on a crate that experiences a
net force of 75 N. If the crate also experiences
an acceleration of 0.50 m/s^2, what is its
weight?

Answers

Answer:

Answer:

M = 75N

0.50 m/s²

M = 150kg

Explanation:

M = F

a6

What is the range of the graph

Answers

Answer:

You're correct the answer is B) [tex]-5 \leq y \leq -1[/tex]

Step-by-step explanation:

The key behind this problem is think about the function [tex]\sqrt[3]{x}[/tex] and think what happen when you plug in values in it.

So we're  going to try with some simply values for evaluate

[tex]\sqrt[3]{-8} = -2[/tex]

[tex]\sqrt[3]-1} = -1[/tex]

[tex]\sqrt[3]{0} = 0[/tex]

[tex]\sqrt[3]{1} = 1[/tex]

[tex]\sqrt[3]{8} = 2[/tex]

How you can see when plug in a negative number the function return a negative number, but when you plug in a positive number the function return a positive number (this isn't a proof of this happen in each value of the given interval, but is a good way of demonstrate the relation). This means that when you plug in a value this value is greater than the value of before, so the function  is increasing it's outputs.

Now this is good because that's mean that the limits of the range are the limits of the domain evaluates in the function (because the smaller input give us the smaller output and the same with the greater). But the given function have different operation in it, so you have to interpret this operations of this way:

When you have a negative value in the [tex]x[/tex] like in this occasion ([tex]\sqrt[3]{-x}[/tex]) the function reflex it's values with respect to the y axis (image put the functions in a mirror a draw the given image in the same cartesian plane).And you have a -3 this is move each value of the function 3 units down.

So with this information you evaluate each limit of the domain [tex]\{-8, 8\}[/tex] in the function and get the limits for the range.  

[tex]f(-8) = \sqrt[3]{-(-8)} -3= \sqrt[3]{8} -3 = 2 -3 = -1[/tex]

[tex]f(8) = \sqrt[3]{-8} -3= -2 -3 = -5[/tex]

So the range of the function in the given interval is equal to [tex]\{-1, -5\}[/tex] in the interval notation is equal to [tex]-5 \leq y \leq -1[/tex]

Two consecutive numbers exist such that the sum of three times the first number and two less than the second number is equal to 144. What are third numbers

Answers

Step-by-step explanation:

two consecutive numbers means that one is larger by 1 than the other number.

so, we have to choices depending on whether the first number (multiplied by 3) is the larger one, or the second number.

to show what I mean, let's start with the second number being the larger one.

we are dealing therefore with x and (x+1).

3x + (x+1) - 2 = 144

4x - 1 = 144

4x = 145

x = 145/4

this is not an integer (but this is necessary to have 2 dedicated consecutive numbers).

so, it is actually not a valid solution.

therefore we are checking the other approach :

we are dealing therefore still with x and (x+1). but now we multiply the other number by 3.

3(x+1) + x - 2 = 144

4x + 1 = 144

4x = 143

x = 143/4

this is still not an integer (but this is necessary to have 2 dedicated consecutive numbers).

so, it is actually not a valid solution either.

and now I am beginning to think you left out some important information in the question.

could it be these 2 numbers are consecutive even or consecutive uneven numbers ?

because then the difference between the both of them is 2 and not 1.

we are dealing therefore with x and (x+2). first attempt to make the smaller number the "first" number :

3x + (x+2) - 2 = 144

4x = 144

x = 144/4 = 36

ah ! now that looks different !

36 and 38 are valid solutions under the changed assumptions. and we are dealing with consecutive even numbers.

let's check :

36×3 + 38 - 2 = 36×3 + 36 = 36×4 = 144

correct.

and fun fact, if we turn this around and make the larger number the "first" number, we are still dealing with x and (x+2), but now we multiply the larger number by 3 :

3(x+2) + x - 2 = 144

4x + 6 - 2 = 144

4x + 4 = 144

4x = 140

x = 140/4 = 35

35 and 37 are also valid solutions under the new assumptions and two consecutive uneven numbers ...

so, please check what your original question (and maybe the headlines and description around it) says. and then pick the right solution.

5.
Identify the vertex of the parabola.
A. (6, 3)
B. (3, 0)
C. (4, -1)
D. (5, 0)

Answers

Answer:

B. (3, 0)

Step-by-step explanation:

It's B. (3,0) because it's on the line of 3 and 0 aka x axis

im stuck on this problem can someone help me? (see photo) ​

Answers

Answer:

I'm thinking the anwer is B

Step-by-step explanation:

I remember doing this problem before :)

(i) Find i in terms of P and A.

(ii) If 2500 is invested 3 years ago has a present value of 2650, find the rate of interest, i (correct to one decimal place)

Answers

Answer:

See below

Step-by-step explanation:

Given formula:

[tex]A=P(1+i/100)^3[/tex]

(i)

Solve for i:

[tex]A/P=(1+i/100)^3[/tex][tex]\sqrt[3]{A/P}=1+i/100[/tex][tex]\sqrt[3]{A/P} -1=i/100[/tex][tex]i=100(\sqrt[3]{A/P} -1)[/tex]

(ii)

P = 2500, A = 2650, find i:

[tex]i =100(\sqrt[3]{2650/2500} -1)[/tex]i ≈ 2.0%

HELP!!!!! QUICK 100 pts to help me!!!!!! A 35 foot ladder rests against a window ledge that is 25 feet above the ground. How far is the base of the ladder from the base of the building? Round your answer to the nearest tenth. Show all work in the "show your work" box.

Answers

Answer:

24.5

Step-by-step explanation:

Apply the pythagorean theorem:

35^2-25^2=c^2

1225-625=c^2

600=c^2

c=24.5

Fill in geometry proofs. ANGLES. ( I WILL GIVE BRAINLIEST! PLS HELP!)

refer to attachment

Answers

Here are the answers

#2

Reflexive sides

#3

Already given in question

#4

Given in the question

#5

By bisector definition

#6

Third angle therom

#7

Angle-Side-Angle

if x = 5 find the value of a) x² b) (x + 3)²

Answers

Answer:

x=5

a)x²

5²=25

b] (x+3)²

(5+3)²

(8)²=64

x=5
a) 5^2 = 25
b) (5+3)^2 = 64

Please help me with this question

Answers

Answer: It's the 3rd one. Secant line

Find the perimeter. Simplify your answer.

Answers

Answer:

The answer is 19s +23

Step-by-step explanation:

You add together all the sides and simplfy down.

4s+10+s+4+4s+10+10s-1

Add all the like terms

until it gets to 19s+23

Answer:

19s + 23

Step-by-step explanation:

P = 2(4s + 10) + s+4+19s-1

P = 8s + 20 + s + 4 + 10s - 1

P = 19s + 23

last time i'm asking about this bc i keep getting this wrong!!

Answers

I think answer is 150, if it’s wrong I’m sorry

FOR A BRAINLIST PLS HURRY

Answers

Answer:

y = x

Step-by-step explanation:

line has a slope 1 and passes through the origin . So the equation is y = x

what is the value of 8x + 2x when x is 6

Answers

Answer:

The answer is 60

Step-by-step explanation:

8x + 2x

x = 6

Substitute the value of x

8(6) + 2(6)

48 + 12

= 60

So basically 8x has a missing number and that missing number is 6 meaning that you need to multiply so you would multipy 8 times 6 and would get 48

Now that you have that answer you would do the next one which is 2 times 6 and thats 12 then you add 48 and 12 together making that 60 and your answer is 60.

Simpler

8 x 6 = 48

2 x 6 = 12

48 + 12 = 60

what is 4x(1+8x) Distributed

Answers

Answer:

4x + 32x²

Step-by-step explanation:

4x(1 + 8x) ← multiply each term in the parenthesis by 4x

= 4x + 32x²

What does this sentence mean? Or write the formula

Find all sets of 2 consecutive positive integers with a sum that is at least 8 and less than or equal to 24.

Answers

Answer:

An odd integer is denoted by 2n+1 where n is an integer.

First odd integer = 2n+1

Next odd integer = 2n+3

8 ≦ (2n+1)+(2n+3) < 24

8 ≦ 2n+1+2n+3 < 24

8 ≦ 4n+4 < 24

Divide through by 4

2 ≦ n+1 < 6

Subtract 1 for all three sides:

1 ≦ n < 5

n ∈ {1,2,3,4}  

Answer:  {2n+1, 2n+3}  {1,3}, {3,5}, {5,7

Step-by-step explanation:

expand and simplify (x-2)(x-3), please help

Answers

Answer:

hope it helps you

(•‿•).........

PLEASE HELP ME I REALLY NEED HELP!!

Answers

Answer:

Yes, based on ASA or AAS

Step-by-step explanation:

Subtract the two angle values of one triangle from 180 to dictate whether the missing angle is equal to the other triangle.

180-63= 117- 45=72

The triangles are equal/congruent because two angles and a side are the same values on both triangles.

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