Find the shortest side of a triangle whose perimeter is 64 if the ratio of two of its sides is 4:3 and the third side is 20 less than the sum if the other two

Answers

Answer 1

Answer:

The shortest side of the triangle is 18

Step-by-step explanation:

Let the sides the triangle be x, y and z.

From the question, the perimeter of the rectangle is 64, that is

x + y + z = 64 ...... (1)

Also, the ratio of two of its sides is 4:3, that is x:y = 4:3, then we can write that x/y = 4/3 ⇒ 3x = 4y ...... (2)

The third side, z, is 20 less than the sum of the other two, that is

z + 20 = x + y ...... (3)

Substitute equation (3) into (1)

Then,

z + 20 + z = 64

2z +20 = 64

2z = 64 - 20

2z = 44

z = 44/2 k

z = 22

From equation (3)

z + 20 = x + y

Then, k

22 + 20 = x +y

42 = x + y

x = 42 - y ...... (4)

Substitute this into equation 2

3x = 4y

3(42-y) = 4y

126 - 3y = 4y

4y + 3y = 126

7y = 126

y = 126/7

y = 18

Substitute this into equation (4)

x = 42 - y

x = 42 - 18

x = 24

∴ x = 24, y = 18 and z = 22

Hence, the shortest side of the triangle is 18.


Related Questions

3. If bº = 110°, what is the value of gº?

Answers

Answer:

hello mate <3

u see here its a quadrialteral

with 4 angles b , d , 70 , g

so b + d + 70 + g = 360

now u see 60 + d = 180 (straight line)

d = 120 and b = 110 ( given)

so

110 + 120 + 70 + g = 360

g + 300 = 360

g = 360 - 300 = 60 degrees option c

brainliest?

Write 128 as a product of its prime factors

Answers

Answer:

The prime factorization of 128 is 2 x 2 x 2 x 2 x 2 x 2 x 2.

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Since, the prime factors of 120 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.

What is 4,327 rounded to the nearest thousand?

Answers

Answer: 4,000

Step-by-step explanation: To round 4,327 to the nearest thousand, we first find the digit in the rounding place, which in this case is the 4 in the thousands place. Next, we look at the digit to the right of the 4, which is 3.

According to the rules of rounding, since the digit to

the right of the rounding place is less than 5, we round down.

So the 4 in the rounding place stays the same

and all digits to the right of the 4 become 0.

So 4,327 rounded to the nearest thousand is 4,000.

1. Three products from renewable resources are​

Answers

Animals, wood, plants

Answer:

biomass energy (such as ethanol), hydropower, geothermal power, wind energy, and solar energy.

Find the missing side lengths

Answers

Answer:

u is 172 and v is 17

Step-by-step explanation:

To find u:

[tex]{ \bf{ \sin( \theta) = \frac{opposite}{hypotenuse} }}[/tex]

feed in the terms:

[tex] \sin(45 \degree) = \frac{17}{u} \\ \\ u = \frac{17}{ \sin(45 \degree) } \\ \\ u = 17 \sqrt{2} [/tex]

To find v:

[tex] \cos( \theta) = \frac{adjacent}{hypotenuse} [/tex]

feed in the terms:

[tex] \cos(45) = \frac{v}{u} \\ \\ v = u. \cos(45) \\ v = (17 \sqrt{2} )÷( \sqrt{2} ) \\ v = 17[/tex]

factorize: xy-3x - 5y + 15

Answers

Answer:

Step-by-step explanation:

xy-3x-5y+15

x(y-3)-5(y-3)

(y-3)(x-5)

"A parabola has the equation = ^ + − . What are the coordinates of the vertex? (You must solve by factoring)!!!!!" I NEED THE ANSWER TO THIS FAST WITH STEPS I'm a grade 10 academic student by the way

Answers

Answer:

1

Step-by-step explanation:

1

please help with number 9!!!

Answers

Answer:

2 + sqrt(3)

Step-by-step explanation:

Roots that contain square roots come in pairs

If there is a root that is a- sqrt(b), there is a root that is a+ sqrt(b)

2 -sqrt(3) means there is a root 2 + sqrt(3)

if three less than one half a number is equal to one-third of the same number, find the number​

Answers

Answer: The number would be 18

Step-by-step explanation:

18/2=9 9-3=6 6*3=18

The equation be (x/2) - 3 = x/3 then, the number of x = 18.

How to estimate the value of x?

To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.

Let x be the number

From the given information, we get

(x/2) - 3 = x/3

The set all the fractions on one side and constants on another side

(x/2) - (x/3) = 3

Multiply by LCM

3x - 18 = 2x

Add 18 to both sides

3x - 18 + 18 = 2x + 18

simplify

3x = 2x + 18

Subtract 2x from both sides

3x - 2x = 2x + 18 - 2x

x =18.

Therefore, the number is x = 18.

To learn more about algebraic expression refer to:

https://brainly.com/question/4541471

#SPJ2

John earns $6 per hour for mowing the lawn. If t represents John's total earnings for h hours of mowing, which equations can be used to model the situation

Answers

Answer:

h=6

Step-by-step explanation:

If i work in a week 2 days cleaning and i will work 4 hours in a day and in 1 hour is 8$ how much will it be in a year

Answers

Answer:

$3072

Step-by-step explanation:

It is given that :

I work for 4 hours everyday, working 2 days a week.

And in 1 hour , I get $8.

Therefore,

1 hour = $8

4 hours = 4 x  8

             = $32

So, in 1 day working for 4 hours, I get $32.

∴ Working 2 days = 32 x 2

                              = $64

In 1 month, there are 4 weeks

So, in 4 weeks (or 1 month), I work for = 4 x 2

                                                               =  8 days

Therefore, in 8 days, I get = 8 x 32

                                            = $256

Now there are 12 months in a year.

So, in 12 months , I will get = 12 x 256

                                            = $3072

Therefore, in 1 year , I will get $3072.

The width of a rectangle measures (2h-6) centimeters, and its length measures (7h+8) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

Answers

Answer:

18h +4

Step-by-step explanation:

The perimeter of a rectangle is given by

P = 2(l+w)  where l is the length and w is the width

  =2( 7h+8 + 2h-6)

Combine like terms

  = 2( 9h+2)

Distribute

   = 18h +4

please help, I'm so confused how to-do this

Answers

Answer:

Step-by-step explanation:

use the quadratic formula : [tex]x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a}[/tex], where ax^2+bx+c=0

[tex]y = \frac{ -(-20) \pm \sqrt{(-20)^2 - 4(1)(50)}}{2(1)}[/tex]

[tex]y = \frac{ 20 \pm \sqrt{400 - 200}}{2}[/tex]

[tex]y = \frac{ 20 \pm \sqrt{200}}{2}[/tex]

y = 17.07106~ or 2.928932~

Given that v=√u*u- 2qs. Make q the subject of the equation. Find the value of q in the equation if v=8, u=12, and s=40​

Answers

Answer:

Step-by-step explanation:

v=√u*u- 2qs

[tex]\sqrt{20}[/tex] x 20 - 2q40 = 8[tex]2\sqrt{5}[/tex] x 20 - 2q40 = 840[tex]\sqrt{5}[/tex] - 2q40 = 8- 2q40 = 8 - 40[tex]\sqrt{5}[/tex]-80q = 8 - 40[tex]\sqrt{5}[/tex] q = (8-40[tex]\sqrt{5}[/tex] ) / -80 = [tex]\frac{-1 + 5\sqrt{5} }{10}[/tex] = 1.018

Above given answer is correct.

so i need help with this pls i suck at algebra

Answers

Answer:

The 5x^2 vs -5x^2 will reflect over "X" axis

the +1 vs -2 will shift the graph down three units

the first answer is the correct answer

Step-by-step explanation:

Setting y = 0 allows you to determine the what
of a graph

Answers

This allows you to find the x intercepts of the function.

  [tex]y=0[/tex] allows you to determine the x-intercept of a graph.

x-intercept and y-intercept:The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.By changing Y to 0 in the equation and figuring out X, you can always determine the X-intercept. Similarly, by putting X to 0 in the equation and solving for Y, you can always determine the Y-intercept.When y is 0, the x-intercept is reached. The graph's intersection with the y-axis, or (0, b), is known as the y-intercept. When x is 0, the y-intercept is reached. When y is 0, the x-intercept is reached.

Therefore, [tex]y=0[/tex] allows you to determine the x-intercept of a graph.

Know more about x-intercept and y-intercept here:

https://brainly.com/question/24363347

#SPJ2

Have fun all !!! This is my trash account. You all can have my points.

Answers

Answer:

Step-by-step explanation:

OK

Answer:

rshjgdlf

FGshjfgsfds

Step-by-step explanation:

GIMME'

the table of values below represents a liner function and show the amount of money in the savings account since she began her part-time job what is her monthly rate of savings​

Answers

Answer:

she saves $24 dollars every month. 36 + 24 =60 +24 =84 +24 =108 +24 =132 :)

The average age of a preschool class is 4.5 years old. If there is one 3-year-old, five 5-year-olds, and two other children both of the same age, what is the age, in years, of the other two children?

Answers

Answer:

3.1

Step-by-step explanation:

5 x5 =25

25+3=28

the other children are 4 years old

Correct answer gets brainliest and 5 star

Answers

Answer:

d

Step-by-step explanation:

Answer:

option D

Step-by-step explanation:

the formula for slope is: y = mx + b

where m = slope & b = y intercept

so in y = -2x + 1,

m (slope) = -2     &      b (y-int) = (0,1)

REALICE LOS SIGUIENTES PROBLEMAS DE ECUACIÓN DE LA RECTA CORRECTAMENTe

1.- Encuentre la ecuación vectorial de la recta si tenemos A(4, -2) y el vector V=(2, 5) paralelo a la recta y que pasa por A


2.- Encuentre la ecuación general de una recta conociendo un punto P(-2 ; 4) y su pendiente m= - 5 y grafique la recta.

Answers

Answer:

1. La ecuación vectorial de la línea es [tex]\begin{bmatrix} & x & \\ & y & \end{bmatrix} =\begin{bmatrix} & 4 & \\ & -2 & \end{bmatrix} + t \times \begin{bmatrix} & 2 & \\ & 5 & \end{bmatrix}[/tex]

2. La ecuación de la recta es, y = -5·x - 6

Step-by-step explanation:

 1. El punto dado en la línea es A (4, -2), el vector paralelo a la línea es (2, 5)

Por tanto, la ecuación vectorial de la línea es;

[tex]\begin{bmatrix} & x & \\ & y & \end{bmatrix} =\begin{bmatrix} & 4 & \\ & -2 & \end{bmatrix} + t \times \begin{bmatrix} & 2 & \\ & 5 & \end{bmatrix}[/tex]

Donde;

t = Cualquier número

2. El punto por el que pasa la recta es P (-2; 4)

La pendiente de la recta, m = -5

Por lo tanto, la ecuación de la línea en forma de punto y pendiente se presenta de la siguiente manera;

y - 4 = (-5) · (x - (-2)) = -5 · x - 10

∴ y - 4 = -5 · x - 10 + 4 = -5 · x - 6

La ecuación de la recta es, y = -5·x - 6

Need help ASAP please

Answers

Answer:

10  

Step-by-step explanation:

1. AB

2 BC

3. CD

4. DE  

5. AC  

6. B D

7.CE

8.AD

9.BE

10. A E

31. Which choice describes the value of m when -5(m + 1) = 23?
А
B.
m 2-3
ms-
6 m2
D.ms-

Answers

Answer:

The correct choice is Option A. m ≥ -28/5

Step-by-step explanation:

factorize. xy^2-y(x-z) -z​

Answers

Answer:

The equation x The equation x 2The equation x 2 +xy+xz+yz can be factorised as follows:The equation x 2 +xy+xz+yz can be factorised as follows:x The equation x 2 +xy+xz+yz can be factorised as follows:x 2The equation x 2 +xy+xz+yz can be factorised as follows:x 2 +xy+xz+yz=(x The equation x 2 +xy+xz+yz can be factorised as follows:x 2 +xy+xz+yz=(x 2The equation x 2 +xy+xz+yz can be factorised as follows:x 2 +xy+xz+yz=(x 2 +xy)+(xz+yz)=x(x+y)+z(x+y)=(x+z)(x+y)The equation x 2 +xy+xz+yz can be factorised as follows:x 2 +xy+xz+yz=(x 2 +xy)+(xz+yz)=x(x+y)+z(x+y)=(x+z)(x+y)Hence, x The equation x 2 +xy+xz+yz can be factorised as follows:x 2 +xy+xz+yz=(x 2 +xy)+(xz+yz)=x(x+y)+z(x+y)=(x+z)(x+y)Hence, x 2The equation x 2 +xy+xz+yz can be factorised as follows:x 2 +xy+xz+yz=(x 2 +xy)+(xz+yz)=x(x+y)+z(x+y)=(x+z)(x+y)Hence, x 2 +xy+xz+yz=(x+z)(x+y)

Answer:

= (y-1) (xy-z)

Step-by-step explanation:

First we expand them -

= xy^2 - xy - yz - z

= xy(y-1)-z(y-1)

= (y-1) (xy-z)

Hope this helped

Use a table of function values to approximate an x-value in which the exponential function exceeds the polynomial
function.
f(x) = 2^(5x-6)
h(x) = 3x^5 - 2x^3 - 4x + 7
x=4
x=7
x = 6
x=5

Answers

Answer: ¿Hablas español porque no entiendo esto? Si lo haces, ¿puedes decirme en español?

Step-by-step explanation:

Hello hello hello hello hello hello hello hello hello hi bye-bye I am so sorry I cannot help you I don’t know math I just need points bye-byeGirls know to bye what no

What is the value of g? ​

Answers

Answer:

56 degrees

Step-by-step explanation:

1. Notice how g is part of a right angle, which equals 90 degrees.

2. Notice how the 34 degree angle on the other side is also part of a 90 angle.

3. Notice how the 2 right angles are vertical to each other, meaning they are the same.

4. Subtract 34 from 90.

5. g=56 degrees

Hope this helps!

-Stella

I think it would be 90 degrees. The g marking looks like it's taking up 2 angles. One of the angles is 34 degrees, because it's opposite to the one marked. Together they look like they form a 90 degree angle.

*It's kind of of hard to see if g is referring to both angle degrees or not.

Yet another calculus question :)


Given [tex]y = x^3 - 2x[/tex] for [tex]x \geq 0[/tex], find the equation of the tangent line to y where the absolute value of the slope is minimized.

I have tried taking both the first and second derivatives and setting them equal to 0 and using that as the answer, but they're incorrect. Could somebody please explain how to complete the question correctly? Thank you so much!

Answers

Answer:  y = (-4/3)*sqrt(2/3)

This is the same as writing [tex]y = -\frac{4}{3}\sqrt{\frac{2}{3}}[/tex]

============================================================

Explanation:

The phrasing "where the absolute value of the slope is minimized" is an interesting way of saying "the tangent slope is 0". This is because absolute values are never negative, so the smallest it can get is 0.

Your teacher has given you

y = x^3 - 2x

which differentiates into

dy/dx = 3x^2 - 2

after using the power rule

The derivative function lets us determine the slope of the tangent. The slope is the dy/dx value. Since we want a slope of 0, we'll set 3x^2-2 equal to zero and solve for x. So you have the correct idea, but you won't involve the second derivative.

dy/dx = 0

3x^2 - 2 = 0

3x^2 = 2

x^2 = 2/3

x = sqrt(2/3)

Notice how I'm ignoring the negative version of this root. This is due to the fact that [tex]x \ge 0[/tex]

-------------------------

Now plug this x value back into the original equation to find its corresponding y coordinate.

y = x^3 - 2x

y = x(x^2 - 2)

y = sqrt(2/3)*( 2/3 - 2 )

y = sqrt(2/3)*( -4/3 )

y = (-4/3)*sqrt(2/3)

Note that x = sqrt(2/3) leads to x^2 = 2/3 after squaring both sides.

-------------------------

Therefore, the equation of this tangent line is y = (-4/3)*sqrt(2/3)

All horizontal lines are of the form y = k, for some constant k. This constant value is basically what number you want the horizontal line to go through on the y axis. That number would be (-4/3)*sqrt(2/3).

Someone help plsssss

Answers

Its either (top to bottom) 1 or 4

what is the answer for 7 to the negitive second power.

Answers

Answer:

the negative just tell you you put a one over the number. Once that's done, the power will be positive, and you can square like normal

Are you asking about  [tex]7^{-2}[/tex]  ?

If so:

A negative in the exponent tells us that we must take the reciprocal of the number, in this case, 7, and then use the exponent like normal:

[tex]7^{-2}[/tex] =

[tex](\frac{1}{7})^{2}[/tex] =

[tex]\frac{1}{49}[/tex],

So our answer is 1/49.

what is the external angle of a polygon where the corresponding interior angle equals 105 degrees

Answers

Answer:

75 degrees maybe.......

Answer:

75 degrees

Step-by-step explanation:

the external angle is between the outside of one of the sides of the angle and the continued line of the second side of the angle.

and because it is measured against a line, where we have a total of 180 degrees for angles, we have

exterior angle = 180 - interval angle = 180-105 = 75

Other Questions
Match the following vocabulary words The probability that Dan buys a sandwich is 0.2.The probability that Dan gets the bus is 0.9.Assuming the events are independent, what is the probability that Dan buys a sandwichand gets the bus? Zoe's Dog Biscuits, inc, has net cash flows from operating activities for the last year of $226 million. The income statement shows that net income in $150 million and depreciation expense is $85 million. During the year, the change in inventory on the balance sheet was an increase of $14 million, change in accrued wages and taxes was an increase of $15 million and change in accounts payable was an increase of $10 million. At the beginning of the year the balance of accounts receivable was $45 million. What was the end of year balance for accounts receivable? A. $20 million B. $25 million C. $45 million D. $65 million What is the value of X? The range of cells in column D and rows 1 to 10 is represented as: 1:10 D1:D10 D:D satellite does not need any energy to revolve around the earth why A convertible preferred stock is convertible at $10, pays a 4% annual dividend, is callable at $110, and is trading at a current market price of $116. Based on these details, what is the parity price of the common stock Help me please!!!!!????? During the light reactions part of photosynthesis, chlorophyll in the chloroplast captures energy from the sun. What is this light energy used for?to release carbon dioxide and use glucose as energyto turn carbon dioxide and chloroplasts to glucoseto combine oxygen and water to make glucoseto cleave water, release oxygen gas, and convert ADP to ATP what is example of application of machine learning that can be imposed in eduction. (except brainly.) During psychiatric assessment, the following are sources of data except: a. Interview. b. Internet and social media. C. Reports from the others. d. Observations A playground merry-go-round has a mass of 120 kg and a radius of 1.80 m and it is rotating with an angular velocity of 0.500 rev/s. What is its angular velocity after a 22.0-kg child gets onto it by grabbing its outer edge Consider an electromagnetic wave propagating through a region of empty space. How is the energy density of the wave partitioned between the electric and magnetic fields?1. The energy density of an electromagnetic wave is 25% in the magnetic field and 75% in the electric field.2. The energy density of an electromagnetic wave is equally divided between the magnetic and electric fields.3. The energy density of an electromagnetic wave is entirely in the magnetic field.4. The energy density of an electromagnetic wave is 25% in the electric field and 75% in the magnetic field.5. The energy density of an electromagnetic wave is entirely in the electric field Help pleas like please ASAP Use the method of cylindrical shells to write out an integral formula for the volume of the solid generated by rotating the region bounded by the curve y = 2x - x^2 and the line y = x about the y-axis. The government has adopted an emissions tax if it: Group of answer choices specifies the type of catalytic converter that must be used to reduce automobile emissions. pays automobile drivers 10 cents for each 10% reduction in automobile emissions. charges automobile drivers 10 cents for each unit of automobile emissions. transfers the ownership of city air to a private firm that charges automobile drivers a profit-maximizing price, based in part on the pollution capacity of the atmosphere. During the Great Depression, a. the pineapple industry finally became highly profitable as world demand for fruits rose. b. Latin America developed a mature regional economy, which exported large quantities of manufactured goods and imported most of its foodstuffs and raw materials. c. revolutions occurred all over Latin America. d. Latin American economies boomed, in contrast to those of the United States and Europe. e. domestic instability led to the creation of dictatorships. A certain heating element is made out of Nichrome wire and used with the standard voltage source of V=120 V. Immediately after the voltage is turned on, the current running through the element is measured at I1=1.28 A and its temperature at T1=25C. As the heating element warms up and reaches its steady-state (operating) temperature, the current becomes I2=1.229 A.Required:Find this steady-state temperature T2. Please help me with this, i need help The function f(x) = One-sixth (two-fifths) Superscript x is reflected across the y-axis to create the function g(x). Which ordered pair is on g(x)?