Point C is located between points B and D. Also BC = 5x + 7, CD = 3y + 4, BD = 38, and BD = 2x + 8y. Find the values of x and y

Answers

Answer 1

Using location of points and a system of equations, it is found that:

The value of x is 3.The value of y is 4.

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

Point C is located between points B and D means that:

[tex]BD = BC + CD[/tex]

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

We are given that:

[tex]BC = 5x + 7[/tex][tex]CD = 3y + 4[/tex][tex]BD = 38[/tex][tex]BD = 2x + 8y[/tex]

From this, two equations can be built.

[tex]2x + 8y = 38[/tex]

Dividing both sides by 2:

[tex]x + 4y = 19[/tex]

[tex]x = 19 - 4y[/tex]

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

Finding y:

[tex]BC + CD = BD[/tex]

[tex]5x + 7 + 3y + 4 = 38[/tex]

[tex]5x + 3y + 11 = 38[/tex]

[tex]5x + 3y = 27[/tex]

Since [tex]x = 19 - 4y[/tex]

[tex]5(19 - 4y) + 3y = 27[/tex]

[tex]95 - 20y + 3y = 27[/tex]

[tex]17y = 68[/tex]

[tex]y = \frac{68}{17}[/tex]

[tex]y = 4[/tex]

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

Finding x:

[tex]x = 19 - 4y = 19 - 4(4) = 19 - 16 = 3[/tex]

The value of x is 3.

The value of y is 4.

A similar problem is given at https://brainly.com/question/10956693


Related Questions

100 POINTS

PLEASE DO THESE FOUR QUESTIONS (even if it’s just one)

1. write a number sentence expressing the value of the missing angle in the diagram below

2. write a number sentence expressing the value of r in the diagram

3. label the diagram below so that one pair of parallel lines, and one pair of equal lines

4. use the index laws to simplify the expression below, giving your answer with positive indices. SHOW ALL WORKING OUT.

Answers

Step-by-step explanation:

1. k = 76°

2. r = 25cm

3. as the drawing attached

one pair of parallel lines : AB and DC

one pair of equal angles : L A and L D

4. (7²× 3`¹)⁴×7^5 / (3² × 7^(-6))³

= (7^8 × 3`⁴)×7^5/ (3² × 7^(-6))³

= (7^13 × 3`⁴)/ (3^6 × 7^(-18))

= (7^(31) × 3^(-10))

= 7^31 / 3^10

Compare and order the numbers below from least to greatest.
4.6, 2.8, V7, V17,

Answers

Answer:

2.8, 4.6, V7, V17

i hope it help n im sorry i can't explain

bài 5: rút gọn
(x +1)^2 – (2x + 1)^2

Answers

[tex](x+1)^2-(2x+1)^2=\\\\=(x^2+2\cdot x\cdot1+1^2)-((2x)^2+2\cdot2x\cdot1+1^2)=\\\\=(x^2+2x+1)-(4x^2+4x+1)=\\\\=x^2+2x+1-4x^2-4x-1=\\\\=x^2-4x^2+2x-4x+1-1=\boxed{-3x^2-2x}[/tex]

What is the product of 3.5 ⋅ 102 and 2.4 ⋅ 103?

Answers

Answer:

3.5 × 102 = 357

2.4 × 103 = 247.2

357 × 247.2 = 88250.4

blake and josh are both saving money for a new bike. the ratio of blake,s saving to josh saving is 3:1 if they have saved 400$, how much has each boy saved

Answers

Answer:

200 each.

Step-by-step explanation:

400 divided by 2 is 200

please help me please ​

Answers

answer:

sorry i don't know the answer but are you an army ?

-3(-3x^2 + 2x)

How do I distribute?

Answers

Answer:

9x^3-3.2x.x

9x^3-3.2x^2

9x^3-6x^2

Answer:

9x^2 - 6x

Step-by-step explanation:

-3(-3x^2 + 2x)

Multiply -3 by the numbers in “( )”

9x^2 - 6x

The typing speeds for the students in a typing class is normally distributed with mean 44 words per minute and standard deviation 6 words per minute. What is the probability that a randomly selected student has a typing speed of less than 38 words per minute

Answers

Answer:

15.87%

Step-by-step explanation:

*Probability-Below 15.87%

Z1=-1

*x-1 38

*µ 44

*σ 6

The probability that a randomly selected student has a typing speed of less than 38 words per minute is 15.87%.

What is z-score?

The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean.

Formula for z-score

z = (x -μ)/σ

Where,

Z is standard score.

x is observed value.

μ is mean of the sample.

σ is standard deviation of the sample.

What is probability?

The area under the normal distribution curve represents probability.

According to the given question.

Mean, μ = 44

Standard deviation, σ = 6

Observed value, x = 38

Therefore, z-score = [tex]\frac{38-44}{6}= -1[/tex]

So, the are P(z > -1) = 15.87%

Hence, the probability that a randomly selected student has a typing speed of less than 38 words per minute is 15.87%.

Find out more information about z-score and probability here:

https://brainly.com/question/25638875

#SPJ2

evaluate the following 1340five minus 242five​

Answers

Answer:

10980 is the correct answer

the perimeter of a triangle is 14x - 4. if two sides measure 3x - 2 and 5x + 3, then how long is the third side?

Answers

Answer:

6x-5

Step-by-step explanation:

14x-4- (3x-2)-(5x+3)= 14x-4-3x+2-5x-3= 6x-5

Calculate Velocity! Help please!!!! It's science? Or mathematics...

Answers

The barracuda swam 14 meters in 2 seconds, so its speed is

(14 m)/(2 s) = 7 m/s

the number is 869214.951 , i need the answers for fractions and decimals and power of 10.

Answers

Answer:

Step-by-step explanation:

Fraction:

[tex]869214.951=\dfrac{869214951}{1000}\\[/tex]

Power of 10:

[tex]869214.951=8.69214951 * 10^{5}[/tex]

How does this work please explain clearly :) also 25 points

Answers

how does what work, you didn’t attach a photo or give choices…

Martinez town is building a volleyball court based on a scale drawing that is 40cm by 80cm and uses the scale 1 cm :22.5cm

Answers

The proportional relationship between drawing court lengths x in centimeters and court lengths in y centimeters is y = 22.5x

Your question is not complete, it seems to be missing the following information;

"write an equation for the proportional relationship between drawing court lengths x in centimeters and court lengths in y centimeters"

The drawing court length is given as;

x = 40 cm or 80 cm

drawing scale = 1 cm : 22.5 cm

The corresponding length of the court is calculated as;

when x = 40 cm;

[tex]y = \frac{22.5}{1} \times 40 cm = 900 \ cm[/tex]

when x = 80 cm;

[tex]y = \frac{22.5}{1} \times 80 \ cm = 1,800 \ cm[/tex]

The proportional relationship between drawing court lengths x in centimeters and court lengths in y centimeters is calculated as;

[tex]\frac{y}{x} = \frac{900}{40} = \frac{1800}{80} \\\\\frac{y}{x} = 22.5\\\\y = 22.5 x[/tex]

Thus, the proportional relationship between the lengths is y = 22.5x

Learn more here: https://brainly.com/question/13329343

23. What is the value of 3.2/0.8​

Answers

Answer:

When you divide 3.2 by 0.8 you get 4.

Find the value of 5u+3 given that -3u-1=8.
Simplify your answer as much as possible.

Answers

Answer:

u=6

Step-by-step explanation:

5u+3=-3u-1=8

COMBINE LIKE TERMS(so 5u and -3u and then combine your positive 4 and your negative 1 then bring down your 8

2u-4=8

opposite inverse so add 4 to 8

2u=12

divide 2 into 12

u=6

so your final answer is 6.

xy = 3k-2, yz-7k+4, xz=4k+38

Answers

Answer:

I have taken out the value of xyz.

Solve the equation for y. Then find the value of Y for each value of X.

y+7x=9;x=-1,0,2

y=?
x=?

(help i hate this math hw)

Answers

Answer:

y=9-7x

If x= -1, y=16

If x= 0, y=9

If x=2, y= -5

Step-by-step explanation:

Because you are solving the equation for y, you want to have y by itself on one side. The only way to do that in this problem is by subtracting the 7x on both sides.

y+7x=9

-7x -7x ---> y=9-7x

The next part of the question says to find the value of Y for each value of X. Using the given X values, we plug them into the equation we just got in order to find Y.

y=9-7(-1) ----> y=16

y=9-7(0) ----> y=9

y=9-7(2) ----> y=-5

Line R is represented by the equation `y=-2x+7`and Line Z is represented by the equation `y=3x-3`. At what point will line R and line Z intersect?

Answers

Answer: (2,3)

Steps:
-2x+7=3x-3
7+3=3x+2x
10=5x
X=2

Y= 3x-3
Y= 3*2 - 3
y= 6-3
Y= 3

why the absolute value of a number will never be negitve

Answers

True because if a number is negative 4 the absolute value will be 4

You start a travelling car wash service. You spend $30 on supplies and plan to charge
$6 for each car you wash. Which of the following equations could be used to find your
profit based on the number of cars you wash?
O y = 6x - 30
O y = 6x
O y = 6x + 30

Answers

Answer:

y= 6x - 30

Step-by-step explanation:

First yu would take the 30 dollars you spent then you will subtract 6 times  how many cars you have done.

FURTHER MATHEMATICS Use determinants to solve the systems of equation:
2x + y + 2z = 13
X + y - 2z = 8
X + 2y + z = 11​

Answers

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2x+1y+2z&=&13\\1x+1y-2z&=&8\\1x+2y+1z&=&11\\\end{array}\right.\\\\\\\Delta=\left| \begin{array}{ccc}2&1&2\\1&1&-2\\1&2&1\end{array}\right| =2*\left| \begin{array}{ccc}1&\frac{1}{2}&1\\1&1&-2\\1&2&1\end{array}\right| =2*\left| \begin{array}{ccc}1&\frac{1}{2}&1\\0&\frac{1}{2}&-3\\0&1&3\end{array}\right| =2*(\frac{3}{2}+3)=9\\\\[/tex]

[tex]\Delta_1=\left| \begin{array}{ccc}13&1&2\\8&1&-2\\11&2&1\end{array}\right| =2*\left| \begin{array}{ccc}13&1&2\\8&1&-2\\\frac{11}{2}& 1&\frac{1}{2}\end{array}\right| =2*\left| \begin{array}{ccc}13&1&2\\-5&0&-4\\\frac{-5}{2}& 0&\frac{5}{2}\end{array}\right| \\\\=2*(-1)*(\frac{-25}{2}-\frac{20}{2}) =45\\[/tex]

[tex]\Delta_2=\left| \begin{array}{ccc}2&13&2\\1&8&-2\\1&11&1\end{array}\right| \\\\\\=\left| \begin{array}{ccc}3&21&0\\3&30&0\\1&11&1\end{array}\right| \\\\\\=1*(90-63) =27\\[/tex]

[tex]\Delta_3=\left| \begin{array}{ccc}2&1&13\\1&1&8\\1&2&11\end{array}\right| \\\\\\=\left| \begin{array}{ccc}0&-1&-3\\0&-1&-3\\1&2&11\end{array}\right| \\\\\\=0\\[/tex]

[tex]\left\{\begin{array}{ccc}x=\dfrac{\Delta_1}{\Delta}=\dfrac{45}{9}=5\\\\y=\dfrac{\Delta_2}{\Delta}=\dfrac{27}{9}=3\\\\z=\dfrac{\Delta_3}{\Delta}=\dfrac{0}{9}=0\\\end{array}\right.[/tex]

A rectangular garden is to be twice as long as it is wide. If 360 yards of fencing, including the gate, will completely enclose the garden, what will be the length of the garden, in yards

Answers

Answer:

ninguna respuesta lo siento pero si es que puedo lo cmletare

You start at (0, 2). You move right 2 units and down 4 units. Where do you end?

Answers

Answer:

(2, -2)

Step-by-step explanation:

Translation left or right adds to x-coordinate, translation up or down adds to y-coordinate.

Given coordinate (0, 2) and translation is 2 units right and 4 units down:

x = 0 + 2 = 2y = 2 - 4 = -2

The end points is (2, -2)

We have to move x co ordinates 2 more and y coordinate 4less

Do it

[tex]\\ \sf\longmapsto (0,2)[/tex]

[tex]\\ \sf\longmapsto (0+2,2+(-4))[/tex]

[tex]\\ \sf\longmapsto (2,2-4)[/tex]

[tex]\\ \sf\longmapsto (2,-2)[/tex]

We will end at (2,-2)

XY=32, YZ=7d, and XZ=74

Answers

The value of d = 6 and the value of YZ = 42

Since XY=32, YZ=7d, and XZ=74

Based on this question, it should be noted that the addition of XY and YZ will equal to the value of XZ. Therefore,

XY + YZ = XZ

32 + 7d = 74

Collect like terms

7d = 74 - 32

7d = 42

Divide through by 7

7d/7 = 42/7

d = 6

Since d is 6, the value of YZ will be:

= 7d = 7 × 6 = 42

In conclusion, the value of d = 6 and the value of YZ = 42.

Read related link on:

https://brainly.com/question/24475076

You are adding two rational numbers with different signs.How can you tell if the sum will be positive, Negative,or Zero

Answers

positive if the positive number is greater than the negative number. negative if the negative number is greater. 0 if the two numbers are opposites of each other. an example would be -5 + 5

help me asap please right now​

Answers

Answer:

-3

Step-by-step explanation:

Answer:

-4.5, -3, 22/7 , 16/5, sqrt(17)

Step-by-step explanation:

Simplify { 36 divided by (9) } divided { (-24) divided 6}

step by step needed

Answers

Answer:

-1

Step-by-step explanation:

{36÷(9)}÷{(-24)÷6} 36/9=4 and (-24)/6=-4

={4}÷{-4} 4/(-4)=-4/4=-1

=-1

help me with my homework

Answers

Answer:

a because I dont know why but some one told me it was this

Answer: A. There are three terms

Concept:

In an algebraic expression, there are several specific terms:

Constant: the individual number that has no variable with it, or in east word, it is isolated.Variable: any unknown value, which is usually presented by alphabets.Coefficients: the numbers that are bounded with a variable, usually in front of a variable.Terms: the number of individuals present in the expression, which is constants and [variable + coefficients].Like terms: terms that have the same variables and powers.

If you are still confused, you may refer to the attachment below for a graphical explanation.

Solve:

a. There are three terms. [tex]\boxed{FALSE}[/tex]

- 14b

- -7

- 8b

- b

There are in total four individuals, which means there are four terms.

b. There is one constant term. [tex]\boxed{TRUE}[/tex]

- 14b is a [variable + coefficient]

- -7 is a [constant]

- 8b is a [variable + coefficient]

- b is a [variable]

Therefore, there is one constant term.

c. The coefficients are 14, 8, and 1 [tex]\boxed{TRUE}[/tex]

- 14b →→→ 14 is the [coefficient]

- -7 →→→ is a [constant]

- 8b →→→ 8 is the [coefficient]

- b →→→ 1 is the [coefficient]

Therefore, 14, 8, and 1 are coefficients.

d. Three of the terms are like terms [tex]\boxed{TRUE}[/tex]

- 14b →→→ b is the [variable]

- -7 →→→ is a [constant]

- 8b →→→ b is the [variable]

- b →→→ b is the [variable]

Since 14b, 8b, and b share the common variable, there are three like terms.

Hope this helps!! :)

Please let me know if you have any questions

what is the value of x when the distance between the points (-2,-3) (-3,x) is equal to 5​

Answers

Answer:

(-3,-4)

Step-by-step explanation:

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