find the measure of each segment

Answers

Answer 1

The value of each line segment is found as 26 units.

What is defined as the mid point?A midpoint is a point in the center of a line connecting two points. The two points of reference are the line's endpoints, and the midpoint is located between the two. The midpoint splits the line connecting such two points in half. Furthermore, a line drawn to bisect the line connecting these two points passes through midpoint.

For the given question.

The line is given as DE and the mid point of line is D.

Thus,

CD = DE .....eq 1

The value of each term are given as;

CD = 2x + 7

DE = 4(x - 3)

Put the value in equation 1.

2x + 7 = 4(x - 3)

2x + 7 = 4x - 12

Bring variables and constants on the different sides.

4x - 2x = 7 + 12

2x = 19

x = 9.5

Put the value in each side;

CD = 2×9.5 + 7 = 26 unitsDE = 4(9.5 - 3) = 26 units

Thus, the value of each line segment is found as 26 units.

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Related Questions

16 1 point
Triangle congruence SSS is being shown?
True
False
|||
+||

Answers

Answer:

True

Step-by-step explanation:

SSS is being shown because the two sides are known by congruence marks, and the third side is known because it is equal--the two triangles are sharing it.

copy and complete each problem
/20 = 11/55

Answers

Answer:

[tex]\frac{4}{20}[/tex] = [tex]\frac{11}{55}[/tex]

Step-by-step explanation:

[tex]\frac{x}{20}[/tex] = [tex]\frac{11}{55}[/tex] cross multiply and solve for x

55x = 11(22)

55x = 220 Divide both sides by 55

x = 4

A couple of friends decide to race each other. Emmet can run 6 yards per second, whereas Ayana can run 9 yards per second. Because he is slower, Emmet also gets a head start of 30 yards. Shortly after they start running, Ayana will catch up to Emmet. How far will Ayana have to run?Write a system of equations, graph them, and type the solution.

Answers

We know the formula d=rt where d is distance, r is rate and t is time

Emmet:

d = 6 yd/s * t

Ayana:

d = 9 yd/s * t

We give Emmet 30 less yards to run

Emmet:

d - 30 = 6 yd/s * t

d = 6t + 30

Setting the equations equal to each other

9 * t = 6t + 30

Subtract 6t from each side

9t-6t = 30

3t = 30

Divide by 3

3t/3 = 30/3

t = 10 seconds

It will take 10 seconds for Ayana to catch up

Ayana:

d = 9 yd/s * t

d = 8 * 10 = 90 yds

the length of a rectangle is 13 centimeters less then four times it’s width it’s area is 35 centimeters find the dimensions of the rectangle

Answers

Solution:

The area of a recatngle is expressed as

[tex]\begin{gathered} \text{Area of rectangle = L}\times W \\ \text{where} \\ L\Rightarrow\text{length of the rectangle} \\ W\Rightarrow\text{ width of the rectangle } \end{gathered}[/tex]

Given that the length of the rectangle is 13 centimeters less than four times its width, this implies that

[tex]L=4W-13\text{ ---- equation 1}[/tex]

Tha area of the rectangle is 35 square centimeters. This implies that

[tex]36=L\times W\text{ --- equation 2}[/tex]

Substitute equation 1 into equation 2. Thus,

[tex]\begin{gathered} 36=L\times W \\ \text{where} \\ L=4W-13 \\ \text{thus,} \\ 36=W(4W-13) \\ open\text{ parentheses} \\ 36=4W^2-13W \\ \Rightarrow4W^2-13W-36=0\text{ ---- equation 3} \\ \end{gathered}[/tex]

Solve equation 3 by using the quadratic formula expressed as

[tex]\begin{gathered} W=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}_{} \\ \text{where} \\ a=4 \\ b=-13 \\ c=-36 \end{gathered}[/tex]

thus, we have

[tex]\begin{gathered} W=\frac{-(-13)\pm\sqrt[]{(-13)^2-(4\times4\times-36)}}{2\times4}_{} \\ =\frac{13\pm\sqrt[]{169+576}}{8} \\ =\frac{13\pm\sqrt[]{745}}{8} \\ =\frac{13}{8}\pm\frac{\sqrt[]{745}}{8} \\ =1.625\pm3.411836016 \\ \text{thus,} \\ W=5.036836016\text{ or W=}-1.786836016 \end{gathered}[/tex]

but the width cannot be negative. thus, the width of the recangle is

[tex]W=5.036836016[/tex]

From equation 1,

[tex]\begin{gathered} L=4W-13 \\ \end{gathered}[/tex]

substitute the obtained value of W into equation 1.

Thus, we have

[tex]\begin{gathered} L=4W-13 \\ =4(5.036836016)-13 \\ =20.14734-13 \\ \Rightarrow L=7.14734 \end{gathered}[/tex]

Hence:

The width is

[tex]5.036836016cm[/tex]

The length is

[tex]7.14734cm[/tex]

question In photograph

Answers

The equation that represents the relationship between x and y in the table is (L.) y = -5x + 3.

What is an Equation in Math?

In mathematics, an equation is a relationship between two expressions that are expressed as equality on each side of the equal to sign.

Given in the table is the relationship between x and y respectively.

Substitute the values of x in the respective equations to find the value of y, the resulting value which matches the value of y in the table determines the correct equation.

J. y = -5x -27

⇒ For x = -3, y = -5(-3) - 27 = 15 -27 = -12 ≠ 18

K. y = -5x + 18

⇒ For x = -3, y = -5(-3) + 18 = 15 + 18 = 33 ≠ 18

L. y = -5x + 3

⇒ For x = -3, y = -5(-3) + 3 = 15 + 3 = 18 ≈ 18

For x = -1, y = -5(-1) + 3 = 5 + 3 = 8

For x = 2, y = -5(2) + 3 = -10 + 3 = -7

For x = 6, y = -5(6) + 3 = -30 + 3 = -27

All the values of x and y in the table satisfy the equation y = -5x + 3. Hence this is the required equation that represents the relationship.

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Estimate the time it would take you to drive 278 miles at38 miles per hour. Round to the nearest hour

Answers

Speed formula:

[tex]s=\frac{d}{t}[/tex]

d is the distance

t is the time

As you need to find a time having the distance and speed, solve the equation above for t:

[tex]\begin{gathered} t\cdot s=d \\ t=\frac{d}{s} \end{gathered}[/tex]

Use the given data to find the time:

[tex]\begin{gathered} t=\frac{278mi}{38mi/h} \\ \\ t=7.31h \\ \\ t=7h \end{gathered}[/tex]Then, it would take you 7 hours to drive 278 mi at 38mi/h

Y=1/3x+2 standard form

Answers

3y - x = 6 is standard form for the given equation

What is standard form of linear equation ?The typical form for linear equations with two variables is Ax+By=C.For instance, the linear equation 2x+3y=5 is in standard form. Finding both intercepts of an equation in this style is quite easy (x and y).This form is also very useful when trying to solve systems of two linear equations.Calculation

y = 1/3x + 2

3y = x + 6

3y - x = 6 is standard form

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how do we do this one there two parts to i t

Answers

Given:

[tex]8\sqrt{y}=x-5y[/tex]

Find: differentiation

Explanation: on differentitaion with respect to x

[tex]\begin{gathered} 8\sqrt{y}=x-5y \\ \frac{8}{2}y^{\frac{-1}{2}}\frac{dy}{dx}=1-5\frac{dy}{dx} \\ 4y^{\frac{-1}{2}}\frac{dy}{dx}+5\frac{dy}{dx}=1 \\ (4y^{\frac{-1}{2}}+5)\frac{dy}{dx}=1 \\ \frac{dy}{dx}=\frac{1}{4y^{\frac{-1}{2}}+5} \end{gathered}[/tex]

[tex]\begin{gathered} \frac{-4}{2}y^{\frac{-3}{2}}\frac{dy}{dx}\frac{d^2y}{dx^2}+5\frac{d^2y}{dx^2} \\ 0=(-2y^{\frac{-3}{2}}\frac{dy}{dx}+5)\frac{d^2y}{dx^2} \\ \frac{d^2y}{dx^2}=0 \end{gathered}[/tex]

put the value of

[tex]\frac{dy}{dx}[/tex]

we get,

[tex]\begin{gathered} (-2\frac{y^{\frac{-3}{2}}}{4y^{\frac{-1}{2}}+5}+5)\frac{d^2y}{dx^2}=0 \\ \frac{d^2y}{dx^2}=0 \end{gathered}[/tex]

Admission to a state fair is $10, and each ride ticket costs $2.50. Write an en

Answers

EXPLANATION

Let's call t to the number of tickets and c to the total cost, the appropiate relationship would be:

c = 2.5t + 10

The variable in the expression represents the number of tickets.

why is 10'15 equal to 10'11? explain ur thinking. ___ 10'4

Answers

[tex]\frac{10^{15}}{10^4}=10^{11}\text{ for the following reasons:}[/tex][tex]To\text{ calcultate }\frac{10^{15}}{10^4}\text{ you would have to apply exponent rule}[/tex]

Exponent rule is the following:

[tex]\frac{x^a}{x^b}=x^{a-b}[/tex][tex]\text{Therefore, if for }\frac{10^{15}}{10^4}\text{ a is 15 and b is 4, therefore:}[/tex][tex]\frac{10^{15}}{10^4}=10^{15-4}[/tex][tex]So,\text{ }10^{\mleft\{15-4\mright\}}=10^{11}[/tex]

Quadratic Factoring: Demonstrate solving some quadraticequations using the following methods: factoring, taking theroot, and completing the square.

Answers

The Solution:

Let's solve with the Factoring Method:

[tex]x^2-x-6=0[/tex][tex]\begin{gathered} x^2-3x+2x-6=0 \\ x(x-3)+2(x-3)=0 \\ (x+2)(x-3)=0 \end{gathered}[/tex][tex]\begin{gathered} x+2=0\text{ or }x-3=0 \\ x=-2\text{ or }x=3 \end{gathered}[/tex]

Solving by the Completing the Square:

[tex]\begin{gathered} x^2-x=6 \\ x^2-x+(\frac{1}{2})^2=6+\frac{1}{4} \\ \\ (x-\frac{1}{2})^2=\frac{25}{4} \end{gathered}[/tex]

Take the square root of both sides.

[tex]\begin{gathered} x-\frac{1}{2}=\sqrt{(\frac{25}{4})} \\ \\ x=\frac{1}{2}\pm\frac{5}{2}=\frac{1\pm5}{2} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{1+5}{2}=\frac{6}{2}=3 \\ \\ \\ x=\frac{1-5}{2}=\frac{-4}{2}=-2 \end{gathered}[/tex]

Therefore, the answers is:

[tex]x=-2\text{ or }x=3[/tex]

Just give me the answer please, my device is at 10%

Answers

Solve for x

We can use sine

[tex]\begin{gathered} \sin 48^0=\frac{x}{17} \\ \text{Cross multiply} \\ x=17\times\sin 48^0 \\ x\text{ =17}\times0.7431448 \\ x=12.6\text{ } \end{gathered}[/tex]

Let a represent the row number in this pattern. Write a rule that tells you the number of dots, d, in row n (Hint: Your rule should begin with "d=") Row 1 Row 2 Row 3 Row 4

Answers

The rule to show the number of dots in the pattern is

d = 2a

What is a pattern?

A pattern is a repetition of items, when the repetition is in ordered then the pattern can be forecasted.

The given pattern is ordered by the rule at which it was formed. The rule helps to forecast the number of dots in the next row

How to get the rules of the pattern

The information given in the question include:

Let a represent the row number in this patternA picture image shoeing the rows and dotsYour rule should begin with "d="

row 1 = 2 dots

row 2 = 4 dots

row 3 = 6 dots

it can be seen that

2 * number of rows = number of dots

Hence:

d = 2 * a

d = 2a

checking the rule for the 4th row

d = 2 * 4

d = 8

counting the dots confirms the rule is okay

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Order the following from least to greatest: 0.232, 1.2, 1.09, 0, 3, 0.9

Answers

Answer:

0, 0.232 , 0.9 , 1.09, 1.2 , 3

How many triangles can be formed by joining the vertices of a 10-sided polygon?

Answers

The total number of triangles formed by joining vertices of 10-sided polygon is given by the combination of 10 sides taken at 3, i.e. selection of 3 points from 10 points ( because a triangle has 3 vertices). This gives

[tex]10C3=\frac{10!}{3!(10-3)!}=\frac{10!}{3!\cdot7!}=\frac{10\cdot9\cdot8}{6}=\frac{720}{6}=120[/tex]

Then, the answer is the last option: 120

Show that (3 * 8 * x)⁷ = 6⁷ * 4⁷ * x⁷

Answers

Answer:

Q.E.D.

Explanation:

Given the expression

[tex](3\times8\times x)^7[/tex]

We want to show that it is equal to the right-hand side.

Now, we note that: 8 = 2 x 4

Substituting 8 = 2 x 4, we have:

[tex]=(3\times2\times4\times x)^7[/tex]

We then go further to get:

[tex]=(6\times4\times x)^7[/tex]

Distributing the exponent, we have:

[tex]=6^7\times4^7\times x^7[/tex]

This is the given right-hand side of the equation as required.

Jason provided the following work when asked to convert 0.105 to its
simplest fraction form.
1. Why did Jason get the problem wrong?
2. Provide the work for properly writing the decimal in its simplest fraction
form.
Jason's Work:
0.105=

105/1000

21/200

Answers

Jason provided the work when asked to convert 0.105 to its simplest fraction form which is; 21/200

How to convert from decimal to fraction?

For conversion from decimal to fraction, we write it in the form a/b such that the result of the fraction comes as the given decimal. To get the decimal of the form a.bcd, we will count the digits that are there after the decimal point; then we write 10 raised to that many power as the denominator and the considered number without any decimal point as the numerator.

Given that Jason's Work:

0.105

Jason provided the work when asked to convert 0.105 to its simplest fraction form which could be;

0.105 = 105/1000

= 21/200

Hence, Jason provided the work when asked to convert 0.105 to its simplest fraction form which is; 21/200

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Brianna's teacher asks her if these two expressions 3x + 5 and 4x are equivalent.Brianna says the expressions are equivalent because the value of each expression is 20 when x = 5.Is Brianna correct synlainthink ASAP please

Answers

Step 1

Given data

Expression 1 = 3x + 5

Expression 2 =

(−1/2x+7/10)−(−3/4x−1/5)

Answers

The expression (−1/2x + 7/10) − (−3/4x − 1/5) has a value of 1/4x + 9/10 when simplified

How to evaluate the expression?

From the question, the expression is given as

(−1/2x+7/10)−(−3/4x−1/5)

Rewrite the expression properly to make it legible

So, we have

(−1/2x + 7/10) − (−3/4x − 1/5)

Expression the above parameter as an equation

This is represented as

(−1/2x + 7/10) − (−3/4x − 1/5) = (−1/2x + 7/10) − (−3/4x − 1/5)

Open the brackets

So, we have the following equation

(−1/2x + 7/10) − (−3/4x − 1/5) = −1/2x + 7/10 + 3/4x + 1/5

Collect the like terms in the equation

(−1/2x + 7/10) − (−3/4x − 1/5) = 3/4x − 1/2x + 7/10 + 1/5

Evaluate

(−1/2x + 7/10) − (−3/4x − 1/5) = 1/4x + 9/10

The expression cannot be further simplified

Hence, the solution to the expression (−1/2x + 7/10) − (−3/4x − 1/5) is 1/4x + 9/10

Answers

Answer:

The sum in summation notation is:

[tex]\sum ^4_{r\mathop{=}0}(-1)^r(4Crx^{4-r}y^r)[/tex]

The expansion is:

[tex]81x^{20}-12x^{15}y^3+\frac{2}{3}x^{10}y^6-\frac{4}{243}x^5y^9+\frac{1}{6561}y^{12}[/tex]

Explanation:

Given the expression:

[tex](3x^5-\frac{1}{9}x^3)^4[/tex]

In summation notation, this can be written as:

[tex]\sum ^4_{r\mathop=0}(-1)^r(4Crx^{4-r}y^r)[/tex]

The simplified terms of the expression is:

[tex]\begin{gathered} 4C0(3x^5)^{\mleft\{4-0\mright\}}(\frac{1}{9}y^3)^0-4C1(3x^5)^{\mleft\{4-1\mright\}}(\frac{1}{9}y^3)^1+4C2(3x^5)^{\mleft\{4-2\mright\}}(\frac{1}{9}y^3)^2-4C3(3x^5)^{\mleft\{4-3\mright\}}(\frac{1}{9}y^3)^3+4C4(3x^5)^{\mleft\{4-4\mright\}}(\frac{1}{9}y^3)^4 \\ \\ =(3x^5)^4-4(3x^5)^3(\frac{1}{9}y^3)+6(3x^5)^2(\frac{1}{9}y^3)^2-4(3x^5)^{}(\frac{1}{9}y^3)^3+(\frac{1}{9}y^3)^4 \\ \\ =81x^{20}-12x^{15}y^3+\frac{2}{3}x^{10}y^6-\frac{4}{243}x^5y^9+\frac{1}{6561}y^{12} \end{gathered}[/tex]

Consider the following relation: (1,12) ,(3, 8) , (3, 11) , (6, 9) , (7, 11) . Whichordered pair could be removed so thatthe relation is a function?Group of answer choices

Answers

Answer: Rajesh Kumar

Step-by-step explanation I took the wok to poland

which of the following describes the two spheres A congruentB similarC both congruent and similarD neither congruent nor similar

Answers

The two spheres are similar since they have a proportion of their radius. This proportion is 9/6 (3/2) or 6/9 (2/3).

They are not congruent. They do not have the same radius.

Therefore, the spheres are similar.

Quantum Logic recently expanded its operations at a cost of $450,000. Management expects that the value of the investment will grow at a rate of 8% per year compounded quarterly for the next 5 years. Find the future value of the investment

Answers

Given:

Quantum Logic recently expanded its operations at a cost of $450,000.

So, P = 450,000

The rate of growth = r = 8% = 0.08

compounded quarterly, n = 4

We will find the future value of the investment (A) after t = 5 years

We will use the following formula:

[tex]A=P\cdot(1+\frac{r}{n})^{nt}[/tex]

Substitute with the given values:

[tex]\begin{gathered} A=450,000\cdot(1+\frac{0.08}{4})^{4\cdot5} \\ \\ A=450,000\cdot1.02^{20}\approx668,676.33 \end{gathered}[/tex]

So, the answer will be:

The future investment = $668,676.33

Which graph represents an exponential function

This is algebra two graphing exponential functions

Answers

Answer: The Curved Line on Top

Step-by-step explanation: A positive-valued function of a real variable. So the top one

Just learned about this in Algebra 1 about 4 days ago.

Hello, may I please have some help with this question. Thank you.

Answers

The total distance that Kim walked in 3 days is 6 2/3 miles. We would convert this distance to mixed numbers. To do this, we would multiply 6 by 3 and add 2. The denominator would still be 3. It becomes

20/3 miles

If she walked 20/3 miles in 3 days, the number of miles that she walked per day would be

total distance/number of days

It becomes

(20/3) / 3

If we change the division sign to multiplication, it means that we would flip 3 such that it becomes 1/3. Thus, we have

20/3 * 1/3 = 20/9

= By converting to mixed numbers, we would find how many 9's are in 20. It is 2. The remainder is 20 - 18 = 2

Thus, the answer is

2 2/9 miles per day

Solve the compound inequality. Graph the solution-7 *x+3<4-The solutions are(Type an inequality or a compound inequality. Sim

Answers

Answer:

[tex]-10\leqslant x<1[/tex]

Explanation:

To solve compound inequalities, we do the same as in an equation or inequality: we need to do the same operation in all places.

We want to solve for x:

[tex]-7\leqslant x+3<4[/tex][tex]-7-3\leqslant x+3-3<4-3[/tex][tex]-10\leqslant x<1[/tex]

And that's the answer

Based on the two data sets represented below, complete the following sentences.Options: "greater" or "less"

Answers

We can check that the median of the dataset T is 14, and its mean is also close to 14, while the median of the dataset U is 17 and its mean is close also close to 17. We can also check that the range of the dataset T is 14 and the data is more concentrated at its center, while the range of the dataset U is 20 and the data is more dispersed.

Therefore, we can state that The center of Data Set T is less than the center of Data Set U, and the spread of Data Set T is less than the spread of Data Set U.

for each of the following polynomial functions, write the equation of a different polynomial function that has the same key characteristic. explain your thinking.

Answers

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Draw the given graph.

STEP 2: Get the function plotted on the graph.

[tex]undefined[/tex]

Solve for x. Write the reasons next to each step.Submit723x+10

Answers

x = 26/3

Explanation:

We would apply the mid-segment theorem:

The base of the smaller triangle = 1/2 (the base of the bigger triangle)

The base of the smaller triangle = 3x + 10

the base of the bigger triangle = 72

3x + 10 = 1/2(72)

Reason: Mid segment is parallel to the base of the large triangle. And it is equal to half the length of the base of the large triangle

simplifying:

3x + 10 = 72/2

3x + 10= 36

subtract 10 from both sides:

3x + 10 - 10 = 36 - 10

3x = 26

DIvide both sides by 3:

3x/3 = 26/3

x = 26/3

or x = 8 2/3

Angel Corporation produces calculators selling for $25.99. Its unit cost is $18.95. Assuming a fixed cost of $80,960, what is the breakeven point in units?

Answers

The breakeven point of Angel Corporation equals to 11,500 units.

How do we get the breakeven point?

Given that the unit price is $25.99, so if they sell a x units, then, the revenue is: R(x) = $25.99*x

Given that the cost per unit is $18.95, plus a fixed cost of $80,960, then, the cost of x units is: C(x) = $80,960 + $18.95*x

Now, the breakeven point is a value of x such that the cost is equal to the revenue, so we need to solve:

$25.99*x = $80,960 + $18.95*x

$25.99*x - $18.95*x = $80,960

$7.04*x = $80,960

x = $80,960/$7.04

x = 11,500 units