Subtract.
5x²-5x+1
(2x² +9x-6)
OA. 3x² - 4x+7
OB. 3x² + 4x-5
OC. 3x² +14x-5
OD. 3x²-14x+7
SUBMIT

Answer:

x = [tex]\frac{2}{3}[/tex] , x = 1

Step-by-step explanation:

(x - [tex]\frac{5}{6}[/tex] )² = [tex]\frac{1}{36}[/tex] ( take square root of both sides )

x - [tex]\frac{5}{6}[/tex] = ± [tex]\sqrt{\frac{1}{36} }[/tex] = ± [tex]\frac{1}{6}[/tex] ( add [tex]\frac{5}{6}[/tex] to both sides )

x = [tex]\frac{5}{6}[/tex] ± [tex]\frac{1}{6}[/tex] , then

x = [tex]\frac{5}{6}[/tex] - [tex]\frac{1}{6}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]

x = [tex]\frac{5}{6}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{6}{6}[/tex] = 1

Vertical Angles Theorem is the reason for step 3 of this proof. Hence, option D is correct.

Theorem of vertical angles or angles that are vertically opposing According to the theorem, two opposing vertical angles that are created when two lines cross one other are always equal to one another.

As AE = EC and BE = ED (by the definition of bisection) suggest that triangles AEB and CED are congruent (by the SAS criterion for congruence),

It is claimed in step 3 of the provided proof that mAEB = mCED. The corresponding angles of two triangles are equal when they are congruent. Since mAEB = mCED, it follows that the measure of angle AEB must be equal to the measure of angle CED.

This step is crucial because it proves the equality of the respective angles in the congruent triangles AEB and CED. This equality is then utilized in step 4 to prove that the two triangles satisfy the SAS criterion, which is a congruence criterion.

Steps 5 through 11 then employ the congruence of triangles AEB and CED to demonstrate that the quadrilateral ABCD is a parallelogram.

Thus, option D is correct.

For more information about Vertical Angles Theorem, click here:

https://brainly.com/question/18868430

#SPJ7

The complete question is given below-

What is the reason for step 3 of this proof?Given: and bisect each other.

Prove: Quadrilateral ABCD is a parallelogram.

Proof:

Statement Reason

1. and bisect each other. given

2. AE = EC

BE = ED definition of bisection

3. mAEB = mCED

4. ABE CDE SAS criterion

5. ACD CAB Corresponding angles of congruent triangles are congruent.

6. converse of Alternate Interior Angles Theorem

7. mBEC = mAED Vertical Angles Theorem

8. BEC DEA SAS criterion for congruence

9. DBC BDA Corresponding angles of congruent triangles are congruent.

10. converse of Alternate Interior Angles Theorem

11. Quadrilateral ABCD is a parallelogram. definition of a parallelogram

a Alternate Interior Angles Theorem

B. Corresponding angles in congruent triangles are congruent.

C. For parallel lines cut by a transversal, corresponding angles are congruent.

D. Vertical Angles Theorem

E. SAS criterion for congruence

[tex]~~~~~\sin \theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\\ \implies \sin x = \dfrac{HI}{GI}\\\\\\\implies \sin x = \dfrac{39}{62}\\\\\\\implies x= \sin^{-1} \left( \dfrac{39}{62} \right)\\\\\\\implies x =38.9^{\circ}[/tex]

Answer:

ABCD=EF

Step-by-step explanation:

A. Z

B. <

C. S

D. >

E. =

F. 2

55? 35

Answer:

The answer is 1001101

Step-by-step explanation:

77 base 10 to base 2 is 1001101

Answer:Flying potatox x plus y yes

Step-by-step explanation:

Answer:

the answer is 1/4 if the question is a fraction

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{11\% of 953.23}}{\left( \cfrac{11}{100} \right)953.23}\implies 104.86[/tex]

Answer:

the area of the problem is 20

Using the together rate, it is found that it will take 1.71 hours for Bella and Jordan to rake the leaves.

It is the sum of each separate rate.

In this problem, the rates are given as follows:

Hence:

[tex]\frac{1}{x} = \frac{1}{3} + \frac{1}{4}[/tex]

[tex]\frac{1}{x} = \frac{4 + 3}{12}[/tex]

[tex]x = \frac{12}{7}[/tex]

x = 1.71.

It will take 1.71 hours for Bella and Jordan to rake the leaves.

More can be learned about the together rate at https://brainly.com/question/25159431

#SPJ1

The probabilities are:

The probability of getting a particular color of marble, is given by the quotient between the number of marbles of that color and the total number of marbles.

Here we have:

So the total number is 5 + 7 + 4 + 8 = 24.

Then:

If you want to learn more about probability, you can read:

https://brainly.com/question/251701

#SPJ1

Leah's family took a road trip to Mount Rushmore. Leah fell asleep 44% of the way through the trip. the total length of the trip is 190.08 miles.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

Leah's family took a road trip to Mount Rushmore. Leah fell asleep 44% of the way through the trip.

If Leah fell asleep after they had traveled 132 miles

So,

44% of 132

= 0.44  x 132

= 58.08

Add in the miles they already traveled

132 + 58.08

= 190.08

Thus, the total length of the trip is 190.08 miles.

Learn more about percent here:

https://brainly.com/question/11549320

#SPJ1

The function that is positive for the entire interval [–3, –2] is the graph of the function (b)

See attachment for the proper representation of the available options

For a function to be positive on the interval [-3,-2];

It means that the y values must be in the positive quadrant from x = -3 to x =-2

From the list of options, we have:

The y values from x = -3 to x =-2 is at the positive quadrant for the second graph i.e. option B

Hence, the function that is positive for the entire interval [–3, –2] is the graph of the function (b)

Read more about functions and graphs at:

https://brainly.com/question/4025726

#SPJ1

Answer:

3=1×5-2

Step-by-step explanation:

you minus 5-2 is 3 and one threes three

Step-by-step Explaination:

Diameter = 1.8 cm

Radius (r) = 1.8/2 = 0.9

According to formula...

Area of circle = π(r)^2

= 3.142 * 0.9 * 0.9

= 2.54502 cm

The total cost for a person who purchases a car share and uses it for 72 hours is $1207.

The total cost is a function of the yearly fee and the cost per hour.

Total cost = yearly fee + (total hours the car was used for x cost per hour)

$199 + (72 x $14)

$199 + $1008 = $1207

To learn more about total cost, please check: https://brainly.com/question/25717996

#SPJ1

Step-by-step explanation:

C(4,2)

Use combinations formula,

c(n,r)=n!/r!(n-r)!

c(n,r)=4!/2!(2!)

[tex]c = \frac{4 \times 3 \times 2 \times 1 }{2 \times 1 \times 2 \times 1} [/tex]

[tex]c = 3 \times 2 \times 1[/tex]

[tex]c = 6[/tex]

An expression is defined as a set of numbers, variables, and mathematical operations. The term that best describes 3 is coefficient.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The value of 3 in the expression, 9 + 4(x + 2) - 3x, is that it is the coefficient of x in the third term.

Hence, the term that best describes 3 is coefficient.

Learn more about Expression:

https://brainly.com/question/13947055

#SPJ1

Answer: 0.088

Step-by-step explanation:

There are two ways. My way is complicated, but never wrong!

0.22 converted to a fraction is 22/100,

explanation: you know this because the denominator must be 10, 100, 1000, 10000 etc... and must be one more digit than the numerator.

and 0.4 into a fraction is 4/10. but we have to have same denominators so we multiply 4/10 by 2 4 x 10 = 40; 10 x 10 = 100.

now multiply...

40   x   22  =  880

100       100      100

and turn it into a decimal, by reversing how we turned it into a decimal.

so it's 0.088!

This is not the line of best fit because the line is not through the middle of the data points.

What is line of best fit?

The line of best fit is a line through a scatter plot of data points that best expresses the relationship between those points.

In this case, this is not the line of best fit because the line is not through the middle of the data points.

Learn more about best fit on:

https://brainly.com/question/23100748

#SPJ1

step by step explanation :

to converting yard to inches you have to multiply whatever number u are given in yard by 36 to get your figure in inches

o multiply whatever number u are given in yard by 36 to get your figure in inches so we multiply 6 *36 to give us 216

o multiply whatever number u are given in yard by 36 to get your figure in inches so we multiply 6 *36 to give us 216answer:

216

Answer:

19

Step-by-step explanation:

7x +2 = 135. Vertically opposite angles

7x=133

x=19

Answer:

length of PR is [tex]4\sqrt{5}[/tex]

Is an isosceles triangle

because PQ is congruent to QR

Step-by-step explanation:

Calculate length of P(-6,0) R(2,4)

=> apply distance formula

[tex]\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

[tex]\sqrt{\left(2-\left(-6\right)\right)^2+\left(4-0\right)^2}[/tex]

[tex]4\sqrt{5}[/tex]

Calculate length of P(-6,0) Q(-3,4)

[tex]\sqrt{\left(-3-\left(-6\right)\right)^2+\left(4-0\right)^2}[/tex]

= 5

5(PQ) = 5(QR)

The amount of money each of Mr Mokwebo 's two sons; Tokelo and Refentse will get is R116 and R95 respectively.

Total amount needed = Tokelo's money + Refentse's money

253 = x + (x - 21)

253 = x + x - 21

253 = 2x - 21

253 - 21 = 2x

232 = 2x

divide both sides by 2

x = 232/2

x = 116

Therefore,

Tokelo's money = x = R116

Refentse's money = x - 21

= 116 - 21

= R95

Learn more about equation:

https://brainly.com/question/2972832

#SPJ1

Component form of u is (-18,13) and The magnitude of u is 22.2

A vector is a two-dimensional entity with both magnitude and direction. A vector can be visualized geometrically as a directed line segment.

The component form of a vector is an ordered pair that describes the change in x and y values

This is mathematically expressed as (Δx, Δy) where Δx=x₂-x₁ and Δy=y₂-y₁

Given ;

Initial points of the vector as (14,-6)

The terminal point of the vector is (-4,7)

Here x₁=14,x₂=-4, y₁=-6,y₂=7

The component form of the vector u is (-4-14,7--6) =(-18,13)

Finding the Magnitude of the vector

u=√(x₂-x₁)²+(y₂-y₁)²

u=√-18²+13²

u=√324+169

u=√493

u=22.2

Therefore the Component form of u is (-18,13) and The magnitude of u is 22.2

To know more about vectors follow

https://brainly.com/question/25705666

#SPJ1

Answer:

b. g(t) = 200 - 4t

Step-by-step explanation:

I don't know how to explain this, but here is the answer.

The mean number is 8.7 and the outliers 1 and 2 reduce the mean value

The dataset is given as:

10, 12, 8, 11, 13, 9, 2, 1, 9, and 12​.

The mean number is calculated using:

Mean = Sum/Count

So, we have:

Mean = (10+ 12+ 8+ 11+ 13+ 9+ 2+ 1+ 9+12​)/10

Evaluate

Mean = 8.7

Hence, the mean number is 8.7

Outliers are relatively far from other data elements of the dataset

In the given dataset, 1 and 2 are far from other data element.

So, the outliers are 1 and 2

Because 1 and 2 smaller than other data elements, they affect the mean by reducing the mean value

Read more about outliers at:

https://brainly.com/question/3631910

#SPJ1

Answer:87/10 is the answer because there are no tens

Step-by-step explanation:

Answer:19 for first answer. Second answer is subtract 16 from both sides

Step-by-step explanation:76/4 first answer

Answer:

5000

makes the best sense