Please help me bef9yer9h

Please Help Me Bef9yer9h

Answers

Answer 1

Answer:

y = -6x + 7.5

Explanation:

To find perpendicular bisector equation:

Given points: B(-2, 1), C(4, 2)

First find slope:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\sf slope: \dfrac{2-1}{4-(-2)} } = \dfrac{1}{6}[/tex]

Then the perpendicular slope will be negatively inverse.

[tex]\sf perpendicular \ slope \ (m) : -(\dfrac{1}{6} )^{-1} = -6[/tex]

Then find the mid point coordinates between BC:

[tex](x_m, y_m)= \sf (\dfrac{x_1 + x_2}{2} , \dfrac{y_2 + y_1}{2} )[/tex]

[tex](x_m, y_m) = \sf (\dfrac{-2 + 4}{2} , \dfrac{1 + 2}{2} )[/tex]

[tex](x_m, y_m) = \sf ( 1 , 1.5 )[/tex]

Then find equation:

y - yₘ = m(x - xₘ)

y - 1.5 = -6(x - 1)

y = -6x + 6 + 1.5

y = -6x + 7.5

Answer 2

The answer is y = -6x + 15/2.

First, find the slope of BC.

m = Δy/Δx

m = 2 - 1 / 4 - (-2)

m = 1/6

Hence, the slope of the perpendicular bisector will be the negative reciprocal of the given line.

m' = - (1/ [1/6])

m' = -6

Now, find the midpoint of BC.

M = (-2 + 4 / 2, 2 + 1 / 2)

M = (1, 3/2)

Now, we can find the equation of the perpendicular bisector using the point slope form of equation.

y - y₁ = m (x - x₁)

y - 3/2 = -6 (x - 1)

y - 3/2 = -6x + 6

y = -6x + 15/2


Related Questions

Wayne borrowed sh. 50,000 from a
bank that charged compound interest
at the rate of 12% p.a. How much did
she pay back at the end of 30 months?

Answers

Answer:15000

Step-by-step explanation:50,000 x 0.12=6,000 X 2=12,000

6000 divided by 2= 3,000

12 + 12=24+6=30

What values of a and b make the equation true? startroot 648 endroot = startroot 2 superscript a baseline times 3 superscript b baseline endroot

Answers

The values of a and b which make the equation true are; a = 3 and b = 4 respectively.

What are indices in maths?An index, or a power, is the small floating number that goes next to a number or letter. The plural of index is indices. Indices show how many times a number or letter has been multiplied by itself.

From the question; the expression given is;

[tex]\sqrt{648} = \sqrt{2^{a} * 3^{b} }[/tex]

In essence; we have;

648 = 2^a × 3^b

By expression of of 648 as the product of its lowest factors; we have;

648 = 2 × 2 × 2 × 3 × 3 × 3 × 3.

In which case; we have;

648 = 2³ × 3⁴

Ultimately, the values of a and b which make the equation true are 3 and 4 respectively.

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The complete question is -

What values of a and b make the equation true? StartRoot 648 EndRoot = StartRoot 2 Superscript a Baseline times 3 Superscript b Baseline EndRoot a = 3, b = 2 a = 2, b = 3 a = 3, b = 4 a = 4, b = 3

What is the value of the expression below when w= 5 and x =9

Answers

The value of the expression 9w + 5x when w= 5 and x =9 is 90

Algebraic expression

9w + 5x

When

w = 5 and x = 9

9w + 5x

= 9(5) + 5(9)

= 45 + 45

= 90

Complete question:

What is the value of the expression below when w = 5 and x = 9? 9w + 5x

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Pentagon ABCDE ~ LMNOP. Find the value of x and the measure of Lc.

Answers

The value of x is 6 and the measure of ∠C is 86 degrees

How to solve for x and the measure of c?

The complete question is added as an attachment

Given that:

ABCDE ~ LMNOP

It means that we have the following equivalent ratio

ED : BC = PO : MN

This gives

8 : 6 = 12 : x

Express as fraction

6/8 = x/12

Multiply both sides by 12

12 *  6/8 = x

Evaluate

9 = x

Rewrite as

x = 9

Also

ABCDE ~ LMNOP implies that the corresponding angles are equal

The corresponding angle of C is N

And, we  have:

N = 86

This implies that

C = 86

Hence, the value of x is 6 and the measure of ∠C is 86 degrees

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Hey I appreciate the help thank you

Answers

Answer:

60 degrees

Step-by-step explanation:

The sum of the interior angles of a triangle are 180.  The bottom triangle give you two of the angle measurements (43 and 35)  Take 180 - 43 -35 = 102.  Angle E is 102.  Vertical angles are congruent so that mean that we can use that to find angle a.  Again, the sum of the interior angles adds up to 180.  180 - 102 - 18 gives us the measurement of angle a (60)

WILL MAKE BRAINLIEST!! What will the coordinates of triangle are RST after it is translated four units right and three units up type your answer in as a coordinate pair X, Y for each point enter your answer and also provide a one sentence explanation that describes how are you determine your answer review the Rubik be slow to see how you will be evaluated?

Answers

The coordinates of triangle RST after it is translated four units right and three units up are (0, 5), (7, 8) and (0, -1)

How to determine the coordinates?

From the figure, the coordinates of the triangle RST are:

R = (-4, 2)

S = (3, 5)

T = (-4, -4)

The rule of translation is given as:

Four units rightThree units up

This is represented as:

(x, y) = (x + 4, y + 3)

So, we have:

R' = (-4 + 4, 2 + 3) = (0, 5)

S' = (3 + 4, 5 + 3) = (7, 8)

T = (-4 + 4, -4 + 3) = (0, -1)

Hence, the coordinates of triangle RST after it is translated four units right and three units up are (0, 5), (7, 8) and (0, -1)

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Jeanette needed a large number of responses for her survey about taste preferences so she chose to do an internet survey. A significant problem she may have is _____

Answers

A significant problem is her sample will not be representative for her survey when she needed a large number of responses for her survey about taste preferences so she chose to do an internet survey.

what is internet survey ?

An Internet survey is a structured questionnaire that your target audience fills out over the internet, typically by filling out a form. The length and format of online surveys can vary. The data is saved in a database, and the survey tool usually includes some level of data analysis in addition to review by a trained expert.

Survey Advantages:

Unlike traditional surveys, internet surveys allow businesses to collect information from a large number of people at a low cost. When you conduct an internet survey, you will have the opportunity to learn:

Who are your customers?

What your users want to achieve?

What information are your users looking for?

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Margie is practicing for an upcoming tennis tournament. Her first serve is good 20 out of 30 times on average. Margie wants to know the estimated probability that her first serve will be good at least four of the next six times she serves. How could she design a simulation for this scenario

Answers

Probability that Margie's first serve will be good at least four of the next six times she serves is 0.68

What is Binomial Distribution in Probability?

Assume that n independent replications of a random experiment with exactly two outcomes are performed. Success has a probability of [tex]p[/tex], while failure has a probability of [tex]q[/tex]. Assume that out of these n times, we will experience success [tex]x[/tex] times and failure [tex]n-x[/tex] times. There are [tex]^nC_x[/tex] different ways in which we can succeed. If, [tex]X[/tex] has a binomial distribution, then,

[tex]P(X=x)=p(x)[/tex]

                  [tex]=[/tex] [tex]^nC_xp^xq^{n-x}[/tex]

for [tex]x[/tex] = 0, 1,..., n. Here,  [tex]q=1-p[/tex]. A binomial variate is any such random variable [tex]X[/tex]. A group of n separate Bernoullian trials is known as a binomial trial. Binomial distribution requirements:

There are just two outcomes, success and failure, for each trial.The quantity "[tex]n[/tex]" of trials is finite.The trials run separately from one another.

For each trial, the odds of success [tex]p[/tex], or failure [tex]q[/tex], remain constant.

Given,

Probability of good serves = Success

⇒ [tex]p=\frac{20}{30}[/tex]

⇒[tex]p=\frac{2}{3}[/tex]

Failure = [tex]q[/tex]

⇒ [tex]q=1-p[/tex]

⇒ [tex]q=1-\frac{2}{3}[/tex]

⇒ [tex]q=\frac{1}{3}[/tex]

Number of trials [tex]= n[/tex]

[tex]n=6[/tex]

Probability of at least four good serve = [tex]P(4 < X < 6)[/tex]

According to the binomial distribution,

Therefore,

[tex]P(4 \leq X \leq 6)=P(X=4)+P(X=5)+P(X=6)[/tex]

                      [tex]=[/tex] [tex]^6C_4(\frac{2}{3}) ^4(\frac{1}{3})^2+ ^6C_5(\frac{2}{3}) ^5(\frac{1}{3})^1+^6C_6(\frac{2}{3}) ^6(\frac{1}{3})^0[/tex]

                      [tex]=[/tex] [tex]15\times\frac{16}{729} +6\times\frac{32}{729} +1\times\frac{64}{729}[/tex]

                      [tex]=[/tex] [tex]\frac{496}{729}[/tex]

                      [tex]= 0.68[/tex]

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A red team, blue team and green team were playing a game. The 3 people on the red team each lost 15 points. The 6 people on the blue team each gained 14 points. The 5 people on the green team each lost 11 points.

1. What is the total gain/loss for each team? Write your answer as a integer.

Team red:
Team blue:
Team green:

2. The twist in this game is that you need to multiply your final score by -6. Who won the game and what was their final score? The team with the greatest integer wins.

Team————wins with———-points.

Answers

1.
Team red: 3(-15) =-45 (Loss)

Team blue: 6(14) =84 (Gain)

Team Green: 5(-11) =-55 (Loss)

2.

Team red: 3(-15)(-6) =270 points

Team blue: 6(14)(-6) =-504 points

Team Green: 5(-11)(-6) =330 points

Team Green wins with 330 points.

Hope it helps : )

PLS HELP ASAP!!!



Enter the correct answer in the box. Write your answer in the form y=mx+b, using the appropriate inequality symbol in place of the equal sign.

What inequity is show in the graph??

Answers

Answer:

y>4x+1

Step-by-step explanation:

We got two simple steps for this question:

1.Find the equation(y=mx+b):

I want to test these two points on my formula:

(0, 1), (–1, –3)

[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{1 - ( - 3)}{0 - ( - 1)} = \frac{4}{1} = 4[/tex]

so we just calculated our m and now it time for b

[tex]y = 4x + b = = = > 1 = 4(0) + b = = = > b = 1[/tex]

So your criterion is y=4x+1

2.

we are looking for ys greater than xs so your answer is gonna be y>4x+1

What is the perimeter of the contest area on the judo mat?
(please be quick)

Answers

Here you gooo , don’t forget to voteee

The perimeter of the contest area on the judo mat will be 32 meters.

What is the perimeter of the square?

For a square with a side length of a unit, we get:

Perimeter of the square = 4a unit

The side length of square is 8 m.

Then the perimeter of the contest area on the judo mat will be

P = 4 x 8

P = 32 m

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NEED HELP ASAP PLEASEE!!!!!!!!!
QUESTION #1
The decimal number 6.05 can be read as "six and five-hundredths."


True

False


QUESTION #2

The decimal number 11.8 can be read as "eleven and eight tens."


True

False

Answers

The statement 6.05 can be read as "six and five-hundredths" is true and 11.8 can be read as "eleven and eight tens" is false

Place value

6.05

6 = ones

0 = tenths

5 = Hundredth

6.05 = six and five-hundredths

11.8

1 = Tens

1 = Ones

8 = tenths

11.8 = eleven and eight tenths

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multiplicacion 5(3x-2)

Answers

Answer: 15x-2

Step-by-step explanation: ?

Answer:

15x - 10

Step-by-step explanation:

[tex]5(3x-2)=5(3x)+5(-2)=15x-10[/tex]

Hope this helps

Simplify. Show work.
3² x 5 + 4 =

Answers

Answer:

49

Step-by-step explanation:

[tex]3^{2} *5+4[/tex]

= [tex]9*5+4[/tex]        Simplify the exponents.

= [tex]45+4[/tex]           Multiplication.

= 49                Addition.

Answer:

49

Step-by-step explanation:

1. Whenever there is an exponent, we solve that first. 3^2 is 9.

2. In an equation, multiplication, and division is first, and since there is no division in the equation, we do the multiplication first. 9 x 5 is 45.

3. We finish by adding 4 to 45, which is 49.

Solving equations with fractions- how do i solve this

Answers

Answer:

23/75

Step-by-step explanation:

8/15 + x = 21/25

x = 21/25 - 8/15

now we need to bring both fractions to the same denominator (bottom part), so that we can do the subtraction.

what is the least common multiple (LCM) of 25 and 15 ? that will be the common denominator.

I usually use the prime factor factorization of the involved numbers.

15 : 3, 5 (15 = 3×5, there are no smaller prime factors)

25 : 5, 5 (25 = 5×5, there are no smaller prime factors)

the LCM is the combination of the longest chains of each prime factor :

3×5×5 = 75

so, we bring both fractions to 75 denominators.

how many 1/75th are 1/25 ? as 25×3 = 75, we have 3/3 × 1/25 = 3/75 (= 1/25).

so,

21/25 = 21×3/75 = 63/75

how many 1/75th are 1/15 ? as 15×5 = 75, we have 5/5 × 1/15 = 5/75 (= 1/15).

so,

8/15 = 8×5/75 = 40/75

remember, we have to multiply the numerator and the denominator by the same value to keep the original value of the fraction unchanged.

and now our equation looks like

x = 63/75 - 40/75 = 23/75

PLEASE HELP IM SUPER STUCK

Answers

Answer:

[tex]y = \frac{1}{4} x + 9[/tex]

Step-by-step explanation:

All lines take the form

[tex]y = mx + c[/tex]

Where m is the gradient (or slope), and c is the y-intercept. To find the gradient if a line perpendicular to another, we must find the negative reciprocal of the other line. The gradient of the line given is -4, so our negative reciprocal is 1/4.

To find our y-intercept, we must find the point where the line crosses the y-axis (in other words, when the X coordinate is 0). Helpfully, the coordinate given is already at this point, so we can simply take the y coordinate from here, and we know our y-intercept is 9. Putting this altogether, our equation is:

[tex]y = \frac{1}{4} x + 9[/tex]

If a hypothesis is tested at the α=0.05 level of significance, what is the probability of making a type i error?

Answers

The probability of making a type i error is also α = 0.05 or 5% of error.

For the given question,

A Type I error occurs when a significance test results in the rejection of a true null hypothesis. By one common convention, if the probability value is below 0.05, then the null hypothesis is rejected.

The null hypothesis assumes no cause and effect relationship between the tested item and the stimuli applied during the test. The probability of making a type I error is represented by the alpha level (α), which is the p-value below which you reject the null hypothesis.

Thus, If a hypothesis is tested at the α=0.05 level of significance, then the probability of making a type i error is also α=0.05 or 5% of error.

Hence we can conclude that the probability of making a type i error is also α = 0.05 or 5% of error.

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Se vendieron un total de 430 boletos para la obra de teatro escolar. Los boletos eran o de adulto o de estudiante. Se vendieron 70 boletos de estudiante menos que boletos de adulto. ¿Cuántos boletos de adulto fueron vendidos?

Answers

Resolviendo un sistema de ecuaciones, veremos que se vendieron 250 boletos de adulto.

¿Cuántos boletos de adulto fueron vendidos?

Definamos las variables:

x = boletos de adulto vendidos.y = boletos de estudiantes vendidos.

Se vendieron un total de 430 boletos, entonces:

x + y = 430

Y se vendieron 70 boletos de estudiante menos que boletos de adulto:

y = x - 70

Tenemos el sistema de ecuaciones:

x + y = 430

y = x - 70

Para resolverlo, podemos reemplazar la segunda ecuación en la primera:

x + y = 430

x + (x - 70) = 430

2x = 430 + 70 = 500

x = 500/2 = 250

Se vendieron 250 boletos de adulto.

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On a coordinate plane, square P Q R S is shown. It has points (0, 4), (4, 4), (0, 0), and (4, 0).

Prove the diagonals of the square with vertices P(0, 4), Q(4, 4), R(0, 0), and S(4, 0) are perpendicular bisectors of each other.
Step 1: Calculate the slope of the diagonals.

The slope of diagonal PS is

.

The slope of diagonal QR is

.

Step 2: Calculate the midpoint of the diagonals.

The midpoint of PS is

.

The midpoint of QR is

.

The diagonals of the square are perpendicular bisectors because the diagonals are

.

Answers

The slope of diagonal PS is  -1 and the slope of diagonal QR is 1 based on the information about the coordinate plane.

How to illustrate the information?

Step 1: Calculate the slope of the diagonals.

The slope of diagonal PS is  -1

The slope of diagonal QR is 1

Step 2: Calculate the midpoint of the diagonals.  

The midpoint of PS is (2,2)

The midpoint of QR is  (2,2)

The diagonals of the square are perpendicular bisectors because the diagonals are perpendicular and share the same midpoint

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Answer:

1. The slope of diagonal PS is -1.

2. The slope of diagonal QR is 1.

3. The midpoint of PS is (2,2).

4. The midpoint of QR is (2,2).

5. The diagonals of the square are perpendicular bisectors because the diagonals are perpendicular and share the same midpoint.

Step-by-step explanation: I just did it on edge 2023. Hope this helps!

Help please im bad at math!

Answers

Hello, the solution is in this photo.

The correct answer is 300

Answer:

300cm^2

Step-by-step explanation:

Replace pie by 3. 3(10)^2 which equals to 300cm^2. 10 is radius.

Can someone help me please

Answers

Answer:

D. (4,0) and (-4,0)

C. there is one discontinuity at x=3

Step-by-step explanation:

Roots can be found by setting f(x)=0:

f(x)=(x^2-16)/(x^2-2x-3)

0=(x^2-16)/(x^2-2x-3), multiply both sides by x^2-2x-3 to get rid of the denominator

0=x^2-16, use difference of squares to factor it

0=(x+4)(x-4)

x=4,-4

Therefore the roots are (4,0) and (-4,0)

Discontinuities are when f(x) is undefined, and f(x) is undefined when something is divided by 0

Set the denominator equal to 0:

0=x^2-6x+9, use the form a^2 - 2ab + b^2 to factor

0=(x-3)^2

x=3

Therefore, there is a discontinuity at x=3

PLEASE HEPP IM STUCK

Answers

Answer:

m = -4

Step-by-step explanation:

We are given that a line intersects the points (-2, 9) and (3, -11).

We want to write the slope of this line.

The slope (m) can be found using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points.

Even though we have everything we need to calculate the slope, let's label the values of the points to avoid any confusion & mistakes.

[tex]x_1=-2\\y_1=9\\x_2=3\\y_2=-11[/tex]

Now substitute these values into the formula (remember that the formula has subtraction).

m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{-11-9}{3--2}[/tex]

Simplify.

m=[tex]\frac{-11-9}{3+2}[/tex]

Subtract the values on top.

m=[tex]\frac{-20}{3+2}[/tex]

Now add the values on the bottom together.

m=[tex]\frac{-20}{5}[/tex]

Now divide -20 by 5.

m = -4

please help me 5 Points

Answers

a. Area of A = 20 ft²

Area of B = 16 ft²

Area of C = 12 ft²

Area of A = 24 ft²

b. The surface area of the triangular prism = 96 ft².

How to Find the Surface Area of a Right Triangular Prism?

The surface area of the triangular prism given in the diagram = area of A + B + C + D.

a.

Area of A (rectangle) = (length)(width) = (10)(2) = 20 ft²

Area of B (rectangle) = (length)(width) = (8)(2) = 16 ft²

Area of C (rectangle) = (length)(width) = (6)(2) = 12 ft²

Area of A (rectangle) = 1/2(base)(height) = 1/2(6)(8) = 24 ft²

b. The surface area of the triangular prism = 20 + 16 + 12 + 2(24) = 96 ft².

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Can someone help me please. (TROLLS WILL BE REPORTED!!!)

Answers

Answer:

B.) 54π units²

Step-by-step explanation:

First, we need to find the height of the cone. We can do this using the Pythagreom Theorem.

a² + b² = c²                              <----- Pythagreom Theorem

3² + b² = 15²                            <----- Insert side lengths

9 + b² = 225                            <----- Solve 3² and 15²

b² = 216                                   <----- Subtract 9 from both sides

b = 14.7 units                          <---- Take square root of 216

Now, we can use the surface area of a right cone equation to find the final answer.

r = 3 units

h = 14.7 units

SA = πr(r + √(h² + r²))                              <----- Surface Area equation

SA = π(3)(3 + √(14.7² + 3²))                     <----- Insert values

SA = π(3)(3 + √(216 + 9))                         <----- Solve 14.7² and 3²

SA = π(3)(3 + √225)                                <----- Add 216 and 9

SA = π(3)(3 + 15)                                     <----- Take square root of 225

SA = π(3)(18)                                            <----- Add 3 and 15

SA = 54π units²                                     <----- Multiply 3 and 18

find a linear and an exponential equation that matches f(2)=12 and f(4)=48

Answers

The exponential  equation that matches the coordinate is 3(2)^x while the linear equation is y = 6x

Exponential equation

The standard exponential equation is expressed as y= ab^x

where

a is the base

x is the exponent

Given the coordinates (2, 12) and (4, 48)

12 = ab^2

48 = ab^4

Find the ratio

4 = b^2

b = 2

Sice ab^2 = 12

4a = 12

a = 3

The exponential  equation that matches the coordinate is 3(2)^x

For the linear equation

The standard form is y = mx + b

m is the slope = 48-12/4-2
Slope = 12/2

Slope = 6

For the y-intercept

12 = 6(2) + b

b = 0

Hence the required linear equation is. y = 6x

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Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 90 people in the 18-21 age bracket and finds that 76 of them respond and 14 refuse to respond. When 263 people in the 22-29 age bracket are contacted, 240 respond and 23 refuse to respond. Assume that 1 of the 353 people is randomly selected. Find the probability of getting someone in the 22-29 age bracket or someone who agreed to respond.

Answers

The probability of getting someone in the 22-29 age bracket or someone who agreed to respond is 0.96.

What is probability?

The rate of possible outcomes to the total outcomes is said to be the probability.

P(E) = n(E)/n(S)

E - event and S -sample space

we have,

P(A or B) = P(A) + P(B) - P(A and B)

Calculation:

It is given that,

Pollsters are concerned about declining levels of cooperation among persons contacted in surveys.

The data is listed below:

(Age group)                Response - agreed         Response - refused   Total

18-21                            76                                     14                                 90

22-29                          240                                   23                                263

Total                            316                                    37                                353

So, consider the required events

Age group (22-29) as A and someone who agreed to respond as B

Thus, the probabilities are calculated as below:

P(A) = n(A)/n(S) = 263/353

P(B) = n(B)/n(S) = 316/353

P(A and B) = n(A and B)/n(S) = 240/353

Substituting all these in the formula we get,

P(A or B) = P(A) + P(B) - P(A and B)

               = 263/353 + 316/353 - 240/353

               = 339/353

               = 0.96

Therefore, the required probability is 0.96.

Refer similar probability problem here:

https://brainly.com/question/21329462

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What is the image of (-4,-4) after a dilation by a scale factor of 2 centered at the origin?

Answers

Answer:

multiply x and y coordinates by 2 since its a whole number dilation (make bigger basically) ... (-8,6)

Step-by-step explanation:

Assuming a level of significance of 0.01, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines

Answers

Answer: Yes, there is

Step-by-step explanation:

Use the interactive tool to find which of the following expressions have a sum of 6. Check all that apply.
8 + 2
(–4) + (-2)
(–3) + 9
7 + (–1)

Answers

The expressions that have a sum of 6 are Options C and D

How to determine the sum

In this case, we use the following rules

(-) + (-) = -

(+) + (+) = +

(+) + (-) = -

(-) + (+) = -

From the first case

8 + 2 = 10

(-4) + (-2) = -4 + -2 = -6

(-3) + 9 = -3 + 9 = 6

7 + (-1) = 7 - 1 = 6

Thus, the expressions that have a sum of 6 are Options C and D

Learn more about mathematical signs here:

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quadratic formula. pls help

Answers

Answer:

[tex]x=-1,\frac{5}{7}[/tex]

Step-by-step explanation:

1) Split the second term in [tex]7{x}^{2}+2x-5[/tex] into two terms.

1 - Multiply the coefficient of the first term by the constant term.

[tex]7\times -5=-35[/tex]

2 - Ask: Which two numbers add up to 2 and multiply to -35?

7 and -5.

3 - Split 2x as the sum of 7x and -5x.

[tex]7x^2+7x-5x-5[/tex]

2)  Factor out common terms in the first two terms, then in the last two terms.

[tex]7x(x+1)-5(x+1)=0[/tex]

3) Factor out the common term x+1.

[tex](x+1)(7x-5)=0[/tex]

4) Solve for x.

1 - Ask: When will (x+1)(7x-5) equal zero?

When x + 1 0 or 7x-5=0

2 - Solve each of the 2 equations above.

[tex]x=-1,\frac{5}{7}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{What are the quadratic formulas?}[/tex]

[tex]\bullet\rm{\ \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]

[tex]\bullet\rm{\ ax^2 + bx + c = 0}[/tex]

[tex]\huge\textbf{What are we solving for?}[/tex]

[tex]\rm{7x^2 + 2x - 5 = 0}[/tex]

[tex]\huge\textbf{What do we have to do?}[/tex]

[tex]\rm{7x^2 + 2x - 5 = 0}[/tex]

[tex]\huge\textbf{Factor the LEFT side of the given}\\\\\huge\textbf{equation:}[/tex]

[tex]\rm{(7x - 5)(x + 1) = 0}[/tex]

[tex]\rm{(7x - 5) \times (x + 1) = 0}[/tex]

[tex]\huge\textbf{Set 0 to the factors:}[/tex]

[tex]\rm{7x - 5 = 0\ or\ x + 1 = 0}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\rm{x = \dfrac{5}{7}\ or\ x = -1}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{\mathsf x = \dfrac{5}{7}\ or\ \mathsf{x} = -1}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

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