MULTIPLE CHOICE: write the equation of a line that is perpendicular to the given line and that passes through the given point.

3x + 9y = 8; (-9, 1)

A.) y = -3x + 28
B.) y = 1/3x + 28
C.) y = 3x + 28
D.) y = 1/3x - 12

Answer:

A= –5x2 + 4x – 7y + 14 = 0

C= 9x2 – 12xy + 4y2 + 4x – y + 5 = 0

D= 12x + 6y – 5y2 + 14 = 0

Step-by-step explanation:

I finished the assignment from Edge2020

The equation which would produce a parabola from the provided options are equation first and forth,

[tex]-5x^2 + 4x - 7y + 14 = 0[/tex]

[tex]12x + 6y -5y^2 + 14 = 0[/tex]

To of identify the type of conic section from an equation whether it is parabola, or not, let suppose the equation as,

[tex]Ax^2+By^2+Cx+Dy+E=0[/tex]

If In this equation,

Either [tex]A=0[/tex] or [tex]B=0[/tex], but not both. Then it is the equation of parabola.

The first equation is,

[tex]-5x^2 + 4x - 7y + 14 = 0[/tex]

There is no square term of y. Thus, this is the equation of parabola.

The second equation is,

[tex]-x^2 + 6x + y^2 - 8 = 0[/tex]

This is not the equation of parabola, as there is two square terms of variable x and y.

The third equation is,

[tex]9x^2 - 12xy + 4y^2 + 4x - y + 5 = 0[/tex]

Similar to the second equation, here is also two square terms of different variable. Thus, it is not a equation of parabola.              

The fourth equation is,

[tex]12x + 6y -5y^2 + 14 = 0[/tex]

This equation is the equation of parabola, as there is only a single square term.

The fifth equation is,

[tex]20x^2 + 10xy - y^2 + 3x - 6y + 5 = 0[/tex]

This is now the equation of parabola because of two square terms.

Hence, the equation which would produce a parabola from the provided options are equation first and forth,

[tex]-5x^2 + 4x - 7y + 14 = 0[/tex]

[tex]12x + 6y -5y^2 + 14 = 0[/tex]

Learn more about the conic section here;

https://brainly.com/question/8320698

Given,

Total number of votes casted = 42,000

The winner received 3/5 of the votes.

To find,

How many votes did the winner not receive.

Solution,

Votes received by the winner is :

[tex]\dfrac{3}{5}\times 42000\\\\=25200[/tex]

Votes didn't received by the winner = Total votes - votes received

= 42,000 -25200

= 16800

Hence, 16800  votes is not received by the winner.

Answer:

The population mean (μ) = 26.

Step-by-step explanation:

a) Data and Calculations:

The population characteristics = 20 and 36

Total population of interest = 56 (20 + 36)

Number of groups in the population = 2

Therefore, the population mean (μ) = 56/2 = 28

b) Based on the parameters given in this example, the population mean equals the average of the group characteristic (attention span of individuals in minutes) or item of interest.  The population mean is calculated by adding the values of the group characteristic and then dividing the result by the number of values.

Answer:

[tex]1. x=27\\2. x=30[/tex]

Step-by-step explanation:

[tex]1.\ We\ are\ given\ that,\\Point\ W\ belongs\ to\ line\ VX\ or\ Point\ W\ lies\ in\ the\ line\ VX.\\Point\ Y\ belongs\ to\ line\ XZ\ or\ Point\ Y\ lies\ in\ the\ line\ XZ.\\\angle WXY=90\\Now\ let's\ consider\ \triangle XYW.\\We\ observe\ that,\\\angle XWY\ and\ \angle VWY\ form\ a\ linear\ pair\ and\ hence\ are\ supplementary.\\Hence,\\\angle XWY\ + \angle VWY\ =180\\\angle XWY=180- \angle VWY\\Substituting\ \angle VWY=6x\ in\ the\ equation\ (\angle XWY=180- \angle VWY),\\[/tex][tex]\angle XWY=180-6x\\Now\ \ \angle XWY\ and\ \angle WXY\ are\ interior\ angles\ opposite\ to\ \angle WYZ.\\\\Hence,\ from\ the\ 'Exterior\ Angle\ Property',\ we\ know\ that,\ the\\ measure of\ the\ \exterior\ angle\ is\ equal\ to\ the\ sum\ of\ the\ interior\ opposite\\ angles.\\Hence,\\\angle XWY + \angle WXY= \angle WYX\\Substituting\ \angle XWY=(180-6x),\ \angle WXY=90,\ \angle WYX=4x,\\(180-6x)+90=4x\\-6x-4x=-90-180 \\-10x=-270\\x=\frac{-270}{-10}\\x=27[/tex]

[tex]2. We\ are\ given\ that,\\Point\ N\ belongs\ to\ the\ line\ KO\ or\ Point\ N\ lies\ on\ the\ line\ KO.\\\angle LNM=45, \angle ONM=105, \angle NLM=90\\Hence,\\As\ we\ observe\ that,\\\angle LNM,\angle ONM\ and\ \angle KNL\ lie\ on\ the\ line\ KO\ and\ are\ hence,\\ supplementary.\\Hence,\\\angle LNM + \angle ONM\ + \angle KNL =180\\Substituting\ \angle LNM=45, \angle ONM=105,\\45+105+ \angle KNL=180\\150+ \angle KNL=180\\\angle KNL=180-150\\\angle KNL=30[/tex]

[tex]Hence\ by\ considering\ \triangle NML,\\\angle LNM + \angle NLM + \angle NML=180\ [Angle\ Sum\ Property\ Of\ A\ Triangle]\\Hence\ by\ substituting\ \angle LNM=45, \angle NLM=90,\\45+90+\angle NML=180\\135+\angle NML=180\\\angle NML=180-135\\\angle NML=45\\Now,\ as\ we\ observe\ that\ \angle KNM= \angle KNL+ \angle LNM\\Hence\ by\ substituting\ \angle KNL=30, \angle LNM=45,\\\angle KNM=30+45\\\angle\ KNM=75\\[/tex]

[tex]Now,\ consider\ \triangle\ KNM,\\\angle NKM+ \angle KNM + \angle NMK=180 [Angle\ Sum\ Property\ Of\ A\ Triangle]\\Hence\ substituting\ \angle NKM=45, \angle KNM=75 , \angle NMK=2x,\\45+ 75 + 2x=180\\120+2x=180\\2x=180-120\\2x=60\\x=\frac{60}{2}\\x=30[/tex]

Answer:

12x+10

Step-by-step explanation:

9x+3x=12x

and

4+6=10

Answer:

C

Step-by-step explanation:

If the parabola opens upward, it has a minimum.

If it opens downwards, it has a maximum.

Every quadratic function either has a maximum or minimum value is true, because the graph of a quadratic function is a parabola that either opens downwards or upwards.

A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. Since the highest degree term in a quadratic function is of the second degree, therefore it is also called the polynomial of degree 2.

Three properties that are universal to all quadratic functions:

1) The graph of a quadratic function is always a parabola that either opens upward or downward (end behavior).

2) The domain of a quadratic function is all real numbers.

3) The vertex is the lowest point when the parabola opens upwards; while the vertex is the highest point when the parabola opens downwards.

According to the question

Every quadratic function either has a maximum or minimum value.

As per the properties of Quadratic Function

This statement is true as

i> the graph of a quadratic function is a parabola  

ii> The vertex is the lowest point when the parabola opens upwards or the vertex is the highest point when the parabola opens downwards.

Hence, Every quadratic function either has a maximum or minimum value is true, because the graph of a quadratic function is a parabola that either opens downwards or upwards.

To know more about Quadratic Function and its properties here:

https://brainly.com/question/2193294

#SPJ3

Answer:

Okay!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

The answer is 14

Step-by-step explanation:

Folow order of operations and when doing multipactiona or subtraction or division and addition, make sure to go from left to right

Answer:

14

Step-by-step explanation:

I hope this helps!

Answer:

15

Step-by-step explanation:

45÷3

This is the correct awnser

Answer:

The greatest number of 15 inches pieces that can be cut from 5 rolls of length 9 feet is: 35

Step-by-step explanation:

Given

Total length of one roll of ribbon = 9 feet

As the pieces have to be cut into inches, we will convert the measurement in feet to inches

As there are 12 inches in one feet, 9 feet will be equal to:

9*12 = 108 inches

Now first of all, we have to see how many 15 inches pieces can be cut from one role

So,

[tex]=\frac{Length\ of\ roll}{Length\ of\ piece}\\=\frac{108}{15}\\=7.2[/tex]

So the seamstress can cut 7 15-inch long pieces from a roll.

Now given that he has to cut from 5 rolls, the total number of 15-inch pieces will be:

[tex]= 5 * 7 =35[/tex]

Hence,

The greatest number of 15 inches pieces that can be cut from 5 rolls of length 9 feet is: 35

Answer:

Answer:

5.7909 * 10^7

Step-by-step explanation:

Scientific notation uses a number from 1 to under 10 and an integer power of 10.

57,909,000 = 5.7909 * 10,000,000 = 5.7909 * 10^7

Answer:

a. [tex]f(a) = -0.03a +1.53[/tex]

b. See Explanation

c. The slope is reasonable but the p intercept is not

d. [tex]f(20) = 93\%[/tex]     [tex]f(30) = 63\%[/tex]    [tex]f(40) = 33\%[/tex]   [tex]f(50) = 3\%[/tex]

Step-by-step explanation:

Given

[tex]a = age[/tex]

[tex]p = probability\ of\ marriage[/tex]

[tex]a = 45[/tex] when [tex]p = 18\%[/tex]

[tex]a = 25[/tex] when [tex]p = 78\%[/tex]

Solving (a): The linear function

We start by calculating the slope, m

[tex]m = \frac{p_2 - p_1}{a_2 - a_1}[/tex]

[tex]m = \frac{78\% - 18\%}{25- 45}[/tex]

[tex]m = \frac{60\%}{-20}[/tex]

[tex]m = -3\%[/tex]

[tex]m = -0.03[/tex]

The function is then calculated as follows

[tex]p - p_1 = m(a - a_1)[/tex]

This gives:

[tex]p - 18\% = -0.03(a - 45)[/tex]

[tex]p - 0.18 = -0.03(a - 45)[/tex]

[tex]p - 0.18 = -0.03a +1.35[/tex]

Solve for p

[tex]p= -0.03a +1.35+0.18[/tex]

[tex]p= -0.03a +1.53[/tex]

Hence,

[tex]f(a) = -0.03a +1.53[/tex]

Solving (b): Interpret the slope and the p intercept

The slope is calculated as:

[tex]m = -0.03[/tex]

And it implies that, there is a 3% reduction in change of getting older as women get older

The p intercept implies that, there is a 1.53 chance for 0 years old female child to get married.

Solving (c): Is (b) reasonable

The slope is reasonable.

However, the p intercept is not because of the age of the woman

Solving (d): Determine f(20), f(30), f(40), f(50)

We have that:

[tex]f(a) = -0.03a +1.53[/tex]

[tex]f(20) = -0.03 * 20 + 1.53[/tex]

[tex]f(20) = -0.6 + 1.53[/tex]

[tex]f(20) = 0.93[/tex]

[tex]f(20) = 93\%[/tex]

[tex]f(30) = -0.03 * 30 + 1.53[/tex]

[tex]f(30) = -0.9 + 1.53[/tex]

[tex]f(30) = 0.63[/tex]

[tex]f(30) = 63\%[/tex]

[tex]f(40) = -0.03 * 40 + 1.53[/tex]

[tex]f(40) = -1.2 + 1.53[/tex]

[tex]f(40) = 0.33[/tex]

[tex]f(40) = 33\%[/tex]

[tex]f(50) = -0.03 * 50 + 1.53[/tex]

[tex]f(50) = -1.5 + 1.53[/tex]

[tex]f(50) = 0.03[/tex]

[tex]f(50) = 3\%[/tex]

Step-by-step explanation

2.5 cups = 5servings

x cups = 8servings

2.5*8 = 5*x

20 = 5x

divide both sides by the coefficient of x

20/5 = 5x/5

4 = x

i.e x = 4

Answer:

2) no

3) yes

Step-by-step explanation:

i think. sorry if im wrong

Answer:

2 No

3 Yes

Step-by-step explanation:

x = ky

Substitute the values of x and y to check if it's proportional. Then solve for k. If k is the same for all 4 equations, then 2 is proportional.

6 = -2k, k = 6/-2, k = -3

7 = -1k, k = 7 / -1, k = -7

8 = 0k, k = 8 / 0, k = 0

9 = k, k = 9

2 is not proportional.

Substitute the values of x and y to check if it's proportional. Then solve for k. If k is the same for all 4 equations, then 3 is proportional.

-70 = -10k, k = -70 / -10, k = 7

-56 = -8k, k = -56 / -8, k = 7

-14 = -2k, k = -14 / -2, k = 7

-7 = -k,  k = -7 / -1, k = 7

3 is proportional.

Answer: 18

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

Answer:

Because when your finding a point on the x line going left goes towards the negative side, like a number line. So for the y line think of it like the number line but going up is positive and going down is negative.

so if we wanted to go right 6 units and down 3 units it would written as:

(x+6,y-3) Because going right on the x line is like adding 6 units and going down on the y line is like subtracting 3 units for this example

Step-by-step explanation:

Answer:

Following are the solution to this question:

Step-by-step explanation:

please find the graph image in the attached file.

Given value:

[tex]AB= c= 1744 \ miles\\\\BC= a= 2451 \ miles\\\\AB= s= 714 \ miles[/tex]

using the law of cosines:  

[tex]\cos A = \frac{s^2+c^2-a^2}{2bc}\\\\[/tex]

        [tex]=\frac{714^2+1744^2-2451^2}{2 \times 714 \times 1744}\\\\= -0.9862[/tex]

[tex]A=cos^{-1} (-0.9862)\\\\A= 170.47^{\circ}[/tex]

[tex]\cos B = \frac{a^2+c^2-b^2}{2ac}\\\\=\frac{2451^2+1744^2-714^2}{2 \times 2451 \times 1744}\\\\= 0.9988\\\\B=cos^{-1} (0.9988)\\\\B= 2.7641^{\circ}\\\\[/tex]

[tex]\cos C = \frac{a^2+c^2-b^2}{2ac}\\\\=\frac{2451^2+1744^2-714^2}{2 \times 2451 \times 1744}\\\\= 0.9988\\\\C=cos^{-1} (0.9988)\\\\C= 2.7641^{\circ}[/tex]

Answer:

We conclude that the percent of decrease = 20%

Step-by-step explanation:

Given

Using the formula

Percent of decrease = ( amount of decrease / orignal amount × 100 ) %

                                   = ( 786 / 3930 × 100 ) %

                                    = ( 0.2 × 100 ) %

                                    = 20%

Therefore, we conclude that the percent of decrease = 20%

Answer:

it goes by  +4 and -4

Step-by-step explanation:

Answer:

The unemployment rate would be 5.5%.

Step-by-step explanation:

It is given that,

The Canadian labor force as of 2019 was 32.7 million.

There were 30.9 million employed

We need to find the unemployment rate.

Unemployed = labor force - employed

= 32.7 - 30.9

= 1.8 million

[tex]\text{unemployment rate}=\dfrac{\text{unemployed}}{\text{labor force}}\times 100\\\\=\dfrac{1.8}{32.7}\times 100\\\\=5.5\%[/tex]

So, the unemployment rate would be 5.5%.

Answer:

17 4/7

Step-by-step explanation:

we'll need to divide 123 by 7

123/7= 17 R 4

But she can't have an extra 4 miles out so,

17 4/7

Answer:

B

Step-by-step explanation:

B is the best example where substitution is the best method since you already have one where y = something and you can plug -2/7x + 11 into the bottom equation for y and solve it that way. A and C make you get x or y by itself first first substitution would work and D already gives you the answers. B is the best since its already set in that format.

Answer:

The area of the circle is [tex]\mathbf{6.25\pi}[/tex]

Step-by-step explanation:

Area of a Circle

A circle of radius r has an area calculated by the following formula:

[tex]A=\pi r^2[/tex]

The diameter of a circle is twice the radius, thus the radius is half the value of the diameter.

A given circle has a diameter of 5 inches.

The radius of this circle is r = 5/2 = 2.5 inches.

Thus, the area is calculated below:

[tex]A=\pi 2.5^2 = 6.25\pi[/tex]

The area of the circle is [tex]\mathbf{6.25\pi}[/tex]

Answer:

Solving the equation [tex]-\frac{7}{10}=\frac{3a}{4}-\frac{13}{20}[/tex] we get: [tex]\mathbf{a=-\frac{1}{15} }[/tex]

Step-by-step explanation:

We need to solve the equation:

[tex]-\frac{7}{10}=\frac{3a}{4}-\frac{13}{20}[/tex]

And find the value of a

Solving the equation: [tex]-\frac{7}{10}=\frac{3a}{4}-\frac{13}{20}[/tex]

First we will be Switching sides

[tex]\frac{3a}{4}-\frac{13}{20}=-\frac{7}{10}[/tex]

Now, for finding value of a we will be adding 13/20 on both sides

[tex]\frac{3a}{4}-\frac{13}{20}+\frac{13}{20}=-\frac{7}{10}+\frac{13}{20}[/tex]

[tex]\frac{3a}{4}=-\frac{7}{10}+\frac{13}{20}[/tex]

Now, on right hand side, Taking LCM of denominators i.e 10 and 20, we get 20 and simplifying:

[tex]\frac{3a}{4}=\frac{-7*2+13}{20}\\\frac{3a}{4}=\frac{-14+13}{20}\\\frac{3a}{4}=\frac{-1}{20}[/tex]

Now, multiply both sides by 4/3

[tex]\frac{3a}{4}\times \frac{4}{3} =\frac{-1}{20}\times \frac{4}{3}\\a=\frac{-1}{5}\times \frac{1}{3}\\a= \frac{-1}{15}[/tex]

So, solving the equation [tex]-\frac{7}{10}=\frac{3a}{4}-\frac{13}{20}[/tex] we get: [tex]\mathbf{a=-\frac{1}{15} }[/tex]

Answer:

x = 30

Step-by-step explanation:

Look at triangle LMN.

m<NLM + m<M + m<MNL = 180

90 + m<M + 45 = 180

m<M = 45

Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

<ONM is an exterior angle of triangle KMN.

The remote interior angles are <K and <M.

m<K + m<M = m<ONM

2x + 45 = 105

2x = 60

x = 30

Answer: x = 30

Answer:

-5-4

Step-by-step explanation:

Let me know if I am wrong, if I am I apologize.

Have a good one.