What is the equation of a line whose slope is 2 and passes through the point (-6,9)

Answer:

The first choice

Step-by-step explanation:

Area of a triangle is 1/2x base x height

the base is 10 and height is 24

26 is the hypotenuse but it is not used in calculating the area

Hope this helps :)

Answer:

1/2 times 10 times 24

Step-by-step explanation:

The hypotenuse is across the right angle so it can’t be included in the area of the triangle which is 26 and 10^2 + 24^2=26^2 by Pathagorean Theron

Answer:

it should be -4=x.

Answer: -4

Step-by-step explanation:

Answer:

The value of α is 0.05.

Step-by-step explanation:

A poll of 1000 adults was conducted to determine their favorite pie.

The poll result states that among the 1000 ​respondents, 14 ​% chose chocolate​ pie, and the margin of error was given as plus or minus 3 percentage points.

[tex]\hat p=\text{Sample Proportion of adults who chose chocolate pie} = 0.14\\\hat q=\text{Sample Proportion of adults who did not chose chocolate pie}\\=1-\hat p\\=0.86\\n=\text{Sample size}=1000\\E=\text{Margin of Error}=0.03\\p=\text{Population Proportion of adults who chose chocolate pie}[/tex]

The confidence level is 95%.

Determine the value of significance level, α as follows:

[tex]\text{Confidence Level}=(1-\alpha)\%\\\\95\%=(1-\alpha)\%\\\\0.95=(1-\alpha)\\\\\alpha=1-0.95\\\\\alpha=0.05[/tex]

Thus, the value of α is 0.05.

Answer:

as probability of this is higher than 0.05 level this is not significantly high number .

Step-by-step explanation:

we have here a binomial distribution with the following data:

p = 0.76 and n = 8

therefore probability that a least 7 of the 8 adults require eyesight correction is P (X> = 7)

 P (X> = 7) = P (X = 7) + P (X = 8) = nCr * (p) ^ (n) * (1-p) ^ (n-r)

= (8C7) * (0.76) ^ 8 * (0.24) ^ (8-7) + (8C8) * (0.76) ^ 8 * (0.24) ^ (8-8)

nCr = n! / (r! * (n-r)!

replacing:

(8C7) = 8! / (7! * (8-7)!) = 8

(8C8) = 8! / (8! * (8-8)!) = 1

P (X> = 7) = 8 * 0.0267 + 1 * 0.11130 = 0.325

as probability of this is higher than 0.05 level this is not significantly high number .

Answer/Step-by-step explanation:

Let's highlight the dimensions of the bedroom and living room using the information given in the question:

==>Squared Bedroom dimensions:

Side length = w = x ft

Area = x*x = x²

==>Rectangular living room dimensions:

width = side length of the squared bedroom = x

length = (x + 9) ft

Area = L*W = x*(x+9) = x² + 9x

Now let's match each given expression with what they represent:

==>"the monomial, x, a factor of the expression x² + 9x" represents "the width of the carpet in the living room"

As we have shown in the dimensions of the squared bedroom above.

==>"the binomial, (x + 9), a factor of the expression x² + 9x" represents "the length of the carpet in the living room" as shown above in the dimensions for living room

==>"the second-degree term of the expression x² + 9x" represents "the area of the carpet in the bedroom"

i.e. the 2nd-degree term in the expression is x², which represents the area of the carpet of the given bedroom.

==>"the first-degree term of the expression x2 + 9x" represents "the increase in the area of carpet needed for the living room".

i.e. 1st-degree term in the expression is 9x. And it represents the increase in the area of the carpet for the living room. Area of bedroom is x². Area of carpet needed for living room increased by 9x. Thus, area of carpet needed for living room = x² + 9x

Answer:

Option D

Step-by-step explanation:

We are given the following equations -

[tex]\begin{bmatrix}-5x-12y-43z=-136\\ -4x-14y-52z=-146\\ 21x+72y+267z=756\end{bmatrix}[/tex]

It would be best to solve this equation in matrix form. Write down the coefficients of each terms, and reduce to " row echelon form " -

[tex]\begin{bmatrix}-5&-12&-43&-136\\ -4&-14&-52&-146\\ 21&72&267&756\end{bmatrix}[/tex]  First, I swapped the first and third rows.

[tex]\begin{bmatrix}21&72&267&756\\ -4&-14&-52&-146\\ -5&-12&-43&-136\end{bmatrix}[/tex]  Leading coefficient of row 2 canceled.  

[tex]\begin{bmatrix}21&72&267&756\\ 0&-\frac{2}{7}&-\frac{8}{7}&-2\\ -5&-12&-43&-136\end{bmatrix}[/tex]  The start value of row 3 was canceled.

[tex]\begin{bmatrix}21&72&267&756\\ 0&-\frac{2}{7}&-\frac{8}{7}&-2\\ 0&\frac{36}{7}&\frac{144}{7}&44\end{bmatrix}[/tex]       Matrix rows 2 and 3 were swapped.

[tex]\begin{bmatrix}21&72&267&756\\ 0&\frac{36}{7}&\frac{144}{7}&44\\ 0&-\frac{2}{7}&-\frac{8}{7}&-2\end{bmatrix}[/tex]      Leading coefficient in row 3 was canceled.

[tex]\begin{bmatrix}21&72&267&756\\ 0&\frac{36}{7}&\frac{144}{7}&44\\ 0&0&0&\frac{4}{9}\end{bmatrix}[/tex]

And at this point, I came to the conclusion that this system of equations had no solutions, considering it reduced to this -

[tex]\begin{bmatrix}1&0&-1&0\\ 0&1&4&0\\ 0&0&0&1\end{bmatrix}[/tex]

The positioning of the zeros indicated that there was no solution!

Hope that helps!

Answer:

The population under consideration in the data set are all the adults in the United States.

Step-by-step explanation:

Sampling

This is a common statistics practice, when we want to study something from a population, we find a sample of this population.

For example:

I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents.

The population of interest are all the residents of New York State.

In this question:

Sample of 765 adults in the United states.

So the population under consideration in the data set are all the adults in the United States.

Answer: -150

Step-by-step explanation: The result of a multiplication problem is called the product so we know that we will be multiplying here.

When multiplying integers, if the signs

are different, the product is negative.

So a positive times a negative always equals a negative.

Therefore, (+25) · (-6) is -150.

Answer: -150

Step-by-step explanation: took the unit test on edge

ith 0 identical marbles permitted to be included in any of the jars, An expression can be developed to determine the total of marbles in jar arrangements, which is:

E = [(n+j -1)!]*{1/[(j-1)!]*[(n)!]}, where n = number of identical balls and j =number of distinct jars, the contents of all of which must sum to n for each marbles in j jars arrangement. With n = 7 and j = 4. E = 10!/(3!)(7!) = 120= number of ways 7 identical marbles can be distributed to 4 distinct jars such that up to 3 boxes may be empty and the maximum to any box is 7 balls.i think is the answer

Answer:

3x - 300

Step-by-step explanation:

Expand the brackets or use distribute law.

Answer:

solution,

[tex]3(x - 100) \\ = 3 \times x - 3 \times 100 \\ = 3x - 300[/tex]

hope this helps..

Answer:

4a^2+4ab+b^2

Step-by-step explanation:

To find the square we multiply the expression with itself

(2a+b)×(2a+b) = 4a^2+4ab+b^2

Answer:

Step-by-step explanation:

Total amount of yogurts made by Stacy = 1.5 Litres

Volume of each cups to be filled with yogurts = 125mL = 125*10⁻³Litres

To get the number of cups Stacy can fill for her to exhaust 1.5Litres can be gotten using the relationship;

Number of cups = Total volume of yogurts made/Volume of each cup

Number of cups = 1.5/125*10⁻³

Number of cups = 1.5/0.125

Number of cups = 12 cups

Number of cups Stacy can fill is 12 cups

Answer:

Step-by-step explanation:

We know that'

GCF × LCM = Product of given number

1. Two numbers have a GCF of 2

= 2 × LCM = Product of given number

LCM = Product of given number / 2

LCM is half of given product.

2. Two numbers have an LCM of 2

= GCF × 2 = Product of given number

GCF = Product of given number / 2

GCF is half of given product.

3. Two numbers have a GCF of 3

= 3 × LCM = Product of given number

LCM = Product of given number / 3

LCM is one-third of given product.

4. Two numbers have an LCM of 10

= GCF × 10 = Product of given number

GCF = Product of given number / 10

GCF is one-tenth of given product.

Answer:

tan =-1

Step-by-step explanation:

tan(θ)=sen(θ)/cos(θ)

so

[tex]tan(angle)=\frac{\frac{-\sqrt{2} }{2} }{\frac{\sqrt{2} }{2} } }\\\\tan(angle)=-1[/tex]

Answer:

Step-by-step explanation:

[tex]cos \: \: theta \: = \frac{ \sqrt{2} }{2} = \frac{1}{ \sqrt{2} } = cos \: \frac{\pi}{4 } [/tex]

[tex]cos \: (2\pi \: - \frac{\pi}{4} ) \: \: ( \frac{3\pi}{2} < theta < 2\pi)[/tex]

[tex] = cos \: \frac{7\pi}{4} [/tex]

Theta = 7π / 4

[tex]sin \: theta = sin \: \frac{7\pi}{4} [/tex]

[tex] = sin \: (2\pi \: - \frac{\pi}{4} )[/tex]

[tex] - sin \: \frac{\pi}{4} [/tex]

[tex] = \frac{ - 1}{ \sqrt{2} } [/tex]

[tex] = - \frac{ \sqrt{2} }{2} [/tex]

Finding tan theta:

[tex]tan \: theta = tan \: \frac{7\pi}{4} [/tex]

[tex] =tan \: (2\pi - \frac{\pi}{4} )[/tex]

[tex] = - tan \: \frac{\pi}{4} [/tex]

[tex] = - 1[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

Answer is given below with explanations.

Step-by-step explanation:

Answer is option 1) 85 : 51

[tex]given \: that \: \\ triangle \: SPT \: is \: similar \: to \: triangle \: QPR \\ corresponding \: sides \: of \: similar \: \\ triangles \: are \: in \: proportion \\ then \: \\ \frac{SP}{ QP} = \frac{PT }{ PR} \\ \frac{3x}{3x + 24} = \frac{51}{85} \\ taking \: reciprocal \: on \: both \: sides \\ \frac{3x + 24}{3x} = \frac{85}{51} [/tex]

Option 1 is correct.

HAVE A NICE DAY!

THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.

Answer:

33

Step-by-step explanation:

The probability you will pick a green or a pink marble is:

3/4

Multiply 3/4 with 44.

3/4 × 44

= 33

Answer:

1. 1/x = 8

Answer = 8x-1

2. 8x+1=3

Answer ; x=1/4

3. 7= 14/X

Answer ; x = 2

4.1/2x^2 = 2

Answer ;x=2

Step-by-step explanation:

[tex]\frac{1}{x} =8 \\8x = 1\\\\\\8x+1=3\\Collect -like- terms \\8x =3-1\\8x = 2\\Divide -both -sides- by ;8\\\frac{8x}{8} =\frac{2}{8} \\x = 1/4\\\\\\7= \frac{14}{x} \\Cross -multiply\\7x =14\\Divide-both-sides-by-7\\x = 2\\\\\\\frac{1}{2} x^{2} =2\\\frac{x^{2} }{2} =2\\Cross-multiply\\x^{2} =4\\Squre-root -both-sides\\\sqrt{x^2}=\sqrt{4} \\x = 2\\[/tex]

Answer:

1. 1/x=8 ⇒ 8x= 1

2. 8x+1= 3⇒ x=1/4

3. 7= 14/x ⇒ x =2

4. 1/2x^2= 2 ⇒ x=2 this is a repeat of one above

None is matching x=1/2

Answer:

The equation for a parabola with vertex at the origin and a directrix at x = 1/48 is [tex]x= \frac{1}{12}\cdot y^{2}[/tex].

Step-by-step explanation:

As directrix is a vertical line, the parabola must "horizontal" and increasing in the -x direction. Then, the standard equation for such geometric construction centered at (h, k) is:

[tex]x - h = 4\cdot p \cdot (y-k)^{2}[/tex]

Where:

[tex]h[/tex], [tex]k[/tex] - Horizontal and vertical components of the location of vertex with respect to origin, dimensionless.

[tex]p[/tex] - Least distance of directrix with respect to vertex, dimensionless.

Since vertex is located at the origin and horizontal coordinate of the directrix, least distance of directrix is positive. That is:

[tex]p = x_{D} - x_{V}[/tex]

[tex]p = \frac{1}{48}-0[/tex]

[tex]p = \frac{1}{48}[/tex]

Now, the equation for a parabola with vertex at the origin and a directrix at x = 1/48 is [tex]x= \frac{1}{12}\cdot y^{2}[/tex].

This is the value 40 million

================================================

Explanation:

You could use a calculator, or you could do it mentally. The second approach will have us note that 4*1 = 4, and then we tack on 7 zeros since we have two zeros in 400 and five zeros in 100,000 giving a total of 2+5 = 7

So that means 400*100,000 = 40,000,000 = 40 million

-------

You could also use scientific notation

400 = 4 x 10^2

100,000 = 1 x 10^5

400*100,000 = (4x10^2)*(1x10^5)

400*100,000 = (4*1) x (10^2*10^5)

400*100,000 = 4 x 10^(2+5)

400*100,000 = 4 x 10^7

400*100,000 = 40,000,000

The exponent of 7 means we move the decimal point 7 spots to the right to go from 4.0 to 40,000,000

Answer:

240cm³

Step-by-step explanation:

First, let's assume the entire shape is full rectangular prism without that has the middle being cut out.

What this means is that, to get the volume of the solid made out of clay, we would calculate the solid as a full rectangular prism, then find the volume of the assumed middle cut-out portion. Then find the difference between both.

Let's solve:

Find the volume of the rectangular prism assuming the solid is full:

Volume of prism = width (w) × height (h) × length (l)

w = 4cm

h = 7cm

l = 3+6+3 = 12cm

Volume of full solid = 4*7*12 = 336cm³

Next, find the volume of the assumed cut-out portion using same formula for volume of rectangular prism:

w = 4cm

h = 7-3 = 4cm

l = 6cm

Volume of assumed cut-out portion = 4*4*6 = 96cm³

Volume of solid made from clay = 336cm³ - 96cm³ = 240cm³

Answer:

15%

Step-by-step explanation:

percentage error equals to

(error / actual length) x 100

error = 1.5

actual length = 10

answer equals 15%

Answer:

Conservation of natural resources is the intelligent and wise use of natural resources in order to last longer.

The conservation of natural resources refers to the sustainable management of natural resources such as water, air, land, and forests. It means that these resources are used in a way that meets the needs of present and future generations. The conservation of natural resources requires the use of technology, policies, and practices that are environmentally sound and economically feasible.

Hope this helps :)

Answer:

Step-by-step explanation:

The spread of the height of each person in the group depends on the standard deviation. A low standard deviation means that the heights are closer to the mean than that of a high standard deviation. If an individual is picked, the probability of picking one who is more than 68 inches tall is small as this depends on the number of individuals in this category. The probability of picking a sample of four people who average more than 68 inches tall would be higher since average would be taken. Therefore, it is more likely to pick a sample of four people who average more than 68 inches tall

Answer: n=2

Step-by-step explanation: 4n-2n=4

4(2)-2(2)=

8-4=4

Answer:

n=2

Step-by-step explanation:

Step by Step Solution:

More Icon

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    4*n-2*n-(4)=0  

Step by step solution :

STEP

1

:

Pulling out like terms

1.1     Pull out like factors :

  2n - 4  =   2 • (n - 2)  

Equation at the end of step

1

:

STEP

2

:

Equations which are never true

2.1      Solve :    2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

2.2      Solve  :    n-2 = 0  

Add  2  to both sides of the equation :  

                     n = 2

Answer:

C) (-2, 4), (6,8) is the correct answer.

Step-by-step explanation:

Given that line segment AB:

A (-3, 6) and B (9, 12) is dilated with a scale  factor 2/3 about the origin.

First of all, let us calculate the distance AB using the distance formula:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Here,

[tex]x_2=9\\x_1=-3\\y_2=12\\y_1=6[/tex]

Putting all the values and finding AB:

[tex]AB = \sqrt{(9-(-3))^2+(12-6)^2}\\\Rightarrow AB = \sqrt{(12)^2+(6)^2}\\\Rightarrow AB = \sqrt{144+36}\\\Rightarrow AB = \sqrt{180}\\\Rightarrow AB = 6\sqrt{5}\ units[/tex]

It is given that AB is dilated with a scale factor of [tex]\frac{2}{3}[/tex].

[tex]x_2'=\dfrac{2}{3}\times x_2=\dfrac{2}{3}\times9=6\\x_1'=\dfrac{2}{3}\times x_1=\dfrac{2}{3}\times-3=-2\\y_2'=\dfrac{2}{3}\times y_2=\dfrac{2}{3}\times 12=8\\y_1'=\dfrac{2}{3}\times y_1=\dfrac{2}{3}\times 6=4[/tex]

So, the new coordinates are A'(-2,4) and B'(6,8).

Verifying this by calculating the distance A'B':

[tex]A'B' = \sqrt{(6-(-2))^2+(8-4)^2}\\\Rightarrow A'B' = \sqrt{(8)^2+(4)^2}\\\Rightarrow A'B' = \sqrt{64+16}\\\Rightarrow A'B' = \sqrt{80}\\\Rightarrow A'B' = 4\sqrt{5}\ units = \dfrac{2}{3}\times AB[/tex]

So, option C) (-2, 4), (6,8) is the correct answer.

Answer:

A) 0.989

B) 0.875

Step-by-step explanation:

Let the X denote height measurements of ten year old children.

Thus, X follows the Normal distribution with mean = 56.2 inches and standard deviation = 3.3 inches.

A) we have to find the probability that a randomly chosen child has a height of less than 63.75 inches.

That is;

P(X < 63.75)

using z score formula, we have;

Z = (X - μ)/σ

Where, μ is mean and σ is standard deviation.

Thus;

Z = (63.75 - 56.2)/3.3

Z = 2.288

From z distribution table, we have the value as approximately 0.989

B) Similarly, using z score formula, we have;

Z = (X - μ)/σ

Where, μ is mean and σ is standard deviation.

Thus;

we have to find the probability that a randomly chosen child has a height of more than 60 inches.

Z = (60 - 56.2)/3.3

Z = 1.1515

From z-tables, the value is approximately 0.875

Answer:

Let the number of children taken to the movies  = x

Let the number of adults taken to the movies  = y

Lets talk about Matinee tickets first:

so 4$ per child/adult

4x + 4y [tex]\leq[/tex] 80    (since the budget is 80$, we can spend 80$ , hence the less- than or equal-to)

4(x+y)[tex]\leq[/tex] 80

x + y [tex]\leq[/tex] 40

So, for the matinee show, the sum of number of children and adults should be less than or equal to 40

Lets talk about the Evening show:

so 6$/child and 8$/adult

6x + 8y [tex]\leq[/tex] 100

2(3x + 4y) [tex]\leq[/tex] 100

3x + 4y [tex]\leq[/tex] 50

So, for the Evening show, the sum of 3 times the number of children and 4 times the number of adults should not exceed 50

Answer:

x = 7

y = 8

Step-by-step explanation:

4y-4 = 28

4y = 32

y = 8

10x+65 = 135

10x = 70

x = 7

Answer:

Step-by-step explanation:

(4y-4)=28

4y=32

y=8

(10x+65)=135

10x=70

x=7

Answer:

B and C

Step-by-step explanation:

In order to know your x and y intercept, first rearrange your equation in the form ax+by=c

NB c should always be one so if you rearrange and c is not one, divide the whole equation by the no. represented by c, then to know your x and y intercepts look at the reciprocal of the coefficients of x and y

For example

B. -4x+2y= -6

divide the whole equation by -6 to get

2/3x-1/3y=1

hence the x intercept will be the reciprocal of the coefficient of x which is 3/2

y intercept will be the reciprocal of the coefficient of y which is -3

so if you look at the line, the equation applies

The same will apply to C

The solution is : B and C,

B. -4x+2y= -6 and, C. y = 3x - 2, could be the equation of the graph shown below.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

In order to know your x and y intercept, first rearrange your equation in the form ax+by=c

NB c should always be one so if you rearrange and c is not one, divide the whole equation by the no. represented by c, then to know your x and y intercepts look at the reciprocal of the coefficients of x and y

For example

B. -4x+2y= -6

divide the whole equation by -6 to get

2/3x-1/3y=1

hence the x intercept will be the reciprocal of the coefficient of x which is 3/2

y intercept will be the reciprocal of the coefficient of y which is -3

so if we look at the line, the equation applies

The same will apply to C. y = 3x - 2

This has positive slope and negative y-intercept, which are the characteristics of our graph.

Therefore this choice is correct.

Hence, B. -4x+2y= -6 and, C. y = 3x - 2, could be the equation of the graph shown below.

To learn more on Equation 0f Straight-Line click:

brainly.com/question/11116168

#SPJ7

Answer:

12

Step-by-step explanation:

The way to find the slope side of a traingle is

A^2+B^2=C^2  Next you substitute

5^2+B^2=13^2  Next simplify

25+B^2=169  Next use the subtraction property of equality

B^2=144  Next find the square root

B=12

Hope this helps :)

Answer:

height =12

Step-by-step explanation:

use Pythagorean theorem for right angle triangle:

a²+b²=c²

a²=c²-b²

a²=13²-5²

a²=144

a=√144-=12