A line passes through the given points. Write an equation for the line in point-slope form. Then rewrite the equation in slope-intercept form. (4, –2), (9, –8)

Answer:

Step-by-step explanation:

a:b = 3:2    ⇒   a = 3x  and  b = 2x

a - b = 5

3x - 2x = 5

x = 5

a = 3•5 = 15

b = 2•5 = 10

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Calculate the slope of the line m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (1, - 2)

m = [tex]\frac{-2-2}{1+1}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]

Answer:

176m²

Step-by-step explanation:

When we are asked to find the outer surface area of a geometric shape, it means to find the Lateral or Curved Surface Area of the shape. We are given two shapes above.

Step 1

Find the Outer surface area of the cone

Outer / Lateral surface area of a cone =

πrl

Where l = √r² + h²

r = 4 m

h = 3m

Outer surface area = 22/7 ×√4² + 3²

= 22/7 × √16 + 9

= 22/7 × √25

= 22/7 × 5

= 62.83185m²

Step 2

Find the outer surface area of a cylinder

= 2πrh

π = 22/7

r = 4m

h = 4.5

π = 22/7

Outer surface area of a cylinder = 2 × 22/7 × 4 × 4.5

= 113.09734m²

Step 3

The Outer Surface Area of the Tent = Outer Surface Area of the cone + Outer Surface Area of the cylinder

= 62.83185m² + 113.09734m²

= 175.92919m²

Approximately ≈ 176m²

Therefore, the outer surface area of the tent = 176m²

Answer:

b)b+2

Step-by-step explanation:

3+2=5

5+2=7

so for the next iteration 2is added.

Answer:

358

Step-by-step explanation:

In 1995, the boys were 50 %

Take the number of people at the convention in 1995 ( 716)

and multiply by 50%

716 * 50%

716 * .50

358

Answer:

b. 358

Step-by-step explanation:

First, find what percentage of attendees were boys in 1995:

By reading the graph, we can see 50% were boys.

In the table, we can see that there were 716 attendees in 1995.

To find how many boys attended in 1995, find 50% of 716.

716(0.5) = 358

Answer:

Sine, Cosine and Tangent are  main functions used in Trigonometry .

They  are based on a Right-Angled Triangle.

It helps to give a name to each side of a right triangle:

"Opposite" ;  side opposite to the angle θ

"Adjacent"; side adjacent (next to) to the angle θ,

"Hypotenuse" ; the longest side

Step-by-step explanation:

Sine, Cosine and Tangent (are often shortened as sin, cos and tan)

They are used in calculation by;

[tex]Sin \alpha = \frac{Opposite}{Hypotenuse}\\ \\Cos \alpha = \frac{Adjacent}{Hypotenuse}\\ \\Tan \alpha = \frac{Opposite}{Adjacent}[/tex]

To remember how to apply them , we use

SOHCAHTOA

soh

cah

toa

Answer:

2n+7

Step-by-step explanation:

First lets find the common difference which is 2, now we can use this formula to find the nth term.

an = a1 + (n - 1 ) d

an= 9+(n-1)2

=9+2n-2

=2n+7

To check let's insert n=5, 2(5)=10+7=17.

15+2=17!

Answer:

La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos es de $13.90

Step-by-step explanation:

La información dada son;

El valor de la máscara = $ 1.25

El valor del paquete de jabones = $ 2.00

El valor del gel de alcohol = $ 3.00

La cantidad que le quedaba después de pagar = $ 7.65

Por lo tanto, tenemos;

La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos = La cantidad que le quedaba después de pagar + El valor del gel de alcohol + El valor del paquete de jabones + El valor de la mascarilla

Por lo tanto;

La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos = $ 7.65 + $ 3.00 + $ 2.00 + $ 1.25 = $ 13.90.

Answer:

Step-by-step explanation:

The graph of function f(x)+2 is moved 2 units up compared to the graph of f(x).

It means the x-coordinate is the same and the y-coordinate of f(x)+2 is increased by adding 2 to y-coordinate of f(x).

-8 + 2 = -6

Answer:

[tex]D=-5y^2[/tex]

Step-by-step explanation:

We have the equation:

[tex]\displaystyle -15y^4=D(3y^2)[/tex]

And we want to find D such that the equation is true.

So, we can divide both sides by 3y². This will yield:

[tex]\displaystyle D=\frac{-15y^4}{3y^2}[/tex]

We can split this into:

[tex]\displaystyle D=\frac{-15}{3}\cdot\frac{y^4}{y^2}[/tex]

Simplify. Hence:

[tex]D=-5y^2[/tex]

Answer:

  Bobby has $300 in the yearbook fund and earns $13.50 for each yearbook sold.

Step-by-step explanation:

The value of the expression when x is zero is 300. For each increment of 1 in x, the value of the expression increases by 13.50. This best matches the scenario ...

  Bobby has $300 in the yearbook fund and earns $13.50 for each yearbook sold.

Answer:

Answer would be D

Step-by-step explanation:

The measure of the length UX will be 76.53 units. Then the correct option is D.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The measure of the length UX will be given by sine of angle 6°.

  sin 6° = UR / UX

0.1045 = 8 / UX

     UX = 76.53 units

Then the correct option is D.

More about the trigonometry link is given below.

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Answer:

Step-by-step explanation:

I'll use x  instead of theta.

So we have:

sin x / ( 1 + cos x) + (1 +cos x) / sinx

The LCM is sin x(1 + cos x) so we have

sin^2 x + (1 + cos x)^2 /  sin x(1 + cos x)

= sin^2 x + cos^2x + 2 cos x + 1 /  sin x(1 + cos x)

Now sin^2x + cos^2x = 1 so:

= 2 + 2 cos x /  sin x(1 + cos x)

= 2(1+ cos x) /  sin x(1 + cos x)

The 1 + cos x is common so we have:

2 / sin x

= 2 cosec x.

Answer: Capable

Step-by-step explanation: The capability of a process could be exaplained as a measure of the ability of a process to produce part within specified limits by making use of statistical measurement. In determining if a certain process is capable or not, the value of process capability (Cp) is measured, in most cases, a process is deemed capable by having a Cp value of 1.33 or higher.

Cp formula :

(Upper specification limit(USL) - Lower specification limit(LSL) ) / 6* standard deviations

Diameter = 10 mm ± 0.5 mm

Standard deviation = 0.1mm

USL = 10 + 0.5 = 10.5

LSL = 10 - 0.5 =. 9.5

Cp = (10.5 - 9.5) / 6*0.1

Cp = 1/0.6

Cp = 1.6666

Cp = 1.67

Hence, the process is capable

Answer:

y<−13

y−9>4+2y

Simplify both sides of the inequality

y−9>2y+4

Subtract 2y from both sides

y−9−2y>2y+4−2y

−y−9>4

Add 9 to both sides.

−y−9+9>4+9

−y>13

The divide both sides by -1

Answer:

[tex]\boxed{y < -13}[/tex]

Step-by-step explanation:

Hey there!

To solve for y we‘ll combine like terms and use the communicative property.

y - 9 > 4 + 2y

+9 to both sides

y > 13 + 2y

-2y to both sides

-y > 13

Divide -1 by both sides

y < -13

Hope this helps :)

let the consecutive multiples be 7(n-1) , 7n and 7(n+1)

so 7(n-1)+7n+7(n+1)=777

or 3n=111,

n=37

252,259,266

[tex]7n+7n+7+7n+14=777\\21n=756\\n=36\\\\7n=252\\7n+7=259\\7n+14=266[/tex]

252,259,266

Answer:

7x + 2

Step-by-step explanation:

Answer:

All real numbers

Step-by-step explanation:

Adding f(x) and g(x) together gets you, (4x-5) + (3x-7) = 7x - 12

If you graph this function you get a slanted line, which extends forever so the domain will be all real numbers.

Answer:

  22. The surface area is 1/9 of its original value

  24. The surface area is 120 m^2 less than its original value.

Step-by-step explanation:

22. For similar figures, the surface area is proportional to the square of the linear dimension scale factor. Multiplying all linear dimensions by 1/3 will result in reducing the surface area to (1/3)^2 = 1/9 of its original value.

__

24. As above, the scaled base surface area will be (1/4)^2 = 1/16 of its original value. Since one dimension of the lateral area is multiplied by 4 and the other dimension is multiplied by 1/4, the net effect on that area is multiplication by (1/4)(4) = 1. That is, the lateral area will remain unchanged.

The overall surface area will be reduced by 15/16 of the area of the bases. The area of the bases is (2)(1/2)(8 m)(16 m) = 128 m^2. The changed figure will have a surface area that is 120 m^2 smaller.

Answer:

The cube only belongs to the x and not 2x.

The statement will only be true if there is a bracket around the 2x.

log₃(2x)³= 3log₃2x

logarithm power rule:

logₐ(x)^y = y ∙ logₐ(x)

Answer:

see explanation

Step-by-step explanation:

Given

[tex]log_{5}[/tex] 2x³

= [tex]log_{5}[/tex] 2 + [tex]log_{5}[/tex] x³

= [tex]log_{5}[/tex] 2 + 3[tex]log_{5}[/tex] x

Answer:

4 cm

Step-by-step explanation:

Volume of milk

LBH

L= 8, B= 5 and H =12

5×8×12=480

After rotation

L= 8, B=15 and H=x

V=LBH

480=8×15×x

480=120x

x=4cm

Answer:

The depth of the milk is 4cm when turned

Step-by-step explanation:

First we need to figure out how much milk is inside the container. We can do this by finding the volume it takes up. The milk's depth is 12cm so the height is 12 instead of 15. The length and width remain the same (5 and 8)

5x8x12=480 cm^3

The volume of the milk is 480, so when the carton is turned, the milk's volume still is the same

When it is turned, the base changes. Now it is 8 and 15 for the length and width. We just need to find the height.

8x15xh=480

120h=480

h=4

The depth of the milk is 4cm when turned

Answer:

C. C only

Step-by-step explanation:

Well to determine if the given graphs are functions we need to do the vertical line test to all the graphs,

A. This fails the vertical line test because the vertical line could pass through 2 points on the lines.

B. this also fails because a vertical line could pass through 2 points.

C. This passes because the vertical line doesn’t touch 2 points.

Answer:

2

Step-by-step explanation:

Looking at the graph, it is 2.

6/12 and 4/8 are equal fractions, as, when simplified, they share a simplified fraction.

Note that what you do to the denominator, you do to the numerator. Find common denominators for both fractions:

(4/8)/(2/2) = 2/4

(6/12)/(3/3) = 2/4

As you can tell, when they share a common denominator (4), the numerators are the same as well (3).

~

Answer:

C. X-Y X-Y

Step-by-step explanation:

The question asks to identify the least amount of discount on the conference registration. If the registration discount is at least half of the possible saving of ROB then all attendees will stay within the block. X is the block rate and Y is the non block rate. The saving for staying two nights outside the block is 2 (X-Y)

Answer:

$635

Step-by-step explanation:

$5x7 birdhouses=$35want

So, $35+$600=$635 total!

I hope this helps you!

Multiplication is the process of multiplying. The cost of building 7 birdhouses will be $635.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

The cost of the birdhouse is the sum of the fixed cost, which is the setup cost of the business of $600, and the variable cost is the cost that is needed to make a single house, therefore, $5.

Now, the total cost of making n number of houses will be,

Cost of making n house = Fixed cost + variable cost

                                        = $600 + $5(n)

Further, the table can be filled using the above formula by substituting the value of n for the number of houses. Therefore,

Number of bird houses     Total cost to build

       1                                     $600+$5(1) = $605

       2                                    $600+$5(2) = $610

       3                                    $600+$5(3) = $615

       4                                    $600+$5(4) = $620

       5                                    $600+$5(5) = $625

       6                                    $600+$5(6) = $630

       7                                    $600+$5(7) = $635

Hence, the cost of building 7 birdhouses will be $635.

Learn more about Multiplication here:

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Six hundred thousand

Hope it helps :)

Answer:

Positive

Step-by-step explanation:

negative times negative is postive positive times negative is negative

Answer:

A positive.

Step-by-step explanation:

Let's replace these with numbers.

-1 · 2  · (-3)

A negative times a positive will always equal a negative. So, we have:

-2 · (-3)

Any numbers with the same sign (positive or negative)  multiplied by each other will equal a positive. Since we have two negatives and we're multiplying them, our result will be a positive number.

6

Hope this helps!! <3 :)

Answer: (-1,-3)

Step-by-step explanation:

midpoint formula [tex]\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]

[tex]\left(x_1,\:y_1\right)=\left(-3,\:-2\right),\:\left(x_2,\:y_2\right)=\left(1,\:-4\right)[/tex]

[tex]\left(\frac{1-3}{2},\:\frac{-4-2}{2}\right)[/tex]

[tex](\frac{-2}{2},\frac{-6}{2})[/tex]

-2/2=-1

-6/2=-3

So the midpoint is (-1,-3)

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[tex](x-9)^2=15\\x-9=\sqrt{15} \vee x-9=-\sqrt{15}\\x=9+\sqrt{15} \vee x=9-\sqrt{15}[/tex]