From a room temperature of 42 degrees, the temperature dropped by 20 degrees, then rose by 75 degrees and finally dropped by 1 degree. What is the temperature after the given changes?
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Answer:

[tex]\displaystyle y-1=\frac{1}{3}(x+3)[/tex]

Step-by-step explanation:

Equation of a Line

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

The table shows the relation between x and y. It contains the following points

(-3,1), (6,4), (12,6), (30,12).

Taking the two first points, we find the equation of the line:

[tex]\displaystyle y-1=\frac{4-1}{6+3}(x+3)[/tex]

[tex]\displaystyle y-1=\frac{3}{9}(x+3)[/tex]

Simplifying:

[tex]\displaystyle y-1=\frac{1}{3}(x+3)[/tex]

To ensure the rest of the points belong to the line, we test them:

For the point (12,6):

[tex]\displaystyle 6-1=\frac{1}{3}(12+3)[/tex]

[tex]\displaystyle 5=\frac{1}{3}(15)[/tex]

5=5

Since equality is true, the point belongs to the line.

For the point (30,12):

[tex]\displaystyle 12-1=\frac{1}{3}(30+3)[/tex]

[tex]\displaystyle 11=\frac{1}{3}(33)[/tex]

11=11

Since equality is true, the point belongs to the line.

Thus, the equation of the line is:

[tex]\mathbf{\displaystyle y-1=\frac{1}{3}(x+3)}[/tex]

Answer:

9) 15

Step-by-step explanation:

Answer:

the smaller number is 13 and the larger number is 67

Answer:

-23

Step-by-step explanation:

the equation of the line is y=-2/3x-23 so the b in the equation (y=mx+b) is the y int so that is -23

Answer:

B

Step-by-step explanation:

Answer:

f=2 c=4

Step-by-step explanation:

8 times 2 equals 16 plus 2 times 4 equals 24 in total.

Answer: A

Step-by-step explanation:

Answer:

(0,-1)

Step-by-step explanation:

because the line crosses through (0,-1) the vertex is (0,-4)

Answer:

B. 16.4°

Step-by-step explanation:

reference angle = x = [tex] \theta [/tex]

Side length opposite to x = 20 ft = opp

Adjacent side length = 68 ft = adj

Apply the following trigonometric ratios formula:

[tex] tan(\theta) = \frac{opp}{adj} [/tex]

Plug in the values into the formula

[tex] tan(x) = \frac{20}{68} [/tex]

[tex] tan(x) = 0.2941 [/tex]

[tex] x = tan^{-1}(0.2941) [/tex]

[tex] x = 16.3886 [/tex]

x = 16.4° (nearest tenth)

Answer:

B. 16.4

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

Answer:

y = 150x + 400

Explanation:

Slope intercept form is :    y = mx + b

B is the y intercept, you can also think of it like a starting value, in this case Susan starts with $400 dollars

M is the slope, you can also think of it like a value that is consistently changing over time, in this case Susan saves(or earns) $150 each month.

If you want to figure how much money she will have in a certain number of months, plug the number of months (x), into the x in     y = 150x + 400.

Answer: 500

Step-by-step explanation:

The remainder of the question is:

How many units does the company need to sell to reach the target profit?

The required sales to break even will be calculated as:

= (Fixed cost + Required profit) / ( Price per unit - Variable cost)

= (120000 - 80000) / (100 - 20)

= 40000/80

= 500

The company needs to sell 500 units.

Answer:

for the second question , all you have to do is substitute , the first point plotted is x and the second point is b , ploy those points in the equation and remember that to find x we make y= 0 and to find y we make x =0

Answer:

The answer is letter F po

Step-by-step explanation:

Use the formula

(b2)2 in order to create a new term. Solve for x

by using this term to complete the square.

Exact Form:x=±√17+5

Answer:

12yd = 36ft

Why: For every 1 yard you have 3 feet

2 yards=6 3=9 and so on

Step-by-step explanation:

12 yards = 36 feet

if this answer is correct:

give a like and rate me 5

Answer:

y=-3x+5

Step-by-step explanation:

y=mx+b

m=(-4-2)/(3-1)=-3

b=y-mx

b =-4 - (3)(-3)

b=-4+9

b=5

Answer: $22.50, but rounded to the nearest dollar its $23.00 Hope this helps :)

Step-by-step explanation: The unit rate it 1/0.75

Answer:

The interest on the investment is $16,170.93811

Step-by-step explanation:

The rule of the compound interest is [tex]A=P(1+\frac{r}{n})^{nt}[/tex], where

∵ The investment is $45,000

∴ P = 45,000

∵ The interest on the investment is compounded annually at 5.25%

∴ r = 5.25% = 5.25 ÷ 100

∴ r = 0.0525

∴ n = 1 ⇒ compound annually

∵ It is for 6 years

∴ t = 6

→ Substitute them in the rule above

∵ [tex]A=45,000(1+\frac{0.0525}{1})^{1(6)}[/tex]

∴ [tex]A=45,000(1.0525)^{6}[/tex]

∴ A = 61,170.93811

∵ I = A - P, where I is the interest

∴ I = 61,170.93811 - 45,000

∴ I = 16,170.93811

∴ The interest on the investment is $16,170.93811

Given :

The ratio of collectable cards Deshawn owns to cards that Stephanie owns is 5:2.

Stephanie has 36 cards.

To Find :

How will the ratio of Deshawn's cards to Stephanie's cards change if they both sell half there cards.

Solution :

Number of card Deshawn had, n = 5/2 × 36

n = 90 .

Number of card after they sell half there cards :

[tex]n_D = \dfrac{90}{2}=45[/tex]

[tex]n_S=\dfrac{36}{2}=18[/tex]

Therefore, new ratio is [tex]\dfrac{45}{18}=5 : 2[/tex].

So, new ratio will be same.

Answer:

$0.15

Step-by-step explanation:

Cost of each pounds of banana = $0.80

Number of pounds of banana = 2 1/4 pounds

Total cost of banana = $0.80 × 2 1/4 pounds

= 0.80 × 9/4

= 0.80 × 2.25

= 1.8

Total cost of banana = $1.8

Cost of each pounds of strawberry = $1.10

Number of pounds of strawberry = 1 1/2 pounds

Total cost of strawberry = $1.10 × 1 1/2 pounds

= 1.10 × 3/2

= 1.10 × 1.5

= 1.65

Total cost of strawberry = $1.65

How much more did Megan spend on bananas than on strawberries?

Total cost of banana - Total cost of strawberry

= $1.8 - $1.65

= $0.15

Answer:

$0.15

Step-by-step explanation:

Cost of each pounds of banana = $0.80

Number of pounds of banana = 2 1/4 pounds

Total cost of banana = $0.80 × 2 1/4 pounds

= 0.80 × 9/4

= 0.80 × 2.25

= 1.8

Total cost of banana = $1.8

Cost of each pounds of strawberry = $1.10

Number of pounds of strawberry = 1 1/2 pounds

Total cost of strawberry = $1.10 × 1 1/2 pounds

= 1.10 × 3/2

= 1.10 × 1.5

= 1.65

Total cost of strawberry = $1.65

How much more did Megan spend on bananas than on strawberries?

Total cost of banana - Total cost of strawberry

= $1.8 - $1.65

= $0.15

Step-by-step explanation:

Answer:

If the lines BC and DE are parallel, the value of c is c=-2

Step-by-step explanation:

We are given line segment BC with end points B(2, 2) and C(9,6) and line segment DE with endpoints  D(c, -7) and E(5, -3).

Using slope formula: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex] we can find point c

When 2 lines are parallel there slope is same.

So, Slope of line BC =Slope of Line DE

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

We have:

[tex]x_1=2, y_1=2, x_2=9, y_2=6 \ for \ line \ BC \ and \\\x_1=c, y_1=-7, x_2=5, y_2=-3 \ for \ line \ DE \[/tex]

Putting values and finding c

[tex]\frac{6-2}{9-2}=\frac{-3-(-7)}{5-c}\\ \frac{4}{7}=\frac{-3+7}{5-c} \\ \frac{4}{7}=\frac{4}{5-c} \\Cross \ multiply:\\4(5-c)=4*7\\20-4c=28\\-4c=28-20\\-4c=8\\c=\frac{8}{-4}\\c=-2[/tex]

So, If the lines BC and DE are parallel, the value of c is c=-2

Answer:

Step-by-step explanation:

Bisect means in half so both angles equal each other, meaning the equations equal each other.

2x+7 = 4x-9

Subtract 4x from both sides

-2x+7 = -9

Subtract 7 from both sides

-2x = -16

x = 8, so the answer is the third choice

Bisect means in half so both angles equal each other, meaning the equations equal each other.

2x+7 = 4x-9

Subtract 4x from both sides

-2x+7 = -9

Subtract 7 from both sides

-2x = -16

x = 8, so the answer is the third choice

Total amount, T = $100 million.

Cost of wheat per ton, C = $300 .

Price per fighter plane, c = $15 million.

Now,

Price of 5 fighter planes, P = $( 15 × 5 ) = $75 million.

Amount left = $( 100 - 75 ) = $25 million.

So,

Number of tons of wheat government can buy is :

[tex]n=\dfrac{25\times 1000000}{300}\\\\n = 83333.33\ tons[/tex]

Therefore, number of tons of wheat the government can afford is 83333.33 tons.

Hence, this is the required solution.

Answer:

1,254.54

Step-by-step explanation:

Answer:

1,254.54

Step-by-step explanation:

Step-by-step explanation:

7.90.

Answer:

The better deal is $32.05/15 gal

Step-by-step explanation:

Divide:

56/25

=2.24

32.05/15

=2.13666667

=2.14

Answer:

Here are 5 (2,4), (3,6), (1,2), (4,8), (5,10)

Step-by-step explanation:

Part (a)

The resultant vector is the vector formed by adding the two vectors a and b. So we effectively add the corresponding components.

You can use the parallelogram law as a visual alternative.

Adding a and b leads to

a+b = (3i-2j) + (pi-2pj)

a+b = (3i+pi) + (-2j-2pj)

a+b = (3+p)i - (2+2p)j

Define vector d to be d = a+b so we can use it later below.

Recall that parallel vectors point in the same direction. This means the ratio of their components or coordinates are equal.

We can say the following

(x coord of d)/(x coord of c) = (y coord of d)/(y coord of c)

(3+p)/(2) = (-(2+2p))/(-3)

Let's solve for p

(3+p)/(2) = (-(2+2p))/(-3)

(3+p)/(2) = (2+2p)/3

3(3+p) = 2(2+2p) .... cross multiply

9+3p = 4+4p

4p+4 = 3p+9

4p-3p = 9-4

p = 5

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

Part (b)

Since p = 5, from part (a), we can determine vector b

b = pi - 2pj

b = 5i - 2*5j

b = 5i - 10j

Then add vectors a and b to get

a+b = (3i-2j) + (5i - 10j)

a+b = (3i+5i) + (-2j - 10j)

a+b = (3+5)i - (2+10)j

a+b = 8i - 12j

Or we can say

a+b = (3+p)i - (2+2p)j  .... from part (a)

a+b = (3+5)i - (2+2*5)j ... plugging in p = 5

a+b = 8i - 12j

Note the ratio of the components of vector d and vector c are such

(x coord of d)/(x coord of c) = (y coord of d)/(y coord of c)

8/2 = -12/(-3)

4 = 4

This helps confirm the answer

You could also graph the vectors c = 2i - 3j and d = 8i - 12j to note the two lines produce the same slope -3/2. We can see that -12/8 = -3/2. Lines of the same slope are parallel lines

a.

The value of p is 5

Since vector a = 3i - 2j and vector b = pi - 2pj, the resultant of vectors a and b is R = a + b

= 3i - 2j + pi - 2pj

= (3 + p)i - 2(1 + p)j

Since R is aparallel to vector c = 2i - 3j, it implies that the cross product of R and c is zero.

The cross product of two vectors a and b is a × b = absinФ where a and b are the magnitudes of a and b and Ф is the angle between them.

So, R × c = [(3 + p)i - 2(1 + p)j] × [2i - 3j]

= (3 + p)i × 2i + (3 + p)i × (-3j) + (-2(1 + p)]j × 2i + (-2(1 + p)]j×(-3j)

= 0 - 3(3 + p)k - 4(1 + p)(-k) + 0

= -3(3 + p)k + 4(1 + p)k

= [-3(3 + p) + 4(1 + p)]k

= [-9 - 3p + 4 + 4p)]k

= [-9 + 4 - 3p + 4p)]k

=  [-5 + p]k

[-5 + p]k = RcsinФ.

Since R and c are parallel, Ф = 0°

So, Rcsin0° = Rc × 0 = 0

So,   [-5 + p]k = 0

-5 + p = 0

p = 5

The value of p is 5

b.

The resultant of vectors a and b is R = 8i - 12j

Since p = 5 and the resultant of vectors a and b is R = (3 + p)i - 2(1 + p)j

Substituting the value of p = 5 into r, we have

R = (3 + p)i - 2(1 + p)j

R = (3 + 5)i - 2(1 + 5)j

R = 8i - 2(6)j

R = 8i - 12j

So, the resultant of vectors a and b is R = 8i - 12j

Learn more about resultant of vectors here:

https://brainly.com/question/14358602