The area of a rectangle is less than 81 square centimeters. The length of the rectangle is 9 centimeters and the width is x centimeters. Select the possible value(s) of x.

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

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

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:

B

Step-by-step explanation:

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:

1,254.54

Step-by-step explanation:

Answer:

1,254.54

Step-by-step explanation:

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:

f=2 c=4

Step-by-step explanation:

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

Answer:

the smaller number is 13 and the larger number is 67

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:

Function B

Step-by-step explanation:

✍️Rate of change for Function A:

Using any two pairs from the table of values given, say, (0, 1) and (4, 2):

Rate of change = [tex] \frac{y_2 - y_1}{x_2 -x_1} = \frac{2 - 1}{4 - 0} = \frac{1}{4} [/tex]

Rate of change for function A = ¼ = 0.25

✍️Rate of change for Function B:

Equation for Function B is given in the slope-intercept format, y = mx + b.

m = slope = rate of change.

Therefore, the function, y = 0.75x - 2 has a rate of change of 0.75.

Rate of change of Function B = 0.75.

✅0.75 if greater than 0.25, therefore, Function B has the greater rate of change.

The function which has a greater rate of change or slope is required.

Function B has a greater rate of change.

Rate of change is given by

[tex]m=\dfrac{\Delta y}{\Delta x}[/tex]

The ordered pairs for the first function are

[tex](0,1),(4,2),(8,3),(12,4)[/tex]

Slope

[tex]m=\dfrac{2-1}{4-0}=\dfrac{1}{4}=0.25[/tex]

Since, it is a linear equation the slope will be equal for all ordered pairs.

The point slope form of a line is

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

where

m = Slope or rate of change

c = y intercept

Here, the equation is

[tex]y=0.75x-2[/tex]

The slope is 0.75.

Function B has a greater rate of change.

Learn more:

https://brainly.com/question/20423510?referrer=searchResults

https://brainly.com/question/25413713?referrer=searchResults

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:

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

Step-by-step explanation:

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:

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:

n/56 divided by 3/24 would be 1/7n

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.

Step-by-step explanation:

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:

A = $4360.515918 which rounded to the nearest penny is $4360.52

Step-by-step explanation:

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:

9) 15

Step-by-step explanation:

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:

The diameter of the virus will appear as 1.2 × 10⁻⁴ meters when viewed under the microscope

Step-by-step explanation:

From the question,

A microscope is set so it makes an object appear 6 × 10² times larger than its actual size. That is, when an object is viewed with the aid of the microscope, the object will be 6 × 10² times larger than its actual size.

Now, to determine how large the diameter of a virus that has a diameter of 2 × 10 ⁻⁷ meters will appear when viewed under the microscope, we will multiply the diameter of the virus by  6 × 10².

That is, 2 × 10 ⁻⁷meters × 6 × 10² = 1.2 × 10⁻⁴ meters

Hence, the diameter of the virus will appear as 1.2 × 10⁻⁴ meters when viewed under the microscope.

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:

$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