Write the equation for an exponential function, in the form y=a•b^x, whose graph passes through the coordinate points (1,7.5) and (3,16.875)

Answer:

8

Step-by-step explanation:

Answer: 8

Step-by-step explanation:

The smallest number that's in the domain of f ° g is x = 0.

The function f(x) = √(9x) represents the square root of 9x.

The function g(x) = x + 7 represents adding 7 to x. To find the smallest number that is in the domain of f ° g, we need to determine the values of x that satisfy both f(x) and g(x).

We can start by looking at the domain of g(x), which includes all real numbers. So any value of x will work for g(x).

Next, we need to consider the domain of f(x). Since taking the square root of a negative number is not defined in the real number system, we must ensure that 9x is positive or zero.

So we set 9x ≥ 0 and solve for x: x ≥ 0. This means any non-negative value of x will work for f(x).

Now, to find the smallest number in the domain of f ° g, we need to find the intersection of the domains of f(x) and g(x).

Since any value of x will work for g(x) and only non-negative values of x will work for f(x), the smallest number that satisfies both functions is x = 0.

Answer:

Third option: 28

Step-by-step explanation:

You need to remember the following identity:

[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]

In the right triangle shown in the figure, you can identify:

[tex]\alpha=30\°\\opposite=14\\hypotenuse=x[/tex]

Then, you need to substitute the corresponding values into  [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]:

 [tex]sin(30\°)=\frac{14}{x}[/tex]

Now, you can solve for "x":

[tex]xsin(30\°)=14\\\\x=\frac{14}{sin(30\°)}\\\\x=28[/tex]

Answer:

The value of x is 28 units

Step-by-step explanation:

Given a right angled triangle with one side 14 units and one angle 30°

we have to find the value of x

By trigonometric ratios

[tex]\sin \theta=\frac{Perpendicular}{Hypotenuse}[/tex]

[tex]\sin 30^{\circ}=\frac{14}{x}[/tex]

[tex]\frac{1}{2}=\frac{14}{x}[/tex]

[tex]x=14\times 2=28 units[/tex]

Hence, the value of x is 28 units.

Option C is correct

Answer:

(C) 19x+6^2+2

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

edge 2021

Answer:

They paid $2.85 for each burger and $1.8 for each order of fries

Step-by-step explanation:

It will be solved simultaneously,

let x represent burger and y represent fries

John's order gives the first equation

3x + 2y = 12.15   ........(1)

Emily's order gives the second equation

4x + 3y = 16.80 ..........(2)

multiply equation (1) by 3 and equation (2) by 2 so as to eliminate y

9x + 6y = 36.45 ....... (3)

8x + 6y = 33.6 ........... (4)

subtract equation (4) from (3)

9x - 8x + 6y -6y = 36.45 - 33.6

x = 2.85

substitute x= 2.85 in equation (1)

3(2.85) + 2y = 12. 15

8.55 + 2y = 12.15

2y = 12.15 -8.55

2y = 3.6

y = 1.8

Answer:

Cost of burger = $2.85 and Cost of fries =   $ 1.80.

Step-by-step explanation:

Given  : john order 3 burgers and 2 fries for $12.15. Emily bought 4 burgers and 3 fries for $16.80.

To find : How much did the pay for each burger and order of fries.

Solution : We have given 3 burgers and 2 fries for $12.15.

Let the cost of 1 burger = x .

Let the cost of 1 Fries = y .

3 x + 2 y = $12.15 ------(1)

4 x + 3 y =  $16.80-----(2)

On multiplying (i) by 4 and (ii) by 3 and subtracting the equation .

12x + 8y = $48 .60

(-)12x +(-) 9y = (-)$50 .40

_____________

0 -y = -$ 1.80

y =  $ 1.80.

3x + 2(1.80) = $12.15 .

3x + 3.60 = 12.15

3x = 12.15 -  3.60

3x = 8.55

On dividing both sides by 3.

x = $2 .85

Therefore, Cost of burger = $2.85 and Cost of fries =   $ 1.80.

Answer: 8/9

Hope it helped!

Answer:

8/9

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 72 and 81 is 9

72 ÷ 9

81 ÷ 9

= 8/9

Answer:

Step-by-step explanation:

B or C depending on how many bags you have

A reasonable tip for an airport skycap is generally $2 per bag, reflecting both the service provided and the quantity of luggage.

The question asks about the appropriate tip amount for an airport skycap. A common guideline for tipping skycaps is $2 per bag, which is considered to be a reasonable amount. Tipping $5 per bag may be considered generous in many cases, and a flat rate of $2 in total could be seen as insufficient unless you only have one bag. The tip should reflect the quality of service provided and the number of bags. The provided information regarding airline costs and opportunity costs of time at airports is not directly related to tipping skycaps but does highlight the broader context of airport expenses and the value of time for air travelers.

Answer:

3) 3a - 2 + 3 = -2

   3a            = -2 + 2 - 3 = -3

   a              = -3/3 = -1

4) m/-6 - 18 - 4 = -16

   m/-6             = -16 + 18 + 4 = 6

   m                  = 6 · (-6) = -36

5) x/-2 - 4 + 22 = -28

   x/-2              = -28 + 4 - 22 = -46

   x                   = -46 · (-2) = 92

6) -13 = 5 + 20m - 2m

   -13 = 5 + 18m

   -18 = 18m

   m  = -18/18 = -1

7) -2(2p - 1) = -14

   -4p + 2   = -14

   -4p          = -14 - 2 = -16

   p              = -16/(-4) = 4

8) -1(8x + 20) = 12

   -8x - 20      = 12

   -8x              = 12 + 20 = 32

   x                  = 32/(-8) = -4

9) -49 = 7(2x + 3)

   -49 = 14x + 21

   -14x = 49 + 21 = 70

   x                     = 70/-14 = -5

10) 3(8h - 4) + 17 = -19

     24h - 12 + 17 = -19

     24h               = -19 + 12 - 17 = -24

     h                   = -24/24 = -1

Answer:

$51200

Step-by-step explanation:

Simply do this: 2¹⁰ × 50. You are doing this because you are doubling it for each year that goes by.

I am joyous to assist you anytime.

Answer:

The volume of the prism is [tex]1,299\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the prism is equal to

[tex]V=BL[/tex]

where

B is the area of the triangular base

L is the length of the prism

we have

[tex]L=30\ in[/tex]

Find the area of the base B

The area of a equilateral triangle is equal to

[tex]B=\frac{1}{2}(10)^{2} sin(60\°)[/tex]

[tex]B=25\sqrt{3}\ in^{2}[/tex]

substitute

[tex]V=(25\sqrt{3})(30)=1,299\ in^{3}[/tex]

The volume of the traingular prism is 1,280.85 in³.

The volume of the prism is determined using the following formulas as show below;

V = Bh

where;

Base area is calculated as follows;

[tex]A = \frac{a^2\sqrt{3} }{4} \\\\A = \frac{10^2 \times \sqrt{3} }{4} \\\\A = 25\sqrt{3} \ in^2[/tex]

[tex]L^2 = (\frac{a}{2} )^2 + h^2\\\\h^2 = L^2 - (\frac{a}{2} )^2\\\\h^2 = 30^2 - (\frac{10}{2} )^2\\\\h^2 = 875\\\\h = \sqrt{875} \\\\h = 29.58 \ in[/tex]

V = 25√3 x 29.58

V = 1,280.85 in³

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Answer:

Question 1: b Question 2: yes

Step-by-step explanation:

The variable must go with 7+1/3 calculate time for all the levels. Then add 5+1/6. It must be less than or equal to because you want to play all 6 levels. You can play all 6 when you plug in 6 as the variable. It is less than 60

Answer:

i was a little unclear about your sugar amount..

Step-by-step explanation:

if the amount was 1 1/4 ( 1 cup and 1/4 cup) them the answer would be 12

12 x 1.25 = 15

if the sugar amount was just 1/4 cup of sugar the answer would be 60

.25 x 15 = 60

In order to t² - t -2 = 0 become into this (t - 2)(t + 1) = 0, we have to know that a  polynomial of the form ax² + bx + c = 0 can be factored as a(x + r1)(x + r2) = 0, where r1 and r2 are the roots of the equation ax² + bx + c = 0 and we can find them using the Quadratic Formula.

Let's solve the equation step-by-step.

t² - t -2 = 0 has the form at² + bt + c = 0, so can be factored as a(t + r1)(t + r2) = 0. With a = 1, b = -1, and c = -2

Step 1. Use the Quadratic Formula to find the roots r1 and r2.

t =  −b ± √b²−4ac/2a

t = -(-1) ± √(-1)²−4(1)(-2)/2(1)

t = 1 ± √1+8/2

t = 1 ± √9/2 where r1 = 1 + √9/2 and r2 = 1 - √9/2

Step 2. Calculate the roots r1 and r2

r1 = 1 + √9/2 = 2

r2 = 1 - √9/2 = -1

Step 3. Write the factored equation a(t + r1)(t + r2) = 0, with a = 1 and the values of r1 and r2 with opposite signs.

1(t - 2)(t + 1) = 0

(t - 2)(t + 1) = 0

Answer:

the 1st one in the 2nd row

Step-by-step explanation:

The balance of a $4000 loan at a 3% annual interest rate compounded monthly after three payments of $200 each is $3428.58.

To find the balance after the third payment of a $4000 loan, compounded monthly at an annual interest rate of 3%, we must first determine the monthly interest rate. The annual rate of 3% means a monthly rate of 0.25% (3%/12 months). Next, we'll apply the loan payment process three times to calculate the remaining balance.

The balance after the third payment is $3428.58.

Answer:

moderate negative

Step-by-step explanation:

a perfect would be a rate, I believe.

The statement which best describes the association between variables X and variable Y is:

          moderate negative association

Since  by looking at the scatter plot we see that the Y-value is decreasing with the increasing x-value i.e. the two variables are in inverse proportion.

Hence, the two variables has a negative association.

Also, when we will draw a line of best fit we will observe that not all the data points will lie on the trend line but they will be closely related to the line of best fit.

Hence, the relationship is moderate.

             Hence the answer is:

           Moderate negative association.

Answer:

The measure of angle KLM is 62°

Step-by-step explanation:

* Lets revise the properties of the rhombus

- The rhombus has 4 equal sides in length

- Every two opposite angles are equal in measure

- The two diagonals bisect each other

- The two diagonals perpendicular to each other

- The two diagonals bisect the vertices angles

* Lets solve the problem

∵ JKLM is a rhombus

∴ m∠MJK = m∠KLM ⇒ opposite angles in the rhombus

∵ JL and KM are diagonals in the rhombus and intersect each

   other at N

∴ JL bisects ∠MJK

∴ m∠KJL = m∠MJN

∵ m∠KJL = (2x + 5)°

∵ m∠MJN = (3x - 8)°

∴ 2x + 5 = 3x - 8 ⇒ subtract 2x from both sides

∴ 5 = x - 8 ⇒ add 8 to both sides

∴ 13 = x

∴ The value of x = 13

∵ m∠KJL = (2x + 5)° ⇒ substitute the value of x

∴ m∠KJL = 2(13) + 5 = 26 + 5 = 31°

∵ m∠KJL = 1/2 m∠MJK

∴ m∠MJK = 2 m∠KJL

∴ m∠ MJK = 2 × 31° = 62°

∵ m∠MJK = m∠KLM ⇒ opposite angles in the rhombus

∴ m∠KLM = 62°

Answer:

2

Step-by-step explanation:

7 divided by 4 equals 1.75 then round to nearest tenth you get 2.

the answer is 1.8 because 1.75 is getting rounded by the 7 place which is the tenths place

Answer:

Sample Response: Find the area of the rectangle. Then, find the area of the circle. The diameter is given, so take half that to get the radius. Multiply the area of the circle by half. Subtract the area of the half circle from the area of the rectangle.

Step-by-step explanation:

i did it.

Answer:

Sample Response: Find the area of the rectangle. Then, find the area of the circle. The diameter is given, so take half that to get the radius. Multiply the area of the circle by half. Subtract the area of the half circle from the area of the rectangle.

Step-by-step explanation:

make sure to inlcued

- area of rectangle

- half the diameter for the radius

- half the area of the circle

- subtract the area of the half circle from the area of the rectangle

Answer:

Let's solve your system by substitution.

x=5;y=−7

Step: Solve x=5 for x:

x=5

Step: Substitute 5 for x in y=−7:

y=−7

y=−7

Answer:

x=5 and y=−7

x=3;y=2x−1

Step: Solve x=3 for x:

x=3

Step: Substitute 3 for x in y=2x−1:

y=2x−1

y=(2)(3)−1

y=5(Simplify both sides of the equation)

Answer:

x=3 and y=5

Let's solve your system by substitution.

y=6x+3;y=5x+4

Step: Solve y=6x+3 for y:

y=6x+3

Step: Substitute 6x+3 for y in y=5x+4:

y=5x+4

6x+3=5x+4

6x+3+−5x=5x+4+−5x(Add -5x to both sides)

x+3=4

x+3+−3=4+−3(Add -3 to both sides)

x=1

Step: Substitute 1 for x in y=6x+3:

y=6x+3

y=(6)(1)+3

y=9(Simplify both sides of the equation)

Answer:

x=1 and y=9

2x+3y=2;y=x−6

Step: Solve y=x−6 for y:

y=x−6

Step: Substitute x−6 for y in 2x+3y=2:

2x+3y=2

2x+3(x−6)=2

5x−18=2(Simplify both sides of the equation)

5x−18+18=2+18(Add 18 to both sides)

5x=20

divide both sides by 5

5x/5 and 20/5

x=4

Step: Substitute 4 for x in y=x−6:

y=x−6

y=4−6

y=−2(Simplify both sides of the equation)

Answer:

x=4 and y=−2

Final answer:

To determine the number of one-point and two-point shots made by a basketball team that scored 92 points from 55 shots, set up a system of equations. Solve the system to find that the team made 18 one-point shots and 37 two-point shots.

Explanation:

Finding the Number of One-Point and Two-Point Shots

Let's define x as the number of one-point shots and y as the number of two-point shots. We then have the following system of equations based on the information provided:

x + y = 55 (Total number of successful shots)

1x + 2y = 92 (Total points scored)

To solve for x and y, we can use either substitution or elimination methods.

Using substitution:

Solve the first equation for x: x = 55 - y.

The team made 18 one-point shots and 37 two-point shots.

Answer:

Step-by-step explanation:

[tex]x,y-\text{positive integers}\\\\\text{The system of equations:}\\\\\left\{\begin{array}{ccc}x+y=10&\text{subtract}\ y\ \text{from both sides}\\xy=21\end{array}\right\\\\\left\{\begin{array}{ccc}x=10-y&(1)\\xy=21&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\(10-y)(y)=21\qquad\text{use the distributive property}\ a(b-c)=ab-ac\\\\10y-y^2=21\qquad\text{subtract 21 from both sides}\\\\-y^2+10y-21=0\qquad\text{change the signs}\\\\y^2-10y+21=0\\\\y^2-3y-7y+21=0\\\\y(y-3)-7(y-3)=0[/tex]

[tex](y-3)(y-7)=0\iff y-3=0\ \vee\ y-7=0\\\\y-3=0\qquad\text{add 3 to both sides}\\\\y=3\\\\y-7=0\qquad\text{add 7 to both sides}\\\\y=7\\\\\text{Put the value of}\ y\ \text{to (1):}\\\\x=10-3=7\ or\ x=10-7=3[/tex]

Answer:

The equation is equal to 78°-x=56°

The decrease in temperature is 22°

Step-by-step explanation:

Let

x-----> the decrease in temperature

we know that

The equation that represent this situation is equal to

78°-x=56°

Solve for x

x=78°-56°

x=22°

Answer:

The required equation is [tex]78^\circ F-t=56^\circ F[/tex]

The decrease in temperature is 22°F.

Step-by-step explanation:

Given : The temperature in Springfield at 10:00 a.m. was 78°F. During the day, it dropped to 56°F.

To find : Write and solve an equation to  find the decrease in temperature ?

Solution :

We have given that temperature is dropped i.e. there is decrease in teh temperature.

Let the decrease in the temperature be 't'.

According to question,

The temperature in Springfield at 10:00 a.m. was 78°F. During the day, it dropped to 56°F.

i.e. the required equation is [tex]78^\circ F-t=56^\circ F[/tex]

Solve,

[tex]t=78^\circ F-56^\circ F[/tex]

[tex]t=22^\circ F[/tex]

The decrease in temperature is 22°F.

Answer:

24ft^3

Step-by-step explanation:

Hope it helped you!

Answer:

24 ft.

Step-by-step explanation:

Someone please show a quicker way! (Done inefficiently in my head.)

((1.5 x1.2) + (((1.2 x .5)/2) x 2)) x 10 = 24

Answer:

BC = 11

Step-by-step explanation:

Substitute x = 5 into the expression for BC

BC  = 2x + 1 = (2 × 5) + 1 = 10 + 1 = 11

11 is the answer good luck

Answer:

[tex]\large\boxed{\left(-\dfrac{1}{2},\ -1\right)}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a midpoint:}\\\\\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)\\\\================================\\\\A(1,\ -3),\ B(-2,\ 1)\\\\\text{Substitute:}\\\\x=\dfrac{1+(-2)}{2}=\dfrac{-1}{2}=-\dfrac{1}{2}\\\\y=\dfrac{-3+1}{2}=\dfrac{-2}{2}=-1[/tex]

Answer:

[tex](\frac{-1}{2} ,-1)[/tex]

Step-by-step explanation:

line segment AB has endpoints A(1,-3) and B(-2,1).

To find the midpoint of AB we use formula

[tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]

A(1,-3) is (x1,y1) , B(-2,1) is (x2,y2)

Plug in the values in the formula

[tex](\frac{1-2}{2} ,\frac{-3+1}{2} )[/tex]

[tex](\frac{-1}{2} ,\frac{-2}{2} )[/tex]

[tex](\frac{-1}{2} ,-1)[/tex]

Answer:

Step-by-step explanation:

The square of the sum of the first five positive integers:

(1 + 2 + 3 + 4 + 5)² = 15² = 225

The sum of the first positive perfect square:

1² + 2² + 3² + 4² + 5² = 1 + 4 + 9 + 16 + 25 = 55

225 - 55 = 200

The positive difference between the square of the sum of the first five positive integers and the sum of the first five positive perfect squares is 170. This is obtained by taking the sum of first five numbers, squaring the sum and subtracting the sum of first five perfect squares.

The sum of first five positive integers = 1+2+3+4+5 = 15

Square of the sum of the first five positive integers = 15² = 225

The sum of the first five positive perfect squares =1²+2²+3²+4²+5²

                                                                                 =1+4+9+16+25

                                                                                 =55

The positive differenece = 225-55=170

Hence the positive difference between the square of the sum of the first five positive integers and the sum of the first five positive perfect squares is 170.

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The flow rate is 2 quarts per minute. There are 4 quarts in a US gallon, so 2 quarts divide 4 quarts per US gallon = 0.5 gallons per minute There are 60 seconds in a minute, so the flow rate is 0.5 gallons per minute divide 60 seconds per minute = 0.0083 gallons per second

Converting 2 quarts per minute to gallons per second requires the use of two conversion factors. First, quarts are converted to gallons by dividing by 4. Then, minutes are converted to seconds by dividing by 60. After performing these steps, it is found that 2 quarts per minute is approximately equal to 0.00833 gallons per second.

The student is asking to convert a flow rate from quarts per minute to gallons per second. There are a few fundamental conversions you need to use to find the answer. Firstly, remember that 1 gallon (gal) is equivalent to 4 quarts (qt). So, to convert the quarts to gallons, divide the quarts by 4. Secondly, there are 60 seconds in a minute; thus, you have to convert the minutes to seconds by dividing by 60.

Let's go step-by-step:

Therefore, 2 quarts per minute is approximately equal to 0.00833 gallons per second.

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System of equations helps us to compare two real-life problems. The system of equations will have no solution.

Inconsistent System

A system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

A system of the equation to be Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

A system of the equation to be Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.

As the systems of two-equations are given, therefore, the two equations are:

Now, if we plot the two-equation on the graph, we will find that the lines of the two equations are parallel. therefore, the system of equations will have no real solution or will have no solution.

Hence, the system of equations will have no solution.

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