Please answer all these questions and number each question you answered to get 60 points

Answer:Im pretty sure the slope is 2.

Step-by-step explanation:

Answer:

  (x -14)² +(y -7)² = 1²

Step-by-step explanation:

You want the equation of the circle that represents the border of a logo centered 14 m right and 7 m up from the lower left corner of a soccer field. The logo is 2 m in diameter.

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

Since the origin of the coordinate system is the lower left corner of the field, the center is located at (h, k) = (14, 7). The diameter of 2 m means the radius is 1 m. Using these values in the equation, it becomes ...

  (x -14)² +(y -7)² = 1²

Answer:

x-axis

Step-by-step explanation:

the point is the format of (x,y)

Every point on the x-axis has a y-coordinate of 0

Answer:

D

Step-by-step explanation:

i took it

Answer:

d

Step-by-step explanation:

my stats teacher went over it

Answer:

800 grams flour ÷ 5 grams flour/biscuit = 160 biscuits

160 biscuits × 3 grams butter/biscuit = 480 grams butter

160 biscuits × 2 grams sugar/biscuit = 320 grams sugar

Katie needs 320 grams sugar.

Kate needs 270g of sugar to make the maximum number of biscuits possible.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Now, Based on the ratio of flour, butter, and sugar of 5:3:2, we can determine that Kate needs;

⇒ 800g + 550g

= 1350g of the mixture.

Hence, For find out the amount of sugar needed, we need to determine the proportion of sugar in the mixture.

We can do this by adding up the ratio numbers;

(5+3+2) = 10.

Then we can divide each ratio number by the total (10) to get the proportion of each ingredient.

So the proportion of sugar in the mixture is 2/10. To find out how much sugar Kate needs, we can set up a proportion:

2/10 = x/1350

We can solve for x by cross-multiplying:

2 × 1350 = 10x

2700 = 10x
x = 270

Therefore, Kate needs 270g of sugar to make the maximum number of biscuits possible.

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Answer:

97

Step-by-step explanation:

I used the law of cosines:  \(t^{2} =s^{2} +u^{2} -2tu cos (t)\)

Let plug the numbers in :  t^2=\(13^{2} +84^{2} -2(13)(84)cos (165)\) which approx is 97 to the nearest inch.

The length of 't' is approximately 69 inches.

To find the length of t, we can use the Law of Cosines, which states that for any triangle with sides a, b, and c and opposite angles A, B, and C, respectively:

a²= b² + c² - 2bc cos(A)

In this case, we want to find the length of t, which is opposite to the given angle ∠T. We know that:

u = 84 inches (opposite to angle ∠U)

s = 13 inches (opposite to angle ∠S)

∠T = 165°

Let's substitute these values into the Law of Cosines:

t² = u²+ s²- 2us cos(T)

t²= (84)²+ (13)² - 2(84)(13) cos(165°)

t²= 7,056 + 169 - 2(84)(13)(cos(180°-15°))

t²= 7,225 - 2(84)(13)(cos(15°))

t²= 7,225 - 2(84)(13)(0.9659)

t²= 7,225 - 2,485.68

t² = 4,739.32

t ≈ 68.86

Rounding to the nearest inch, the length of t is approximately 69 inches.

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Step-by-step explanation:

1. use PEMDAS (Parentheses, Exponent, Multiplication & Division, Addition & Subtraction). you would do 3/4 divided by 3/8 first.

  3/4 / 3/8 = 2  

2. add 2 to -2 1/2 (or if it's easier to understand, do 2 minus 2 1/2)

  -2 1/2 + 2 = -1/2     OR       2- 2 1/2 = -1/2

answer is -1/2

At the same rate as his 100-meter freestyle swim in the 2012 Olympics, Nathan Adrian could have completed one loop of a 25-meter pool in 11.88 seconds.

The idea of proportionality can be applied. The time it would take Nathan Adrian to complete one lap in a 25-meter pool is known to be 47.52 seconds for the 100-meter freestyle. Since the tempo is constant while the distance varies, we can establish a ratio:

100 meters / 47.52 seconds = 25 meters / x seconds

where x is the unknown time for one lap in the 25-meter pool.

To solve for x, we can cross-multiply:

100 meters * x seconds = 47.52 seconds * 25 meters

100x = 1188

Dividing both sides by 100, we get:

x = 11.88 seconds

Therefore, at the same rate as his 100-meter freestyle swim in the 2012 Olympics, Nathan Adrian could have completed one loop of a 25-meter pool in 11.88 seconds.

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Answer:

CAB is 37 degrees

Step-by-step explanation:

90 + 53 = 143

180 - 143 = 37

It will cost $412.50 for equipment for all stations.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Dan orders supplies for the science lab. Each of the 30 stations in the chemistry lab needs 5 feet of rubber tubing. If rubber tubing sells for $8.25 per yard.

The cost will be calculated as below,

3 feet = 1 yard

5 x 30 = 150 feet

8.25 per yard = cost

150/ 3 = 50 yards (total tubing needed)

50 x 8.25 = $ 412.50

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Answer:

x = 1

Step-by-step explanation:

5(2x - 8) + 15 = -15

First, let's move the 15 to the opposite side of the equation. We'll do this by subtracting 15 from BOTH sides of the equation.

5(2x - 8) + 15-15 = -15-15

5(2x-8) + 0 = -30

5(2x-8) = -30

Now let's expand that first term.

5(2x)-5(8) = -30

10x - 40 = -30

Now let's move the -40 to the opposite side of the equation. We'll do this by ADDING 40 to both sides of the equation.

10x - 40 + 40 = -30 + 40

10x -0 = 10

10x = 10

Now to solve for x, we divide BOTH sides by 10 to "isolate the variable" aka get x alone.

10x/10 = 10/10

x = 1

The answer is x = 1.

Let's check if our answer is correct!

Original equation: 5(2x - 8) + 15 = -15

Substitute 1 for x.

5(2*1-8) + 15 =

5(2-8) + 15 =

5(-6) + 15 =

-30 + 15 = -15 >>> which is exactly what we started with! So x is 1.

We will be able to put out $36598.19. The solution has been obtained by using the concept of present value of annuity.

The present value of an annuity is the current value of its anticipated future payments at a given rate of return, or discount rate. With higher discount rates, the annuity's present value falls.

We are given that $400,000 are saved for retirement. The account earns  6% interest.

Using present value of annuity,

⇒Present value of annuity due = P + P \([\frac{1-(1+r)^{-(n-1)} }{r}]\)

⇒400,000 = P + P \([\frac{1-(1+0.06)^{-(15-1)} }{0.06}]\)

⇒400,000 = P [1 + 9.295]

⇒P = 400,000/10.9295

⇒P = $36598.19 (approx.)

Hence, we will be able to put out $36598.19.

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Answer:

a number greater than any assignable quantity or countable number (symbol ∞).

Step-by-step explanation:

Answer:

I belive it's Y = 3/2x - 1

Part A) The equation that you can use to solve for x is D) 800 = x(40) + 1.25x(8)

Part B) Based on the above equation, the normal hourly rate is $16.

An equation is an algebraic statement of the equality or equivalence of two or more mathematical expressions.

Mathematical expressions combine variables with numbers and operands without the equal symbol (=).

The normal rate = x

The overtime rate = 1.25x

The normal working hours per week = 40 hours

The number of hours worked for the week = 48 hours

The overtime hours = 8 hours (48 - 40)

The total earnings for the week = $800

800 = x(40) + 1.25x(8)

800 = 40x + 10x

800 = 50x

x = $16

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Answer:

$173.59

Step-by-step explanation:

54.11+51.96+67.52=173.59

Answer:

$170!

Step-by-step explanation:

Add: $54.11 + 51.96= 106.07

Then: 106.07 +  67.52 = $173

Round it!= 173 rounded to the nearest tenth!

Answer: $170

Hope this helps!! -3-ll

Answer:

2/5

Step-by-step explanation:

Answer:

√3√ab

Step-by-step explanation:

Please look in the attachment! Hope this helps! :D

Answer:

56

Step-by-step explanation:

Answer:

45.5

Step-by-step explanation:

5x7=35

3/2x3/2 = 4.5

7-3=4

4/2x3/2=6

35+4.5+6= 45.5

The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

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Gianna is 90 miles far away in 3 hours of driving.

She drove in total of 180 minutes.

The speed can be defined as the rate at which an object covers some distance. Speed can be measured as the distance traveled by a body in a given period of time. The SI unit of speed is m/s.

Given,

Gianna drives 5 miles in 10 minutes

Speed per minute = 5/10 = 0.5 miles/minute

Gianna drove in total for 3 hours

1 hour = 60 minutes

3 hours = 60 × 3 = 180 minutes

Distance Gianna drove in 180 minutes = speed per minute × time

                                                                = 0.5 × 180

                                                                = 90 miles

Hence, Gianna drove 90 miles in 3 hours, 180 minutes is total time she drove.

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Answer:

Rational.

Step-by-step explanation:

Irrational are these.

\(\sqrt{2} , \sqrt{5}\) ,π

Yes, the given number is a rational number.

Rational numbers are numbers that can be written in the form p/q, where p and q are integers and q≠0.

Given that, a number 2.4444...

Repeating decimals are considered rational numbers because they can be represented as a ratio of two integers.

Hence, 2.4444 is a rational number.

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Answer

Explanations:

1a) The standard form of the equation of a circle is expressed using the formula shown below;

where:

(a, b) is the centre of the circle

"r" is the radius of the circle

The radius of the circle will be the distance from the center (3,-7) and the point located on the circle at (-4,1). This can be gotten using the distance formula as shown:

Substitute the radius and the centre (3, -7) into the formula for the equation of a circle as shown:

This given the required equation of the circle

2) In order to check whether the point (7, 6) lies on the circle, we will simply substitute the coordinate point in the resulting equation as shown:

Since the result is not equal to 113, this shows that the point (7,6) is NOT on the circle



The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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The experimental probability of choosing a student who walks to school is given by 0.15625 or 15.625%.

Given data ,

The experimental probability of choosing a student who walks to school can be calculated by dividing the number of students who walk to school by the total number of students in Joe's class.

Number of students who walk to school = 5

Total number of students in the class = 32

Experimental probability = Number of students who walk to school / Total number of students

= 5 / 32

P = 0.15625

Hence , the experimental probability of choosing a student who walks is 0.15625 or 15.625%.

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Answer:

9,2 and 2,9

Step-by-step explanation:

x+y=11

xy=18

Since they are asking for integers you can simply look through and see what integers multiply out to 18 and then check if they add up to 11. The answers for x and y are 9 and 2. but 9 can be for y as well and 2 can be for x.

How to solve it algebraically

18/y=x

x+y=11(insert 18/y for x)

18/y+y=11(factor it)

(y^2+18)/y=11(multiply both sides by y)

y^2+18=11y (subtract both sides by 11y)

y^2-11y+18=0

complete the square

y^2-11y    = -18

(-11/2)^2=121/4 (add in on both sides)

y^2-11y+121/4=49/4

(y-11/2)^2=49/4 (square root both sides)

y-11/2=±7/2

y=11/2±7/2

y=9 or y=2

so

x=9 or x=2

Hope this helps :)

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