If Julie needs 3 and 1/4 cups of oatmeal how many 1/4 cups of oatmeal will she use

q=4,-1

you need to isolate q

The solution set of the equation is {-4, 2}

Given expression:

[tex]\frac{8}{q} +2=\frac{q+4}{q-1}[/tex]

Solve for q: simplify

[tex]\frac{8}{q} +2=\frac{q+4}{q-1}\\\frac{8+2q}{q}=\frac{q+4}{q-1}\\(8+2q)(q-1)=(q(q+4)\\8q-8+2q^{2} -2q=q^{2} +4q\\2q^{2} +6q-8 =q^{2}+4q\\q^{2} +2q-8=0[/tex]

Factorize the quadratic equation to solve q

[tex]q^{2} +4q-2q-8=0\\q(q+4)-2(q+4)=0\\(q+4)=0, (q-2)=0\\q= -4, 2[/tex]

Therefore, The solution set of the equation is {-4, 2}

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After all the deductions and exemptions, the total taxable​ income of Homer Simpson is $46,700.

Given that, income of Homer and his wife = $60000 and interest earned = $1200.

In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.

Adding this to total income, we have total taxable amount = 60000+1200 = $61200

Now, investment in tax deferred savings plan = $2500

This amount will be subtracted from total taxable income, so amount becomes = 61200-2500 = $58700

Subtract the exemptions and deductions = $12000

That is, amount becomes = 58700-12000 = $46700

Hence, the net taxable income is $46,700.

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Homer Simpson's taxable income is determined by subtracting his tax-deferred savings and total deductions from his total income. His taxable income comes to $46,700. The percentage of tax he pays depends on the U.S income tax bracket he falls under.

To calculate Homer Simpson's taxable income, we need to consider their total income, deductions, and investments. Homer's total income is the sum of his salary, $60,000 and the interest earned, $1200. So, the total income equals $60,000 + $1200 = $61,200.

Next, we subtract the total deductions which include the tax-deferred savings plan and the total deductions and exemptions they have, from the total income. Thus, the taxable income equals $61,200 - $2,500 (savings plan) - $12,000 (deductions and exemptions) = $46,700.

The U.S income tax code is based on a progressive system, so knowing the taxable income can help determine the income tax bracket Homer falls under. Given the figures, Homer's income is in the bracket that is taxed at 22% as per the 2020 basic tax tables from the Internal Revenue Service.  However, it is important to take into consideration any changes in tax laws or additional deductions they might have.

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Answer:

A   $4025

B  $2415

C  $1610

Step-by-step explanation:

Part A

I=PRT

I = 23000* .035 * 5

 = 4025

You will pay $4025

Part B

I =PRT

= 23000 *.035 * 3

= 2415

You will pay $2415

Part C

Take the amount from Part A and subtract The amount from Part B and that is the amount you will save.

4025-2415=1610

A   $4025

B  $2415

C  $1610

Step-by-step explanation:

Part A

I=PRT

I = 23000* .035 * 5

= 4025

You will pay $4025

Part B

I =PRT

= 23000 *.035 * 3

= 2415

You will pay $2415

Part C

Take the amount from Part A and subtract The amount from Part B and that is the amount you will save.

4025-2415=1610

The rocket splashes down after 43 seconds.

The rocket peaks at 2400. meters above sea-level.

Step 1

We realise that the rocket will hit the ground when our function [tex]h(t)=0[/tex] , i.e [tex]-4.9t^2+202t+318=0.[/tex]

Step 2

Use the quadratic formula to solve for the time. For the general quadratic equation [tex]at^2+bt+c=0[/tex], the general solution to the equation is

[tex]t=\frac{-b\pm\sqrt{b^2-4ac}}{2a} .[/tex]

In our case, the quadratic equation [tex]h(t)=-4.9t^2+202t+318=0[/tex] has a solution

[tex]t=\frac{-202\pm\sqrt{202^2-4((-4.9)(318))}}{2(-4.9)} \\t=-1.52,t=42.74.[/tex]

Step 3

In this step we pick the value of [tex]t[/tex] that makes physical sense. Since the NASA team launced the rocket at [tex]t=0[/tex], the rocket reaches the bottom when [tex]t=42.74[/tex]. This can be rounded up to [tex]43[/tex] seconds.

Step 1

The first step is to realist that since the coefficient of the quadratic term is negative, the graph of this function will face downwards. From this we can gather that the maximum value of this function occurs at the vertex.

Step 2

In this step we calculate the t coordinate of the of the vertex of this function. For any quadratic equation [tex]h(t)=at^2+bt+c[/tex] , the vertex occurs when ,

[tex]t=-\frac{b}{2a}.[/tex]

For the equation [tex]h(t)=-4.9t^2+202t+318[/tex] , the vertex occurs when ,

[tex]t=-\frac{202}{2(-4.9)}=20.61.[/tex]

Step 3

We substitute the value of [tex]t[/tex] from step 2 above into [tex]h(t)[/tex] to get the maximum value of this function.  This calculation is shown below,

[tex]h(20.61)=-4.9(20.61)^2+202(20.61)+318=2399.84m.[/tex]

This can be rounded up to 2400m.

Answer: 345.9 ounces

I'm really sorry that I took a long time. I got carried away. Hopefully my work was correct though.

A= about 354 square feet~ (rounded)

The stage can be split into two shapes. The first is a trapezoid and the formula to find the area for it would be A=(b₁+b₂)/2 and then multiple by the height. b₁ would be 17 and b₂ is 20 and the height is 13. 17+20 is 37. 37/2 is 18.5. 18.5 times 13 is 240.5. Area of the trapezoid is 240.5 square feet. Then we need to find the area of the semicircle. The formula is A=(πr²)2. r is the radius which is half of the diameter. The diameter is 17 so the radius is 8.5. π is about 3.14 if you don't have a calculator. 8.5 squared is 72.25. 72.25 times 3.14 is 226.865. 226.865/2 is 113.4325. The area of the half circle is 113.4325. Just add these two areas to get 353.9325. So I think the area is pretty much 353.9325 but might be slightly different because some values I said were rounded. Either way the answer should be similar.

I forgot you said you needed help fast and got carried away. Sorry if I wasn't fast enough and hopefully I did my math correctly.

Answer:

The rate of change of water in the pool is 400 gallons / hour

Step-by-step explanation:

We are given

At 6:00 AM:

there were 400 gallons of water in the pool

so,

[tex]N_1=400[/tex]

At 11:00 AM:

there were 2400 gallons of water in the pool

so,

[tex]N_2=2400[/tex]

now, we can find time between

t=11-6=5 hours

now, we can use formula

rate of change of water in pool is

=( change in water quantity)/( total time)

so, we get

[tex]=\frac{N_2-N_1}{t}[/tex]

now, we can plug values

[tex]=\frac{2400-400}{5}[/tex]

[tex]=\frac{2000}{5}[/tex]

[tex]=400[/tex]

So,

The rate of change of water in the pool is 400 gallons / hour

Answer:

  y = 4x^2 -31x -8

Step-by-step explanation:

The roots tell you that (x +1/4) and (x -8) will be factors. We can eliminate the fraction by multiplying that factor by 4. Then our polynomial with integer coefficients is ...

  (4x +1)(x -8) = 4x^2 -31x -8

As an equation, this could be ...

  y = 4x^2 -31x -8

Answer:

(A)

[tex]C_n=3+2n[/tex]

(B)

[tex]C_1_0=23[/tex]

Step-by-step explanation:

(A)

we are given

[tex]C_n_+_1=C_n+2[/tex]

[tex]C_1=5[/tex]

Firstly, we will find few terms

[tex]C_2=C_1+2[/tex]

[tex]C_2=5+2[/tex]

[tex]C_2=7[/tex]

[tex]C_3=C_2+2[/tex]

[tex]C_3=7+2[/tex]

[tex]C_3=9[/tex]

[tex]C_4=C_3+2[/tex]

[tex]C_4=9+2[/tex]

[tex]C_4=11[/tex]

so, we will get terms as

5, 7 , 9 , 11

we can see that this is arithematic sequence

First term =5

common difference =d=7-5=2

now, we can use nth term formula

[tex]C_n=C_1+(n-1)d[/tex]

now, we can plug values

[tex]C_n=5+2(n-1)[/tex]

[tex]C_n=5+2n-2[/tex]

[tex]C_n=3+2n[/tex]

(B)

we can plug n=10

[tex]C_1_0=3+2\times 10[/tex]

[tex]C_1_0=23[/tex]

Answer:

c

Step-by-step explanation:

Answer:

the maximum height of the ball= 256 feet

7 seconds

Step-by-step explanation:

The quadratic function h ( t ) = − 16t^2 + 96t + 112 models the ball's height about the ground, h ( t ) , in feet, t seconds after it was thrown.

a= -16 , b= 96  and c= 112

To find maximum height , we find vertex

[tex]x= \frac{-b}{2a}=\frac{-96}{2(-16)}= 3[/tex]

Now plug in 3 for 't' in h(t)

[tex]h(t) = -16t^2 + 96t + 112[/tex]

[tex]h(t) = -16(3)^2 + 96(3)+ 112=256[/tex]

Hence vertex is (3, 256)

the maximum height of the ball= 256 feet

(b) when the ball hits the ground then height becomes 0

so we plug in 0 for h(t)  and solve for t

[tex]0 = -16t^2 + 96t + 112[/tex]

Apply quadratic formula

[tex]t=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]

Plug in all the values a= -16 , b= 96  and c= 112

[tex]t=\frac{-96+-\sqrt{96^2-4(-16)(112)}}{2(-16)}[/tex]

t= -1  and t= 7

time cannot be negative. So it will take 7 second to hit the ground.

The maximum height of the ball is 160 feet and it takes 4 seconds for the ball to hit the ground.

The quadratic function h(t) = -16t^2 + 96t + 112 represents the height of the ball above the ground (h(t)) in feet after t seconds since it was thrown. To find the maximum height of the ball, we need to determine the vertex of the quadratic function. The vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by the formula x = -b/2a, where x represents the time and a and b are coefficients in the quadratic equation.

In this case, the coefficient a = -16 and b = 96. Plugging these values into the formula, we get t = -96/(2 * -16) = 3 seconds. Substituting this value into the quadratic function, we find h(t) = -16(3^2) + 96(3) + 112 = 160 feet. Therefore, the maximum height of the ball is 160 feet.

To determine how many seconds it takes until the ball hits the ground, we need to find the time when h(t) = 0. Setting the quadratic equation equal to zero and solving for t, we get -16t^2 + 96t + 112 = 0. This equation can be solved using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula.

Applying the quadratic formula, we have t = (-b ± √(b^2 - 4ac)) / 2a. Plugging in the values of a = -16, b = 96, and c = 112, we get t = (-96 ± √(96^2 - 4(-16)(112))) / (2 * -16). Evaluating this expression, we get two solutions: t = 4 and t = 7. Therefore, the ball takes 4 seconds to reach the ground after being thrown.

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The total cost of the meal is $8. A 15% tip on this amount is $1.20.

The total cost of the meal is the cost of the cheeseburger ($5.50) plus the cost of the milkshake ($2.50), giving a total of $8. To calculate a 15% tip, we multiply the total cost by 0.15. So, JJ should leave a tip of $8 * 0.15 = $1.20.

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Answer:

Step-by-step explanation:

Let "Hannah" = h, and her sister = s

h = 2s

h +  s ≤ 18

Plug in 2s for h in the second equation.

(2s) + s ≤ 18

Simplify

2s + s ≤ 18

3s ≤ 18

Isolate the variable (s). Divide 3 from both sides

(3s)/3 ≤ (18)/3

s ≤ 18/3

s ≤ 6

2) The oldest Hannah's sister can be is 6 years

~

Answer:

12 years old

Step-by-step explanation:

1) 2x+x=18

2) Now solve 2x+x=18

Add alike terms

3x=18

Now divide both sides by 3 (3x/3 and 18/3)

x=6

So Hannah is 6 years old. Her sister must be 12.

Answer: B) Adjacent interior angle

As the name implies, the angle is inside the triangle and it is adjacent (ie next to) the exterior angle. Contrast this with a remote interior angle, which is also inside the triangle, but it is not adjacent to the exterior angle in question. Alternate interior angles won't apply here because we don't have a set of parallel lines with a transversal cut.

Answer:

In 30 minutes:

The minute hand moves a distance of 25.13 inches

In 20 minutes:

The minute hand moves a distance of 16.76 inches

Step-by-step explanation:

When 60 minutes are completed, the minute hand of the relog makes a complete revolution. The distance s that the minute hand travels when making a complete revolution is:

[tex]s = 2\pi r[/tex] Where r is the radius of the circumference, and in this case, the radius of the minute hand.

So:

[tex]s = 16 \pi[/tex]

s = 50.27 inches.

In 30 minutes (which is half of 60) the minute hand covers only half a revolution. Then the distance traveled in 30 minutes is [tex]\frac{1}{2}(s) = 25.13[/tex] inches

In 20 minutes (which is one third of 60) the minute hand only travels a third of a complete revolution. Then the distance traveled in 20 minutes is [tex]\frac{1}{3}(s) = 16.76[/tex] inches

We calculate the distance traveled by the minute hand of a clock by using the arc length formula from geometry. Using the length of the hand as the radius and the angle covered as a fraction of 360 degrees (converted into radians), we can determine the distances for 30 and 20 minutes as 8π inches and 16/3 π inches respectively.

The subject of our question involves the calculation of arc lengths (distances) moved by a clock hand, an aspect of geometry. We'll be treating the minute hand of a clock as a line segment that sweeps out a circular path. The arc length formula will be utilized here, which is given by the equation L = rθ, where L is the arc length, r is the length of the minute hand (as the radius), and θ is the angle covered by the minute hand.

In a span of a whole hour or 60 minutes, the minute hand completes a full 360° circle. So, for 30 minutes, it covers half the circle which equates to 180°. This degree measure needs to be converted to radians because our formula uses radian measure. 180° equals π radians.

With r = 8 inches and θ = π, we substitute these values into our formula to get L = 8π inches for 30 minutes.

The same concept applies for 20 minutes. In this case, the hand covers a third of the circle which is (360/3)=120°, this is (2/3)π in radian. Substituting r = 8 inches and θ = (2/3)π into our formula, we get L = 16/3 π inches for 20 minutes.

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Answer:

option-C

Step-by-step explanation:

We are given

graphs -- I , V , VI have same starting point

it means that it has same initial values

Suppose, we are given exponential function as

[tex]f(x)=a(b)^x[/tex]

Here , 'a' is initial value

we can see that initial value of graph-I is 30

so, all other graphs must also have 30 initial value

so, graphs

[tex]e,\delta , \phi[/tex]  have same initial value =30

so, option-C.......Answer

Answer:

8 sets of twenty sandwiches.

Step-by-step explanation:

first you find the answer to 3 x __ = __ lets make the answer 24. That makes the other blank 8. Now subtract 24 from 184 and you should get 160. Divide 160 by 20 and you'll get how many set the customer ordered of twenty sandwiches. Multiply by twenty and you will get the whole amount they ordered.

Answer:

Caterer males 3 extra sandwiches for every 20 sandwiches. That means Caterer makes 23 sandwiches for every 20 ordered sandwiches. Therefore is ratio form we can write it,

23:20

Now we need to check if Caterer makes total 184 sandwiches for a customer then ordered sandwiches will be,

[tex]23:20=184:x[/tex]

Where x represents the number of sandwiches ordered.

[tex]23:20=184:x\\\frac{23}{20}=\frac{184}{x}[/tex]

Now we need to solve it for x;

[tex]\frac{23}{20}=\frac{184}{x}\\x=\frac{184X20}{23}\\ x=160[/tex]

therefore ordered Sandwiches are 160.

Step-by-step explanation:

Answer:

25 ounces.

Step-by-step explanation:

We have been given that a metal alloy is made by mixing 12 ounce of metal C with 13 ounce of metal D.

To find the total weight of the alloy we will add the weight of metal C and weight of metal D.

[tex]\text{The total weight of the alloy}=\text{Weight of metal C + Weight of metal D}[/tex]

[tex]\text{The total weight of the alloy}=12\text{ ounce}+13\text{ ounce}[/tex]

[tex]\text{The total weight of the alloy}=25\text{ ounce}[/tex]

Therefore, the total weight of alloy is 25 ounces.

Answer:

5/6 is your correct answer..

Step-by-step explanation:

Answer:

D) 120

Step-by-step explanation:

720- 135-115-110-140-100=120

Answer:

49

Step-by-step explanation:

7^x

If x=2

7^2

49

Answer:

1/5

Step-by-step explanation:

We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices  A(−3, 4), B(−1, 12) and C(4, −2) to the image triangle A'B'C' with vertices A' (−0.6, 0.8), B' (−0.2, 2.4) and C' (0.8, −0.4).

Center of dilation is at the origin.

To find the scale factor, we will divide the corresponding vertices of the image and pre-image.

A (−3, 4) ---> A' (−0.6, 0.8) = [tex]\frac{-0.6}{-3} , \frac{0.8}{4}=(\frac{1}{5} , \frac{1}{5})[/tex]

B(−1, 12) ---> B' (−0.2, 2.4) = [tex]\frac{-0.2}{-1} , \frac{2.4}{12} = (\frac{1}{5} , \frac{1}{5})[/tex]

C(4, −2) --->  C' (0.8, −0.4) = [tex]\frac{0.8}{4} , \frac{-0.4}{-2} = (\frac{1}{5} , \frac{1}{5})[/tex]

Therefore, the scale factor of the dilation is 1/5.

Answer:

AC is 96 units

Answer:

B) 0.85

Step-by-step explanation:

By definition, complementary angles add to 90 degrees.

The given angle 58 degrees is complementary to 90-58 = 32 degrees. The two angles 58 and 32 add to 90.

Therefore, cos(32) = 0.848 = 0.85

The complementary angle to 58° is 42° and the cosine value of 42° is 0.74.

Given: angle 58°.

let the angle complementary to 58° be x.

By the definition of complementary angles, we can write:

⇒ x + 58° = 90°

⇒ x = 90° - 58°

⇒ x = 42°

Therefore, the angle complementary to 58° is 42°.

Now, we have to find the cosine value of 42°.

⇒ cos (42°) = 0.74

Therefore, the cosine value of 42° that is the complementary angle to 58° is 0.74.

Hence, the best answer will be option (A).

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Answer:

The zeros of a graph form the factors of the function. When we multiply the factors out and add the exponents up in the final function, we have the highest exponent known as the degree.

Step-by-step explanation:

A polynomial graph has several features we look for to determine the equations.

Answer:

Need the graph for final answer. Use the values of the graph to substitute into the slope formula and simplify.

Step-by-step explanation:

The average rate of change is the amount over an interval the outputs change in a ratio to the input change. In a linear function, this is constant and called slope. In all other function, it is called the average rate of change because the rate of change varies over the interval. We use the same formula for the average rate of change as we do slope. First we need both the input and output values of the function over the interval.

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

Substitute the values for your function into the slope formula and simplify.

Answer:

is there a graph

Step-by-step explanation:

Answer: c-5 cm, 2 cm, 2 cm.

Final answer:

40 child tickets and 95 adult tickets were sold.

Explanation:

Let's assume the number of child tickets sold is x.

According to the problem, the number of adult tickets sold is 15 more than twice the number of child tickets. So the number of adult tickets sold is 2x + 15.

The total income from ticket sales is $1,340. The income from child tickets is $5 times the number of child tickets and the income from adult tickets is $12 times the number of adult tickets.

Therefore, we can express the total income as the sum of the income from child tickets and adult tickets:

$5x + $12(2x + 15) = $1,340

Simplifying the equation:

$5x + $24x + $180 = $1,340

$29x = $1,340 - $180

$29x = $1,160

Dividing both sides by 29:

x = $1,160/$29

x = 40

So, the number of child tickets sold is 40, and the number of adult tickets sold is 2x + 15 = 2(40) + 15 = 80 + 15 = 95.

Therefore, 40 child tickets and 95 adult tickets were sold.