Lina invested $7,800 in a mutual fund at a simple interest rate of 4.35%. She earned $1,696.50 in interest. How long (in years) was the money invested?

Answer:

(2i,0) (-2i,0)

(1,0) (-1,0).

Step-by-step explanation:

The graph below shows that there are only 2 real solutions at x = 1 and x = - 1

Expressed as points, these two are (1,0) and (-1,0). However that is not the complete answer. There are 2 complex points.

y = x^4 + 3x^2 - 4

y = (x^2 - 1)(x^2 + 4)

These two binomials can be equated to 0

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

Answer:$88

Step-by-step explanation:

multiply 80 dollars by 10% then add that answer to 80 dollars and that gives you 88 dollars

Answer:

Based on the number of cookies each girl made and if Kristina and Liz made the same number of cookies, then Heather made 4.2 dozen cookies.

Step-by-step explanation:

In order to find the number of cookies that Heather made, you need to set up two equations that represent the number of cookies that Kristina and Liz each made.  Since Kristina made 2.4 dozen less than 6 times as many dozen as Heather, we can represent that with the equation  6c - 2.4.  Since Liz made 1.8 dozen more than 5 times as many dozen as Heather, we can represent that with the equation 5c + 1.8.  We can set both equations equal to each other since Liz and Kristina made the same number, so 6c - 2.4 = 5c + 1.8.  Solving for 'c', which represents how many dozen cookies Heather made, we get 4.2  

Let's assign a variable to represent the number of dozens of cookies Heather made. We'll call this variable \( H \).

According to the problem:
- Kristina made \( 6 \times H - 2.4 \) dozen cookies.
- Liz made \( 5 \times H + 1.8 \) dozen cookies.

We are also given that Kristina and Liz made the same number of cookies, so we can set these two expressions equal to each other to find the value of \( H \):

\[ 6H - 2.4 = 5H + 1.8 \]

Now, we'll solve this equation for \( H \).

Step 1: Isolate the variable \( H \) on one side.
To do this, we'll first subtract \( 5H \) from both sides of the equation:

\[ 6H - 5H - 2.4 = 5H - 5H + 1.8 \]
\[ H - 2.4 = 1.8 \]

Step 2: Now we need to get \( H \) alone, so we'll add \( 2.4 \) to both sides:

\[ H - 2.4 + 2.4 = 1.8 + 2.4 \]
\[ H = 4.2 \]

So, Heather made \( 4.2 \) dozen cookies.

To ensure this is the correct number of dozens Heather made, we can plug this value back into the original expressions for Kristina and Liz's cookies to verify that they made the same amount:

Kristina: \( 6 \times 4.2 - 2.4 = 25.2 - 2.4 = 22.8 \) dozen cookies
Liz: \( 5 \times 4.2 + 1.8 = 21 + 1.8 = 22.8 \) dozen cookies

Both Kristina and Liz made 22.8 dozen cookies, confirming our solution that Heather made 4.2 dozen cookies.

Answer:

no solution

Step-by-step explanation:

1. Substitute the value of  into the equation. y = y + 6 + 4

2. Solve. the system has no solution because y = y.

Answer:

222.7 minutes

Step-by-step explanation:

You multiply 26.2 by 8.5

Answer:9.5 is the anser

Step-by-step explanation:

Answer:

$7. Based on the assumption that both offices paid the same amount for delivery, the difference in the total cost paid is due to the difference in the number of turkey sandwiches ordered, which is 4. The cost of each sandwich is a quarter of this difference in cost.

Step-by-step explanation:

In mathematical working, the explanation above can be written in the form of equations, where we work to solve the value of a variable. In this case, we are interested to find the value of t.

Define variables:

Let the cost of a turkey sandwich be $t while the delivery fee be $d.

Form 2 equations:

Assuming that the sandwich stores charges the same delivery fee for both offices,

4t + d= 33 -----(1)

8t + d= 61 -----(2)

Solve by elimination:

(2) - (1):

4t= 61 - 33

4t= 28

Divide both sides by 4:

t= 7

Thus, each turkey sandwich adds $7 to the cost of the delivery.

To find out how much each turkey sandwich adds to the cost of delivery, we need to determine the cost of delivery in both cases and subtract it from the total price paid by each office.

To find out how much each turkey sandwich adds to the cost of delivery, we need to determine the cost of delivery in both cases and subtract it from the total price paid by each office.

For the first office, they paid $33 for 4 turkey sandwiches. Let's assume the cost of delivery is 'x'. So the equation to represent the total cost is: 4x + 33 = total cost.

Similarly, for the second office, they paid $61 for 8 turkey sandwiches. Let's assume the cost of delivery is 'y'. So the equation to represent the total cost is: 8y + 61 = total cost.

Now we can solve both equations to find the values of 'x' and 'y' which will represent the cost of delivery. Once we have those values, we can calculate how much each turkey sandwich adds to the cost of delivery by dividing the cost of delivery by the number of turkey sandwiches ordered.

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624.75

first get the numeric values simplified

2/13h=0.153h

so 18.20÷0.153=119

meaning he earned 119 dollars every hour

now you can multipy this number with 5.25 to get the answer which is 624.75 dollars

Answer:

I think it would be linear because its really easy?!

Step-by-step explanation:

Answer:

[tex]x=8[/tex]

Step-by-step explanation:

In similar triangles, corresponding sides' ratio are equal.

We can set up a ratio of [tex]\frac{SideAB}{Side XY}=\frac{SideCA}{Side ZX}[/tex]

Hence, we can write (and solve):

[tex]\frac{Side AB}{Side XY}=\frac{Side CA}{SideZX}\\\frac{2}{4}=\frac{x+7}{4x-2}\\2(4x-2)=4(x+7)\\8x-4=4x+28\\8x-4x=28+4\\4x=32\\x=\frac{32}{4}=8[/tex]

So, x = 8

Answer:

y = -3/2 x -15

Step-by-step explanation:

–3x–2y=30

To get the equation is slope intercept form y=mx+b, we need to solve for y

Add 3x to each side

–3x+3x–2y=3x+30

-2y = 3x+30

Divide  by -2

-2y/-2 = 3x/-2 + 30 /-2

y = -3/2 x -15

The slope is -3/2 and the y interceot us -15

Answer:

20 is the answer.

Step-by-step explanation:

Substitute 3 in for x and -2 in for y.

4(3) - (-2 to the third power)

12 - -8 = 12 + 8

The answer is 20

Please mark brainliest as that would really help out :3

The perimeter of the polygon is 110 feet and the area is 360 square feet.

The polygon consists of a rectangle and a right triangle. To find the perimeter, we add the lengths of all sides. The length of the rectangle is 20 feet and its width is 15 feet, so the perimeter of the rectangle is 2 * (20 + 15) = 70 feet. The length of the base of the right triangle is 8 feet and the hypotenuse is 17 feet. The other side of the triangle is the height, which is given as 15 feet. Therefore, the perimeter of the polygon is 70 + 8 + 15 + 17 = 110 feet.

To find the area, we calculate the area of the rectangle and the triangle separately and then add them together. The area of the rectangle is length * width = 20 * 15 = 300 square feet. The area of the right triangle is 0.5 * base * height = 0.5 * 8 * 15 = 60 square feet. Therefore, the area of the polygon is 300 + 60 = 360 square feet.

Answer:

First box: 6x

Second box: 24

Step-by-step explanation:

9(16)=6x

144 = 6x   | divide by 6

144/6 = 6x/6

24 = x

Answer:

X-intercept:(-4/3,0)

Y-intercept:(0,-3/2)

Step-by-step explanation:

The x-intercept is (-4/3, 0) and the y-intercept is (0, -3/2).

To find the x-intercept of the equation 8y= -9x-12, we substitute y with 0 and solve for x. This gives us:

8(0) = -9x-12

0 = -9x-12

-9x = 12

x = -12/9

x = -4/3

Therefore, the x-intercept is (-4/3, 0).

To find the y-intercept, we substitute x with 0 and solve for y. This gives us:

8y = -9(0)-12

8y = -12

y = -12/8

y = -3/2

Therefore, the y-intercept is (0, -3/2).

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Answer:

2 1/2

Step-by-step explanation:

You divide and there are 2 two’s that can go into 5 with a remainder of 1

Answer: 2 1/2

Step-by-step explanation:

divide 5/2

you get 1 as a remainder and two at the top

2 1/2

Answer:

There seems to be a typo error but still this has solution.

Let the number be = x

A positive real number is 6 less than another. Means the second will be [tex](x+6)[/tex]

The sum of the square of the two numbers is 38.

[tex]x^{2} +(x+6)^{2} =38[/tex]  

=> [tex]x^{2} +36+12x+x^{2} =38[/tex]

=> [tex]2x^{2}+12x+36 =38[/tex]

=> [tex]2x^{2}+12x=2[/tex]

=> [tex]2x^{2}+12x-2=0[/tex]

Taking out 2 common;

=> [tex]x^{2}+6x-1=0[/tex]

Solving this quadratic equation, we get;

[tex]x=-3+\sqrt{10}[/tex] and [tex]x=-3-\sqrt{10}[/tex]

As positive number is needed, we have [tex]-3+\sqrt{10}[/tex]

or x = [tex]\sqrt{10}-3[/tex]

x = 0.162277

And other number is 6.162277.

Given:

Question:

Find out the numbers.

Problem-solving:

Let us use [tex]\boxed{ \ x \ }[/tex] to represent the positive real number.

This positive real number is 6 less than another. The other number is [tex]\boxed{ \ x + 6 \ }[/tex]

The sum of the square of the two numbers is 38, i.e., [tex]\boxed{ \ x^2 + (x + 6)^2 = 38 \ }[/tex]

Let us work on expanding it.

[tex]\boxed{ \ x^2 + (x + 6)^2 = 38 \ }[/tex]

Recall that [tex]\boxed{ \ (a + b)^2 = a^2 + 2ab + b^2 \ }[/tex]

[tex]\boxed{ \ x^2 + x^2 + 12x + 36 = 38 \ }[/tex]

[tex]\boxed{ \ 2x^2 + 12x + 36 - 38 = 0 \ }[/tex]

[tex]\boxed{ \ 2x^2 + 12x - 2 = 0 \ }[/tex]

Both sides are divided by two.

[tex]\boxed{ \ x^2 + 6x - 1 = 0 \ }[/tex]

Let us solve the equation by using the quadratic formula.

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

[tex]\boxed{ \ x = \frac{-6 \pm \sqrt{6^2 - 4(1)(-1)}}{2(1)} \ }[/tex]

[tex]\boxed{ \ x = \frac{-6 \pm \sqrt{36 + 4}}{2} \ }[/tex]

[tex]\boxed{ \ x = \frac{-6 \pm \sqrt{40}}{2} \ }[/tex]

[tex]\boxed{ \ x = \frac{-6 \pm 2\sqrt{10}}{2} \ }[/tex]

[tex]\boxed{ \ x = \frac{-6}{2} \pm \frac{2\sqrt{10}}{2} \ }[/tex]

[tex]\boxed{ \ x = -3 \pm \sqrt{10} \ }[/tex]

[tex]\boxed{ \ x_1 = -3 + \sqrt{10} \ . \ . \ . \ x_1 > 10 \ }[/tex] this is fulfilled.

[tex]\boxed{ \ x_2 = -3 - \sqrt{10} \ . \ . \ . \ x_2 < 10 \ }[/tex]

[tex]\boxed{ \sqrt {10} = 3.162 \ }[/tex]

Notes:

[tex]\boxed{ \ ax^2 + bx + c = 0, \ \ \ \ \  a \neq 0 \ }[/tex] is a quadratic equation in standard form.

Methods of solving quadratic equations include:

Keywords: a positive real number is 6, less than another, if the sum of the square, 38, then finds, quadratic equation, methods, factoring, the zero product property, the square root, completing, the quadratic formula

Answer:

32 jelly beans were in the bag

Step-by-step explanation:

We know 75% is 3/4 and that she ate 24, so divide 24 by 3 then multiply it by 4:

24/3= 8

8 x 4 = 32

Final answer:

By dividing the number of jelly beans Jayla ate (24) by 75% and scaling it up to 100%, we determine that the bag initially contained 32 jelly beans.

Explanation:

Jayla ate 75% of the jelly beans in the bag, which equaled 24 jelly beans. To find out how many jelly beans were in the bag originally, we need to find what amount corresponds to 100% if 75% is 24 jelly beans. We perform this calculation by dividing the amount eaten (24 jelly beans) by the percentage she ate (75%), and then multiplying by 100% to scale it up to the total amount.

The calculation goes as follows: (24 / 0.75) = 32. This means there were originally 32 jelly beans in the bag before Jayla ate any.

The equation of line passes through the point (1, 2) will be;

⇒ y = 7x - 5

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (1, 2).

And, The slope is,

⇒ m = 7

Now,

Since, The equation of line passes through the point (1, 2).

And, Slope of the line is,

⇒ m = 7

Thus, The equation of line with slope 7 is,

⇒ y - 2 = 7 (x - 1)

⇒ y - 2 = 7x - 7

⇒ y = 7x - 7 + 2

⇒ y = 7x - 5

Therefore, The equation of line passes through the point (1, 2) will be;

⇒ y = 7x - 5

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Answer:

A.) Linear

B.) Continuous function

Step-by-step explanation:

Its linear because it is not all over the place and continuous because it does not stop it will keep going because it is a ray  

Answer: The graph is A) Linear

The graph represents a B) Continuous function.

Step-by-step explanation:

Since we have given a figure which depicts the total cost of purchasing blueberries at Blue Basket Farm at certain price per pound.

Since the graph is linear .

As we can write it as :

At x = 1, y = 4

At x = 2 , y = 8

At x = 3, y = 12

So, it will become

[tex]y=kx[/tex], where k = 4 units.

So, it is linear graph.

The graph is continuous function as it does not break any where and it is unbroken line.

hence,  the graph is A) Linear

The graph represents a B) Continuous function.

Answer:

B(m)=A(m)-D(m)

B(m)=176m

Step-by-step explanation:

we are given

Walking on his own, the distance, D, in feet, that Roberto can cover in M, minutes is given by the function

D(m)=264m

When he walks on the moving sidewalk at the airport, the distance, A, in feet, that he can cover in m m minutes is given by the function

A(m)=440m

B is the distance, in feet, that Roberto would travel on the moving sidewalk in  m minutes if he were standing still

moving sidewalk distance = standstill distance + walking distance

A(m)=D(m)+B(m)

so, we get

B(m)=A(m)-D(m)

now, we can plug values

B(m)=440m-264m

B(m)=176m

Final answer:

To find the distance B(m) that Roberto would travel on a moving sidewalk in m minutes if he stood still, one must subtract the function for walking alone D(m) from the function for walking on a moving sidewalk A(m). Thus, B(m) is calculated as B(m) = A(m) - D(m), resulting in B(m) = 176m.

Explanation:

The student needs to find the formula for the distance B(m) that Roberto would travel on the moving sidewalk in m minutes if he stands still, in terms of the functions D(m) and A(m). The function D(m) = 264m represents the distance Roberto covers by walking on his own in m minutes, and A(m) = 440m represents the distance covered while walking on a moving sidewalk.

Since A(m) represents the combined effect of walking and the moving sidewalk, and D(m) represents just walking, the difference A(m) - D(m) will give us the contribution of the moving sidewalk alone, while Roberto stands still. Thus, the formula for B(m) is:

B(m) = A(m) - D(m)

B(m) = 440m - 264m

B(m) = 176m

The formula B(m) indicates the distance Roberto would cover on the moving sidewalk if he did not walk and just stood still.

Final answer:

The bases of the triangles have a ratio of 3:4.

Explanation:

The areas of two triangles with equal altitudes have a ratio of 3:4. We can set up the equation:

A₁/A₂ = 3/4

Let's denote the bases of the triangles as b₁ and b₂. The formula for the area of a triangle is A = (1/2) * base * height. Since the altitudes are equal, we can write:

A₁ = (1/2) * b₁ * h

A₂ = (1/2) * b₂ * h

Substituting these equations into the ratio, we get:

(1/2) * b₁ * h / (1/2) * b₂ * h = 3/4

Cancelling out the height and simplifying, we find:

b₁ / b₂ = 3/4

Therefore, the bases of the triangles have a ratio of 3:4.

Answer:

[tex]\pi,\ \dfrac{7\pi}{6},\ \dfrac{3\pi}{4},\ \dfrac{4\pi}{3},\ \dfrac{3\pi}{2},\ \dfrac{5\pi}{3},\ \dfrac{7\pi}{4},\ 2\pi.[/tex]

Step-by-step explanation:

Convert each angle in degree measure:

[tex]\dfrac{3\pi}{4}=135^{\circ},\\ \\\pi=180^{\circ},\\ \\\dfrac{7\pi}{6}=210^{\circ},\\ \\\dfrac{5\pi}{3}=300^{\circ},\\ \\\dfrac{7\pi}{4}=315^{\circ},\\ \\\dfrac{4\pi}{3}=240^{\circ},\\ \\\dfrac{3\pi}{2}=270^{\circ},\\ \\2\pi=360^{\circ}.[/tex]

Then

[tex]\cos \dfrac{3\pi}{4}=\cos 135^{\circ}=-\dfrac{\sqrt{2}}{2},\\ \\\cos \pi=\cos 180^{\circ}=-1,\\ \\\cos \dfrac{7\pi}{6}=\cos 210^{\circ}=-\dfrac{\sqrt{3}}{2},\\ \\\cos \dfrac{5\pi}{3}=\cos 300^{\circ}=\dfrac{1}{2},\\ \\\cos \dfrac{7\pi}{4}=\cos 315^{\circ}=\dfrac{\sqrt{2}}{2},\\ \\\cos \dfrac{4\pi}{3}=\cos 240^{\circ}=-\dfrac{1}{2},\\ \\\cos \dfrac{3\pi}{2}=\cos 270^{\circ}=0,\\ \\\cos 2\pi=\cos 360^{\circ}=1.[/tex]

Therefore, the angles in increasing order of their cosines are

[tex]\pi,\ \dfrac{7\pi}{6},\ \dfrac{3\pi}{4},\ \dfrac{4\pi}{3},\ \dfrac{3\pi}{2},\ \dfrac{5\pi}{3},\ \dfrac{7\pi}{4},\ 2\pi.[/tex]

Answer:

Step-by-step explanation:

By increasing her speed from 55 mph to 60 mph, Rachel can save approximately 1.5 hours on her 1034-mile trip from New York to Dayton, Florida.

The subject of this question is Mathematics, specifically dealing with the concept of speed, distance, and time. To answer your question, we need to calculate how long the trip would take at each speed and then find the difference.

First, we calculate the time taken when the average speed is 55 mph. The formula to calculate time is distance divided by speed. So, 1034 miles divided by 55 mph equals about 18.8 hours.

Next, we do the same for 60 mph. 1034 miles divided by 60 mph equals about 17.2 hours.

The difference between the two times will give the time saved by increasing the speed to 60 mph from 55 mph. So, 18.8 hours - 17.2 hours equals 1.6 hours, which is approximately 1.5 hours when rounded to the nearest half hour.

Therefore, Rachel can save about 1.5 hours driving at an average speed of 60 mph compared to 55 mph over the distance of 1034 miles.

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Answer:

The answer is 1.2

Step-by-step explanation:

Answer:

1.2

Step-by-step explanation:

You can use a calculator... Or you can ask google this, "What is 0.324 divided by 0.27?"

0.324 divided by 0.27 is 1.2

[tex]f(x)=x^2-2x-8;\ g(x)=\dfrac{1}{4}x-1\\\\f(x)=g(x)\iff x^2-2x-8=\dfrac{1}{4}x-1\qquad\text{multiply both sides by 4}\\\\4x^2-8x-32=x-4\qquad\text{subtract x from both sides}\\\\4x^2-9x-32=-4\qquad\text{add 4 to both sides}\\\\4x^2-9x-28=0\\\\4x^2-16x+7x-28=0\\\\4x(x-4)+7(x-4)=0\\\\(x-4)(4x+7)=0\iff x-4=0\ \vee\ 4x+7=0\\\\x=4\ \vee\ 4x=-7\\\\\boxed{x=4\ \vee\ x=-\dfrac{7}{4}}[/tex]

Answer:

3/2

Step-by-step explanation:

To find the rate of change

f(x2) - f(x1)

------------------ = rate of change

x2-x1

Looking at the graph

f(15) = 12

f(9) = 3

Substituting this into the equation

12-3

---------

15-9

9

------

6

3/2

The rate of change is 3/2

The average rate of change of a function from x = 9 to x = 15 is calculated by the slope of the secant line, which is (f(15) - f(9)) / (15 - 9). Specific function values are needed to perform this calculation.

To calculate the function's average rate of change from x = 9 to x = 15, you can use the formula for the slope of the secant line between these two points on the graph of the function. This is given by the difference in the function values at these points divided by the difference in x-values:

Average Rate of Change = (f(15) - f(9)) / (15 - 9).

You would need the specific function values f(15) and f(9) in order to calculate this. If the function is linear, like the one represented by f(x) = 7x, you would substitute these x-values into the function to get f(15) = 7*15 and f(9) = 7*9, and then perform the calculation. However, without the actual function values, we cannot complete this calculation.

Answer:

y = 2x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

To find m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (1, 1) and (x₂, y₂ ) = (5, 9)

m = [tex]\frac{9-1}{5-1}[/tex] = [tex]\frac{8}{4}[/tex] = 2

y = 2x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

using (1, 1 ), then

1 = 2 + c ⇒ c = 1 - 2 = - 1

y = 2x - 1 ← equation of line

Answer:

The graph is shown below.

Step-by-step explanation:

Let x be the weight of fruit in pounds and P(x) be the price of fruit.

For fruit weighing greater than or equal to 0.01 pounds and less than or equal to 0.5 pounds, the amount charged is $2.00.

P(x) = $2.00 for 0.01 ≤ x ≤ 0.5

For fruit weighing greater than 0.5 pounds and less than or equal to 1.0 pounds, the amount charged is $3.50.

P(x) = $3.50 for 0.5 < x ≤ 1.0

For fruit weighing greater than 1.0 pounds and less than or equal to 1.5 pounds, the amount charged is $5.00.

P(x) = $5.00 for 1.0 < x ≤ 1.5

For fruit weighing greater than 1.5 pounds and less than or equal to 2.0 pounds, the amount charged is $6.50.

P(x) = $6.50 for 1.5 < x ≤ 2.0

For fruit weighing greater than 2.0 pounds and less than or equal to 2.5 pounds, the amount charged is $8.00.

P(x) = $8.00 for 2.0 < x ≤ 2.5

It is a piecewise floor function. We have open circle on left side of each floor except first floor because the sign of inequality in all other is < .

We have closed circle on right side of each floor because the sign of inequality is ≤ .

The graph is shown below.

Anna earns $8.50 per hour babysitting. For 3, 3.5 and 4 hours of work, she will earn $25.50, $29.75, and $34.00 respectively.

Anna earns $8.50 per hour for babysitting. To calculate her earnings, we simply need to multiply the number of hours she worked by her hourly rate.

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