Write a linear function f with the values f(2)=4 and f(−7)=9. A function is f(x)=

Answer:

y=-3x+5

Step-by-step explanation:

y-y1=m(x-x1)

y-5=-3(x-0)

y-5=-3(x)

y-5=-3x

y=-3x+5

Answer:

Rock phosphate, insoluble phosphates in bone deposits, and dissolved phosphates available to plants

Answer:

As π/7 is in first quadrant and all trig functions are positive there,

so, cos pi/7 is positive.

Step-by-step explanation:

Please check the attached figure a.

As π/7 is in first quadrant and all trig functions are positive there,

so, cos pi/7 is positive.

Keywords: trigonometric function, cos π

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Answer:

Triangle ABC is dilated is dilated with a scale factor of ⅓ with the center of dilation at the point (3,4) resulting in triangle DEC

Step-by-step explanation:

From triangle ABC,

|AC|=3 units

From triangle DEC,

|EC|= 1 unit

Since the two triangles are similar, we can find the scale factor using the ratio of the image length over the corresponding object length.

[tex]scale \: factor = \frac{ |EC| }{ |AC| } [/tex]

Let us substitute the values to get:

[tex]scale \: factor = \frac{1}{3 } [/tex]

When we trace through AD and EB, they will meet at C. Hence C(3,4) is the center of dilation.

Answer:

The answer is 5 years ago.

Step-by-step explanation:

5 years ago the age of the mother was 5 times the daughter's age.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Suppose the current age of the daughter is D while the mother is M.

As per the given, The daughter is 36 years younger than her mother.

D = M - 36

And , M = 50

D = 50 - 36 = 14

Let's say x year age the mother was 5 times the daughter's age.

(M - x) = 5(D - x)

(50 - x) = 5(14 - x)

50 - x = 70 - 5x

-x + 5x = 70 - 50

4x = 20

x = 5

Hence "5 years ago the age of the mother was 5 times the daughter's age".

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Final answer:

C paid Rs. 127,050 for the car.

Explanation:

To find out what C paid for the car, we need to consider the gains made by A and B. A bought the car for Rs.100,000 and spent Rs. 10,000 on repairs. This means A's total cost is Rs. 110,000. A then sells the car to B at a gain of 10%, which means B buys the car for 110% of Rs. 110,000, or Rs. 121,000.

Now, B sells the car to C at a gain of 5%. To find out what C paid, we need to calculate 105% of Rs. 121,000, which gives us Rs. 127,050. Therefore, C paid Rs. 127,050 for the car.

Answer:

This number line

shows the numbers

between 95 and 101.

Step-by-step explanation:

96, 97, 98, 99, and 100 all fall between 95 and 101.

97, 98, 99, and 100 are all greater than 96, so option 2 is incorrect.

96 is less than 97, so option 3 is incorrect.

Answer:

Step-by-step explanation:

P = Q - 7.......Q is the quantity of baskets....and he makes 15 baskets....so sub in 15 for Q and solve for P, the price

P = 15 - 7

P = 8 <====

Answer:

D.$8

Step-by-step explanation:

Firstly, you replace Q with 15. Then you solve the equation.

P=15-7

P=8

Answer: 14ft > 4 1/2 yd

Step-by-step explanation:

Answer:

The ordered pair is not a solution of the system of inequalities

Step-by-step explanation:

we know that

If a ordered pair is a solution of a system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)

we have the system

[tex]x+5y < 16[/tex] ----> inequality A

[tex]x< 8[/tex] ----> inequality B

substitute the value of x and the value of y of the ordered pair in each inequality

ordered pair (6,2)

Verify inequality A

For x=6, y=2

[tex]6+5(2) < 16[/tex]

[tex]16 < 16[/tex] ----> is not true

so

The ordered pair not satisfy the inequality A

therefore

The ordered pair is not a solution of the system of inequalities

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

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

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

By definition, if two lines are perpendicular then the product of their slopes is -1.

We have the following equation of the line:

[tex]y = 2x-5[/tex]

Then [tex]m_ {1} = 2[/tex]

We find [tex]m_ {2}:[/tex]

[tex]m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {2}\\m_ {2} = - \frac {1} {2}[/tex]

Thus, the perpendicular line will be of the form:

[tex]y = - \frac {1} {2} x + b[/tex]

We substitute the given point and find "b":

[tex]-2 = - \frac {1} {2} (8) + b[/tex]

[tex]-2 = -4 + b\\-2 + 4 = b\\b = 2[/tex]

Finally, the equation is of the form:

[tex]y = - \frac {1} {2} x + 2[/tex]

ANswer:

[tex]y = - \frac {1} {2} x + 2[/tex]

Answer:

9.

Step-by-step explanation:

It's given that A = 16. It shows that B = A-7, so that would mean B is 16-7, which is 9.

Final answer:

The quotient when 4x^3 + 2x + 7 is divided by x + 3 is 4x^2 - 10x + 32 with a remainder of -89.

Explanation:

To find the quotient when 4x^3 + 2x + 7 is divided by x + 3, we can use long division. Divide the first term, 4x^3, by x which gives 4x^2. Multiply x + 3 by 4x^2 to get 4x^3 + 12x^2. Subtract this from the original expression to get -10x^2 + 2x + 7. Then, divide -10x^2 by x which gives -10x. Multiply x + 3 by -10x to get -10x^2 - 30x. Subtract this from the previous result to get 32x + 7. Finally, divide 32x by x which gives 32. Multiply x + 3 by 32 to get 32x + 96. Subtract this from the previous result to get -89. Therefore, the quotient when 4x^3 + 2x + 7 is divided by x + 3 is 4x^2 - 10x + 32 with a remainder of -89.

Answer:

x = 65

Step-by-step explanation:

The triangle has 2 congruent sides and is therefore isosceles.

The base angles are congruent, both 25°

Subtract the sum of the base angles from 180° for vertex angle

vertex angle = 180° - (25 + 25)° = 180° - 50° = 130°

Hence x = 130° ÷ 2 = 65

Answer:

41.24 cm²

Step-by-step explanation:

Here is the complete question:  A 3 cm by 3 cm rectangle sits inside a circle with radius of 4 cm. What is the area of the shaded region?

Given: measurement of rectangle is [tex]3\ cm\times 3\ cm[/tex]

          Radius of circle is 4 cm.

We can find the area of shaded region by subtracting area of rectangle from area of circle.

First, lets find the area of rectangle

Formula; Area of rectangle= [tex]length\times width[/tex]

Area of rectangle= [tex]3\ cm\times 3\ cm= 9\ cm^{2}[/tex]

∴ Area of rectangle= 9 cm²

Now, finding the area of circle.

Formula: Area of circle= [tex]\pi r^{2}[/tex] (∵ r is radius)

Area of circle= [tex]3.14\times 4^{2} = 3.14\times 16[/tex]

∴ Area of circle= 50.24 cm²

Next solving to find area of shaded region.

Area of shared region= [tex]\textrm{Area of the circle} - \textrm{Area of the rectangle}[/tex]

Area of shaded region= [tex]50.24\ cm^{2} - 9\ cm^{2} = 41.24\ cm^{2}[/tex]

∴ Area of shaded region= 41.24 cm²

Answer:

x = -5 + 5i, -5 - 5i

Step-by-step explanation:

Answer:

V ≈ 63.4

Step-by-step explanation:

The arc length of the segment becomes the circumference of the cone's base.  Therefore, we can find the radius of the cone:

s = C

(90/360) 2π (10) = 2π r

r = 2.5

The radius of the segment is the slant length of the cone.  So we can use Pythagorean theorem to find the cone's height.

l² = r² + h²

10² = 2.5² + h²

h = √93.75

The volume of the cone is:

V = π/3 r² h

V = π/3 (2.5)² √93.75

V ≈ 63.4

Answer:

see explanation

Step-by-step explanation:

A difference of 2 squares factors in general as

a² - b² = (a - b)(a + b)

(x - 1)² - 25 ← is a difference of squares

with a = x - 1 and b = 5, thus

(x - 1)² - 25

=(x - 1 - 5)(x - 1 + 5) = (x - 6)(x + 4), then

(x - 6)(x + 4) = 0

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 4 = 0 ⇒ x = - 4

Solutions are x = - 4, x = 6

Answer:

641

Step-by-step explanation:

24,358 ÷ 38=641

Hope this helps!!

24,358 / 38 = 641

Use long division to find the answer :)

Hope this helps!

Answer:

1640.

Step-by-step explanation:

1640 would be your best option. As you are much higher than average. 2060 would not be a better option as you are below average in this case.

Answer:2060

Step-by-step explanation: your closest to 2060

Answer:

[tex]t_{n}  = 30 + 7n[/tex], where, n = 0, 1, 2, 3, 4, .........

Step-by-step explanation:

Given the arithmetic sequence in recursive formula.

f(0) = 30 and f(n + 1) = f(n) + 7 ......... (1)

Therefore, putting n = 0 in equation (1) we get f(1) = f(0) + 7 = 30 + 7 = 37 {Since, f(0) is given to be 30}

Again, putting n = 1 in equation (1) we get f(2) = f(1) + 7 = 37 + 7 = 44

And, putting n = 2 in equation (1) we get f(3) = f(2) + 7 = 44 + 7 = 51

and so on.

Therefore, the arithmetic sequence is 30, 37, 44, 51, .......

Therefore, the linear equation of this sequence is given by [tex]t_{n}  = 30 + 7n[/tex], where, n = 0, 1, 2, 3, 4, .........

(Answer)

Answer: 12 girls

Step-by-step explanation: Our first step in this problem is to write down the unit ratio that is involved. In this case, it's girls/boys.

Next, we set up our proportion. We know that at a movie there are 3 girls for every 8 boys so we have 3/8 and we are asked how many girls are at the movie if 32 boys are the movie so that's x/32.

Now we have the proportion 3/8 = x/32.

Notice that the 32 boys must go on the bottom of the second ratio because our unit ratio tells us that we put girls/boys.

Solving from here, we use the means-extremes property to get 3 times 32 to get 96 = 8 times x or 8x. So we have 96 = 8x.

Dividing both sides by 8, we find that 12 = x.

This means that 12 girls are at the movie when 32 boys are at the movie.

Time taken by stone in air is 7 seconds and time taken by stone in water is 5 seconds

Solution:

Let "x" represents the time taken by stone in the air

Given that the stone's entire fall took 12 seconds

Thus, the total time taken by it in both air and water = 12 seconds

time taken by stone in the air = x

time taken by stone in water = 12 - x

In the air, it had an average speed of 16 m/s

average speed in air = 16 m/s

We know that,

distance = speed x time

distance covered by it in air = [tex]16 \times x = 16x[/tex]

distance covered in air = 16x

It had an average speed of 3 m/s before hitting the seabed

average speed in water = 3 m/s

distance covered by it in water = [tex]3 \times (12 - x) = 36 - 3x[/tex]

distance covered in water = 36 - 3x

Then,

Total distance covered = distance covered in air + distance covered in water

Total distance covered = 16x + 36 - 3x = 13x + 36

But, the total distance covered by it = 127 meters ( Given )

Therefore,

13x + 36 = 127

13x = 127 - 36

13x = 91

x = 7

Hence, the time taken by stone in air = x seconds = 7 seconds,

And, the time taken by it in water = 12 - x = 12 - 7 = 5 seconds

Sybil's profit for selling n watermelons is represented by the function P = 2n - 15, which is the result of subtracting her cost function from her revenue function.

The function that represents Sybil's profit, P, for selling n watermelons is found by calculating the difference between her revenue and her costs. The profit function, therefore, is the revenue function R = 6n minus the cost function C = 4n + 15. Executing the subtraction, we get:

P = R - C

P = 6n - (4n + 15)

P = 6n - 4n - 15

P = 2n - 15

This function represents the profit made on selling n watermelons.

Final answer:

The function representing Sybil's profit for selling n watermelons is P = 2n - 15.

Explanation:

Profit can be calculated by subtracting the total cost from the total revenue. In this case, the total revenue function is R = 6n and the total cost function is C = 4n + 15. To find the profit function, we subtract the total cost function from the total revenue function:

P = R - C

P = 6n - (4n + 15)

P = 2n - 15

Therefore, the function representing Sybil's profit for selling n watermelons is P = 2n - 15.

I believe that the answer is 7 because it is in the tens place.

Sorry misunderstood the Question the other user is correct

originally had a 2

Answer:

7 because it is in the 0.1 (1/10 or tenth) place of the number

Answer:

Question 1:

Draw a line that crosses the largest number of dots. Then use the line to check the best prediction of the number of baseballs that will be used if 275 pitches are thrown.

Question 2:

A). y = 1.2x - 6

Question 3:

J). y = [tex]\frac{9}{4}x - 81[/tex]

Question 4:

F). f(n) = -3n + 24 *Although it doesn't work when f(n) = 6 and n = 6*

Step-by-step explanation:

Question 2:

The line passes throught point (5, 0) and is parallel to the line whose equation is y = 1.2x + 3.8

For parallel lines, their values of slope is the same.

So our line, that passes through point (5, 0), also has a slope of 1.2

Taking another point (x, y) on our line;

Slope = change in y ÷ change in x

1.2 = [tex]\frac{y - 0}{x - 5}[/tex]

y = 1.2x - 1.2(5)

y = 1.2x - 6

Question 3:

The line passes x-axis at point (36, 0)

The line is perpendicular to another line whose equation is y = -[tex]\frac{4}{9}x[/tex] + 5

For perpendicular lines, the product of their slopes = -1

Let's say the slope of our unknown line is a ;

Given: The slope of our second line is -4/9

So,

a × -4/9 = -1

a = -1 × -9/4 = 9/4

Taking another point (x, y) on our unknown line;

Slope = change in y ÷ change in x

9/4 = [tex]\frac{y - 0}{x - 36}[/tex]

Cross-multiplying that you get;

y = [tex]\frac{9}{4}x - 81[/tex]

Question 4:

The function that model that situation is f(n) = -3n + 24 though it doesn't work when f(n) = 6 and n = 6

Answer:

A

Step-by-step explanation:

3x+2y=15

-3x

2y=15-3x

divide by 2

y=-3/2x+7.5

Parallel Line = Same Slope

y=-3/2x+b

substitute (5,2)

2=-3/2(5)+b

2=-7.5+b

   +7.5

9.5=b

Final Equation: y=-3/2x+9.5

Lana needs to first convert the equation to slope-intercept form, and then use the parallel line's slope with the provided point in the point-slope formula to find her line's equation.

The correct option for Lana to find an equation for a line that passes through the point (5, 2) and is parallel to the given equation 3x + 2y = 15, is option A.

First, Lana needs to write the given equation in slope-intercept form which is y = mx + b, where m is the slope and b is the y-intercept. To do this, she needs to rearrange the equation by subtracting 3x from both sides and dividing by 2, which gives y = -1.5x + 7.5.

Parallel lines have the same slope, so the slope, m, of Lana's line is -1.5. Now, she uses the point-slope form of a linear equation which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through. Substituting the point (5, 2) and slope -1.5 into this equation, Lana gets y - 2 = -1.5x + 7.5.

She rearranges this to get her final equation.

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Answer:

$2,480

Step-by-step explanation:

Let $x be next year tuition. Aiden will pay $2,400, that is 75% of $x.

$x - 100%

$2,400 - 75%

Write a proportion:

[tex]\dfrac{x}{2,400}=\dfrac{100}{75}\\ \\75x=2,400\cdot 100\\ \\75x=240,000\\ \\x=3,200[/tex]

Next year’s tuition will be $720 more than this year’s, then this year tuition is

[tex]\$3,200-\$720=\$2,480[/tex]

Answer:

16

Step-by-step explanation:

So according to PEMDAS we need to do the work in the parentheses first. 2 plus 2 is 4 so we will put 4 in the parentheses to replace 2 plus 2. Now we will divide 8 by 2 which is 4. since 4 is right next to the parentheses, we need to multiply the 4 by the 4 in the parentheses. 4 times 4 is 16.

Final answer:

The new balance in the checkbook register is $114.04.

Explanation:

To find the new balance in a checkbook register after a deposit and a check are processed, you need to add the deposit to the current balance and then subtract the amount of the check.

Initially, the checkbook register has a balance of $158.

A deposit of $35 is made, and a check for $78.96 is written.

Calculating the new balance involves the following steps:

After completing these steps, the new balance in the register would be $193 - $78.96 = $114.04.

Balancing your checkbook regularly is essential to manage your money efficiently and to avoid fees associated with overdrafts or insufficient funds.