789
Bernie, Eddy and Gery share £450
Bernie gets twice as much as Eddy who gets three times as much as Gery.
Work out how much they each get.​

Answer:

Step-by-step explanation:

The inequality [tex]2y \leq 6[/tex] means [tex]y \leq 3[/tex].

y = 0, satisfies the above inequality, so the arrows will be towards the x axis.

Now, we need to draw 5x < 8 + 4y.

First, lets draw the equation of 5x = 8 + 4y.

y = 1 gives x = 2.4 & y = 0 gives x = 1.6.

Hence, the above equation passes through (2.4, 1) and (1.6, 0).

The point (0, 0) satisfies the inequality 5x < 8 + 4y. Hence, the arrows will be towards the origin.

The solution will be the area of APQ except any point on PQ, as PQ is nothing but the line 5x = 8 + 4y.

Answer:

3 Miles per hour, or .05 Miles per minute

Step-by-step explanation:

Answer: 25%

Step-by-step explanation:

Since 825 people said they would buy the car again, it means they were satisfied with the car

Therefore, the percentage of those satisfied with the car is = (825/3300) x 100 = 25%

Answer:

f(2)= -4

Step-by-step explanation:

f(x)= -x^3 + 6x - 7

f(2) = -2^3 + 6*2 - 7

f(2)= -8 +12 -7

f(2)= 3-7

f(2)= -4

The value of the function f(x)=-x^3+6x-7 at x=2 is -3.

To find the value of the function f(x) = -x^3 + 6x - 7 at x = 2, we substitute the value of x into the function.

So, f(2) = -(2)^3 + 6*(2) - 7 = -8 + 12 - 7 = -3.

Thus, the value of the function at x = 2 is -3. This is a simple algebraic operation involving cubes and multiplication, which are basic arithmetic operations.

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The length of DZ is 4 units ⇒ 3rd answer

Step-by-step explanation:

Triangle X Y Z is cut by line segment C D, where

We need to find the length of DZ

In Δ XYZ

∵ C ∈ XY and D ∈ YZ

∵ CD // XZ

∴ m∠YCD = m∠YXZ ⇒ alternate angles

∴ m∠YDC = m∠YZX ⇒ alternate angles

In Δs YCD and YXZ

∵ m∠YCD = m∠YXZ

∵ m∠YDC = m∠YZX

∵ ∠Y is a common angle

∴ Δ YCD is similar to Δ YXZ by AAA postulate

- There is a constant ratio between their corresponding sides

∴ [tex]\frac{YC}{YX}=\frac{CD}{XZ}=\frac{YD}{YZ}[/tex]

∵ YC = 25 units

∵ CX = 5 units

∵ YX = YC + CX

∴ YX = 25 + 5 = 30 units

∵ YD = 20 units

∵ YZ = YD + DZ

∴ YZ = 20 + DZ

Let us use the ratio of the corresponding side

∵ [tex]\frac{YC}{YX}=\frac{YD}{YZ}[/tex]

∴ [tex]\frac{25}{30}=\frac{20}{20+DZ}[/tex]

- Simplify [tex]\frac{25}{30}[/tex] by dividing up and down by 5

∵ [tex]\frac{25}{30}=\frac{5}{6}[/tex]

∴ [tex]\frac{5}{6}=\frac{20}{20+DZ}[/tex]

- By using cross multiplication

∴ 5(20 + DZ) = 6(20)

∴ 100 + 5 DZ = 120

- Subtract 100 from both sides

∴ 5 DZ = 20

- Divide both sides by 5

∴ DZ = 4 units

The length of DZ is 4 units

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Answer:

on edge the answer is C.

Step-by-step explanation:

bc it is

Answer:

Why is 90 the sum of all factors of 40, including 40? The factors of the number 40 are: 1, 2, 4, 5, 8, 10, 20, 40. If you add them up, you will get the total of 90.

Step-by-step explanation:

2. Given the points A, B, C, D, calculate:

(a) the angle B of the triangle ABC

(b) the area of the triangle ABC

(c) the median BE of the triangle ABC

(d) the height AH of the triangle ABC

(e) the volume of tetrahedron ABCD

(f) the point E so that ABCE is a parallelogram.

A(-1, 2, -3), B(4, -1, 0), C(2, 1, -2), D( 3,4,5)​

Using the balance method, we find a = 15 by isolating the variable a. Substituting a = 15 back into the original equation, we verify the solution.

To solve the equation 12 = 2a - 18 using the balance method, we aim to isolate the variable a on one side of the equation.

Starting with 12 = 2a - 18, we'll first add 18 to both sides to isolate the term with 2a:

[tex]\[12 + 18 = 2a - 18 + 18\]\[30 = 2a\]\\[/tex]

Next, we divide both sides by 2 to solve for a:

[tex]\[\frac{30}{2} = \frac{2a}{2}\]\[15 = a\][/tex]

Now, let's verify the solution by substituting a = 15 back into the original equation:

[tex]\[12 = 2(15) - 18\]\[12 = 30 - 18\]\[12 = 12\][/tex]

Since the left side equals the right side, the solution a = 15 is verified.

Complete Question:

Solve the following equation using balance method and verify 12 = 2a - 18​

There are 1160 pennies and 114 dimes in the piggy bank.

Step-by-step explanation:

Given,

Worth of money = $23.00 = 23*100 = 2300 cents

1 penny = 1 cent

1 dime = 10 cents

Let,

x be the number of pennies

y be the number of cents

According to given statement;

x+10y=2300       Eqn 1

x = 10y+20          Eqn 2

Putting value of x from Eqn 2 in Eqn 1

[tex]10y+20+10y=2300\\20y=2300-20\\20y=2280[/tex]

Dividing both sides by 20

[tex]\frac{20y}{20}=\frac{2280}{20}\\y=114[/tex]

Putting y=144 in Eqn 2

[tex]x=10(114)+20\\x=1140+20\\x=1160[/tex]

There are 1160 pennies and 114 dimes in the piggy bank.

Keywords: linear equation, substitution method

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Final answer:

Joshua has 114 dimes and 1160 pennies in his piggy bank. This was determined by setting up a system of equations based on the values of the coins and the given relationship between the number of dimes and pennies.

Explanation:

The problem presented is a typical algebraic word problem that requires setting up equations based on the given information about dimes and pennies. We are told that the total value of the coins is $23.00 and that the number of pennies is 20 more than 10 times the number of dimes. To solve the problem, we need to use the fact that the value of a dime is 10 pennies, and then set up a system of linear equations to find the number of each type of coin.

Step-by-Step Explanation

Thus, Joshua has 114 dimes and 1160 pennies in his piggy bank.

Answer:

28 minutes

Step-by-step explanation:

d + v = 45

d = v + 11

time to sub

(v + 11) + v = 45

2v + 11 = 45

2v = 45 - 11

2v = 34

v = 34/2

v = 17 minutes.........volleyball

d = v + 11

d = 17 + 11

d = 28 minutes <=== dodge ball

Answer:

28 mins.

Step-by-step explanation:

The population of the moose after 12 years is 7692

Step-by-step explanation:

The form of the exponential growth function is [tex]y=a(b)^{x}[/tex] , where

The table:

→  x  :  y

→  0  :  40

→  1   :  62

→  2  :  96

→  3  :  149

→  4  :  231

To find the value of a , b in the equation use the data in the table

∵ At x = 0 , y = 40

- Substitute them in the form of the equation above

∵ [tex]40=a(b)^{0}[/tex]

- Remember any number to the power of zero is 1 (except 0)

∴ 40 = a(1)

∴ a = 40

- Substitute the value of a in the equation

∴ [tex]y=40(b)^{x}[/tex]

∵ At x = 1 , y = 62

- Substitute them in the form of the equation above

∵ [tex]62=40(b)^{1}[/tex]

∴ 62 = 40 b

- Divide both sides by 40

∴ 1.55 ≅ b

∴ The growth factor is about 1.55

- Substitute its value in the equation

∴ The equation of the population is [tex]y=40(1.55)^{x}[/tex]

To find the population of moose after 12 years substitute x by 12 in the equation

∵ [tex]y=40(1.55)^{12}[/tex]

∴ y ≅ 7692

The population of the moose after 12 years is 7692

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He must save $150 each of the last two months in order to meet his goal.

Step-by-step explanation:

Given,

Amount Colin wants to save = $900

Amount saved each month for 8 months = $75

Amount saved in 8 months = 75*8 = $600

Let,

x be the amount saved each month for remaining two months.

Therefore;

Number of months * Amount saved + Amount saved in 8 months = Total amount to save

[tex]2x+600=900\\2x=900-600\\2x=300[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{300}{2}\\x=150[/tex]

He must save $150 each of the last two months in order to meet his goal.

Keywords: subtraction, division

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Answer:

North Pole

Step-by-step explanation:

Answer:

So your walk of 1 mile West is a complete circle. You then walk 1 mile North, which brings you back to your starting point, (1 + 1/(2pi)) miles from the South Pole. The obvious answer is the North Pole. You're either on the North Pole, or somewhere very near (about 840 feet or less) the South Pole.-step explanation:

Add the whole numbers 4 + 3 = 7

Add the fractions 1/2 + 1/4

Rewrite 1/2 to have a common denominator with 1/4

1/2 = 2/4

Now add 2/4 + 1/4 = 3/4

The answer would be 7 3/4

Answer:

a. y int. = initial amount of coyotes

b. 135 coyotes

Step-by-step explanation:

a. when x = 0, you get y int. = 15 coyotes. This shows that at the very beginning, you had 15 coyotes.

b. 40 years = two 20 year periods. x = 2 after 40 years

y = 15 * (3)^2

y = 135 coyotes

a. y int. = initial amount of coyotes

b. 135 coyotes

a. when x = 0, you get y int. = 15 coyotes.

This represent that at the very beginning, you had 15 coyotes.

b. 40 years = two 20 year periods. x = 2 after 40 years

[tex]y = 15 \times (3)^2[/tex]

y = 135 coyotes

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Answer:

3 boxes.

Step-by-step explanation:

The circular pool has a radius of 16 feet.

So, the circumference of the pool will be 2πr = [tex]2 \times \frac{22}{7} \times 16 = 100..57[/tex] feet.

Therefore, to place a rim around the circular pool with a foam rim Sarah will need 100.57 feet length of foam rim.

Now, the foam rim is  sold in boxes that will cover the length of 40 feet.

Therefore, she will need [tex]\frac{100.57}{40} = 2.51[/tex] ≈ 3 boxes to place around the rim of the pool. (Answer)

Answer:

The cost to rent each chair and each table are $1.5 and $8.75 respectively

Step-by-step explanation:

Let x represent 1 chair

Let y represent 1 table

Therefore

3x + 2y = 22   ------------(1)

5x + 6y = 60   ------------(2)

Multiply (1) by 5 and (2) by 3

15x + 10y = 110   ----------(3)

15x + 18y = 180  ------------(4)

Subtract (3) from (4)

8y = 70

Divide through by 8

y = $8.75

Substitute y = 8.75 in (1)

3x + 2y = 22

3x + 2(8.75) = 22

3x + 17.5 = 22

Collect like terms

3x = 22 - 17.5

3x = 4.5

Divide through by 3

x =$1.5

Final answer:

By setting up a system of linear equations based on the given information and solving it, we determined that the cost to rent each chair is $1.50 and the cost to rent each table is $8.75.

Explanation:

To find the cost to rent each chair and each table from the party rental company, we set up a system of linear equations based on the information given:

Let C be the cost of one chair and T be the cost of one table. We can write the following equations:

Solving this system of equations, we can find the values of C and T. First, multiply the first equation by 3 to eliminate T:

Now we can subtract the second equation from the modified first equation:

With the cost of a chair known, we can substitute back into either equation to find the cost of a table:

The cost to rent each chair is $1.50 and the cost to rent each table is $8.75.

Answer:

It's B,C,D

Step-by-step explanation:

Answer:

its b,c, and d

Step-by-step explanation:

Answer:

4/8 - 2/5 = 1/10

Answer:

24.4

Step-by-step explanation:

diameter=2*radius

=2*12.2

=24.4

Final answer:

The diameter of a circle with a radius of 12.2 is 24.4 units. This is calculated by doubling the radius, using the formula D = 2r.

Explanation:

To determine the diameter of a circle with a radius of 12.2, you simply need to use the relationship between the radius and the diameter of a circle. The diameter is twice the radius, which can be represented by the formula D = 2r, where D is the diameter and r is the radius.

Substituting the value of the radius into the formula gives us:

D = 2 × 12.2

This calculates to:

D = 24.4

Therefore, the diameter of the circle is 24.4 units. Keep in mind that if the radius was given in a specific unit, like meters or centimeters, then the diameter will be in the same unit.

Answer:

58 degrees

Step-by-step explanation:

All triangles measure up to 180 degrees.

180-87-35=58

10 ≤ x ≤ 30, x < 2y, x < 40.

Solution:

Given x is the number of graphing calculators produced daily and

y is the number of scientific calculators produced daily.

Step 1: A company produce atleast 10 and not more than 30 graphing calculators per day.

⇒ 10 ≤ x < 30

Step 2: Each day, the number of graphing calculators cannot exceed twice the number of scientific calculators produced.

⇒ x < 2y

Step 3: The number of scientific calculators cannot exceed 40 per day.

⇒ x < 40

Hence, the constraints are 10 ≤ x ≤ 30, x < 2y, x < 40.

Answer:

See below.

Step-by-step explanation:

The sum of the measures of the interior angles of an n-sided polygon is

(n - 2)180

A pentagon has 5 sides, so for a pentagon, n = 5.

(n - 2)180 = (5 - 2)180 = 3(180) = 540

The sum of the measures of the angles of a pentagon is 540.

You don't show the measures of the 4 angles that are known, so to answer the question, add the 4 given measures and subtract the sum from 540.

Answer:

The finance charge is $6.96.

Step-by-step explanation:

Given:

Dudley Greene's charge account statement shows an unpaid balance of $376.00.

The monthly finance charge  is 1.85 percent of the unpaid balance.

Now, to find the finance charge.

Unpaid balance = $376.00.

Finance charge = 1.85%  of  unpaid balance.

So, to get the finance charge:

1.85% of $376.00.

[tex]=\frac{1.85}{100} \times 376.00[/tex]

[tex]=0.0185\times 376.00[/tex]

[tex]=\$6.96.[/tex]

Therefore, the finance charge is $6.96.

Answer:

The function given by [tex]y = - (2)^{x} + 3[/tex] will have a range of y < 3.

Step-by-step explanation:

The function given by [tex]y = - (2)^{x} + 3[/tex] will have a range of y < 3.

This is because, for any real values of x, the term [tex]- (2)^{x}[/tex] will have a negative value. If we put x = 1, then, [tex]- (2)^{x}[/tex] = - 2, and for x = -1, then [tex]- (2)^{x}[/tex] = - 0.5.

That means [tex]- (2)^{x} < 0[/tex] for all real x.

Hence, [tex]- (2)^{x} + 3[/tex] < 0 + 3

⇒ y < 3 for all real x. (Answer)

Answer:

13104

Step-by-step explanation:

9C2 x 14C3 = 36 x 364

                    = 13104

Answer:

C, 49°.

Step-by-step explanation:

Cause i said so

Answer:

C, 49.

Step-by-step explanation:

Answer:

The answer is in both because, the x goes into 3 accordingly. Also in 30 degrees you move upward, and they both factor into the same equations.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

6 in to 13 ft = 9 in to x ft

6 / 13 = 9 / x.....cross multiply because this is a proportion

(6)(x) = (13)(9)

6x = 117

x = 117/6

x = 19.5 (or 19 1/2) ft <====

Answer: m = [tex]\frac{-1}{11}[/tex]

Step-by-step explanation:

The slope of a line is calculated by :

m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]x_{1}[/tex] = 5

[tex]x_{2}[/tex] = -6

[tex]y_{1}[/tex] = -5

[tex]y_{2}[/tex] = -4

substituting the values , we have :

m = [tex]\frac{-4-(-5)}{-6-5}[/tex]

m = [tex]\frac{-4+5}{-11}[/tex]

Therefore :

slope = [tex]\frac{-1}{11}[/tex]

Answer:

The x-intercept is 4

Step-by-step explanation:

We are given;

The slope of a line as -3/4

y-intercept is 3

We are supposed to determine the x-intercept;

We need to know that;

The slope of a line is given by the ratio of the change in y to the change in x

The coordinates of y-intercept are (0, 3)

Taking the x-intercept as a, then the coordinates of x-intercept is (a, 0)

But;

slope = Δ in y ÷ Δ in x

Therefore;

[tex]\frac{0-3}{a-0}= \frac{-3}{4}[/tex]

Solving for a

[tex]-3a = -12 \\ a =4[/tex]

Therefore, the x-intercept is 4