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Christine went shopping and bought each of her ten nephews a gift, either a video costing $14.95 or a CD costing $16.88. She spent $164.94 on the
gifts. How many videos and how many CDs did she buy

Answer:

f(x) = 3x - 14

Step-by-step explanation:

note that y = f(x), thus rearrange the equation making y the subject.

Given

y - 3x = - 14 ( add 3x to both sides )

y = 3x - 14 , that is

f(x) = 3x - 14 ← in functional notation

Answer:

10.7

Step-by-step explanation:

Let x be the missing side.

The rectangles are similar. Wich means:

● 8/9 = x/12

Cross multiply

● 9x = 8×12

● 9x = 96

Divide both sides by 9

● 9x/9 = 96/9

● x = 10.666

Round it to the nearest unit

● x = 10.7

Answer:

[tex]slope=\frac{1}{2}[/tex]

Step-by-step explanation:

Use the following equation:

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

Rise over run is the change in the y-axis over the change of the x-axis, otherwise known as the slope.

Insert the values:

[tex](1_{x1},2_{y1})\\(5_{x2},4_{y2})[/tex]

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

The slope is [tex]\frac{1}{2}[/tex].

:Done

Answer:

1/2

Step-by-step explanation:

The formula for slope is: y1-y2/x1-x2

The points given are: (x-coordinate, y-coordinate)

In the formula:

y1 is the y-coordinate of the first point

y2 is the y-coordinate of the second point

x1 is the x-coordinate of the first point

x2 is the x-coordinate of the second point

This said, we can plug our points in.

2-4/1-5

Subtract.

-2/-4

Simplify.

-1/-2

The negatives will cancel each other out.

1/2

The slope of the line that cuts through the points (1,2) and (5,4) is 1/2.

Answer:

1.) Neither

2.) Area

3.) Perimeter

4.) Neither

Step-by-step explanation:

Given that the lengths of the rectangle are r and s

The perimeter of the rectangle will be:

Perimeter = 2r + 2s

Perimeter = 2(r+s)

While the area will be:

Area = r × s

Area = rs

For each expression, say whether it gives the perimeter of the rectangle, the area of the

rectangle, or neither.

1. rts = neither

2. r.s = Area of rectangle

3. 2r + 2s = Perimeter of rectangle

4.72 +82 = neither.

Answer:

The correct option is;

45°

Step-by-step explanation:

By angle sum theorem, we have that the sum of angles in a triangle = 180°

Therefore, we have;

When the interior angles of the triangle are constructed to be 60° and 75°, we have by the angle sum theorem;

The third angle + 60° + 75° = 180°

Which gives;

The third angle  = 180°- 60° - 75° = 180°- 135° = 45°

The measurement of the third angle by the angle sum theorem will be 45°

The correct option is ∠third angle = 45°.

Answer:

Step-by-step explanation: 2cos3 theta=1. Cos 3theta=1/2. Since cos 60°= 1/2. Therefore cos 3theta=cos 60°. Theta=20°.

can we chat girl in comment

Answer:

Option B is the correct option.

Step-by-step explanation:

[tex] \mathrm{ - \frac{4}{5} \div 2}[/tex]

[tex] \mathrm{dividing \: a \: negative \: and \: a \: positive \: equals \: a \: negative \:. \: ( - ) \div ( + ) = ( - )}[/tex]

[tex] \mathrm{ - \frac{4}{5} \div 2}[/tex]

[tex] \mathrm{dividing \: is \: equivalent \: to \: multiplying \: with \: the \: reciprocal}[/tex]

[tex] \mathrm{ - \frac{4}{5} \times \frac{1}{2} }[/tex]

[tex] \mathrm{reduce \: the \: numbers \: with \: G.C.F \: 2}[/tex]

[tex] \mathrm{ - \frac{2}{5} }[/tex]

Hope I helped!

Best regards!

The quotient of  -4 /5 divide 2 would be equal to -2/5 in simplified form.

Quotients are the number that is obtained by dividing one number by another number. We can use the fact that division can be taken as multiplication but with the denominator's multiplicative inverse.

We have been given that  -4 /5 divide 2

Thus, we have to divide the terms as;

-4 /5   ÷ 2

Therefore,  -4 /5 x 1/ 2

-2/5

Hence, the quotient of  -4 /5 divide 2 would be equal to -2/5 in simplified form.

Learn more about the quotient;

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Answer:C=d/ab

Step-by-step explanation:

D=abc

D/ab=abc/ab (both side divided by ab)

Ab cancel by ab and c= d/ab remains

The solution of the given equation D = ABC for C will be D/(AB).

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

The equation must be constrained with some constraints.

As per the given equation,

D = ABC

The value of the above equation for C will be as,

D = (AB)C

C = D/(AB)

Hence "The solution of the given equation D = ABC for C will be D/(AB)".

For more about the equation,

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Answer:

-20

Step-by-step explanation:

First thing you do is set up your equation:

y-17= -37

+17   +17        Next you add 17 to both sides

-------------        Follow your integer rules

y= -20

We can check this by putting it back into the solution

-20-17= -37  Integer Rules

                     You use KCC aka Keep Change Change

= -20+ -17= -37

Answer:

True.

Step-by-step explanation:

Cheetahs can reach speeds of 109.4–120.7 km/h (68.0–75.0 mph), and some have been recorded at over 80mph. The cheetah can accelerate from 0 to 96.6 km/h (60.0 mph) in under three seconds, though endurance is limited.

The second fastest land animal is the Pronghorn antelope at 98kph (60mph).

Answer:

It is a Fact because it can run 70mph or 112kph

Answer:

volume before reducing is 8 times the volume after reducing

Step-by-step explanation:

volume before reducing=

V=4/3πr³=

V=4/3π(9)³=972π cm³

diameter reduced to half=18/2=9 cm

radius=d/2=9/2=4.5 cm

volume of sphere when diameter reduced by 1/2=

V=4/3πr³

v=4/3 (π)(4.5)³=121.5π

Answer:

The volume of a sphere whose diameter is 18 centimeters is 972  π cubic centimeters. If its diameter were reduced by half, its volume would be 1/8  of its original volume.

Step-by-step explanation:

Correct for plato :)

Answer:

The number of seedlings the three boys planted together is 560 seedlings

Step-by-step explanation:

The possible information in the question are;

Percentage of the seedlings planted by Ali = 40%

Percentage of the seedling planted by Ben = 45%

The percentage of the seedling planted by Cliff = The rest of the seedling

The number of seedling planted by Cliff = 84 siblings

Therefore, the percentage of the seedling planted by Cliff = 100% - 45% - 40% = 15%

Given that Cliff planted 15% of the seedlings, we have;

15% of seedlings Cliff planted = 84

Let X = the total number of seedlings

15/100 × X = 0.15×X = 84

X = 84/0.15 = 560

The total number of seedlings = The number of seedlings the three boys planted together = 560 seedlings.

Answer:

[tex]slope=3[/tex]

Step-by-step explanation:

Use the following equation the find the slope:

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

Rise over run is the change in the y-axis over the change in the x-axis from one point to the other. This is also known as the "slope". Insert the known values:

[tex](-10_{x1},8_{y1})\\\\(-15_{x2},-7_{y2})\\\\\\\frac{-7-8}{-15-(-10)}\\\\\frac{-7-8}{-15+10}[/tex]

Solve:

[tex]\frac{-7-8}{-15+10}=\frac{-15}{-5}[/tex]

Simplify. Two negatives make a positive:

[tex]\frac{-15}{-5}=\frac{15}{5}[/tex]

Simplify fraction by dividing top and bottom by 5:

[tex]\frac{15}{5}=\frac{3}{1} =3[/tex]

The slope is 3.

:Done

The slope of the line that passes through the points (-10, 8) and  (-15, -7) is 3 and thsi can be determined by using the point-slope formula.

Given :

The line that passes through the points (-10, 8) and  (-15, -7).

The following steps can be used in order to determine the slope of the line that passes through the points (-10, 8) and  (-15, -7):

Step 1 - The slope formula when two points are given is:

[tex]\rm m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

where m is the slope and [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the points on the line.

Step 2 - Substitute the known terms in the above formula.

[tex]\rm m = \dfrac{-7-8}{-15+10}[/tex]

Step 3 - Simplify the above expression.

[tex]\rm m = \dfrac{15}{5}[/tex]

m = 3

For more information, refer to the link given below:

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Answer:

The equation would be a quadratic trinomial

Step-by-step explanation:

Step 1: Expand the equation to remove the brackets

0 = 8x² + 3x - 12x² + 1

Step 2: Collect like terms

0 = -4x² + 3x + 1

Step 3: Count number of terms

0 = -4x² + 3x + 1

1 2 3

Therefore there are 3 terms and this is a quadratic equation making the answer B, a quadratic trinomial

Answer:

9

Step-by-step explanation:

f(x) = 2x² – 3x

Let x=3

f(3) = 2 * 3^2 - 3*3

     = 2 *9 - 9

     = 18-9

      = 9

Answer:

Step-by-step explanation:

[tex]f(x) = 2x^2 -3x\\ f(3) = ?\\\\ f(3) = 2(3)^2 -3(3)\\ f(3) = 2(9) - 9\\ f(3) = 18- 9\\ f(3) = 9[/tex]

Answer:

x = 6

Step-by-step explanation:

x + 4 = 10

x = 10 - 4

x = 6

hope it helps

4(1-3x) + 7x -8

Use distributive property:

4 -12x + 7x -8

Now combine like terms:

-5x -4

Answer:

[tex]-5x-4[/tex]

Step-by-step explanation:

With the expression [tex]4(1-3x) + 7x - 8[/tex], we can simplify it down by applying the distributive property, then combining like terms.

[tex]4(1-3x)+7x-8\\\\4-12x+7x-8\\\\4-5x-8\\\\-5x-4[/tex]

Hope this helped!

Answer:

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

● (a)

Let's determine the difference between the outputs of any two inputs that are one unit apart.

Let m be that difference.

2 and 3 are one unit apart since when you substract 2 from 3 you get 1.

● 3-2 = 1

Let's calculate m.

The output of 2 and 3 are respectively 45 and 53.

● m = 53 - 45

● m= 8

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let's determine the difference between the outputs of any two inputs that are 2 units apart.

Let m' be that difference

3 and 1 are 2 units apart since when you substract 1 from 3 you get 2.

● 3-1 = 2

The outputs of 1 and 3 are respectively 37 and 53.

● m'= 53-37

● m' = 16

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let's determine the difference between the outputs of two inputs that are 3 units apart.

Let m" be that difference

0 and 3 are 3 units apart since when you substract 0 from 3 you get 3.

● 3-0 = 3

Let's calculate m":

The outputs of 0 and 3 are respectively 29 and 53

● m" = 53-29

● m" = 24

■■■■■■■■■■■■■■■■■■■■■■■■■■

● m = 8

● m'= 16

● m" = 24

Notice that all these values are multiples of 8.

● 8 = 8×1

● 16 = 8×2

● 24 = 8×3

Notice that each time the difference m is multiplied by the units that are between the inputs.

This is explained by the fact that the function is a linear one.

When the input interval grows the difference between the outputs grows two.

Answer:

Step-by-step explanation:

find the equation of the linear function   in the form of y=mx+b

m=y2-y1/x2-x1 =-3+11/-4+5=8

y=8x+29 ( when x=0, y=b=29)

out put  : -3 and -11 -3-(-11)=8 which is 1 unit

out put : 21 and 5 21-5=16   which is 2 unit (2*8)

output :53 and 29 53-29=24 which is 3 units (3*8)

ratio of change = f(b)-(f(a)/b-a

at point -3 and -11 : f(-3)-f(-11)/-4+5=-3+11/1=8

at point 21 and 5 : 21-5/-1+3=16/2=8

the graph always increasing and always equal 8

Answer:

D + E = F + H

Step-by-step explanation:

We have to identify the two pairs from the give table which have the same result.

These pairs show the relation as A + B = C + D

We take a pair of expressions given in options (D) and (E)

By adding them,

D + E = (-4 + 9i) + (6 - 6i)

         = 2 + 3i

Similarly we add the expressions given in options (F) and (H),

F + H = (-9 + 15i) + (11 - 12i)

         = 2 + 3i

Therefore, D + E = F + H will be the answer.

Answer:  A

Step-by-step explanation:

Notes: Dividing by a fraction means to multiply by its reciprocal.

           The denominator cannot equal zero.

[tex]\dfrac{5a^3bc}{8ab^3}\div\dfrac{-ab^2}{6a^5b}\cdot \dfrac{2a^2b^3}{3b}\qquad \rightarrow a\neq 0,b\neq 0\\\\\\=\dfrac{5a^3bc}{8ab^3}\cdot\dfrac{6a^5b}{-ab^2}\cdot \dfrac{2a^2b^3}{3b}\\\\\\=\dfrac{5\cdot 6\cdot 2\quad a^3\cdot a^5\cdot a^2\quad b\cdot b\cdot b^3\quad c}{8\cdot -1 \cdot 3\quad a\cdot a\qquad b^3\cdot b^2\cdot b \quad}\\\\\\=\dfrac{-60a^{10}b^5c}{-24a^2b^6}\\\\\\=\dfrac{-5a^8c}{2b}[/tex]

Answer:

18.18 min

Step-by-step explanation:

The complete question is

On a cold February morning, the radiator fluid in Stanley’s car is -18F. When the engine is running, the temperature goes up 5.4 F per minute. Approximately how long will it take before the radiator fluid temperature reaches 80 F?

The initial temperature of the engine [tex]T_{1}[/tex] = -18 F

rate of increase in temperature r = 5.4 F/min

Final temperature [tex]T_{2}[/tex]  = 80 F

Difference in temperature ΔT = [tex]T_{1} -T_{2}[/tex] = 80 - (-18) = 98 F

time taken to reach this 80 F will be = ΔT/r

where ΔT is the difference in temperature

r is the rate of change of temperature

time taken = 98/5.4 = 18.18 min

Answer:

B

Step-by-step explanation:

This rectangle appears to have 7 boxes on the bottom, and 3 box for the side.

Since area is base×height

It would be 7×3

Answer:

The answer is D. 5

Step-by-step explanation:

14-(-3)^2=

14-9=5

The value of f(a) = 14 - [tex]a^{2}[/tex] at x = -3 is 5.

We have the following function of [tex]a[/tex] -

f(a) = 14 - [tex]a^{2}[/tex]

We have to determine the value of this function at a = -3.

The value of f(x) = 2x - 3  at x = 3 can be calculated as follows -

f(3) = 2 x 3 - 3 = 6 - 3 = 3

According to the question -

f(a) = 14 - [tex]a^{2}[/tex]

Now, the value of the function f(a) can be calculated as follows -

f(- 3) = 14 - [tex](-3)^{2}[/tex]

f(- 3) = 14 - 9

f(- 3) = 5

Hence, the value of f(a) = 14 - [tex]a^{2}[/tex] at x = -3 is 5.

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Answer:

£13496.80

Step-by-step explanation:

We can ignore the £ sign for now, that is just units.

If we decrease a number by 4.5%, we will have to find [tex]100-4.5=95.5[/tex]% of 14132.77.

We can easily do this by setting up a proportion.

[tex]\frac{x}{14132.77} = \frac{95.5}{100}[/tex]

Multiply 14132.77 by 95.5:

[tex]14132.77\cdot95.5=1349679.535[/tex]

Divide by 100:

[tex]1349679.535\div100=13496.79535[/tex]

Rounding this to two decimal places, it simplifies to 13496.80.

Hope this helped!

Answer:

C

Step-by-step explanation:

Definitely not a! To square a number you multiply it by itself. for example, if you were squaring 3, you would do 3x3.

Not b either! You will have to take the SQUARE ROOT of the number!

C is the right answer, as I said for a.

D is wrong! The perfect square 49 has a sqrt (square root) of 7. That is NOT even, so d cannot be true.

C is the only true statement. Also, if this is right, can I get branliest answer? Thx :)

Answer:

[tex]\frac{14}{55}[/tex]

Step-by-step explanation:

note that

n! = n(n - 1)(n - 2) .... × 3 × 2 × 1

Given

[tex]\frac{8!9!}{5!12!}[/tex]

Cancel the terms from 8! ( 5 × 4 × 3 × 2 × 1 ) with the same terms from

5! ( 5 × 4 × 3 × 2 × 1 ) leaving

8 × 7 × 6 = 336 on the numerator

Similarly

Cancel the terms from 9! and 12!

leaving 12 × 11 × 10 = 1320 on the denominator, thus simplifies to

[tex]\frac{336}{1320}[/tex]

= [tex]\frac{14}{55}[/tex]

Answer:

f(x) = 4x² + 48x + 149

Step-by-step explanation:

f(x) = 4(x + 6)² + 5

The above expression can be written as: f(x) = ax² + bx + c, by doing the following:

1. Expand (x + 6)²

(x + 6)² = (x + 6)(x + 6)

(x + 6)(x + 6)

x(x + 6) + 6(x +6)

x² + 6x + 6x + 36

x² + 12x + 36

(x + 6)² = x² + 12x + 36

2. Substitute x² + 12x + 36 for (x + 6)² in

f(x) = 4(x + 6)² + 5

This is illustrated below:

f(x) = 4(x + 6)² + 5

(x + 6)² = x² + 12x + 36

f(x) = 4(x² + 12x + 36) + 5

Clear bracket

f(x) = 4x² + 48x + 144 + 5

f(x) = 4x² + 48x + 149

Therefore, the standard of the function:

f(x) = 4(x + 6)² + 5

is

f(x) = 4x² + 48x + 149

Answer:

Sequence a) Pattern: (-2) -9, -11, -13, -15, -17

Sequence b) Pattern: (-5) -15, -20, -25, -30, -35

Sequence c) Pattern: (-6) -13, -19, -25, -31, -37

Hope this helps!

Hi there! Hopefully this helps!

-------------------------------------------------------------------------------------------------------------

A (Subtracting by 2): -9, -11, -13, -15, -17.

B(Subtracting by 5): -15, -20, 25, -30, -35

C(Subtracting by 6): -13, -19, -25, -31, -37

Answer: $1398

Step-by-step explanation:

Given , Principal (P) =  $12,500

Rate of interest for 1st year [tex](R_1)[/tex]=  12% =0.12

Rate of interest for 2nd year [tex](R_2)[/tex]=  15% =0.15

Rate of interest for 3rd year [tex](R_3)[/tex]=  18% =0.18

Interest for first year = [tex]I=P\times R_1\times T[/tex]

= [tex]12500\times 0.12\times 1[/tex]

= $1500

Now, For second year new principal [tex]P_2 = \$12,500+\$1,500 =\$14,000[/tex]

Interest for second year = [tex]I=P_2\times R_2\times T[/tex]

= [tex]14000\times 0.15\times 1[/tex]

= $2100

Now, For third year new principal [tex]P_3 = \$14000+\$2,100 =\$16,100[/tex]

Interest for third year = [tex]I=P_3\times R_3\times T[/tex]

= [tex]16100\times 0.18\times 1[/tex]

= $2898

Difference  between the compound interest of the first year and the  compound interest for the third year. = $2898 - $1500 = $1398

Hence, the difference  between the compound interest of the first year and the  compound interest for the third year is $1398 .