Erica had 6 coins in her coin collection. she goes to a coin show and buys some coins. how many dose she have now?

The average rate of change of the function over the interval is 2

Finding the average rate of change

From the question, we have the following parameters that can be used in our computation:

The graph

The interval is given as

From x = -3 to x = 3

The function is a quadratic function

This means that it does not have a constant average rate of change

From the graph

y = -8, when x = -3

y = 4, when x = 3

This means that

f(-3) = -8

f(3) = 4

The average rate is calculated using

Rate = (Change in y values)/(Change in corresponding x values)

So, we have

Rate = (4 + 8)/(3 + 3)

Evaluate

Rate = 2

Hence, the average rate of change is 2

Answer:

c.7 and d.5

Step-by-step explanation:

Given the following equation :

[tex]x^{2}-6x+40=6x+5[/tex]

This equation is equivalent to the following equation :

[tex]x^{2}-6x+40=6x+5[/tex]

[tex]x^{2}-6x+40-6x-5=0[/tex]

[tex]x^{2}-12x+35=0[/tex]

Given an equation [tex]ax^{2}+bx+c=0[/tex] we can find the solutions using the quadratic equation (x1 and x2 are the solutions) :

[tex]x1=\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex]

[tex]x2=\frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]

Using this equations :

[tex]x^{2}-12x+35=0[/tex]

[tex]a=1\\b=-12\\c=35[/tex] ⇒

[tex]x1=\frac{-(-12)+\sqrt{(-12)^{2}-4.(1).(35)}}{2.(1)}=7[/tex]

[tex]x2=\frac{-(-12)-\sqrt{(-12)^{2}-4.(1).(35)}}{2.(1)}=5[/tex]

Given the two solutions x1 and x2 we can write the equation :

[tex]ax^{2}+bx+c=0[/tex] ⇒ [tex]a.(x-x1).(x-x2)=0[/tex] ⇒

[tex]x^{2}-12x+35=0[/tex] is equivalent to

[tex](x-7).(x-5)=0[/tex]

The solutions for this equation are 7 and 5.

Therefore, c.7 and d.5 are the solutions for this exercise.

Answer: The answer is C on Quizizz.

Step-by-step explanation:

The time it takes the rock to reach the canyon floor is after 3.99seconds

The intercept is the point where the axis is equal to zero. Give the quadratic equation that represents the height h (in feet) of an object t seconds after it is dropped expressed as:

h = -16t² + 255

The rock reaches the ground when h(t) = 0. Substitute

h = -16t² + 255

h = -16t² + 255 = 0
16t² = 255
t² = 255/16
t² = 15.9375

t = 3.99seconds

Hence the time it takes the rock to reach the canyon floor is after 3.99seconds

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Answer:

abc(a + b + c)

That's your answer!!!

Answer:

17 cars

Step-by-step explanation:

Mike collects toy cars. He decides to put all of his toy cars in a line so that he can count them.

It is given that 9th car in the line ends up being exactly at the middle of the line.

This statement shows that before and after the middle car there were 8 cars.

So the cars in the line is 8 + 1(middle) + 8 = 17 cars

Mike have total 17 cars.

Option (b) 4(3-x)+6x=3x+12+2x is the equation that has the solution x = all real numbers because it simplifies to an identity, which is true for any value of x.

Among the given equations, the one that has the solution x = all real numbers is essentially an identity, meaning that for any value of x you plug into the equation, the equation will hold true. To determine which equation is an identity, each equation must be simplified.

Let's take option (b) as an example:

4(3−x)+6x=3x+12+2x

4∙3 - 4∙x + 6∙x = 3∙x + 12 + 2∙x

12 - 4∙x + 6∙x = 3∙x + 12 + 2∙x

12 + 2∙x = 5∙x + 12

12 - 12 + 2∙x - 2∙x = 5∙x - 2∙x + 12 - 12

0 = 3∙x - 3∙x

After simplifying, we end up with 0 = 0, which is an identity and is true for all values of x, hence this is the equation where x is all real numbers.

Answer:

{y | y > –4}

Step-by-step explanation:

The range of f(x) = (3/4)^x - 4 is (-∞, -4].

The range of the function f(x) = (3/4)^x - 4 can be determined by finding the minimum and maximum values that the function can reach.

Putting it all together, the range of f(x) is (-∞, -4].

estimate  by rounded to the nearest dollars

2 +1 +5 +2 +3 +9 +1 =  $23

-2

23-2 = 21

 yes the amount is reasonable

Answer: 3+1+5+2+3+9+1-1-1=22

The total on the register is reasonable because if you estimate $21.77 to the nearest dollar you would get $22.00.

Step-by-step explanation:

The decimal form of the given percent 203% is 2.03

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction. The word "percent" means "per hundred." So, whenever you see a number with a percent sign (%), you can imagine it as a fraction,

Percent is from the Latin adverbial phrase per centum meaning “by the hundred.” The Latin phrase entered English in the 16th century.

Example: 10% means 10 out of every 100. So if 10% of 500 people have ice cream, then 50 people have ice cream.

Given that, what is decimal form for the 203 percent,

Since, the percent is any number in its 100th part,

Therefore, 203% = 203/100

Since, it is 100 in the denominator,

The decimal will be put after two digits in the numerator,

Therefore,

203% = 203/100 = 2.03

Hence, the decimal form of the given percent 203% is 2.03

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The function that best represents the graph of the function which is given is:

               [tex]f(x)=(x-3)^2+1[/tex]

From the graph that is provided to us we observe that the graph passes through the point (3,1).

Hence, we will check which of the following function satisfies this point.

a)

[tex]f(x)=(x-3)^3-1[/tex]

when x=3 we see that:

[tex]f(x)=(3-3)^3-1\\\\i.e.\\\\f(x)=-1\neq 1[/tex]

Hence, option: a is incorrect.

c)

[tex]f(x)=(x+3)^3-1[/tex]

when x=3 we have:

[tex]f(3)=(3+3)^3-1\\\\i.e.\\\\f(3)=9^3-1\\\\i.e.\\\\f(3)=729-1\\\\f(3)=728\neq 1[/tex]

Hence, option: c is incorrect.

d)

[tex]f(x)=(x+3)^3+1[/tex]

when x=3 we have:

[tex]f(3)=(3+3)^3+1\\\\i.e.\\\\f(3)=9^3+1\\\\i.e.\\\\f(3)=729+1\\\\f(3)=730\neq 1[/tex]

Hence, option: d is incorrect.

Now we are left with option: b)

i.e.

b)

[tex]f(x)=(x-3)^2+1[/tex]

Also, when x=3 we have:

[tex]f(3)=(3-3)^2+1\\\\f(3)=0+1\\\\f(3)=1[/tex]

Hence, it passes through the point (3,1)

Also, when we will plot this function we observe that it matches the given graph.

We can calculate for the slope of the line using the formula:

m = (y2 – y1) / (x2 – x1)

From the given values:

m = (4,000 – 10,000) ft / (15 – 0) min

m = -400 ft/min

This means that the altitude is decreasing by 400 ft per minute.

> The slope is –400 . This means that the helicopter descends 400 ft each minute.

The simplification form  of the expression 15x+14y+3x+7y is 18x + 21y option (D) 18x + 21y is correct.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

15x+14y+3x+7y

After simplification,

Adding like terms:

= 18x + 21y

Thus, the simplification form  of the expression 15x+14y+3x+7y is 18x + 21y option (D) 18x + 21y is correct.

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Answer: Option 'C' is correct.

Step-by-step explanation:

Since we have given that

Cost for 5 weeks i.e. 15 classes = $108

Cost of per class is given by

[tex]\frac{108}{15}=7.2[/tex]

Cost for 8 weeks i.e. 24 classes = $125

Cost of per class is given by

[tex]\frac{125}{24}=5.21[/tex]

Amount of saving of per class by taking the 8 week class is given by

[tex]7.2-5.21=\$1.99[/tex]

Hence, Option 'C' is correct.

Answer:

The measure of length of equal side is 36 cm each.

B is correct.

Step-by-step explanation:

Isosceles triangle ABC has a perimeter of 96 centimeters.

The base of the triangle is BC and measures 24 cm

We need to find the length of equal side of triangle.

AB=AC

The perimeter of triangle is 96 cm

AB + AC + BC = 96

AB + AB + 24 = 96                          ( ∵ AB=AC)

              2AB = 96-24

              2AB = 72

                AB = 36

Hence, The measure of length of equal side is 36 cm each.

The principle being demonstrated is known as the Symmetric Property, which holds that if an equation or statement is valid, then its switched or flipped version will also be true.

The question refers to a fundamental property in mathematics called the Symmetric Property. The Symmetric Property states that if an equation or statement is true, then its mirror or flipped version will also hold true. In this case, if LM = JK, then under Symmetric Property, it must be true that JK = LM.

For instance: If 5 = 2 + 3, then 2 + 3 = 5.

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Answer:

Step-by-step explanation:dhdjdbfbd

When a system has one answer or in other words, the graphs of the equations intersect one time, the system is called a consistent system of linear equations and therefore the equations are independent.

When a system has no solution meaning, the graphs of the equations don’t interconnect at all, the system is known to be an inconsistent system of linear equations and the equations are independent.

So therefore, the answer is yes.

Answer-

Area of the kite is 14.0 sq.units

Solution-

[tex]\text{Area}_{WXYZ}=\text{Area}_{WXY}+\text{Area}_{WZY}[/tex]

From the graph, in the triangle WXY

Base = WY=4 units,

Height = 3 units

[tex]\text{Area}_{WXY}=\dfrac{1}{2} \cdot base\cdot height=\dfrac{1}{2} \cdot 4\cdot 3=6\ sq.unit[/tex]

From the graph, in the triangle WZY

Base = WY=4 units,

Height = 4 units

[tex]\text{Area}_{WZY}=\dfrac{1}{2} \cdot base\cdot height=\dfrac{1}{2} \cdot 4\cdot 4=8\ sq.unit[/tex]

[tex]\therefore \text{Area}_{WXYZ}=6+8=14\ sq.units[/tex]