12x + 16 = 100
100
(Equation)
Solve it and show your work!
15
Simon & Iris earned money
by selling candy. They
earned $12 by recycling.
They split the total and
each got $100. How much
did they earn selling
candy?
Speaker notes

Using the Factor Theorem, the non-real solutions are given as follows:

[tex]\frac{1 + \sqrt{5}i}{3}, \frac{1 - \sqrt{5}i}{3}[/tex]

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

For this problem, the function is:

f(x) = 3x^5 + 25x^4 + 26x³ - 82x² + 76x - 48.

The function can be written as:

f(x) = g(x)h(x).

In which:

Using a calculator, as the graph is not given, the real solutions are given as follows:

[tex]x_1 = -6, x_2 = -4, x_3 = 1[/tex]

Hence:

g(x) = (x + 6)(x + 4)(x - 1)

g(x) = (x² + 10x + 24)(x - 1)

g(x) = x³ + 9x² + 14x - 24.

f(x) is of degree 5, g(x) of degree 3, hence h(x) is of degree 2 and:

f(x) = g(x)h(x)

3x^5 + 25x^4 + 26x³ - 82x² + 76x - 48 = (x³ + 9x² + 14x - 24)(ax² + bx + c)

Hence:

-24bx + 14cx = 76x

-24b + 28 = 76

-24b = 48

b = -2.

Then the equation with the non-real solutions is:

h(x) = 3x² - 2x + 2.

Which is a quadratic equation with coefficients a = 3, b = -2 and c = 2, thus:

Hence the non-real solutions are:

[tex]\frac{1 + \sqrt{5}i}{3}, \frac{1 - \sqrt{5}i}{3}[/tex]

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The original amount for the laptop that Candace bought when the markup rate is 20% will be $4375.

It should be noted that she added 875 markup amount to the original price and the markup rate used was 20%,

Therefore, 20% of x = 865

0.2x = 875

Divide

x = 875 / 0.2

x = 4375

Therefore, the original amount for the laptop is $4375.

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Answer:

10

Step-by-step explanation:

1 Simplify 10-910−9 to 11.

1+8-7+{(6-(5+4)\div 3)}^{2}-1

1+8−7+(6−(5+4)÷3)

2

−1

2 Simplify 5+45+4 to 99.

1+8-7+{(6-9\div 3)}^{2}-1

1+8−7+(6−9÷3)

2

−1

3 Simplify 9\div 39÷3 to 33.

1+8-7+{(6-3)}^{2}-1

1+8−7+(6−3)

2

−1

4 Simplify 6-36−3 to 33.

1+8-7+{3}^{2}-1

1+8−7+3

2

−1

5 Simplify {3}^{2}3

2

to 99.

1+8-7+9-1

1+8−7+9−1

6 Simplify 1+81+8 to 99.

9-7+9-1

9−7+9−1

7 Simplify 9-79−7 to 22.

2+9-1

2+9−1

8 Simplify 2+92+9 to 1111.

11-1

11−1

9 Simplify.

10

this is what you need?if yes than look and write

Answer:

c

Step-by-step explanation:

Answer:

1(7-6)1/6

Step-by-step explanation:

Answer:

No solution.

Explanation:

Given expression:

when x = 3, y = 4

Substitute these values inside expression:

6(3) + 4(4) = 36

18 + 16 = 36

34 = 36

As the statement "34 = 36" not true. The solution is false or no solution.

Answer:

The given values are wrong.

Step-by-step explanation:

Given information,

→ x = 3

→ y = 4

Solving the given equation,

→ 6x + 4y = 36

→ (6 × 3) + (4 × 4) = 36

→ 18 + 16 = 36

→ 34 ≠ 36

Hence, there is no solution.

Answer: x=21, y=8

Step-by-step explanation:

18y+5=10x-61  ==> 18y+5 and 10x-61 are congruent angle, so they're equal

x+10+10x-61=180 ==> x+10 and 10x-61 are supplementary angles since they're on a straight line(a straight line measures 180 degrees and is called a straight angle), so they add up to 180 degrees.

x+10x+10-61=180

11x-51=180

11x=231

x=21

18y+5=10(21)-61

18y+5=210-61

18y+5=149

18y=144

y=8

From the graph of the function, we have that:

a) The domain is all real values.

b) The range is y ≤ 4.

c) The x-intercepts are x = -4 and x = 1.

d) The y-intercept is y = 3.

e) f(-2) = 3, f(2) = -5.

Hence, for this problem:

a) The domain is all real values.

b) The range is y ≤ 4.

Hence:

c) The x-intercepts are x = -4 and x = 1.

d) The y-intercept is y = 3.

For the graph, when x = -2 y = 3 and when x = 2 y = -5, hence:

f(-2) = 3, f(2) = -5.

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Answer:

10 cups

Step-by-step explanation:

Since 16 cups is twice 8 cups, it needs twice 5 cups of flour which is 10 cups.

We can also use a proportion.

5/8 = x/16

8x = 5 × 16

x = 5 × 2

x = 10

Answer: 10 cups

As per given data of respondents of four locations in the bar graph per40 potential customers , the average number of location chosen per potential customer is equal to 2.5.

As given,

Total number of potential customers =40

Number of  respondents from bar graph

At grocery stores= 40

At drugstores respondents =32

At health food stores =8

At big box stores =20

Average number=(40 +32+8+20)/40

                            = 100 /40

                            =2.5

Therefore, as per given data of respondents of four locations in the bar graph per40 potential customers , the average number of location chosen per potential customer is equal to 2.5.

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[tex] \green\star\:{\underline{\underline{\sf{\orange{Answer:}}}}}[/tex]

¡Hello :D!

To solve the similar terms we must eliminate the parentheses and then put the parentheses back but this time it would be like this: (4 x + x) + ( 2 - 2)

Once we have done that we must restore the ones on the right side which gives us the result of 1 then as we see that there is + in the Parenthesis and another + outside the Parenthesis we do not care + since we are using the law of signs .

We proceed to solve:

[tex]\: \: \: \: \: \: \bold \: \bold \: \bold \: ( \bf4x+2)+(x-2)[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: \bf \bold4x + 2 + x - 2[/tex]

[tex] \: \: \: \: \: \: \: \: \bf\tt( \bf4x + x) + (2 - 2)[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf5x[/tex]

So the result is 5x

I hope I've helped XD

The function is a good model for the data, capacity U. S. nuclear power plants were working in 2014 is 115% and the year when nuclear power plant working with full capacity is 2008.

Given that the table which shows the capacities at which U.S. nuclear power plants are working and a model of the situation is f(t)=0.027t²+0.216t+53.296.

The Scatter plot for our function and points is shown in attached image and the point are highly related to the curve .

So the function is good model.

The year 2014 means t=2014-1970=44

So to get the population,put t=44 in equation

f(t)=0.027(44)²+0.216(44)+53.296

f(t)=0.027(1936)+0.216(44)+53.296

f(t)=52.272+9.504+53.296

f(t)=115.072

And on rounding it we get 115%.

Now, to find year at which capacity is 100% ,put f(t)=100 and solve for t

f(t)=0.027t²+0.216t+53.296=100

0.027t²+0.216t+53.296=100

0.027t²+0.216t+53.296-100=0

0.027t²+0.216t-46.704=0

Now, we will solve this using quadratic formula for f(x) =ax²+bx+c=0

[tex]\begin{aligned}x&=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\end[/tex]

for our function a= 0.027 , b=0.216 ,c=-46.704 substitute this value and we get

[tex]\begin{aligned}t&=\frac{-0.216\pm \sqrt{(0.216)^2-4\times 0.027\times (-46.704)}}{2\times 0.027}\\ &=\frac{-0.216\pm \sqrt{0.046656+5.044032}}{0.054}\\ &=\frac{-0.216\pm \sqrt{5.090688}}{0.054}\\ &=\frac{-0.216\pm 2.256}{0.54}\\ &=37.78, -45.78\end[/tex]

As we all know time cannot be negative so t=-45.78 will be rejected.

So, t=37.78=38

Now, we will find the corresponding year

1970+38=2008

Hence, from the given table the function is a good model for the data, capacity U. S. nuclear power plants were working in 2014 is 115% and the year when nuclear power plant working with full capacity is 2008.

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the required simplified value of given expression 4x = 12x + 32 is x = -4 (hence proved).

Given that,
An expression is given 4x = 12x + 32,
We have to prove x = -4 as of simplified solution.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
4x = 12x + 32
Taking 12x to the left side of the equal sign and it becomes -12x
4x - 12x = 32
Applying subtraction property between 4x and 12
- 8x = 32
Dividing both sides by -6
x = -4

Thus, the required simplified value of the given expression is x = -4 (hence proved).

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The correct option is b. -30x + 32 = 182.

After combining the like terms, the equation that represents -8x + 23 - 22x + 9 = 182 is -30x + 32 = 182, where x = -5.

In its most basic form, an equation is a statement that demonstrates that 2 mathematical expressions have been equal.

Now, as per the given question;

The stated equation in the question is is,

-8x + 23 – 22x + 9 = 182

Considering like terms together;

-8x – 22x + 23 + 9 = 182

Further simplifying;

– 30x + 32 = 182

Subtracting 32 from the both sides.

– 30x + 32 - 32 = 182 - 32

On solving;

– 30x = 150

⇒ x = -5

Therefore, the expression which defined the equation after taking alike terms is -30x + 32 = 182 for which the value of 'x' comes to be -5.

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The complete question is;

Joy is going to solve the equation below which of the following represents the equation after just distributing and combining like terms?

-8x + 23 – 22x + 9 = 182

a. 14x + 32 = 182

b. -30x + 32 = 182

c. 14x + 14 = 182

d. -30x + 14 = 182

The model that best described the statement is an exponential model and the function that models the situation is A(t) = 4^t

The statement is given as:

The above statement is a population function

Population functions are best represented by an exponential function

Hence, the model that best described the statement is an exponential model.

Here, we have

Initial value, a = 1

Rate, r = 3

The function is represented as

A(t) = A * (1 + r)^t

So, we have

A(t) = 1 * (1+3)^t

Evaluate

A(t) = 4^t

Hence, the function that models the situation is A(t) = 4^t

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Answer:

67,500

Step-by-step explanation:

i think this is the answer.

Answer:  67500

This is because 536 is closer to 500 than it is to 600

One way to solve is to follow these steps

2(3b - 2) = 2(2b + 12)

2*3b - 2*2 = 2*2b + 2*12

6b - 4 = 4b + 24

6b-4b = 24+4

2b = 28

b = 28/2

b = 14

Answer:

y= (x+9)^2

Step-by-step explanation:

If h<0 ( negative) then it shifts to the right, if it is is h>0 ( positive number) then it shift to the left!

y = x2

Shift 2 units left:  y = (x+2)2

Then, shift up 9 units:  y = (x+2)2 + 9

Then, reflect in the x-axis:  y = -(x+2)2 - 9

f(x)=x+1 is a formula for a function f(x) that has f(9)=10

What is a simple definition for function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input

a constant function is a function whose (output) value is the same for every input value. For example, the function y(x) = 10 is a constant function because the value of y(x) is 10 regardless of the input value x

if we take f(x)= x+1

then put x=9 we get f(9)= 10

Hence , f(x)=x+1 is a formula for a function f(x) that has f(9)=10

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Answer:

q arrow p, and p arrow q

Step-by-step explanation:

edmentum

Answer:

consider the two number as x and y

first  given condition

x-6 = 3y

i.e. x= 3y + 6  eqn 1

second given condition

x+ y = 38

i.e. x= 38-y  eqn 2

solving eqn 1 and 2

3y + 6 = 38-y

3y + y = 38-6

4y = 32

y = 8

substituting the value of y in eqn 2

x = 38 - y

x= 38-8

x= 30

hence the required numbers are 8 and 30

Six cotton mice has 64%, nine Norway rats has 95%, 17 pine voles has 180%, and two eastern chipmunks has 21% were taken in a 24-hour period from the pie chart.

Given that,

In the figure there is a chart pie chart with 4 parts and 4 colors.

Six cotton mice, nine Norway rats, 17 pine voles, and two eastern chipmunks were taken in a 24-hour period.

We have to find by use the information below to calculate the percentage of each species of captured mammal, and then use that information to name the various pie-shaped sections.

Each value must be converted into a circle's angle for the pie chart.

Total=6+9+17+2=34

Cotton mice=(6/34)×360°=64°

Norway rats=(9/34)×360°=95°

Pine voles=(17/34)×360°=180°

Eastern chipmunks=(2/34)×360°=21°

Therefore, Six cotton mice has 64%, nine Norway rats has 95%, 17 pine voles has 180%, and two eastern chipmunks has 21%.

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Answer:the iconic Indian building named Taj Mahal

Step-by-step explanation:

Step-by-step explanation:

THE THIRD GRAPH IS THE PARABOLA!

HOPE THIS HELPS!

The polar equation r = - 4 · cos θ is equivalent to the equation of the circle (x + 2)² + y² = 2², whose radius is 2 and center is (h, k) = (- 2, 0).

Polar and rectangular forms are related by this relation: (x, y) → (r · cos θ, r · sin θ), where r is the radial distance with respect to the origin and θ is the angle in standard position. We can use this fact to change the given expression into its rectangular form:

r = - 4 · (x / r)

r² = - 4 · x

x² + y² = - 4 · x

y² = - (x² + 4 · x)

y² - 4 = - (x² + 4 · x + 4)

y² - 4 = - (x + 2)²

(x + 2)² + y² = 4

(x + 2)² + y² = 2²

In a nutshell, the polar equation r = - 4 · cos θ is equivalent to the equation of the circle (x + 2)² + y² = 2², whose radius is 2 and center is (h, k) = (- 2, 0).

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The towns are 15600 miles apart.  

The term "map scale" refers to the proportion between a distance on a map and its corresponding distance on the ground. Lets see an example like, On a map with a scale of 1:100,000, one kilometer on the ground is equivalent to one centimeter. The scale of a map refers to the proportion between a distance on a map and its actual distance on the ground. This simple concept is complicated by the fact that scale must vary across a map due to the curvature of the Earth's surface. The concept of size is now important in two different ways as a result of this development.

The size of the producing globe is compared to the size of the Earth in the first technique. a theoretical globe known as the generating globe, upon which the map is projected and the Earth is compressed. The ratio of the size of the Earth to that of the generating globe is known as the nominal scale, also known as the major scale or representative fraction.

∵ 1 inch = 50 miles on the map

∴ 312 inches = 312 * 50 = 15600 miles .

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Answer: 17/14 or 1 3/14 simplified

Step-by-step explanation:

14 is the least common multiple of denominators 7 and 2. Use it to convert to equivalent fractions with this common denominator.

It is not a function because: C) the element 1 is in both the domain and the range.

A relation can be defined as a function if each of the domain values each has exactly one corresponding range value. This means that an element of the domain must not have two different elements from the range that it is related or corresponded to.

In the given function, 1 as an element of the domain is related to two different range elements, 10 and 7. This doesn't satisfy a function property.

Therefore, we can state that: it is not a function because: C) the element 1 is in both the domain and the range.

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