Translate each sentence into an equation.
1.
Three more than four times a number is equal to twelve.
2.
The sum of a number and two is twice the number.
3.
The quotient of a number and twelve is the sum of eight and the number.
4.
Five more than three times a number is equal to eight.
5.
The sum of a number and six is seven times the number.
6.
The quotient of a number and six is equal to nine.
7.
Seven less than a number is two.
8.
Twenty-seven is the product of three and a number.
9.
Twelve less than six times a number is equal to three times the number. ...?

Answer:

7.2+x=19.5

x=19.5-7.2

x=12.2

your welcome

Step-by-step explanation:

Answer:

can confirm that the answer above is correct

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Step-by-step explanation:

Answer:

[tex]h(x)=2x^2+14x-60[/tex]

Step-by-step explanation:

This question can be solved by two methods

Method 1: Substitute x=3 and x=-10 in all the equations and determine which equals to zero (ie., check h(3)=0 and h(-10)=0 for all the equations)

Equation 1

[tex]h(x)=x^2-13x-30[/tex]

[tex]h(3)=3^2-13(3)-30[/tex]

[tex]h(3)=-60[/tex]

As h(3)≠0, Equation 1 is discounted

Equation 2

[tex]h(x)=x^2-7x-30[/tex]

[tex]h(3)=3^2-7(3)-30[/tex]

[tex]h(3)=-42[/tex]

As h(3)≠0, Equation 2 is discounted

Equation 3

[tex]h(x)=2x^2+26x-60[/tex]

[tex]h(3)=2(3)^2+26(3)-60[/tex]

[tex]h(3)=36[/tex]

As h(3)≠0, Equation 3 is discounted

Equation 4

[tex]h(x)=2x^2+14x-60[/tex]

[tex]h(3)=2(3)^2+14(3)-60[/tex]

[tex]h(3)=0[/tex]

[tex]h(x)=2x^2+14x-60[/tex]

[tex]h(-10)=2(-10)^2+14(-10)-60[/tex]

[tex]h(-10)=0[/tex]

As h(3)=0 and h(-10)=0, Equation 4 represents h(x)

Method 2: Solve to find the roots of each equation where h(x)=0 using the quadratic formula. Roots should be x=3,x=-10

The quadratic formula is:

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

where a, b and c are as below

[tex]h(x)=ax^2+bx+c=0[/tex]

Equation 1

[tex]h(x)=x^2-13x-30=0[/tex]

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

[tex]x=\frac{13\±\sqrt{(-13)^2-4(1)(-30)}}{2(1)}[/tex]

[tex]x=15,x=-2[/tex]

As roots are not x=3 and x=-10, Equation 1 is discounted

Equation 2

[tex]h(x)=x^2-7x-30[/tex]

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

[tex]x=\frac{-(-7)\±\sqrt{(-7)^2-4(1)(-30)}}{2(1)}[/tex]

[tex]x=10,x=-3[/tex]

As roots are not x=3 and x=-10, Equation 2 is discounted

Equation 3

[tex]h(x)=2x^2+26x-60[/tex]

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

[tex]x=\frac{-(26)\±\sqrt{(26)^2-4(2)(-60)}}{2(2)}[/tex]

[tex]x=2,x=-15[/tex]

As roots are not x=3 and x=-10, Equation 3 is discounted

Equation 4

[tex]h(x)=2x^2+14x-60[/tex]

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

[tex]x=\frac{-(14)\±\sqrt{(14)^2-4(2)(-60)}}{2(2)}[/tex]

[tex]x=3,x=-10[/tex]

As roots are x=3 and x=-10, Equation 4 represents h(x)

The correct answer is:C. 1,092 people per square mile

To calculate the population density of a state, we divide the total population by the total area. In this case, the state has 1,627,260 people living within 1,490 square miles. We perform the following calculation:

Population Density = Total Population / Total Area

Population Density = 1,627,260 people / 1,490 square miles

When we perform the division, we get approximately 1092.12 people per square mile. Rounding to the nearest whole number, we get a population density of 1,092 people per square mile.

Therefore, the correct answer is:C. 1,092 people per square mile

Using the normal distribution, it is found that:

a) [tex]Z_0 = -1.75[/tex].

b) [tex]Z_0 = 1.96[/tex].

c) [tex]Z_0 = 1.645[/tex].

d) [tex]Z_0 = -0.83[/tex].

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Item a:

This is Z with a p-value of 0.0401, thus [tex]Z_0 = -1.75[/tex].

Item b:

Item c:

Same logic as b, just middle 90%, thus [tex]Z_0 = 1.645[/tex].

Item d:

This is Z with a p-value of 1 - 0.2967 = 0.2033, thus [tex]Z_0 = -0.83[/tex].

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Final answer:

The value of the standard normal random variable Z that satisfies the equation P(-Z0 ≤ Z ≤ Z0) = 0.90 is approximately 1.28.

Explanation:

The z-score that corresponds to the area 0.90 under the standard normal distribution can be found using a z-table or a calculator.

Therefore, the value of the standard normal random variable Z, denoted as Z0, that satisfies the equation P(-Z0 ≤ Z ≤ Z0) = 0.90 is approximately 1.28.

Answer:

Simultaneous Equation

Step-by-step explanation:

A bag contains 18 coins consisting of quarters and dimes. The total value of the coins is $2.85. Which system of equations can be used to determine the number of quarters, q, and the number of dimes, d, in the bag?

To get the number of dimes and the number of quarters q will definitely have to be by simultaneous equation

let the number of dimes be d

let the number of quarters be q

let the cost of quarters/ one  be Q

let the cost of dime/one be  D

q+d=18--------------1

Qq+Dd=2.85.........2

from equation 1

q=18-d

substituting the value of q into equation 2

Q(18-d)+Dd=2.85

if cost of quarters/ one  is given and the cost of dime/one is also given we can go ahead to find

q and d

In this mathematical problem involving a system of equations, we use the information provided about the total number of coins and their total value to form two equations: q + d = 18 and 0.25q + 0.10d = 2.85.

The subject of this question is Mathematics, specifically dealing with a system of equations. Given the problem, the system of equations can be formulated from the conditions that the student has 18 coins in total and their combined value is $2.85. These conditions give us two equations:

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To calculate the height of a sail that is four times as high as it is wide and made from 32 square meters of material, we use the area formula for a triangle and find that the height is 16 meters.

The student's question concerns the height of a sail in the shape of a right triangle, where the sail's height is four times its width and the total area of the sail is 32 square meters. To find the height, we can let the width be x meters, which makes the height 4x meters due to the given ratio.

Using the formula for the area of a triangle, A = bh/2, where b is the base and h is the height, we can write an equation for the area in terms of x: 32 m² = x × (4x) / 2.

Simplifying this, we get 32 = 2x2, which can be further simplified to x² = 16. Taking the square root of both sides gives us x = 4. Therefore, the height of the sail, being four times the width, is 16 meters.

Answer:

50

Step-by-step explanation:

10=20/100*50/1=1000/100=10

To find the x-intercepts, set the trinomial equal to zero and solve for x. Substitute x = 0 to find the y-intercept.

To find the x-intercepts of a trinomial, you need to set the trinomial equal to zero and solve for x.

In the example given (x^2-10x+25), you would set the trinomial equal to zero as follows:

x^2-10x+25 = 0

Now, you can factor the trinomial or use the quadratic formula to solve for x. In this case, the trinomial can be factored as (x-5)(x-5) = 0.

So, the x-intercept is x = 5.

The y-intercept can be found by substituting x = 0 into the trinomial. In this case, when x = 0, the trinomial becomes y = 25.

So, the y-intercept is (0, 25).

The absolute maximum occurs at x = -1, where y = 5. The absolute minimum occurs at x = 1, where y = 1.

To find the absolute extrema of a function on a closed interval, we first need to find the critical points of the function within that interval. The critical points occur where the derivative of the function is equal to zero or does not exist.

In this case, the function is y = 3x^(2/3) - 2x, and the closed interval is [-1, 1].

We can find the derivative of the function:

y' = 2x^(-1/3) - 2

Setting the derivative equal to zero and solving for x:

2x^(-1/3) - 2 = 0

x^(-1/3) = 1

Raising both sides to the power of -3 gives:

x = 1

We found one critical point at x = 1. Now we need to check the endpoints of the closed interval, which are -1 and 1. Evaluating the function at these points:

y(-1) = 3(-1)^(2/3) - 2(-1) = 5

y(1) = 3(1)^(2/3) - 2(1) = 1

Therefore, the absolute maximum of the function occurs at x = -1, where y = 5, and the absolute minimum occurs at x = 1, where y = 1.

To write the inequality 'five less than a number is at least -28' in mathematical symbols, we need to assume the number is 'x' and express 'five less than a number' as 'x - 5'. We then represent 'at least -28' as '≥ -28'. By combining these expressions, we get the inequality x - 5 ≥ -28. To solve it, we add 5 to both sides to isolate the variable 'x' and obtain x ≥ -23.

To write the inequality, we need to translate the phrase 'five less than a number is at least -28' into mathematical symbols. Let's assume the number is represented by 'x'. 'Five less than a number' can be written as 'x - 5'. The phrase 'at least -28' means the number has to be greater than or equal to -28, which can be written as '≥ -28'.

Putting it together, the inequality is: x - 5 ≥ -28.

To solve this inequality, we can add 5 to both sides to isolate the variable 'x'. This gives us: x ≥ -28 + 5, which simplifies to x ≥ -23.

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Tree diagram can be used to represent the sample space. The correct option is option C.

In probability, a tree diagram can be used to represent the sample space. Tree diagrams represent a series of independent events or conditional probabilities.

As it is given that the coin is tossed three times, therefore, the number of stages in the tree diagram will be three, where each time the coin is tossed will result in either heads or tails.

Now, the tree diagram of the coins can be drawn as shown below.

Further, comparing it with our diagram, the only possible option is option c where the number of levels in the tree is three and each toss result in either heads or tails.

Hence, the correct option is option C.

Learn more about Tree Diagram:

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Final answer:

To represent the number of campers attending the camp, use the equation y = mx + c, where y represents the number of campers, m represents the rate of increase, x represents the number of years, and c represents the initial number of campers. Using the given information, solve for the rate of increase (m) and initial number of campers (c). Substitute the values in the equation to find the number of campers attending the camp right now.

Explanation:

To represent the number of campers attending the camp right now, we can use the equation: y = mx + c, where y represents the number of campers attending the camp, m represents the rate at which the number of campers increase, x represents the number of years since 2005, and c represents the initial number of campers in 2005.

From the information provided, we know that in 2005 there were 450 campers and five years later, in 2010, the number of campers rose to 750. We can use these two points to find the values of m and c.

Using the formula: (y2 - y1) / (x2 - x1) = m, we can calculate the value of m as: (750 - 450) / (2010 - 2005) = 60. Therefore, the rate of increase is 60 campers per year. Now, we can substitute the values of m and c in the equation to find the number of campers attending the camp right now. y = 60x + 450.

The linear equation representing the number of campers attending camp each year, starting from 2005 with 450 campers and increasing by 60 campers per year, is C = 450 + 60t, where C is the number of campers and t is the number of years after 2005.

In 2005, there were 450 campers at a camp. Five years later, the number of campers increased to 750. To represent the growth in the number of campers, we can write a linear equation. Assuming the number of campers increases at a constant rate each year, we first find the rate of increase.

Rate of increase per year = (Number of campers in 2010 - Number of campers in 2005) / (2010 - 2005)

Rate of increase per year = (750 - 450) / (5)

Rate of increase per year = 300 / 5 = 60 campers per year

Let's denote C as the number of campers and t as the number of years after 2005. The equation that represents the number of campers is:

C = 450 + 60t

This equation indicates that starting with 450 campers in 2005, every year there are 60 more campers attending the camp.

In the given sets, the concept AB + BC = AC is used to create equations in terms of x. After each equation is solved, you can find the lengths of AB and BC by substituting the value of x into their respective original equations.

For this mathematics problem, you have to make use of the concept that the sum of the parts equals the whole. Specifically, this concept translates to the equation AB + BC = AC, as AC is the entire segment that encompasses both parts AB and BC.

For each of the sets you provided:

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Answer:

The correct answer is D. The simplified form of the expression 7^4 is 2,401.

Step-by-step explanation:

7 ^ 4, that is, the exponentiation of 7 to the fourth power, implies the continuous multiplication of the number 7 for 4 times. Therefore, this number will appear 4 times in a multiplication, whose result will be said number exposed to the fourth power.

Simplified, this operation translates into 7x7x7x7, whose result is 2,401.

The cost function is a linear function that represents the relationship between the total cost and total output. The equation C(x) = $200 + $3600x/20 represents the cost function in this case.

The cost function is a linear function that represents the relationship between the total cost and total output. In this case, the fixed costs are $200 per day, meaning they do not depend on the output. The total costs per day, C(x), can be expressed as the sum of fixed costs and variable costs:

C(x) = FC + VC(x)

Given that the total costs are $3800 per day for a daily output of 20 boards, we can write the equation as:

$3800 = $200 + VC(20)

Now, we can solve for VC(20) to find the variable cost:

VC(20) = $3800 - $200 = $3600

Therefore, the cost function equation is C(x) = $200 + $3600x/20, where x represents the total output per day.

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Answer:

b

Step-by-step explanation:

Answer:

D) Group D

Step-by-step explanation:

A range: 38

B range: 48

C range: 40

D range: 51

To solve the equation 15-28i=3l+(4m)i, separate the real and imaginary parts of the equation and solve for l and m separately.

To solve the equation 15-28i=3l+(4m)i, we can separate the real and imaginary parts of the equation. The real part is 15, and the imaginary part is -28. Similarly, the real part of the right side is 3l and the imaginary part is 4m. Equating the real parts and imaginary parts separately, we get two equations: 15 = 3l and -28 = 4m. Solving these equations will give us the values of l and m.

In the first equation, dividing both sides by 3 gives us l = 5. In the second equation, dividing both sides by 4 gives us m = -7.

Therefore, the solution to the equation 15-28i=3l+(4m)i is l = 5 and m = -7.

Answer:

A. 90° clockwise rotation around point A of pre-image JKL

Step-by-step explanation:

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