The expression that shows the result of that transformation are:
3f(x) = 3.4ˣ
f(3x)=4³ˣ
f(x+3)=4ˣ⁺³
f(x)+3=4ˣ+3.
The given function is f(x) =4ˣ.
We have to find the transformations applied to the function f(x).
Graph transformation involves modifying an existing graph or graphed equation to create a different version of the original graph.
f(x) =4ˣ
We have to find 3f(x), f(3x), f(x+3) and f(x)+3.
3f(x) = 3.4ˣ
f(3x)=4³ˣ
f(x+3)=4ˣ⁺³
f(x)+3=4ˣ+3.
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Simplify by combining Like terms: m + 9 - 4m
Answer:
9-3m
Step-by-step explanation:
m and -4m are like terms, combining them yields (1m-4m) which is -3m. The 9 is a constant.
PLEASE PLEASE HELP I WILL GIVE BRAINLIEST AND MAX POINTS
Answer:
After 5 hours the amount of cells is 35
Step-by-step explanation:
i just graphed it and the point in which they intersect s the x and y values. Hope this helped Happy Holidays
Answer:
35
Step-by-step explanation:
I already commented this
Solve the system of equation by the elimination method {1/3x+1/2y=1/2{1/6x-1/3y=5/6(x,y)=(_, _)
Solution
- The solution steps to solve the system of equations by elimination is given below:
\(\begin{gathered} \frac{x}{3}+\frac{y}{2}=\frac{1}{2}\text{ \lparen Equation 1\rparen} \\ \\ \frac{x}{6}-\frac{y}{3}=\frac{5}{6}\text{ \lparen Equation 2\rparen} \\ \\ \text{ Multiply Equation 2 by 2} \\ 2\times(\frac{x}{6}-\frac{y}{3})=\frac{5}{6}\times2 \\ \\ \frac{x}{3}-\frac{2y}{3}=\frac{5}{3}\text{ \lparen Equation 3\rparen} \\ \\ \\ \text{ Now, }\frac{x}{3}\text{ is common to both Equations 1 and 3.} \\ \\ \text{ We can therefore subtract both equations to eliminate }x. \\ \text{ We have:} \\ \text{ Equation 1 }-\text{ Equation 3} \\ \\ \frac{x}{3}+\frac{y}{2}-(\frac{x}{3}-\frac{2y}{3})=\frac{1}{2}-\frac{5}{3} \\ \\ \frac{x}{3}-\frac{x}{3}+\frac{y}{2}+\frac{2y}{3}=\frac{1}{2}-\frac{5}{3}=\frac{3}{6}-\frac{10}{6} \\ \\ \frac{y}{2}+\frac{2y}{3}=-\frac{7}{6} \\ \\ \frac{3y}{6}+\frac{4y}{6}=-\frac{7}{6} \\ \\ \frac{7y}{6}=-\frac{7}{6} \\ \\ \therefore y=-1 \\ \\ \text{ Substitute the value of }y\text{ into any of the equations, we have:} \\ \frac{1}{3}x+\frac{1}{2}y=\frac{1}{2} \\ \frac{1}{3}x+\frac{1}{2}(-1)=\frac{1}{2} \\ \\ \frac{1}{3}x=\frac{1}{2}+\frac{1}{2} \\ \\ \frac{1}{3}x=1 \\ \\ \therefore x=3 \end{gathered}\)Final Answer
The answer is:
\(\begin{gathered} x=3,y=-1 \\ \\ \therefore(x,y)=(3,-1) \end{gathered}\)help me pliss
which one is supposed to be correct?
The two triangles shown are similar. Find the value of
a
b
2.1
1.4
Answer:a 2.1 similar to 1.4 is 5.6 n answer to your question
Step-by-step explanation:
Answer:
1.5
Step-by-step explanation:
WEEK 2 Direction: Answer the following problems. 1. Jun wanted to know how much ice cream he got in on scoop. The radius of a scoop is 2 inches. Find the volum Use 3.14 for pi. (SHOW YOUR SOLUTION) a) What is asked in the problem? b) What are the given facts? c) What is the formula to be used? d) Number Sentence e) Final answer. (show your solution pls)
We are given the radius of the scoop and asked to find the volume of ice cream in one scoop. By using the formula for the volume of a sphere and substituting the given radius, we can calculate the volume. The final answer is approximately 33.49 cubic inches.
a) The problem asks for the volume of ice cream in one scoop.
b) The given fact is that the radius of the scoop is 2 inches.
c) The formula to be used is the volume of a sphere, which is given by V = (4/3)πr³, where V is the volume and r is the radius.
d) Number Sentence:
- Given: Radius (r) = 2 inches
- Formula: V = (4/3)πr³
- Substituting the value: V = (4/3)π(2)³
- Simplifying: V = (4/3)π(8)
- Evaluating: V = (4/3)(3.14)(8)
- Multiplying: V = 33.49333333 (approx.)
e) Final answer: The volume of ice cream in one scoop is approximately 33.49 cubic inches.
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A neighborhood is trying to set up school carpools, but they need to determine the number of students who need to travel to the elementary school (ages 5-10), the middle school (ages 11-13), and the high school (ages 14-18). A histogram summarizes their findings:
Histogram titled Carpool, with Number of Children on the y axis and Age Groups on the x axis. Bar 1 is 5 to 10 years old and has a value of 3. Bar 2 is 11 to 13 years old and has a value of 7. Bar 3 is 14 to 18 years old and has a value of 4.
Which of the following data sets is represented in the histogram?
{3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4}
{5, 10, 4, 11, 12, 13, 12, 13, 12, 11, 14, 14, 19, 18}
{5, 6, 5, 11, 12, 13, 12, 13, 14, 15, 11, 18, 17, 13}
{3, 5, 10, 11, 13, 7, 18, 14, 4}
The correct answer is that the data set {3, 7, 4} is represented in the given histogram.(option-a)
The given histogram represents the number of children in each age group who need to travel to school. Since the histogram has only three bars, we can conclude that there are only three age groups.
The first bar represents children aged 5-10, of which there are 3. The second bar represents children aged 11-13, of which there are 7. The third bar represents children aged 14-18, of which there are 4.
Therefore, the data set that is represented in the histogram is:
{3, 7, 4}
None of the other data sets given match the values in the histogram. The first data set has duplicate values and is not sorted by age group. The second data set includes ages that are not represented in the histogram. The third data set has values for ages 6, 11, 12, 13, 14, 15, 17, and 18, but the histogram does not have bars for all those ages. (option-a)
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A garden is to designed with a rectangular part in the middle with two semi-circles on the ends.
The dimensions of the rectangular portion are 18.4 feet long and 8.6 feet wide.
a) What is the area of one semi-circle at one end?
b) What is the area of the garden?
c) Find the area in square metres.
Given statement solution is :- a) The area of one semi-circle at one end is 58.09 square feet.
b) The area of the garden is 274.42 square feet.
c) The area in square metres is approximately 58.09 square feet.
The area of the garden is approximately 274.42 square feet, and the area in square meters is approximately 25.49 square meters.
a) To find the area of one semi-circle at one end, we need to calculate the area of a complete circle and then divide it by 2. The formula for the area of a circle is A = πr², where A represents the area and r is the radius.
Since the diameter of the semi-circle is equal to the width of the rectangular portion, which is 8.6 feet, the radius will be half of that, which is 8.6 / 2 = 4.3 feet.
Now we can calculate the area of the semi-circle:
A = (π * 4.3²) / 2
A ≈ 58.09 square feet
b) To find the area of the garden, we need to sum the area of the rectangular portion with the areas of the two semi-circles.
Area of the rectangular portion = length * width
Area of the rectangular portion = 18.4 feet * 8.6 feet
Area of the rectangular portion ≈ 158.24 square feet
Area of the two semi-circles = 2 * (area of one semi-circle)
Area of the two semi-circles ≈ 2 * 58.09 square feet
Area of the two semi-circles ≈ 116.18 square feet
Total area of the garden = area of the rectangular portion + area of the two semi-circles
Total area of the garden ≈ 158.24 square feet + 116.18 square feet
Total area of the garden ≈ 274.42 square feet
c) To convert the area from square feet to square meters, we need to know the conversion factor. Since 1 foot is approximately 0.3048 meters, we can use this conversion factor to convert the area.
Area in square meters = Total area of the garden * (0.3048)²
Area in square meters ≈ 274.42 square feet * 0.3048²
Area in square meters ≈ 25.49 square meters
Therefore, the area of one semi-circle at one end is approximately 58.09 square feet. The area of the garden is approximately 274.42 square feet, and the area in square meters is approximately 25.49 square meters.
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Q1. An industry analyst wants to compare the average salaries of two firms, both to each other and to the industry. Firm A's average salary is 93% of the industry average, Firm B's average salary is $58,000, and the industry average salary is 96% of Firm B's average salary. a. Determine the industry average salary. b. Determine Firm A's average salary. c. Express Firm B's average salary as a percentage of Firm A's average salary. Round the percentage to two decimals.
a.The Industry Average Salary is $55,680. b.The Firm A's Average Salary is $51,718.40 .c. Firm B's average salary is approximately 112.27% of Firm A's average salary.
a. To determine the industry average salary, we can use the information that the industry average salary is 96% of Firm B's average salary. Firm B's average salary is $58,000. Therefore, we can calculate the industry average salary as follows:
Industry Average Salary = 96% of Firm B's Average Salary
= 0.96 * $58,000
= $55,680
b. Firm A's average salary is stated as 93% of the industry average salary. To calculate Firm A's average salary, we can multiply the industry average salary by 93%:
Firm A's Average Salary = 93% of Industry Average Salary
= 0.93 * $55,680
= $51,718.40
c. To express Firm B's average salary as a percentage of Firm A's average salary, we can divide Firm B's average salary by Firm A's average salary and multiply by 100:
Percentage = (Firm B's Average Salary / Firm A's Average Salary) * 100
= ($58,000 / $51,718.40) * 100
≈ 112.27%
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Does the volume of a cone increase more when you double the height of the original or when you double its radius? Explain why.
The volume of a cone increase more when you double the height of the original or when you double its radius. This is true.
What is a cone?A cone is a shape formed by connecting a common point, known as the apex or vertex, to all the points of a circular base with a set of line segments. The height of the cone is the distance from the vertex to the base.
A cone always contains a right angle. To solve for the volume of a cone, we need to get the radius of the cone and its height. radius is the line from the center of the circle of the cone going to the edge of the circle. height is the measurement of the cone from its pointy tip going downward.
The volume of a cone is 1/3πr²h, so if you double the radius the volume would quadruple. So, when the height is doubled, the volume is also doubled.
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(2/5)p=14
Mike sold y boxes of cookies for $5 each. He made at least $200.
What’s the least amount of boxes of cookies he sold?
Answer: 1 =5$
200$=40
Step-by-step explanation:
Answer:
40 boxes
Step-by-step explanation:
200 = 5x
x = 40
A deposit of $225 as an integer
Answer:
225
Step-by-step explanation:
A deposit is positive, so a deposit of $225 as an integer (number) would be 225I hope this helps!
The area model shows 2 1 4
What is 2 x 2 1/4?
2 1/2
2 3/4
4 1/4
4 1/2
Answer:
4 1/2
Step-by-step explanation:Because 2x2 =4 and 2x1/4 = 1/2 so it is 4 1/2
G(x) = x-2/x+2 when g (4)
Answer:
g(4) = 1/3
Step-by-step explanation:
G(x) = x-2/x+2
To find g(4) let x= 4
G(4) = (4-2)/(4+2)
= 2 / 6
Simplifying
= 1/3
g(4) = 1/3
\(\huge \boxed{\color{fuchsia} \tt Question :}\)
\( \rm \dag \: g(x) = \dfrac{x - 2}{x + 2} \: when \: g(4).\)
\(\huge \boxed{\color{fuchsia} \tt Answer :}\)
\( \rm \dag \: g(x) = \dfrac{x - 2}{x + 2} \)
Now, in g(4), x = 4
\( \rm : \implies \: g(4) = \dfrac{4 - 2}{4+ 2} \\ \rm : \implies \: g(4) = \cancel{\dfrac{2}{6}} \\ \rm : \implies \: g(4) = \dfrac{1}{3} \)
\( \tt Hence, \: {\color{cyan}g(4) = \dfrac{1}{3}} \: is \: the \: answer.\)
Can I get help with this, I’m so confused
The linear and exponential equations for the amount of money in the banks indicates;
TCF Bank Equation
y = 100·x + 1000
Well Fargo Bank Equation
y = (1.06)ˣ
The number of years it will take for both accounts to have the same amount of money is about 17 years
What is an exponential equation?An exponential equation is an equation of the form; y = a·bˣ, where the input variable, x is an exponent.
The equation for calculating the amount in each bank, based on the details are;
TCF Bank;
Amount invested = $1,000
Amount added each year = 100·x
The TCF Bank Equation is; y = 100·x + 1000Well Fargo Bank Equation
The percentage of the amount earned as interest each year = 6% = 0.06
The exponential equation for compound interest amount is; y = 1000·(1 + 0.06)ˣ
Therefore; y = 1000·(1.06)ˣ
The Well Fargo Bank Equation is; y = 1000·(1.06)ˣWhen the amount in the two accounts have the same amount of money, we get;
1000·(1.06)ˣ = 100·x + 1000
Therefore; (1.06)ˣ = (100·x + 1000)/1000 = 0.1·x + 1
(1.06)ˣ = 0.1·x + 1
Solving the above equation using the substitution method and graphing indicates that we get;
x = 0, and x ≈ 17.125732
Therefore, it takes about 17 years for the two accounts to have the same amount of money
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What is the value of the expression when m=4, n= -9, p= -2, and q= 12?
Answer:
i dont know
Step-by-step explanation:
B: 1
provostwendall65 if you don't know then don't answer.
Which equation shows y=3x−15 in standard form?
A. 15x−5y=1
B. 15x+5y=−1
C. 5x−15y=1
D. 5x−15y=−1
Answer:
c 5x -15y =1
Step-by-step explanation:
5x-15y=1
-5x -15y= 1 -5x change the signs on both sides of the equation
15y = -1 +5x divide both sides by 15
y = -1/15 + 1/3 x Reorder the terms
y = 3x-15
:)
All options are wrong here.
Given equation is \(y=3x-15\).
the equation given here is in form of \(y=mx+c\) . The general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis) .
We have to write \(y=3x-15 \\\) in standard form.
The standard form for linear equations in two variables is Ax+By=C.
Now we convert \(y=3x-15\) in standard form.
Here \(y=3x-15\\\)
\(y-3x=-15\\\\-y+3x=15\)
\(3x-y=15\)
But no options match with the above standard form of equation.
Hence all options are wrong here.
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How many times can 5 go into 33
Answer:
6 times
Step-by-step explanation:
33÷5
5×5= 25 too little
5×6=30 just right
5×7= 35 too much
Answer:
5,10,15,20,25,30,3- oh wait its only 6 mate... but for a full answer, it would be 6.2
Step-by-step explanation:
i think...
A piece of wood is in the shape of a rectangular prism with a length of 10 inches, a width of 4 inches, and a height of 5 inches. You cut the wood in half to form two pieces of wood, each with a length of 5 inches. What is the percent increase in the total surface area? Round your answer to the nearest hundredth, if necessary. %
Answer: 18.18%
Step-by-step explanation:
First, let's calculate the surface area of the original piece of wood. The surface area (SA) of a rectangular prism is given by the formula:
\($$SA = 2lw + 2lh + 2wh$$\)
where \(\(l\)\) is the length, \(\(l\)\) is the width, and \(\(h\)\) is the height. For the original piece of wood, \(\(l = 10\) inches\), \(\(w = 4\) inches\), and \(\(h = 5\) inches\).
After the piece of wood is cut in half, the length becomes 5 inches, but the width and height remain the same. So, for each of the two new pieces of wood, \(\(l = 5\) inches\), \(\(w = 4\) inches\), and \(\(h = 5\) inches\). The total surface area of the two new pieces of wood is twice the surface area of one of the new pieces.
The percent increase in the total surface area is given by the formula:
\($$\text{Percent Increase} = \frac{\text{New Total SA} - \text{Original SA}}{\text{Original SA}} \times 100\%$$\)
Let's calculate these values.
The percent increase in the total surface area when the piece of wood is cut in half is approximately 18.18%.
Lily owns a van rental she needs to changes the 75 quarts of oil with 8 quarts for each oil change
The number of oil change in total is 10 changes
How to determine the number of oil changeFrom the question, we have the following parameters that can be used in our computation:
Number of quarts of oil = 75 quarts
Rate per change = 8 quarts
The number of oil change can be calculated using the following unit rate equation
The number of oil change = Number of quarts of oil/Rate per change
Substitute the known values in the above equation, so, we have the following representation
The number of oil change = 75 quarts/8 quarts per change
Evaluate the quotient in the above equation, so, we have the following representation
The number of oil change = 9.37500 changes
Round up
The number of oil change = 10 changes
Hence, the number of oil change is 10
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What is the size matrix T?
The size of a matrix is typically described using the number of rows and columns, such as a 3x4 matrix, where there are 3 rows and 4 columns.
Matrices are commonly used in mathematics, engineering, physics, and computer science to represent data, perform calculations, and solve problems. The size of a matrix is an important factor in determining its properties and the operations that can be performed on it.
For instance, if T refers to a transformation matrix used in computer graphics, it could be a 4x4 matrix that describes the translation, rotation, and scaling of a 3D object in space. If T refers to a transition matrix used in Markov chains, it could be a square matrix with dimensions equal to the number of states in the chain.
In summary, the size of a matrix T depends on the context in which it is used, and without additional information, it is not possible to determine its dimensions or properties.
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Inso ice cream machines make a total of 320 gallons in a certain amount of time.
Working together for the same length of time, how many gallons of ice cream can 4
machines make?
The gallons of ice cream 4 machines can make is 650 gallons.
How to find the number of gallons of ice cream 4 machine can make?Two ice cream machines make a total of 320 gallons in a certain amount of time.
Working together for the same length of time, the number of gallons of ice creams 4 machine can make can be calculated as follows:
Therefore,
If 2 ice cream machine = 320 gallons
4 ice cream machine = ?
cross multiply
Hence,
gallons of ice cream made by 4 machines = 320 × 4 / 2
gallons of ice cream made by 4 machines = 1280 / 2\
Therefore,
gallons of ice cream made by 4 machines = 640 gallons
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Determine the general solution of 5 tan 0-6 cos 0 = 0
The general solution for the equation 5tan(θ) - 6cos(θ) = 0 is:
θ = sin⁻¹(2/3) + nπ, where n is an integer.
To determine the general solution of the trigonometric equation 5tan(θ) - 6cos(θ) = 0, we can use algebraic manipulation and trigonometric identities to simplify and solve for θ.
Starting with the given equation:
5tan(θ) - 6cos(θ) = 0
First, we can rewrite the tangent function in terms of sine and cosine:
5(sin(θ)/cos(θ)) - 6cos(θ) = 0
Next, multiply through by cos(θ) to eliminate the denominator:
5sin(θ) - 6cos²(θ) = 0
Using the identity sin²(θ) + cos²(θ) = 1, we can express cos²(θ) as 1 - sin²(θ):
5sin(θ) - 6(1 - sin²(θ)) = 0
Expanding and rearranging terms:
5sin(θ) - 6 + 6sin²(θ) = 0
Rearranging the equation:
6sin²(θ) + 5sin(θ) - 6 = 0
Now, we have a quadratic equation in terms of sin(θ).
We can solve this quadratic equation by factoring or using the quadratic formula.
However, since this equation is not easily factorable, we will use the quadratic formula:
sin(θ) = (-b ± √(b² - 4ac)) / 2a
For our equation:
a = 6, b = 5, c = -6
Plugging these values into the quadratic formula and simplifying, we get:
sin(θ) = (-5 ± √(5² - 4(6)(-6))) / (2(6))
sin(θ) = (-5 ± √(25 + 144)) / 12
sin(θ) = (-5 ± √169) / 12
sin(θ) = (-5 ± 13) / 12.
This gives us two possible solutions for sin(θ):
sin(θ) = (13 - 5) / 12 = 8/12 = 2/3
sin(θ) = (-13 - 5) / 12 = -18/12 = -3/2
Since the range of the sine function is -1 to 1, the second solution (-3/2) is not valid.
Now, to find the values of θ, we can use the inverse sine function (sin⁻¹) to solve for θ:
θ = sin⁻¹(2/3)
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What is the greatest common factor of the polynomial below?
12x²9x
OA. 4x
OB. 3x
OC. 4x²
OD. 3x²
The greatest common factor (GCF) of the polynomial 12x²9x is 3x, therefore option B is correct.
How to Find the Greatest Common Factor of a Polynomial?The Greatest Common Factor (GCF) of a polynomial is the largest factor that all of the terms in the polynomial have in common.
To find the GCF, we need to find the largest factor that both terms have in common. Both terms have a factor of 3x, so that is the greatest common factor. Factoring out 3x from each term gives:
12x²9x = 3x(4x)3(3x) = 3x(4x3)
So the GCF of 12x²9x is 3x.
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Two dice are rolled. Determine the probability of the following. ("Doubles" means both dice show the same number.)
Rolling an even number or doubles
The probability of the Doubles" means both dice show the same number is 36.
What is probability?When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
The probabilities of these two outcomes must be added in order to get the likelihood of rolling an even number or doubles, but since we have already tallied those outcomes twice, the probability of rolling both doubles and an even number must be subtracted. The probability of rolling doubles and an even number is 1/36 since rolling two sixes is the only method to get a double and an even number.
The likelihood of rolling an even number or doubles is thus:
The formula for P(even number or doubles) is P(even number) = P(even number) + P(doubles) - P(even number and doubles) = 1/2 + 1/6 - 1/36 = 19/36.
The odds of rolling an even number or two doubles are 19/36.
Therefore, the probability of the Doubles" means both dice show the same number is 36.
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Solve for p.
4(p+1.25)=725
Enter your answer as a decimal or fraction in simplest form in the box.
p =
$\text{Basic}$
30 pts
Answer:
180.9375
rounded 181
Step-by-step explanation:
firts we multiply by 4 the parentesis
4p+1.25=725
1.25 goes from adding to substracting
4p=725-1.25
then 4 goes to divide
p=723.75/4
so it will be 180.9375
rounded 181
Explain how counting number of girls in five children family can be treated as a binomial experiment. What assumptions are necessary?
This is a binomial experiment and you'll use the binomial probability distribution because:
There are two choices for each birth. Either you get a girl or you get a boy. So there are two outcomes to each trial. This is where the "bi" comes from in "binomial" (bi means 2).Each birth is independent of any other birth. The probability of getting a girl is the same for each trial. In this case, the probability is p = 1/2 = 0.5 = 50%There are fixed number of trials. In this case, there are 5 births so n = 5 is the number of trials.Since all of those conditions above are met, this means we have a binomial experiment.
Some textbooks may split up item #2 into two parts, but I chose to place them together since they are similar ideas.
the product of the square of h and 8
Answer:
\(h ^{2} \: \: and \: \: 64\)
The product of the square of h and 8 is \(8h^{2}\).
We now recognize that we should square the "\(h\)", which makes it "\(h^{2}\)". however, we want to understand the product of \(h^{2}\) an eight. A product is an answer to a multiplication problem, because of this we should multiply those phrases collectively. Consequently, the best expression is (\(h^{2}\)) x \(8\), which can be simplified to \(8h^{2}\)
To find the product of the square of \(h\) and \(8\)
First, the square of \(h\)
In a mathematical language, the square of \(h\) can be written as \(h^{2}\)
Second, the product of the square of \(h\) and \(8\)
When talking about products, you want to refer to multiplication. So, the statement can be written as \(8h^{2}\)
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-6x=48 true and false
The value of x that will make the expression true is -6
Simplifying equationsEquations are expressions separated by an equal sign
Given the equation below
-6x = 48
we need to determine the value of x from the expression
-6x/-6 =48/-6
x = 48/-6
Determine the value of x
x = -6
Hence the value of x that will make the expression true is -6
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school is canceled tomorrow or we are going hiking.
Answer:
School is canceled tomorrow so we are going for hiking