Amber solved the equation −2=10−3(2+6).
Match the property with each of Amber's steps for solving the equation.
Answers
The property use to solve the equation is as follows:
Distributive propertyCombine like termsAdditive property of equalityDivision property of equalityHow to solve equations?The equation can be solved as follows:
−2a = 10 − 3(2a + 6)
Using distributive property,
−2a = 10 − 3(2a + 6)
- 2a = 10 - 6a - 18
According to distributive law, multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together.
Combine like terms
- 2a = 10 - 6a - 18
- 2a = -6a - 8
Using additive property of equality, we will add 6a to both sides of the equation.
The additive property of equality states that if we add or subtract the same number to both sides of an equation, the sides remain equal.
- 2a = -6a - 8
- 2a + 6a = -6a + 6a - 8
4a = - 8
using division property of equality, we will divide both sides of the equation by 4.
The division property of equality states that if both sides of an equation are divided by a common real number that is not equal to 0, the quotients remain equal.
4a = - 8
4a / 4 = -8 / 4
a = - 2
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Related Questions
Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by the function below. Find the tax rate t that maximizes revenue for the government. (Round your answer to three decimal places.)
Answers
The given function for the sales of [tex]S(t) = 7 - 6 \cdot \sqrt[3]{t} [/tex], gives the tax rate that maximizes government revenue as t = 343/512
What is a government tax rate?The tax rate is the percentage of an amount that is paid to the government as tax.
The given function is presented as follows;
[tex]S(t) = 7 - 6 \cdot \sqrt[3]{t} [/tex]
Where;
t = The tax rate on imported shoes
S = The total sales
Taking the total sales as contributing to the government revenue, R(t), we have;
Revenue = R(t)
Which gives;
[tex]R(t) = t \times (7 - 6 \cdot {t}^{ \frac{1}{3} }) [/tex]
At the maximum total sales, we have;
[tex] \frac{dR(t)}{dt} = \frac{d t \times\left(7 - 6 \cdot {t}^{ \frac{1}{3} } \right) }{dt} = 0 [/tex]
[tex]\frac{d t \times\left(7 - 6 \cdot {t}^{ \frac{1}{3} } \right) }{dt} = 7- 8 \cdot \sqrt[3]{t} = 0[/tex]
Which gives;
At maximum revenue, t = (7/8)³
t ≈ 0.669921875
The tax rate that maximizes the government revenue is t = 343/512Learn more about government tax rate here:
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The formula used to convert degrees Celsius to degrees Fahrenheit is
F = C +32.
Convert 77°F to degrees Celsius. Solve the formula for C, and then use it to
convert the temperature.
Which is the correct formula and conversion?
Answers
77°F is equivalent to 45°C as per the given equation.
The correct formula for conversion is,°F = (°C × 9/5) + 32, and 77°F is equivalent to 25°C
This is a problem with the temperature conversion. We can solve this problem by following a few steps.
F = C +32 as per the question and the temperature is given as 77°. We have to convert this temperature to degrees Celsius. We can write C as (F-32).
Hence the formula for C can be written as C = F - 32
Now we can find convert the temperature,
C = F - 32
Or, C = 77 - 32 [ subtracting 32 from both sides ]
Or, C = 45
Here we can conclude that 77°F is equivalent to 45°C as per the question.
The correct formula for conversion is,
°F = (°C × 9/5) + 32
Or, 77 = (C × 9/5) + 32
Or, (C × 9/5) = 77 - 32 [ subtracting 32 from both sides ]
Or, (C × 9/5) = 45 [ multiplying both side with 5/9 ]
Or, C = (45×5) / 9 = 25
According to the correct conversion equation, 77°F is equivalent to 25°C
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if tommy has 34 has apples and she puts them in 3 baskets whats the anwser and with the reminder if it has one
Answers
34 / 3 = 11.3
Answer is 11.3, put a line over the 3 because it’s a repeating decimal
Metric area unit conversion with decimal valuesA rectangular field is 0.35 kilometers long and 0.2 kilometerswide. What is the area of the field in square meters? Do notround your answer.mX 5 ?Conversion facts for length1000 millimeters (mm) = 1 meter (m)100 centimeters (cm) = 1 meter (m)10 decimeters (dm) = 1 meter (m)1 decameter (dam) = 10 meters (m)1 hectometer (hm) = 100 meters (m)1 kilometer (km) = 1000 meters (m) I need help with this math problem.
Answers
Given that
The length of the rectangular field is 0.35 km and the width is 0.2 km. And we have to find the area of this field.
Explanation -
The formula for the area of the rectangle is
[tex]Area=length\times breadth[/tex]On substituting the values we have
[tex]\begin{gathered} Area=0.35\times0.2\text{ km}^2 \\ Area=0.07\text{ km}^2 \end{gathered}[/tex]Since the conversions are given as
[tex]\begin{gathered} 1\text{ km = 1000 m}^{\text{ }}=10^3\text{ m} \\ 1\text{ km}^2=10^6\text{ m} \end{gathered}[/tex]So the required answer in sq meters will be
[tex]\begin{gathered} Area=0.07\times10^6\text{ m}^2 \\ Area=7\times10^4\text{ m}^2=70000\text{ m}^2 \end{gathered}[/tex]So the final answer is 70000 sq meters.Challenge: The price of Stock A at 9 A.M. was $14.76. Since then, the price has been increasing at the rate of $0.09 each hour. At noon the price of Stock B was $15.26. It begins to decrease at the rate of $0.14 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
Answers
In one hour, the prices of the two stocks will be the same.
The price of stock A at 9 a.m. was $14.76.The rate of increase in the price of stock A per hour is $0.09.The price of stock B at 12 p.m. was $15.26.The rate of decrease in the price of stock B per hour is $0.14.Let the number of hours after which the prices of the two stocks become the same be "x".We also need to consider that the price of stock A is given at 9 a.m., whereas the price of stock B is given at 12 p.m.14.76 + (3+x)*0.09 = 15.26 - (x)*0.1414.76 + 0.27 + 0.09x = 15.26 - 0.14x0.23x = 0.23x = 1Thus, the number of hours after which the prices of the two stocks become the same is one hour.To learn more about rate, visit :
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The next model of a sports car will cost 13.8% more than the current model. The current model costs $56,000. How much will the price increase in dollars? What will be the price of the next model?
Answers
Current model is $56,000
New model is 13.8% more expensive
13.8% of 56,000 = 56000*13.8/100 = 772800/100 = 7728
Nex model price = 56000+7728 = 63728
Answers:
The price increase in dollars is $7,728
The price of the next model is $63,728
In the figure below, circle 1 is a unit circle. Circle 2 has a diameter that is one and half times longer than that of circle 1, and circle 3 has a diameter that is twice as long as that of circle 1. If angle Z is equal to 2 radians, what is the length of the arc between points I and J?
Answers
The length of an arc is given by:
[tex]s=r\timesθ[/tex]where r is the radius and θ is the measure of the angle in radians.
To find the radius:
radius in circle 1 = 1 (unit circle)
radius in circle 3 = 2 x 1 = 2.
Hence:
[tex]s=2\times2=4[/tex]ANSWER
the length of the arc between points I and J is 4
hwlp
The length of a rectangle is 6 feet more than twice the width. If the perimeter is 132 feet, find the dimensions.
Answers
Length=
L = 2w + 6
New equation =
P = 2(2w + 6) + 2w
P = 4w + 12 + 2w
P = 12 + 6w
As stated in the question, the perimeter is 132 feet:
So,
132 = 12 + 6w
120 = 6w
W = 20
Now let’s find length using width:
L = 2w + 6
L = 2(20)+ 6
L = 40 + 6
Now we know that
W = 20
L = 46
Find the area of the circle pictured above. Round your answer to the nearest tenth in^2
Answers
Area of the circle is 28.3 in^2
Here, we want to find the area of the circle
Mathematically, the area is;
[tex]\begin{gathered} \text{Area of circle = }\pi\text{ }\times r^2 \\ But\text{ r = }\frac{d}{2} \\ \\ Area\text{ of circle = }\frac{\pi\text{ }\times d^2}{4} \\ \\ from\text{ the question, d = 6 inches} \\ \pi\text{ = }\frac{22}{7} \\ \\ \\ \text{Area of circle = }\frac{\frac{22}{7\text{ }}\text{ }\times6^2}{4} \\ \\ \text{Area of circle = }\frac{22\text{ }\times\text{ 36}}{28} \\ \\ \text{Area of circle = 28.2857} \\ \\ \text{Area of circle = 28.3 in\textasciicircum{}2} \end{gathered}[/tex]Two angles are supplementary. The measure of one angle is x and the measure of the other angle is 4x, find the value of xa. 36b.18c.4d.5
Answers
we know that
If two angles are supplementary, then their sum is equal to 180 degrees
so
In this problem
x+4x=180
solve for x
5x=180
x=36
therefore
the answer is the option A
Part 2
The surface area of a cube is 42 in2. What is the volume of the cube?
Answers
Answer:
7√7 in or 18.52 in=======================
Let the side of the cube be a.
Then its surface area is:
S = 6a²Find the side of the cube:
42 = 6a²a² = 7a = √7Find the volume of the cube:
V = a³ = (√7)³ = 7√7 ≈ 18.52 inThere are 9 athletes at a track meet. How many different ways can they finish first'orsecond?
Answers
For the first place, we have 9 different options from the athletes, then for the second place, we would only have 8 different options, therefore, there are 9x8=72 ways they can finish first or second
351,528.094 in word form
Answers
Three hundred fifty-one thousand five hundred twenty-seven and ninety-four thousandths
If a number is added to the number of 5/6 and twice as much is added to the denominator, the result is 3/5, find the number
Answers
Answer:
[tex]x=7[/tex]Step-by-step explanation:
We have the number:
[tex]\frac{5}{6}[/tex]If a number is added to the numerator and twice as much is added to the denominator and the result is 3/5, we can create the following equation:
[tex]\frac{5+x}{6+2x}=\frac{3}{5}[/tex]Solve for x, using cross multiplication:
[tex]\begin{gathered} 5(5+x)=3(6+2x) \\ 25+5x=18+6x \\ -x=-7 \\ x=7 \end{gathered}[/tex]if Joey drives 222 3/4 miles 3 3/8 hours . if he drives at a constant rate how far will he drive in one hour ?
Answers
Start by making the mixed numbers into fractions using that:
[tex]A\frac{b}{c}=\frac{(A\cdot c)+b}{c}[/tex]According to this:
[tex]222\frac{3}{4}=\frac{(222\cdot4)+3}{4}=\frac{888+3}{4}=\frac{891}{4}[/tex][tex]3\frac{3}{8}=\frac{(8\cdot3)+3}{8}=\frac{24+3}{8}=\frac{27}{8}[/tex]To find the rate we divide the distance over the time
[tex]\frac{\frac{891}{4}}{\frac{27}{8}}=\frac{891\cdot8}{27\cdot4}=\frac{7128}{108}=\frac{66mi}{h}[/tex]The rate idicates that joey drives 66 miles in one hour.
Y varies inversely with the square of x. When x=4, then y=3. Find y when x=2
Answers
Answer:
y = 6
Step-by-step explanation:
y= [tex]\frac{1}{x}[/tex]
3 = [tex]\frac{1}{4}[/tex]k Solve for k by multiplying both sides by 4
12 = k
y = [tex]\frac{1}{2}[/tex](12)
y = [tex]\frac{12}{2}[/tex]
y= 6
LOOK AT THE PICTURE BELOW. Find an approximation for [tex] \sqrt{18} [/tex]
Answers
ANSWER:
[tex]\sqrt[]{18}=4.25[/tex]STEP-BY-STEP EXPLANATION:
We have to calculate the square root of 18, to locate it on the graph, like this:
[tex]\sqrt[]{18}=4.2426\cong4.25[/tex]simplify (4z-13)+(9-9z)
Answers
Answer:
the answer is -5z-4
Step-by-step explanation:
you just combined the like terms
The ratio of boys to girls in Janice's classroom is 3:5, and there are a total of 32 students in the class. Using completesentences, explain how you could draw a tape diagram to represent this situation. In your answer, draw a diagramand make sure to include what quantity each bar represents.
Answers
Teh ratio of boys to girls in JAnice's classroom is 3:5
Total number of students 32
Let the ratio constant is K
So,
The equation will be
3K + 5K=32
8K=32
K=32/8
K=4
So,
the boys will be
4 + 4 + 4 =3K =12
The number of girls will be :
4 + 4 + 4 + 4 + 4 = 5K =20
PLEASE HURRY
What is an equivalent expression for −12(8a − 7b) + 8(4x + 3y)?
Answers
Answer:
-96a + 84b + 32x + 24y
Step-by-step explanation:
if you simplify an answer then it is equivilent to the beggining equation
hope this helped:)
3. Refer to Table 1. Which of the following price floors would be binding in this market?
$1
$2
$3
$4
Answers
Explanation:
The term "binding price floor" means "a price that is above equilibrium".
If the floor is at equilibrium or lower, then buyers and sellers will just go for the equilibrium price (as they naturally would have done anyway) and there's no need for the floor. In such cases, the floor is considered non-binding.
As you pointed out in the table, the equilibrium price is $3 where quantity supplied equals quantity demanded. A binding floor price would be $4 since it's above equilibrium.
A rectangle has a length that is 3 more than twice the width. Its perimeter is 96 inches. Which equation models this? A. 2w + 3 = 96 B. w + 2m + 3 = 96 C. 2(w) + 2(w + 3) = 96 D. 2(w) + 2(2w + 3) = 96
Answers
ANSWER
EXPLANATION
Let the length of the rectangle be L.
Let the width of the rectangle be w.
The length of the rectangle is 3 more than twice the width.
This means that:
L = 3 + (2 * w)
L = 2w + 3
The perimeter of a rectangle is given as:
P = 2w + 2L
The perimeter of the rectangle is 96 inches. This means that:
96 = 2L + 2w
Recall that: L = 2w + 3
=> 96 = 2(w) + 2(2w + 3)
=> 2(w) + 2(2w + 3) = 96
Which is the equation of a circle that is centered at the origin?O (– 1)2 + (y – 1)2 = 4O2? + (y - 1)2 = 2O 2 + y2 = 7Ox+y=8
Answers
Standard equation of circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex][tex]\begin{gathered} \text{If centered at the origin:} \\ (h,\text{ k) = (0, 0)} \\ h\text{ = 0, k = 0} \end{gathered}[/tex][tex]\begin{gathered} \text{The equation of circle becomes:} \\ (x-0)^2+(y-0)^2=r^2 \\ x^2+y^2=r^2 \end{gathered}[/tex]comparing the above equation with the options given:
[tex]\begin{gathered} x^2+y^2=7\text{ has the form} \\ x^2+y^2=r^2,wherer^2\text{= }7 \end{gathered}[/tex][tex]x^2+y^2\text{ = 7 (option C)}[/tex]Which digit represents 100 times the value of the ones place
Answers
Depending upon the position of the digits represent the 100 times the place value of the ones place.
What is place value?
In mathematics, every digit can be defined as a place value in a number. Basically, it is completely depends on the position of the digits in a number. Most of the number has same digits, but their positions are different, which makes the number different.
According to the question, all the digits represents 100 times the place value of the ones place.
Those digits can be defined as [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]. But the position of the digit should be at the 100th place.
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Can you find the area of a square using the given side lengths:
Answers
Answer
• d) 0.01 m²
,• e) 12.25cm²
Explanation
The area of a square (A) is given by:
[tex]A=s^2[/tex]where s represents the side length.
• d) ,s = 0.1 ,m
Replacing the data we get:
[tex]A=(0.1)^2[/tex]Simplifying:
[tex]A=0.01m^2[/tex]• e) ,s = 3.5cm
Replacing the data we get:
[tex]A=(3.5)^2=12.25cm^2[/tex]Use the graph to answer the following questions.how much does the cost of cheese and crease for each ounce Milan buys? What is the slope of the line?
Answers
The graph given is a linear graph,
so that means that the cost of cheese is linearly related to the weight of cheese bought.
The increase in the cost of cheese increase for each ounce Milan buys is, therefore, the slope of the graph;
to find the slope of the graph, we use any two points on the line; i'll be using (4,96) and (2,48)
[tex]\text{slope}=\frac{96-48}{4-2}=\frac{48}{2}=24[/tex]This means that the cost of cheese increases by 24 cents for each ounce Milan buys.
Write the equation for f(x) and g(x). Then identify the reflection that transforms the graph of f(x) to the graph of g(x).
Answers
Given the figure of the functions f(x) and g(x)
The graph of the function is the shown lines
The equation of f(x):
As shown the line of f(x) passes through the points: (-2, 0) and (0, -1)
The slope of the line will be:
[tex]slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-0}{0-(-2)}=\frac{-1}{2}[/tex]The y-intercept = -1
so, the equation of f(x) =
[tex]f(x)=-\frac{1}{2}x-1[/tex]The equation of g(x):
As shown the line of g(x) passes through the points: (-2, 0) and (0, 1)
The slope of the line will be:
[tex]slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{1-0}{0-(-2)}=\frac{1}{2}[/tex]The y-intercept = 1
So, the equation of g(x) will be:
[tex]g(x)=\frac{1}{2}x+1[/tex]Identify the reflection that transforms the graph of f(x) to the graph of g(x).
As shown, the functions are symmetric around the x-axis
And as we can see for the same value of x: g(x) = -f(x)
So, the type of transformation is: Reflection over the x-axis
Museum entrance tickets cost $25. Then each special exhibit a person wishes to visit costs an additional $4. Write an expression that represents the cost to enter the museum and visit any number of special exhibits. Then find the cost for a person to enter and visit three exhibits.
Answers
ANSWER
T = 4x + 25;
T = $37
EXPLANATION
Let the number of special exhibits to be visited be x.
The cost of the musuem entrance ticket is $25 and each special exhibit costs an additional $4.
This means that the cost of cisiting x additional exhibits is:
4 * x = $4x
Therefore, the total cost to enter the musuem and visit any number of special exhibits is:
T = 4x + 25
That is the expression that represents the total cost.
If a person wants to visit three exhibits, it means that:
x = 3
Therefore, the total cost, T, is:
T = 4(3) + 25
T = 12 + 25
T = $37
That is the total cost to enter and visit three exhibits.
What is the rest of the pattern.
3, 6, 10, 15, _, _, _.
Answers
Answer:
3, 6, 10, 15, 21, 28, 36.
Step-by-step explanation:
3 (+3),
6 (+4),
10 (+5),
15 (+6),
21 (+7),
28 (+8),
36
Answer:
If my theory is right the next 3 numbers are 21,28,36
Step-by-step explanation:
Looking at the beginning you see that 3 goes to 6 which is a hop of 3
Then next is 6 to 10 which is a hop of 4
Then next is 10 to 15 which is a hop of 5
So I think it’s going in a chronological number order
So I say the next hops will be 6,7,8
Find the probability.When a single card is drawn from an ordinary 52-card deck, find the probability of getting a heart.A) 1/13B) 1/4C) 1/26D) 1/52
Answers
The probability of getting a red 7 would be; 1/26
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Given that the total number of cards is 52.
WE are asked to find the he probability of getting a red 7
Since there are 2 red 7 cards in the deck of cards.
So, the number of favourable outcomes would be 2.
n (E) = 2
The probability
P(E) = n (E) /n (S)
Therefore, the probability of getting a red 7 will be;
P(E) = n (E) /n (S)
P(E) = 2/52
P(E) = 1/26
Hence, The probability of getting a red 7 would be; 1/26
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