The product of 7 and the cube of a number, N is 7N³
How to find the product of 7 and the cube of a number?
Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
In order to determine the product of 7 and the cube of a number. We need to represent the number with a letter.
Let N represent the number.
Thus, we can then write that the product of 7 and the cube of a number, N is:
7 × N³ = 7N³
Note: product means multiplication
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NO LINKS!!
Please help me with these proofs Part 4
Given:
RC ⊥ OK,RK ≅ KSThe triangles ΔKRO and ΔKCO are right triangles with common leg and congruent hypotenuse. It is sufficient for HL (Hypotenuse - leg) congruence. RK and KC are hypotenuse and OK is common leg.
Statement Reason
RC ⊥ OK GivenRK ≅ KS Given∠1 and ∠2 are right angles Definition of perpendicularOK ≅ OK Reflexive property (common side)ΔKRO ≅ ΔKCO HL congruence ProvedProblem 4Given:
LG bisects ∠GFA,∠F ≅ ∠ATo prove FG ≅ AG, we'll first prove the triangles are congruent by AAS as we have one congruent angle pair, one side is common to both triangles, another pair of congruent angles is formed by the angle bisector. The common side is adjacent to one of the congruent angles but not included.
Statement Reason
LG bisects ∠GFA Given∠F ≅ ∠A Given∠1 ≅ ∠2 Definition of angle bisectorLG ≅ LG Reflexive property (common side)ΔLGA ≅ ΔLGF AAS congruenceFG ≅ AG CPCTCProvedThe slowest mammal is the three-toad sloth.The top speed of a three-toad sloth on the ground is about 1/4 foot per second.The top speed of a giant tortoises on the ground is about 1/3 foot per second.How much longer would it take a three-toad sloth than a giant tortoise to travel 12 feet on the ground?
Answer: 12 seconds
Step-by-step explanation: it takes 4 seconds for the sloth to travel 1 for so 4 times 12 is 48, it takes 3 seconds for the turtle to travel a foot so 3 times 12 is 36 and 48 - 36 is 12, 12 seconds
solve the inequality /2x+1/>=3
Hi there! |2x + 1| (greater than or equal to) 3. So the absolute value of an equation always results in a positive equation. If you haven't done negative integers yet, here..
|-4| = 4
|-3| = 3
|-2| = 2
-4 = -4
-3 = -3
-2 = -2
But when you put the absolute value marks next to them, the value turns positive. :D
So |2x + 1| is greater than or equal to 3. The number for x can be negative, since the equation is always turned positive. |2(-1) + 1| = 3 is 2(1) + 1 = 3. So yes, -1 would work. But then again, positive 1 will work too! The value just can't be zero, since that would be 2(0) + 1 = 3, which is 0 + 1 = 3, not true.
Values have to be [1, +infinity] and [-1, -infinity].
Hope that helps!
What will be your weekly gross pay if your hourly rate is 20 per hour, you work 48 hours and overtime rate is time and a half?
The weekly gross pay is 1040. The solution is obtained using arithmetic operations.
What are arithmetic operations?
There are four basic operations which are listed as follows:
•Addition(‘+’): This operation deals with finding the sum.
•Subtraction(‘-’): This operation deals with finding the difference.
•Multiplication(‘×’): This operation deals with finding the product.
•Division(‘÷’): This operation deals with finding the quotient.
Assumption: Weekly working hours are 40.
Since, the hourly rate is 20 per hour and working hours per week are 40
So, the weekly pay comes out to be 40*20= 800
The overtime rate is time and a half which comes out to be
20*1.5= 30 per hour
The overtime hours are 48-40=8 hours
So, the weekly overtime pay comes out to be 8*30= 240
The total pay= 800+240= 1040
Hence, the weekly gross pay is 1040.
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Give an example of a variable amount.
Variable amount include costs of goods sold (COGS), raw materials and production inputs, packaging, wages and commissions, and certain utilities.
What is variable amount?The investment return payable in addition to the Capital Protected Amount in respect of the Investment Element is referred to as the Variable Amount.Variable costs are costs that change with volume. Raw materials, piece-rate labor, production supplies, commissions, delivery costs, packaging supplies, and credit card fees are examples of variable costs. The variable costs of production are referred to as the "Cost of Goods Sold" in some accounting statements.The variable cost is calculated using the following formula:
Total variable cost = total output quantity x variable cost per unit output.Unit break-even point = Fixed costs/ (Sales price per unit – Variable cost per unit).To learn more about variable amount refer to :
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Blanca is going to use a box that is a rectangular prism for a card box at her son’s birthday party. She will wrap and decorate the box. The dimensions of the box are shown in the diagram.
What is the total surface area of the box in square inches?
The total surface area of the box is 465.5 square inches.
What is a prism?A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
From the figure,
Length = l = 10.5 in
Width = w = 7 in
Height = h = 9.1 in
The total surface area of the box.
= 2 (lw + wh + lh)
= 2 (10.5 x 7 + 7 x 9.1 + 10.5 x 9.1)
= 2 (73.5 + 63.7 + 95.55)
= 2 x 232.75
= 465.5 square inches.
Thus,
The total surface area is 465.5 square inches.
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Graph the line with slope 7 and y-intercept-7
Answer: y = 7x + 7
Step-by-step explanation:
The lines equation is y = 7x + 7
Here is a picture of graphing it (desmos)
f ( x ) = 2 x 2 + x − 2 , evaluate f ( − 4 )
884848383858684848493932929
Can y'all please help, thank you
When a graph is rising, you must first take the derivative, then set it equal to 0, and last determine out which zero values the variable is positive between.
Explain a graph.
A graph depicts how two variables that are mainly characterized along one of a pair of axes at right angles relate to one another. A typical method for depicting the relationships between data is via graphs. While taking up less space, a graph satisfies the goal of representing the data that are either too many or complex to be clearly specified in the text.
The graph demonstrates that the answer increases from x=-1 to x=2, hence the interval is (-1,2) and the decreasing interval starts at x=-1.
When a function is rising, you must first take the derivative, then set it equal to 0, and last figure out which zero values the function is positive between.
According to the available alternatives, the right answer is 2 because x=2 and finishes at x=3.
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GO= 10x - 4
EO = 3x + 8
E is the midpoint of G0. Solve for x and find the length of each segment.
Answer:
4
Step-by-step explanation:
x is equals to 4
..........
Please help me find the perimeter
Answer:
what is the dimensions then I can help
Answer:
HELP you find the perimeter of what? you didnt link it.
Step-by-step explanation:
Write the expressions using exponents 2•2•2
Solution
Step 1:
The number 2 appears 3 times in the multiplication.
Step 2:
So 2 × 2× 2= 8
Step 3:
The expression 8 has a base of 2 and an exponent of 3.
[tex]2 \times 2 \times 2 \\ = {2}^{3} [/tex]
what is the area of the triangle given below 13 by 10
3 pennies are in a fraction of a dollar
Answer:
3/100
Step-by-step explanation:
100 pennies equals 1 dollar so 3 over 100 is the fraction
is 1 over 3 = to 3 out of 3
the correct answer is No
Step-by-step explanation:
it's not equal
Answer:
[tex]\frac{1}{3}\neq\frac{3}{3}[/tex]
Step-by-step explanation:
The two numbers are different
Solve x - 5y = 6 for x.
Answer:
X=5y+6
Step-by-step explanation:
Answer:
the answer is x = 6 + 5y
An Airplane uses the equation y=0.28x+24 to calculate the fare y, in dollars, for a trip of x miles. What is the fare for 500-mile trip?
The fare for a 500-mile trip is 164.
What is the fare for a 500-mile trip?The equation provided in the question is known as a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.
The general form of a linear equation is:
y = mx + b
Where:
m = slope b = interceptIn the equation used to calculate the fare, y=0.28x+24, 0.28 is the variable cost and 24 is the fixed cost.
Cost of a 500-mile trip = y=0.28(500) +24
y = 140 + 24
y = 164
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For. Which boats can you use proportional reasoning to determine the location of the boat after 1 hour
When each set of data values is related by multiplying by a certain factor, the relationship is said to be proportional. A graph, an equation, or some data can all be used to identify proportional relationships.
What is a good illustration of a proportionate relationship?As an illustration of a proportionate relationship in real life, let's look at the following, There is a correlation between the number of gallons of gas we put in our car and the price we will have to pay when we fill up the tank. That is to say, the more gas we use, the more we will have to pay.When each set of data values is related by multiplying by a certain factor, the relationship is said to be proportional. A graph, an equation, or some data can all be used to identify proportional relationships.When each set of data values is related by multiplying by a certain factor, the relationship is said to be proportional.To learn more about proportional relationships refer to:
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I dont get this i get confused on it
The rate of total amount to pounds of meat is 33:11. Option B
The unit rate of total amount to pounds of meat is 3:1. Option F
How to determine unit rate?$33.00 for 11 pounds of meat
The rate of total amount to number of pounds = 33/11
= 33 : 11
The unit rate which refers to the rate of each pound of meat = Total cost / number of pounds
= 33/11
= 3/1
= 3 : 1
Hence, the rate and unit rate of the cost to pounds of meat is 33 : 11 and 3 : 1
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Swimming Pool On a certain hot summer's day, 639 people used the public swimming pool. The daily prices are $1.75 for children and $2.00 for adults. The receipts for admission totaled $1213.75.
How many children and how many adults swam at the public pool that day?
There were
children at the public pool.
On the hot summer day, 639 people used the public swimming pool.
How many children and how many adults swam at the public pool that day?Create two simultanous equations:Let c stand for the number of children that bought a ticket, and a stand for the number of adults that bought a ticket, you get your first equation, beingc+a=508
then, you now create a second equation for the prices of the tickets.(price of childrens tickets)(number of children that swam)+(price of adults tickets)(number of adults that swam) = total money collectedso:1.75c+2.25a=1083.00
now we still know, that a=508−cso we can substitute it into the second formula 1.75c+2.25(508−c)=1083now its just simple algebra1.75c+1143−2.25c=1083
60=0.5c
so: c=120
now we know, that 120 children went to the swimming pool.and we still have the formula from before:a=508−c
so a=388
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Pablo helped in the community garden for 2 3/4 hours this week. That was 1 5/6 equal length shifts because Paola stopped early one day when it started to rain
The single shift is 1.5 hours long if 2+3/4 hours equals 1+5/5 equal length shift.
What is meant by Fraction?Fractions are referred to in mathematics as the components of a whole. The entire can be a single item or a collection of items. When we slice a cake in real life, the portion represents the proportion of the cake that was originally cut. The word "fraction" has its roots in Latin. "Fractus" is the Latin word for "broken." The fraction was first expressed verbally in antiquity. Later, a numerical form was developed.
Paola contributed to the community garden for 2 + 3 / 4 hours this week, or a 1 + 5 / 6 times length of shift.
We must determine the duration of a single shift.
The correct fraction of the given mixed fractions must first be determined.
Numerator and denominator combine to form a fraction.
The numeral that appears above the division symbol is referred to as the numerator, while the numeral that appears below the division symbol is referred to as the denominator.
2+3/4=(8+3)/4=11/4
1+5/6=(6+5)/6=11/6
Let's say a shift lasts for x hours.
So,
11/4=11*x/6
11/4=11/6 x
66/44=x
x=3/2
x=1.5 hours.
As a result, the single shift is 1.5 hours long if 2+3/4 hours equals 1+5/5 equal length shift.
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what is 1+7 please give me the right answer
Answer:
1 + 7 = 8
The answer is 8.
Answer:
1+7=8
Step-by-step explanation:
The sum of the digits of a two-digit number is 7. The number is 10 times its tens digit. Find the number.
Answer:
70
Step-by-step explanation:
We know that the ones digit is zero, and thus the tens digit is 7.
ANSWER ASAP PLEASEEE
Answer:
(1,0)
Step-by-step explanation:
Two nearby towns have experienced changes in their populations over the past several years. Town A had a population of 15,000 residents in 2010 , and the number of residents has since decreased at a rate of 10% per year. Town B had a population of 7,000 residents in 2010 , and the number of residents has since increased at a rate of 400 people per year.
The populations of these two nearby towns, which have experienced population changes (decay and growth) over the past several years, are:
Town A = 15,000 x 0.9^nTown B = 7,000 + 400(n).How does population change?The population of the town may change by increasing or decreasing.
For Town A, the population decreased geometrically. The decrease or decay can be represented as an exponential decay function.
For Town B, the population increased arithmetically. The increase or growth can be represented as an arithmetic function.
Town A Town B
Population in 2010 15,000 7,000
Annual decrease rate 10%
Annual increase rate 400
Number of years n n
Population in n years:
Town A = 15,000 x 0.9^n
Town B = 7,000 + 400(n)
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Question Completion:What are the populations of these two towns after n years?
Simplify the given expression. Write answers with the positive exponents
x²⁸y²⁸ is the simplified form of the expression ( x⁻⁴ / y⁴ )⁻⁷ written in positive exponents.
What is the simplified form of the expression?Given the expression in the question;
( x⁻⁴ / y⁴ )⁻⁷
To simplify, apply the exponent rule;
b⁻ⁿ = 1/bⁿ
( x⁻⁴ / y⁴ )⁻⁷
Replace x⁻⁴ with 1/x⁴
( 1/x⁴ / y⁴ )⁻⁷
( 1/x⁴ × 1/y⁴ )⁻⁷
( ( 1 × 1 ) / ( x⁴ × y⁴ ) )⁻⁷
( 1/x⁴ y⁴ )⁻⁷
Change the sign of the exponent by rewriting the base as its reciprocal.
( x ⁴y⁴ )⁷
Apply product rule;
( bᵃ mᵇ)ⁿ = bᵃⁿ × mᵇⁿ
( x⁴ y⁴ )⁷
x⁴ ˣ⁷ × y⁴ ˣ⁷
x²⁸ × y²⁸
x²⁸y²⁸
Therefore, the simplified form of the expression is x²⁸y²⁸.
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Answer:
y^28 x^28
Step-by-step explanation:
Simplify the following:
(1/(x^4 y^4))^(-7)
(1/(x^4 y^4))^(-7) = (y^4/x^(-4))^7:
(y^4/x^(-4))^7
Multiply each exponent in y^4/x^(-4) by 7:
(y^(7×4))/((x^(-4))^7)
7×4 = 28:
y^28/(x^(-4))^7
Multiply exponents. (x^(-4))^7 = x^(-4×7):
y^28/x^(-4×7)
-4×7 = -28:
y^28/x^(-28)
Multiply the numerator of y^28/x^(-28) by the reciprocal of the denominator. y^28/x^(-28) = y^28 x^28:
Answer: y^28 x^28
8 + 13 + –85 = ??????????????????????????????????
Answer:
=-64
Step-by-step explanation:
8+13-85 = 21-85 = -64
Answer:
= -64
Step-by-step explanation:
+ * - = -
+ -85 = -85
then:
8 + 13 + -85 = 8 + 13 - 85 = 21 - 85
= -64
The relationship between the mass m in
kilograms of an organism and its metabolism P in
Calories per day can be represented by P = 73.3m³.
Find the mass of an organism that has a metabolism of
586.4 Calories per day.
Given that the relationship between the mass m in kilograms of an organism and its metabolism P in Calories per day can be represented by P = 73.3m^3
What does a math equation mean?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
We can use this equation to find the mass of an organism that has a metabolism of 586.4 calories per day.
P = 73.3m^3
586.4 = 73.3m^3
m^3 = 8
m = ∛8
m = 2
So the mass of an organism that has a metabolism of 586.4 calories per day is 2 kilograms.
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An inequality equivalent to: 6x+12≥48
A.
3x+6≥24.
B.
3x+12≥24.
C.
3x+12≥18.
D.
3x+21≥24.
An inequality equivalent to 6x+12≥48 is 3x+6≥24.
What is inequality?
Inequality means not equal. Generally, if two values are not equal, we use the “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.
This is because dividing both sides of the original inequality by 6 results in 3x + 6 ≥ 24.
In option B, C and D, the inequality is not equivalent to the original inequality, as they have different values on one side of the inequality sign.
In option B: 3x+12≥24, the left side of the inequality is greater than the left side of the original inequality.
In option C: 3x+12≥18, the right side of the inequality is lesser than the right side of the original inequality.
In option D: 3x+21≥24, the left side of the inequality is greater than the left side of the original inequality and the right side of the inequality is greater than the right side of the original inequality.
Hence, An inequality equivalent to 6x+12≥48 is 3x+6≥24.
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25. FIND THE ERROR In the system a + b = 7 and 1.29a + 0.49b = 6.63, a represents pounds of apples and b represents pounds of bananas a person bought. Guillermo and Cara are finding and interpreting the solution. Is either correct? Explain your reasoning. Guillermo 1.29a + 0.49b = 6.63 1.29a +0.49(a + 7) = 6.63 1.29a + 0.49a + 3.43 = 6.63 1.78a = 3.2 a = 1.8 a + b = 7, so b = 5.2. The solution (1.8, 5.2) means that 1.8 pounds of apples and 5.2 pounds of bananas were bought.
Cara 1.29a + 0.49b = 6,63 1.29(7-b) + 0.49b = 6.63 9.03 1.296 + 0.496 = 6.63 -0.8b = -2.4 b=3 The solution b = 3 means that 3 pounds of apples and 3 pounds of bananas were bought. uolunteers. The ratio of boys to girls is 7:5.
The error is to find the solution of system of equations.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The system of equations are,
⇒ a + b = 7 .. (i)
And 1.29a + 0.49b = 6.63 .. (ii)
Now, We can solve the system of equations as;
Here, The system of equations are,
⇒ a + b = 7
⇒ a = 7 - b .. (i)
And, ⇒ 1.29a + 0.49b = 6.63 .. (ii)
Substitute the value of a from (i) in (ii), we get;
⇒ 1.29a + 0.49b = 6.63
⇒ 1.29(7 - b) + 0.49b = 6.63
⇒ 9.03 - 1.29b + 0.49b = 6.63
⇒ - 0.8b = 6.63 - 9.03
⇒ - 0.8b = - 2.4
⇒ 0.8b = 2.4
⇒ b = 2.4 / 0.8
⇒ b = 3
And, From (i);
⇒ a = 7 - b .. (i)
⇒ a = 7 - 3
⇒ a = 4
Hence, The solution is, 4 pounds of apples and 3 pounds of bananas were bought.
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