Your answer 1) A teacher asked the class to solve the equation 3(x + 2) = 21. Robert wrote 3x + 6 = 21 as his first step. Which property did he use? associative property
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1) A teacher asked the class to solve the equation 3(x + 2) = 21. Robert wrote 3x + 6 = 21 as his first step. Which property did he use? associative property
The property used was Distributive property
so
3(x + 2) = 21
3x+3*2=21
3x+6=21
answer isDistributive propertyIf we have3(x+2)applying distributive property means, that you multiply the number outside the parenthesis by each number inside the parenthesisso3*x+3*23x+6Related Questions
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Which values from the set satisfy this inequality?
-5 - 3x > 10
{-15, -10, -5, 0, 5, 10, 15}
Answers
The values from the set satisfy this inequality include -15, and -10,
Which values from the set satisfy this inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
The values from the set satisfy this inequality will be:
-5 - 3x > 10
-5 - 3(-10) > 10
-5 + 30 > 10
25 > 10
Also,
-5 - 3x > 10
-5 - 3(-15) > 10
-5 + 45 > 10
40 > 10
The correct options are -10 and -15.
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what's the answer for this equation
x^3 - 3x^2 + 3x - 1 > 3/2x(x - 1)
Answers
hello
the answer to the question is:
x³ - 3x² + 3x - 1 > (3/2)x(x - 1)² ---->
(x - 1)³ > (3/2)x(x - 1)² ----> x - 1 > (3/2)x ---->
(1/2)x < - 1 ----> x < 2
Find the value that makes the equation true 18x-23=1+6x
Answers
Question 1 0.1 pts The initial cost of a pickup truck is $12,659 and will have a salvage value of $3,580 after five years. Maintenance is estimated to be a uniform gradient amount of $135 per year, with zero dollar for first year maintenance. The operation cost is estimated to be $0.2 per mile for 344 miles per month. If the interest rate is 12%, what is the annual equivalent cost (AEC) for the truck? Enter your answer as follow: 123456
Answers
The annual equivalent cost (AEC) for the pickup truck is $4,308. We found the equivalent uniform annual cost (EUAC) first.
To calculate the AEC, we need to first find the equivalent uniform annual cost (EUAC) which includes both the initial cost and the present value of the maintenance and operation costs.
Find the present value of maintenance costs over five years using the gradient formula:
PV maintenance = A * [(1+i)^n - (1+i- g)^n] / [i - g]where A = $135, i = 12%, g = 0, n = 5
PV maintenance = $501.21
Find the present value of operating costs over five years using the present value formula:
PV operation = C * [1 - (1 + i)^-n] / iwhere C = $0.2/mile * 344 miles/month * 12 months/year = $827.52/year, i = 12%, n = 5
PV operation = $3,322.08
Find the EUAC using the formula:
EUAC = (initial cost + PV maintenance + PV operation) * A/Pwhere A/P = [(1+i)^n * i] / [(1+i)^n - 1]
EUAC = ($12,659 + $501.21 + $3,322.08) * 0.1464EUAC = $2,219.77Finally, convert the EUAC to AEC by adding the present value of the salvage value and multiplying by the interest rate:
AEC = (EUAC + PV salvage) * iwhere PV salvage = $3,580 / \((1+i)^5\)
AEC = ($2,219.77 + $2,267.03) * 0.12AEC = $4,308.Learn more about Cost and Estimate:
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PLEASE HELP!!! MARKING AS BRAINLIST
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The probability that a randomly selected point within the circle falls in the red-shaded triangle is given as follows:
0.23.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The radius of a circle is the distance between the center and a point on the circumference of the circle, hence it is given as follows:
r = 13.
Then the area of the circle is given as follows:
A = π x 13² = 530.93.
The area of a right triangle is given as half the multiplication of the sides, hence:
A = 0.5 x 24 x 10 = 120.
Hence the probability is of:
p = 120/530.93 = 0.23.
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if a population of a town is recorded at 1,200 in the year 2000 and the population increases by exactly 50 people each year, what will be the population of the town in 2026? Be careful to treat the year 2000 as the beginning; let x be the number of years since the year 2000.
Answers
The required population of the town in 2026 will be 2,500.
We can use the given equation model:
Population = 1,200 + 50x
where x is the number of years since the year 2000.
To estimate the population in 2026, we need to find the value of x when the year is 2026.
2026 - 2000 = 26
So x = 26.
Now we can substitute x = 26 into the equation to find the population in 2026:
Population = 1,200 + 50x
Population = 1,200 + 50(26)
Population = 2,500
Therefore, the population of the town in 2026 will be 2,500.
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If x=yand yz, which statement must be true
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On the given statement, the transitive property is applicable. Thus option A is correct option.
According to the statement
we have to find that the which statements are true in the form of given statement.
So, For this purpose, we know that the
A property is called transitive property, if x, y and z are the three quantities, and if x is related to y by some rule, and y is related to z by the same rule, then we can say x is related to z by the same rule.
And the given equation is
x=y and y = z
from this it is clear that the x= z.
then transitive property is perfect for this.
So, On the given statement, the transitive property is applicable. Thus option A is correct option.
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Disclaimer: This question was incomplete. Please find the full content below.
Question:
If x=y and y = z, which statement must be true
A. Transitive property applicable here
B . Associative property applicable here
C . Distributive property applicable here
D . Identity property applicable here
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Question 1 of 10
Which expressions are equivalent to the one below? Check all that apply.
log 2-log 4
A. log(¹)
B. log 1
C. log(2) + log(¹)
D. log 2
Answers
"The correct option is C." The only expression that is equivalent to log 2 - log 4 is option C: log(2) + log(¹).
The expression "log 2 - log 4" can be simplified using logarithmic properties. Specifically, the property states that "log(a) - log(b) = log(a/b)." Applying this property to the given expression, we have "log 2 - log 4 = log(2/4) = log(1/2) = -log(2)."
The expression log 2 - log 4 can be simplified using logarithmic properties. Let's analyze each option:
A. log(¹): This expression is not equivalent to log 2 - log 4. The logarithm of 1 is 0, but it does not cancel out the terms log 2 and log 4.
B. log 1: This expression is equivalent to 0, but it does not cancel out the terms log 2 and log 4.
C. log(2) + log(¹): This expression is equivalent to log 2 + 0, which simplifies to just log 2. It is not equivalent to log 2 - log 4.
D. log 2: This expression is not equivalent to log 2 - log 4. It represents the logarithm of 2, but it does not account for the subtraction of log 4.
Option C, "log(2) + log(¹)," again uses an exponentiation notation without an exponent and is not a valid mathematical expression.
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Find the sum of the first 6 terms of the sequence: –3, 1, 5, 9, . . .A) 45B) 42C) 48D) 25
Answers
SOLUTION
From the sequence give
–3, 1, 5, 9, . . .
The first term, a = -3
The common difference, d = 4 (gotten by adding 4 to the next term).
The number of terms required n = 6.
Formula for sum of an arithmetic sequence is given by
\(S_n=\frac{n}{2}\lbrack2a+(n-1)d\rbrack\)Substituting these values into the equation above we have
\(\begin{gathered} S_n=\frac{n}{2}\lbrack2a+(n-1)d\rbrack \\ S_6=\frac{6}{2}\lbrack2\times-3+(6-1)4\rbrack \\ S_6=3\lbrack-6+(5)4\rbrack \\ S_6=3\lbrack-6+20\rbrack \\ S_6=3\lbrack14\rbrack \\ S_6=42 \end{gathered}\)Hence, the answer is 42, option B
Estimate the line of best fit using two points on the line (4,6) (9,10)
Answers
Answer:
y=4/5x+2 4/5
Step-by-step explanation:
i just took the test
Question 3 (1 point)
Karl wants to find the width RQ of a river. He starts at point R, and walks
perpendicular along the edge of the river 42 ft and marks point S. He then walks 28
ft further and marks point T. He turns 90° and walks until his location (point U), point
S, and point Q are collinear. Suppose TU= 68 ft. What is the width of the river in
feet?
Answers
The width RQ of the river is approximately 61.98 ft.
To find the width RQ of the river, we can use the properties of perpendicular lines and collinearity.
Given that Karl starts at point R and walks perpendicular along the edge of the river 42 ft to point S, we can draw a line segment RS of length 42 ft.
From point S, Karl walks 28 ft further to point T. We can draw another line segment ST of length 28 ft.
Now, Karl turns 90° from point T and walks until his location (point U), point S, and point Q are collinear. Let's denote the length of this line segment as UQ.
From the given information, we know that TU = 68 ft.
Since U, S, and Q are collinear, we can form a right triangle by connecting UQ and US.
The length of UQ can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, we have:
UQ² = TU² - US²
UQ² = 68² - 28²
UQ² = 4624 - 784
UQ² = 3840
Taking the square root of both sides, we have:
UQ = √3840
UQ ≈ 61.98 ft
Therefore, the width RQ of the river is approximately 61.98 ft.
Note: It's important to keep in mind that this solution assumes the river is a straight line and that Karl's path is perpendicular to the river's edge. In reality, the river's edge may not be perfectly straight, and the path Karl walks may not be exactly perpendicular.
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Graph the quadrilateral with the given vertices in the coordinate plane.
Answers
Because EF = GH = 4, EF≅GH, Because these are vertical line segments, their are slope undefined and they are parallel. EF and GH are opposite sides that are equal and parallel. So, EFGH is a parallelogram by the definition of a parallelogram.
What is a parallelogram?
A parallelogram is a simple quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposite or facing sides are equal in length, and its opposite angles are equal in size.
Given that E(-3,0), F(-3,4), G(3,-1),H(3,-5)
The quadrilateral is attached below.
The distance between two points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].
The length of EF is √[(-3 -(-3))² + (4- 0)²] = √4² = 4
The length of GH is √[(3 -3)² + (-1- (-5))²] = √4² = 4
Therefore, EF = GH = 4
The line segments are congruent.
The line segments are vertical, thus the slope of the line is undefined.
If opposite sides are equal and parallel, then the quadrilateral is a parallelogram.
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An insurance policy charges a regular risk premium, , at Years 0,1,2,3,…,9 from today. The policy pays a claim of 2 (i.e. × ) in 15 Years from today. Calculate the value of (to 2 decimal places), assuming an interest rate of 2% per annum.
Answers
Answer:
x = 12.29
Step-by-step explanation:
present value of the claim = x² / (1 + 2%)¹⁵ = 0.743x²
present value of the 10 premiums:
x + x/1.02 + x/1.02² + x/1.02³ + x/1.02⁴ + x/1.02⁵ + x/1.02⁶ + x/1.02⁷ + x/1.02⁸ + x/1.02⁹ = x + 0.9504x + 0.9612x + 0.9423x + 0.9238x + 0.9057x + 0.888x + 0.8706x + 0.8535x + 0.8368x = 9.1323x
0.743x² = 9.1323x
x² / x = 9.1323 / 0.743
x = 12.29
Answer
x = 12.29
Step-by-step explanation:
Given that the policy claims x² in 15 years, at 2% = 0.02, the present value of the claim is given as:
x²/(1 + 0.02)^15
= x²(1/1.02)^15
= 0.743x²
The present value of the 10 premiums:
x + x/1.02 + x/1.02² + x/1.02^3 + x/1.02^4 + x/1.02^5 + x/1.02^6 + x/1.02^7 + x/1.02^8 + x/1.02^9
= x + 0.9504x + 0.9612x + 0.9423x + 0.9238x + 0.9057x + 0.888x + 0.8706x + 0.8535x + 0.8368x
= 9.1323x
Now,
0.743x² = 9.1323x
x²/x = 9.1323/0.743
x = 12.29
This is what we are looking for.
put more than 5 points & will mark branliest.
Which fraction is equivalent to a repeating decimal?
A. 1/10
B. 1/15
C. 1/16
D. 1/20
Answers
Answer:
c. 1/16 = 0.0625 is ur answer buddy
What is the total weight of candy in a 5/6 pound bag site
Answers
We can see here that the total weight of candy in a 5/6 pound bag site is 377 grams.
What is weight?Weight is a measure of the force exerted by gravity on an object. It is the measure of how heavy an object is. Weight is typically expressed in units such as pounds or kilograms. The weight of an object can vary depending on the gravitational force acting on it.
There are 16 ounces in a pound.
Thus, a 5/6 pound bag of candy weighs
5/6 × 16 = 13.3 ounces.
If you want to know the weight in grams, 13.3 ounces is equal to 377 grams.
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PLEASE HELP I WILL GIVE 30 POINTS
Answers
The area of the base is 615.75 mm².
We can use the formula for the volume of a cylinder to find the height:
V = πr²h
Plugging in the given values:
980 = π(14)²h
Solving for h:
h = 980 / (π(14)²)
h ≈ 1.86 mm
Now, The area of the base is given by:
A = πr²
A = π(14)²
A ≈ 615.75 mm²
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If the base price of a concert ticket is $30, and a handling surcharge of 15% is added to the price, what is the total cost of the ticket? *
Answers
Answer:
34.50$
Step-by-step explanation:
30 * 0.15 = 4.50Then we add this surcharge (4.50$) to the base price of the ticket (30$) to get the total value of (34.50$).
Answer:
$34.50
Step-by-step explanation:
Handling surcharge = 15% of 30
\(=\dfrac{15}{100}*30\)
= $ 4.50
Total price = base price + handling surcharge
= 30 + 4.50
= $ 34.50
Which type of relationship is indicated by the residual plot? Non-linear relationship. Linear relationship Exponential relationship
Answers
The type of relationship that is indicated by the residual plot is given as follows:
Non-linear relationship.
How to classify the functions?A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.
A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.
For this problem, we have an alternative pattern, where the function neither multiplied nor added/subtracted by a constant value when the input is increased by one, hence we merely classify the relationship as a non-linear relationship.
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Pls help me (its a png)
Answers
Answer:
\((-2.9)^{8}\)
Step-by-step explanation:
\((-2.9)\) · \((-2.9)^{7}\)
We add the power of the two numbers. 1 + 7 = 8
So, the answer is \((-2.9)^{8}\)
Help me solve these two problems! Show the work
Answers
Answer:
see explanation
Step-by-step explanation:
2
4x² + 64 ← factor out the common factor of 4 from each term
= 4(x² + 16)
3
(a - 10)² = 121 ( take square root of both sides )
a - 10 = ± \(\sqrt{121}\) = ± 11 ( add 10 to both sides )
a = 10 ± 11
then
a = 10 - 11 = - 1
a = 10 + 11 = 21
A pole that is 3.3m tall casts a shadow that is 1.44m long. At the same time, a nearby building casts a shadow that is 47.75m long. How tall is the building? Round your answer to the nearest meter.
Answers
Answer:
20.8 would be the answer
Step-by-step explanation:
mathmatically indication example with solution
Answers
A mathematically indication example would be to solve the equation 3x + 2 = 14 for the value of x. The solution would be 4.
How to solve the equation ?Looking for a mathematically indication example, we can consider a simple mathematical equation with one variable and solve it.
The equation would be 3 x + 2 = 14.
So we can solve for the equation to be :
3x + 2 - 2 = 14 - 2
3x = 12
3 x / 3 = 12 / 3
x = 4
In conclusion, the mathematically indication example would be 3x + 2 = 14 and the value of x would be 4.
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Nvm I found the answer
Answers
Find the area of the composite figure below.
6 9
15
Answers
Answer:
180
Step-by-step explanation:
Triangle: 1/2BH
Square: BH
1. Split up the shapes
2. Use the area formula for square and triangle
Square area: 135
Triangle area: 45
3. Add
I need word form and decimal
(I already shaded it in so that is all I need
Answers
The shading is correct for each of the three problems. Nice work.
==========================================
Problem 13
Word form = one tenth
Decimal form = 0.1
Explanation: The 1 is in the tenths place for the decimal value 0.1 to represent the fraction 1/10.
==========================================
Problem 14
Word form = eighty-five hundredths
Decimal form = 0.85
Explanation: The 8 is in the tenths place, and the 5 is in the hundredths place. Overall, 0.85 represents 85 out of 100, aka 85/100.
==========================================
Problem 15
Word form = thirty-nine thousandths
Decimal form = 0.039
Explanation: The second zero is in the tenths place. The 3 is in the hundredths place. The 9 is in the thousandths place. The decimal represents 39/1000 which you can think of it as 039/1000.
Eighty five hundredths, 0.85
Thirty nine thousandths, 0.039
Hope this helps!!!
ASAP NEED HELP DESCRIBE AND GET CORRECT a) You are using the equation 4(p – 7) = 44 to determine how many pictures can be saved at one time to the photo stream on your cell phone. Describe the operations in the order that you will perform them to solve the equation. (3 points)a) You are using the equation 4(p – 7) = 44 to determine how many pictures can be saved at one time to the photo stream on your cell phone. Describe the operations in the order that you will perform them to solve the equation. (3 points)
Answers
Answer:
p = 18
Step-by-step explanation:
4(p – 7) = 44
Divide each side by 4, using the division property of equality
4(p – 7)/4 = 44/4
p-7 = 11
Add 7 to each side using the addition property of equality
p-7+7 = 11+7
p = 18
Answer:
he is right the guy above me
Step-by-step explanation:
What is the lowest common multiple of 10 and 12
Answers
Answer:
Your answer would be 60.
Step-by-step explanation:
12 doesn't equal anything that ten can equal until it reachest 60, therefore 60 is the least common multiple.
12 x 5 = 60
10 x 6 = 60
Last week Rachel walked 235 miles per day on each of the 7 days. During the same week, she also jogged 534 miles per day on 4 days. What is the total number of miles Rachel walked and jogged last week?
Answers
Answer:it should'nt be hard :)
Step-by-step explanation:
Answer:
3,781 miles
Step-by-step explanation:
Do 235x7 and 534x4. then add the two together. srry if im wrong btw. the total should be 3,781 .-.
This is a conversion graph between litres and gallons. Use the graph to convert 60 gallons to litres
Answers
Disclaimer: The conversion graph is missing in the question.
60 gallons is equal to 227.125 litres.
Refer to the attached image for the conversion of litres to gallons.
And gallons to litres.
In this image, a vertical line is drawn from the given value of gallon until it meets the cross line. And then a horizontal line is drawn, which touches the litres line.
At the point at which this horizontal line touches the litres line, that value is considered as the corresponding litres for the given gallons.
Similarly, a vertical line is drawn from the litres line until it meets the cross line. And then a vertical line is drawn, which touches the gallons line.
At the point at which this vertical line touches the gallons line, that value is considered as the corresponding gallons for the given litres.
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Show that the angle bisector of an equilateral triangle is perpendicular to the base
Answers
To show that the angle bisector of an equilateral triangle is perpendicular to the base, we can assume an equilateral triangle with sides ABC. Next, we can get an angle bisector in the middle represented by BD which becomes perpendicular to the base BC.
How to prove that the angle bisector is perpendicular to baseAfter getting the angle bisector, we would see that the line segment BD, divides angle BAC into two equal angles, each measuring 30 degrees. Now, we can draw a perpendicular line from point D to the base BC.
We could also draw a line E, which is the perpendicular line that intersects the base BC. We want to show that BD is perpendicular to BC, which means we need to show that angle BDE is a right angle.
Since the sum of angles BDA and ADE is 90 degrees (they form a right angle), and the sum of angles BAD, ABD, and BDA is 180 degrees, it follows that angle BDE must be a right angle.
Therefore, we have shown that the angle bisector of an equilateral triangle is perpendicular to the base.
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