The three consecutive even integers are 10, 12, and 14.
Given that three consecutive even number the sum of the smallest integer and twice the median is 20 more than the largest integer.
Let's represent the three consecutive even integers as follows:
The smallest integer: x
The median integer: x + 2 (since it's consecutive and even)
The largest integer: x + 4 (since it's consecutive and even)
Now, we can set up the equation based on the given information:
"The sum of the smallest integer and twice the median is 20 more than the largest integer."
This can be expressed as:
x + 2(x + 2) = (x + 4) + 20
Now, we can solve for x:
x + 2x + 4 = x + 24
Combine like terms:
3x + 4 = x + 24
Subtract x from both sides:
2x + 4 = 24
Subtract 4 from both sides:
2x = 20
Now, divide by 2:
x = 10
So, the smallest integer is 10, the median integer is x + 2 = 12, and the largest integer is x + 4 = 14.
Therefore, the three consecutive even integers are 10, 12, and 14.
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Explain how to compare 0.7 and 5/8.
A rectangle has a length of 6cm by 8cm. Which is the length of a diagonal of the rectangle?
A.10cm
B.14cm
C.24cm
D.28cm
E.48cm
Answer:
Your answer would be A 10cm
A(n) _______________ force can cause an object to change its speed and/or direction.
PLEASE HELP! What is the equation of this line? y = 2x y=−12x y=12x y=−2x Graph of a line passing through the origin and the point begin ordered pair 2 comma 4 end ordered pair
we know that
The line passing through the origin [tex](0,0)[/tex] and the point [tex](2,4)[/tex]
If the equation of the line passes through the origin
then
the equation of the line represent a direct variation
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
The constant k is equal to the slope m
with the point [tex](2,4)[/tex] find the constant of proportionality k
[tex]y/x=k[/tex]
substitute
[tex]4/2=k[/tex]
[tex]k=2[/tex]
The linear equation is equal to
[tex]y=2x[/tex]
therefore
the answer is
[tex]y=2x[/tex]
The required equation of the line passing through the origin and point (2, 4) is y = 2x.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at
x = 0.
Given, a line passes through origin (0, 0) and point (2, 4).
So slope is = (y₂ - y₁)/(x₂ - x₁) = (4 - 0)/(2 - 0) = 2.
Let the required equation of the line be y = mx + b.
∴ 4 = 2×2 + b.
b = 0.
So, the equation is y = 2x + 0 ⇒ y = 2x.
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What value of c makes the statement true? -2x3(cx3 + x2) = -10x6 - 2x5
Answer: The required value of c that makes the given statement true is 5.
Step-by-step explanation: We are given to find the value of c that makes the following statement TRUE :
[tex]-2x^3(cx^3+x^2)=-10x^6-2x^5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the value of c, we need to equate the coefficients of the same powers of the unknown variable x.
From equation (i), we have
[tex]-2x^3(cx^3+x^2)=-10x^6-2x^5\\\\\Rightarrow -2cx^{3+3}-2x^{3+2}=-10x^6-2x^5\\\\\Rightarrow -2cx^6-2x^5=-10x^6-2x^5.[/tex]
Equating the coefficients of [tex]x^6[/tex] on both sides of the above equation, we get
[tex]-2c=-10\\\\\Rightarrow c=\dfrac{-10}{-2}\\\\\Rightarrow c=5.[/tex]
Thus, the required value of c that makes the given statement true is 5.
Which of the following best defines the two quantities that are measured to find the call rate of a phone company? The quantity of price measured in dollars depends on the quantity of time measured in minutes. The quantity of time measured in minutes depends on the quantity of price measured in dollars. The quantity of time measured in minutes depends on the quantity of speed measured in calls per minute. The quantity of speed measured in calls per minute depends on the quantity of time measured in minutes.
Answer:
A. the quantity of price measured in dollars depends on the quantity of time measured in minutes.
Step-by-step explanation:
The following best defines the two quantities that are measured to find the call rate of a phone company:
A. the quantity of price measured in dollars depends on the quantity of time measured in minutes.
In this way we can determine that how much money will it cost in dollars for each minute of phone call.
What is the simplified form of the following expression? (y8)(y2) y10 y6 y16 y64
The simplified form of the expression (y^8)(y^2) is y^10, found by applying the laws of exponents that dictate adding the exponents when multiplying with the same base.
Explanation:The simplified form of the expression (y8)(y2) can be found using the laws of exponents which state that when multiplying two powers with the same base, you add the exponents. Here, since the base is y, and we have exponents 8 and 2, we add them together:
y8 × y2 = y8+2
This simplifies to y10, which is the compressed form of the given expression.
Final answer:
To simplify the expression (y⁸)(y²), use the rule of exponents which says that you add the exponents when multiplying powers with the same base, resulting in y¹⁰.
Explanation:
The question requires simplifying an algebraic expression with exponents. The given expression is (y⁸)(y²). To simplify this, we use the rule of exponents which states that when multiplying two powers with the same base, you add the exponents. Therefore, y⁸ × y² = y⁸₊²} = y¹⁰
13(21−3a)=6−a
no solution
−1
0
all real numbers
Answer:
No solution hope this helps:)
Step-by-step explanation:
Matt is five years older than twice his cousin Andy’s age. The sum of their ages is less than 35. Let x represent Andy's age.
Final answer:
To represent the relationship between Matt and Andy's ages mathematically, let x be Andy's age, and express Matt's age as 2x + 5. The inequality x + (2x + 5) < 35 simplifies to x < 10, indicating Andy's age must be less than 10.
Explanation:
The question involves creating an inequality to represent the relationship between Matt and Andy's ages, where Matt is five years older than twice Andy's age, and the sum of their ages is less than 35.
Let x represent Andy's age. The formula for Matt's age would be 2x + 5. To find the range of possible values for Andy's age, you would write the inequality x + (2x + 5) < 35.
Solving this inequality involves combining like terms and isolating the variable x.
Step 1: Combine like terms.
x + 2x + 5 < 35
Step 2: Simplify the inequality.
3x + 5 < 35
Step 3: Subtract 5 from both sides to isolate the term with x.
3x < 30
Step 4: Divide both sides by 3 to solve for x.
x < 10
This tells us that Andy's age must be less than 10 for the conditions to be met.
What is the solution to the equation 5(x - 3) + 7 = 5x - 8?
A.-8
B.0
C.All real numbers
D.No solution
Suppose the measure of an angle is 67 degrees what is the measure of its complementary angle
the greatest common factor of 162, 378, and 414
hello i was trying to get the understanding on how is 4-6+6=4,,,,,,,my answer (4-6=2+6=8) but me being in high school i know its not that easy.... So someone please break it down please???
A quantitative variable that has a finite or countable number of values is called
A quantitative variable with a countable number of values is known as a discrete variable, which includes whole number counts such as the number of yellow M&Ms or total M&Ms in a sample
A quantitative variable that has a finite or countable number of values is called a discrete variable. Quantitative discrete data such as the number of phone calls received each day can only take certain numerical values, which are typically integers like zero, one, two, or three. This is different from continuous data, which can take any value within a certain range, like weight or percentage values that can include fractions and decimals.
For example, in the case of counting M&Ms, the number of yellow M&Ms and the total number of M&Ms would be discrete data because they can only be whole numbers. In contrast, the weight of the M&Ms in ounces and the percentage that are red are examples of continuous data because these can take on any value, including fractions, within the range.
The distinction between discrete and continuous data is important for selecting appropriate statistical methods for analysis, as certain methods are more suitable for discrete data, while others are better for continuous data
What is the value of x?
A. 68°
B. 62°
C. 112°
D. 124
I need help with the functions and graphing
Andy is scuba diving.He starts at sea level and then descends 10 feet in 2 1/2 minutes.
a. how would you represent Andy's descend as a unit rate? Express your answer as an integer.
b. How much feet can he descend in 6 minutes?
If 3 is added to twice a number and this sum is multiplied by 2, the result is the same as if the number is multiplied by 3 and 4 is added to the product. what is the number?
The unknown number(n) is equal to - 2 satisfying asked statement.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let the unknown number be 'n'.
Given, If 3 is added to twice a number,
and this sum is multiplied by 2,
the result is the same as if the number is multiplied by 3
and 4 is added to the product.
∴ (2n + 3)×2 = n×3 + 4.
4n + 6 = 3n + 4.
4n - 3n = 4 - 6.
n = - 2.
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what is the light from a lazer pointer a point, line, line segment, ray or plane?
Find the middle term of ([tex]( x^{2}+2) ^{20}
[/tex]
The measure of a and the measure of b are complementary. the measure of a is 8 times the measure of
b. find the measurement of each angle.
Please help with this! Thanks!
B: measure of BCD=45; acute
C: measure of BCD=90; right
D: measure of BCD=42; acute
E: measure of BCD=17; acute
3x-6 = 2x+11
3x = 2x+17
x = 17
3(17)-6 = 45
2(17)+11 = 45
45+45 = 90
answer is C 90 degrees:right
The area of a rectangle is 440 square inches. The length of the rectangle is 29 inches more than its width. What is the length of the rectangle?
the length of the rectangle is either -11 inches or 40 inches.
Let the length of the rectangle be L.Let the width of the rectangle be W.Given the following data;
Area of rectangle = 440 square inchesTranslating the word problem into an algebraic equation, we have;
[tex]L = W + 29[/tex]
To find the length of the rectangle;
Mathematically, the area of a rectangle is given by the formula;
[tex]Area = L * W[/tex]
Substituting the values into the formula, we have;
[tex]440 = (W + 29) * W\\\\440 = W^{2} + 29W[/tex]
Rearranging the equation, we have;
[tex]W^{2} + 29W - 440 = 0[/tex]
W e would solve the quadratic equation by factorization;
[tex]W^{2} + 40W - 11W - 440 = 0\\\\W(W + 40) - 11(W + 40)\\\\(W + 40)(W- 11)[/tex]
Width, W = -40 0r 11 inches.
Next, we would find the length of the rectangle;
When Width, W = -40;
[tex]L = W + 29[/tex]
[tex]L = -40 + 29[/tex]
Length, L = -11 inches
When Width, W = 11;
[tex]L = W + 29[/tex]
[tex]L = 11 + 29[/tex]
Length, L = 40 inches
Therefore, the length of the rectangle is either -11 inches or 40 inches.
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Which algebraic expression has no like terms?a.-x+4y-6x+9 B.-4x+y+4y C.-3xy-8+xy+y^2 D.-x+7+3xy-4y
Answer:D
Step-by-step explanation:
Two complementary angles are expressed as 4x - 16 and 2x 10. find the number of degrees in each angle.
Two complementary angles are given as 4x - 16 and 2x + 10. Solving for x we find x = 16. Substituting x into the expressions for the angles, we find the angles to be 48 and 42 degrees.
Explanation:The task here is to find the value of two angles that are complementary. Given the expressions for the angles are 4x - 16 and 2x + 10. As complementary angles, they sum up to 90 degrees. Hence, mathematically, we can express this as (4x - 16) + (2x + 10) = 90.
Solving the equation, combine like terms to get 6x - 6 = 90. Then, add 6 to both sides to get 6x = 96. Divide each side by 6 to find x, hence x = 16.
Substitute x = 16 into 4x - 16, therefore the first angle is 4×16 - 16 = 48 degrees. Similarly, substitute x = 16 into 2x + 10, hence the second angle is 2×16 + 10 = 42 degrees. The angles are thus 48 and 42 degrees, which adds up to 90).
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Toss a fair coin 10 times what is the probability of getting 7 heads
A copy machine makes 44 copies per minute. how long does it take to make 154 copies?
Final answer:
It takes 3.5 minutes for a copy machine to make 154 copies at a rate of 44 copies per minute.
Explanation:
To find out how long it takes for a copy machine to make 154 copies at a rate of 44 copies per minute, we need to perform a division calculation. First, we divide the total number of copies needed (154 copies) by the rate at which the machine produces copies, which is 44 copies per minute.
The calculation is as follows:
154 copies ÷ 44 copies per minute = 3.5 minutes.
This means it would take the copy machine 3.5 minutes to produce 154 copies.
please round to the nearest tenth if possible.
jackson wants to divide 3\4 pound box of trail mix into small bags each of the bags will hold 1/12 pound of trail mix how many bags of trail mix can jackson fill
express 3.01 as a mixed number
Answer:
3 1/100
hope this is helpful!