Final answer:
The solution to the system of equations x + 2y = 7 and x - 2y = -1 is found by eliminating y, yielding x=3 and y=2, which is option B, (3, 2).
Explanation:
The solution to the system of equations x + 2y = 7 and x - 2y = -1 can be found by adding or subtracting the two equations to eliminate one of the variables. By adding the two equations, we eliminate y and get 2x = 6, which results in x = 3. Substituting x = 3 back into either of the original equations yields y = 2. Therefore, the solution to the system is (3, 2), which corresponds to option B.
EVEN OR ODD FUNCTIONS HELP! PLS!
Which of the graphs represent an even function? I think it's the first one.
Even and Odd Functions U3L2
1. f(x)=-x^2/x^4-25
2. The function is neither even nor odd.
3. The graph is symmetric about the origin.
4. 2ND graph from the question's photos (looks like mcdonalds logo)
youre welcome !
Solve y over negative 2 + 5 = 13.
an airplane takes off at a rate of 2,000 feet per minute. how long will it take the plane to reach 50,000 feet
Three collinear point
Your gross weekly salary is $800.00. Your federal income tax deduction is $53. The Social Security tax is 6.2%. The Medicare tax is 1.45% of gross pay. The state tax is 1.5% of gross pay. Each week you have $28.40 deducted for medical insurance and $12.00 for a health savings account. What is your net pay?
The net weekly pay is $633.4
How to determine the net pay?The gross pay is given as:
Gross = $800.00
The deductions are:
Federal income tax deduction = $53.Social Security tax = 6.2%. Medicare tax = 1.45%State tax = 1.5%Medical insurance = $28.40Health savings account = $12.00The net pay is then calculated as:
Net pay = 800.00 - (53 + 6.2% * 800 + 1.45% * 800 + 1.5% * 800 + 28.40 + 12.00)
Evaluate
Net pay = 633.4
Hence, the net weekly pay is $633.4
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Fill in the blanks to write an equation in slope-intercept form representing the function shown in the table.
y =
x +
The slope intercept equation which models the data in the table given ls y = 3x + 1
General form of a slope - intercept equation :
y = bx + c ; b = slope ; c = interceptSlope can be calculated thus:
Slope = (y2 - y1) /(x2 - x1)
Slope = (-2 + 8) / (-1 + 3)
Slope = 6/2 = 3
Taking any pair of points, we can calculate the intercept, c :
y = 3x + c
10 = 3(3) + c
10 = 9 + c
c = 10 - 9
c = 1
Therefore, the slope - intercept equation is y = 3x + 1
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Karen calculates the volume of cylinder A with a radius of 3 inches, and a height of 6 inches. The volume of this cyliner is 54pi inches cubed. Cylinder B also had a radius of 3 inches, but the height is doubled. What is the relationship between the volumes of the two cylinders?
Determine the axis of symmetry and the vertex of the given function. y = 2x2 − 12x + 21 Axis of symmetry: x = Vertex: ( , )
Answer:
The vertex of the function is (h,k)=(3,3)
The axis of symmetry is x=3.
Step-by-step explanation:
Given : Function [tex]y=2x^2-12x+21[/tex]
To find : Determine the axis of symmetry and the vertex of the given function.
Solution :
The quadratic function is in the form, [tex]y=ax^2+bx+c[/tex]
On comparing, a=2 , b=-12 and c=21
The vertex of the graph is denote by (h,k) and the formula to find the vertex is
For h, The x-coordinate of the vertex is given by,
[tex]h=-\frac{b}{2a}[/tex]
[tex]h=-\frac{-12}{2(2)}[/tex]
[tex]h=\frac{12}{4}[/tex]
[tex]h=3[/tex]
For k, The y-coordinate of the vertex is given by,
[tex]k=f(h)[/tex]
[tex]k=2h^2-12h+21[/tex]
[tex]k=2(3)^2-12(3)+21[/tex]
[tex]k=18-36+21[/tex]
[tex]k=3[/tex]
The vertex of the function is (h,k)=(3,3)
The x-coordinate of the vertex i.e. [tex]x=-\frac{b}{2a}[/tex] is the axis of symmetry,
So, [tex]x=-\frac{b}{2a}=3[/tex] (solved above)
So, The axis of symmetry is x=3.
The ages of mark and adam add up to 28 years total. mark is 20 years older than adam. how many years old is adam
Adam is 4 years old. This conclusion is reached by setting up a system of equations based on the information that Mark and Adam's ages add up to 28 years and Mark is 20 years older than Adam.
The student is asking how old Adam is, given that the total age of Mark and Adam is 28 years, and Mark is 20 years older than Adam. To solve this, we can set up a system of equations. Let Mark's age be represented by M and Adam's age be represented by A. The two equations based on the given information would be:
M + A = 28 (The sum of their ages is 28)M = A + 20 (Mark is 20 years older than Adam)Now, substituting the second equation into the first one, we get:
A + 20 + A = 28
This simplifies to:
2A + 20 = 28
Subtracting 20 from both sides, we have:
2A = 8
Dividing both sides by 2, we find:
A = 4
So, Adam is 4 years old.
Rotating a polygon in Quadrant II 270° clockwise is the same as
A) rotating it 90° clockwise.
B) rotating it 180° clockwise.
C) rotating it 90° counterclockwise.
D) rotating it 270° counterclockwise.
Defined by two lines or rays diverging from a common point.
A) arc
B) angle
C) parallel lines
D) perpendicular lines
What are two lines in the same plane that do not intersect?
A) angle
Eliminate
B) line segment
C) parallel lines
D) perpendicular lines
Solve the inequality. x - 5 ≤ -6
A. x ≤ -1
B. x ≤ -6/5
C. x ≤ - 11
D. x ≤ 11
Stanley ran a 5 kilometer race in 30 minutes.What was his speed in kilometers per hour?Round to the nearest tenth
True or false: the sum of relative frequencies in a distribution always equals 1.
Samantha has two pieces of cloth. One piece is 72 inches wide and the other piece is 90 inches wide. She wants to cut both pieces into strips of equal width that are as wide as possible. How wide should she cut the strips
d=11/5(p-15) solve for p
Point Q is the midpoint of GH. GQ=2x+3, and GH=5x−5 .
What is the length of GQ?
Enter your answer in the box.
____ units
The length of GQ is 25/3 units.
Explanation:To find the length of GQ, we need to equate GQ to GH and solve for x. Since Q is the midpoint of GH, the lengths GQ and QH are equal. Therefore, we have the equation:
2x + 3 = 5x - 5
Subtract 2x from both sides:
3 = 3x - 5
Add 5 to both sides:
8 = 3x
Divide both sides by 3:
x = 8/3
To find the length of GQ, substitute the value of x back into 2x + 3:
GQ = 2(8/3) + 3
GQ = 16/3 + 3
GQ = 16/3 + 9/3
GQ = 25/3 units
need hlp wit these math prob
see attached picture for answer:
for the format you need it would be 1.5x +-y = 12
which shows the set(s) the number 2.77 is an element of?
The correct answer is option a. 2.77 is an element of the set real numbers.
To determine which set(s) the number 2.77 is an element of, let's analyze each option:
1. Real numbers: The set of real numbers includes all rational and irrational numbers. This means any number that can be placed on the number line, including integers, fractions, and decimals. Since 2.77 is a decimal number, it is indeed a real number.
2. Real numbers and natural numbers: While 2.77 is a real number, natural numbers are a subset of real numbers that consist of all positive integers (1, 2, 3, ...). Since 2.77 is not a positive integer, it is not a natural number. Therefore, this option is incorrect because 2.77 is not a natural number.
3. Natural numbers and whole numbers: As mentioned, natural numbers are positive integers. Whole numbers include all natural numbers and the number 0 (0, 1, 2, 3, ...). Since 2.77 is neither a natural number nor a whole number, this option is incorrect.
4. Null set: The null set (or empty set) contains no elements. If 2.77 were in the null set, it would imply that the null set is not empty, which contradicts the definition of the null set. Therefore, this option is incorrect.
The complete question is
"Which shows the set(s) the number 2.77 is an element of?
a. real numbers
b. real numbers and natural numbers
c. natural numbers and whole numbers
d. null set"
The dimensions of a rectangular bin are consecutive integers. If the volume of the bin is 4896 cubic inches, what are the dimensions of the bin?
cubed root of 4896 = 16.98
round to 17
17-1 = 16
17 +1 = 18
16* 17 *18 = 4896
bin is 16 in x 17 in x 18 in
Answer:
The dimension of the rectangle is [tex]16\times 17\times 18[/tex]
Step-by-step explanation:
Given : The dimensions of a rectangular bin are consecutive integers. If the volume of the bin is 4896 cubic inches.
To find : What are the dimensions of the bin?
Solution :
The dimensions of a rectangular bin are consecutive integers.
Let the consecutive integers are x,x+1,x+2
So let, length, l=x
Breadth b=x+1
Height h=x+2
The volume of the bin is
[tex]V=l\times b\times h[/tex]
[tex]4896=x\times (x+1)\times (x+2)[/tex]
[tex]4896=(x^2+x)(x+2)[/tex]
[tex]4896=x^3+2x^2+x^2+2x[/tex]
[tex]x^3+3x^2+2x-4896=0[/tex]
Plot the equation graphically to find the value of x.
Refer the attached figure below.
The value of x is 16.
So, Length is l=16
Breadth is b=x+1=16+1=17
Height is h=x+2=16+2=18
The dimension of the rectangle is [tex]16\times 17\times 18[/tex]
The sum of the interior angles of a triangle is_______. 360° 180° 270° 540°
Which statement is true statement about rotation?
A. The image is smaller than the preimage.
B. The image overlaps the preimage.
C. The image is larger than the preimage
D. The image and preimage are congruent.
Answer:
The correct option is D. The image and preimage are congruent.
Step-by-step explanation:
Let us understand the this concept with the help of an example.
Consider the figure 1:
From the figure 1, it is clear that the size of image doesn't change.
Thus, option A and C are invalid.
Or we can say that, the image and preimage remain the same.
Therefore, the correct option is D. The image and preimage are congruent.
Whats the area of a circle with the diameter of 20 feet.
Find the difference of functions s and r shown below. r(x) = –x² + 3x
s(x) = 2x + 1 (s – r)(x) =
-x^2+3x-2x+1
(-x^2+3x)-2x+1
(2x+1)-(x^2 + 3x)
2x+1-x^2+3x
Answer:
(2x + 1) - (–x² + 3x) is difference .
Step-by-step explanation:
Given : r(x) = –x² + 3x and s(x) = 2x + 1
To find : Find the difference of functions s and r .
Solution : We have given that r(x) = –x² + 3x and s(x) = 2x + 1.
Difference :
(s – r)(x) = s(x) - r(x)
=(2x + 1) - (–x² + 3x)
= 2x +1 + x²-3x
= x²-x +1.
Therefore, (2x + 1) - (–x² + 3x) is difference .
The difference of the function is (2x+1)-(x^2 + 3x)
Difference of functions
Given the following functions
r(x) = –x² + 3x
s(x) = 2x + 1
Taking the difference of the function will give:
(s – r)(x) = 2x - 1 - (-x^2 + 3x)
Expand
(s – r)(x) = 2x - 1 + x^2 - 3x
(s – r)(x) = x^2 - x - 1
Hence the difference of the function is (2x+1)-(x^2 + 3x)
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Solve the following equation. Then place the correct number in the box provided. Leave answer in terms of a mixed number.
6(2P - 1) > 5P + 2
Answer:
p>[tex]\frac{8}{7}[/tex]
Step-by-step explanation:
The equation is 6(2 P-1) > 5 P +2
6(2 P-1)> 5 P+2
6×2 P-6×1> 5 P+2
12 P-6> 5 P+2
12 P - 5 P > 2+6
7 P > 8
P > [tex]\frac{8}{7}[/tex]
P is greater than[tex]\frac{8}{7}[/tex]
Hence, the correct answer is p greater than [tex]\frac{8}{7}[/tex]
The stage manager of a school play creates a rectangular acting area of 42 square yards. String lights will outline the acting area. To the nearest whole number, how many yards of string lights does the manager need to enclose this area?
Use the listing method to write the following set.
{x | x ∈ N, x < 3}
(A.) {1, 2, 3}
(B.) {0, 1, 2, 3}
(C.) {1, 2}
The probability that a driver is speeding on a stretch of road is 0.27. what is the probability that a driver is not speeding?
Answer: 0.73 since 1 - 1.27 = 0.73 so the drivers probability of not speeding is 0.73 hope it helps
If probability that a driver is speeding on a stretch of road is 0.27 then probability that a driver is not speeding is 0.73.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that the probability that a driver is speeding on a stretch of road is 0.27.
Probability(Speeding)=0.27
We need to find the probability that a driver is not speeding.
Probability(Not Speeding)=1-Probability(Speeding)
One minus zero point two seven
=1-0.27
We get zero point seven three
=0.73
Hence, if probability that a driver is speeding on a stretch of road is 0.27 then probability that a driver is not speeding is 0.73.
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When you are comparing two sets of data, and one set is strongly skewed and the other is symmetric, which measures of the center and variation should you choose for the comparison?
When comparing two sets of data, choose the median for skewed data and mean with standard deviation for symmetric data.
When comparing two sets of data where one is strongly skewed and the other is symmetric, for the comparison, it is advisable to choose the median as the measure of the center for the skewed data since it is resistant to outliers, and the mean and standard deviation for the symmetric data to give an overall representation of the data.
12-5x-4kx=y solve for x
Indicated operation on 1 2/3 + 5 3/8