A rectangle is transformed according to the rule r0, 90º. the image of the rectangle has vertices located at r'(–4, 4), s'(–4, 1), p'(–3, 1), and q'(–3, 4). what is the location of q?
Answer:
Clockwise vertices of q' ( -3 ,4) →→ q( 4 , 3 ).
Counter clock wise rule : q' (-3 ,4 ) →→ q( -4 , -3 ).
Step-by-step explanation:
Given : rectangle has vertices located at r'(–4, 4), s'(–4, 1), p'(–3, 1), and q'(–3, 4)
To find : transformed according to the rule 90º , what is the location of q?
Solution : we have given that
vertices located at r'(–4, 4), s'(–4, 1), p'(–3, 1), and q'(–3, 4).
By the rule of 90º rotation clock wise rule : (x ,y ) →→ ( y , -x )
90º rotation counter clock wise rule : (x ,y ) →→ ( -y , x ).
Then Clockwise vertices of q' ( -3 ,4) →→ q( 4 , 3 ).
counter clock wise rule : q' (-3 ,4 ) →→ q( -4 , -3 ).
Therefore, Clockwise vertices of q' ( -3 ,4) →→ q( 4 , 3 ).
counter clock wise rule : q' (-3 ,4 ) →→ q( -4 , -3 ).
The graph of y= x^2 is changed to y= x^2 - 3. How does this change in the equation affect the graph?
A.) the parabola shifts 3 units up.
B.) the parabola shifts 3 units down.
C.) the parabola becomes 3 units under
D.) the parabola becomes 3 units narrower.
The way it changes the graph is that the parabola shifts 3 units down.
Transformation of functionGraph of a quadratic function are parabolic in nature. The parent function is given as:
f(x) = x²
If the graph of the function is changed to y= x^2 - 3, this shows that the parent function was shifted down by 3 units.
Hence we can conclude that the way it changes the graph is that the parabola shifts 3 units down.
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Find the volume of the solid bounded above by the plane z = y + 8, below by the xy-plane, and on the sides by the circular cylinder x2 + y2 = 64.
The volume of the solid is found by integrating the area of circular cross-sections of the cylinder across its height affected by the plane z = y + 8. The integration from y = 0 to y = 8 and then doubling the result gives a volume of 12288π cubic units.
Explanation:To find the volume of the solid bounded above by the plane z = y + 8, below by the xy-plane, and on the sides by the circular cylinder x2 + y2 = 64, we can use the method of cross-sectional areas.
The equation x2 + y2 = 64 represents a circle with radius 8 in the xy-plane. The cross-sectional area of the cylinder at any height y is a circle's area, which is πr2. Since the radius r is 8, the area A is 64π.
The solid is bounded above by the plane, which means the height of this solid at any point (x, y) on the xy-plane is z = y + 8. To find the volume, we integrate the area over the range of y values within the cylinder, which are from -8 to 8. Keeping the symmetry in mind, we can double the integral from 0 to 8 to account for the full height.
So, the volume V is calculated as:
V = 2 × ∫0864π(y+8) dy
When you integrate, you get:
V = 2 × 64π[½ y2 + 8y]08
V = 2 × 64π[32 + 64]
Finally, simplifying the expression:
V = 2 × 64π(96)
V = 12288π cubic units.
This is the volume of the solid.
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Please help me thank you! PLEASE SHOW ALL WORK TOO!
I have 4 questions.
PLEASE HELP FAST AND SHOW ALL WORK!
Is the line through points P(-8-10) and Q(-5,-12) perpendicular to the line through points R(9,-6) and S(17,-5)? Explain.
The lines through points P and Q and points R and S are not perpendicular.
To determine if the line through points P(-8, -10) and Q(-5, -12) is perpendicular to the line through points R(9, -6) and S(17, -5), we need to calculate the slopes of both lines and check if they are negative reciprocals of each other. The slope of a line (m) through two points (x1, y1) and (x2, y2) is given by the formula m = (y2 - y1) / (x2 - x1).
For line PQ:
mPQ = (-12 + 10) / (-5 + 8) = -2 / 3
For line RS:
mRS = (-5 + 6) / (17 - 9) = 1 / 8
Now, the product of the slopes of two perpendicular lines is -1. Let's check if the product of mPQ and mRS is -1:
mPQ * mRS = (-2 / 3) * (1 / 8) = -2 / 24 = -1 / 12
Since -1 / 12 is not equal to -1, the lines are not perpendicular. Therefore, the line through points P and Q is not perpendicular to the line through points R and S.
TRUE OR FALSE : A pair of pants has been marked down from $36 to $27 . The percent decrease is 25%
The sixth graders are taking a field trip to the zoo. There are 591 sixth graders, and each bus holds 48 people. How many buses will be needed for the trip?
Find the value of x. If necessary, round to the nearest tenth.
Jaime wants to display her math test scores by using either a line plot or a stem and leaf plot. Her test scores are:
93, 95, 87, 90, 84, 81, 97, 98.
Which best explains what type of graph will better display the data?
a stem and leaf plot because the data can be grouped into sets of 10
a stem and leaf plot because each data point contains two digits
a line plot because there are only a few data points
a line plot because the numbers are all clustered near each other
Answer:
A
Step-by-step explanation:
hope it helps!!!!!!!
Answer:
A on edge 2020
Step-by-step explanation:
A security alarm requires a four-digit code. The code can use the digits 0–9 and the digits cannot be repeated.
Which expression can be used to determine the probability of the alarm code beginning with a number greater than 7?
A.(2P1)(9P3)/10P4
B.(2C1)(9C3)/10C4
C.(10P1)(9P3)/10P4
D.(10C1)(9C3)/10C4
Answer: A is the right answer. The probability of the alarm code beginning with a number greater than 7 =[tex]\frac{^2P_1\times\ ^9P_3}{^{10}P_4}[/tex].
Step-by-step explanation:
Given:A security alarm requires a four-digit code. The code can use the digits 0–9 and the digits cannot be repeated.
there is only 2 numbers which are greater than 7 i.e. 8 and 9. ∴ there is 2 possibility for first place.
For the remaining 3 digits there is 9 possibilities (including 1 which would left after choosing 1 from first place )
No of ways for the alarm code beginning with a number greater than 7=[tex]^2P_1\times\ ^9P_3[/tex]
Total ways of code with 4 digits=[tex]^{10}P_4[/tex]
Therefore the probability of the alarm code beginning with a number greater than 7 =[tex]\frac{^2P_1\times\ ^9P_3}{^{10}P_4}[/tex].
The cost in dollars of a class party is 59 + 13n, where n is the number of people attending. what is the cost for 44 people?
Seventeen less than four times a number is twenty-seven find the number
Identify the variation as direct, inverse, joint or combined.
y = 7x
Answer:
y =7x , follows the direct variation.
Step-by-step explanation:
Direct variation states that a relationship between two variables in which one is a constant multiple of the other. In other words, when one variable changes the other changes in proportion to the first.
If y is directly proportional to x i.e, [tex]y \propto x[/tex] or
y = kx .....[1] where k is the constant variation
Given : y = 7x
On comparing this with equation [1] we get;
k(constant of variation) = 7
therefore,
it follows the direct variation as [tex]y \propto x[/tex] or
y = 7x where k =7 is the constant of variation.
Therefore, y =7x follows the direct variation.
b(n)=-8-2(n-1) find the 9th term in the sequence
Answer:
-24
Step-by-step explanation:
We are given that
[tex]b(n)=-8-2(n-1)[/tex]
We have to find the 9th term in the sequence.
Substitute n=1
Then, we get
[tex]b(1)=-8[/tex]
Substitute n=2
Then,we get
b(2)=-8-2(2-1)=-8-2=-10
n=3
b(3)=-8-2(3-1)=-8-4=-12
[tex]d_1=b(2)-b(1)=-10-(-8)=-2[/tex]
[tex]d_2=b(3)-b(2)=-12-(-10)=-2[/tex]
[tex]d_1=d_2=d=-2[/tex]
When the difference between two consecutive terms is constant then, the sequence is called arithmetic sequence.
Therefore, the given sequence is in A.P
The nth term of A.P is given by
[tex]a_n=a+(n-1)d[/tex]
We have, [tex]a=b(1)=-8[/tex]
[tex]d=-2[/tex]
n=9
Substitute the values in the formula
[tex]a_9=-8+(9-1)(-2)=-8-16=-24[/tex]
[tex]a_9=b(9)=-24[/tex]
Megan is constructing the bisector of AB¯¯¯¯¯. She has already constructed two arcs as shown.
What should Megan do for her next step?
Use the straightedge to draw XY←→.
Place the point of the compass on point A and draw an arc, using AX as the width for the opening of the compass.
Place the point of the compass on point X and draw an arc, using AX as the width for the opening of the compass.
Use the straightedge to draw AX←→ and BX←→.
Kalahira is correct but the letters at the end might confuse you.
Correct answer:
Use the straightedge to draw XY←→.Ruby is visiting San Francisco. From her hotel she walks 4 blocks east and 2 blocks north to a coffee shop. Then she walks 5 blocks west and 1 block north to a museum. Where is the museum in relation to her hotel?
Answer:
The museum is 1 block west and 3 blocks north from the hotel.
Step-by-step explanation:
First of all, Ruby goes Northeast to a coffe shop, walking 4 blocks to the east and 2 blocks to the north. Then, she goes 5 blocks to the west, and 1 block to the north.
Therefore, she walks:
-3 blocks north
-4 blocks east
-5 blocks west
As east and west are contrary, we have to substract the lower number to the higher one in order to know the difference between both directions (5 W - 4 E = 1 W). As a result, Ruby finally moved west by 1 block.
Finally, we know that the museum is 1 block west and 3 blocks north from the hotel.
An Expression that represents 40% of a number is 40n
Which statement is always true?
a. linear pairs of angles are congruent
b. vertical angles are supplementary
c. adjacent angles are complementary
d. adjacent linear pairs of angles are supplementary?
The statement that is always true is: D. adjacent linear pairs of angles are supplementary.
What are Linear Pairs of Angles?Linear pairs of angles are angles that lie on the straight line. The sum of a linear pair is always 180 degrees, thus, they are regarded as supplementary angles.
Therefore, the statement that is always true is: D. adjacent linear pairs of angles are supplementary.
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Which of the sums below can be expressed as 6(3 + 9)?
18 + 54
18 + 9
9 + 15
6 + 54
The longer leg of a right triangle is 1inch longer than the shorter leg. the hypotenuse is 9inches longer than the shorter leg. find the side lengths of the triangle.
The Pythagorean theorem is applied to a right triangle with the longer leg being one inch longer than the shorter leg and the hypotenuse being nine inches longer than the shorter leg. The side lengths of the triangle are found to be 5 inches, 6 inches, and 14 inches.
Explanation:The subject of this question is mathematics, specifically the part of geometry that deals with right triangles and the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c), is equal to the sum of the squares of the other two sides (a and b), i.e., a² + b² = c².
In this problem, the longer leg (a) is represented as b = a + 1 and the hypotenuse (c) as c = a + 9. If you substitute these two equations into the Pythagorean theorem, you get (a + 1)² + a² = (a + 9)². Solving this equation gives a = 5 inches.
Substituting a = 5 inches into the expressions for b and c, we get b = 6 inches and c = 14 inches. Therefore, the sides of the triangle are 5 inches, 6 inches, and 14 inches.
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How many solutions can be found for the linear equation? 10(x + 6) 2 - 9 = (15x + 1) 3 - 8
The given linear equation will have only one possible solution
What is function?A function is a relation between a dependent and independent variable. We can write the examples of functions as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given is to find the total number of solutions for the linear equation -
10(x + 6) 2 - 9 = (15x + 1) 3 - 8
A linear equation is a equation of degree one. The number of solutions of a equation are equal to its degree. So, the given linear equation will have only one solution.
Therefore, the given linear equation will have only one possible solution.
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choose the expressions that are equal to 5.92+3.48
Identify the horizontal asymptote of f(x) = quantity 6 x minus 7 over quantity 11 x plus 8.
Twice a number is equal to negative four. Which equation could be used to find the number? 2n = 4 2n = -4n 2n - 4 2n = -4
This graph shows the cost of buying dried fruit.
What is the slope of the line and what does it mean in this situation?
Select from the drop-down menus to correctly complete each statement.
The slope of the line is ____. This means that every of dried fruit costs $____.
the correct answer is =
The slope of the line is 3.5
This means that every pound
of dried fruit cost $3.50
Slope of the line is 3.5. This means that every of dried fruit costs $3.5 per lb.
From the graph attached,
Points shown on the graph are (4, 14) and (8, 28).
Since, slope of a line passing two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, slope of the line passing through (4, 14) and (8, 28) will be,
Slope = [tex]\frac{28-14}{8-4}[/tex]
= [tex]\frac{14}{4}[/tex]
= 3.5
This means that every of dried fruit costs $3.5 per lb.
Therefore, slope of the line is 3.5. This means that every of dried fruit costs $3.5 per lb.
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Keisha is reading a 325-page book at a rate of 25 pages per day. Use a point-slope equation to determine
whether she will finish reading the book in 10 days.
Determine whether the function ƒ(x) = x(x3 − x) is even, odd or neither.
For the inverse variation equation xy = k, what is the value of x when y = 4 and k = 7? 3 28
Answer:
The value of x is [tex]\frac{7}{4}[/tex].
Step-by-step explanation:
It is given that the inverse variation equation is
[tex]xy=k[/tex] ..... (1)
The value of y is 4 and the value of k is 7.
Substitute y=4 and k=7 in equation (1).
[tex]x\times 4=7[/tex]
Divide both sides by 4.
[tex]\frac{x\times 4}{4}=\frac{7}{4}[/tex]
[tex]x=\frac{7}{4}[/tex]
Therefore the value of x is [tex]\frac{7}{4}[/tex].
85% of all cars sold in chicago are some color other than black. if three hundred black cars were sold in chicago, how many cars were sold there?
Show all work please
Final answer:
To find the total number of cars sold in Chicago, we can use percentages and proportions. We can set up a proportion and solve for the unknown variable. The total number of cars sold in Chicago is 1700.
Explanation:
To solve this problem, we can use the concept of percentages and proportions. We are given that 85% of all cars sold in Chicago are some color other than black, and we also know that 300 black cars were sold. We need to find the total number of cars sold in Chicago.
First, let's find the ratio of black cars to colored cars. Since the percentage of colored cars is 85%, the percentage of black cars would be 100% - 85% = 15%. We can express this as a ratio by writing it as 15/100.
Now, let's set up a proportion:
x/300 = 85/15
Next, we can cross-multiply and solve for x:
15x = 300 * 85
x = (300 * 85) / 15
x = 1700
Therefore, the total number of cars sold in Chicago is 1700.
Maggie earns money from working at the pet store and answering phones. She earns $10 each hour she works at the pet store and $0.25 for each phone call she answers. Maggie answered 60 phone calls and earned $115 last week.
Part A: Create an equation that will determine the number of hours she worked at the pet store. (3 points)
Part B: Solve this equation justifying each step with an algebraic property of equality. (6 points)
Part C: How many hours did Maggie work at the pet store last week? (1 point)
Can you solve Part B