let g(x) be a vertical shift of f(x)=-x up 4 units followed by a vertical stretch by a factor of 3. Write the rule for g(x).
A function assigns the values. The function g(x) can be written as g(x) = -3x + 12.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given the function f(x)=-x, now since a transformed function g(x) is produced by shifting the function 4 units upwards and vertical stretch by a factor of 3. Therefore, g(x) can be written as,
Vertical Shift by 4 units,
f(x)+4
Vertical stretch by a factor of 3
g(x) = 3(f(x) + 4)
g(x) = -3x + 12
Hence, the function g(x) can be written as g(x) = -3x + 12.
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how many sets of 5 students can be selected out of 30 students?
Answer:
142 506
Step-by-step explanation:
here the order does not matter
Then
we the number of sets is equal to the number of combinations.
Using the formula :
the number of sets is 30C5
[tex]C{}^{5}_{30}=\frac{30!}{5!\left( 30-5\right) !}[/tex]
[tex]=142506[/tex]
There are 142506 ways in which 5 students can be selected out of 30 students.
How can a certain number of individuals be selected using a combination?The selection of 5 students out of 30 students can be achieved with the use of combination since the order of selection is not required to be put into consideration.
By using the formula:
[tex]\mathbf{^nC_r = \dfrac{n!}{r!(n-r)!}}[/tex]
where;
n = total number of individual in the set = 30r = number of chosing individuals to be selected = 5[tex]\mathbf{^nC_r = \dfrac{30!}{5!(30-5)!}}[/tex]
[tex]\mathbf{^nC_r = \dfrac{30!}{5!(25)!}}[/tex]
[tex]\mathbf{^nC_r = 142506}[/tex]
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In order to create a system of equations that has the same solution as the system
x+y=4
2x+y = 7
complete three steps.
1
Step 1: Multiply the equation x + y = 4 by _[blank A]__.
Step 2: Add the equations 2x + y = 7 and _[blank B]_.
Step 3: Write the new system of equations as _[blank C]__.
Match each blank with the system or statement that correctly fills in that blank.
#Step1
Multiply by -2It will result -2x-2y=-8
#2
-2x-2y=-8#3
add
-y=-1y=1Find x
x+1=4x=3The area of a square is given by and the perimeter is given by , where s is the side length of the square.
If the side length of a square is 4 inches, its area is
square inches and its perimeter is
inches.
The area of the square is 16 square inches and its perimeter is 16 inches.
What is Area of square ?
A square is a two-dimensional geometric shape with four equal sides and four right angles. The area of a square is the measure of the region enclosed by the square. The area is expressed in square units, such as square inches, square meters, or square feet.
The area of a square is given by the formula:
A = s²
where A is the area and s is the length of a side.
If the side length of the square is 4 inches, the area can be calculated as:
A = 4² = 16 square inches.
The perimeter of a square is given by the formula:
P = 4s
where P is the perimeter and s is the length of a side.
If the side length of the square is 4 inches, the perimeter can be calculated as:
P = 4 x 4 = 16 inches.
Therefore, the area of the square is 16 square inches and its perimeter is 16 inches.
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What is the line that has a slope of -2/3 and passes through point -3,-1?
Answer:
y = (- 2/3)x - 3
Step-by-step explanation:
y = mx + c
y = (- 2/3)x + c
Now let's substitute the values (-3,-1)- 1 = (- 2/3)(-3) + c
-1 = 2 + c
c = - 3
Therefore,
y = (-2/3)x - 3
Answer:
y = -2/3x - 3
Step-by-step explanation:
y = mx + b
y = y coordinate → given: - 1
m = slope → given: - 2/3
x = x coordinate → given: - 3
b = y intercept → need to find
y = -2/3x + b → -1 = -2/3(-3) + b
-1 = 2 + b
subtract 2 from both sides
-1 - 2 = 2 - 2 + b
-3 = b
y = -2/3x - 3
Suppose f(x) = x² and g(x)= (1/5x)^2
Which statement best compares the graph of g(x) with the graph of f(x)?
A. The graph of g(x) is the graph of f(x) shifted units left.
B. The graph of g(x) is the graph of f(x) vertically stretched by a
factor of 5.
OC. The graph of g(x) is the graph of f(x) horizontally stretched by a
factor of 5.
D. The graph of g(x) is the graph of f(x) horizontally compressed by a
factor of 5.
Answer:
B. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.
For what value of x is line m parallel to line n?
Answer:
[tex]x=10[/tex]
Step-by-step explanation:
Here, we can use an angle rule.
We see that angles [tex](8x+50)[/tex]° and 130° are under a sort of F shape, where lines m and n are the horizontal parts of the letter and where the diagonal line is the vertical part of the letter.
This means we can use the rule:
Corresponding angles are equal.
This means that:
[tex]8x + 50 = 130[/tex]
We can now use this equation we have formed to solve for [tex]x[/tex]:
[tex]8x + 50 = 130\\8x = 80\\x = 10[/tex]
Therefore, our final answer is [tex]x=10[/tex].
Jamie is walking her neighbors’ dog while they are away. She is keeping track of the total number of blocks she walks over time.
A 2-column table with 3 rows. Column 1 is labeled Minutes with entries 6, 14, 20. Column 2 is labeled Blocks with entries 3, 7, 10.
Does the table represent a proportional relationship?
Yes, because both columns are written in ascending order.
Yes, because the values in the second column are less than the values in the first column.
Yes, because the ratios are equivalent between each pair of values.
No, because the values in the table do not increase by the same amount in each row.
Answer:
Yes, the relation is proportional because the ratios are equivalent between each pair of values
Step-by-step explanation:
Proportional relationships are relationships with equal ratios.
Entries in the respective columns are:
column 1 (Minutes) column 2 (Blocks) Ratios
6 3 1/2
14 7 1/2
20 10 1/2
As the ratio of Blocks and Minutes is same for every row,
the given table represent a proportional relationship.
hence, option c is correct.
Yes, because the ratios are equivalent between each pair of values.
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Answer: Yes, the relation is proportional because the ratios are equivalent between each pair of values :)
What is The Value Of X
Answer:
X = 92 degrees
Step-by-step explanation:
the angles of a triangle all add up to 180 degrees, so 40 plus 180-132 = 88
180-88= 92 so X = 92
Find the range of values of x for which
[tex]2{x}^{2} \geqslant 9x + 5[/tex]
See attached images for work.
What's your annual income if you're unemployed?
Answer:
$46,819 is the average unemployed salary
URGENTTT...A survey asks teachers and students whether they would like the new school mascot to be a pirate or a moose. This table shows the results:
The option second "No, they are not independent because P(student)≈ 0.82 and P(student pirate) ≈ 0.94" is the correct option (B) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have a table given that shows the survey asks teachers and students whether they would like the new school mascot to be a pirate or a moose.
The probability of a person that is a student:
P(student) = (75+15)/110 = 0.83
The probability:
P(student|pirate) = 75/80 = 0.93
The probability of both events is different.
Thus, the option second "No, they are not independent because P(student)≈ 0.82 and P(student pirate) ≈ 0.94" is the correct option (B) is correct.
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The Ferris Wheel has a diameter of 30 meters, the center is 19 meters off the ground and it makes 2 revolutions per min.
Draw this Ferris Wheel, labeling the radius, height, and center. Supposing the minimum height of the Ferris Wheel occurs when t=0, write the sinusoidal function for the height as a function of time. Last graph on a coordinate plane, label the key points.
The sinusoidal function for the height as a function of time will be h= -15 cos (πt/15)+19 meter
As the Ferris wheel starts with the rider from the bottom position (which is the minimum point in the cycle), we can represent the position of the rider with a negative cosine function.
The general form of the cosine function representing the displacement of the rider is:
f(t) = a cos(bt+c) + d, where:
amplitude = |a| which is the distance that travels above and below the midpoint
period = 2 π/|b| which is the time period i.e. time required to complete one cycle
-c/b is the phase shift.
d = vertical displacement of the function
Given the diameter of the wheel is 30 m, then r = 30/2 = 15 m.
So the distance that travels above and below the midpoint is the radius for which a=15. As we have the negative cosine function, a = -15.
The time period is 0.5min. As it is given the frequency is 2 revolutions per min for which b= 2(2π) rad/min.= 4π/60 rad/sec.= π/15 rad/sec.
The rider starts from the bottom position, so there will be no phase shift, so c=0
Given that the center of the wheel is 19 m above the ground, so d=19m
Therefore the equation will be
height of rider as function of time(t) = h = -15 cos (πt/15)+19 meter
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find area of shape below to 1 dp
The shape will have a surface area of 189.25 cm². There are two distinct pieces to the figure: a rectangle and a semicircle.
What is the area?The space filled by a flat form or the surface of an item is known as the area.
The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.
The figure is divided into two parts one is a rectangle and the second is a semicircle.
Area of figure = Area of rectangle + Area of a semicircle
Area of figure = L × B + (πr²/2)
A = 10 cm × 15 cm + (3.14 ×(5)^2/2)
A= 189.25 cm²
Hence the area of the shape will be 189.25 cm²
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Example 1.29 Initially, a box contains three white and five red balls. Balls
are drawn at random from the box. Whenever a red ball is drawn, it is placed
back into the box together with one extra red ball. Whenever a white ball is
drawn, it is placed back into the box together with two extra white balls. What
is the probability that the first three balls are drawn out of the box alternated
in colour?
Using it's concept, it is found that there is a 0.1541 = 15.41% probability that the first three balls are drawn out of the box alternated in colour.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Considering the situation described, the ways that alternate colored balls can be taken with the probabilities given as follows:
R(5/8) - W(3/9) - R(5/11).W(3/8) - R(5/10) - W(5/11).Hence the probability that the first three balls are drawn out of the box alternated in colour is given by:
[tex]p = \frac{5}{8} \times \frac{3}{9} \times \frac{5}{11} + \frac{3}{8} \times \frac{5}{10} \times \frac{5}{11} = 0.0689 + 0.0852 = 0.1541[/tex].
0.1541 = 15.41% probability that the first three balls are drawn out of the box alternated in colour.
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tôi là người Việt Nam ai giúp giải bài này nha bài 2 ạ
Multiply (5z + 6)(2z + 1)(2z - 1)
Pls help and explain WELL ty
Answer:
[tex]\huge\boxed{\sf 20z\³ + 24z\² - 5z - 6}[/tex]
Step-by-step explanation:
Given expression:= (5z + 6)(2z + 1)(2x - 1)
Using formula (a + b)(a - b) = a² - b²= (5z + 6)[(2z)² - (1)²]
= (5z + 6)(4z² - 1)
Distributing
= 5z (4z² - 1) + 6(4z² - 1)
= 20z³ - 5z + 24z² - 6
Arrange
= 20z³ + 24z² - 5z - 6
[tex]\rule[225]{225}{2}[/tex]
What is the length of DE?
A A
12
DXE
A. 6
B. 8
C. 5
D. 7
Answer:
A
Step-by-step explanation:
these two triangles are similar
therefore corresping sides are proportionate
12/8=9/x
12x=72
x=72/12=6
Answer:
the answer is 6
Step-by-step explanation:
i hope this is helpful
Find the average rate of change of f(x) = -3x² + 1 over each of the following intervals.
(a) From 2 to 4
(b) From -2 to 0
(c) From 2 to 5
The average rate of change of f(x) = -3x² + 1 over each of the given intervals are; -18, 6 nd 38
How to find the average rate of change?We are given the function;
f(x) = -3x² + 1
(a) From 2 to 4;
f(2) = -3(2)² + 1
f(2) = -12 + 1
f(2) = -11 (2, -11)
f(4) = -3(4)² + 1
f(4) = -47 (4, -47)
Slope = (-47 - (-11))/(4 - 2)
Slope = -36/2
Slope = -18
(B) From -2 to 0;
f(-2) = -3(-2)² + 1
f(2) = -12 + 1
f(2) = -11 (-2, -11)
f(4) = -3(0)² + 1
f(4) = 1 (0, 1)
Slope = (1 - (-11))/(0 - (-2))
Slope = 12/2
Slope = 6
(C) From 2 to 5;
f(2) = -3(2)² + 1
f(2) = -12 + 1
f(2) = -11 (2, -11)
f(5) = -3(5)² + 1
f(5) = -74 (0, -74)
Slope = ((-74) - 2)/(0 - 2)
Slope = -76/-2
Slope = 38
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The graph of which function has an axis of symmetry at x = 3?
f(x) = x2 + 3x + 1
On a coordinate plane, a parabola opens up. It goes through (negative 4, 5), has a vertex at (negative 1.75, 6.75), and goes through (1, 5).
f(x) = x2 – 3x – 3
On a coordinate plane, a parabola opens up. It goes through (negative 2, 7), has a vertex at (1.75, 5), and goes through (5, 7).
The graph of the function has an axis of symmetry at x = 3 will be D. f(x) = x² - 6x - 1. On a coordinate plane, a parabola opens up, it goes through (0, negative 1), has a vertex at (3, negative 10) and goes through (6, 0).
What is axis of symmetry?It should be noted that the axis of symettry is the line that divides an object into two equal halves.
Here, the graph of the function has an axis of symmetry at x = 3 is option D. On the coordinate plane, a parabola opens up, it goes through (0, negative 1), has a vertex at (3, negative 10) and goes through (6, 0).
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Answer: D. f(x) = x² - 6x - 1
Right on Edge 2023 :)
Find the value of x in each case:
x = 90°
2x = 180°
Step-by-step explanation:
angle VTS= angle TSR (alternate angle)
now in ∆TRS,
2x + x + x = 360° (angle sum property of ∆)
4x = 360°
x = 90°
You buy 2 shirts and 1 pair of pants for $34. Your friend buys 3 shirts and 3 pairs of pants for $69. What is the price of 1 shirt and 1 pair of pants
You buy 3 shirts and 1 pair of pants for $32. Your friend buys 2 shirts and 3 pairs of pants for $40. How much did each item cost?
First let’s define a shirt as X and pants as Y!
In the first scenario, the equation will be 3X + Y =$32
In the second scenario, the equation will be 2X + 3Y = $40
Now because we have two different variables (X & Y) let’s solve for one of them (Ex: Y) to simplify the equations!
3X + Y= $32—> subtract 3X on both sides of the equation
-3X. - 3X
Net result: Y= 32- 3X
Now we can insert this into the second equation 2X + 3Y = $40 in order to solve for X variable
2X + 3(32-3X) = $40
2X + 96 - 9X = $40 —> simplify the equation
-7X + 96 = $40 —> substrate 96 from both sides
-7X = -56 —> divide both sides by -7
X= 8
Now reinsert 8= X into 3X + Y = $32
3(8) + Y = $32
24+ Y = $32 —> substract 24 from both sides
y = 8
ANSWER: X= 8, Y= 8
Find y.
Help me please:))
Answer:
y = 47
Step-by-step explanation:
All of the angles in a triangle must add up to 180. The angle marked 3y can help us find the missing angle of the triangle: 180-3y
Then you can make an equation to help solve for y:
50 + (2y-3) + (180-3y) = 180
Combine like terms:
227-y=180
y = 47
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: y=47 \degree[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \:(2y - 3) + 50 = 3y[/tex]
[tex]\qquad \tt \rightarrow \:2y - 3 + 50 - 3y = 0[/tex]
[tex]\qquad \tt \rightarrow \:2y - 3y + 47 = 0[/tex]
[tex]\qquad \tt \rightarrow \: - y = - 47[/tex]
[tex]\qquad \tt \rightarrow \:y = 47 \degree[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
5 positive integers that have a mode of 2, a median of 5, a mean of 6 and a range of 10.
2,2,5,9,12
The numbers should be 2, 2, 5, 9 and 12.
What is mean, mode and median?
The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.
The median is the middle value in a list ordered from smallest to largest. The mode is the most frequently occurring value on the list.
Let us take numbers 2, 2, 5, 9 and 12.
Mean = 192+2+5+9+12)/5mean = 30/5
mean= 6
mode = 2median = 5range = 12-2range = 10.
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Circle Q is shown. Line segments P Q and R Q are radii. The length of R Q is 6. Angle P Q R is 45 degrees. Sector P Q R is shaded.
Which statements are true about circle Q? Select three options.
The ratio of the measure of central angle PQR to the measure of the entire circle is One-eighth.
The area of the shaded sector is 4 units2.
The area of the shaded sector depends on the length of the radius.
The area of the shaded sector depends on the area of the circle.
The ratio of the area of the shaded sector to the area of the circle is equal to the ratio of the length of the arc to the area of the circle.
The statements that are true about circle Q are:
The ratio of the measure of central angle PQR to the measure of the entire circle is 1/8.The area of the shaded sector depends on the length of the radius.The area of the shaded sector depends on the area of the circle.How to explain the circle?The measure of the central angle is 45°. The measure of the entire circle is 360°. This makes the ratio of the central angle to the entire circle 45/360 = 9/72 = 1/8
To find the area of the shaded sector, this will be:
A = πr² = π(6²) = 36π
1/8(36π) = 36π/8 = 18π/4 = 9π/2 = 4.5π square units. This is not 4 square units.
The ratio of the area of the shaded sector to the area of the circle would not be the same as the ratio of the length of the arc to the area of the circle.
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Answer:
1,3,4
Step-by-step explanation:
15 trucks can carry 26,850 kg weight. Find the weight carried by one truck.
[tex] \huge\underline{\underline{\boxed{\color{blueviolet}{ANSWER}}}}[/tex]
★ 15 trucks can carry 26,850 kg weight
★ We've to find the weight carried by one truck
[tex]\huge \pink {\overline{ \quad \quad \quad \quad \quad \quad \quad\quad \quad}}[/tex]
[tex] \sf{Number \: of \: trucks = 15 }[/tex]
[tex] \sf{Weight \: carried \: by \: one \: truck = \frac{26,850Kg}{15} }[/tex]
[tex] \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:= 1790Kg[/tex]
Therefore , the weight carried by one truck is 1790 kg
please help asap!!!
Rewrite the following equation as a function of x.
Answer:
B
Step-by-step explanation:
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:f(x)= 9280 - 20x [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{1}{16} x + \cfrac{1}{320} y - 29 = 0[/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{1}{16} x + \cfrac{1}{320} y = 29[/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{20 x+ y}{320} = 29[/tex]
[tex]\qquad \tt \rightarrow \: 20x + y = 29 \sdot320[/tex]
[tex]\qquad \tt \rightarrow \: y = 9280 - 20x[/tex]
[tex]\qquad \tt \rightarrow \: f(x) = 9280 - 20x[/tex]
[tex] \textsf{Correct option - A } [/tex]Answered by : ❝ AǫᴜᴀWɪᴢ ❞
13 7in 7in 7in volume and surface area pyramid
The Volume and Surface Area of Prism is 294 in² and 114.33 in³.
What is pyramid?A large structure built especially in ancient Egypt that usually has a square base and four triangular sides meeting at a point and that contains tombs.
Surface rea of rectangular prism,
= 2( lb +bh +lh)
= 2 ( 7*7 + 7*7+ 7*7)
= 2 ( 49+49+49)
= 2*3*49
= 294 in²
Now, Volume,
= bhl/3
= 7*7*7/3
= 114.33 in³
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What is the length of the line?
Choose 1 answer: A. 7 B. The square root of 10 C. Square root of 29 D.Square root of 21
Answer:
C
Step-by-step explanation:
= The square root of (5^2+2^2)= The square root of 29 ---> C
لیا
Use the drawing tools to form the correct answer on the graph.
Graph the line that represents this equation:
y + 2 = (x+2)
Drawing Tools
Select
Point
Line
P
K
Click on a fool to begin drawing.
17
-10
-8
-6
-4
4
10-
8
06000
Undo
Resef
The graph is plotted and attached in the attachment. The given equation is a linear equation with the intercept 0.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation one variable is present then the equation is known as the linear equation in one variable.
If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as y = mx + c.
Given equation;
y + 2 = (x+2)
Rearrange the equation;
y + 2 = x+ 2
y=x
The standard equation for the straight line is;
y = mx + c
Where c is the intercept and m is the slope
After comparing the given equation with the standard equation we get;
m = 1
c =0
Hence,the graph is plotted and attached in the attachment.
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