The horizontally compressed function is [tex]\(\text{g(x)} = x^2 + 6\)[/tex]. The correct option is OC. [tex]\(\text{g(x)} = x^2 + 6\)[/tex].
To horizontally compress the function [tex]f(x) = x^2[/tex], we can modify the equation by introducing a horizontal compression factor. Let's call the compressed function [tex]g(x)[/tex].
The general equation for a horizontally compressed function can be expressed as [tex]g(x) = f(ax)[/tex], where a is the compression factor.
In this case, we want to compress [tex]f(x) = x^2[/tex]. Let's choose a compression factor of [tex]\frac{1}{2}[/tex].
Therefore, the equation for [tex]g(x)[/tex] would be:
[tex]\[ g(x) = f\left(\frac{x}{2}\right) = \left(\frac{x}{2}\right)^2 \][/tex]
Simplifying this equation, we have:
[tex]\[ g(x) = \frac{x^2}{4} \][/tex]
Hence, the equation of [tex]g(x)[/tex] is:
[tex]\[ \text{g(x)} = \frac{x^2}{4} \][/tex]
So, the correct option is OC. [tex]\(\text{g(x)} = x^2 + 6\)[/tex].
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What are the sums? Complete the equations.
-80+30=
80+ (-30) =
15% of what number is 3?
Answer:
Step-by-step explanation:
15 % of x = 3
[tex]\frac{3x}{20} = 3\\ x = 20[/tex]
Answer:
20
Step-by-step explanation:
Find 1% 3 : 15 = 0.2Find 100% 0.2 × 100 = 20%or solve with an expression
3 : 15 × 100 =
0.2 × 100 =
20
or solve with an equation3 : 15 = x : 100
x = 3 × 100 : 15
x = 20
Graph the circle (x - 3)^2 + (y + 3)^2= 36.
The circle on a graph by drawing the center point and then drawing a circle around it with a radius of 6.
To graph the circle with the equation (x - 3)² + (y + 3)² = 36, we can start by finding the center and radius of the circle.
The equation of a circle in standard form is (x - h)² + (y - k)² = r² (h, k) represents the center of the circle and r represents the radius.
Comparing the given equation with the standard form, we can see that the center of the circle is (3, -3) and the radius is √36 = 6.
Using this information, we can proceed to plot the circle on a graph:
Plot the center point: (3, -3).
From the center point, move 6 units in each direction (up, down, left, and right) to determine the points on the circle.
Up: (3, -3 + 6) = (3, 3)
Down: (3, -3 - 6) = (3, -9)
Left: (3 - 6, -3) = (-3, -3)
Right: (3 + 6, -3) = (9, -3)
Connect the plotted points to form a circle.
The resulting graph should look like this:
| • (3, 3)
|
| •
| •
__|_____________________________
|
|
|
|
| • (3, -3)
The center of the circle is denoted by a solid dot (•) in the graph and the other points lie on the circumference of the circle.
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Given AC is congruent to BD and angle CAB is congruent to angle DBA.
Prove triangle ABC is congruent to triangle BAD
By the Side-Angle-Side (SAS) congruence criterion, triangle ABC is congruent to triangle BAD.
To prove that triangle ABC is congruent to triangle BAD based on the given information, we can apply the Side-Angle-Side (SAS) congruence criterion.
AC is congruent to BD (Side)
angle CAB is congruent to angle DBA (Angle)
To prove triangle ABC congruent to triangle BAD using the SAS congruence criterion, we need to show that they share two congruent sides and a congruent angle between them.
Side AB is common to both triangles.
Side AC is congruent to BD (given).
angle CAB is congruent to angle DBA (given).
By satisfying the SAS congruence criterion, we can conclude that triangle ABC is congruent to triangle BAD.
The SAS congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
In this case, we have side AB in common, and side AC is congruent to BD, along with angle CAB being congruent to angle DBA.
Therefore, all the conditions of the SAS criterion are satisfied.
Hence, we can conclude that triangle ABC is congruent to triangle BAD based on the given information.
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The quadratic functions f(x) and g(x) are described in the table.
x f(x) g(x)
−6 36 4
−5 25 1
−4 16 0
−3 9 1
−2 4 4
−1 1 9
0 0 16
1 1 25
2 4 36
In which direction and by how many units should f(x) be shifted to match g(x)?
Left by 4 units
Right by 4 units
Left by 8 units
Right by 8 units
The direction that the quadratic function f(x) is to be translated is to the left and the units is 4.
Here given two functions, f(x) and g(x).
General form of the quadratic function is,
ax² + bx + c.
It is clear that, f(x) is simply the square of the x values.
f(x) = x²
Since g(x) is the translation of the function f(x) and the value of g(x) = 0, when x = -4,
g(x) = (x + 4)²
That is,
g(x) = f(x + 4).
So f(x) is shifted left by 4 units.
Hence f(x) is shifted left by 4 units.
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Consider polygon ABCD, shown below.
B
C
E
A
G
F
D
Select all the ways that describe rigid transformations that take AEFD to CFEB.
The rigid transformations that can take AEFD to CFEB are translation, rotation, and reflection.
To describe the rigid transformations that take polygon AEFD to CFEB, we need to identify the transformations that preserve the shape and size of the polygon. Here are some possibilities:
Translation: A translation involves moving the entire polygon without changing its orientation or shape. If we shift polygon AEFD to the right, it will align with polygon CFEB. Therefore, translation is one way to achieve this transformation.
Rotation: If we rotate polygon AEFD around a fixed point, such as the center of the polygon or a vertex, by a certain angle, it can align with polygon CFEB. A rotation preserves the shape and size of the polygon.
Reflection: A reflection involves flipping the polygon across a line, resulting in a mirror image. If we reflect polygon AEFD across a line of reflection, it can match polygon CFEB.
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please help! thank uu ~ :)
Answer: It has ans an equal chance of 50-50
Step-by-step explanation: There are 10 of each type, leaving 20 total, half of the candy is Cherry, the other half is Strawberry.
A company invests $760,000 a year for 8 years at 5.2% annual rate. How much interest will they earn?
$316,160.00
Step-by-step explanation:Interest is the amount of money earned on an initial investment.
Simple Interest
Since the question does not talk about being compounded, we can assume the company is earning simple interest. Simple interest is the amount of money earned on the principal. The principal is the initial investment. Additionally, interest is earned at a specific rate; in this case, the rate is 5.2% each year.
Interest Formula
The formula to find the amount of interest earned is I = Prt. In this formula, I is the amount of interest earned, P is the principal, r is the rate as a decimal, and t is the time in years. To find the interest earned, all we need to do is plug in the information we know.
I = 760,000 * 8 * 0.052I = $316,160The account will earn $316,160 of interest.
We can also determine the total of the account by using the formula A = P (1 + rt). If we solve this formula, we can figure out that the account total is $1,076,160.
A boat's value over time is given as the function f(x) and graphed below. Use A(x) = 400(b) +0 as the parent function. Which graph shows the boat's value increasing at a rate of 25% per year? (2 points)
Graph is attach below for this question and the equation of this graph is
A(x) = 400(1.25)ˣ +0
We have,
In mathematics, "graph" can refer to (at least) two different things. In elementary mathematics, the term "graph" indicates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty).
Given that the boat's value increasing at a rate of 25% per year.
So after each year the value becomes = 1 + 25% = 1 + 0.25 = 1.25 of the previous year.
So the equation becomes: A(x) = 400(1.25)ˣ +0
Since, b = 1.25 > 1, so A(x) is a increasing function. And for every value of x, A(x) < 0.
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The radius of a circle is 15 kilometers. What is the angle measure of an arc 7 kilometers long?
Answer:
26.74 degrees!
Step-by-step explanation:
The formula you can plug the numbers into is:
angle = L / r
Angle = the central angle
L = the length of the arc
r = radius of the circle
Write x2 + 6x − 3 = 0 in the form of (x − a)2 = b, where a and b are integers. (1 point)
(x + 6)2 = 3
(x + 6)2 = 12
(x + 3)2 = 6
(x + 3)2 = 12
Answer:
Step-by-step explanation:
What is the measure in radians for the central angle of a circle whose radius is 8 cm and intercepted arc length is 5.6 cm? Enter your answer as a decimal in the box. radians
Answer:
The measure of the central angle in radians is 5.6/8 = 0.7 radians.
In one part of a rainforest in South America, 3/5 of the frogs are poisonous. What fraction of the frogs are not poisonous?
2/5 of the frogs in that portion of the South American rainforest are not poisonous.
How to calculate the fraction of frogs that are not poisonous in South American rainforestOn the off chance that 3/5 of the frogs in a rainforest in South America are poisonous, at that point, the remaining division speaks to the frogs that are not poisonous.
To discover this division, we subtract the division of poisonous frogs from 1 (which speaks to the complete):
1 - 3/5 = 5/5 - 3/5 = 2/5
Hence, 2/5 of the frogs in that portion of the rainforest are not poisonous. This fraction represents the parcel of frogs that don't have poisonous characteristics.
It is important to note that this calculation expects that all frogs within the rainforest are either poisonous or notpoisonous, and there are no other conceivable outcomes or middle states.
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d) Shiva bought a second-hand motorcycle for Rs 1,53,200. He spent Rs 1,200 to repair it and sold it to Bishnu at 8% loss. How much did Bishnu pay for it?
Bishnu selling price paid Rs 1,42,048 for the motorcycle.
To find out how much Bishnu paid for the motorcycle, we need to calculate the selling price after the 8% loss.
Let's start with the purchase price: Shiva bought the second-hand motorcycle for Rs 1,53,200.
Then, Shiva spent Rs 1,200 to repair it. So, the total cost for Shiva becomes:
Total cost = Purchase price + Repair cost
= Rs 1,53,200 + Rs 1,200
= Rs 1,54,400
Now, to calculate the selling price after an 8% loss, we need to subtract 8% of the total cost from the total cost:
Loss = 8% of Total cost
= 8/100 * Rs 1,54,400
= Rs 12,352
Selling price = Total cost - Loss
= Rs 1,54,400 - Rs 12,352
= Rs 1,42,048
Therefore, Bishnu selling price paid Rs 1,42,048 for the motorcycle.
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please help me out with explanation
Sorry for bad handwriting
if i was helpful Brainliests my answer ^_^
Answer:
891 cm³
Step-by-step explanation:
Since they are the same shape with only their sizes different, that means they have a proportionate ratio so:
2673 / 9 = V / 3
Now make V the formula of the subject:
V = 2673 / 9 TIMES 3 = 891.
Which statements is true and justify your answer
Answer:
Step-by-step explanation:
Given ABC with A(0, 5), B(1, -3), and C(-3, 3), select all the terms that apply to the triangle.
A. Acute
B. Right
C. Obtuse
D. Equilateral
E. Isosceles
F. Scalene
Thanks!
Based on the given information, we cannot determine if the triangle is acute, right, or obtuse (A, B, C). However, we can conclude that the triangle is scalene (F).
How to determine the type of triangleTo determine the terms that apply to triangle ABC with vertices A(0, 5), B(1, -3), and C(-3, 3), we can analyze the properties of the triangle based on its side lengths and angles.
Side Lengths:
AB: Distance between points A(0, 5) and B(1, -3)
BC: Distance between points B(1, -3) and C(-3, 3)
AC: Distance between points A(0, 5) and C(-3, 3)
Using the distance formula, we can calculate the side lengths:
AB = [tex]\sqrt{ (1 - 0)^2 + (-3 - 5)^2)} = \sqrt{(1^2 + (-8)^2} = \sqrt{65}[/tex]
BC = [tex]\sqrt{((-3 - 1)^2 + (3 - (-3))^2} = \sqrt{((-4)^2 + 6^2)} = \sqrt{52}[/tex]
AC = [tex]\sqrt{((-3 - 0)^2 + (3 - 5)^2)} = \sqrt{(-3)^2 + (-2)^2)} = \sqrt{13}[/tex]
We can conclude that the triangle is not equilateral (D) since all sides have different lengths. We can also conclude that the triangle is not isosceles (E) since no two sides have the same length. Therefore, the triangle is classified as scalene (F).
In summary, based on the given information, we cannot determine if the triangle is acute, right, or obtuse (A, B, C). However, we can conclude that the triangle is scalene (F).
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Can someone help me on 3-6?
Directions: Find the volume of each figure. Round the nearest hundredth.
Using the formula of volume of a sphere and hemisphere, the volume of the figures are given as;
1. 2144.57 m³
2. 696.6 m³
3. 20569.1m³
4. 2637ft³
5. 56.5km³
6. 6381.79 in³
What is volume of sphere?The volume of a sphere is given as 4/3πr³
Where π is a constant whose value is equal to 3.14 approximately. “r” is the radius of the hemisphere.
1. The volume of the sphere is;
v = 4/3 * 3.14 * 8³ = 2144.57m³
2. The volume of the sphere is;
v = 4/3 * 3.14 * (11/2)³ = 696.6m³
3. The volume of the sphere is;
v = 4/3 * 3.14 * 17³ = 20569.1m³
4. The volume of the hemisphere is;
v = 2/3 * 3.14 * 10.8³ = 2637ft³
5. The volume of the hemisphere is;
v = 2/3 * 3.14 * 3³ = 56.5km³
6. The volume of the hemisphere is;
v = 2/3 * 3.14 * (29/2)³ = 6381.79in³
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I need help with question 4
The output of the exponential function when x = 5 is given as follows:
f(5) = 96.
How to define an exponential function?An exponential function has the definition presented as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The parameter values for this problem are given as follows:
a = 3, as when x = 0, f(x) = 2.b = 2, as when x is increased by one, f(x) is multiplied by two.Hence the function is given as follows:
[tex]f(x) = 3(2)^x[/tex]
The numeric value at x = 5 is given as follows:
[tex]f(5) = 3(5)^x = 96[/tex]
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In triangle MNO, o = 8 inches, m0=48° and mM=28°. Find the length of n, to the
nearest 10th of an inch.
The length of side m is, 5.1 inches.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
In ΔMNO,
⇒ o = 8 inches, m ∠M = 28° and m ∠O = 48°.
Now, Let the length of side m = x
So, By sine rule, we get;
[tex]\rightarrow \sf \dfrac{sin \ M}{m} = \dfrac{Sin \ O}{o}[/tex]
Substitute all the values, we get;
[tex]\sf \rightarrow \dfrac{sin \ 28^\circ}{x} = \dfrac{sin \ 48^\circ}{8}[/tex]
[tex]\sf \rightarrow \dfrac{0.47}{x} = \dfrac{0.74}{8}[/tex]
[tex]\sf \rightarrow x=\dfrac{ 0.47 \times 8}{0.74}[/tex]
[tex]\sf x = 5.08\thickapprox 5.1 \ inches[/tex]
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Find the amount if $300 is invested at 8% compounded monthly for 16 months.
Amount =
Step-by-step explanation:
Amount = Principal ( 1 + i) ^n i = decimal interest per month = .08/12
n = 16 months
amount = $ 300 ( 1+ .08/12)^16 = $ 333.65
Which of these contexts describes a situation that is certain?
Rolling an even number on a standard six-sided die, numbered from 1 to 6.
Spinning a spinner divided into four equal-sized sections colored red/green/yellow/blue and landing on red or yellow or green or blue.
Winning a raffle that sold a total of 100 tickets if you bought 0 tickets.
Reaching into a bag full of 5 strawberry chews and 15 cherry chews without looking and pulling out a pineapple chew.
The context which describes a certain situation from the given is spinning a spinner divided into four equal-sized sections colored red/green/yellow/blue and landing on red or yellow or green or blue.
Certain probability or certain situation is defined as the situation where the event is sure to happen.
Rolling an even number on a standard six-sided die, numbered from 1 to 6.
The die can be rolled to odd number. Soo it is uncertain.
Spinning a spinner divided into four equal-sized sections colored red/green/yellow/blue and landing on red or yellow or green or blue.
This is a certain situation since the spinner will surely land on any of the four colors.
Winning a raffle that sold a total of 100 tickets if you bought 0 tickets.
This is not possible.
Reaching into a bag full of 5 strawberry chews and 15 cherry chews without looking and pulling out a pineapple chew.
This is also not possible.
Hence the certain situation is spinning a spinner.
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A conveyor belt carries supplies from the first floor to the second floor which is 23 feet higher. The belt makes a 60 degree angle with the ground.
How far do the supplies travel from one end of the conveyor belt to the other? Round your answer to the nearest foot.
27 feet
33 feet
13 feet
40 feet
The distance traveled by the supplies is given as follows:
27 feet.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:
Sine of angle = opposite side/hypotenuse.Cosine of angle = adjacent side/hypotenuse.Tangent of angle = opposite side/adjacent side = sine/cosine.The distance is the hypotenuse of the right triangle, while the height of 23 feet is opposite to the angle of 60º.
Applying the sine ratio, we have that:
sin(60º) = 23/x
x = 23/sine of 60 degrees
x = 27 feet.
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I need help right now can someone help me ple
The Area of Rhombus QRST is 78.32 in².
We know the formula of Area of Rhombus
= 1/2 x product of diagonals
We have, QS = 8.8 and RT = 17.8
So, Area of Rhombus QRST
= 1/2 x QS x RT
= 1/2 x 8.8 x 17.8
= 78.32 in²
Thus, the Area of Rhombus QRST is 78.32 in².
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What is the strength of the association between the two
variables in the scatter plot?
Select from the drop-down menu to correctly complete the
statement.
The strength of association is Choose...
Strong or weak
Need help with pie chart
a. The category that was chosen as approximately 1/4 will be Cat.
b. The percentage that choose other or cat will be 35%.
c. The percentage that choose dog is 16%
a. It should be noted that to determine the category chosen by approximately one-fourth of the community, we need to look for the corresponding section of the pie chart. This shows the cat.
b. The percentage that choose other or cat will be:
= 10% + 25%
= 35%.
c. The percentage that choose dog is:
= 32% / 2
= 16%
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Which of the following steps would you perform to the system of equations
below so that the equations have opposite y-coefficients?
4x+2y=4
12x - y = 26
3 kg of cheese costs £7.50
What is the cost of 6.5 kg of cheese?
Answer: £16.25
Step-by-step explanation:
In order to find the answer we will use a method called unitary method, it is very simple and you must know it as it's repeatedly given in Year 7 and 8 here's the explanation
Cost of 3kg= £7.50
Cost of 1 kg = £7.50÷3
=2.5
Cost of 6.5kg = 2.5×6.5 = £16.25
A bag has 6 blocks in it.
Jerry picks a block out of
the bag 60 times. He gets
the green block 43 times.
Based on these results how
many blocks to you expect
to be green? Explain your
reasoning.
We can expect 258 blocks in the bag to be green.
We have to given that,
A bag has 6 blocks in it. Jerry picks a block out of the bag 60 times. He gets the green block 43 times.
Since, We know that Jerry picked a block out of the bag 60 times, and got the green block 43 times.
So the probability of picking a green block is:
P = 43/60
P = 0.7167
This means that out of every 60 blocks picked, there are 43 green.
Now, For this probability to estimate the number of green blocks in the bag.
since, Jerry picked 60 blocks 6 times
When, we assume that the bag contains a total of 360 blocks , we can multiply this total by the probability of getting a green block:
360 x 0.7167 = 258.012
Thus, We can expect 258 blocks in the bag to be green.
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What is the strength of the association between the two
variables in the scatter plot?
Select from the drop-down menu to correctly complete the
statement.
The strength of association is Choose...
Strong or weak
A weak correlation between the two variables is depicted by the scatter plot in the supplied image.
The trend line's points are widely dispersed, which suggests that there is little correlation between the variables.
In a scatter plot, the degree of connection between the two variables can be classified as strong or weak.
A weak correlation indicates that there is a lot of scatter around the trend whereas a high relationship indicates that there is very little scatter in comparison to the trend's movement.
Thus, the given association is weak correlation.
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