The endpoints of line segment AB are A (9,4) and B (5,-4). Then endpoints of its image after dilation are A' (6,3) and B' (5,-4). Find the scale factor and explain
Answer:To find the image of B, first find the scale factor for the dilation. The scale factor should be greater than 1 because the image of A is farther from the origin than A. Divide the coordinates of the image of A by the coordinates of A: –6/–4 = 3/2 and 9/6 = 3/2, so the scale factor is 3/2. Now, apply the dilation to B by multiplying the coordinates by 3/2 to get ((3/2)(1), (3/2)(4)), or (3/2, 6).
Hope I helped
Ryan earns $7.50 an hour doing yard work if you were 12 hours a week during an 11 week summer break how much money will Ryan earn in all
7.58 rounded to the nearest tenth place
Rafael walks 2.5 km every day. How far does he walk in 9 days?
Given the number, two-fifths, generate its equivalent forms as a fraction, a decimal, and a percent. In addition, give a real world example in which each form might be used
The surface area of a snowball melting decreases at a rate of 6cm/min. how is the volume changing when the radius is 3
Lines a and b are parallel. What is the measure of angle s? Enter your answer in the box. s = ∘∘ Horizontal parallel lines a and b intersect with another line making eight angles, the top right angle of line a is labeled one hundred fifty eight degrees, and the top left angle of line b is labeled X degrees
Answer:
Measure of angle s is 22°
Step-by-step explanation:
Given that lines a and b are parallel. Horizontal parallel lines a and b intersect with another line making 8 angles, the top right angle of line a is labeled 158° and the top left angle of line b is labeled s degrees
we have to find the measure of angle s.
As ∠1 and 158° and on straight line hence are supplementary
i.e ∠1+158°=180°
⇒ ∠1=180°-158°=22°
Also, angle s and ∠1 are alternate interior angles.
As a and b are parallel then alternate interior angles are equal.
Hence, ∠s=∠1=22°
Measure of angle s is 22°
The factored form of 4a3b5 − 16a5b2 + 12a2b3 is ?
Answer:
The factored form of [tex]4a^3b^5-16a^5b^2+12a^2b^3[/tex] is [tex]4a^2b^2\left(ab^3-4a^3+3b\right)[/tex].
Step-by-step explanation:
To find the factored form of [tex]4a^3b^5-16a^5b^2+12a^2b^3[/tex] you must:
Apply exponent rule: [tex]a^{b+c}=a^ba^c[/tex]
[tex]a^2b^3=a^2b^2b,\:a^5b^2=a^2a^3b^2,\:a^3b^5=a^2ab^2b^3[/tex]
So, we can write our expression as [tex]4a^2ab^2b^3-16a^2a^3b^2+12a^2b^2b[/tex].
Next, rewrite 12 as [tex]3\cdot \:4[/tex] and -16 as [tex]4\cdot \:4[/tex]
[tex]4a^2ab^2b^3+4\cdot \:4a^2a^3b^2+3\cdot \:4a^2b^2b[/tex]
Factor out common term: [tex]4a^2b^2[/tex]
Therefore,
[tex]4a^3b^5-16a^5b^2+12a^2b^3= 4a^2b^2\left(ab^3-4a^3+3b\right)[/tex]
8/10 divided by 1 5/6
An artist agrees to paint a landscape painting at $0.30 per square inch. If the painting is 13 inches by 17 inches, how much should the artist charge?
area of painting = 13 * 17 = 221 square inches
221 * 0.30 = 66.30
the price would be $66.30
Where a is the frontal area of the ball (πd2/4), and cd is the drag coefficient (0.47 for a sphere). what is the drag force on the ball?
Pls help me with these three! Thanks!
2x^3-18x
factor completely
a triangle is classified as equilateral triangle when it has
Answer:
Three sides with the same length because that is what an equilateral triangle is.
Step-by-step explanation:
An electric current, I, in amps, is given by I=cos(wt)+√8sin(wt), where w≠0 is a constant. What are the maximum and minimum values of I
The maximum value of the electric current is [tex]I_{max}=\dfrac{1}{3}[/tex]
the minimum value of the electric current is [tex]I_{min}=-\dfrac{1}{3}[/tex]
The given expression for electric current is [tex]I=\cos(\omega t)+\sqrt{8}\sin(\omega t)[/tex] where [tex]\omega \neq 0[/tex].
Differentiate the given function with respect to [tex]t[/tex]-
[tex]\dfrac{dI}{dt}=\dfrac{d(\cos(\omega t)+\sqrt 8 \sin(\omega t))}{dt}\\\dfrac{dI}{dt}=-\omega \sin(\omega t)+\sqrt 8 \omega \cos(\omega t)[/tex]
Equate the derivative to 0-
[tex]\dfrac{dI}{dt}=0\\-\omega \sin(\omega t)+\sqrt 8 \omega \cos(\omega t)=0\\\sin(\omega t)=\sqrt 8 \cos (\omega t)\\\tan (\omega t)=\sqrt 8\\\omega t=\tan^{-1}\sqrt 8\\\omega t=2n\pi-2\tan^{-1}\sqrt 2}\\or,\\\omega t=2n\pi+2\tan^{-1}\sqrt {1/2}}[/tex]
[tex]2n\pi[/tex] is the period of sine and the cosine trigonometric function.
So, the maximum value of the electric current is
[tex]I_{max}=\cos(2\tan^{-1}\sqrt {1/2})\\I_{max}=\dfrac{1}{3}[/tex]
Also, the minimum value of the electric current is
[tex]I_{min}=\cos(2\tan^{-1}\sqrt {2})\\I_{min}=-\dfrac{1}{3}[/tex]
Learn more about maximum and minimum values of the functions here:
https://brainly.com/question/13581879?referrer=searchResults
Tell whether the two rates form a proportion
7 inches in 9 hours; 42 inches in 54 hours
explain how you got the answer/show your work
The rates of 7 inches per 9 hours and 42 inches per 54 hours do form a proportion, as demonstrated by cross-multiplying the two ratios which resulted in equal cross products (378 inch-hours on both sides).
Explanation:To determine if the two rates form a proportion, we need to compare the ratios of inches to hours for both scenarios. For the first rate, we have 7 inches in 9 hours, and for the second rate, we have 42 inches in 54 hours. A proper proportion exists when two ratios are equivalent.
Let's set up our two ratios:
First ratio: 7 inches / 9 hoursSecond ratio: 42 inches / 54 hoursNow, we will test if these ratios form a proportion by creating a fraction out of each ratio and then cross-multiplying.
(7 inches / 9 hours) = (42 inches / 54 hours)
Cross multiply:
7 inches * 54 hours = 378 inch-hours
42 inches * 9 hours = 378 inch-hours
Since the cross products are equal, the two rates indeed form a proportion.
Which investment has the least amount of risk? standard deviation = $450, expected return = $4,500 standard deviation = $600, expected return = $400 standard deviation = $500, expected return = $800 standard deviation = $400, expected return = $5,000?
The amount of interest you pay does not depend on the method the lender uses to calculate interest.
True or False
Answer:
FALSE
Step-by-step explanation:
The amount of interest paid depends on the method adopted by the lender. There are several methodologies for applying interest, so that each sector will adhere to the most convenient modality. The interest paid by you will be the result of this choice and may for example have a daily, monthly, semi-annual or annual impact. Obviously all interest charged must be clearly described in a contract and must be considered legal in the state legal apparatus.
Daisy is shipping a package to her daughter, Molly. If the box’s dimensions are equal, and the length is 3 feet long, what is the volume of the box in cubic feet?
A. 1
B. 3
C. 9
D. 27
Let f(x) = 4x-5 and g(x) = 3x, find (fog)(x)
Please answer the question
At the store deli, Rita spent $13.45 on 5 pounds of cheese. How much would it cost to buy 2 pounds of cheese?
Answer:
The cost would be $ 5.38.
Step-by-step explanation:
Given,
The price of 5 pounds of cheese = $ 13.45,
So, the price of 1 pounds of cheese = [tex]\frac{\text{Price of }5\text{ pounds of cheese}}{5}[/tex]
[tex]=\frac{13.45}{5}[/tex]
[tex]=\$ 2.69[/tex]
Thus, the price of 2 pounds of cheese = 2 × price of each pound of cheese
= 2 × 2.69
= $ 5.38
Niko uses 12 marshmallows and 8 graham crackers to make 4 s'mores. Drag marshmallows and graham crackers into the box to show how many Niko needs to make 3 s'mores.
Answer: Niko needs 9 marshmallows and 6 graham crackers to make 3 s'mores.
Step-by-step explanation:
Let x be the number of marshmallows , y be the number of graham crackers and z be the number of s'mores.
Then according to given question
Niko uses 12 marshmallows and 8 graham crackers to make 4 s'mores
gives the equation 12x+8y=4z
If we divide whole equation by 4 , we get the quantity of x and y to make z such that
[tex]\frac{1}{4}(12x+8y)=\frac{1}{4}(4z)\\\Rightarrow3x+2y=z[/tex]
Now to make 3 s'mores, we need to multiply the equation by 3 such that
[tex]3\times(3x+2y)=3\times\ z\\\Rightarrow\ 9x+6y=3z[/tex]
Thus Niko needs 9 marshmallows and 6 graham crackers to make 3 s'mores.
In the diagram, g ∥ h, m∠1 = (4x + 36)°, and m∠2 = (3x – 3)°.What is the measure of ∠3?
what is the axis of symmetry for the graph of y-4x=7-x^2
what is the answer to simplify 9 yards: 9 feet
A farmer estimates that he has 9,000 bees producing honey on his farm. The farmer becomes concerned when he realizes the population of bees seems to be decreasing steadily at a rate of 5% per year. If the number of bees in the population after x years is represented by f(x), which statements about the situation are true? Check all that apply. The function f(x) = 9,000(1.05)x represents the situation. The function f(x) = 9,000(0.95)x represents the situation. After 2 years, the farmer can estimate that there will be about 8,120 bees remaining. After 4 years, the farmer can estimate that there will be about 1,800 bees remaining. The domain values, in the context of the situation, are limited to whole numbers. The range values, in the context of the situation, are limited to whole numbers.
Answer:
Step-by-step explanation:
The function f(x) = 9,000(0.95)x represents the situation.
After 2 years, the farmer can estimate that there will be about 8,120 bees remaining.
The range values, in the context of the situation, are limited to whole numbers.
The true representation of the declining bee population is f(x) = 9,000(0.95)^x, accounting for a 5% annual decrease. The function and expected number of bees after 2 years are correct if rounded to approximately 8,120. The domain and range values are limited to whole numbers in this context.
Explanation:The given situation of the farmer noticing a decrease of bees in his population can be represented by a mathematical function that models the decline. This function is f(x) = 9,000(0.95)^x, which correctly represents a 5% annual decrease in the bee population.
After analyzing the situation:
The statement f(x) = 9,000(1.05)^x is false because it suggests a 5% increase rather than a decrease.The correct function, as mentioned before, is f(x) = 9,000(0.95)^x.After 2 years, the population of bees expected can be calculated: f(2) = 9,000(0.95)^2 ≈ 8,122.5, which, when rounded to a whole number due to the context, is about 8,123 bees remaining, making this statement true if it refers to approximately 8,120 bees.After 4 years, using the function, the statement that there will be about 1,800 bees remaining is false; the correct calculation would yield a higher number.The domain values are limited to whole numbers since you cannot have a fraction of a year.The range values are also limited to whole numbers as you cannot have a fraction of a bee.Learn more about Exponential Decay here:https://brainly.com/question/2193799
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Which line has a mistake in the following steps.
12 - 6(8 / 4)
12 - 6(2)
6(2)
12
When creating a scatterplot, if the points are too close together to see the relationship, how could you adjust your graph?
A.
decrease your scale values
B.
increase your scale values
C.
plot more points
D.
plot fewer points
One-fourth equals the quotient of a number and 8. Find the number.
16.99 cap; 20% discount