The coordinates of the transformed figure are: A ’(-1, -2), B ’(-3, -2), C ’(-2, 4)
When a shape is rotated, it must be rotated through a point, here itis rotated around the origin
The coordinates of the triangle is given as:
A(1, 2), B(3, 2), C(2, 4) is rotated 90 degree
The rule of 90 degrees clockwise rotation is:
x, y = -x, -y
So, we have:
A(1, 2) which becomes (-1, -2)
B(3, 2), which becomes (-3, -2)
C(2, 4) which becomes (-2, -4)
Hence, the coordinates of the transformed figure are:
A ’(-1, -2), B ’(-3, -2), C ’(-2, 4)
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A soup company is looking at two designs for a new can. Can a have a diameter of 8 centimeters and a height of 15 centimeters. Can B has diameter of 10 centimeters and a height of 12 cm. How much greater of the volume of can B then can A? Use 3.14 for π and give the difference to The nearest cubic centimeter. To the nearest cubic centimeter, volume to Cube B is ______ centimeters.
Given:
The diameter of can A is, d(A) = 8 cm.
The height of can A is, h(A) = 15 cm.
The diameter of can B is, d(B) = 10 cm.
The height of can B is, h(B) = 12 cm.
The objective is to find how much greater is volume of can B than can A.
Explanation:
The general formula for volume of a can is,
[tex]V=\pi r^2h[/tex]To find volume of A:
The volume of can A can be calculated as,
[tex]V(A)=\pi(\frac{d_A}{2})^2\times h_A\text{ . . .. . .. (1)}[/tex]On plugging the given values in equation (1),
[tex]\begin{gathered} V(A)=3.14\times(\frac{8}{2})^2\times15 \\ =753.6\operatorname{cm}^3 \end{gathered}[/tex]To find volume of B:
The volume of can B can be calculated as,
[tex]V(B)=\pi(\frac{d_B}{2})^2h_B\text{ . . . . .(2)}[/tex]On plugging the given values in equation (2),
[tex]\begin{gathered} V(B)=3.14\times(\frac{10}{2})^2\times12 \\ =942\operatorname{cm}^3 \end{gathered}[/tex]To find difference:
The difference between volume of can A and can B will be,
[tex]\begin{gathered} V(B)-V(A)=942-753.6 \\ =188.4\operatorname{cm}^3 \end{gathered}[/tex]Hence, the volume of can B is greater than can A by 188.4 cm³.
Rochelle needs to pack a picture frame that measures 7 3/8 inches on each side will it be into a box that measures 7.4 inches on each side
A picture frame that is 7 3/8 inches wide on each side needs to be packed into a box that is 7.4 inches wide on each side. It would not consequently fit.
Given that,
A picture frame that is 7 3/8 inches wide on each side needs to be packed into a box that is 7.4 inches wide on each side.
Picture frame length is 7 3/8, or 7.4 inches.
Box length is 7.4 inches.
Therefore, it is clear from the about that the box's length is shorter than the picture frame's length.
It would not consequently fit.
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At a sale this week, a table is being sold for $400. This is a 36% discount from the original price.
What is the original price?
Using the concept of Percentage, the original price of the table is $625.
What is Percentage?A Percentage means a ratio with the second part being 100. Percentage refers to parts per hundred. The term is derived from the Latin phrase per centum, which means "per hundred." In mathematics, the symbol % stands for percent.
Example: 50% means 50 out of every 100. So if 50% of 200 students are girls, then there are 100 students who are girls.
We know that,
Table was sold at $400.
Discount given is 36% then the table is sold at,
100% - 36% = 64%
Let the original price be p then,
64% of p = 400
That gives,
p = [tex]\frac{40000}{64}[/tex]
p = 625
Hence, The original price of the table is $625.
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Name the set of 4 consecutive odd integers starting with -3 ( put the set in braces [ ] and put commas between the elements of the set. )
Solution
For this case we need to find 4 consecutive odd integers so we can do this:
-3, -3+2, -3+2+2, -3+2+2+2
Solving we got:
[-3,-1, 1, 3]
Determine whether or not the following correspondences specify a function, and explain your reasoning in writing
Recall that a relation is a function if for every value on the domain there is only one value on the range.
(a) Notice that for every value on the domain, there is only one value on the range:
For the value 0 in the domain, there is the value 5 in the range.
For the value 1 in the domain, there is the value 6 in the range.
For the value 2 in the domain, there is the value 7 in the range.
For the value 3 in the domain, there is the value 7 in the range.
Therefore the relation represented by the given graph in a) is a function.
(b) Notice that for the value 3 in the domain there are two values in the range, 6 and 7, therefore, the relation represented by the graph in b) is not a function.
Answer:
(a) Function.
(b) Not a function.
A friend lends you $260, which you agree to repay with 3% interest.How much will you have to repay?How much of that was interest?
To answer this question we will use the following formula to compute the x% of y:
[tex]y\times\frac{x}{100}.[/tex]Since you have to repay with 3% interest, then you have to pay 103% of the original amount.
The 103% of 260 is:
[tex]260\times\frac{103}{100}=267.80.[/tex]Now, notice that the interest is the difference between the original amount and the above result:
[tex]I=267.80-260=7.80.[/tex]Answer:
How much will you have to repay? $267.80.
How much of that was of interest? $7.80.
select all input values for which f(x)=2.choose all answers that apply:A.) x= -7B.) x=0C.) x=4D.) None of the above
The expression f(x) = 2 refers to all the x-value that make y = 2.
According to the given graph, the value is x = -7 because that's where y = 2.
Hence, the answer is A.how many ways can Aileen choose 2 pizza toppings from a menu of 19 toppings if each topping can be chosen once ?
Answer:
[tex]171\text{ ways}[/tex]Expalnation:
From what we have here, there are 19 toppings to choose from
To choose the first topping, there are 19 choices to select from
For the second topping selected, since repetition is not allowed, there would be 17 toppings to choose from
Thus, the total number of ways will be according to the combination rule as follows:
[tex]\begin{gathered} ^nC_r\text{ = }\frac{n!}{(n-r)!r!} \\ ^{19}C_2\text{ = }\frac{19!}{(19-2)!2!}\text{ = 171 ways} \end{gathered}[/tex]3/9 divided by 10/50
To be able to divide the two fractions as given,
A spring is oscillating vertically according to the equation y=3cos(2t-pi) where y is the displacement in feet and t is time in seconds. At what time will the spring be 2 ft. high? Round your answer to the nearest tenth.
we have the equation
[tex]y=3cos(2t-pi)[/tex]For y=2 ft
substitute in the given equation
[tex]\begin{gathered} 2=3cos(2t-p\imaginaryI) \\ cos(2t-p\mathrm{i})=\frac{2}{3} \end{gathered}[/tex]Solve for t
using a calculator
2t-pi=0.84
2t=0.84+pi
2t=3.98
t=1.99 -----------> round to one decimal place
t=2.0 sec
The answer is option CI need help please!!!! I need the answer like right now please!! Thank you!!!
I need help with this practice Can you solve, please explain step-by-step, *as I am new to this branch/topic of math*
Explanation
This is Algeba, an aspect of Math
We are told to find th correct optionthat satisfies the condition of a and b
Given that
a =5 and b =8
To go about this, we will simply substitute a = 5 and b=8 into each of the equation and cross-check the value with 104
Let us check for the first option
[tex]\begin{gathered} 8+a+8+b \\ 8+5+8+8=29 \\ since\text{ 29 is not equal to 104, then this is a wrong answer} \end{gathered}[/tex]Option B
[tex]\begin{gathered} 8+a+8b \\ 8+5+8(8)=8+5+64=77 \\ since\text{ 77 is not equal to 104, then this is wrong also} \end{gathered}[/tex]Option C
[tex]\begin{gathered} 8a+8+b=8(5)+8+8=40+16=56 \\ since\text{ 56 is not equal to 104, then this is also wrong} \end{gathered}[/tex]Option D
[tex]\begin{gathered} 8a+8b=8(5)+8(8)=40+64=104 \\ \\ 104\text{ is EQUAL to 104} \\ This\text{ is correct} \end{gathered}[/tex]Therefore, the anser is
(x^4)+(5x^2)+4=1 i need help on how to do this
A biker is making a turn around the corner. The biker's speed remained constant at 12 miles per hour during the entire turn. Which of the following statements describes the forces on the biker?
The forces were balanced to keep the biker with a constant speed.
The forces were unbalanced as the biker made the turn.
The forces were balanced due to the biker's inertia.
The forces were unbalanced due to the action-reaction pair required to turn.
The forces were balanced due to the biker's inertia. Option C.
Objects that move in circles or along circular orbits experience a centripetal force. That is there is a physical force pushing or pulling an object toward the center of the circle. The centripetal force that causes the car to spin in a circle is generated by the friction between the tires and the road surface. A minimum coefficient of friction is required. Otherwise, the car will travel a curve with a larger radius and leave the lane.
As the motorcycle climbs the loop friction forces act along the direction of travel to prevent gravity from slowing it down. As the motorcycle descends the loop friction forces act against the direction of motion preventing acceleration due to gravity. Whenever the velocity increases at the same rate, we are moving with constant acceleration. Centripetal force supports the circular motion. One idea is that if the road is smooth the car can't make a circle.
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Answer: The forces were balanced due to the biker's inertia.
Step-by-step explanation:
option c
compare f(0) and g(0)g(x)=|2x-8|-11f(0) is =, <, or > than g(0)
Let's begin by listing out the given information:
For the graph of f(x), we will pick out two coordinates that lie along the straight line. We have:
[tex]undefined[/tex]the part of Ray and Kelley's roller coaster is a curved pattern that can be represented by a polynomial function. I will upload the complete question. because it is to much to type.
Thus, the answer is Kelsey is the one who is correct. Because the number of intercepts is different from the number of zeroes.
1) Examining the question, we take into consideration that not all intercepts are zeroes of the polynomial.
In a third-degree polynomial function, there is another kind of intercept. The y-intercept.
2) So, we can tell that there is no way for both of them to be correct.
3) Thus, the answer is Kelsey is the one who is correct. Because the number of intercepts is different from the number of zeroes.
In 1995, the standard bus fare in Chicago was $1.50. In 2008, the standard bus fare was $2.40.Find the percent increase. Round to the nearest tenth of a percent
Given that:
- The standard bus fare was $1.50 in 1995.
- The standard bus fare was $2.40 in 2008.
You need to use the following formula, in order to find the percent increase:
[tex]PercentageIncrease=\frac{Final\text{ }Value-Initial\text{ }Value}{|Initial\text{ }Value|}\cdot100[/tex]In this case, you can identify that:
[tex]\begin{gathered} Final\text{ }Value=2.40 \\ Initial\text{ }Value=1.50 \end{gathered}[/tex]Therefore, substituting values into the formula and evaluating, you get:
[tex]\begin{gathered} PercentageIncrease=\frac{2.40-1.50}{|1.50|}\cdot100 \\ \\ PercentageIncrease=\frac{0.9}{1.50}\cdot100 \end{gathered}[/tex][tex]\begin{gathered} PercentageIncrease=0.6\cdot100 \\ \\ PercentageIncrease=60\text{ \%} \end{gathered}[/tex]Hence, the answer is:
[tex]PercentageIncrease=60\text{ \%}[/tex]A microwave company claims that their microwaves can pop popcorn in under 2.25 minutes. After 134 randomly chosen microwaves were sampled, it was found that the mean time to pop popcorn was 2.5 minutes, with a standard deviation of .25 minutes. Using the information provided, determine if this claim should be rejected?A. Reject the null hypothesis. There is not enough evidence to oppose the microwave company's claim.B. Reject the null hypothesis. There is enough evidence to oppose the microwave company's claim.C. Fail to reject the null hypothesis. There is not enough evidence to oppose the microwave company's claim.D. Fail to reject the null hypothesis. There is enough evidence to oppose the microwave company's claim.
ANSWER
A. Reject the null hypothesis. There is not enough evidence to oppose the microwave company's claim.
EXPLANATION
The claim is that the microwave can make popcorn in under 2.5 minutes. Hence, the statistical hypotheses are:
[tex]\begin{gathered} H_0\colon\mu\ge2.25 \\ H_1\colon\mu<2.25 \end{gathered}[/tex]where H0 = null hypothesis
H1 = the hypothesis we are interested in proving
The level of significance of the test is not given, hence, we can assume that the level of significance of the test is 5%:
[tex]\alpha=5\%=0.05[/tex]Since the sample size is n = 134, we can use the approximation to the standard normal distribution to calculate the test statistic:
[tex]z=\frac{\bar{x}-\mu}{\frac{S}{\sqrt[]{n}}}[/tex]For the given sample:
[tex]\begin{gathered} n=134 \\ \bar{x}=2.5\text{ min} \\ S=0.25 \\ \mu=2.25\text{ min} \end{gathered}[/tex]Hence, we have that:
[tex]\begin{gathered} z=\frac{2.5-2.25}{\frac{0.25}{\sqrt[]{134}}} \\ z=\frac{0.25}{\frac{0.25}{11.5758}} \\ z=0.25\cdot\frac{11.5758}{0.25} \\ z=11.5758 \end{gathered}[/tex]Now, we have to find the p-value.
If the p-value is greater than the significance level, the decision is to not reject the null hypothesis.
If the p-value is less than the significance level, the decision is to reject the null hypothesis.
For any z-score value greater than 3, the accumulated probability is 0.99999 and for any value below -3, the accumulated probability is 0.
We have that the z-score is 11.5758. This means that:
[tex]\begin{gathered} P(z>11.58)=1-P(z<11.57)=1-0.99999 \\ \Rightarrow P(z>11.58)=0.00001 \end{gathered}[/tex]As we can see, the p-value is less than the significance level, so the decision is to reject the null hypothesis.
This means that the alternative hypothesis:
[tex]H_1\colon\mu<2.25[/tex]is right (or stays) and so, the claim of the company is right.
Hence, the correct answer is option A.
please help me answer the question in the image. thank you for any help and explanations you can give me!
We can solve this type of question using trigonometric functions. Here, we use sine of the angle of take-off with the horizontal runway.
[tex]\begin{gathered} \sin 10^o=\frac{500}{c} \\ c=\frac{500}{\sin 10^o} \\ c=\frac{500}{0.1736} \\ c=2880.18 \end{gathered}[/tex]Thus, the distance that the plane has traveled is equal to 2880 ft.
What is the solution of 0.2x - 4 - 2x < -0.4 and 3x + 2.7 <3
Answers:
1) x > - 2
2) x < 0.1
Explanatt
The given inequalities are:
1) 0.2x - 4 -2x < -0.4
2) 3x + 2.7 < 3
Solution to number 1:
0.2x - 4 - 2x < -0.4
Collect like terms
0.2x - 2x < -0.4 + 4
-1.8x < 3.6
Divide both sides by 1.8
[tex]\begin{gathered} \frac{-1.8x}{1.8}<\frac{3.6}{1.8} \\ -x\text{ < }2 \\ x\text{ > -2} \end{gathered}[/tex]Solution to number 2:
3x + 2.7 < 3
Collect like terms
3x < 3 - 2.7
3x < 0.3
Divide both sides by 3
[tex]\begin{gathered} \frac{3x}{3}<\frac{0.3}{3} \\ x\text{ < 0.1} \end{gathered}[/tex]PLEASE HELP IM SICK AND I DONT UNDERSTAND.DUE IN 30 MINS!!!!!!
The value of x is -12 and the pair of interior angles are: 130 and 50 degrees.
Given, a transversal is passed by the parallel lines.
Hence consecutive interior angles are formed.
Each pair of internal angles on the same side of a transversal are supplementary, or they add up to 180°, if the transversal meets two parallel lines.
therefore, x+142 + x + 62 = 180°
arrange the variables one side
2x + 142 + 62 = 180
add the constants.
2x + 204 = 180
2x = 180-204
2x = -24
x = -12
interior angle 1 = x+142
= -12+142
= 130°
interior angle 2 = x+62
= -12+62
= 50°
Hence the value of x is -12.
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k(-1,3)5-2 -14321(0, 1)y1.1, 3) (2, 3)1 2613VXAnalyze the graph of the exponential decay function.The initial value isThe base, or rate of change, isThe domain isD
The general expression for an exponential function is the following:
[tex]y=ab^x[/tex]where b represents the base of the function.
In this case, notice that the graph of the function passes through the points (0,1) and (1,1/3), then, with these points we can find the values of a and b:
[tex]\begin{gathered} (0,1): \\ 1=ab⁰\Rightarrow a=1 \\ (1,\frac{1}{3}): \\ \frac{1}{3}=b¹\Rightarrow b=\frac{1}{3} \end{gathered}[/tex]therefore, we have that:
the initial value is a = 1
the base is b = 1/3
the domain of the function is all real numbers.
how can I construct a tally table to represent the data?
Answer:
a)
To construct a tally table, we will have to present the table ranging from 150 to 156
b)
The probability of choosing a student not more than 153 in height means
[tex]\begin{gathered} Pr(h\leq153) \\ Pr(h\leq153)=\frac{n(h\leq153)}{n(S)} \\ (h\leq153)=1+5+10+16=32 \\ n(S)=50 \\ Pr(h\leq153)=\frac{n(h\leq153)}{n(S)}=\frac{32}{50}=\frac{16}{25} \end{gathered}[/tex]Hence,
The probability of picking not more than 153cm in height is = 16/25
b ii)
To figure out the probability greater than 153cm in height
[tex]\begin{gathered} Pr(h>153) \\ Pr(h>153)=\frac{n(h>153)}{n(S)} \\ n(h>153)=10+6+2=18 \\ n(S)=50 \\ Pr(h>153)=\frac{n(h>153)}{n(S)}=\frac{18}{50}=\frac{9}{25} \end{gathered}[/tex]Hence,
The probability of height greater than 153cm = 9/25
Veronica owes a clothing store $1800, but until she makes a payment, she pays 4% interest per month.What is Veronica's monthly interest payment?
The interest Veronica has to pay monthly is:
1,800 * 0.04 = I think you can calculate this, Km.
Which pairs of non- overlapping angles share a ray to make a right angle? Select all that apply.
From the figure the pairs of angles that share a ray to make a right angle are:
[tex]\begin{gathered} \measuredangle EGK\text{ and }\measuredangle KGF \\ \measuredangle\text{FGJ and }\measuredangle JGH \end{gathered}[/tex]Answer: Option 1 and Option 4.
draw examples of each figure: - 2 perpendicular lines-AB AC ray on same line-EW intersecting with EMI'll upload picture
Part c
N 11
2 perpendicular lines
see the figure below
N 12
see the figure below
N 13
see the figure below
please put answers for sin, cos, tan, cot, sec, and csc
If we measure the angle in the clockwise direction:
Therefore, this point is:
[tex](-1,0)[/tex]Since the cosine and sine functions are given by:
[tex]\begin{gathered} \sin (\theta)=\frac{opposite}{_{\text{ }}hypotenuse} \\ \cos (\theta)=\frac{adjacent}{_{\text{ }}hypotenuse} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} \sin (-\pi)=\frac{0}{1}=0 \\ \cos (-\pi)=\frac{1}{-1}=-1 \end{gathered}[/tex]Since:
[tex]\begin{gathered} \cot (\theta)=\frac{adjacent}{_{\text{ }}opposite}\to\cot (-\pi)=-\frac{1}{0}=_{\text{ }}undefined \\ \csc (\theta)=\frac{hypotenuse}{_{\text{ }}opposite}\to\csc (-\pi)=\frac{1}{0}=_{\text{ }}undefined \end{gathered}[/tex]Therefore, we can conclude that cotangent and cosecant are undefined for - π
[tex]\begin{gathered} \tan (\theta)=\frac{opposite}{_{\text{ }}adjacent}=\frac{0}{-1}=0 \\ \sec (\theta)=\frac{hypotenuse}{_{\text{ }}adjacent}=\frac{1}{-1}=-1 \end{gathered}[/tex]
Find how much money needs to be deposited now into an account to obtain $7,400 (Future Value)
in 10 years if the interest rate is 7% per year compounded monthly (12 times per year).
The final amount is $
Round your answer to 2 decimal places
Given a certain rate of return, present value (PV) is the current value of a future sum of money or stream of cash flows.
$ 3,682.21 is the present value.
How to find the present value?A future sum of money or stream of cash flows' present value (PV), assuming a given rate of return, is their current value.
Future value is converted to present value by using either a discount rate or the interest rate that would be earned if an investment were made.
Present Value = FV/(1+r/n)^nt
Solution:
Present Value = FV/(1+r/n)^nt
Present Value = 7400/(1+7/12)^10*12
Present Value = 7400/(19/12)^120
Present Value = 7400/(1.58)^120
Present Value = 7400/2^120
Present Value = $ 3,682.21
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Find the area of a square with a side length x when x is equal to the given value. Are the area of a square and the length of its side directly proportianal? Justify your answer. x=3 in.
Answer:
9 in
It is portions because the area will always be the square of a side
Step-by-step explanation:
all sides of a square are the same so we can just multiply 3 by 3 to make 9.
Hopes this help please mark brainliest
Answer: The answer is 9 inches
Step-by-step explanation:
The answer is nine inches but the sides are not proportional.
Find the value of xOptions are 110, 80, 35, 40
The sum of all angles in a triangle is 180º. Therefore:
[tex]\begin{gathered} 180=\text{ 30 + \lparen3x-10\rparen + x} \\ 180=\text{ 30 +3x -10 + x} \\ 180\text{ = 20 + 4x} \\ 180\text{ - 20 = 4x} \\ 160=\text{ 4x} \\ \\ \frac{160}{4}=\text{ x} \\ \\ 40=\text{ x} \end{gathered}[/tex]X will be 40º.
