The surface area of the dilated prism is 9 times the surface area of the original prism.
If the surface area of a triangular prism is dilated at a scale factor of 3, it means that every dimension of the prism's surface area is multiplied by 3.
When a two-dimensional shape is dilated by a scale factor, the area is multiplied by the square of the scale factor.
In this case, the scale factor is 3, so the surface area of the dilated prism is (3²) times the surface area of the original prism.
Therefore, the surface area of the dilated prism is 9 times the surface area of the original prism.
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Iris’s checking account pays simple interest at 5% per year. She has $175 in her account. Write a linear function to model the amount of money in her checking account at any time t
Her checking account balance at every given time is represented by the linear function 175 + 8.75t
What is a interest?The basic interest formula is as follows: Interest is equal to P, R, and T. P is the principal sum (the beginning balance). Interest rate, R (usually per year, expressed as a decimal). T = Number of intervals of time (generally one-year time periods).An interest is just the additional sum borrowed when one borrows money or saves money.In this situation, the checking account offers simple interest at a rate of 5% annually. Her account has $175 in it.
The amount of money in the account at anytime will be:
= 175 + (PRT/100)
P = principal
R = rate
T = time
= 175 + [(175 × 5 × t)/100]
= 175 + 8.75t
The function is 175 + 8.75t
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Solve the compound inequality n+2≤−5 and n+6≥−6
The solution of the inequality are n ≤ -7 and n ≥ -12.
How to solve compound inequality?A compound inequality is an inequality that combines two simple inequalities.
Therefore, let's solve the compound inequality individually.
n + 2 ≤ −5 and n + 6 ≥ −6
Hence,
n + 2 ≤ − 5
subtract 2 from both sides of the inequality
n + 2 - 2 ≤ − 5 - 2
n ≤ -7
n + 6 ≥ −6
subtract 6 from both sides of the inequality
n + 6 ≥ −6
n + 6 - 6 ≥ −6 - 6
n ≥ -12
Therefore, n ≤ -7 and n ≥ -12
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What is the formula of substitution reaction?
Let's assume that the reaction is taking place between alkyl bromide and the nucleophile is OH- , then the formula for substitution reaction will be , R-Br + OH− => R-OH + Br− .
Nucleophiles are known as organisms that are strongly linked to an area of positive charge in the form of an ion or a molecule. These are believed to be fully charged or to have negative ions on a molecule. Cyanide ions, water, hydroxide ions, and ammonia are common examples of nucleophiles.
Electrophiles are compounds which are involved in the electrophilic substitution process. They are the molecules that transfer a pair of electrons during the creation of a covalent bond.
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How many images will be formed if 2 mirrors are kept at an angle of 72?
The number of images formed by two mirrors kept at an angle of 72° are;
5 images, If the object is positioned symmetrically between the mirrors
4 images if the object is placed asymmetrically between the mirrors
How can the number of images formed by two mirrors placed at an angle be found?The formula that can be used to find the number of images formed, n, when two mirrors are placed at a specified angle, θ, to each other is presented as follows;
If [tex]\dfrac{360^{\circ}}{\theta}[/tex] is an even number, the number of images formed is obtained using the formula;
[tex]n = \dfrac{360^{\circ}}{\theta} -1[/tex]If [tex]\dfrac{360^{\circ}}{\theta}[/tex] is an odd number, the number of images formed is obtained using the formula;
[tex]n = \dfrac{360^{\circ}}{\theta} -1[/tex]If [tex]\dfrac{360^{\circ}}{\theta}[/tex] is an odd number, and the position of the object is asymmetric, the number of images formed is obtained using the formula;
[tex]n = \dfrac{360^{\circ}}{\theta}[/tex]When θ = 72°, we get;
[tex]n = \dfrac{360^{\circ}}{72^{\circ}} = 5[/tex], which is an odd number, therefore;
If the object is placed symmetrically between the two mirrors, the number of images formed is therefore;
[tex]n = \dfrac{360^{\circ}}{72^{\circ}}-1 = 4[/tex]
If the object is placed asymmetrically between the two mirrors, the number of images formed is [tex]n = \dfrac{360^{\circ}}{72^{\circ}} = 5[/tex]
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Discuss the difference between r and p.
Choose the correct answers below.
r represents the ____
p represents the ___
r represents the sample correlation coefficient.
p represents the population correlation coefficient.
A statistical concept known as the correlation coefficient helps in establishing a relationship between expected and actual values gained through statistical experimentation.
The estimated correlation coefficient's value explains how much the expected and actual values match.
The correct answers are
r represents the sample correlation coefficient
The interpretation of sample correlation coefficient (r) depends on how the sample data are collected.
A statistical concept known as the correlation coefficient helps in establishing a relationship between expected and actual values gained through statistical experimentation.
p represents the population correlation coefficient.
With a large simple random sample, the sample correlation coefficient is an unbiased estimate of the population correlation coefficient (p)
A correlation coefficient of 1 is perfect positive correlation
A correlation coefficient of -1 is perfect negative correlation
A correlation coefficient of 0 indicated the variables do not have any direct relationship.
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Discuss the difference between r and p. Choose the correct answers below.
r represents the _____
1. sample correlation coefficient thing
2. critical value for the correlation coefficient.
3. population correlation coefficient.
p represents the _____
1. critical value for the correlation coefficient.
2. population correlation coefficient.
3. sample correlation coefficient.
EXPRESS 7 + 12x -3x^2 in the form a+b(x+c)^2
Answer:
19 - 3(x - 2)²
Step-by-step explanation:
7 + 12x - 3x² ( rearrange terms in x )
7 - 3x² + 12x ( factor out - 3 from each of the x- terms )
= 7 - 3(x² - 4x)
using the method of completing the square on x² - 4x
add/subtract ( half the coefficient of the x- term )² to x² - 4x
= 7 - 3(x² + 2(- 2)x + 4 - 4)
= 7 - 3(x - 2)² - 3(- 4)
= 7 - 3(x - 2)² + 12
= 19 - 3(x - 2)² ← in the form a + b(x + c)²
with a = 19 , b = - 3 , c = - 2
Here's a box plot that summarizes the number of pencils in each student's desk.
H+++
0 2 4
+++
6
6
8
Number of pencils
Find the range of the data.
+++H
pencils
10 12 14
The range of the data on the boxplot is 12
How to determine teh rangeFrom the question, we have the following parameters that can be used in our computation:
The box plot
The range is calcilated as
Range = Maximum - Minimum
From the plot, we have
Maximum = 12
Minimum = 0
Substitute the known values in the above equation, so, we have the following representation
Range = 12 - 0
Evaluate
Range = 12
Hence, the range is 12
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Which of the following is additive inverse of 3 2?
The additive inverse of 3/2 is -3/2 as the sum of both value is 0 which is additive identity.
An additive inverse of a number is the number that when added to the original number, results in a sum of zero. In other words, it is the opposite of the original number on the number line. In the case of a fraction, the additive inverse is found by multiplying the numerator and denominator by -1. The additive inverse of 3/2 is -3/2 because 3/2 + (-3/2) = 0. This is true for any number in any form, whether it be an integer, a decimal, or a fraction.
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Complete question:
what is additive inverse of 3/2?
4x^2-24=20x Help Solve by factoring show and explain steps please
Which system has no solution y=-3x+8 6c+2y=-4.5i
Answer:6c+2y=4.5i
Step-by-step explanation:
i am pretty sure it that answer is because you cant add 2 variables in a problem well 2 different variable
hope its right
Given: AABC with = CB
Prove: DE AC
7
What is the missing step in this proof?
OA. ZBAC ZACB
OB.
ZBDE ZDEB
ZADE ZDEC
OD. ZBAC BDE
OE. ZABC ZDBE
O C.
Answer: It seems that the missing step in this proof would be option "OB" ZBDE ZDEB ZADE ZDEC,
Step-by-step explanation:
It's showing that the angles are equal and the angles are congruent. The reason is that by definition, congruent angles have the same degree measure and by using the Angle-Angle Similarity Criterion we can prove that if two angles of one triangle are congruent to two angles of another triangle, the two triangles are similar.
It is important to note that this statement can only be used when the two figures are similar and it is not sufficient for congruency. Therefore, a missing step in this proof would be to prove that the figures are similar before using the Angle-Angle Similarity Criterion.
The statement given is "AABC with = CB" and the conclusion is "DE AC." The question is asking for the missing step in the proof that shows how these two statements are related.
NASA's InSight is a robotic lander designed to study the deep interior of Mars. The solar panels on InSight are shaped like regular decagons. Find the measure of each interior angle of the solar panels. Then find the measure of each exterior angle.
Interior angle: ?
Exterior angle: ?
An interior angle of a regular decagon is given by the formula (n-2) * 180 / n, where n is the number of sides. Since a decagon has 10 sides, the measure of each interior angle is (10-2) * 180 / 10 = 160 degrees.
The measure of each exterior angle of a regular polygon is given by the formula 360 / n, where n is the number of sides. So in the case of a decagon, each exterior angle measures 360 / 10 = 36 degrees.
What is the relationship between squaring and getting the square root?
Finding a number's square root is the equivalent as squaring it, or the opposite process. When you multiply the square root of a given integer by itself, you get the original number. Since 8 x 8 equals 64, as fact, 8 is the square root of 64.
What is square roots?It is possible to multiply an integer by its square root in order to obtain the original value. Square root of, end square root is the symbol for this mathematical concept. Contrary to squaring, finding a number's square root is the reverse. For instance, 3 is squared at 9, 32, and its square root at 9, which is 9, is equal to 3. It is simple to multiply by 9 since it is a perfect square.
Thus, there is a reverse relationship between squaring and getting the square root.
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Three vehicles recorded the following information about their trips.
Van:500 miles in 7.5 hours
Truck:300 miles in 5 hours
Car:400 miles in 5.5 hours
Find the unit rate miles/hour for the van.
The unit rate of miles/hour taken by the van is 66.67 miles/hr.
What is unit rate?A unit rate is a price for one unit of something. This is written as a ratio with a denominator of one. A unit rate compares one amount to one unit of another amount. Unit rates include miles per hour, cost per item, and calories per serving.Here given that,
The records of the trip of three vehicles are:
Van:500 miles in 7.5 hours
Truck:300 miles in 5 hours
Car:400 miles in 5.5 hours
We have to find unit rate miles/hour of the van.
So ,
Van covers 500 miles in 7.5hrs.
To find the unit rate,
Unit rate = total distance covered / total time taken
By substituting the values,
unit rate = 500/7.5
= 66.67 miles/hr
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There are 623 calories in seven ounces of a certain ice cream. How many calories are there in two pounds?
1 pound
=
16 ounces
1 pound=16 ounces
Before you try that problem, answer the question below.
How many ounces will you need to find the number of calories for?
There are 2,848 calories in two pounds of a certain ice cream.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
There are 623 calories in seven ounces of a certain ice cream.
Since, We know that;
⇒ 1 pound = 16 ounces
Hence, We get;
⇒ 2 pounds = 32 ounces
Here, Amount of ice cream in 7 ounces = 623 calories
Hence, Amount of ice cream in 32 ounces = 623 × 32 / 7
= 2,848 calories
Thus, Amount of ice cream in 1 pounds = 2,848 calories
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Determine a series of transformations that would map Figure V onto Figure W.
The required equation of transformation from figure V to figure W is (-x, y+3).
What is the transformation of geometry over the coordinate plane?Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.
Here,
From the figure, it is clearly seen that first the figure gets mirrored on the y-axis, so the translation in the horizontal direction is given as -x. Now after forming the image across the y-axis the figure is translated up by 3 units so vertical translation is given as y +3.
Combine translation is given as {-x, y+3}
Thus, the required equation of transformation from figure V to figure W is (-x, y+3).
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lines x and y are parallel write an equation that represents the relationship between a and g
The required equation that represents the relationship between b and e exists m<b + m<e = 180.
What is meant by supplementary angles?Two angles are called supplementary when their measures add up to 180 degrees.
If the sum of two angles is 180 degrees then they are said to be supplementary angles, which form a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.
The required equation that represents the relationship between b and e exists m<b + m<e = 180
From the given diagram, we can see that the line x and y are cut by a transversal. This shows that the following statements exists true;
m<b and m<g exists supplementary
i.e m<b + m<g = 180
Also m<b and m<f are equal (alternate interior angle)
m<b = m<d (vertically opposite angle)
Also, since m<d and m<e are supplementary angles (angle on a straight line), then m<b and m<e are also supplementary.
Therefore, the required equation that represents the relationship between b and e exists m<b + m<e = 180.
The complete question is:
Lines x and y are parallel. Write an equation that represents the relationship between b and e. Explain how you know this equation is always true. Your explanation should use AT LEAST TWO of the following terms: vertical angles, corresponding angles, congruent, supplementary.
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Which equation has the solutions x = startfraction negative 3 plus-or-minus startroot 3 endroot i over 2 endfraction? 2x2 + 6x + 9 = 0 x2 + 3x + 12 = 0 x2 + 3x + 3 = 0 2x2 + 6x + 3 = 0.
The equation that has the solutions [tex]\frac{-3 \pm \sqrt{3}i }{2}[/tex] will be a) 2x² + 6x + 9
Here we have to find the equation which has roots
[tex]\frac{-3 \pm \sqrt{3}i }{2}[/tex]
This means that the factors of the roots will be
[tex]x+\frac{3 + \sqrt{3}i }{2}[/tex] and [tex]x+\frac{3 - \sqrt{3}i }{2}[/tex]
Now since all our options are quadratic equations, they have to be a product of these 2 factors and ONLY an additional numerical co-efficient
Hence we get
[tex][x+\frac{3 + \sqrt{3}i }{2}][x+\frac{3 - \sqrt{3}i }{2}][/tex]
rearranging this will give us
[tex][x+\frac{3}{2} + \frac{ \sqrt{3}i }{2}][x+\frac{3}{2} - \frac{ \sqrt{3}i }{2}][/tex]
using the formula
a² - b² = (a + b)(a - b) we get
(x + 3/2)² - (√3i/2)²
= x² + 9/4 + 3x + 9/4 [since i² = -1]
Hence we get x² + 3x + 9/2
= a) 2x² + 6x + 9
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Correct Question
Which equation has the roots
[tex]\frac{3 \pm \sqrt{3}i }{2}[/tex]
a) 2x² + 6x + 9 = 0
b) x² + 3x + 12 = 0
c) x² + 3x + 3 = 0
d) 2x² + 6x + 3 = 0.
Roger received $200 for his birthday. He wants to use the money to buy new clothes for
work. He can buy pants for $30 and shirts for $20. He wants at least 6 new items. Which
combinations of shirts and pants can he buy?
Answer:
Step-by-step explanation: He can get 150 worth of clothes
He can buy 3 new shirts and 3 pairs of new pants!
Can someone help me please Assap?
Step-by-step explanation:
[tex]\frac12(8k+12k^2+6k^3)\\=4k+6k^2+3k^3\\[/tex]
Rearrange into descending order:
[tex]\boxed{3k^3+6k^2+4k}[/tex]
How do you find the image of a point across a line?
The point's x and y coordinates may be switched to create the point's image around the line y=x. As an illustration, consider the picture of the point (a,b) about the line y=x: (b,a).
What is image coordinate system?A main image's spatial reference is specified by an image coordinate system. No distortions appear when a main picture is presented in its own image coordinate system, and secondary images and features can be projected onto the primary image using its image coordinate system.
The point B(l,m) is the point that corresponds to the point P in the line mirror ax+by+c=0 such that PB is perpendicular to ax+by+c=0 and the midpoint L of PB falls on the line ax+by+c=0.
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please help!! will give brainliest! only help if you know how to do this! (statistics and two-way tables)
A representative sample is one that is drawn at random from the population and is large enough to provide accurate data.
What is sample?A population refers to the entire population about which you want to draw conclusions. A sample is the specific group from which you will collect data. The sample size is always less than the total population size.A sample is a subset of the population that is representative of the whole. A sample is sometimes required because accessing the entire population is not always feasible or cost effective.For instance, suppose a researcher is investigating the impact of inflation on US families. It is not possible to reach all of the families in the United States. As a result, the researcher would use a representative sample of US families. This is referred to as a sample.To learn more about sample refer to :
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Burger Mania ell 10 chicken nugget for $1. 50,At thi rate how much hould a family pack of 45 chicken nugget
The cost of a family pack of 45 chicken nuggets = 6.75 dollars
Given that Burger Mania sells 10 chicken nuggets for $1. 50
First we find the cost of one chicken nugget.
10 chicken nuggets = 1. 50 dollars
So, 1 chicken nugget = (1.50) / 10 dollars
= 0.15 dollars
= 15 cents
We need to find the cost of 45 chicken nuggets.
Using Unitary method the cost of 45 chicken nuggets would be,
45 × 0.15 = 6.75 dollars
Therefore, at given rate a family pack of 45 chicken nuggets must be 6.75 dollars
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Solve: 2.5x-3=18
be sure to show your work
Which equation shows the value of -1.5 - 2.75
The value of the given expression is -4.25
What is an expression?
Expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.
Given that, an expression, -1.5 - 2.75
= -1.5 - 2.75
= -1.5 + (-2.75)
= -4.25
Hence, the correct expression is -1.5 + (-2.75) = -4.25
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Mr. Walker used proportions and the following example to teach students how to calculate speeds: An F-15 Eagle travels at a speed of 1,875 miles per hour for 3.5 hours. Which distance solves the proportion he used?
Answer:
6,562.5 miles
Step-by-step explanation:
The proportion is 1,875 miles/1 hour.
At that speed, the distance can be calculated when the time is known, which is 3.5 hours in this case:
(1,875 miles/hr)*(3.5 hr) = 6562.5 miles
Pls help asap it’s making me type so how’s u
Your day going?
The equation in point-slope form for the line passing through (3, -8) with a slope of -3 is y = -3x + 1
What is the slope?
The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).
The point-slope form of the equation of a line is:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
We are given that the line passes through the point (3, -8) and has a slope of -3, so we can substitute these values into the point-slope form:
y - (-8) = -3(x - 3)
Simplifying the equation, we get:
y + 8 = -3x + 9
Subtracting 8 from both sides, we get:
y = -3x + 1
Therefore, the equation in point-slope form for the line passing through (3, -8) with a slope of -3 is:
y - (-8) = -3(x - 3)
which simplifies to:
y + 8 = -3x + 9
or in slope-intercept form:
y = -3x + 1
Hence, the equation in point-slope form for the line passing through (3, -8) with a slope of -3 is y = -3x + 1
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Owen is going to invest in an account paying an interest rate of 5.7% compounded continuously. How much would Owen need to invest, to the nearest hundred dollars, for the value of the account to reach $122,000 in 14 years?
Answer:
Hence, your answer will be:
P ≈ $54900
Step-by-step explanation:
Owen is going to invest in an account paying an interest rate of 5.7% compounded continuously. How much would Owen need to invest, to the nearest hundred dollars, for the value of the account to reach $122,000 in 14 years?
Compounded Continuously:
A = Pe^rt
Given Values:
A = 122000 t = 14 r = 0.057
Plug In:
122000 = Pe^0.057(14)
Plug In:
122000 = Pe^0.798
Evaluate In Calculator Using e Button:
122000 = P(2.221094295)
Divide By: 2.221094295
122000 / 2.221094295 = P(2.221094295) / 2.221094295
Use Calculator:
54927.87959894 = P
Round to The Nearest Hundred Dollars:
P ≈ $54900
Sierra ha a bottle with 2 cup of orange juice left. I thi enough to make 6 frozen juice bar? Explain
No, it depends upon the size of the bottle but it's not enough for a normal bottle to make 6 frozen juice bars.
No, 2 cups of orange juice is not enough to make 6 frozen juice bars. Each frozen juice bar typically requires a certain amount of juice, and it is likely that 6 bars would require more than 2 cups of juice. To be sure, you would need to check the recipe or packaging for the frozen juice bars to determine the exact amount of juice required per bar.
It is also important to note that even if the juice is enough to make 6 bars, it might not yield the same taste as desired because of the lack of enough juice, also the freezing process might not work as well as it should because of the small quantity of juice.
Therefore, It is not enough as it depends upon the size of the bottle but it's not enough for a normal bottle to make 6 frozen juice bars.
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What is the image of (-3,-4) after a dilation be a scale factor of 4 centered at the origin?
The image of the point (-3,-4) after a dilation with a scale factor of 4 centered at the origin is (12,-16).
What is triangle dilation?Generally, Dilation is a method for producing figures with a similar appearance.
By multiplying the distances between each point with the scale factor, each point is extended outwards from the center point D.
(Towards the outside in the event that the scale factor is greater than 1) To alter the profile of the triangle, move the points A, B, and C respectively.
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Answer:(-12, -16)
Step-by-step explanation:
I took the test