In the diagram, OP = 2 and OP’ = 8. Find the scale factor of the dilation. a) 1/4 b) 1/2 c) 4 d) 6
Answers
Answer:
c
Step-by-step explanation:
Consider the ratio of image to original, that is
scale factor = [tex]\frac{OP'}{OP}[/tex] = [tex]\frac{8}{2}[/tex] = 4 → C
The scale factor of the dilation will be option C; 4.
What is the scale factor?The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.
Since the scaling is done by multiplication of some constant, that constant is called scale factor.
Dilation of a figure will leave its sides get scaled (multiplied) by same number.
Let suppose if a rectangle is dilated, and its sides were of length = L and width = W, then its dilated version would be having length = Ln, and width = Wn where n is the factor of scaling.
Let that constant be 's'.
Then we have:
[tex]s \times x = y\\s = \dfrac{y}{x}[/tex]
Consider the ratio of image to original, that is;
Scale factor = OP'/OP
OP'/OP = 8/2 = 4
Hence, the scale factor of the dilation will be option C; 4.
Learn more about scale factors here :
https://brainly.com/question/8765466
#SPJ2
Related Questions
I need help I don't understand I was on a streak and now this stupid problem is just unsolvable I just want to finish this stupid work and play gtao
Answers
Explanation:
Area of rectangle A: 48
Area of rectangle B: 96
48/96 = 4/8 = 1/2
Ratio of the area of rectangle A and B is 1:2
Answer:
the ratio is 1:3
Step-by-step explanation:
Shape A can be transformed to shape B by a reflection in the x-axis followed by a translation (c, d) find the value of c and the value of d
Answers
Answer:
c = -6
d = -1
Step-by-step explanation:
In the picture attached, the question is shown.
Shape A is composed of the points:
(3, 2)
(5, 2)
(3, 5)
Reflection across the x-axis transforms point (x, y) into (x, -y). Applying this transformation to shape A:
(3, 2) → (3, -2)
(5, 2) → (5, -2)
(3, 5) → (3, -5)
Translation (c, d) transforms (x, y) into (x+c, y+d). The point (3, -2) in the pre-image (before translation) corresponds to point (-3,-3) in the image (after translation). Therefore:
(3, -2) → (3+c, -2+d) → (-3,-3)
3+c = -3
c = -3 -3 = -6
-2+d = -3
d = -3+2 = -1
If I have 2 steel rods, one with 17% purity and one with 25% purity. How much should I take (in kgs) from each bar?
Answers
Answer:
250 kg of 17% and 150 kg of 25%
Step-by-step explanation:
For answering this, we do it by proportions.
take the difference
17% === 20% === 25%
3 5
Then ratio
17% :25% = 5:3
For 400 kg,
17% = 5/(5+3) * 400 = 250 kg
25% = 3/(5+3) * 400 = 150 kg.
Above is a mental method, no calculation or pencil need.
I will edit to give an algebraic method.
Algebraic method:
Given:
17% rods and 25% rods.
Need to make 400 kg of 20% rods.
Let
A=weight of 17% rods
B=weight of 25% rods
to make 20% rods, we need
( 0.17A + 0.25B ) / (A+B) = 0.20 ............(1)
But we know that
A+B=400 .............(2)
substitute
B=400-A in (1)
( 0.17A + 0.25 (400-A) ) / 400 = 0.20
Cross multiply and simplify
(0.17-0.25)A +100 = 80
-0.08A = -20
A = -20 / (-0.08)
A = 250 ...........(3) (17% rods)
substitute (3) in (2)
B = 400-250 = 150 (25% rods)
Same answer as mental calculations
Even simpler albebra, same answer!
Given:
17% rods and 25% rods.
Need to make 400 kg of 20% rods.
Let
W=weight of 25% rods
400-W = weight of 17% rods
To make 20% purity rods, we need to have 400*0.2=80 kg of pure metal, which is
0.25W + 0.17(400-W) = 80
Expand and simplify
0.25W + 68 - 0.17W = 80
0.08W = 80-68 = 12
W = 12/0.08 = 150 (25% rods)
400-W = 250 kg (17% rods)
Answer:
245432
Step-by-step explanation:
Angela uses cup of strawberries to make of a liter of smoothie. What is the unit rate in cups of strawberries per liter of smoothie?
Identify the domain of the function shown in the graph.
5
O A. -1 5x53
O B. 25x37
Ο Ο Ο
O C. All real numbers
D. X23
Answers
Answer:
[2, 6].
Step-by-step explanation:
Notice that there is a red line (graph) only for [2, 6]. Thus, the domain of this function is [2, 6].
A car travels at 60 miles per hour. If d is the distance traveled and t is the time in hours: Write a function for the distance traveled d in t hours. What is the dependent variable? What is the independent variable? Make a table with at least 5 coordinate pairs. Graph the coordinate pairs and draw the function
Answers
Answer:
Step-by-step explanation:
d= distance
t= time
The independent variable is t, time. The distance the car travels depends on the time in hours spent travelling. The dependent variable is d, distance. Here is a table with 5 coordinate pairs that can be used.
(T) (D)
1 30
2 60
3 90
4 120
5 150
These are the coordinate pairs for the function. When we use division and determine the rate of change, we can determine that the average rate of speed (MPH) is 30 MPH.
A random sample of 145 students is chosen from a population of 4,250 students. The mean IQ in the sample is 130, with a standard deviation of 7. Using a margin of error of 0.95%, what is the 90% confidence interval for the students' mean IQ score?
Answers
Answer:
Approximately, the 90% confidence interval for the students' mean IQ score is between 129.045 - 130.956
Step-by-step explanation:
The formula to use to solve this question is called the Confidence Interval formula.
Confidence interval =
x ± z × ( σ/ (√n) )
Where:
x = the sample mean = 130
z = the z-value for 90% confidence = 1.645
σ = standard deviation = 7
n = sample size = 145
130 ± 1.645 × (7/√145)
130 ± 0.9562687005
130 - 0.9562687005 = 129.0437313
130 + 0.9562687005 = 130.9562687005
Therefore, approximately, the 90% confidence interval for the students' mean IQ score is between 129.045 - 130.956
If the picture looks a little weird, just zoom in and it should be fixed.
Answers
Answer:
c
Step-by-step explanation:
got it right
What is the volume of the pyramid
150ft^3
540 ft^3
432 ft^3
48 ft^3
Answers
Answer:
Option (4)
Step-by-step explanation:
To calculate the volume of a pyramid we use the formula,
V = [tex]\frac{1}{3}(\text{Area of the base})(\text{Height of the pyramid})[/tex]
Area of the square base = (Side)²
= (6)²
= 36 square ft
Height of the pyramid 'h' = [tex]\sqrt{l^{2}-(\frac{\text{Side length of the base}}{2})^{2}}[/tex] [By Pythagoras theorem]
h = [tex]\sqrt{5^{2}-3^{2}}[/tex]
h = [tex]\sqrt{16}[/tex]
h = 4 ft
Therefore, volume of the given pyramid = [tex]\frac{1}{3}(36)(4)[/tex]
= 48 cubic ft
Option (4). 48 ft³ will be the answer.
Check all solutions to the equation. If there are no solutions, check "None."
x=-81
Answers
Answer:
none
Step-by-step explanation:
If a squared variable is equal to a negative number, all of the solutions are imaginary
There are no real solutions
Answer:
The correct answer is none.
if the parent function is y=2x, which is the function of the graph?
a. y = 0.5(2)^x+1 - 3
b. y = 0.5(2)^x-1 - 3
c. y = 0.5(2)^x+1 + 3
d. y = 0.5(2)^x-1 + 3
Answers
Answer:
The answer is option B.[tex]y = 0.5 {(2)}^{x - 1} - 3[/tex]
Hope this helps you
1. Write the standard form of the line that passes through the given points. (7, -3) and (4, -8)
2. Write the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to 2 x + y = -5.
3. Write the equation of the line, in standard form, that has an x-intercept of 2 and is parallel to 2x + y = -5
Answers
Answer:
1. [tex]-5x+3y+44=0[/tex]
2. [tex]2x+y-2=0[/tex]
3. [tex]2x+y-4=0[/tex]
Step-by-step explanation:
Standard form of a line is [tex]Ax+By+C=0[/tex].
If a line passing through two points then the equation of line is
[tex]y-y_1=m(x-x_1)[/tex]
where, m is slope, i.e.,[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex].
1.
The line passes through the points (7,-3) and (4,-8). So, the equation of line is
[tex]y-(-3)=\dfrac{-8-(-3)}{4-7}(x-7)[/tex]
[tex]y+3=\dfrac{-5}{-3}(x-7)[/tex]
[tex]y+3=\dfrac{5}{3}(x-7)[/tex]
[tex]3(y+3)=5(x-7)[/tex]
[tex]3y+9=5x-35[/tex]
[tex]-5x+3y+9+35=0[/tex]
[tex]-5x+3y+44=0[/tex]
Therefore, the required equation is [tex]-5x+3y+44=0[/tex].
2.
We need to find the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to [tex]2 x + y =-5[/tex].
Slope of the line : [tex]m=\dfrac{-\text{Coefficient of x}}{\text{Coefficient of y}}=\dfrac{-2}{1}=-2[/tex]
Slope of parallel lines are equal. So, the slope of required line is -2 and it passes through the point (0,2).
Equation of line is
[tex]y-2=-2(x-0)[/tex]
[tex]y-2=-2x[/tex]
[tex]2x+y-2=0[/tex]
Therefore, the required equation is [tex]2x+y-2=0[/tex].
3.
We need to find the equation of the line, in standard form, that has an x-intercept of 2 and is parallel to [tex]2x + y =-5[/tex].
From part 2, the slope of this line is -2. So, slope of required line is -2 and it passes through the point (2,0).
Equation of line is
[tex]y-0=-2(x-2)[/tex]
[tex]y=-2x+4[/tex]
[tex]2x+y-4=0[/tex]
Therefore, the required equation is [tex]2x+y-4=0[/tex].
HURRRYYYY FIRST GETS BRAINLLEST Janine wrote the numbers 1-100 and placed them in a bag. If she selects a number without looking, what is the probability that the number is even and greater than 80? Input your answer as a decimal or fraction.
Answers
Answer:
1/10 or ( 0.1 )
Step-by-step explanation:
no. of even no.s greater than 80 = 10
Total no.of numbers = 100
So P(no. of even no.s greater than 80) = 10/100 = 1/10
Answer:
There are 10 even numbers greater than 80.
So Probability of getting an even numbers greater than 80 is 10/100 (1/10)
Hope it helps you. Please mark Brainliest :)
Have a nice day PPLS!!!!!!!
State if a triangle is acute, obtuse, or right.
3 am
3 am
5 cm
A) Acute
B) Right
C) Obtuse
ANSWER QUICK 10 POINTS!!
Answers
Answer:
Acute.
Step-by-step explanation:
This is a right angle:
|_ (Basically angle makes an "L" shape and equals to 90 degrees)
This is an obtuse angle:
\_ (Basically like a fat/big angle that is greater than 90 degrees)
This is an acute angle:
/_ (Basically "a-cute" angle that is small and is less than 90 degrees)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Hope that helps and maybe earns a brainliest! :)
Classify the object in real life by what type of polygon it is. State if it is concave or convex, and explain why. Also write the sum of the interior angles. If the polygon is regular what would the measure of the interior and exterior angles be? a. Stop sign b. Tripod c. Computer screen d. School crossing sign e. The dome of a capitol building f. A cell in a honeycomb g. Describe the difference between a concave and convex polygon. h. What is a regular polygon? i. How do you calculate the sum of the interior angles?
Answers
Answer:
see below for classification
concave: angles less than 180°
regular: sides and angles congruent
sum = 180°(n -2)
Step-by-step explanation:
A) The given shapes are classified and described in the attachment. (A polygon is a plane figure, so a "tripod" and a "dome" are not polygons.)
__
B) A convex polygon has interior angles that measure less than 180°. A concave polygon has one or more reflex angles.
__
C) A regular polygon has all angle measures congruent, and all side lengths congruent.
__
D) The sum of interior angles can be calculated from the formula ...
angle sum = 180° · (n -2) . . . . where n is the number of sides
What is one of the solutions to the following system? StartLayout Enlarged left-brace 1st Row y minus 3 = x 2nd row x squared minus 6 x + 13 = y EndLayout (–5, 2) (–2, 1) (2, 5) (8, 5)
Answers
Answer:
The solution of given equation is (2,5)
Step-by-step explanation:
The equations give to us are:
y - 3 = x
or
y = x + 3
y = x² - 6x + 13
We can find the solution of the given system of equations by substituting each point in both of the equations. The point which satisfies both of the equation will be the solution of the the system of given equation.
Substitute (2,5) in both equations
y = x+3
5 = 2+3
5 = 5
TRUE
y = x² - 6x + 13
5 = 2² -6(2) + 13
5 = 5
TRUE
Similarly, we can also check the rest of the points, which come as FALSE.
Therefore, the solution of given equation is (2,5)
Answer:
Answer is C
Step-by-step explanation:
Help, My parents can’t even help me. I’m really stuck. In the SuperLottery, three balls are drawn (at random) from ten white balls numbered from 1 to 10, and one SuperBall is drawn (at random) from ten red balls numbered from 11 to 20. When you buy a ticket, you choose three numbers from 1 to 10, and one number from 11 to 20. If the numbers on your ticket match at least two of the white balls or match the red SuperBall, then you win a super prize. What is the probability that you win a super prize?
Answers
Answer:
This is an extremely easy question. Your correct answer is 1/7,200 or 0.01389%
Step-by-step explanation:
Since you have to choose the three numbers and one super ball to be able to win the lottery, your chances of getting 3 white numbers is 1/10 x 1/9 x 1/8 = 1/720
The chances of getting the super ball is 1/10
And the chances of winning the jackpot is 1/720 x 1/10 = 1/7,200 = 0.01389%
Which statement is true regarding the graphed functions?
Answers
Answer:
C
Step-by-step explanation:
You can look them up in the graphs.
f(2) means "where is the blue graph when x=2?", and you can see it is at y=0.
A password has to use the following format: LDDDDLLL, where L can be any of the upper case letters in the alphabet, and D can be any digit including 0. None of the digits or letters can repeat. What is the probability that a random password uses only vowels (A,E,I,O,U) and odd numbers (1,3,5,7,9)? Show work but do not evaluate. What is the probability that the password spells the word “MATH?”
Answers
Answer:
Only vowels and odd numbers:
[tex]P = \frac{5}{26} *\frac{4}{25}* \frac{3}{24}* \frac{2}{23} *\frac{5}{10}* \frac{4}{9} *\frac{3}{8} *\frac{2}{7}[/tex]
Spells math:
[tex]P = \frac{1}{26} *\frac{1}{25}* \frac{1}{24}* \frac{1}{23}[/tex]
Step-by-step explanation:
We have four letters, so the probability that one letter is a vowel is 5/26 (we have 5 vowels in a total of 26 letters), then the second letter has a probability of 4/25 of being a vowel (1 vowel used), and so on (third letter being vowel = 3/24 and fourth letter being vowel = 2/23)
Then, for the digits, we do the same, one digits has 5/10 probability of being odd, then the second digit has 4/9, the third has 3/8 and the fourth has 2/7.
So the final probability would be:
[tex]P = \frac{5}{26} *\frac{4}{25}* \frac{3}{24}* \frac{2}{23} *\frac{5}{10}* \frac{4}{9} *\frac{3}{8} *\frac{2}{7}[/tex]
To find the probability that the password spells the word “MATH", each letter has to be a specific letter, so the first letter has 1/26 probability, the second has 1/25, and so on:
[tex]P = \frac{1}{26} *\frac{1}{25}* \frac{1}{24}* \frac{1}{23}[/tex]
The number of passwords with only vowels and odd numbers is 1/125580 and the probability that a password spells MATH is 1/358800
How to determine the probabilityThe password format is given as:
LDDDDLLL
Since no character can be repeated, then the total number of different password using the format is:
Total = 26 * 10 * 9 * 8 * 7 * 25 * 24 * 23
Total = 1808352000
Also using the format, the number of passwords with only vowels and odd numbers is:
Total = 5 * 5 * 4 * 3 * 2 * 4 * 3 * 2
Total = 14400
The probability is then calculated as:
[tex]p = \frac{14400}{1808352000}[/tex]
Simplify
[tex]p = \frac{1}{125580}[/tex]
The number of password that spells MATH is:
Total = 1 * 10 * 9 * 8 * 7 * 1 * 1 * 1
Total = 5040
So, the probability that a password spells MATH is:
[tex]p = \frac{5040}{1808352000}[/tex]
Simplify
[tex]p = \frac{1}{358800}[/tex]
Hence, the probability that a password spells MATH is 1/358800
Read more about probability at:
https://brainly.com/question/25870256
What is the image of (2,-2) after a dilation by a scale factor of 5 centered at the
origin?
Answers
Answer:
(10, -10)
Step-by-step explanation:
since the point is at the origin, simply multiply.
2 * 5 = 10
-2 * 5 = -10
Answer:
(10, -10)
Step-by-step explanation:
multiple both X and Y by 5
then you get 10,-10 i hope your not mad if this is wrong
Identify the simplified form of the expression (m 5/2 n 7/2)2 A) m n2 B) m5 n C) m2 n5 D) m5 n7
Answers
Answer:
D) m^5·n^7
Step-by-step explanation:
The applicable rule for exponents is ...
(a^b)^c = a^(b·c)
__
[tex](m^{\frac{5}{2}}n^{\frac{7}{2}})^2=m^{\frac{5}{2}\cdot2}n^{\frac{7}{2}\cdot2}=\boxed{m^5n^7}[/tex]
I am interested in the how, not just an answer. Who can show me the correct solution path?
Answers
Which of these phrases contain a variable? Check all that apply.
O A. The length of the hallway
O B. Twelve ounces of tea
O C. The weight of the wombat
O D. Seven cups of flour
Answers
Answer:
The length of the hall way
the weight of the wombat
The weight of the wombat
Helen drives 195 miles in 3 hours.
a) What is her average speed in mph?
Matthew drives at an average speed of 62 mph for 5 hours.
b) How many miles does Matthew drive?
Answers
Answer:
a) What is her average speed in mph?
= 65 mph
b) How many miles does Matthew drive?
=310 miles
Step-by-step explanation:
The average speed in meters per hour (mph) of Helen is 65 miles per hour
Given:
Total distance = 195 miles
Time taken = 3 hours
Average speed = Total distance ÷ Time taken= 195 miles ÷ 3 hours
= 65 miles per hour
If Matthew drives at an average speed of 62 mph for 5 hours.
Total distance between traveled = Average speed × Time taken
= 62 mph × 5 hours
= 310 Miles
Therefore the total miles Helen traveled in 5 hours at the rate of 62 mph is 310 miles
Read more:
https://brainly.com/question/8406966
What is this expression in simplified form?
(8/10)(8/5)
OA 64/50
OB. 16/50
OC. 80/2
OD. 320/2
Answers
Answer:
A.64/50
Step-by-step explanation:
8/10*8/5
64/50
The least simplified form of the equation is 32/25
The simplified form of expression is option (D) 64/50 is the correct answer.
What is simplification of an expression?Simplification of an expression is the process of writing an expression in the most efficient and compact form without affecting the value of the original expression. It involves, multiply out the brackets and then simplify the resulting expression by collecting the like terms.
For the given situation,
The expression is (8/10)(8/5)
The simplified form of expression is
⇒ [tex](\frac{8}{10} )(\frac{8}{5} )[/tex]
⇒ [tex]\frac{64}{50}[/tex]
Hence we can conclude that the simplified form of expression is option (D) 64/50 is the correct answer.
Learn more about simplification of an expression here
https://brainly.com/question/13730519
#SPJ3
What is the initial value of the equation shown?
y = -7x - 6
-13
-7
-6
-1
Answers
Answer:
-6
Step-by-step explanation:
Just did the test and -6 was the right answer.
given f(x) = 3/2x - 5 and g(x) = x^2 + 2x find x (the input) if g(x) = 0 ( the output 0 ) there are 2 answers
Answers
Answer:
x = 0 , x = -2
Step-by-step explanation:
The function given to us is:
f(x) = 3/2x - 5
g(x) = x² + 2x
We have to find the input x, for which the output of the function g(x) becomes 0.
It means that there is no use for the function f(x) in this question, so discard it
Substitute g(x) = 0 into the given equation of g(x):
g(x) = x² + 2x
0 = x² + 2x
Take x common from both the terms:
x(x+2) = 0
Thus, the values of x can be written as:
x = 0 , x + 2 = 0
x = 0 , x = -2
Determine the length of BC . ANSWERS: A) 12.25 units B) 24.71 units C) 19.00 units D) 5.57 units
Answers
Answer:
A) 12.25 units
Step-by-step explanation:
From Pythagorean theorem:
AB² + BC² = 25²6² + BD² = BC²19² + BD² = AB²Defining:
x = AB²y = BC²z = BD²The system of equations is:
x + y = 625 (eq. 1)
36 + z = y (eq. 2)
361 + z = x (eq. 3)
Replacing equation 3 into 1:
361 + z + y = 625
From equation 2:
z = y - 36
Replacing it into equation 1:
361 + y - 36 + y = 625
2y = 625 + 36 - 361
y = 300/2
y = 150
Finally:
BC = √y
BC = √150
BC = 12.25 units
Does the graph represent a function?
Answers
Answer:
yes
Step-by-step explanation:
Need help solving triangle in picture
Answers
Answer:
see explanation
Step-by-step explanation:
Using the sine ration on the left, right triangle
sin35° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{a}{8.6}[/tex] ( multiply both sides by 8.6 )
8.6 × sin35° = a , thus
a ≈ 4.93 cm
a + b = 15.7, so
4.93 + b = 15.7 ( subtract 4.93 from both sides )
b = 10.77
-------------------------------------------------------------
Using the cosine ratio on the left, right triangle
cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{y}{8.6}[/tex] ( multiply both sides by 8.6 )
8.6 × cos35° = y , so
y ≈ 7.04 cm
Using Pythagoras' identity on the right, right triangle
c² = b² + y² = (10.77)² + (7.04)² = 115.99 + 49.56 = 165.55
Take the square root of both sides )
c = [tex]\sqrt{165.55}[/tex] ≈ 12.87 cm
Harold has $20.00 to spend. He decided to buy a shirt for $15.95 and spend the rest on packs of gum. If each pack of gum costs $1.99, how many packs of gum can Harold buy?
Answers
Answer:
2 or less packs
Step-by-step explanation:
15.99 + 1.99g < 20.00 where g is the number of packs of gum
Subtract 15.99 from each side
15.99 + 1.99g - 15.99 < 20.00-15.99
1.99g < 4.01
Divide by 1.99
1.99g/1.99 < 4.01/1.99
g < 2.015075377
Harold must buy whole packs so g =2 or less