Answers
Answer:
[tex]\frac{4}{3}[/tex]
Explanation:
This can be seen as asking what can you multiply by 3 to get 4.
[tex]3[/tex] × [tex]scale factor[/tex] [tex]= 4[/tex]
To solve this, you divide both sides by 3 to leave the scale factor alone on the side, getting our answer!
[tex](3[/tex] × [tex]scale factor)[/tex] ÷ [tex]3 = 4[/tex] ÷ [tex]3[/tex]
[tex]scale factor[/tex] [tex]= 4[/tex] ÷ [tex]3[/tex] [tex]or[/tex] [tex]\frac{4}{3}[/tex]
You can also convert it to a proper fraction or a decimal.
[tex]\frac{4}{3} = 1\frac{1}{3} = 1.333...[/tex]
So given triangle DEF : triangle RST, the scale factor is [tex]\frac{4}{3}[/tex] ([tex]x[/tex] is 12 by the way).
The scale factor represents the ratio of corresponding side lengths between the two triangles. Here the scale factor is [tex]\frac{3}{4}[/tex].
To calculate the scale factor divide each corresponding side's length in one triangle by its corresponding side's length in the other. Calculate the ratio of any two corresponding sides. For each of the corresponding sides, repeat this step.
Scale factor = Length of corresponding side in Triangle 1 / Length of corresponding side in Triangle 2
Here, according to the diagram we can write:
4 × Scale Factor = 3
or Scale Factor = [tex]\frac{3}{4}[/tex]
The scale factor can be rounded to the desired number of decimal places.
Scale Factor = [tex]\frac{3}{4} =0.75[/tex]
which means that the lengths of the sides in ΔDEF are 0.75 times the lengths of the corresponding sides in ΔRST.
So, we can also write: [tex]\frac{EF}{ST}=\frac{x}{16}=\frac{3}{4}[/tex]
or, x = 12
Therefore, for given ΔDEF : ΔRST, the Scale Factor is [tex]\frac{3}{4}[/tex].
To know more about scale factor,
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Related Questions
A juice company gives prizes to anyone finding specially marked caps on its bottles. You and your friends buy 60 bottles of juice. You find 4 of the bottles have a winning cap. What is the experimental probability of winning a prize in the contest? Express your answer as a fraction in simplest form.
Answers
Answer:
[tex]\Huge \boxed{ \text{$\frac{1}{15}$}}[/tex]
Step-by-step explanation:
Experimental probability is the probability calculated by performing actual experiments and observing the outcomes. In this case, the experiment is buying juice bottles and checking if they have a winning cap.
You and your friends bought 60 bottles of juice.You found 4 of them had winning caps.To find the experimental probability, we need to divide the number of winning caps (favourable outcomes) by the total number of bottles (possible outcomes).
The experimental probability can be expressed as a fraction:
[tex]\frac{ \text{ \huge Number of Winning Caps}}{\text{ \huge Total Number of Bottles}}[/tex]
Now, let's plug in the numbers you provided:
[tex]\huge \text{ $\frac{4}{60}$}[/tex]
To simplify this fraction, we need to find the greatest common factor (GCF), of the numerator (4) and the denominator (60) and then divide both by the HCF. The HCF of 4 and 60 is 4. So, we divide both the numerator and the denominator by 4:
[tex]\huge \text{ $\frac{4 \div 4}{60 \div 4}$= $\frac{1}{15}$}[/tex]
So, the experimental probability of winning a prize in the contest is [tex]\frac{1}{15}[/tex]. This means that, based on your experiment, there is 1 chance in 15 of finding a winning cap when buying a bottle of juice.
________________________________________________________
Answer: hope this helps ♡
The experimental probability of winning a prize in the contest is 1/15.
Step-by-step explanation:
We want to write the probability of winning a prize in the contest.
Here, the number of bottles with a winning cap is 4 and the total (number of bottles) is 60.
Hence, we will write that the experimental probability of winning a prize in the contest is 4/60.
4/60 simplified is: [tex]\frac{4}{60}=\frac{4 divided by 4}{60dividedby4} = \frac{1}{15}[/tex]
Olivia was asked to factor the following expression completely:
[tex]x^3-x+3x^2y-3y[/tex]
[tex]x(x^2-1)+3y(x^2-1)[/tex]
[tex](x + 3y)(x^2 - 1)[/tex]
How can you check Olivia’s work to show the answer is or is not correct. If Olivia is not correct, explain to Olivia where her mistake is and how to fix it.
Answers
She used factorisation method using
And factorised it well
She can check her answer by completing her answer into a solution
If she gets what the equation was from the beginning
She’s correct
The table shows the multiplication of two linear expressions. Select the correct reason for each step.
Reason 1:
Reason 2:
Reason 3:
Reason 4:
Answers
Answer:
Step-by-step explanation:
reason 1:
opening of brackets to solve the expression
reason 2:
in multiplication order is followed i.e. the number always lead the variable in the expression
reason 3:
for clarification brackets are added to multiply like terms i.e. numbers with numbers and variable with the variable
reason 4:
the solved and simplified expression is delivered as a result
Please help me! im on an assignment an cant figure it out
Answers
Step-by-step explanation:
The difference beteen 9.2 ounces and 8.1 ounces is 1.1 ounces
and the difference in price is .49
so 1.1 ounces cost .49
$ .49 / 1.1 oz = $ .445 per ounce
Then Reid's bowl should cost 7.8 oz * $ .445 / oz = $3.47
A rectangle field has an area of 300 square meters and a perimeter of 80 meters. What are the length and width of the field?
Answers
Answer:
l + w = 40, lw = 300
l(40 - l) = 300
40l - l² = 300
l² - 40l + 300 = 0
(l - 30)(l - 10) = 0
l = 30, w = 10
The length of the field is 30 meters, and the width of the field is 10 meters.
10 is the width
30 is the length
What is the area to this?
Answers
Answer:
The Area of the polygon is 36m².
Step-by-step explanation:
Area of the polygon= Area of rectangle + Area of triangle
Diagram
______________
l. l \
3m |. 3m l. \
|. l. /
|_____________ l /
11m. 2m
( 13m).
Area of rectangle= Length × Width
= 11m × 3m
= 33m²
Area of triangle= ½ × base × height
To find the height= 13m - 11m = 2m
= ½ × 3 × 2
= ½ × 6
= 3m²
Area of the polygon= 33m² + 3m² = 36m²
please write a function for the points (1/3,0) (-2 3/4,0) and (0,-5) and explain the steps.
thank you!
Answers
The function for the points are y = -15x - 5
How to determine the functionFrom the information given, we have that;
The points are;
(1/3,0) (-2 3/4,0) and (0,-5)
Using the point-slope form of a linear equation, we have;
y - y₁ = m(x - x₁)
Such that;
m is the slope of the liney - y₁ and (x - x₁) are the pointsUsing (1/3, 0) and (0, -5), we have that the slope is;
m = (0 - (-5))/0 -1/3)
expand the bracket
= 5 / (-1/3)
= -15
Now, take any of the given points and substitute the values
Using (1/3, 0), we get;
y - 0 = -15(x - 1/3).
y = -15x - 5.
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The function for the points solved by (1/3,0) (-2 3/4,0) and (0,-5) solved by point slope form is [tex]a=-15b-5[/tex]
We have given the points:
(1/3,0) (-2 3/4,0) and (0,-5)
Using the formula of linear equation
[tex]a-[/tex][tex]a_{1}[/tex][tex]=x[b-b_{1}][/tex]
Where we will consider (1/3,0) = [tex]a-a_{1}[/tex] and (0,-5) = [tex]b-b_{1}[/tex]
that is 1/3 = [tex]a[/tex], 0 = [tex]a_{1}[/tex] and
0 = [tex]b[/tex], -5 = [tex]b_{1}[/tex]
[tex]x[/tex] refers to the slope of line (take any variable)
Now for finding the value of [tex]x[/tex],
[tex]x=a-a_{1}/b-b_{1}[/tex]
inserting the values,
[tex]x=[0-[-5]]/[0-1/3]\\x= -15[/tex]
Substitute the value of [tex]x[/tex] in the equation
[tex]a-0=-15[b-1/3][/tex]
By simplifying the equation, we get
[tex]a=-15b-5[/tex]
To know more about functions and points:
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You flip a coin.
What is P(heads)?
Write your answer as a fraction or whole number.
Answers
If the probability of no rain tomorrow is 30%, what is the probability that it will rain tomorrow? Express your answer as a percent.
Answers
Answer:
70%
Step-by-step explanation:
Since the probability of no rain tomorrow is 30%, that means 30% of the probability is taken up by the chance of no rain.
Since the total probability always adds up to 100%, that means the remaining 70% of the probability must be for rain.'
So the probability that it will rain tomorrow is 70%.
You can verify this with a probability tree diagram:
Total Probability = 100%
No Rain - 30%
▼
More Likely event
▲
Rain - 70%
Since the chance of no rain is 30%, that leaves 70% for the chance of rain.
The probability that it will rain tomorrow is 70%.
What is probability?
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.
Given the problem, we need to find the probability that it will rain tomorrow.
Since, the probability of no rain tomorrow is 30%, the probability that it will rain tomorrow is 100% - 30% = 70%.
Hence, the probability that it will rain tomorrow is 70%.
Learn more on probability at:
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Please help me! I really need help
Answers
They are not the same shape, and angles are not proportional. I hope i’m a little help.
Answer: They are not the same shape.
Step-by-step explanation: The given figures have two different shapes that is the first one is square in which all the four sides are equal while the second shape is a rectangle in which the the opposite sides are equal, thus making both the figures different from each other.
The length of a bacterial cell is about 3 x 10^−6 m, and the length of an amoeba cell is about 4.5 x 10^−4 m. How many times smaller is the bacterial cell than the amoeba cell? Write the final answer in scientific notation with the correct number of significant digits. Step by Step needed!
2 x 10^2
2 x 10^3
0.7 x 10^1
6.67 x 10^2
Answers
Answer:
Step-by-step explanation:
Okay, so first you take 3 × 10∧-6m back to its decimal form, giving you 0.000003. Also, take 4.5×10∧-4m back to its decimal form giving you 0.00045. You then divide 0.00045 by 0.000003 giving you 6.66666 but we then take it to 6.67 × 10∧2 which is the answer.
Factor the following expressions completely. Show and check all work on your own paper.
[tex]2x^2-18x-20[/tex]
Answers
Answer:
2( (x - 10) (x + 1)
Step-by-step explanation:
First factor out a 2
2([tex]x^{2}[/tex] - 9x - 10) Then you are trying to find two number that add to -9 and multiply to -10 (-10 and 1)
2(x - 10) ( x + 1)
Helping in the name of Jesus.
