Step-by-step explanation:
Okay! Since these are similar figures we need to find the scale factor in order to answer this question.
We have a triangle with sides 7, 4, and 9. The longest side is 9. This corresponds with the longest side on the similar triangle, which is 36. So to find the scale factor we divide 36 by 9. The scale factor is 4.
Now to find the shortest side of the bigger triangle, we have to find the length of the shortest side on the smaller one which is 4. Since our scale factor is 4, we multiply 4 by 4 to get 16.
The length of the shortest side of the similar triangle is 16
The shortest ide is 16
The volume of a cone is 20π cubic meters. What is the volume of a cylinder with the same base and height?
[tex]\bf \begin{array}{lrlll} \stackrel{\textit{volume of a cone}}{\cfrac{\pi r^2 h}{3}\qquad \implies \qquad \cfrac{\pi r^2 h}{3}}=20\pi&\qquad \qquad \stackrel{\textit{volume of a cylinder}}{\pi r^2 h\qquad \implies \qquad 3\left(\cfrac{\pi r^2 h}{3} \right)} \\\\\\ &3(20\pi ) \\\\\\ &60\pi \\\\\\ &\approx 188.5 \end{array}[/tex]
Write the absolute value inequality in the form
|x−b| c that has the solution set x≤−9 or x≥−5.
Answer:
[tex]\large\boxed{|x+7|\geq2}[/tex]
Step-by-step explanation:
Look at the picture.
[tex]|x-a|\geq b\\\\a=\dfrac{-9+(-5)}{2}=\dfrac{-14}{2}=-7\\\\b=-9-(-7)=-9+7=-2\\b=-5-(-7)=-5+7=2\\\\|x-(-7)|\geq2\\\\|x+7|\geq2\\\\Check:\\\\|x+7|\geq2\iff x+7\geq2\ \vee\ x+7\leq-2\qquad\text{subtract 7 from both sides}\\\\x+7-7\geq2-7\ \vee\ x+7-7\leq-2-7\\\\x\geq-5\ \vee\ x\leq-9\qquad CORRECT\ :)[/tex]
Answer: This is the correct answer bc RSM said so. Thank You So Much
Step-by-step explanation:
Evaluate following the correct order of operations.
17 - 5 + 8
16
20
30
4
PEMDAS has addition before subtraction there for you would do 5+8=13 then 17-13 which equals 4
BODMAS is the shortened way of telling the order
Bracket
Of
Division
Multiplication
Addition
Subtraction
Therefore addition should be done first
17 - 5+8=17-13=4
Someone please help me with math..i need help...
➷ 3) It would be option D as x is larger than 12 but not equal to it (hence the circle is not filled in)
4) It would be option C as x is smaller then -15 and can be equal to it (hence the circle is filled in)
✽➶ Hope This Helps You!
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3) D
x > 12 (x is bigger than 12)
4) C
[tex]x \leqslant - 15[/tex]
(x is equal to, or is smaller than -15)
A college graduate expects to earn a salary of 60000 during the first year after graduation and receive a 4% raise every year after that what is the total income he will have received after ten years?
The college graduate will have received a total income of $699,848.22 after ten years, starting with a salary of $60,000 and increasing by 4% each year.
Explanation:To find the total income the college graduate will have received after ten years, we need to calculate the salary for each year and sum them up. The first year salary is $60,000. After that, the salary increases by 4% each year. To calculate the salary for each subsequent year, multiply the previous year's salary by 1.04. Here are the calculations for each year:
Year 1: $60,000Year 2: $60,000 * 1.04 = $62,400Year 3: $62,400 * 1.04 = $64,896Year 4: $64,896 * 1.04 = $67,491.84Year 5: $67,491.84 * 1.04 = $70,190.95Year 6: $70,190.95 * 1.04 = $72,999.66Year 7: $72,999.66 * 1.04 = $75,923.45Year 8: $75,923.45 * 1.04 = $78,967.79Year 9: $78,967.79 * 1.04 = $82,138.35Year 10: $82,138.35 * 1.04 = $85,440.18Now, sum up the salaries for each year:
Total income after ten years = $60,000 + $62,400 + $64,896 + $67,491.84 + $70,190.95 + $72,999.66 + $75,923.45 + $78,967.79 + $82,138.35 + $85,440.18 = $699,848.22
Therefore, the college graduate will have received a total income of $699,848.22 after ten years.
The college graduate will receive a total income of approximately $720,360 over ten years.
1. To calculate the total income a college graduate will receive over ten years with an initial salary of $60,000 and a 4% annual raise, we can use the formula for the sum of a geometric series.
Initial salary (first year): $60,000Annual raise: 4%The salary for each year can be expressed as a geometric sequence where the first term (a) is $60,000 and the common ratio (r) is 1.04.We need to find the sum of the first ten terms of this geometric series.2. The formula for the sum of the first n terms of a geometric series is given by:
Sum = a(1 - [tex]r^{n}[/tex]) / (1 - r)
3. Substituting the given values:
a = 60,000, r = 1.04, n = 10
Sum = 60,000 * (1 - [tex]1.04^{10}[/tex]) / (1 - 1.04)
Sum = 60,000 * (1 - 1.48024) / ( -0.04)
Sum = 60,000 * (-0.48024) / (-0.04)
Sum = 60,000 * 12.006
Sum ≈ 720,360
4. Total Income:
Thus, the total income received after ten years is approximately $720,360.
Please help with this |4x−1|=7 (x is NOT 2 and 1.5)
Answer:
see explanation
Step-by-step explanation:
The absolute value always returns a positive result, however the expression inside can be positive or negative, that is
4x - 1 = 7 OR 4x - 1 = - 7
4x - 1 = 7 ( add 1 to both sides )
4x = 8 ( divide both sides by 4 )
x = 2
OR
4x - 1 = - 7 ( add 1 to both sides )
4x = - 6 ( divide both sides by 4 )
x = [tex]\frac{-6}{4}[/tex] = - [tex]\frac{3}{2}[/tex] = - 1.5
Solutions are x = - 1.5 or x = 2
help solve pls ^-^
1.23 = x – 9.5
2.12 = k – 4.3
3.r – 20 = 32
4.d – 10 = 25
5.n – (-8) = -18
6.c – (-2.6) = -14.9
Step-by-step explanation:
[tex]1.\ x-9.5=1.23\qquad\text{add 9.5 to both sides}\\\\\boxed{x=10.73}\\\\2.\ k-4.3=12\qquad\text{add 4.3 to both sides}\\\\\boxed{k=16.3}\\\\3.\ r-20=32\qquad\text{add 20 to both sides}\\\\\boxed{r=52}\\\\4.\ d-10=25\qquad\text{add 10 to both sides}\\\\\boxed{d=35}\\\\5.\ n-(-8)=-18\\\\n+8=-18\qquad\text{subtract 8 from both sides}\\\\\boxed{n=26}\\\\6.\ c-(-2.6)=-14.9\\\\c+2.6=-14.9\qquad\text{subtract 2.6 from both sides}\\\\\boxed{c=-17.5}[/tex]
based on the graph below, how would you describe the curve?
Answer:
It's A.
Step-by-step explanation:
For every value of x there is one value of y - we can draw a vertical line through any value of x and it will pass through only one value of y.
Therefore it is a one-to-one function.
Answer:
Option A
Step-by-step explanation:
The curve given is an increasing curve cutting x axis once and y axis once.
Any vertical line cuts only once the curve. Hence this is a function only.
We find that for every y in the range there is only one x corresponding to that.
Hence this curve is not a many to one curve. It is not linear because it is not a straight line. It is a function.
Hence only correct option is
a) The curve is a one to one function.
The store sells 24 candy bars for $12.
Select the three unit rates that can be used to describe this sale.
(A.) $0.50 per candy bar
(B.) 2 candy bars per dollar
(C.) $6 per dozen
(D.) 10 candy bars per $5
Answer the answer is b 12 divided by 24 is 2
Step-by-step explanation:
Answer:
(A.) $0.50 per candy bar
(B.) 2 candy bars per dollar
(C.) $6 per dozen
Step-by-step explanation:
The store sells 24 candy bars for $12 . The three unit rate that can be used to describe this sale are
Let us confirm for option A
24 candy bars sale for $12
1 candy bar will sale for ?
cross multiply
12/24 = 1/2 = $0.5
A is right and it is a unit rate
Let us confirm for option B
24 candy bars sale for $12
2 candy bars will sale ?
(2 × 12)/24 = 24/24 = $1
B is right and it is a unit rate
Let us confirm for option C
Note that a dozen is 12 bars
24 candy bars sale for $12
12 candy bars will sale ?
(12 × 12)/24 = 144/24 = $6
C is right and it is a unit rate
Let us confirm for option D
24 candy bars sale for $12
10 candy bars sale for ?
(10 × 12) /24 = 120/24 = $5
Option d is wrong it is not a unit rate. The unit rate here should be 2 candy bar per dollar.
the interest earned on an account varies directly with the balance in the account. if an account with a balance of $200 earns $12.5 in interest, find the amount of interest earned on an account with a balance of 500
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \stackrel{\textit{\underline{I}nterest varies with \underline{b}alance}}{I=kb}\qquad \qquad \textit{we know that } \begin{cases} b=200\\ I=12.5 \end{cases} \\\\\\ 12.5=k200 \implies \cfrac{12.5}{200}=k\implies \cfrac{~~\frac{125}{10}~~}{\frac{200}{1}}=k\implies \cfrac{125}{10}\cdot \cfrac{1}{200}=k \\\\\\ \cfrac{1}{16}=k \qquad \qquad \textit{therefore}\qquad \boxed{I=\cfrac{1}{16}b} \\\\\\ \textit{when b = 500, what is \underline{I}?}\qquad I=\cfrac{1}{16}(500)\implies I=\cfrac{125}{4}\implies I=31.25[/tex]
(3x3 - 2x2 + 4) - (2x2 + 14) = A) 3x3 - 10 B) 3x3 + 10 C) 3x3 - 4x2 - 10 D) 3x3 - 2x2 + 18
I think it’s C. But I’m not A 100 sure
Answer:
The Answer Would be (C. 3x3 - 4x2 - 10)
Step-by-step explanation:
Like terms are those terms which have same variable to the same power.
Find the difference of the following:
Remove the parenthesis we get;
Combine like terms;
Therefore, the difference of is,
How do you find slope?
Answer:
rise/run
Example:
say the lines is going 3 up and 4 to either side, the slope would be 3/4 :)
Answer:
Step-by-step explanation:
Step One: Identify two points on the line.
Step Two: Select one to be (x1, y1) and the other to be (x2, y2).
Step Three: Use the slope equation to calculate slope.
Let's say that points (15, 8) and (10, 7) are on a straight line. What is the slope of this line?
Step One: Identify two points on the line.
In this example we are given two points, (15, 8) and (10, 7), on a straight line.
Step Two: Select one to be (x1, y1) and the other to be (x2, y2).
It doesn't matter which we choose, so let's take (15, 8) to be (x2, y2). Let's take the point (10, 7) to be the point (x1, y1).
Step Three: Use the equation to calculate slope.
Once we've completed step 2, we are ready to calculate the slope using the equation for a slope.
We said that it really doesn't matter which point we choose as (x1, y1) and the which to be (x2, y2). Let's show that this is true. Take the same two points (15, 8) and (10, 7), but this time we will calculate the slope using (15, 8) as (x1, y1) and (10, 7) as the point (x2, y2). Then substitute these into the equation for slope.
Subtract (x+8)-(-3x-5)
[tex]\bold{Hey\ there!}\\ \\\bold{(x+8)-(-3x-5)} \\ \bold{Distribute\downarrow} \\ \bold{x(-3x)=-3x^2} \\ \bold{x(-5)=5x} \\ \bold{8(-3x)=-24x} \\ \bold{8(-5)=-40} \\ \\ \bold{We\ get:x+8+3x+5} \\ \bold{Combine\ the\ like\ terms\downarrow} \\ \bullet \ \bold{x \& 3x} \\ \bullet \ \bold{8\&5} \\ \\ \bold{Substitute\ the\ x\ by \ itself\ is\ 1}[/tex]
[tex]\bold{1x+3x=4x} \\ \bold{8+5=13} \\ \\ \\ \boxed{\boxed{\bold{Answer:4x+13}}}\checkmark \\ \\ \bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy \ your\ day!} \\ \\ \\ \\ \frak{LoveYourselfFirst:)}[/tex]
Mr. and Mrs. Jones have a patio that they want to rearrange. They want to put flower pots in the largest corner of their patio, but they do not know which corner of their patio has the largest angle. Mr. and Mrs. Jones only have the measurements of the sides of the patio area. The diagram is a sketch Mrs. Jones drew of the patio. Find which corner of the patio has the largest angle.
A.
corner G
B.
corner H
C.
corner I
D.
corner F
Answer:
it is b. corner H according to my test results
Step-by-step explanation:
explain what opposites are and give examples of real world situations
Answer:
Opposites in the numbers world refer to numbers that have the same absolute value, but one is negative, while the other is positive.
For a real world example, consider if you have your friend 5 dollars. The amount you have in the transaction is the opposite of the amount he has in the transaction.
The opposite of a number X is that number that when added to X produces zero. The opposite of X is denoted with −X.
The opposite of a number has the same absolute value as the number but an opposite sign. For example, the opposite of 1 is equal to −1 because 1 + (−1) = 0.
The opposite of zero is zero. This is the only number whose opposite is equal to itself. So zero is the neutral element with regard to addition.
In turn, the opposite of a complex number corresponds to a rotation of 180°.
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If DC = 12 and AT = 10, then B _____ R. Choose the relationship symbol to make a true statement. < = >
Answer:
>
Step-by-step explanation:
12 s bigger thn 10.
Answer:
>
Step-by-step explanation:
What is the value of x?
Answer:
x = 7
Step-by-step explanation:
Similar
The two triangles
1) the one making up the peak of the large triangle
2)the large triangle
are similar. That is because the 2 bases are parallel and corresponding angles are equal. The third angle at the peak is common. So by AAA they are similar.
Proportion
Therefore the sides are in proportion.
5/40 = 3/(2x + 10)
Solution
Cross multiply
5*(2x + 10) = 40*3
Remove the brackets on the left. Combine the right.
10x + 50 = 120
Subtract 50 from both sides
10x + 50 - 50 = 120 - 50
10x = 70
Divide by 10
10x/10 = 70/10
x = 7
A jar contains 4 red marbles, 4 green marbles, and 5 blue marbles.
If we choose a marble, then another marble without putting the first one back in the jar, what is the probability that the first marble will be blue and the second will be green?
Answer:
20/156 or 5/39
Step-by-step explanation:
the first part of the equation will be:
5/13 (5 is how many blue and 13 is altogether)
the next part of this equation is the green marble. Because we didn't put the blue marble back, the next part of the equation will be:
4/12 (4 is how many green and 12 is altogether now that one blue was taken out)
and from there, you multiply 5/13 with 4/12, with will give you 20/156, or 5/39 if you simplify.
jack rolled a die 3 times and got 2 each time. What is the probability he will get 2 on the next roll?
if the die has six sides, the probability that he will roll 2 again is 1/6 since there’s only one 2 out of the six sides
The probability jack will get 2 on the next roll is 1/6.
What is probability?It is the ratio that determines how likely a certain event can occur within a set of possible events.
The probability that jack might roll a 2 can be shown below:The given dice has 6 sides.
The number 2 occurs only on one side of a die.
Therefore, if he were to roll the dice one more time, the probability that he would get 2 can be given by 1/6.
Therefore, the probability that jack will get 2 on the next roll is 1/6.
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Mean And Median of 12,10,11,9,9,10,12,9,8,7,9,10
Answer:
The median is 9.5 and the mean is 9.6667
Step-by-step explanation:
what is the total cost, with 8% sales tax, of a $75 pair of shoes
Answer:
$81
Step-by-step explanation:
The total cost would be cost + cost(tax), or cost(1 + tax).
So here, it would be 75(1 + 0.08).
That is equal to $81.
Given a square with side lengths represented by the function f(x)=2x+5, find the square.
A. 2x^2+10x+25
B. 4x^2+20x+25
C. 4x^2+20x+10
D. 2x^2+5x+10
Answer:
[tex]B. 4x^2+20x+25[/tex]
Step-by-step explanation:
The length of the side:
[tex]2x+5[/tex]
In a square all sides have the same length.
And the area of a square is given by the formula:
[tex]Area=(length)^2[/tex]
so, substituting that the length is [tex]2x+5[/tex]
[tex]Area=(2x+5)^2[/tex]
and we solve this squared binomial with the formula:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
in this case [tex]a=2x[/tex] and [tex]b=5[/tex]
thus, we get:
[tex]Area= (2x)^2+2(2x)(5)+(5)^2[/tex]
and solving:
[tex]Area=4x^2+20x+25[/tex]
which is option B.
Find the length of the line segment that joins the points (2,5) and (9,8)
Answer:
=5sqrt(2)
Step-by-step explanation:
The length of a line segment is given by
d = sqrt( (x2-x1)^2 + (y2-y1)^2 )
= sqrt( (9-2)^2 + (8-5) ^2)
= sqrt(7^2 + 3^2)
= sqrt(49+9)
= sqrt(50)
=sqrt(2*25)
We know that sqrt(ab) = sqrt(a)sqrt(b)
sqrt(25)sqrt(2)
=5sqrt(2)
The answer is 5sqrt of 2
You have 36 apples to share with your friends. If each friend gets exactly 2 apples, which equation could you use to solve for the number of friends, nn?
A)n/2=36
B) 2n=36
C) 36n=2
D)36×2=n
Solution :
Since there are 36 apples
There are n friends
Since each friend gets 2 apples.
So, n friends get apples= 2n
Answer:
B) 2n = 36
Step-by-step explanation:
Each friend receives 2 apples.
n number of friends receive 2n apples.
2n is the total number of apples, and it equals 36.
The equation is
2n = 36
Answer: B) 2n = 36
An airplane covers 94 miles in 1/6 of n hour. The plane can cover how many miles in 6 hours
Answer:
3,384 miles
Step-by-step explanation:
If can cover 94 miles in 1/6 of an hour. (1/6 hour)*6 = 1 hour, so multiply 94 by 6 to see how far the plane will travel in 1 hour.
94(6) = 564 miles in one hour
Multiply that by 6 to see how far the plane travels in 6 hours
564(6) = 3,384 miles
The airplane can cover 3,384 miles in 6 hours.
What is the formula for finding distance when the speed and time are given?The formula for finding the distance covered is:
Distance = speed*time
We can find the distance that the plane can cover as follows:It is given that it can cover 94 miles in 1/6 hours.
This should be converted to per hour.
For this, multiply the distance by 6.
94 miles * 6 = 564 miles
The speed of the plane is 564 miles per hour.
The distance that the plane covers in 6 hours = 564 miles per hour * 6 hours
= 3,384 miles.
Therefore, we have found that the plane can cover 3,384 miles in 6 hours.
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What are you required to do when you want to use a discount membership to save money
use the discount?
this is really confusing
you are required to apply to the terms and conditions of the discount stuff.
What are the various methods of solving systems of equations and how do we find the solutions(s)?
Answer:
1-ELIMINATION.
2- SUBSTITUTION.
3- GRAPHING.
Step-by-step explanation:
Methods:
1- Elimination:
- Line up the variables.
- To cancel out one of the variables, you need to make that the coefficient of that variable opposite. For example:
[tex]\left \{ {{3x+y=1} \atop {-3x+4y=3}} \right.[/tex]
As you can see, the coefficient of x in the first eqation is 3 and -3 in the second option.
- Add the equations.
- Solve for the the variable that is still present.
- Substitute the value of the variable obtained into one of the original equations.
- Solve for the other variable.
2- Substitution:
- Solve for one of the variables from any of the equations of the system.
- Substitute into the other equation for that variable.
- Solve for the other varible to find its value.
- Substitute the value obtained into any of the original equations and solve for the other variable.
3- Graphing:
- Rewrite the equations as equtions of the line slope intercept form ([tex]y=mx+b[/tex], where m is the slope nd b the y-intercept).
- Graph each line.
- Then:
If there ir an intersection point of the two lines, then that point is the solution to the system
If the lines are the same, there are infinitely many solutions.
If the lines are parallel, then there is no solution
A. 38
B. 62
C.100
D.190
Answer:
The answer is 190.
Step-by-step explanation:\
500/100 = 5
5*38 = 190
Hope this helps. Please mark as brainliest.
Answer:
190
Step-by-step explanation:
38% of the plants in the garden are trees. 38% of a total of 500 plants comes out to 190 trees.
rewrite these in increasing order of length: 537 km, 790 dm, 41 cm, 8 mm, 788 m
Answer: [tex]8mm,\ 41cm,\ 790dm,\ 788m,\ 537km[/tex]
Step-by-step explanation:
To solve this problem you must:
1. Write the lenghts given in the problem in the same units.
2. Let's convert all the units to meters. Then:
537 km to m:
[tex](537km)(\frac{1,000}{1km})= 537,000m[/tex]
790 dm to m:
[tex](790dm)(\frac{1m}{10dm})=79m[/tex]
41 cm to m:
[tex](41cm)(\frac{1m}{100cm})=0.41m[/tex]
8 mm to m:
[tex](8mm)(\frac{1m}{1,000mm})=8*10^{-3}m[/tex]
Now you rewrite them in increasing order:
[tex]8mm,\ 41cm,\ 790dm,\ 788m,\ 537km[/tex]
Answer:
The correct order is,
8mm, 41 cm, 790 dm, 788m, 537 km
Step-by-step explanation:
It is given some measures of lengths
537 km, 790 dm, 41 cm, 8 mm, 788 m
Convert this into single unit
we can convert this into Meter
1). 537 km = 537000 m
2). 790 dm = 79 m
3). 41 cm = 0.41 m
4). 8 mm = 0.008 m
5). 788 m = 788 m
From this we get the correct order,
8mm, 41 cm, 790 dm, 788m, 537 km
What is greater 12 gallons or 50 quarts
50 quarts is greater than 12 gallons.
Given that, 12 gallons and 50 quarts.
Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
We know that, 1 quarts = 0.25 gallons
Here, 50 quarts = 50×0.25
= 12.5 gallons
So, 12.5 gallons > 12 gallons
Therefore, 50 quarts is greater than 12 gallons.
To learn more about the metric conversion visit:
brainly.com/question/21244256.
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