Answer:
7.5 Miles.
Step-by-step explanation:
3 + 4.5 = 7.5 Miles.
∆ABC has side lengths of 10 units, 20 units, and 24 units. ∆XYZ is similar to ∆ABC, and the length of its longest side is 60 units. The perimeter of ∆XYZ is units. If the height of ∆ABC, with respect to its longest side being the base, is 8 units, the area of ∆XYZ is square units.
Answer: Perimeter = 135 units Area = 1200 Square units
Step-by-step explanation: I think you want the perimeter and area of XYZ so that's what I will answer for.
First, we are given that ABC and XYZ are proportional and that their longest sides are 24 units and 60 units respectively.
Using this, we can say XYZ = ABC * 5/2 (60/24 = 5/2)
Therefore, the other two sides of XYZ are 50 and 25.
We can get the perimeter using 60 + 50 + 25, that equals 135 units
Next, since the height of ABC was 8 units with 24 units being its base, it's likely safe to say the height = 1/3 base
We will apply with to triangle XYZ, height = 1/3 * 60 = 20
20 units * 60 units = 1200 square units
The perimeter and area of the ΔXYZ are 135 units and 600 sq. units. Where similar triangles are related by a scale factor.
How to find the scale factor for similar triangles?The ratio of their respective sides of two similar triangles gives the scale factor. I.e.,
Consider ΔABC and ΔDEF are two similar triangles
Then its scale factor = DE/AB = EF/BC = DF/AC
The scale factor is also defined as follows:
(Scale factor)² = (Area of the triangle DEF)/(Area of the triangle ABC)
or
Scale factor = (perimeter of ΔDEF)/(perimeter of ΔABC)
Finding the scale factor:Given that the sides of the triangle ABC are 10 units, 20 units, and 24 units. The longest side is 24 units.
The triangle XYZ has the longest side of length 60 units.
Since ΔABC ~ ΔXYZ
So, the ratio of their longest sides gives the scale factor. I.e.,
Scale factor = 60/24 = 2.5
Calculating the perimeter of the ΔXYZ:The perimeter of the ΔXYZ is calculated by
Scale factor = (perimeter of the ΔXYZ)/(perimeter of the ΔABC)
⇒ 2.5 = (perimeter of the ΔXYZ)/(10 + 20 + 24)
⇒ perimeter of the ΔXYZ = 2.5 × 54
∴ the perimeter of the ΔXYZ = 135 units
Calculating the area of the ΔXYZ:The area of the ΔXYZ is calculated by
(Scale factor)² = (area of the ΔXYZ)/(area of the ΔABC)
So, the area of the ΔABC, whose height h = 8 units and base b = 24 units is
Area of the ΔABC = 1/2 × b × h
= 1/2 × 24 × 8
= 96 sq. units
Thus,
(Scale factor)² = (area of the ΔXYZ)/(area of the ΔABC)
⇒ (2.5)² = (area of the ΔXYZ)/(96)
⇒ area of the ΔXYZ = (2.5)² × 96
∴ area of the ΔXYZ = 600 sq units
Thus, the perimeter and area of the ΔXYZ are 135 units and 600 sq. units.
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what best describes the sequence 256,128,64,32
Answer:
It's a geometric sequence.
Step-by-step explanation:
Note that the next term = the previous term multiplied by 0.5.
This is a geometric sequence with first term 256 and common ratio 0.5.
The nth term = 256(0.5)^(n-1).
Your parents allow you to borrow a car to get to your part-time job, but you have to pay for a tank of gas each month. Gasoline costs $2.76/gallon and the tank takes 15 gallons. You have 2 coworkers who are each willing to pay for a quarter of a tank each month to carpool with you to work. How much do you save each month? $20.70 $16.46 $18.55 $15.91
By having two coworkers pay for a quarter of the tank each, the student saves $20.70 per month on gasoline.
The question asks us to calculate how much a student would save on gasoline for a month by having two coworkers pay for a quarter of a tank each. With gasoline costing $2.76\/gallon and the tank capacity of 15 gallons, the cost of a full tank is 15 gallons x $2.76\/gallon = $41.40.
Each coworker would pay for a quarter of that amount, which is 0.25 x $41.40 = $10.35. Since there are two coworkers, the total contribution would be 2 x $10.35 = $20.70. Therefore, the student saves $20.70.
If 3p-q=6 and 2p+3q=4 find q
Answer:
q=-6 and q=4/3 or 1.33Step-by-step explanation:3p-q=63(0)-q=6(Substitute 0 for p)-q=6(Divide by -1)q=-62p+3q=42(0)+3q=4(Substitute 0 for p)3q=4(Divide by 3)q=4/3 or 1.33Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Name Score
Julia 650
Andrew 550
Jason 380
Cathy 720
Jessica 710
Robert 550
The table gives the scores of 6 students from a class of 25 in a competitive exam. The point estimate of the mean score for the students is
Answer:
The mean point estimate is 593
Step-by-step explanation:
650 + 550 + 380 + 720 + 710 + 550 = 3560
3560/6 = 593.33
Answer:
593.3
Step-by-step explanation: plato family
Which of the following equations represents an ellipse with a minor axis of length 10 and foci located at (3,6) and (7,6)?
Answer:
It is choice A.
Step-by-step explanation:
The general form is (x - h)^2 / a^2 + (x - k)^2/b^2 = 1 where (h, k) is the center, 2a = major axis and 2b = minor axis.
The ellipse in the question has a^2 > b^2 so the major axis is parallel to the x axis.
The minor axis which is parallel to the y-axis is of length 10 so b^2 = (1/2 * 10)^2
= 25 so we can eliminate C.
The center of the ellipse = the midpoint of a line joining the focii so it is:
( 3+ 7)/2, 6)
= (5,6).
As (h, k) is the center we have h = 5 and k = 6.
So it is choice A.
The equation of the eclipse will be [tex]\frac{(x-5)^2}{29} +\frac{(y-6)^2}{25} =1[/tex] i.e. option A.
What is equation of the ellipse?The standard equation of the ellipse is [tex]\frac{(x-h)^2}{a^2} +\frac{(y-k)^2}{b^2} =1[/tex].
Here,
(h, k) is the center, and 2a and 2b are major and minor axis.
We have,
Length of minor axis = 10
i.e. 2b = 10
And, b = 5
And,
Foci (c) located at (3,6) and (7,6),
i.e. Major axis is parallel to x-axis. [Because y is constant]
And,
The foci (c) always lie on the major axis.
And,
c² = a² - b²
Now,
The center of an ellipse is the midpoint of both the major and minor axes, i.e. the midpoint of a line joining the foci (c),
i.e. Center [tex]=( \frac{x_1 + x_2 }{2}, \frac{y_1 + y_2}{2}) =( \frac{3+7}{2}, \frac{6+6}{2}) =(5, 6)[/tex]
Now,
Foci (c) = 5 - 3 = 2
So,
c² = a² - b²
i.e.
2² = a² - 5²
4 = a² - 25
⇒ a² = 29
And, b² = 5² = 25
So,
h = 5 and k = 6
Now,
Putting the values in the standard form of equation of the ellipse,
i.e.
[tex]\frac{(x-h)^2}{a^2} +\frac{(y-k)^2}{b^2} =1[/tex]
i.e.
[tex]\frac{(x-5)^2}{29} +\frac{(y-6)^2}{25} =1[/tex]
So, this is the equation of the eclipse i.e. option A.
Hence, we can say that the equation of the eclipse will be [tex]\frac{(x-5)^2}{29} +\frac{(y-6)^2}{25} =1[/tex] i.e. option A.
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The basic formula to calculate a student's GPA is the
Answer:
The basic formula to calculate a student's GPA is the addition of all grade points in completed courses divided by the number of classes completed.
A student's GPA is calculated by adding up the numeric equivalent of each grade and dividing by the total number of classes. For example, using a system where A = 4, B = 3, C = 2, D = 1 and F = 0, a student with one A and one B would have a GPA of (4+3)/2 = 3.5.
Explanation:The basic formula to calculate a student's GPA (grade point average) typically involves totalling the numeric representation of each individual grade, and then dividing that total by the total number of classes taken.
For instance, if we use a regular American system where A = 4, B = 3, C = 2, D = 1 and F = 0, and a student has one A and one B, their GPA would be the sum of these points (4 + 3 = 7) divided by the number of classes (2) which equals 3.5. Therefore, this student's GPA is 3.5.
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The polynomial 6x2 + x − 15 has a factor of 2x − 3. What is the other factor?
3x − 5
3x + 5
4x − 5
4x + 5
Answer:
[tex](3x+5)[/tex]
Step-by-step explanation:
The given polynomial expression is:[tex]6x^2+x-15[/tex]
We compare to [tex]ax^2+bx+c[/tex] and have a=6,b=1,c=-15
The product [tex]ac=6\times -15=-90[/tex]
Two factors of -90 that sums to 1 are -9 and 10
We split the middle term to get:
[tex]6x^2+10x-9x-15[/tex]
[tex]2x(3x+5)-3(3x+5)[/tex]
[tex](3x+5)(2x-3)[/tex]
Therefore the other factor is:
[tex](3x+5)[/tex]
Answer: B
Step-by-step explanation:
The formula to determine energy is E=1/2mv2? What is the formula solved for v?
Answer:
v = √( [tex]\frac{2E}{m}[/tex] )
Step-by-step explanation:
E=1/2mv²
v² = ( [tex]\frac{2E}{m}[/tex] )
v = √( [tex]\frac{2E}{m}[/tex] )
Answer:
[tex]v=\sqrt{\frac{2E}{m}}[/tex]
Step-by-step explanation:
[tex]E= \frac{1}{2} mv^2[/tex]
Solve the equation for v
To remove fraction , multiply both sides by 2
[tex]2 \cdot E= \frac{1}{2} mv^2 \cdot 2[/tex]
[tex]2E=mv^2[/tex]
Divide both sides by 'm' to isolate v^2
[tex] \frac{2E}{m}=v^2[/tex]
Now to remove square from V, we take square root on both sides
[tex]\sqrt{\frac{2E}{m}} =v[/tex]
[tex]v=\sqrt{\frac{2E}{m}}[/tex]
If f(x) = 4x2 and g(x) = x+1, find (*•g)(x).
Answer:
(f · g)(x) = 4x³ + 4x²Step-by-step explanation:
(f · g)(x) = f(x) · g(x)
We have f(x) = 4x² and g(x) = x + 1. Substitute:
(f · g)(x) = (4x²)(x + 1) use the distributive property
(f · g)(x) = (4x²)(x) + (4x²)(1)
(f · g)(x) = 4x³ + 4x²
the percent of working students increased 21.7% to 8.9%, what was the percent prior to increase
Answer:
Approximately 7.3%.
Step-by-step explanation:
What is percentage increase?
[tex]\displaystyle \text{Percentage Increase} = \frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}} \times 100\%[/tex].
For this question:
[tex]\text{Percentage Increase} = 21.7\%[/tex],[tex]\text{Final Value} = 8.9\% = 0.089[/tex], and[tex]\text{Initial Value}[/tex] needs to be found.Let [tex]\text{Initial Value} = x[/tex].
[tex]\displaystyle \frac{0.089 - x}{x} = 0.217[/tex].
Assume that [tex]x \ne 0[/tex]. Multiply both sides of the equation by [tex]x[/tex]:
[tex]0.089 - x = 0.217x[/tex].
Add [tex]x[/tex] to both sides of the equation:
[tex]0.089 = (1 + 0.217)x[/tex].
[tex]\displaystyle x = \frac{0.089}{1 + 0.217} = 0.0731 \approx 7.3\%[/tex].
In other words, the initial percentage is approximately 7.3%.
What is the slope of the line represented by the equation y=-3x+1?
When a line is represented in the slope intercept formula as in the question you must remember that it is always set up like so...
y = mx + b
m is the slope and b is the y-intercept of the line
Since in the equation y = -3x + 1 the m is -3 then the slope is -3
Hope this helped!
~Just a girl in love with Shawn Mendes
Lucy can assemble a computer by herself in 35 minutes. Manny does the same job in 50 minutes. How long will it take them to assemble a computer working together?
Answer:
Step-by-step explanation:
I think its 15 I just subtracted the two numbers
Answer: about 20.6 minutes
Step-by-step explanation:
Given : Lucy can assemble a computer by herself in 35 minutes.
Manny does the same job in 50 minutes.
Let t be the time taken by both of them working together.
Then, we have
[tex]\dfrac{1}{t}=\dfrac{1}{35}+\dfrac{1}{50}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{35+50}{35\times50}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{85}{1750}\\\\\Rightarrow\ t=\dfrac{1750}{85}=20.5882352941\approx20.6[/tex]
Hence, it will take approx 20.6 minutes to assemble a computer working together.
Factor the polynomial:
x^2 + 5x − 14 =
x^2 − 10x + 16 =
Answer:
the first one is: (x-2)(x+7)
the second one is: (x-2)(x-8)
I had this question and got it right.
To factor the polynomial x^2 + 5x - 14, use the method of finding two numbers that multiply to give the constant term and add up to give the coefficient of x. For x^2 - 10x + 16, use the same method to find the two numbers.
Explanation:To factor the polynomial x^2 + 5x - 14, we look for two numbers that multiply to give the constant term (-14) and add up to give the coefficient of x (5). In this case, the numbers are 7 and -2. So we can rewrite the polynomial as (x + 7)(x - 2).
To factor the polynomial x^2 - 10x + 16, we look for two numbers that multiply to give the constant term (16) and add up to give the coefficient of x (-10). In this case, the numbers are -2 and -8. So we can rewrite the polynomial as (x - 2)(x - 8).
use the squared identities to simplify sin^2x cos^2x
Answer:
[tex]\frac{1-cos^2(2x)}{4}[/tex]
Step-by-step explanation:
We have the following expression
[tex]sin^2x *cos^2x[/tex]
Whe know that:
[tex]sin^2(x) = \frac{1-cos(2x)}{2}\\\\cos^2(x)=\frac{1+cos(2x)}{2}[/tex]
Now replace these equations in the main expression and simplify
[tex](\frac{1-cos(2x)}{2})*(\frac{1+cos(2x)}{2})[/tex]
[tex](\frac{(1-cos(2x))(1+cos(2x))}{4})[/tex]
Apply the following property
[tex](a + b) (a-b) = a ^ 2 -b ^ 2[/tex]
Then
[tex](\frac{(1-cos(2x))(1+cos(2x))}{4})=\frac{1^2-cos^2(2x)}{4}[/tex]
Finally:
[tex](\frac{(1-cos(2x))(1+cos(2x))}{4})=\frac{1-cos^2(2x)}{4}[/tex]
Eight friends ate 5/8 of a bag of chips what fraction of the bag did each person eat assuming that they each ate the same amount?
Given: 8 friends ate (5/8)TH fraction of a bag of chips.
And Each one ate the same fraction.
Then; The fraction of chips consumed by one person is (1/8)TH of (5/8)
i.e. =
[tex] \frac{1}{8} ( \frac{5}{8} ) \\ = \frac{5}{64} [/tex]
Hope it helps...
Regards;
Leukonov/Olegion.
Answer:
Option B. [tex]\frac{5}{64}[/tex] of the bag.
Step-by-step explanation:
Eight friends ate [tex]\frac{5}{8}[/tex] of a bag of chips in the same amount.
We have to find the quantity that each person ate the chips.
Each friend ate = [tex]\frac{5}{8}[/tex] ÷ 8
= [tex]\frac{5}{8}[/tex] × [tex]\frac{1}{8}[/tex]
= [tex]\frac{5}{64}[/tex]
Therefore, each friend ate [tex]\frac{5}{64}[/tex] of the bag of chips.
Option B is the answer.
Drag each tile to the correct box.
Find the y-intercept of each exponential function and order the functions from least to greatest y-intercept.
Answer:
The functions ordered from least to greatest y-intercept are
1) h(x) -----> y-intercept -1
2) g(x) ----> y-intercept 1
3) f(x) ----> y-intercept 2
Step-by-step explanation:
we know that
The y-intercept (or initial value) is the value of y when the value of x is equal to zero
Part 1) Find the y-intercept of g(x)
Remember that the initial value of the fuction is equal to the y-intercept
a=1 -----> is the initial value
therefore
The y-intercept of g(x) is 1
Part 2) Find the y-intercept of f(x)
Observing the table
For x=0
f(x)=2
therefore
The y-intercept of f(x) is 2
Part 3) Find the y-intercept of h(x)
Observing the graph
For x=0
h(x)=-1
therefore
The y-intercept of h(x) is -1
Answer:
1 3 2
Step-by-step explanation:
solve |2x-5|=4 pleasee
Answer:
x = 1/2 and x = 9/2
Step-by-step explanation:
To solve this equation: |2x-5|=4 we need two evaluate two cases:
|2x-5| = 2x-5 when x>5/2 ✅
|2x-5| = -2x+5 when x<5/2✅
Then, if x>5/2:
2x-5 = 4 ➡ x = 9/2
Then, if x>5/2:
-2x+5 = 4 ➡ x = 1/2
Then, the two solutions are: x = 1/2 and x = 9/2
Answer:
X= 1/2
Step-by-step explanation:
PLS HELP! WILL GIVE BRAINLIEST.
Answer:
Rotation of 90 degrees clockwise and then Dilation (scale factor) of 0.5
If triangle abc is similar to triangle mno how do I solve for value of missing side
ABC 1.2cm and 3.0cm
Mno 0.96 and x
Answer:
=2.4 cm
Step-by-step explanation:
In similar plane figures, the ratio of corresponding sides is a constant.
This constant is the linear scale factor.
In the provided example, 1.2cm corresponds to 0.96 while 3.0 corresponds to x
Thus, 1.2 cm/0.96 cm=3.0 cm/x
x=(3.0 cm×0.96 cm)/1.2 cm
=2.4 cm.
Answer:
1.44 cm
Step-by-step explanation:
n the diagram, what is mVSR?
Not enough information, please attach a photo next time.
Easy!!!
if f(x)=-9x-9 and g(x)=√x-9, find f(g)(10)
I have 8 other problems and everyone says this is really easy but I don't get it and I'm freaking out
Step-by-step explanation:
f(g(10))
This is called a composite function. It's when you plug one function into another.
First, find g(10):
g(x) = √(x-9)
g(10) = √(10-9)
g(10) = √1
g(10) = 1
Then plug that into f(x):
f(x) = -9x - 9
f(g(10)) = -9 g(10) - 9
f(g(10)) = -9 (1) - 9
f(g(10)) = -9 - 9
f(g(10)) = -18
What’s equivalent to z+(z+6)
Answer:
2z + 6
Step-by-step explanation:
Since nothing can be done with the brackets we can take those out. We would end up with
z + z + 6
As you can see we have two z's and we can add those together. This would give us our answer:
2z + 6
A circle is centered at the point (5, -4) and passes through the point (-3, 2).
The equation of this circle is (x + )2 + (y + )2 =
.
Reset
Answer:
(x-5)^2+(y+4)^2=100
Step-by-step explanation:
As we know the given points
Center = (5, -4)
and
Point on circle = (-3,2)
The distance between point on circle and center will give us the radius of circle
So,
The formula for distance is:
[tex]\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1})^{2}}\\Taking\ center\ as\ point\ 1\ and\ the\ other\ point\ as\ point\ 2\\d=\sqrt{(-3-5)^{2}+(2-(-4))^{2}}\\d=\sqrt{(-8)^{2}+(2+4)^{2}}\\d=\sqrt{(-8)^{2}+(6)^{2}}\\\\d=\sqrt{64+36}\\d=\sqrt{100} \\ d=10\\So\ the\ radius\ is\ 10[/tex]
The standard form of equation of circle is:
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where h and k are the coordinates of the center. So putting in the value:
[tex](x-5)^{2}+(y-(-4))^{2}=(10)^{2}\\(x-5)^{2}+(y+4)^{2}=100[/tex]
17. A grab bag contains 3 football cards and 7 basketball cards. An experiment consists of taking one card out
of the bag. replacing it, and then selecting another card. What is the probability of selecting a football
card and then a basketball card? Express your answer as a decimal.
a 0.21
b 0.23
c 0.49
d 0.09
The probability of selecting a football card and then a basketball card from the grab bag is (a) 0.21.
We employ the idea of independent events to calculate probability. Given that there are 3 football cards among the total of 10 cards, the chance of choosing one during the initial draw is [tex]\frac{3}{10}[/tex]. The likelihood of choosing a basketball card on the second draw is [tex]\frac{7}{10}[/tex] since the card is changed before the second draw. When these probabilities are added together, the result is [tex]\frac{3}{10}* \frac{7}{10} = \frac{21}{100}[/tex] = 0.21. As a result, option (a) corresponds to the right response, which is 0.21.
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wich expression is equivalent 1/4-3/4x
Answer:1/4(1-3x)
Step-by-step explanation:
If y varies inversely as x and y = 18 when x = 4, what is y when x = 242
Answer:
y = [tex]\frac{36}{121}[/tex]
Step-by-step explanation:
Given that y varies inversely as x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
To find k use the condition y = 18 when x = 4
k = yx = 18 × 4 = 72, so
y = [tex]\frac{72}{x}[/tex] ← equation of variation
When x = 242, then
y = [tex]\frac{72}{242}[/tex] = [tex]\frac{36}{121}[/tex]
At a market Denine buys a bag of 6 mangoes for 15 pesos. What is the unit
price for 1 mango?
Answer:
2.5 pesos/mango
Step-by-step explanation:
You are looking for the price per mango. "Per" means to divide.
Price per mango means to divide the price of all the mangoes by the number of mangoes.
(15 pesos)/(6 mangoes) = (5 pesos)/(2 mangoes) = 2.5 pesos/mango
Colleen plans to print x pictures from her camera at a drug store. The expression $0.2x represents the cost of developing the pictures if she is not a member of the store’s photography club. If she is a member, then the total cost is given by $0.15x + $10. How much more will Colleen pay by not being a member if she develops 350 pictures
Answer:
$7.5
Step-by-step explanation:
If Colleen develops 350 pictures (x):
1. If member, cost is:
[tex]0.15x + 10\\=0.15(350)+10\\=62.5[/tex]
2. If not a member, cost is:
[tex]0.2x\\=0.2(350)\\=70[/tex]
Hence, Colleen pays 70 - 62.5 = 7.5 more by not being a member.
Answer:
$7.5.
Step-by-step explanation:
We have been given that Colleen plans to print x pictures from her camera at a drug store.
The difference of cost for non-member and member would be difference of both expressions as:
[tex]0.2x-(0.15x+10)=0.05x-10[/tex]
To find the difference for developing 350 pictures without being member and non-member, we will substitute [tex]x=350[/tex] in expression [tex]0.05x-10[/tex]:
[tex]0.05(350)-10=17.5-10=7.5[/tex]
Therefore, Colleen will pay $7.5, while not being a member and developing 350 pictures.
What is the 5th term in the binomial expansion
(a+b)^7
Answer:
5th term is 35a^4b^3
Step-by-step explanation:
We need to find the 5th term in binomial expansion (a+b)^7
The binomial theorem is:
[tex](x+y)^n = \sum_{n=0}^{k} {n\choose k}x^ky^{n-k}[/tex]
We are given
x=a,
y =b
n=7
and k= 4 since we have to find 5th term but k starts from zero
putting the values
[tex]={7\choose 4}a^4b^{7-4}\\={7\choose 4}a^4b^{3}\\=\frac{7!}{4!(7-4)!}a^4b^3\\=35a^4b^3[/tex]
So, 5th term is 35a^4b^3
Answer:
On Apex
Step-by-step explanation:
35a^4 b^3