Answers
8
Explanation
as the triangles are similar we can set a proportion
Step 1
Let
[tex]\text{ratio}=\frac{\text{longest side}}{\text{smallest side}}[/tex]so
a) for triangle FIM
[tex]\begin{gathered} \text{ratio}=\frac{\text{longest side}}{\text{middle side}} \\ ratio_1=\frac{FM}{FI}=\frac{6}{4}=\frac{3}{2} \\ ratio_1=\frac{3}{2} \end{gathered}[/tex]b) for triangle LAK
[tex]\begin{gathered} \text{ratio}=\frac{\text{longest side}}{\text{smallest side}} \\ ratio_2=\frac{LK}{LA}=\frac{12}{LA} \\ ratio_2=\frac{12}{LA} \end{gathered}[/tex]as the tringles are similar, the ratios are similar
hence
[tex]\begin{gathered} \text{ratio}_1=ratio_2 \\ \frac{3}{2}=\frac{12}{LA} \end{gathered}[/tex]Step 2
now, solve for LA
[tex]\begin{gathered} \frac{3}{2}=\frac{12}{LA} \\ \text{cross multiply } \\ 3\cdot LA=12\cdot2 \\ 3LA=24 \\ \text{divide both sides by 3} \\ \frac{3LA}{3}=\frac{24}{3} \\ LA=8 \end{gathered}[/tex]therefore, the answer i
8
I hope this helps you
Related Questions
you invest 1,000 in an account that pays simple interest of 3% for 10 years. what is the amount of money you'll have at the end of the 10 years?
Answers
Given data:
The given principal is P=1,000.
The given rate of interest is r=3%.
The given time is t=10 years.
The expression for the final amount after 10 years is,
[tex]A=P+\frac{P\times r\times t}{100}[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} A=1,000+\frac{1,000\times3\times10}{100} \\ =1,300 \end{gathered}[/tex]Thus, the final amount after 10 years is 1,300.
You invest $1000 in an account that has an annual interest rate of 4%, compounded quarterly for 12 years. How much money will you have after the 12 years? $3138.43 O $3237.27 O $1601.03 O $1612.23
Answers
The compound interest formula is given by
[tex]A=P(1+\frac{r}{n})^{n\times t}[/tex]where A is the resulting amount after t years, P is the present value (or principal amount) , r is the annual interest rate and n is the number of compounding periods per year.
From the given information, we have that
[tex]\begin{gathered} P=1000 \\ r=0.04 \\ n=4\text{ (quaterly=4 times per year)} \\ t=12\text{ years} \end{gathered}[/tex]By substituting these values into the formula, we have
[tex]A=1000(1+\frac{0.04}{4})^{4\times12}[/tex]which gives
[tex]\begin{gathered} A=1000(1.01)^{48} \\ A=1000(1.6122) \\ A=1612.226 \end{gathered}[/tex]Therefore, by rounding to the nearest thousandth, the answer is $1612.23, which corresponds to the last option.
The water level in a lake was monitored and was noted to have changed −213 inches in one year. The next year it was noted to have changed −116 inches. What was the total change in the water level over the two years? Enter your answer as a simplified mixed number by filling in the boxes.
Answers
are those fractions??
Out of a group of 120 students, 28 said they ski and 52 said they snowboard. Sixteen of thestudents said they do both. If a student is chosen at random, find the probability that theysnowboard given they ski (Hint: Draw a Venn Diagram).
Answers
Given:
The total number of students = 128 students.
The number of students who play ski, N(S)= 28 students.
The number of students who play snowboard, N(B)= 52 students.
The number of students who play both ski and snowboard, N(S and B)= 16 students.
[tex]N(S\cap B)=16[/tex]Required:
We need to find the probability that they snowboard given they ski.
Explanation:
The ven diagram.
Consider the Conditional probability formula.
[tex]P(\frac{S}{B})=\frac{N(S\cap B)}{N(B)}[/tex][tex]Substitue\text{ }N(S\cap B)=16\text{ and N\lparen B\rparen=52 in the formula.}[/tex][tex]P(\frac{S}{B})=\frac{16}{52}[/tex][tex]P(\frac{S}{B})=\frac{4}{13}[/tex]Final answer:
The probability that they snowboard given they ski is 4/13.
Multiply. Simplify, you may leave the numerator and denominator in answer in factored form.
Answers
Step 1
Given;
Step 2
Multiply
[tex]\frac{x^3+1}{x^3-x^2+x}\times\frac{3x}{-15x-15}=\frac{3x^4+3x}{-15x^4-15x}[/tex]Simplify
[tex]\frac{3x\left(x+1\right)\left(x^2-x+1\right)}{-15x\left(x+1\right)\left(x^2-x+1\right)}=-\frac{1}{5}[/tex]Answer;
[tex][/tex]Will someone please help me with this? I tried getting help but it didn’t work
Answers
Pattern A Step 0 Step 1 pattern A or pattern B) shows a quadratic relationship?Step 2 Step 3 8 Pattern B Step 0 Step 1 Step 2 Step 3 2 a. How many dots will there be in Step 4 of each pattern? Pattern A = 16 dots Pattern B = 16 dots b. Which pattern (
Answers
Looking at pattern A, the rate at which the number of dots in increasing is linear. The common difference between the number of dots in consecutive steps is 2. The sequence formed is
4, 8, 12.......
The common difference is 8 - 4 = 12 - 8 = 4
Thus, the number of dots in step 4 is
12 + 4 = 16
Looking at pattern B, the sequence formed is
2, 3, 6, 11
3 - 1 = 1
6 - 3 = 3
11 - 6 = 5
We can see that the difference between consecutive terms is increasing by a constant value, 2. This means that the difference between the fourth term and the third term is 5 + 2 = 7
Thus, the number of dots in step 4 is
11 + 7 = 18
b) A quadratic sequence is one in which the second difference between any two consecutive terms is constant. The constant value for the second difference in pattern B is 2
Thus, pattern B is shows a quadratic relationship
Find the equation of the line with the following:slope = 2/5; passes through (-3, 1)
Answers
Answer:
[tex]y=\frac{2}{5}x+\frac{11}{5}[/tex]Explanation:
Given the slope and a point on the line, we use the point-slope form to find the equation of the line:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ m=\frac{2}{5} \\ (x_1,y_1)=(-3,1) \end{gathered}[/tex]Substitute the given values:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-1=\frac{2}{5}(x-(-3)) \\ y-1=\frac{2}{5}(x+3) \\ y=\frac{2}{5}(x+3)+1 \\ y=\frac{2}{5}x+\frac{6}{5}+1 \\ y=\frac{2}{5}x+\frac{11}{5} \end{gathered}[/tex]The equation of the line in slope-intercept form is:
[tex]y=\frac{2}{5}x+\frac{11}{5}[/tex]Which letrero Best represents √27 on the number line.
Answers
You have the following number
√27
In order to determine which letter best represent the previous number, you take into account the following square roots:
√25 = 5
√36 = 6
Then, you can consider that √27 is a number in between 5 and 6, because √27 in anumber in between √25 and √36.
The only letter that is in between 5 and 6 on the number line, is the letter C.
Hence, letter C best represents √27
A jeweler has found that the monthly revenue received from selling a pair of earrings at a cost of d dollars each is given by the polynomial −7d2+180d. Find the monthly revenue received when d=17 dollars.
Answers
The monthly revenue is $1037
What is a linear equation in one variable?
A linear equation in one variable is equation whose degree is one and there is only one variable present.
We are given the monthly revenue received from selling a pair of earrings at a cost of d dollars is given by equation [tex]-7d^{2}+180d[/tex]
We have to find the monthly revenue received when the cost is $17
That is d=17
Now we substitute d=17 in the given equation to find the monthly revenue
We get,
[tex]-7d^{2}+180d\\[/tex]
⇒[tex]-7(17^{2})+180(17)\\[/tex]
⇒ -2023+3060
⇒1037
Hence the monthly revenue earned is $1037
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Robin and Dovey have four pet pigeons that they train to race. They release the birds at Robin's house and then drive to Dovey's to collect them. To drive from Robin's to Dovey's, because of one-way streets, they go 3.1 km north, turn right and go 1.7 km east, turn left and go 2.3 km north, turn right and go 0.9 km east, turn left and go 1.2 km north, turn left and go 4.1 km west, and finally turn left and go 0.4 km south. How far do the pigeons have to fly to go directly from Robin's house to Dovey's house? Round your answer to the nearest tenth. (HINT: draw a picture!) *
Answers
Let the north and east with a positive sign, so, the south and west are negative signs
Because of one-way streets, they go 3.1 km north, turn right and go 1.7 km east, turn left and go 2.3 km north, turn right and go 0.9 km east, turn left and go 1.2 km north, turn left and go 4.1 km west, and finally turn left and go 0.4 km south.
So, the resultant horizontal distance = 1.7 + 0.9 - 4.1 = -1.5 km
The resultant vertical distance = 3.1 + 2.3 + 1.2 - 0.4 = 6.2 km
So, the direct distance will be calculated using Pythagorean theorem :
So, the distance d =
[tex]\begin{gathered} d=\sqrt[]{(-1.5)^2+(6.2)^2}=\sqrt[]{2.25+38.44} \\ \\ d=\sqrt[]{40.69}=6.37887 \end{gathered}[/tex]Rounding the answer to the nearest tenth
so, the answer is : 6.4 km
Amrita wants to raise more than $200 for a charity by walking dogs in her neighborhood. She charges $7 per walk.What is an inequality that can be used to find the number of walks, w, that Amrita needs to complete?
Answers
Given:
Amrita wants to raise more than $200 for a charity.
She charges $7 per walk.
[tex]\begin{gathered} 7w>200 \\ \end{gathered}[/tex]Find the area of the shadedSector in terms of π12 90
Answers
Consider the following figure:
A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then theunit cost is given by the function C (x) = 0,3x2 -96x+14,848. How many cars must be made to minimize the unit cost?Do not round your answer
Answers
Answer:
[tex]160\text{ cars}[/tex]Explanation:
Here, we want to get the number of cars to be made so as to minimize the unit cost
What we have to do here is to find the first derivative of the given cost function
Mathematically, we have that as:
[tex]C^{\prime}(x)\text{ = 0.6x -96}[/tex]To get the minimum x value, we simply set the first derivative to zero and solve for x
Mathematically, that would be:
[tex]\begin{gathered} 0\text{ = 0.6x-96} \\ 0.6x\text{ = 96} \\ x\text{ = }\frac{96}{0.6} \\ x\text{ = 160 } \end{gathered}[/tex]Solve the equation. Justify each step using the word bank provided. *Properties may be used more than once!
Given
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Distributive Property
Combine
Like Terms
Justifications for each step:
2(x − 4) − 9 = 3(2x + 1) + 4
HELP PLEASE
Answers
The result of the equation 2(x − 4) − 9 = 3(2x + 1) + 4 by using the distributive property is x = -6
The equation is
2(x − 4) − 9 = 3(2x + 1) + 4
The distributive property states that multiplying the sum of two or more variables by a number will provide the same result as multiplying each variable individually by the number and then adding the products together.
The distributive property of the addition
A(B + C) = AB + AC
The distributive property of the subtraction
A(B - C) = AB - AC
The equation is
2(x − 4) − 9 = 3(2x + 1) + 4
Apply the distributive property
2x-8-9 = 6x+3+4
2x-17 = 6x+7
Rearrange the like terms and combine it
2x-6x = 7+17
-4x = 24
x = -6
Hence, the result of the equation 2(x − 4) − 9 = 3(2x + 1) + 4 by using the distributive property is x = -6
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The slope of the line is given by the variable m. Slowly drag the m slider to the right. How does this changethe line?
Answers
2.
As you can see:
Rise = 2
Run = 2
Slope = 2
Use the long division method to find the result when 8x3 + 14x2 11x - 8 is divided by 2x + 1. If there is a remainder, express the result in the form q(a) +
Answers
Let's develop a synthetic division
As you can observe, the division is exact because its reminder is zero.
Hence, the answer is-
[tex]\frac{8x^3+14x^2-11x-8}{2x+1}=4x^2+5x-8[/tex]Select the equations below that are equivalent to -6 = -20 - v
Answers
Given
[tex]-6=-20-v[/tex]- For -72 = 9(-20 - v):
[tex]\begin{gathered} -\frac{72}{9}=\frac{9(-20-v)}{9} \\ -8=-20-v \end{gathered}[/tex]The equation is not equivalent
- For -90 = 15(-20 - v):
[tex]\begin{gathered} \frac{-90}{15}=\frac{15(-20-v)}{15} \\ -6=-20-v \end{gathered}[/tex]The equation is equivalent
- For 5 * -6 = -100 - 5v:
Common factor 5
[tex]\begin{gathered} -30=5(-20-v) \\ \frac{-30}{5}=\frac{5(-20-v)}{5} \\ -6=-20-v \end{gathered}[/tex]The equation is equivalent
- For 3 * -6 = -60 - 3v:
Common factor 3
[tex]\begin{gathered} -18=3(-20-v) \\ \frac{-18}{3}=\frac{3(-20-v)}{3} \\ -6=-20-v \end{gathered}[/tex]The equation is equivalent
Answer:
-90 = 15(-20 - v)
5 * -6 = -100 - 5v
3 * -6 = -60 - 3v
I need to factor this expression (7th grade math):26x + 18
Answers
SOLUTION:
Required: To factorize the expression:
Solving:
[tex]\begin{gathered} 26x\text{ + 18} \\ \text{First we find the GCF of each terms of the binomial. The greatest co}mmon\text{ factor betwe}en\text{ 26x and 18} \\ 2(13x\text{ + 9)} \end{gathered}[/tex]Final answer:
The final answer is 2(13x + 9)
How can you find the next digit in the quotient?
Bring down the ? to show there are 2 tens
? ones that still need to be divided.
Answers
Bring down the next digit 6 to show there are 2 tens and 6 ones that still need to be divided.
This method of dividing is called the long division method.
In this, we divide the dividend with the divisor and get a quotient and a remainder.
The steps involved are given below :
1. Take the dividend's first digit from the left. Determine whether this digit is bigger than or equal to the divisor.
2. Then divide it by the divisor and write the result as the quotient on top.
3. Subtract the result from the digit and record the difference in the box below.
4. Reduce the dividend by the following digit (if present).
5. Repeat the above steps.
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od 2 - 7th Grade Math) Simplify the following expressions: (9x + 3) - (5x - 7) (1 Point) Enter your answer
Answers
Simplifying the expression, we have:
[tex]\begin{gathered} (9x+3)-(5x-7) \\ =9x+3-5x+7 \\ =(9x-5x)+(3+7) \\ =4x+10 \end{gathered}[/tex]So the simplified expression is 4x + 10.
helpppppppp ur gurlll out
Answers
Answer:
Step-by-step explanation:
2(x-3) + 21 = -3
So:
My first step is to open the brackets
2x - 6 + 21 = -3
Then I plus two numbers in the equation:
2x + 15 = -3
Third step is: 2x = -3 - 15
2x = -18
The value of x that makes the equation true is:
x = -18/2
x = -9
What is the mean absolute deviation of 10,4,12,4,2,10,10,6
Answers
3.25 is the mean absolute deviation of 10,4,12,4,2,10,10,6
What is Mean absolute Deviation?Mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean. Mean absolute deviation is a way to describe variation in a data set.
Given data:
10,4,12,4,2,10,10,6
Using the formula
Mean Absolute deviation = ∑(xi - x)/n
Mean = (10+ 4+ 12 +4+ 2+ 10 + 10+6)/8
= 58 / 8
= 7.25
Now,
10-7.25 = 2.75
4-7.25= -3.25
12-7.25=4.75
4-7.25=-3.25
2-7.25=-5.25
10-7.25=2.75
10-7.25=2.75
6-7.25=-1.25
mean absolute deviation=(2.75+3.25+4.75+3.25+5.25+2.75+2.75+1.25)/8
=26/8
=3.25
Hence 3.25 is the mean absolute deviation of 10,4,12,4,2,10,10,6.
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j
knjfjfjfjfjfjf help me solve this thanks !!
Answers
Answer:
132 degrees
Step-by-step explanation:
102+30 = 132
Need help w whole paper
Answers
Answer:
it is 1+1=2 and 8+x(1230+8723)=27t9230
Step-by-step explanation:
its easy for me
The quadratic equation d = -t2 + 4t + 33 models the depth of water, d, in feet
in a flood channel t hours after a rainstorm.
a. Solve the equation -t2 + 4t+ 33 = 0.
b. Approximate the positive solution found in part (a) to two decimal
places.
c. Interpret the answer to part (b) in terms of the problem.
Answers
a. The solution of the equation is t = 2 ± √37.
b. The approximation of the positive solution is 8.08.
c. The interpretation is that the depth of the water is 0 feet after 8.08 hours of the rainstorm.
We are given a quadratic equation. The equation is given below :
d = -t² + 4t + 33
The equation models the depth of the water "d" in a flood channel "t" hours after a rainstorm.
a. We have to solve the equation :
-t² + 4t + 33 = 0
t² - 4t - 33 = 0
t = 2 ± √37
b. We need to approximate the positive solution found in part (a) to two decimal places. The positive solution is t = 2 + √37.
t = 2 + 6.08
t = 8.08
c. The depth of the water is 0 feet after 8.08 hours of the rainstorm.
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Which of the following graphs represents the reflection of the point ( -3, 5) over the x-axis? I have to send you the other 2. It’s 4 altogether.
Answers
We have to identify the graph that represents the reflection of the point (-3,5) over the x-axis.
A reflection over the x-axis can be defined by the following rule: if we have a point (x,y), the image point after the reflection will have the same x-coordinate but the opposite of the y-coordinate.
It can be expressed as:
[tex]P=(x,y)\longrightarrow P^{\prime}=(x,-y)[/tex]Then, the image point for (-3,5) will be:
[tex](-3,5)\longrightarrow(-3,-5)[/tex]Then, this can be represented in a graph as:
This matches the following graph:
The box plots below show the number of goals that two hockey players, Sam and Barry, Scored each season during their careers.Select all that are TRUE1) Barrys data is nearly symmetrical2) the median is Sams data is more than Barrys data3) Sam scored more goals in one season than berry did.4) Barrys chart shows more variable than Sams5) Sams distribution is skewed left
Answers
From the given distribution, it is clear that
Sam scored more goals in one season than berry did.
and
Barrys data is nearly symmetrical
A rocket is launched straight up with a velocity of 8.36. What would be the velocity when it lands?
Answers
If the rocket is launched straight up with a velocity of 8.36 then at the velocity of landing the speed of the rocket will also be 8.36.
Given that the rocket is launched straight up with a velocity of 8.36.
We are required to find the velocity when the rocket lands.
Velocity is basically the directional speed of a object in motion as an indication of its rate of change in position as observed from a particular frame of reference.
When the velocity of rocket while it goes up is 8.36 then the velocity when it lands is also 8.36 because if the velocity will increase then the rocket will crash also.
Hence if the rocket is launched straight up with a velocity of 8.36 then at the velocity of landing the speed of the rocket will also be 8.36.
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Solve -4x + 3 > 23 or 7x - 6 > 22
Answers
Answer:
-4x + 3 > 23 Answer is x<-5
Step-by-step explanation:
