State if the triangles in each pair of similar. If so, State how you know they are similar and complete the similarity statement.
Answers
Answer:
Step-by-step explanation:
They are not similar. If they were, ∠LMF and ∠GHF would both have the same angle measure and they do not.
Final answer:
Mathematics question on similar triangles; triangles are similar if they have congruent corresponding angles and proportional sides obtained through AA, SSS, or SAS criterion. A similarity statement describes the correspondence of the vertices.
Explanation:
The question provided falls within the subject of Mathematics, specifically within the study of geometry and the concept of similar triangles. To determine if two triangles are similar, we must check if they have the same shape, which implies that their corresponding angles are equal and their corresponding sides are in proportion. In other words, two triangles are similar if their corresponding angles are congruent and the lengths of their corresponding sides are proportional. This can be verified by angle-angle similarity (AA), side-side-side similarity (SSS), or side-angle-side similarity (SAS). The similarity statement provides the order of correspondence of vertices between similar triangles.
When evaluating if triangles BAO and B1A1O are similar, we must compare their corresponding angles and sides. If the given information indicates that at least two angles of one triangle are congruent to two angles of another triangle (AA criterion), or that the sides are proportional (SSS or SAS criterion), then the triangles are similar. For instance, if ∠BAO ≅ ∠B1A1O and ∠BOA ≅ ∠B1O1A1, then by the AA criterion, the triangles are similar, and we could write the similarity statement as triangle BAO ∼ triangle B1A1O.
Related Questions
John wants to pay off a $2,100 bill in the next 13 months. What is the approximate amount that he will have to set aside each month to reach his goal?
$154
$167
$162
$187
Answers
Answer:the approximate amount that he will have to set aside each month to reach his goal is $162
Step-by-step explanation:
Total amount of bill that John wants to pay off js $2,100. $2,100 bill in the next 13 months. To determine the amount that he will have to set aside each month to reach his goal, we would divide the total bill by the number of months. It becomes
2100/13 = 161.538
The approximate amount is $162
Answer:
$162
Step-by-step explanation:
$2,100/13
A recent article in the Cincinnati Enquirer reported that the mean labor cost to repair a heat pump is $90 with a standard deviation of $22. Monte’s Plumbing and Heating Service completed repairs on two heat pumps this morning. The labor cost for the first was $75 and it was $100 for the second. Assume the distribution of labor costs follows the normal probability distribution. Compute z values for each.
Answers
Answer:
Z value for the first pump = -0.68
Z value for the second pump = 0.45
Step-by-step explanation:
Data provided in the question:
Mean labor cost to repair a heat pump = $90
Standard deviation = $22
Labor cost for the first, X₁ = $75
Labor cost for the Second, X₂ = $100
Now,
Z value for the first pump = [X₁ - Mean] ÷ Standard deviation
thus,
Z value for the first pump = [ $75 - $90] ÷ $22
= - 0.68
Z value for the second pump = [X₁ - Mean] ÷ Standard deviation
thus,
Z value for the second pump = [ $100 - $90] ÷ $22
= 0.45
Answer:
z1= -0.6818
z2= 0.45
Step-by-step explanation:
Mean labor cost to repair the heat pump is μ= $90
standard deviation σ= $22
Labor cost for the first heat pump X_1= $75
labor cost for the second heat pump is X_2= $100
z value for the first heat pump
[tex]z_1= \frac{X_1-\mu}{\sigma}[/tex]
⇒ [tex]z_1= \frac{75-90}{22}[/tex]
= -0.6818
z value for the second heat pump
[tex]z_2= \frac{X_2-\mu}{\sigma}[/tex]
⇒[tex]z_2= \frac{100-90}{22}[/tex]
= 0.45
A 85cm snowman melts and loses 3cm in height for every hour the sun shine and the sun shine only 6.5 hours a day. How many days will it take for the snowman to melt
Answers
Answer:
Step-by-step explanation:
The initial height of the snowman is 85 cm. snowman melts and loses 3cm in height for every hour the sun shine and the sun shine only 6.5 hours a day. This means that the height that the snowman loses in a day would be
3 × 6.5 = 19.5 cm
Therefore, in a day, the snowman loses 19.5 cm in height. Therefore,
the number of days that it will take the snowman to melt would be
85/19.5 = 4.36 days
A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average rate of 3 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?
A. 0.5< t < 0.75
B. 1.75< t < 2.0
C. 2.0 < t < 2.5
D. 2.5 < t < 3.0
E. 3 < t < 3.5
Answers
Answer:
C. 2.0 < t < 2.5
Step-by-step explanation:
Diameter of track (D) = 2 miles, Average rate (A) = 3 miles per hour
A = distance/ time
time (t) = distance/A
distance around the track (circumference) = πD = 3.142 × 2 miles = 6.284 miles
t = 6.284miles/3miles/hour = 2.1 hour
Therefore, 2.0 < t < 2.5
On a final exam, 75 percent of a class had scores that were greater than 70, and 60 percent of the class had scores that were less than 85. What percent of the class had scores that were greater than 70 but less than 85 ?
Answers
Answer:
The answer is 35.
35% of the class had scores that were greater than 70 but less than 85.
Step-by-step explanation:
Let's assume the number of students in the class =100
If 75% of the class scored greater than 70, then, it means 25% (100-75) of the scores were less than or equal to 70
In other words, 25 scores were less than or equal to 70.
If 60% of the class had scores that were less than 85, then, it means 40%(100-60) of the scores were greater than or equal to 85
Therefore, of the 100 scores, 25 scores were LESS THAN OR EQUAL to 70, and 40 scores were GREATER THAN OR EQUAL to 85.
We've now accounted for 65 (25+40) scores, which means the remaining 35 (100-65) scores must be between 70 and 85.
Answer:
The answer is 35.
35% of the class had scores that were greater than 70 but less than 85.
Step-by-step explanation:
Let's assume the number of students in the class =100
If 75% of the class scored greater than 70, then, it means 25% (100-75) of the scores were less than or equal to 70
In other words, 25 scores were less than or equal to 70.
If 60% of the class had scores that were less than 85, then, it means 40%(100-60) of the scores were greater than or equal to 85
Therefore, of the 100 scores, 25 scores were LESS THAN OR EQUAL to 70, and 40 scores were GREATER THAN OR EQUAL to 85.
We've now accounted for 65 (25+40) scores, which means the remaining 35 (100-65) scores must be between 70
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The number of fish caught during a fishing tournament b. The number of textbook authors now sitting at a computer c. The political party affiliation of adults in the United States d. The square footage of a house e. The number of free dash throw attempts before the first shot is made f. The weight of a Upper T dash bone steak
Answers
Answer:
a. Discrete
b. Discrete
c. Not a random variable
d. Continuous
e. Discrete
f. Continuous
Step-by-step explanation:
The discrete random variable is countable while continuous random variable is measurable.
a. The number of fish caught is a discrete random variable because these are countable.
b. The number of text book authors are also countable so it is a discrete random variable.
c. The political party affiliation of adults is not a random variable because the political party affiliation depends on person's interest and it cannot be randomly assigned to person. Also random variable is the numerical outcome of random experiment whereas political affiliation is the categorical variable that results in non numerical responses such as Democrat, Republicans etc.
d. The square footage of a house is measurable and so it is a continuous random variable.
e. The number of free dash throw attempts are countable so it is a discrete random variable
f. The weight of Upper T dash bone steak is measurable and so it is a continuous random variable.
The number of fish caught during a fishing tournament is a discrete random variable, while the square footage of a house is a continuous random variable. The other examples are not random variables.
Explanation:a. The number of fish caught during a fishing tournament is a discrete random variable. The values of the variable are obtained by counting the number of fish caught.
b. The number of textbook authors now sitting at a computer is not a random variable. It is a fixed number and does not vary.
c. The political party affiliation of adults in the United States is not a random variable. It can be determined by surveying adults or analyzing existing data.
d. The square footage of a house is a continuous random variable. The values of the variable are obtained by measuring the size of the house.
e. The number of free-throw attempts before the first shot is made is a discrete random variable. The values of the variable are obtained by counting the number of attempts.
f. The weight of an Upper T-bone steak is a continuous random variable. The values of the variable are obtained by measuring the weight of the steak.
A baby was born and then began to gain weight at a rate of 1.5 pounds per month. After 4 months, the baby's weight was 16 pounds. Write an equation for the function W ( t ) , W(t), representing weight, in pounds, of the newborn baby t t months after birth.
Answers
Answer:
w=1.5t+12
Step-by-step explanation:
that's the right answer
The equation for the function W(t) representing the weight of the newborn baby t months after birth is W(t) = 16 + 1.5t
To solve this problem
We can make use of the given data.
The infant gained weight at a pace of 1.5 pounds each month, reaching 16 pounds at the end of 4 months. With this knowledge, the equation can be written as follows:
W(t) = Initial weight + (Rate of weight gain per month) * (Number of months)
W(t) = 16 + (1.5 * t)
So, the equation for the function W(t) representing the weight of the newborn baby t months after birth is W(t) = 16 + 1.5t
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In the XY-Plane above, the circle has center (h,k) and radius 10. What is the value of k?
Answers
Answer:
k = +/- 6
Step-by-step explanation:
In the XY-Plane above, the circle has center (h,k) and radius 10. What is the value of k?
The concluding part of this question will be
Two coordinates are given, (4,0) and (20,0)
equation of a circle
([tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]
We can then have two equations of the circle and solve simultaneously
([tex](4-h)^{2} +(-k)^{2} =10^{2}[/tex] .............................1
([tex](20-h)^{2} +(-k)^{2} =10^{2}[/tex] ......................................2
combining the two equation to solve
(20-h)^2 - (4-h)^2 = 0
20^2 - 40h +h^2 -4^2 + 8h -h^2 = 0
20^2 - 42 = 32h
h = 12
(4-12)^2 + (-k)^2 = 100
k^2 = 36
k = +/- 6
PLEASE HELP WITH QUESTION!!!!!
Find the sum of the series:
Answers
The sum of the given series [tex]\sum _{a=1}^{10}\:\left(2a+2\right)[/tex] is 130.
Step-by-step explanation:
The sum of series need to be found is [tex]\sum _{a=1}^{10}\:\left(2a+2\right)[/tex] .
Apply sum rule,
[tex]\sum x_n+y_n=\sum x_n+\sum y_n[/tex]
[tex]\sum _{a=1}^{10}\:\left(2a+2\right).[/tex] =[tex]\sum 2a+\sum 2[/tex].
Apply the constant multiplication rule,
[tex]\sum c\cdot a_n=c\cdot \sum a_n[/tex] .
[tex]\sum 2\cdot a=2\cdot \sum a[/tex].
[tex]\sum _{a=1}^{10}n[/tex] = 1+2+3+4+5+6+7+8+9+10.
[tex]\sum _{a=1}^{10}n[/tex] = 55.
[tex]\sum 2\cdot a[/tex]=2×55.
[tex]\sum 2\cdot a [/tex]=110.
To find [tex]\sum _{a=1}^{10}2[/tex],
Apply sum rule, [tex]\sum _{k=1}^n\:a\:=\:a\cdot n[/tex] ,
[tex]\sum _{a=1}^{10}2[/tex] =2×10.
[tex]\sum _{a=1}^{10}2[/tex] = 20.
[tex]\sum _{a=1}^{10}\:\left(2a+2\right)[/tex] = 110+20.
[tex]\sum _{a=1}^{10}\:\left(2a+2\right)[/tex] =130.
Use matrices to determine the vertices of the reflected figure. Then graph the image and the pre-image on the same coordinate grid.
Triangle XYZ with vertices X(2, -9), Y(-6, 0) and Z(-5, -5), reflected over the y-axis.
A.
B.
C.
D.
(pictures below)
Answers
Answer:
see below for the matrix multiplicationgraph CStep-by-step explanation:
Reflection across the y-axis is a left-right reflection that changes only the sign of the x-coordinate. The transformation matrix (as for any rotation and/or reflection) can be 2-dimensional, and can left-multiply the coordinate matrix that has coordinate pairs as column vectors. The transformed coordinates show up as column vectors in the result matrix.
The only graphs showing left-right reflections are those of choices C and D. Only choice C has the points properly plotted on the graph.
The correct answer is graph C, or the third option.
Just got it right on edge 2020, hope this helps!! :)
Make a Venn Diagram from the following information to answer below question?25 students played soccer 4 boys played soccer and baseball 3 girls played soccer and baseball 10 boys played baseball 4 girls played baseball 9 students played tennis 3 boys played soccer and tennis 3 girls played soccer and tennis 3 boys played baseball and tennis 1 girl played baseball and tennis 1 boy played all three sports 1 girl played all three sports How many students played soccer, but not baseball or tennis?
Answers
To find the number of students who played soccer but not baseball or tennis, we need to analyze the given information and use the formula A = (A ∩ B) + (A ∩ C) + (A - A ∩ B ∩ C). Substituting the given values, we find that 32 students played soccer but not baseball or tennis.
Explanation:To determine how many students played soccer but not baseball or tennis, we need to analyze the information given in the Venn diagram provided. Let's label the regions of the Venn diagram:
A represents the set of students who played soccer.
B represents the set of students who played baseball.
C represents the set of students who played tennis.
From the given information, we know that:
A = 25A ∩ B = 4A ∩ C = 3B = 10B ∩ C = 4C = 9A ∩ B ∩ C = 1To find the number of students who played soccer but not baseball or tennis, we need to calculate the value of A without the intersection of the other sets. Using the formula:
A = (A ∩ B) + (A ∩ C) + (A - A ∩ B ∩ C),
we can substitute the given values:
A = 4 + 3 + (25 - 1)
A = 32
Therefore, 32 students played soccer but not baseball or tennis.
PLEASE HELP
Which system of inequalities is represented by the graph?
A. y less than or equal to-2x+4 and y greater than or equal to x-6
B. y less than or equal to2x+4 and y greater than or equal to -x -6
C. y less than or equal to 2x-4 and y greater than or equal to -x-6
D. y less than or equal to 2x+4 and y greater than or equal to -x+6
Answers
Answer:
The answer to your question is letter B
Step-by-step explanation:
Process
1.- Find two points of each line
Line A (-2, 0) (-1, 2)
Line B (-1. - 5) (-6, 0)
2.- Find the slope and equation of each line
Line A
[tex]m = \frac{2 - 0}{-1 + 2}[/tex]
[tex]m = \frac{2}{1}[/tex]
m = 2
y - 0 = 2(x + 2)
y = 2x + 4
Line B
[tex]m = \frac{0 + 5}{-6 + 1}[/tex]
[tex]m = \frac{5}{-5}[/tex]
m = -1
y - 0 = -1(x + 6)
y = -x - 6
3.- Find the inequalities
Line A, we are interesteed in the lower area of the line, so the inequality is
y ≤ 2x + 4
Line B, we are also interested in the lower area of the line so the inequality is
y ≥ - x - 6
Answer:B
Step-by-step explanation:
Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?
A. $506.00
B. $726.24
C. $900.00
D. $920.24
E. $926.24
Answers
Answer:
E. $926.24
Step-by-step explanation:
The total amount of interest paid is shown below:
1. For 6 months, the interest would be
= Invested amount × interest rate
= $10,000 × 2%
= $200
2. For 12 months, the interest would be
= (Invested amount + interest paid for 6 months) × interest rate
= ($10,000 + $200) × 3%
= $10,200 × 3%
= $306
3. For 18 months, the interest would be
= (Invested amount + interest paid for 6 months + interest paid for 12 months ) × interest rate
= ($10,000 + $200 + $306) × 4%
= $420
Now the total interest would be
= $200 + $306 + $420.24
= $926.24
At the used bookstore, Keisha bought 24 novels. If 3/8 of the book the books are mystery novels and the rest are science fiction novels, how many science fiction novels did Keisha buy?
Answers
Keisha bought 15 science fiction novels.
Step-by-step explanation:
Given,
Number of novels bought by Keisha = 24
Mystery novels = 3/8 of total novels
Mystery novels = [tex]\frac{3}{8}*24=\frac{72}{8}[/tex]
Mystery novels = 9
Let,
x represent the number of science fiction novels.
Mystery novels + Science fiction novels = Total novels
[tex]9+x=24\\x=24-9\\x=15[/tex]
Keisha bought 15 science fiction novels.
Keywords: fraction, addition
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if the sum of the interior angles of a regular n-gon is 900 degrees, then n=what?
Answers
Answer:
n=7
Step-by-step explanation:
let n be number of sides.
(n-2)180=900
n-2=900/180=5
n=5+2=7
The common stock of Manchester & Moore is expected to earn 13 percent in a recession, 6 percent in a normal economy, and lose 4 percent in a booming economy. The probability of a boom is 5 percent while the probability of a recession is 45 percent. What is the expected rate of return on this stock?
Answers
Answer:
8.65%
Step-by-step explanation:
Given information:
Recession Return = 13%
Normal Return = 6%
Boom Return = -4%
Probability of a recession = 45 %
Probability of a boom = 5 %
Probability of a normal = 100 - 45 - 5 = 50%
We need to find the expected rate of return on this stock.
Expected rate of return is the sum of products of probability and returns of each state of economy.
Expected rate of return [tex]=13\%\times 45\%+6\%\times 50\%+(-4\%)\times 5\%[/tex]
[tex]=5.85\%+3\%-0.2\%[/tex]
[tex]=8.65\%[/tex]
Therefore, the expected rate of return on this stock is 8.65%.
When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?
Answers
Final answer:
When a positive integer x, which leaves a remainder of 5 when divided by 9, is multiplied by 3, the remainder when 3x is divided by 9 is 6.
Explanation:
When the positive integer x is divided by 9, the remainder is 5. To determine the remainder when 3x is divided by 9, we should remember that when two positive numbers multiply, the result has a positive sign. So multiplying x by 3, we get 3x. The initial information tells us that x = 9n + 5 for some integer n. Thus, 3x equals 3(9n + 5), which simplifies to 27n + 15. This expression can be further broken down as 27n + 9 + 6, which is the same as 9(3n + 1) + 6. Therefore, when 3x is divided by 9, it is the same as dividing this expression by 9, which leaves us with a remainder of 6. Hence, the remainder when 3x is divided by 9 is 6.
Identify the monomial function described as odd or even, and indicate whether a is positive or negative.
Answers
Answer:
Case 1: As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) decreases.
It is an 'odd' function with 'positive' a.
Case 2: As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) decreases.
It is an 'even' function with 'negative' a.
Case 3: As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) increases.
It is an 'even' function with 'positive' a.
Case 4: As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) increases.
It is an 'odd' function with 'negative' a.
Step-by-step explanation:
Let us consider a monomial function:
f(x) = axⁿ
Case 1:
As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) decreases.
This happens only if a is 'positive' and n is 'odd'. So, it is an 'odd' function with 'positive' a.
Case 2:
As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) decreases.
This happens only if a is 'negative' and n is 'even'. So, it is an 'even' function with 'negative' a.
Case 3:
As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) increases.
This happens only if a is 'positive' and n is 'even'. So, it is an 'even' function with 'positive' a.
Case 4:
As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) increases.
This happens only if a is 'negative' and n is 'odd'. So, it is an 'odd' function with 'negative' a.
Keywords: monomial function, odd function, even function
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Identify the monomial function described as odd or even, and indicate whether a is positive or negative.
QUESTION 4 of 5: You have insurance premiums of $250 due quarterly. How much will you pay annually?
Answers
Answer:
$1000
Step-by-step explanation:
quarterly is 1/4
12/4 is 3
so every 3 months you pay $250
annually is the whole year so 250*4
Answer:
1000
Step-by-step explanation:
a rectangular picture 16 inches by 20 inches has a frame of uniform width. Find the width of the frame if the total area of the picture and the frame is 672 square inches
Answers
Answer: 22
Step-by-step explanation:
The area of the picture =l×b = 20×16=320
The length of the frame is 16
If the width is x ( and it's uniform)
672- 320= 352
Area of the frame = 16× x=352
x=352/16
x = 22
Total width is 42 inch.
Given that,
Length of picture is 16 inch and width is 20 inch.Total area with frame is 672 sq in.We need to find the width of frame.According to the scenario, computation of the given data are as follows,
Total area of picture = 16 [tex]\times[/tex] 20 = 320 sq in.
So Frame area = 672 - 320 = 352
Now, length of frame = 16
Let, width of frame = w
So, 16 [tex]\times[/tex] w = 352
W = 352 [tex]\div[/tex] 16
W = 22 inch
So total width is 22 + 20 = 42 inch.
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find the radius of the oblique cylinder (PLEASE HELP EXTRA POINTS)
Answers
Answer:
The radius of the oblique cylinder is 4 cm.
Step-by-step explanation:
Given:
The volume of the oblique cylinder = [tex]192 \pi cm^3[/tex]
Height of the cylinder = 12 cm
To Find:
Radius of the oblique cylinder = ?
Solution:
we know that the volume of the oblique cylinder
=>[tex]\text{base area of the cylinder} \times \text{height of the cylinder}[/tex]------------------------------(1)
where base area of the cylinder is the area of the circle
so area of the circle = base area
[tex]\pi r^2[/tex] = base area---------------(2)
Substituting (2) in (1)
[tex]192 \pi = \pi r^2 \times height[/tex]
[tex]192 \pi = \pi \times r^2 \times height[/tex]
[tex]192 \pi = \pi \times r^2 \times 12[/tex]
[tex]\frac{192 \pi}{ \pi \times 12}= r^2[/tex]
[tex]\frac{192}{12}= r^2[/tex]
[tex]16= r^2[/tex]
[tex] r^2 =16[/tex]
[tex] r =\sqrt{16}[/tex]
r=4
The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the _____.
a. variance
b. standard error
c. residual
d. predicted interval
Answers
Answer:
Option C. Residual
Step-by-step explanation:
Residuals are defined as:
Residual is the error that are not explained by the regression line.It is defined as the difference between observed value of dependent variable and the predicted variable.Residual = Observed value - Predicted value[tex]e = y_{\text{observed}}- \hat{y}[/tex], where e is the residual.Residuals are the unexplained differences.Thus,
The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the residuals.
Option C. Residual
The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the residual.
The following information should be considered:
Residual should be the error i.e. not described by the regression line. It shows the difference between the observed value and the predicted value.Therefore we can conclude that option c is correct.
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Thomas brings over 1/2 of his marble collection. He divides these marbles equally among 3 friends. What fraction of Thomas's entire marble collection did each friend get?
Answers
Answer:
Each of the three friends will get one-sixth of the Thomas's enitre marble collection.
Step-by-step explanation:
Fraction of the total marble collection brought by Thomas = [tex]\frac{1}{2}[/tex]
Now, Thomas divides these marbles equally among his three friends. So, each of the three friends will get one-third of the total marble collection brought by Thomas.
Fraction of total marble collection got by each friend = [tex]\frac{1}{3} \;of\;fraction\;of\;total\;marble\;collection\;brought\;by\;Thomas[/tex]
= [tex]\frac{1}{3}\times\frac{1}{2}=\frac{1}{6}[/tex]
∴ Each of the three friends of Thomas will get one-sixth of his entire collection of marbles.
Triangles Q R S and X Y Z are shown. Angles Q S R and X Z Y are right angles. Angles Q R S and X Y Z are congruent. The length of Y Z is 9, the length of X Z is 12, and the length of hypotenuse X Y is 15. Given △QRS ~ △XYZ, what is the value of tan(Q)? Three-fifths Three-fourths Four-fifths Four-thirds
Answers
Answer:
Three-fourths
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
∠QSR≅∠XZY ---> given problem
∠QRS≅∠XYZ ---> given problem
so
△QRS ~ △XYZ ----> by AA Similarity theorem
Remember that, if two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
That means
[tex]\frac{QS}{XZ}=\frac{QR}{XY}=\frac{RS}{YZ}[/tex]
∠Q≅∠X
∠R≅∠Y
∠S≅∠Z
In the right triangle XYZ
Find the tangent of angle X
[tex]tan(X)=\frac{YZ}{XZ}[/tex] ---> opposite side angle X divided by adjacent side angle X
substitute the given values
[tex]tan(X)=\frac{9}{12}[/tex]
Simplify
[tex]tan(X)=\frac{3}{4}[/tex]
Remember that
∠Q≅∠X
so
[tex]tan(Q)=tan(X)[/tex]
therefore
[tex]tan(Q)=\frac{3}{4}[/tex] ---->Three-fourths
Among all pairs of numbers with a sum of 232, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms.
Answers
Answer:
Step-by-step explanation:
232/2=116
so 116,116 has maximum product
Allison works for a computer software company. She earns \$225$225dollar sign, 225 per week plus \$25$25dollar sign, 25 for each software package that she sells that week. If she wants to earn at least \$400$400dollar sign, 400 this week, what is the minimum number of software packages that she must sell this week?
Answers
Answer:
7 software packages
Step-by-step explanation:
Given,
Signing amount = $ 225,
Additional amount for each software package = $ 25
Thus, the total amount for x software packages = signing amount + additional amount for x packages
= 225 + 25x
If total amount ≥ $ 400
225 + 25x ≥ 400
25x ≥ 400 - 225
25x ≥ 175
[tex]\implies x \geq \frac{175}{25}=7[/tex]
Hence, the minimum number of software packages that she must sell would be 7.
Final answer:
Alison needs to sell at least 7 software packages this week on top of her base salary to earn at least $400.
Explanation:
Alison wants to earn at least $400 this week by selling software packages. She earns a base $225 per week plus $25 for each software package sold. To determine the minimum number of software packages Alison must sell, we subtract her base salary from her desired earnings for the week:
Required earnings (>=$400) - Base salary ($225) = Sales required from software packages
$400 - $225 = $175
Now divide the sales required from software packages by the amount earned per package:
$175 / $25 = 7
Therefore, Alison needs to sell at least 7 software packages to meet her goal of $400
A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 187, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?
A. 22B. 33C. 55D. 77E. 88
Answers
Answer:
B. 33
Step-by-step explanation:
Let the number of Fuji trees be F, the number of gala be G and the total number of trees be x.
10% cross pollinated, this means 1/10 cross pollinated or 0.1x
Number of Fuji plus cross pollinated is 187.
And cross pollinated is 3/4 of total or let’s say 0.75 of total which is 0.75x
Now, adding 0.1x + 0.75x would equal 187
0.85x = 187
x = 187/0.85 = 220 trees
The total number of trees is 220.
The number of gala trees is thus 220 - 187 = 33 trees
The population of locusts in a certain swarm doubles every two hours. If 4 hours ago there were 1,000 locusts in the swarm, in approximately how many hours will the swarm population exceed 250,000 locusts?A. 6B. 8C. 10D. 12E. 14
Answers
4 hours ago = 1,000
2 hours ago = 2,000
Now = 4,000
In 2 hours = 8,000
In 4 hours = 16,000
In 6 hours = 32,000
In 8 hours = 64,000
In 10 hours = 128,000
In 12 hours = 256,000
The answer would be D. 12 hours.
Rebecca moves to a large city that had two event stadiums. The larger stadium can hold 4.5 times 10^4 people, which is about 15 times as many people as the smaller stadium can hold. Which expression could represent the approximate amount of people the smaller stadium can hold?
Answers
Answer:
3,000 people
Step-by-step explanation:
Total number of people larger stadium can hold equals 4.5 times [tex]10^{4}[/tex] people,
which equals 45,000 people.
Now,
it is given that larger stadium can hold 15 times more people than small stadium .
So, smaller stadium will hold 15 times less people than the larger stadium ,
Which equals , [tex]\frac{45000}{15}[/tex] = 3,000 people.
Thus ,
Smaller stadium can hold a total of 3,000 people.
A regular hexagon is inscribed in a circle, the diameter of the circle is d; what is the circumference of the hexagon ?
Answers
Answer:
3d
Step-by-step explanation:
A regular hexagon has six equivalent triangles, each triangle having one side of that of the hexagon. if the diameter of the circle in which the hexagon is inscribed is d , then its radius will be
[tex]r=\frac{d}{2}[/tex]
this radius also happens to be one of the side of the equivalent triangle whose one side is also the side of hexagon. since length of one side of hexagon is
[tex]\frac{d}{2}[/tex]
the circumference of the hexagon will be [tex]6 (\frac{d}{2} )\\\\thus \\circumference \\of \\hexagon = 3d[/tex]