Determine whether the given triangles are similar. Justify your answer. If they are similar write a similarity statement. How do you do this?
Answers
Similar shapes may or may not have equal lengths
Triangles ABC and PRQ are similar by SSS
The corresponding sides on both triangles are:
AB = 8, and PQ = 6
AC = 12, and PR = 9
BC = 12, and QR = 9
Divide the corresponding sides, to determine the scale factor (k)
[tex]k = \frac{6}{8} = \frac{9}{12} = \frac{9}{12}[/tex]
Evaluate the quotients
[tex]k = 0.75 = 0.75 = 0.75[/tex]
Given that the scale factors are equal.
Hence, both triangles are similar by SSS
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Related Questions
What’s twice the difference of a number and 8 is at least -20 using x as a variable into a inequality please help!!!
Answers
Wayne is solving a system of linear equations.
y= -3/4x+5
X= -2
To solve this system, he graphed the line y= - 3/4x+5
When Wayne graphs the line x= -2, at which point will he find the solution of this system of linear equations?
Answers
A vet weighs two puppies. The small puppy weighs 4 2/3 pounds. The large puppy weighs 4 2/3 times as much as the small puppy. How much does the large puppy weigh?
Answers
4 2/3 times the small puppies weight = large puppy weight
4 2/3 × 4 2/3 or 4 2/3^2 = 21.77777.... or in mixed number is 21 7/9 lbs
Answer:
21
Step-by-step explanation:
there are 5280 feet in a mile. how many feet are in 7/11 of a mile
Answers
=5280 * 7/11
=(5280*7)/11
=36,960/11
=3,360 feet in 7/11 mile
Hope this helps! :)
To find the number of feet in 7/11 of a mile, you multiply 5280 (the number of feet in a mile) by 7/11. The answer is 3360 feet.
Explanation:To calculate how many feet are in 7/11 of a mile, you first have to understand that there are 5280 feet in one mile. If you need to find out the feet in a fraction of a mile, you can multiply this number of feet in one mile by that fraction. In this case, the fraction is 7/11. So, the calculation would go as follows:
5280 feet/mile * 7/11 mile = 3360 feet.
Therefore, 7/11 of a mile is equivalent to 3360 feet.
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A monument in the shape of a right triangle sits on a rectangular pedestal that is 5 meters high by 11 meters long. The longest side of the triangular monument measures 61 meters. How high off the ground is the top of the monument?
Answers
Answer:
65 meters off the ground.
Step-by-step explanation:
The height of the monument is 9.80 m
Explanation:To find the height of the monument, we can use the Pythagorean theorem. The rectangle on the pedestal forms a right triangle with the longest side of the monument being the hypotenuse. Let's call the height of the monument 'h'. Using the Pythagorean theorem, we have:
[tex]h^2 = (11^2) - (5^2)[/tex]
[tex]h^2 = 121 - 25[/tex]
[tex]h^2 = 96[/tex]
[tex]h = \sqrt{96[/tex]
h ≈ 9.80 meters
What is the value of 83?
Answers
50 points 3/8 x 54
Answers
first multiply 54 and 3 together
54 x 3 = 162
Then divide 162 and 8 together
162/8 = 20.25
20.25 is your answer
hope this helps
Plz help!I don’t understand
Answers
The diagram means that parallelograms come in two kinds: rectangles and rhombuses.
So,
.. all rhombuses are parallelograms
.. all rectangles are parallelograms
.. no rectangles are rhombuses
This diagram only recognizes parallelograms that are rectangles and rhombuses. There are also other kinds of parallelograms, but those are not shown here.
The scale on a map is 1:500000
Two towns are 7cm apart on the map
work out the actual distance between the map
Give your answer in kilometres
Answers
it mean:
1cm : 500000 cm
(500000×7) cm = 3500000 cm (real distance between the two towns, in cm)
if
1 Km = 100000 cm
3500000 /100000 = 35 Km (real distance between the two towns, in Km)
The actual distance between the two towns, considering that they are 7cm apart on a map with a scale of 1:500000, is 35 kilometers.
Explanation:
In the given scenario, you're being asked to find the actual distance between two towns based on their distance on a map, using the map's scale, which is 1:500000. This means 1 cm on the map is equivalent to 500000 cm on the ground.
Since the towns are 7 cm apart on the map, the actual distance on the ground will be 7 (distance on the map) multiplied by 500000 (scale of the map), i.e., 3500000 cm. Since there is 100000 cm in 1 km, you convert the distance to kilometers by dividing by 100000. Hence, the actual distance is 3500000/100000 = 35 km.
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1.Subtract
5/8 - 1/6
Express your answer in simplest form.
2.Subtract
6/7 - 3/5
A. 3/12
B. 9/35
C. 3/7
D. 3/35
3. Add
5 3/8 + 4 1/4
4. Add
2 5/6 + 3 3/4
Express your answer in simplest form
5. Subtract
3 1/4 - 1 5/8
Please Help ASAP I have to get the done before 10:00
Answers
2. 9/35
3. 9 5/8
4. 6 7/12
5. 1 5/8
2)B)9/35
3)9 1/8
4)3 1/12
5)dunno, sry
Hope I helped for numbers 1-4! :)
The value of a boat is $23,400. It loses 8% of its value every year. Find the approximate monthly percent decrease in value. Round your answer to the nearest hundredth of a percent.
(NOT 67%)
Answers
Final answer:
The approximate monthly percent decrease in value is 0.67%.
Explanation:
To find the approximate monthly percent decrease in value, we need to first calculate the annual percent decrease. We know that the boat loses 8% of its value every year. So, the annual percent decrease is 8%.
To find the monthly percent decrease, we need to divide the annual percent decrease by 12 (since there are 12 months in a year).
Therefore, the approximate monthly percent decrease in value is 0.67%.
Final answer:
The approximate monthly percent decrease in value of the boat that depreciates at 8% annually is 0.65% when rounded to the nearest hundredth of a percent.
Explanation:
To find the monthly percent decrease in value of a boat that costs $23,400 and depreciates 8% annually, we need to calculate the equivalent monthly rate. The formula for monthly depreciation is (1 - (1 - annual depreciation rate)^(1/12)). In this case, the annual depreciation rate is 0.08 for 8%. Applying the formula, we get:
Monthly depreciation = 1 - (1 - 0.08)^(1/12) = 1 - (0.92)^(1/12)
= 1 - (0.92)^(0.08333...)
= 1 - 0.99347... (value calculated using a calculator)
= 0.00653... or 0.653% (after converting to a percentage).
To round to the nearest hundredth of a percent, we get approximately 0.65% monthly depreciation. This is the approximate monthly percent decrease in the boat's value.
A survey asked 10 boys and 10 girls how many hours they spent playing video games the previous week. The number of hours are given in the line plots.
Two line plots one above the other, both are labeled from two to twenty by twos. The top line plot is labeled Boys and it has three Xs above ten, two Xs above fifteen and one X above eight, twelve, thirteen, fourteen and twenty. The bottom line plot is labeled Girls and it has three Xs above four, two Xs above ten and one X above three, six, seven, eight and fifteen.
Select from the drop-down menus to complete each statement.
Answers
The range of boys and girls is 12 hours.
The median for boys is 12.5 hours
The median for girls is 6.5 hours.
What is a range in a set of data?The range is the difference between the highest value and the lowest value of a given set of data.
We have,
From the line plot,
Boys:
Hours Number of boys
1
2
3
4
5
6
7
8 x
9
10 x x x
11
12 x
13 x
14 x
15 xx
16
17
18
19
20 x
Girls:
Hours Number of girls
1
2
3 x
4 xxx
5
6 x
7 x
8 x
9
10 xx
11
12
13
14
15 x
Now,
Range:
Boys:
= Longest time - Shortest time
= 20 - 8
= 12 hours
Girls:
= 15 - 3
= 12 hours
Median:
Boys:
= 8, 10, 10, 10, 12, 13, 14, 15, 15, 20
= 12.5
Girls:
= 3, 4, 4, 4, 6, 7, 8, 10, 10, 15
= 6.5
Thus,
The range is the same for both boys and girls.
The median for boys is 12.5.
The median for girls is 6.5.
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The complete question:
Find the range and median for both boys and girls.
Solve the system of linear equations by substitution.
x=2y+7
3x−2y=3
Answers
First equation
x = 2y + 7
Second equation
3x - 2y = 3
Substitute x with (2y + 7) in the second equation
3x - 2y = 3
3(2y + 7) - 2y = 3
use distributive property
3(2y) + 3(7) - 2y = 3
6y + 21 - 2y = 3
add like terms
6y - 2y + 21 = 3
4y = 3 - 21
4y = -18
y = -18/4
y = -4.5
Substitute y with its value, which is -4.5, in the first equation
x = 2y + 7
x = 2(-4.5) + 7
x = -9 + 7
x = -2
The solution is
(x,y) = (-2, -4.5)
solve the linear system using substitution. SHOW WORK HELP ME PLEASE
Answers
An architect has a scale drawing of an addition that is to be added to a house with a scale of 1 inch : 2 feet. If the drawing is 6 inches by 10 inches, how big is the addition to the house going to be?
Answers
In order for us to solve this problem, we will be needing to form a ratio just like the ones the question provides to us. In case you don't quite understand how to do it, don't fret and watch me explain it. I will also be attaching an image with all the work shown in case you need extra help.
As we know, the scale of the house is 1 inch : 2 feet. First of all, let's balance the unit sizes by converting 2 feet into inches, thus making the problem much easier.
One foot is 12 inches, meaning that two feet should be two times more than 12 inches.
[tex]12(2)=24[/tex]
Great! We can now form the balanced ratio. It is going to be 1 inch : 24 inches. Now, let's form an actual ratio with plugged in unknown variable in order for us to solve for it.
[tex] \frac{1}{24} : \frac{6}{x} [/tex]
According to the ratio, our numerator on the right side is six time bigger than numerator on the left side, meaning that our denominator on the right side is six times bigger than denominator on the left side as well. Keeping this in mind, let's solve for it.
[tex]24(6)=144[/tex]
Awesome! One of the sides is 144 inches. We are left with only one side which is 10 inches on the scale. Let's form the same ratio and solve for it.
[tex] \frac{1}{24} : \frac{10}{x} [/tex]
Just like we did in our last step, let's multiply the left denominator with the right numerator.
[tex]24(10)=240[/tex]
We now know values of two sides, and we can set it as our answer.
Answer:144 by 240 inches is the size of the house.
a number is added to 9. the result is then multiplied by 4 to give a new result of 120. what is the number ?
Answers
A number is added to 9. << Since we don't know the name of the number, we will call it x.
A number is added to 9 = x + 9
Then they say the result is then multiplied by 4 to give a new result of 120.
We need to turn this into an equation.
(x + 9) * 4 = 120
Use the distributive property
(x)(4) + (4)(9) = 120
4x + 36 = 120
Add 36 to both sides
4x + 36 - 36 = 120 - 36
4x = 84
x = 84/4
x = 21
Thus, the number is 21
I hope the details are clear to understand. If you don't understand something, please feel free to leave a comment down bellow...
As always, I am here to help!
Answer:
n=21
Step-by-step explanation:
Ik im late but hopefully it can help other people :)
The equation is :
4(9+n)=120
n+9=120/4
n+9=30
n+9-9=30-9
n=21
Please rate... Thankyou :)
if you take one 10 minute shower a day, how many gallons of water are used
Answers
If you take a 10-minute shower each day, you would use approximately 25 gallons of water.
Explanation:The average person in the U.S. uses approximately 100 gallons of water per day, which includes daily activities such as cooking, washing dishes and clothes, flushing the toilet, and bathing. If you take a 10-minute shower each day, you would use a certain amount of water.
To calculate the amount of water used during a 10-minute shower, you would need to know the flow rate of your showerhead. On average, a showerhead has a flow rate of 2.5 gallons per minute. So, multiplying the flow rate by the duration of the shower gives us:
2.5 gallons/minute * 10 minutes = 25 gallons
Therefore, if you take one 10-minute shower a day, you would use approximately 25 gallons of water.
Number 8 question please answer
Answers
.. 2*(1 1/3 +3) = 2*(4 1/3) = 8 2/3 . . . . feet
Then the lateral area is
.. (6 ft)*(8 2/3 ft) = (48 +4) ft^2 = 52 ft^2
The area of the top is
.. (3 ft)*(1 1/3 ft) = (3 +1) ft^2 = 4 ft^2
The total area Fran wants to paint is
.. total area = lateral area + top area
.. = (52 ft^2) + (4 ft^2) = 56 ft^2
Selection C is appropriate.
Elena always puts 5/12 of the money she makes at work in her savings account. If she made $192 at work, how much money did she put in her savings account?
Answers
=80
her saving is $80
If she made $192 at work. Then the amount of money she puts in her savings account will be $80.
What is division?Division means the separation of something into different parts, sharing of something among different people, places, etc.
Elena always puts 5/12 of the money she makes at work in her savings account. If she made $192 at work.
Then the amount of money she puts in her savings account will be
→ 5/12 x 192
→ 80
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What is 1,289,845 rounded to the nearest ten thousand?
Answers
1,289,845 rounded to the nearest ten thousand is 1,290,000.
Explanation:To round 1,289,845 to the nearest ten thousand, we need to look at the digit in the ten thousandth place, which is the 8 in this case. If the digit is 5 or greater, we round up, and if it is less than 5, we round down. Since the 8 is greater than 5, we round up. To do this, we keep the digit in the ten thousandth place as it is and change all the digits to the right of it to zeros. Therefore, 1,289,845 rounded to the nearest ten thousand is 1,290,000.
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I’m rohmbus ABCD, AB= 14 and AC= 26. Find the area of the rhombus to the nearest tenth.
Answers
we know
In a rhombus ABCD , AC = 26 , AB = 14
the diagonals of a rhombus are perpendicular bisectors of each other
AX = XC = 13. triangle ABX is a right triangle with hypotenuse 14.
From the pythagoras theorem AB² = AX² + BX²
14² = 13² + BX²
196 = 169 + BX²
27 = BX²----- > BX=√27
BX = 5.20
The four triangles formed by construction of the diagonals are all congruent since the diagonals are perpendicular bisectors.
Total area of the rhombus is 4 times of ABX triangle
the answer is the option D) 135.1 units ²
help please really don't understand
Answers
All you have to do is plug the values into the formula:
6^2 + 8^2 = c^2
36 + 64 = c^2
100= c^2
Now find the square root of 100, which is 10. So, the missing measure is 10 inches.
Ryan and his friends flip 4 coins. What is the probability that they will flip 2 heads and 2 tails?
Answers
results in total. That is 24
or 16
Alex is adding square-foot tiles on the floor in his laundry room. If the space he wants to fill is 7 feet long and 6 feet wide, how many square-foot tiles will he need to fill the area?
A) 12 tiles
B) 26 tiles
C) 36 tiles
D) 42 tiles
Answers
you are given that the room is 7 x 6 feet
that is the area is 42 ft^2
A tile is 1ft^2
so you will need 42 tiles for the room
D.) 42 tiles
Hope this helps
please help! what is the value of K
Answers
[tex]g(x)=k*f(x)[/tex]
k * f = g
kf = g
Solve for K, divide both sides by f
kf/f = g/f
K = g/f
I hope this helps!
What is the area of this figure? Drag and drop the appropriate number into the box. A = cm² 108 135 189 318 A shape made up of a square with the length measuring 9 centimeters and a height measuring 9 centimeters. There are two equally sized right triangles attached to the square. The base of each triangle measures 9 centimeters. The height of each triangle measures 12 centimeters. The remaining side of each triangle measures 15 centimeters.
Answers
.. (9 cm)^2 = 81 cm^2.
The two triangles together will have area
.. (9 cm)*(12 cm) = 108 cm^2.
The sum of the areas of those three shapes is
.. 81 cm^2 +108 cm^2 = 189 cm^2
Answer:
the answer is 189
1. Describe how the figures are alike.
2. Describe how the figures are different.
Answers
All figures are in 3-D form. But the base of each polygonal prism is different.
What is Geometry?One of the first areas of mathematics is geometry, along with maths. It is preoccupied with spatial characteristics including the separation, form, size, and relative placement of objects. A geometer is a mathematician who specializes in shape.
A prism is a solid form that is enclosed by plane faces on all of its sides. A prism has two different kinds of faces. Bases refer to identical top and bottom faces. The name "prism" refers to the form of these bases.
All figures are in 3-D form. And all the figures are polygonal prism.
But the base of each polygonal prism is different.
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Darrel loaned his friend $2500 to help him with his business. If his friend pays Darrel back in 1 year with 15% simple interest, how much will he owe Darrel altogether?
Answers
Answer: $2875
Step-by-step explanation:
The formula to calculate the simple interest is given by :-
[tex]S.I.=P\times r\times t[/tex], where P is the principal amount , r is the rate of interest and t is the time period.
Given: Principal amount = $2500
Rate of interest = 15%=0.15
Time period = 1 year
Now, the simple interest gained by Darrel after 1 year will be :-
[tex]S.I.=2500\times 0.15\times 1=\$375[/tex]
Now, the total amount his friend owed altogether= [tex]P+I=2500+375=\$2875[/tex]
A cylinder has a radius of 30 ft and a height of 19 ft. What is the exact surface area of the cylinder?
A.
1200π ft2
B.
1260π ft2
C.
1800π ft2
D.
2940π ft2
Answers
The exact surface area of the cylinder with a radius of 30 ft and height of 19 ft is calculated using the formula 2πr(h + r), resulting in an area of 2940π ft², which matches option D.
To find the exact surface area of a cylinder, we use the formula that states the surface area (SA) is SA = 2πr(h + r), where r is the radius and h is the height of the cylinder. Given that the radius (r) is 30 ft and the height (h) is 19 ft, we plug these values into the formula:
SA = 2π(30)(19 + 30)
SA = 2π30(49)
SA = 60π(49)
SA = 2940π ft²
Therefore, the exact surface area of the cylinder is 2940π square feet, which corresponds to option D.
after painting his porch jamil had a 1/4 can of paint left the radius of the can is 8 cm and the height is 20 cm he wants to put the remaining paint into a smaller can with a radius of 5 cm
what does the height of the smaller can need to be to hold all the paint.
Answers
Answer:
The height of small can need to be 12.8 cm to hold all the paint
Step-by-step explanation:
- Jamil had a 1/4 can of paint left
- The radius of the can is 8 cm and its height is 20 cm
- He wants to put the remaining paint into a smaller can with a
radius of 5 cm
- We need to find the height of the smaller can
- The volume of the paint in the larger can is the same volume of paint
will put in the smaller can
- Lets find the volume of the paint in the larger can
∵ The volume of the paint in the larger can = 1/4 its volume
∵ The can is shaped a cylinder
∵ Volume the cylinder = πr²h, where r is the radius of it and h its height
∵ r = 8 cm and h = 20 cm
∴ The volume of the paint = [tex]\frac{1}{4}\pi (8)^{2}(20)=320\pi[/tex] cm³
- Same amount of paint will put in the smaller can
∵ r = 5 cm and V = 320π cm³
∴ 320π = π(5)²h
- Divide both sides by π
∴ 320 = 25 h
- divide both sides by 25
∴ h = 12.8 cm
* The height of small can need to be 12.8 cm to hold all the paint
The height of the smaller can need to be to hold all the paint will be 12.8 cm.The term height is frequently used to describe someone's or something's height.
What is the height?Height is defined as the vertical distance between an object's top and bottom. It is measured in centimeters, millimeters, meters, and other units.
From the given conditions;
The volume of the paint in the larger can is,[tex]\rm V_L[/tex]
The volume of the paint in the smaller can is,[tex]\rm V_S[/tex]
The volume of the cylinder is, V
The radius of the can is,r= 8 cm
The height is,h=20 cm
The volume of the paint in the larger can is found as;
[tex]\rm V_L = \frac{1}{4} V \\\\ V=\pi r^2 h \\\\ V_L= \frac{1}{4} \pi (8)^2 (20) \\\\ V_L = 320 \pi \ cm^3[/tex]
The volume of the larger can is equal to the volume of the smaller can;
[tex]\rm V_S = V_L \\\\ 320 \ \pi \ cm^3=\pi r^2 h \\\\ \pi \ cm^3=\pi (5)^2 h \\\\ 320=25h \\\\ h =12.8 \ cm[/tex]
Hence the height of the smaller can need to be to hold all the paint will be 12.8 cm.
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