4. triangle FBT is similar to triangle ADQ with a scale factor of 5/3. Complete the table below.
Sides Angles
BF = 15 B = 85
BT = F = 40
FT = 21 T =
AD = 9 A =
DQ = 6 D =
AQ = Q = 55
Answers
Triangle FBT is similar to triangle ADQ with a scale factor of 5/3. AD = 9; BF = 15, DQ = 6; BT = 10, FT = 21; AQ = 12.6
∠F = ∠A = 40°, ∠Q = ∠T = 55°, ∠B = ∠D = 85°
What are similar triangles?Similar triangles are triangles that have the same shape and the ratio of their corresponding sides are in the same proportion. Corresponding angles are equal.
triangle FBT is similar to triangle ADQ with a scale factor of 5/3.
AD = 9; BF = 9 * 5/3 = 15
DQ = 6; BT = 6 * 5/3 = 10
FT = 21; AQ = 21 * 3/5 = 12.6
∠F = ∠A = 40°, ∠Q = ∠T = 55°, ∠B = ∠D = 85°
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How do I use the intermediate value theorem to prove every polynomial of odd degree has at least one real root?
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Answer:
Step-by-step explanation:
Find the measure of the red arc or chord in ⊙C
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Answer: 75
Step-by-step explanation:
The measure of the red arc or chord is 75 degrees
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
From the given figure we observe that ∠ACB is vertical angle of ∠ECD
∠ECD = 75 degrees
∠ECD = ∠ACB as they are vertical angles
∠ACB = 75 degrees
∠ACB is the central angle.
The central angle of an arc is the central angle subtended by the arc. The measure of an arc is the measure of its central angle.
So measure of arc AB is 75 degrees
Hence, the measure of the red arc or chord is 75 degrees
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Help picture below problem 6
Answers
Answer:
g is 37
Step-by-step explanation:
supplementary means two angles that add up to 180°
180-143=37
[tex] \rm \sum_{n = 1}^{ \infty } \frac{( - {1)}^{n + 1} }{n \binom{2n}{n} } \\ [/tex]
Answers
Recall the well-known series
[tex]\displaystyle 2 \arcsin^2(x) = \sum_{n=1}^\infty \frac{(2x)^{2n}}{n^2 \binom{2n}n}[/tex]
Replace x with √x :
[tex]\displaystyle 2 \arcsin^2(\sqrt x) = \sum_{n=1}^\infty \frac{(4x)^n}{n^2 \binom{2n}n}[/tex]
Differentiate both sides:
[tex]\displaystyle -\frac{\arcsin(\sqrt x)}{2\sqrt{x-x^2}} = \sum_{n=1}^\infty \frac{(4x)^n}{n \binom{2n}n}[/tex]
Multiply by 4x :
[tex]\displaystyle -\frac{4x \arcsin(\sqrt x)}{2\sqrt{x-x^2}} = \sum_{n=1}^\infty \frac{(4x)^{n+1}}{n \binom{2n}n}[/tex]
All the series I've mentioned converge for |x| < 1, so we can take x = -1/4 to find the value of the sum we want.
[tex]\displaystyle \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n \binom{2n}n} = -\frac{4 \times \left(-\frac14\right) \arcsin\left(\sqrt{-\frac14}\right)}{2\sqrt{-\frac14-\left(-\frac14\right)^2}} = -\frac{\arcsin\left(\frac i2\right)}{\frac{\sqrt5\,i}2}} = \boxed{\frac2{\sqrt5} \mathrm{arsinh}\left(\frac12\right)}[/tex]
where
[tex]\arcsin\left(\frac i2\right) = z \iff 2\sin(z) = -2i\sinh(iz) = i \implies z = i \, \mathrm{arsinh}\left(\frac12\right)[/tex]
A construction company is building the house shown below. They need to use a scale
of 1 in: 8f (1 inch = 8 feet). They measured the drawing to find that that the height of
the building is 2.5 in.
1.) Explain to the construction workers how they would use this information to
calculate the height of the final building.
2.) What is the height of the final building?
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Answers
Using proportions, we have that:
The height of the building is found using a rule of three.The height is of 20 feet.What is a proportion?
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The scale is of 1 inch = 8 feet. What is the height for 2.5 inches? The rule of three is given by:
1 inch - 8 feet.
2.5 inches - x feet
Applying cross multiplication, the height in feet of the final building is given by:
x = 8 x 2.5 = 20 feet.
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The height of the building is calculated by representing 1 inch as 8 feet. The final building has a height of 20 feet.
What is scaling?Scaling is the increase or decrease in the height of an object by a scale factor k.
Given that the scale used is:
1 inch = 8 feet. Hence:
Since the height of the building is 2.5 in, hence:
Height of the final building = 2.5 in * 8 ft per 1 in = 20 feet
The height of the final building is 20 feet.
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The side of the clip on a clip board appears to be a right triangle. The
leg lengths are 2 millimeters and 2.1 millimeters and the hypotenuse
is 2.9 millimeters. Is the side of the clip a right triangle?
Answers
Answer:
Yes, it is a right triangle.
Step-by-step explanation:
Answer:
Yes, this is a right triangle.
Step-by-step explanation:
For this, you would use the Pythagorean theorem a^2 + b^2=c^2
Here we have 2^2+2.1^2=2.9^2
So we must check to see if that checks out. What we find is that both sides are equal to 8.41 which means we have a right triangle.
1. Which unit multiplier should be used to change feet to inches?
A 1ft/12in
B 12in/1ft
C 12ft/1in
D 1in/12ft
E 12in/12in
2. Which unit multiplier should be used to change quarts to gallons?
A 8 qt/ 1 gal
B 1 gal/ 8 qt
C 1 gal/ 4 qt
D 2 qt/4 qt
3. Which unit multiplier should be used to change feet to yards?
A 1 yd/ 36 inch
B 3ft/3ft
C 1 yd/ 3 ft
D 1 yd/ 2 feet
4. When using unit multipliers, the name of the measure in the numerator should be the same as:
a.
the name in the denominator
b.
the name of the given amount
c.
the name of the unit in the desired answer
d.
the larger of the units of measure given
e.
the smaller of the units of measure given
5. The term used to multiply by when converting measures should always be:
Select one:
a.
less than the given measure
b.
greater than the given measure
c.
greater than one
d.
less than one
e.
equal to one
6. How many unit multipliers are required to change square feet to square inches?
Select one:
a.
1
b.
2
c.
3
d.
12
e.
144
7. How many unit multipliers are required to change cubic yards to cubic feet?
Select one:
a.
1
b.
2
c.
3
d.
9
e.
12
8. Sam stacked a pile of wood that was four feet deep, four feet high, and 16 feet long. How many cords of wood does he have?
Answers
The required unit multipliers that should be used to change feet to inches is: 12 in/1 ft
What is Unit Multiplier?Unit multipliers are used to convert one unit of measurement to another by the multiplication of the measure we're converting by a unit multiplier that cancels out the other units, retaining only the preferred choice or desired answer.
From the given information:
The required unit multiplier that should be used to change feet to inches is: 12in/ 1ftThe required unit multiplier that should be used to change quarts to gallons is: 1gal/ 8qtThe required unit multiplier that should be used to change quarts to gallons is: 1yd/3 ftHowever, it is important to note that when using unit multipliers, the name of the measure in the numerator should be the same as the name of the unit in the desired answer.
The term used to multiply by when converting measures should always be less than the given measure.
The required unit multiplier to convert square feet to square inches is 144The required unit multiplier to convert cubic yard to cubic feet is 27The cord of wood can be determined by multiplying the length, depth and height of the wood together, then dividing the answer but 128.
Thus, the cord of the wood = (4 ft × 4 ft × 16 ft)/128
The cord of the wood = 2 cords.
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The sphere below has a radius of 25 cm.
O
25 cm
Work out the volume of the sphere.
Give your answer correct to 1 decimal place.
Volume of sphere= tr3
cm3
Answers
Answer:
65449.8 cm3
Step-by-step explanation:
We start with the volume formula for a sphere: 4/3 πr3
We start with subbing in 25 to r, then we cube 25, which is equal to 15625.
We multiply 4/3 and pi. And lastly we multiply what we got by 15625 and either round the answer or fphaving fixed your calculator.
Regis leans a 10-foot ladder against a wall. The base of the ladder makes a 65 angle with the ground.
(a)
What is the distance, In feet, from the base of the ladder to the base of the wall? Round to the nearest tenth of a foot.
(b) Regis needs to move the ladder so that it reaches a window 9.6 feet above the ground.
How many feet closer to the building does he need to move the base of the ladder?
Answers
The distance, In feet, from the base of the ladder to the base of the wall is 4.2 ft.
He needs to move the ladder 0.1 ft closer to the base of the building.
The situation forms a right angle triangle.
Right angle triangleRight angle triangle has one of its angles as 90 degrees. The sides and angle can be found using trigonometric ratios.
The length of the ladder is the hypotenuse of the triangle formed. Therefore, the distance, In feet, from the base of the ladder to the base of the wall can be calculated as follows;
cos 65° = adjacent / hypotenuse
cos 65° = d / 10
d = 10 × 0.42261826174
d = 4.22618261741
d = 4.2 ft
She needs to move the ladder so it reached a window 9.6 feet above the ground. Therefore, the distance from the base of the ladder and the wall is as follows;
cos 65 = d / 9.6
d = 9.6 × 0.42261826174
d = 4.05696
d = 4.1
Therefore, he needs to move the ladder 0.1 ft closer to the building.
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Examine the equation and solution method shown below. Indentify the error and then solve the equation using a valid solution method.
1. Find and explain the error in the solution method.
2. Solve the equation 3(3x+6+x)=1 using a valid solution method.
3. Explain each step in your solution method. Why is your method valid?
Pls Help. 100 points
Answers
3 ( 3x + 6 + x ) = 1
Step 1, apply distributive method.
9x + 18 + 3x = 1
Step 2, simplify the following
12x + 18 = 1
Step 3, Change side
12x = -17
Final answer
x = -17/12
The error/mistake was in step 2 where [ 9x +3x = 12x ]
Recheck the answer
3 ( 3x + 6 + x ) = 1
3 ( 3(-17/12) + 6 + -17/12 ) = 1
1 = 1
Hence proved our solution is correct.
Answer:
Question 1
The error is in step 2. They have subtracted [tex]3x[/tex] from the left side of the equation, yet only subtracted 3 from the right side.
Questions 2 & 3
Solve:
[tex]3(3x + 6 + x) = 1[/tex]
Apply the distributive law [tex]a(b + c) = ab + ac[/tex] :
[tex]\implies 9x + 18 + 3x = 1[/tex]
Collect and combine like terms:
[tex]\implies 9x + 3x+ 18 = 1[/tex]
[tex]\implies 12x + 18 = 1[/tex]
Subtract 18 from both sides:
[tex]\implies 12x + 18 - 18 = 1 - 18[/tex]
[tex]\implies 12x = -17[/tex]
Divide both sides by 12:
[tex]\implies \dfrac{12x}{12}=-\dfrac{17}{12}[/tex]
[tex]\implies x=-\dfrac{17}{12}[/tex]
......................................
Answers
Answer:
D. f(x) = x - 4
Step-by-step explanation:
If you plug in the x values for the expression x - 4:
3 - 4 = -1
4 - 4 = 0
5 - 4 = 1
6 - 4 = 2
This means that the function rule is f(x) = x - 4
Hope this helps :)
a rectangular garden is 1.25 meters wide and 3.4 meters long. what is the area of the garden?
Answers
Area = length x width
Area = 1.25 x 3.4 = 4.25 square meters
Julie's grades for this term test are 85' 88' and 97. In addition for the three tests that Julie already had, there will b just one more test. Julie needs to earn at least ________ point for the last test to get no less than A for the term. "A" means the average of 93 or more.
Answers
The score Julia has to have on her last test to have an A for the term is 102.
What is the least score?The first step is to determine the sum of her scores on the first three tests: 85 + 88 + 97 = 270
Now determine the score on the last test that would give an average of 93
(270 + x)/ 4 = 93
270 + x = 93 x 4
372 - 270 = x
x = 102
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the table shows the letter grades in science class for a random sample of 300 sixth grade students. Find the relative frequency for each letter grade to complete the table. Use pencil and paper. What additional information does the relative frequency give that the frequency doesn't? Explain.
Answers
Answer:
0.12,0.16,0.37,0.2,0.15
Step-by-step explanation:
A. 36 divided by 300 = 0.12
B. 49 divided by 300 = 0.16
C. 111 divided by 300 = 0.37
D. 60 divided by 300 = 0.2
F. 44 divided by 300 = 0.15
Two cars, one traveling north and
one traveling east leave a city.
The car traveling north goes X
miles while the car traveling east
has gone ×+4 miles. If the
distance between the cars at this
moment is 20 miles find the
distance the car traveling east has
traveled.
Answers
The sides of a fair number cube are labeled 1, 2, 3, 4, 5, and 6. What is the theoretical probability that the number cube will land with the number 5 facing up?
Answers
Answer:
Probability that the number cube will land with the number 5 facing up
=5/6
Hope this helps, just used my mind
Step-by-step explanation:
Please mark me brainliest if correct
3 1/6 + 8 2/9 - 1 1/2 =?
Answers
Answer:
9 8/9
Step-by-step explanation:
Chicago is home to 2.706 million people and the city sees approximately 55 million visitors each year. China has a population of 1.393 billion. If their visitors were proportional to Chicago, how many visitors could China expect? Write your answer in scientific notation rounded to two decimal places. Provide your answer below: x 10^ visitors
Answers
China could expect a quantity of visitors of 8.512 × 10⁶ in Chicago.
How to apply direct proportions
A direct proportion is a direct relationship between two variables, which in this case is represented between the quantity of tourists in the city of Chicago and the population of the country of origin.
Let suppose the existence of direct proportionality and world has a population of 9000 million people, the quantity of Chinese visitors in the city of Chicago is determined by the following formula:
x = (1.393 × 10⁹ / 9 × 10⁹) × 55 × 10⁶
x = 8.512 × 10⁶
China could expect a quantity of visitors of 8.512 × 10⁶ in Chicago. [tex]\blacksquare[/tex]
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A production process produces 2.5% defective parts. A sample of five parts from the production process is selected. What is the probability that the sample contains exactly two defective parts?
Answers
Using the binomial distribution, it is found that there is a 0.0058 = 0.58% probability that the sample contains exactly two defective parts.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, we want P(X = 2) with p = 0.025, n = 5, hence:
[tex]P(X = 2) = C_{5,2}.(0.025)^{2}.(0.975)^{3} = 0.0058[/tex]
There is a 0.0058 = 0.58% probability that the sample contains exactly two defective parts.
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find rate
a)the interest of Re.1 of 1 month is 1 paisa.
b)the interest of re.1 of 1 month is 2 paisa
Answers
Step-by-step explanation:
A.) Correct Answer: 12%
Given , Principle = ₹ 1 , Time = 1 month = ( 1 / 12 ) year and SI = 1 paisa = ₹ ( 1 / 100 )
As we know that ,
Rate =SI × 100Principal × Time
Rate =(1 ÷ 100) × 100= 12% p.a.1 × (1 ÷ 12)
B.) Correct Answer:
Answer:
See below ↓
Step-by-step explanation:
a) I = Prt
r = I/Ptr = 0.01/1x(1/12)r = 0.12r = 12%b)
r = I/Ptr = 0.02/1x(1/12)r = 0.24r = 24%Can someone please help me with this question.
Answers
Answer:
I think option B is the correct answer
I think it will help you.
Answer:
C
Step-by-step explanation:
Hope this helps
I’m not sure the steps to figure out the problem. X = 2 to x =4
Answers
Answer:
you have to put the Y in the formula or make a comparison
You randomly choose one of the morales.Without replacing the first marble, you choose a second marble. What is the probability of choosing red and then green?
P(Red and green)=1/4*1/4=1/16
(I really need help)
Answers
P(A and B) = P(A) x P(B after A)
Choose the first marble
The total number of hypothetical marbles are, hypothetically speaking, 4 on a hypothetical basis, and there is one red marble.
P(red)=1/4
Choose the second marble
Without hypothetically replacing the hypothetical first marble, you choose the hypothetical marble, hypothetically speaking. So, the total hypothetical number of marbles are, hypothetically, 3, and there is, hypothetically, one green marble.
P(green) = 1/3
The probability of choosing red and then, hypothetically, green is:
P(red and green) = P(red) x P(green)
=1/4 x 1/3
= 1/12
P(red and green) is hypothetically equal to 1/12 on a hypothetical account.
Final hypothetical answer: 1/12
can someone pls help me with this. WILL MARK BRAINLIEST
Answers
Answer:
I would say B. 6 inches, 8 inches, 10 inches.
Step-by-step explanation:
They are all 2 times difference.
3 · 2 = 6
4 · 2 = 8
5 · 2 = 10
A gym has 12 exercise stations, including 4 weightlifting benches.
What is the probability that a randomly selected exercise station will be a weightlifting bench?
Answers
probability : 1/3
Explanation:
total people : 12weightlifting benches : 4probability = selected/total
Here,
probability = 4/12 = 1/3 = 0.33E=Weightlifting bench
So
P(E)=4/12P(E)=1/3Help help help help math
Answers
Answer:
(-8, 12)
Step-by-step explanation:
Dilation of point (-4, 6) about point (0, 0)
Scale factor = 2
Image coordinate:
(-8, 12)
hope this helps and is right!! p.s. i really need brainliest :)
Find the area of the triangle.
Answers
Answer:
14 m²
Step-by-step explanation:
14m² is ur answer
If u need solution do let me know in the comments
What is the value of x in the equation –2.4x = 8.4?
Answers
Answer:
x= 3.5
Step-by-step explanation:
2.4 x= 8.4
x= 8.4 /2.4
x= 3.5
Answer:
X= -3.5
Step-by-step explanation:
You are trying to find what x is, and x is being multiplied with -2.4. The easiest way to find the answer is to divide 8.4 by -2.4. This way, you will get your answer of -3.5. Because two negatives make a positive when you multiply, 8.4 is not negative.
How I solved this.
-2.4x = 8.4
8.4=total
-2.4= Needs to be multiplied with x
x=?
8.4/-2.4=-3.5
Check your work:
-2.4(-3.5)=8.4
Final answer:
x= -3.5
I hope this helps!
-No one
Modern Electronics offers a one-year monthly installment plan for a big screen TV. The payment for the first month is 882, and then it increases by 4% each month for the rest of the year. Which expression can be used to find the total amount paid in the first 12 months?
Answers
✿————✦————✿
Answer: A
[tex]62=\frac{12(1.04^{12}-1) }{1.04-1}[/tex]
✿————✦————✿
Rewrite the expression without using a negative exponent.
1/3n^-4
Answers
Answer:n^4/3
Step-by-step explanation: