Answers
f(3) = 3375
The answer is 3375
Related Questions
what is the product? (9t-4)(-9-4)
Answers
Answer: The product of [tex](9t-4)(-9-4)[/tex] is -117t+52.
Explanation:
The given expression is,
[tex](9t-4)(-9-4)[/tex]
Simplify the above expression.
[tex](9t-4)(-13)[/tex]
Use distributive property t simplify the above expression.
[tex](9t-4)(-13)=9t\times (-13)-4\times(-13)[/tex]
[tex](9t-4)(-13)=117t+52[/tex]
Therefore, the product of [tex](9t-4)(-9-4)[/tex] is -117t+52.
1. Given a || b , c || d, and . Find the measure of angles 1 through 12 in the complex figure.
Answers
To solve all of the angles that are listed you are going to have to set up and solve several equation involving supplementary angles and angles around traversals around parallel lines.
For example, you could set up the equation:
3 + 4 + 69 = 180
Also, angle 9 is 116 because they are alternate interior angles.
Also, angle 11 is 116 because the are corresponding angles.
Also, angle k can be solved with the equation: k + 12 + 90 = 180.
Good luck
In summary:
- Angle 1 = Angle 2 = Angle 3 = Angle 4 = 69°
- Angle 5 = Angle 6 = Angle 7 = Angle 8 = 116°
- Angle 9 = Angle 10 = 69°
- Angle 11 = Angle 12 = 116°
Let's analyze the complex figure with parallel lines and transversals. We have two parallel lines, a and b, intersected by two transversals. I'll break down the problem step by step:
1. Angle 1: This angle is formed by the intersection of a and the transversal. It is an **alternate interior angle** with the angle measuring 69°. Therefore, **Angle 1 = 69°**.
2. **Angle 2**: It is also an alternate interior angle with the same measure as **Angle 1**. Hence, **Angle 2 = 69°**.
3. **Angle 3**: This angle is formed by the intersection of **b** and the transversal. It is a **corresponding angle** to **Angle 1**. Therefore, **Angle 3 = 69°**.
4. **Angle 4**: It is a corresponding angle to **Angle 2**. Thus, **Angle 4 = 69°**.
5. **Angle 5**: This angle is formed by the intersection of **c** and the transversal. It is an **alternate interior angle** with the angle measuring **116°**¹. Therefore, **Angle 5 = 116°**.
6. **Angle 6**: It is also an alternate interior angle with the same measure as **Angle 5**. Hence, **Angle 6 = 116°**.
7. **Angle 7**: This angle is formed by the intersection of **d** and the transversal. It is a **corresponding angle** to **Angle 5**. Therefore, **Angle 7 = 116°**.
8. Angle 8: It is a corresponding angle to Angle 6. Thus, Angle 8 = 116°.
9. Angle 9: It is a vertical angle to Angle 1. Therefore Angle 9 = 69°.
10. Angle 10: It is a vertical angle to Angle 2. Thus Angle 10 = 69°.
11. Angle 11: It is a vertical angle to Angle 5. Therefore, Angle 11 = 116°.
12. Angle 12: It is a vertical angle to Angle 6. Thus, Angle 12 = 116°.
This is really confusing... making my head hurt. I don't understand it AT ALL. If I get this one wrong, and all the other three like this, I'm gonna fail my test.
Can you figure out number 8 please and show how you got it?
Answers
You're working with a geometric problem where the probability of success is constant in each trial. This is related to the situation where you repeatedly ask students if they live within a five-mile radius. The problems you've mentioned seem to involve figuring out specifics related to degrees and interpreting figures.
Explanation:It sounds like you're dealing with a geometric problem. Geometric problems often involve situations where the probability of success or failure stays constant across trials. For example, you inquire if a person lives within five miles of you - the probability is fixed, regardless of the number of people you ask.
Let's decipher it step by step. Firstly, visualize each instance (trial) as the asking of a question to a student and consider success as the event where the student lives within five miles. Probability of success then stays the same every time you ask.
In problem 91, it's important to understand the degrees involved. The first part mentions 88.6°. Without the full problem, it's hard to give a direct answer here, but angles often play a part in geometry and trigonometry problems, it could be related to that. As for the figures mentioned (Car X, the hash marks) they would likely be visible on a diagram accompanying your problem and would inform the solution.
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What was the original price if:
a
after increasing by 30% it became $520?
Answers
130% x = 520 Change a % to a decimal
(130/100) x = 520
1.3 x = 520 Divide by 1.3
x =520 / 1.3
x = 400
So the original cost of the item was 400 dollars.
Answer:
Original price was $400.
Step-by-step explanation:
Let the original price = x dollars.
It is given that the new price is obtained by increasing the original price by 30% i.e. 0.3
As, the new price is $520.
So, we have the relation,
[tex]x+0.03x=520[/tex]
i.e. [tex]1.3x=520[/tex]
i.e. [tex]x=\frac{520}{1.3}[/tex]
i.e. x = 400
Hence, the original price was $400.
please help. i get two diff ans.
If the interest rate is 3% and a total of $4,370.91 will be paid to you at the end of 3 years, what is the present value of that sum? A) $3900, B) $3947 C) $3,977.40 D) $4000,
Answers
A person at ground level measures the angle of elevation to the top of a building to be 74°. If at this point the person is 34 feet away from the base of the building, then how tall is the building?
Please round to the tenths place.
Please show work/steps and provide units with your answer.
Answers
Mark a line going from the base of the building to the person 34 feet.
Draw another line from the person to the top of the building. Label the angle between the two lines as 74o
Tan(74) = o / a
Tan(74) = o/34
o = 34*Tan (74)
o = 34 * 3.49
o = 118.6
The building is 118.6 feet tall.
Jack just opened a checking account at the bank. Within the first month, he deposited three checks for $34.98, $51.02, and $51.22. He withdrew $3.23 for new pencils, $4.22 for cards, and $9.79 for movies from his account in the same month.
Order the rational numbers from least to greatest and explain your reasoning.
At the beginning of the month Jack’s balance was $98. What was his balance at the end of the
month after all of his deposits and withdrawals? Show your work, no credit will be given for just an
answer.
Answers
34.98
51.02
51.22
Total income = 137.22 $
Now, let's find the amount of expenses:
3.23
4.22
9.79
Total expenses = $ 17.24
The balance at the end of the month is:
Initial amount + total income-total expenses
Substituting:
98 + 137.22-17.24 = 217.98 $
Answer:
his balance at the end of the month after all of his deposits and withdrawals is:
$ 217.98
The formula for the area of a triangle is A = 1/2bh, where b is the length of the base and h is the height. The equation solved for h is h =2a/b The formula for the area of a triangle is A = bh, where b is the length of the base and h is the height. The equation solved for h is h = . Find the height of a triangle that has an area of 30 square units and a base measuring
12 units. 3 units 5 units 8 units 9 units
Answers
the answer is 5 units i know this because i just took a test with this question
Using a directrix of y = −2 and a focus of (2, 6), what quadratic function is created?
Answers
directrix y=-2
focus (2,6)
y=1/(2(6-(-2)) * (x-2)²+(6+(-2))/2
or y=(x-2)²/16+2
You are paying 11% interest on a credit card balance of $2,000. Which of the following best estimates the interest you are paying each month?
a) $11.00
b) $13.33
c) $15.33
d) $18.33
Will fan and medal,
Answers
$220/12 (months in a year)=$18.33
d) $18.33
Help: Scientists think the _____ is a solid iron with a layer of liquid iron surrounding it.
1. Outer core
2. Inner core
3. Mantle
4. Crust,
Answers
A is an acute angle in a right triangle, Given that Sin A= 7/25, what is the ratio for Cos A? Enter your answer in the box as a fraction in simplest form.
Answers
7² + x² = 25²
x² = 25² - 7²
x² = 576
x = 24
The adjacent side of the triangle is 24
Given that sin A = [tex] \frac{7}{25} [/tex]
Since sin A = [tex] \frac{o}{h} [/tex]
We can conclude that o = 7 and h = 25
cos A = [tex] \frac{a}{h} [/tex]
cos A = [tex] \frac{24}{25} [/tex]
[tex] \sin A = \dfrac{7}{25} = \dfrac{opp}{hyp} [/tex]
[tex] a^2 + b^2 = c^2 [/tex]
[tex] a^2 + 7^2 = 25^2 [/tex]
[tex] a^2 = 625 - 49 [/tex]
[tex] a = \sqrt{576} [/tex]
[tex] a = 24 [/tex]
[tex] adj = a = 24 [/tex]
[tex] \cos A = \dfrac{adj}{hyp} [/tex]
[tex] \cos A = \dfrac{24}{25} [/tex]
Find the volume of a cylinder with a radius of 5 cm and a height of 10 cm. Then, find the volume of the cylinder if the radius is increased to 10 cm. Leave your answers in term of pi.
Answers
[tex]v= \pi r^{2} h[/tex]
where v = volume of cylinder, r = radius, and h = height of cylinder.
1) Radius = 5 cm, height = 10 cm. Plug these values into the equation.
[tex]v= \pi 5^{2} (10) = 250 \pi [/tex]
2) Radius = 10 cm, height = 10 cm.
[tex]v= \pi 10^{2} (10) = 1000 \pi[/tex]
Volume of cylinder is 250πcm³ and volume of the new cylinder is 1000πcm³.
How to determine the volume of the cylinder?The volume of the cylinder can be determined by multiplying area of base with height of the cylinder.
V=πr²*h
where r is the radius of base of the cylinder and h is the height of the cylinder.
following this above formula in given problem,
radius of the base of the cylinder= 5cm
height of the cylinder=10cm
volume= V=πr²*h= π5²*10= 250π cm³
Now the radius of the cylinder is increased to 10cm.
now r=10cm
height of the cylinder=10cm
volume= V=πr²*h= π10²*10= 1000π cm³
Therefore volume of cylinder is 250πcm³ and volume of the new cylinder is 1000πcm³.
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Consider the incomplete paragraph proof. Given: Isosceles right triangle XYZ (45°–45°–90° triangle) Prove: In a 45°–45°–90° triangle, the hypotenuse is times the length of each leg. Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem, a2 + b2 = c2, which in this isosceles triangle becomes a2 + a2 = c2. By combining like terms, 2a2 = c2. Which final step will prove that the length of the hypotenuse, c, is times the length of each leg? Substitute values for a and c into the original Pythagorean theorem equation. Divide both sides of the equation by two, then determine the principal square root of both sides of the equation. Determine the principal square root of both sides of the equation. Divide both sides of the equation by 2.
Answers
2a^2= c^2
If we have square root
√2a^2=√c^2
a√2= c
Answer:
Step-by-step explanation:
In a 45°–45°–90° triangle, the hypotenuse is times the length of each leg. Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem that is:
[tex]a^{2}+b^{2}=c^{2}[/tex], which in this isosceles triangle becomes [tex]a^{2}+a^{2}=c^{2}[/tex] as a=b in isosceles triangle.
By combining the like terms, [tex]2a^{2}=c^{2}[/tex]
Now, we will determine the principal square root of both sides of the equation,
[tex]c=\sqrt{2}a[/tex] (since a is positive)
Divide both sides of the equation by 2, we get
[tex]\frac{c}{2}=\frac{\sqrt{2}a}{2}[/tex]
[tex]\frac{c}{2}=\frac{a}{\sqrt{2}}[/tex]
[tex]c=\frac{2a}{\sqrt{2}}[/tex]
[tex]c=\sqrt{2}a[/tex]
Now, as a=b, then [tex]c=\sqrt{2}b[/tex]
Select the type of equations.
consistent
equivalent
inconsistent
Answers
simplify: 27k^5m^8/(4k^3)(9m^2)
Answers
In your notebook, set up the following addition using a vertical format and find the sum of the given polynomials.
7b + 3, -4b + 5 and -3+2
A.) 10b + 2
B.) 10
C.) 0
D.) b - 8
Please explain.
Answers
Selection B properly describes the sum.
Answer:
Terms containing b are added; terms not containing b are added. The sum of the b terms is 0, because 7-4-3 = 0. That leaves only the constant 3+5+2=10.
Selection B properly describes the sum.
Step-by-step explanation:
Find the area of a parallelogram with a height 15 cm and a base of 18 and 2/3 cm
Answers
The formula for area of a parallelogram is [tex]A = bh[/tex], where [tex]b[/tex] is the base and [tex]h[/tex] is the height.
You're given the values of both the base and the height, so you can just plug these values into the formula for area. It will be easier to multiply if we convert the mixed number to an improper fraction first, so I'll do that.
[tex]18 \frac{2}{3} = \frac{56}{3} [/tex]
[tex]A = bh[/tex]
[tex]A = \frac{56}{3} *15[/tex]
[tex]A= \frac{56}{3} * \frac{15}{1} [/tex]
[tex]A= \frac{840}{3} [/tex]
[tex]A=280[/tex]
Answer:
The area of the parallelogram is 280 cm².
What would a monthly payment be on a purchase of $12000 car at 4.9% for 5 years?
Answers
Answer: it's 225.41 but your answer helped!
Step-by-step explanation:
The monthly payment will be $249
Firstly, we will calculate the simple interest which will be:
= PRT/100
where,
P = principal = $12000
R = rate = 4.9%
T = time = 5 years
Simple Interest = PRT/100
= ($12000 × 4.9 × 5)/100
= $294000/100
= $2940
Then the total amount to be repaid will be: = Principal + Interest
= $12000 + $2940
= $14940
We'll convert 5 years to months and this will be: = (5 × 12) = 60 months.
The monthly payment will then be:
= $14940/60
= $249
In conclusion, the monthly payment will be $249
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Find the amount paid for the loan.
$2400 at 10.5% for 5 years
Answers
Final answer:
$3,919.24
Explanation:
To calculate the total amount paid for a loan of $2,400 at an interest rate of 10.5% over 5 years, we will assume the interest compounds annually for simplicity. The formula to find the future value of a loan including interest is P(1 + r)^n, where P is the principal amount ($2,400), r is the annual interest rate (10.5% or 0.105), and n is the number of years (5).
Plugging the numbers into the formula gives us $2,400(1 + 0.105)^5. Calculating this gives us approximately $3,919.24. Therefore, the total amount paid for the loan over 5 years would be $3,919.24.
To find the amount paid on a $2400 loan at 10.5% interest for 5 years, calculate the simple interest and add it to the principal. The total interest is $1260, bringing the total repayment amount to $3660 over 5 years.
To find the amount paid for the loan of $2400 at 10.5% interest for 5 years, one would typically use the formula for the compound interest or an installment payment plan depending on whether the loan is paid off in a lump sum at the end of the term or through regular payments over the term. However, you have not specified the method of repayment (lump sum or installments), so let's consider a simple interest scenario which is often used for short-term loans.
The simple interest can be calculated as:
I = PRT
Where:
I = Interest
P = Principal amount ($2400)
R = Annual interest rate (10.5% or 0.105 in decimal)
T = Time in years (5)
Using the formula:
I = $2400 × 0.105 × 5 = $1260
Therefore, the total interest paid over 5 years is $1260. To find the total amount paid for the loan, add the interest to the principal:
Total Amount Paid = Principal + Interest
Total Amount Paid = $2400 + $1260 = $3660
The borrower would have to pay a total of $3660 after 5 years.
A recipe for punch says to use 4 1/2 of lemonade for each cup of ginger ale. If you use 1 2/5 cups of ginger ale, how much lemonade should you use?
Answers
Hi guys can you help me factor these two equations?
5x^2-13x-6
4x^4 – 28x^3 + 48x^2
please show your work on both of them, and thank you so much!
(Edit I have to repost this question bc i really need it answered. I'm offering more points now!
Answers
Not Factored: (5x^2 - 13x - 6)
Factored: (5x + 2 )(x - 3)
There is no real "work" to be shown for this, you can see that
1) Seperating 5x^2 into 5x and x will get you the equation in the form:
(5x ) (x ) = 5x^2 +
2) To complete this factor you need to guess which two numbers will add together to give you - 13x and multiply to form -6 (from the original unfactored equation). The numbers that will do this are 2 and 3
3) You can plug in negative or positives of those numbers to make sure they give you the exact results you need.
For example testing -2 and 3 you will get: (5x - 2) (x + 3 ) = 5(x^2) - 2x + 15x - 6 = 5x^2 +13x - 6. This is NOT the same as the unfactored equation. So you know -2 and 3 is the wrong choice. Choosing 2 and -3 will give you the answer instead.
As i said, there's no actual "work" to show this, you have to make guesses and try to factor it.
-------------------------------------------------------------------------------------------------
Problem # 2
Not Factored: 4x^4 - 28x^3 + 48x^2
Factored: 4x^2 (x^2 - 7x + 12) =
4x^2 (x - 3) (x - 4)
To solve this, you factor out the 4x^2 from the entire equation. Then you can further factor the quadratic equation by seperating x^2 into (x )(x ) and guessing for which numbers will add to -7x and multiply to 12
barb is making a bead necklace. she strings 1 white bead, then 3 blue beaads, then 1 white bead, and so on. write the numbers for the first eight beads that are white. what is a rule for the pattern.,
Answers
(-6)^-12(-6)^5(-6)^2
Answers
if your simplifying your answer is the same.
if your multiplying your answer is also the same.
hope i helped :D
Arrange the summation expressions in increasing order of their values.
Answers
[tex]\sum_{i=1}^{4}4(5)^{i-1} = (4(5)^{1-1}) + (4(5)^{2-1}) + (4(5)^{3-1}) + (4(5)^{4-1})[/tex]
[tex]=4+20+100+500 = 624 [/tex]
[tex]\sum_{i=1}^{5}3(4)^{i-1} = (3(4)^{1-1}) + (3(4)^{2-1}) + (3(4)^{3-1}) + (3(4)^{4-1}) + (3(4)^{5-1})[/tex]
[tex]=3+12+48+192+768=1023[/tex]
[tex]\sum_{i=1}^{2}5(6)^{i-1} = (5(6)^{1-1}) + (5(6)^{2-1})[/tex]
[tex]=5+30=35[/tex]
[tex]\sum_{i=1}^{4}5^{i-1} = (5^{1-1})+(5^{2-1})+(5^{3-1})+(5^{4-1}) [/tex]
[tex]=1 + 5+ 25+125 = 156[/tex]
So, our totals are: 624, 1023, 35, and 156. So clearly, 1023 > 624 > 156 > 35. W can write it as (your answer):
[tex]\sum_{i=1}^{2}5(6)^{i-1} <\sum_{i=1}^{4}5^{i-1} <\sum_{i=1}^{4}4(5)^{i-1} < \sum_{i=1}^{5}3(4)^{i-1} [/tex]
Hope this helps! If anything is confusing, you can always DM me.
∑ 4 * 5^(i-1) = 4 + 20 + 100 + 500 = 624
∑ 3 * 4^(i-1) = 3 + 12 + 48 + 192 + 768 = 1,023
∑ 5* 6^(i-1) = 5 + 30 = 35
∑ 5^(i-1) = 1 + 5 + 25 + 125 = 156
Answer:
∑ (i=1, 2) 5 * 6^(i-1) < ∑ (i=1, 4) 5^(i-1) < ∑ (i=1, 4) 4 * 5^(i-1) <
< ∑ (i=1, 5) 3 * 4^(i-1)
What is the area of a regular hexagon with a side length of 4 m? Enter your answer in the box. Round only your final answer to the nearest hundredth.
Answers
A= a^2 (3√3)/2
we replace a with 4
A=41.57
The area of a regular hexagon with a side of 4m is 24√3.
Side of the regular hexagon = 4m
What is a regular hexagon?A Regular hexagon is a polygon with 6 equal sides.
We know that a regular hexagon with a side p comprises 6 equilateral triangles with a side p.
So, the area of a regular hexagon with side p= area of 6 equilateral triangles with side p.
So, the area of a regular hexagon with side p = [tex]6*\frac{\sqrt{3} }{4} p^{2}[/tex]
The area of a regular hexagon with a side of 4m = [tex]6*\frac{\sqrt{3} }{4} 4^{2}[/tex]
The area of a regular hexagon with a side of 4m =24√3.
Therefore, The area of a regular hexagon with a side of 4m is 24√3.
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Which of these denominations in no longer made in the United States?
A. $1000
B. $50
C. $2
D. $100
Answers
Answer:
$1000
Step-by-step explanation:
A delivery truck is transporting boxes of two sizes: large and small. the combined weight of a large box and a small box is 95 pounds. the truck is transporting 50 large boxes and 65 small boxes. if the truck is carrying a total of 5275 pounds in boxes, how much does each type of box weigh?
Answers
Final answer:
By setting up a system of linear equations from the given conditions, we can determine that a large box weighs 60 pounds, and a small box weighs 35 pounds.
Explanation:
To solve the problem involving the weights of large and small boxes being transported by a delivery truck, we can set up a system of linear equations. Let L represent the weight of a large box and S represent the weight of a small box. We know from the problem statement the following:
A large box plus a small box weighs 95 pounds: L + S = 95
Total weight of all boxes: 50L + 65S = 5275
Now we can solve this system of equations by substitution or elimination. If we solve the first equation for L, we get L = 95 - S. Substituting this into the second equation gives us:
50(95 - S) + 65S = 5275
Expanding and simplifying the equation, we get:
4750 - 50S + 65S = 5275
15S = 5275 - 4750
15S = 525
S = 35
Now that we have the weight of the small box, we can substitute it back into the first equation to find the weight of the large box:
L + 35 = 95
L = 60
Therefore, a large box weighs 60 pounds, and a small box weighs 35 pounds.
the function f(x)=2^x and g(x)=f(x)+k. if k=2, what can be concluded about the graph?
the graph of g(x) is shifted vertically...
2 units to the left of the graph of f(x)...
Answers
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units up.
To graph y = f (x) -k, move the graph of k units down.
We have then:
f (x) = 2 ^ x
g (x) = f (x) + k
if k = 2
then,
the graph of g (x) is shifted vertically 2 units up
Answer:
the graph of g (x) is shifted vertically 2 units up
Answer:
Its shifted verticlly 2 and to the left 2.
Step-by-step explanation:
Its verticlly because when it says 2^x its going up if it said -2^x it would go down.
It goes left because it is 2^x=? so if you put it on the other side its negative which makes it to the left.
sav meh pl0x ty fam
Mean: 42
Median: 38
Range: 52
Mean Deviation: 11.23
Shift 1
18
25
56
42
29
38
54
47
35
30
Shift 2
23
19
50
49
67
34
30
59
40
33
Shift 3
19
22
24
40
45
29
33
29
39
59
Shift 4
21
23
25
40
35
19
70
40
22
23
The summary statistics for all of the workers at a steel factory are shown. Four sample groups were taken from each of the four shifts. For which sample group is the mean closest to the population mean?
A) Shift 1
B) Shift 2
C) Shift 3
D) Shift 4
Answers
Mean: 42
Median: 38
Range: 52
Mean Deviation: 11.23
To obtain the sample that is closest to the mean we shall proceed as follows:
Shift 1:
18,25,56,42,29,38,54,47,35,30
The mean of the sample is:
(18+25+56+42+29+38+54+47+35+30)/10
=374/10
=37.4
Shift 2:
23, 19, 50, 49, 67,34,30,59,40, 33
The mean is:
(23+19+50+49+67+34+30+59+40+33)/10
=404/10
=40.4
Shift 3:
Shift 3
19, 22, 24, 40, 45, 29, 33, 29, 39, 59
The mean of the values
(19+22+24+40+45+29+33+29+39+59)/10
=339/10
=33.9
Shift 4:
21, 23, 25, 40, 35, 19, 70, 40, 22, 23
The mean of the values is:
(21+23+25+40+35+19+70+40+22+23)/10
=318/10
=31.8
From the calculations, the sample that has mean that is close to population mean is Shift 2