The value of c such that the line y = 9/4 x + 9 is tangent to the curve y = c x is 9/4. This is because a line is tangent to a curve when it touches the curve at exactly one point, hence the slope of the given line (9/4) will be equal to the value of c, which is the slope of the curve.
Explanation:The problem asks us to find the value of c such that the line y = 9/4 x + 9 is tangent to the curve y = c x. A line is tangent to a curve when it touches the curve at exactly one point. In this context, the slope of the given line (9/4) will be equal to the value of c since in the line equation y = c x, c is the slope. So the value of c is 9/4.
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identify the property that is being applied at each step to simplify the expression.
PLEEEAAASSSSEEEE HEEEELLLPPPPP
WOULD BE GGRRRREEEAAAATTTTLLLLYYYY APPRECIATED!!!!!!!!!!!!!!!!!
4^-5 *(4*9)^5*9^-3=4^-5*(4^5*9^5)*9^-3
=(4^-5*4^5)*(9^5*9^-3
=4^0*9^2
=1*9^2
=9^2
=81
The expression simplifies using multiple properties of exponents, including the power of a product, properties of exponents for multiplication and division, the zero exponent property, and squaring.
Explanation:The expression you're asking about applies multiple properties of exponents to simplify the given expression. To start, applying the power of a product property, it simplifies [tex](4*9)^5[/tex] to [tex]4^5*9^5[/tex]. Following that, the property of exponents for division is used to combine [tex]4^{-5[/tex] and [tex]4^5[/tex], leading to [tex]4^0[/tex], as well as [tex]9^5[/tex] and [tex]9^{-3[/tex], resulting in [tex]9^2[/tex]. The zero exponent property translates [tex]4^0[/tex]into 1. Lastly, the square of 9 gives the end result of 81.
In summary, these are the properties applied: power of a product, properties of exponents for multiplication and division, zero exponent property, and squaring.
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What is the exact volume of the cone?
28π in³
563π in³
1963π in³
196π in³
28π in^3
56/3π in^3
196/3π in^3
196π in^3
These are the numbers they meant to put and the answer is 196/3 in^3.
Use
A=P(1+rn)nt
A=P(1+rn)nt where:
A = the amortized amount (total loan/investment amount over the life of the loan/investment)
P = the initial amount of the loan/investment
r = the annual rate of interest
n = the number of times interest is compounded each year
t = the time in years
Find how long it takes a $2,200.00 investment to earn $210.00 in interest if it is invested at 10% compounded monthly.
It will take ___ years. (Round answer to 3 decimal places.)
It will take approximately 1.459 years for a $2,200.00 investment to earn $210.00 in interest if it is invested at 10% compounded monthly.
Explanation:To find how long it takes a $2,200.00 investment to earn $210.00 in interest if it is invested at 10% compounded monthly, we can use the formula A = P(1+rn)^(nt). Plug in the values: A = 2200 + 210 = 2410, P = 2200, r = 0.10 (10%), n = 12 (compounded monthly), and t = ?
2410 = 2200(1 + 0.10/12)^(12t). Divide both sides by 2200 to isolate the expression:
1.095 = (1 + 0.10/12)^(12t). Take the natural logarithm of both sides to remove the exponent:
ln(1.095) = 12t * ln(1 + 0.10/12). Solve for t:
t = ln(1.095) / (12 * ln(1 + 0.10/12)). Use a calculator to find the value of t, which is approximately 1.459 years when rounded to 3 decimal places.
the diameter of a circle is 40 m find the area of the circle in term of pie?
40
Answer: The required area of the given circle is [tex]400\pi~\textup{m^2}.[/tex]
Step-by-step explanation: We are given that the diameter of a circle i 40 m.
We are to find the area of the circle in terms of pie.
We know that
the AREA of a circle with radius of length r units is given by
[tex]A=\p r^2.[/tex]
Since the diameter of the given circle is 40 m, so the length of the radius is given by
[tex]r=\dfrac{40}{2}=20~\textup{m}.[/tex]
Therefore, the AREA of the circle is given by
[tex]A=\pi r^2=\pi\times 20^2=400\pi~\textup{m}^2.[/tex]
Thus, the required area of the given circle is [tex]400\pi~\textup{m}^2.[/tex]
Rearrange the formula V = 1 3 πr2h for h.
Answer:
The answer is A. Thanks
Step-by-step explanation:
Making 'h' the subject , the expression obtained is h = 3V/ πr²
Given the volume formula :
V = 1/3 πr²hTo make 'h' the subject
multiply both sides by 3
3V = πr²h
divide both sides by πr² in other to isolate 'h'
3V/ πr² = πr²h/πr²
h = 3V/ πr²
Therefore, making 'h' the subject , the expression obtained is :
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A 24-ounce mocha beverage with whipped cream has 25% of the calories allowed on a 2,000-calorie-per-day diet. What percentage of a 2,500-calorie-per-day diet would this same drink constitute?
Answer:
c
Step-by-step explanation:
Lisa had 1750 stamps. Mark had 480 fewer stamps than Lisa. Lisa gave some stamps to Mark. Now Mark has three times as many stamps as Lisa. How many stamps did Mark have at first? How many stamps does Lisa have now? Explain.
how can you use compensation to find 8 x 903?
Determine whether each of these functions from {a, b, c, d} to itself is one-to-one.
a.f(a)=b,f(b)=a,f(c)=c,f(d)=d
b.f(a)=b,f(b)=b,f(c)=d,f(d)=c
c.f(a)=d,f(b)=b,f(c)=c,f(d)=d
Mr. James wants to build a walkway around his school garden. The width of his garden is one-third the length. The perimeter of the school garden is 32 feet. What is the length and width of his garden?
L=3W
2(3W+W)=32 feet
8W=32 feet
W=4 feet
L=3W
L=3* 4 feet
L=12 feet
The width is 4 feet, the length is 12 feet.
Shan's dumpling house can produce 100 dumplings using one worker and 175 dumplings using two workers. what is the marginal product of the second worker?
a.25 dumplings
b.75 dumplings
c.175 dumplings
d.275 dumplings
The marginal product of the second worker is b. 75 dumplings.
To find the marginal product of the second worker, we need to determine how many additional dumplings the second worker is able to produce compared to the first worker. The marginal product (MP) of a worker is calculated as follows
[tex]\[ MP = \text{Total production with two workers} - \text{Total production with one worker} \][/tex]
Given:[tex]\[\]\[ \text{Total production with one worker} = 100 \text{ dumplings} \]\[ \text{Total production with two workers} = 175 \text{ dumplings} \][/tex]
Substitute the given values into the formula:[tex]\[\]\[ MP = 175 \text{ dumplings} - 100 \text{ dumplings} \]\[ MP = 75 \text{ dumplings} \][/tex]
Una piscina completamente llena se puede vaciar por un desagüe en 10 horas, y por otro, en 15 horas. Si se abren ambos de desagüe simultáneamente. en cuanto tiempo variarán la piscina?
piano and pipe organs contain keyboard a portion of which is shown Express the ratio of Black Keys to white keys in the picture above three different ways to simplify if possible Final Solution in a complete sentence
Black keys 6
white keys 8
The ratio should be 3:4
Given that,
Black keys 6 and white keys 8Based on the above information, the calculation is as follows:
= 6:8
= 3:4
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What is the volume in cubic yards of a greenhouse that is 35 feet long, 10 feet wide, and 10 feet high?
Final answer:
To determine the volume of a greenhouse, multiply its length, width, and height to find its volume in cubic feet, then convert to cubic yards using the conversion factor of 1 cubic yard being equivalent to 27 cubic feet. The volume for the given dimensions is approximately 129.63 cubic yards.
Explanation:
The volume of a structure, including a greenhouse, is calculated by multiplying its length by its width by its height. The first step is to calculate the volume in cubic feet, then convert cubic feet to cubic yards knowing that 1 cubic yard equals 27 cubic feet. Here's how to calculate the volume of the given greenhouse:
Multiply the length, width, and height in feet to get the volume in cubic feet: 35 ft x 10 ft x 10 ft = 3500 cubic feet.Convert cubic feet to cubic yards using the conversion factor (1 cubic yard = 27 cubic feet): 3500 cubic feetTherefore, the volume of the greenhouse is 129.63 cubic yards.
The weight of 10,000 identical samples of a substance is 10 pounds. What is the weight of 100 samples?
Answer: 0.1
Step-by-step explanation: Okay. So, the weight of 10,000 samples is 1 pound. To find the weight of each sample, we can do 10/10,000, which would give us 0.001. Each sample weighs 0.001 pound. We can multiply that times 100 to find the weight of 100 samples. 0.001 * 100 = 0.1. The weight of 100 samples is 0.1 pound.
How would you Evaluate. 5⋅ 4 0
Write words to match the expression, 3 + (4 × 12)
Convert this improper fraction to a mixed number. 56/5 11 r 1 11 1/5 11.2 5/56
Allen is given three lengths of rope: 4 feet, 8 feet, and 15 feet. Can Allen form a triangle with side lengths of 4 feet, 8 feet, and 15 feet using these three pieces of rope
Answer:the answer is B No,set of side length does not satisfy triangle inequality theorem
Step-by-step explanation:
The bookshelf was bought at a wholesale price of $147.00, and Gabriela Furniture Store Marie up all Furniture by 60%.At what price should the manager sell the bookshelf ?
27 students in all 4:5 packed lunch. how many students packed lunch
Debra is on the swim team. Each day she swims 850m. How many kilometers does she swim each day?
Lisa wants to buy a phone card for $5. Company X charges $0.49 for the first minute and $0.16 for each additional minute. Company Y charges $0.57 for the first minute and $0.12 for each additional minute. If Lisa makes just one call, which phone company gives her more minutes for $5? How many more minutes?
The ling family wants to purchase a television that costs $449. The store that sells the television has multiple locations in different counties. The sales tax for each county is shown. Complete the table below by arranging the counties from least to greatest sales tax rate. Write each sale tax as a percent
Find p((5 on green die and 3 on red die) or (3 on green die and 5 on red die)). (enter your answer as a fraction.)
The probability of rolling a 5 on the green die and a 3 on the red die, or a 3 on the green die and a 5 on the red die is calculated by summing their individual probabilities, leading to a final probability of 1/18.
To solve this probability question, we will use the fundamental counting principle and basic probability rules. We have two six-sided dice, one green and one red. The question specifies two separate events:
The green die shows a 5 and the red die shows a 3.
The green die shows a 3 and the red die shows a 5.
Since each face on a fair six-sided die has an equal chance of appearing, the probability of getting any specific number is 1/6. When we roll two dice, the probability of any specific outcome is (1/6) x (1/6), which simplifies to 1/36.
Since there are two independent events that satisfy the question, we can add the probabilities of each event occurring:
Probability of a 5 on green die and 3 on red die = 1/36
Probability of a 3 on green die and 5 on red die = 1/36
Adding them up, we get 1/36 + 1/36 = 2/36, which simplifies to 1/18. Therefore, the probability of getting either a (5 on the green die and 3 on the red die) or (3 on the green die and 5 on the red die) is 1/18.
The initial number of views for a blog was 20. The number of views is growing exponentially at a rate of 20% per week. What is the number of views expected to be four weeks from now? Round to the nearest whole number.
Answer : The number of views expected to be four weeks from now is, 42
Step-by-step explanation :
Formula for exponential growth is :
[tex]y=a(1+r)^x[/tex]
where,
y = exponential growth = ?
a = initial amount of growth = 20
r = growth rate = 20% = 0.20
x = number of time intervals that have passed = 4
Now put all the given values in the above formula, we get:
[tex]y=20\times (1+0.20)^4[/tex]
[tex]y=41.475\aaprox 42[/tex]
Thus, the number of views expected to be four weeks from now is, 42
solve for f. f²-121=h²+22h
the sum of six consecutive integers is 387. what is the sixth number in the sequence
Help me asap!
please help
cross multiply:
21*9 = 189
7*q = 7q
so you have 189/7q
divide 189 by 7 to get q
189 / 7 =27
q = 27
Cases are normally sold full. There were three partially full cases that could be combined to make full cases. The cases were 11/16, 5/16 and 7/16 full.