Here is a graph of water used, w , in gallons and time in the shower, t , in minutes. What are two constants of proportionality for the proportional relationship?

Answer:

-1

Step-by-step explanation:

We need to find the value of tan² 70° -sec² 70°​.

We know that,

\(\sec^2\theta-\tan^2\theta=1\) ...(1)

We can write the given expression as :

tan² 70° -sec² 70° = -(-tan² 70° +sec² 70°)

=-(sec² 70°-tan² 70°)

Using identity (1)

=-(1)

= -1

Hence, the value of the given expression is -1.

Answer:

1. a. A

2. c. C

3. a. A > C

Step-by-step explanation:

Absolute value is the translation of the number inside | ? | into a positive number.

Examples:

| -245 | = 245

| -47 | = 47

| 69 | = 69

| 21 | = 21

| -4 | = 4

Answer:

835.66m^2 (to 2d.p)

Step-by-step explanation:

Firstly split the shape up so you get a rectangle and 2 circles.
Find the area of the circle:
formulae = πr^2
14/2=7
7^2=49
49π*2 (as there is two circles)= 98
98π=307.876
Find the circumference of the circle
formulae = dπ
14π=43.98
43.98 is the height of the rectangle
43.98*12=527.79 (rounded to 1d.p)
Area of rectangle is 527.79
Area of two circles is 307.876
Add them together = 835.66m^2 (to 2d.p)

Answer:

836cm^2

Step-by-step explanation:

For the sides, do 14/2 to find the radius (r) which is 7.

7^2 x pi = 153.9380400259 (formula for area of a circle is pi x r^2)

Multiply this by 2 to account for both sides of the cylinder.

For the cross-section of the cylinder, do 2 x pi x the radius (7) x 12 (the length, or l) which gets you 527.787565803085.

527.787565803085 + (153.9380400259 x 2) = 835.663645854885, rounded to 836 centimetres squared.

Hope this helps :D

Answer:

3^3

The answer is a.3^3

The scale factor k for the sphere's volume in order to arrive at the volume of the new sphere is 3^3, the correct option is A

Suppose the initial measurement of a figure was x units.

And let the figure is scaled and new measurement is of y units.

Since the scaling is done by multiplication of some constant, that constant is called scale factor. Let that constant be 's'.

Then we have:

\(s \times x = y\\s = \dfrac{y}{x}\)

Thus, scale factor is the ratio of the new measurement to the old measurement.

Given;

Radius is multiplied by 3

In order to arrive at the volume of new sphere the factor must be greater or equal to 3

So,

Scale factor=x*k

=3^3

Therefore, the scale factor k will be 3^3

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Answer:

b) x=25

Step-by-step explanation:

If B is a midpoint, then segments AB and BC should be equal to each other.  

Then you can make an equation making both segments equal to one another:

2x-8=x+17

2x-x=17+8

x=25

Answer:

Neither because the number 55 squared is in between 7. (7*7=49) and 8. (8*8=64). When cubed, it is in between 3. (3*3*3=27) and 4. (4*4*4=64) Therefore, the number 55 cannot be perfectly squared or cubed. (You can put it in your own words)

Answer:neither

Step-by-step explanation:

because 55 is neither

Answer:

C. I and III

Step-by-step explanation:

The 2 at the upper left means the divisor is x - 2.

The result at the bottom means the quotient is 3x^2 - 4x + 2.

Answer: C. I and III

Answer:

ii=8(20+3)

ii=160+3

ii=163

a=8*23

a=184

Answer:

Step-by step answer

Formula A= ^h b/2

Please search area of a triangle. It will provide answer.

Answer:

The company charged $500 for its services,and Mia gives the movers a 16% tip. Now, we can add the tip amount to the cost of the service to find the total amount Mia paid: Total amount = Cost of service + Tip amount = $500 + $80 = $580

Step-by-step explanation:

a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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Let's denote the three numbers A, B, and C.

Given that the highest common factor (HCF) of these three numbers is 8 and their sum is 80, we can consider possible combinations of numbers that satisfy these conditions.

Since the HCF is 8, all three numbers must be divisible by 8. Additionally, the sum of the numbers is 80, so we need to find combinations of three numbers that satisfy both conditions.

Let's list the possible combinations:

These are the four possible sets of three numbers that satisfy the given conditions: (8, 16, 56), (16, 8, 56), (24, 8, 48), and (8, 24, 48).

The radius of convergence is a-R a+R = 6+12 =18 and 6-12 = -6 for the |6x 12/<78 and diverges if |6x 12| 78.

The set of actual numbers x wherein the collection converges is the c program language period of convergence. If there exists a actual wide variety R such that the collection converges for |x−a|R, then R is the radius of convergence.

The radius of convergence is 1/2 of of the duration of the c program language period of convergence. If the radius of convergence is R then the c program languageperiod of convergence will consist of the open c program languageperiod: (a − R, a + R). To discover the radius of convergence, R, you operate the Ratio Test.

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Answer:

Step-by-step explanation:

Alright.

Question 4:

a) area of triangle is width * length

so (2m + 3)(4m-4)

8m^2 -8m +12m -12

A = 8m^2 + 4m - 12

b) trapezoid area formula: A=[(a+b)/2](h)

where a and b are the bases.

[(x+1)+(3x+1) / 2](2x+2)

[(x+1+3x+1) / 2] ( 2x+2)

[(4x +2)/2](2x+2)

(2x + 1)(2x+2)

4x^2 + 4x + 2x + 2

A = 4x^2 + 6x + 2

Next question:

I'm not sure what is the differences of each set of data. so I'm gonna skip this question.

Next question:

5) a) notice the x values. it moves from left to right. Notice the y values, it moves from down to up. if you picture this in your mind, you're gonna conclude that the parabola opens downward.

b) Notice the x values. it moves from left to right.

notice the y values. Between  -2 < x < -1 the parabola opens upward. Then from x = 0 again it opens downward.

c) notice the y values. from -2 < x < -1 as well as for x = 0 the parabold opens upward.

From 0 < x < 1 as well as for x = 2, the parabola opens downward.

The storage can hold approximately 10.94 cubic meters of grain.

Unit conversion is the process of converting a quantity expressed in one set of units to an equivalent quantity expressed in another set of units. For example, converting a length from feet to meters, or converting a temperature from Celsius to Fahrenheit.  

To convert cubic yards to cubic meters, multiply the given volume in cubic yards by this conversion factor to obtain the equivalent volume in cubic meters.  

Here we have

Adam’s family maintains storage that can hold 14.3 yd³ of grain.

Given that 1 yard is approximately equal to 0.9144 meters

To convert cubic yards (yd³) to cubic meters (m³),

Use the conversion factor:

1 yd³ = (0.9144 m)³

So, we can convert 14.3 cubic yards of grain to cubic meters as follows:

14.3 yd³ x (0.9144 m/yd)³ ≈ 10.94 m³

Rounding this answer to the nearest hundredth gives us:

10.94 m³ rounded to the nearest hundredth = 10.94 m³

Therefore,

The storage can hold approximately 10.94 cubic meters of grain.

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In the equation:

the leading coefficient, a, is equal to -3. Given that a is less than zero, then the parabola has the shape of a ∩. Therefore, it has a maximum.

To find the maximum, we need to find the vertex (h, k) of the parabola.

The x-coordinate, h, is found as follows:

The y-coordinate, k, is found substituting the value of h into the equation of the parabola, as follows:

Then, the maximum is placed at (-2, 4)

Answer:

Step-by-step explanation:

Given

We can see from the equations that

So greater use of unit B brings greater profit. We don't want any unit is left over, so get this equation.

Is the equation set to indicate use of the units A and B

Solving we get

It this case all the units are used and profit is maximum

Answer:

95

Step-by-step explanation:

For average you just add all the numbers together and divide by how many numbers there are.

88+95+97+100=380

380÷4=95

The average of the given data is 95.

Average is defined as the ratio of the sum of the number of the data sets to the total number of the data. The average actually determines the middle value of the data.

Given that Jenny's test grades are 88, 95, 97, and 100. The average of the numbers will be calculated by adding all the numbers and dividing it by the total count of the numbers.

For average you just add all the numbers together and divide by how many numbers there are.

Average = ( 88+95+97+100 ) / 4

Average = 380 / 4

Average = 95

Therefore, the average of the given data is 95.

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Answer:

The mean prior to the given set of numbers would be \(58.8\).

How So?

1. Knowing this, first order the set from least to greatest.

\(22, 35, 44, 63, 63, 71, 80,92\)

2. Then, add up all the values.

\(22+35+44+63+71+80+92=470\)

3. Finally, divide 470 by 8 (the number of values in the set).

\(470\) ÷ \(8 = 58.75\)

4. Round 58.75, leaving you with the following solution:

\(58.75=58.8\) ←Our Final Solution / Mean

______________________________________________

Hope this helps!

4

p=2(l+b)

p=2(6+2)

p=16

p=4l

16=4l

l=4

9514 1404 393

Answer:

  x^3 -4x^2 +12x -27

Step-by-step explanation:

Use the distributive property.

  = (x^2 -x +9)(x) +(x^2 -x +9)(-3)

  = x^3 -x^2 +9x -3x^2 +3x -27

  = x^3 -4x^2 +12x -27 . . . . . collect terms

The required present value needed now to get $700 after 4 years at 11% compounded monthly is $451.73.

To find the present value of $600 after 4 years at 7% compounded monthly, we can use the formula for compound interest:

Compound Interest =P(1+r/n)^rt

Substituting the given values, we get:

Compound Interest =600 (1+7/n)^4

Simplifying this equation, we get

P = 600 / 1.487

P = 451.73

Therefore, the present value needed now to get $600 after 4 years at 7% compounded monthly is $451.73.

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The amount of budget cut from last year's budget which was $166,245 will be $54860.85 which is nearly  $55,415 from the given option. Hence the correct option is (B).

The percentage is the 1 of the hundred or simply the amount or value of any number or data in the range of 100 called percentage.

For example, if Ramesh got 87 marks out of 150 then it required a lot of attention to drawing a conclusion about Ramesh's marks but if I say Ramesh got 58% then it will be easier to think and draw any conclusion.

Given that last year budget was $166,245 and the cut was 33% so it means it will be 0.33 of the $166,245 so

$166,245 × .33 = $54860.85 but in option, it is not mentioned so the nearest answer among the option will be (B).

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Hello!

We will go tu use the pythagorean theorem!

So:

BA² = BC² + AC²

AC² = BA² - BC²

AC² = 52² - 20²

AC² = 2304

AC = √2304

AC = 48

There's missing information. What does f(x) approach as x approaches negative infinity and infinity?

Answer:

1st answer: The polynomial function for this graph is of

odd degree and the leading coefficient is negative

2nd answer: The polynomial function for this graph is of even

degree and the leading coefficient is negative

Degree and Leading Coefficient

Step-by-step explanation:

3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:

3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup

Since there are 1 cup in each term, we can rewrite it as:

3 cups + (1/2) cup

Now, we can express each term as a multiplication expression:

3 cups = 3 * 1 cup = 3

(1/2) cup = (1/2) * 1 cup = 1/2

Putting it all together, the multiplication expression is:

3 * 1 cup + (1/2) * 1 cup = 3 + 1/2

Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

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