Fill in the blank question.
A bathtub contains 6012
gallons of water. When the drain plug is pulled, the tub drains at an average rate of 4.5 gallons per minute. In how many minutes will the amount of water in the bathtub be 24.5 gallons?

( f - g )(x) = 10x - 17 and ( f ° g)(-6)  = 60. The answers are option D and B

Different types of function demands different ways of solving them. Different types are simple function, function by substitution and function of function.

Given that

f(x) = [tex]x^{2}[/tex] + 9x - 14 and g(x) = [tex]x^{2}[/tex] - x + 3

( f - g )(x) will be the difference between f(x) and g(x)

( f - g )(x) = [tex]x^{2}[/tex] + 9x - 14 - ( [tex]x^{2}[/tex] - x + 3)

( f - g )(x) =  [tex]x^{2}[/tex] + 9x - 14 -  [tex]x^{2}[/tex] + x - 3

( f - g )(x) = 10x - 17

Also, if f(x) = [tex]3x^{2}[/tex] - 15 and g(x) = 1 - 2/3 x

( f ° g)(-6) means that we will evaluate g at -6, then evaluate f at the result of g(-6)

g(-6) = 1 - 2/3 (-6)

g(-6) = 1 + 4

g(-6) = 5

f(g(-6)) = 3([tex]5^{2}[/tex]) - 15

f(g(-6)) = 3 x 25 - 15

f(g(-6)) = 75 - 15

f(g(-6)) = 60

Therefore, ( f - g )(x) = 10x - 17 and ( f ° g)(-6)  = 60

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Answer:

x = 157/60

Step-by-step explanation:

x + 2/3 - x + 1/5 = x - 3/4 - 1

x - x - x = -2/3 - 1/5 - 3/4 - 1

-60x/60 = -40/60 - 12/60 - 45/60 - 60/0

-60x = -40 - 12 - 45 - 60

-60x = -157

x = -157/-60

x = 157/60

157/60 + 2/3 - 157/60 + 1/5 = 157/60 - 3/4 - 1

2/3 + 1/5 = 157/60 - 3/4 - 1

40/60 + 12/60 = 157-60 - 45/60 - 60/60

40 + 12 = 157 - 45 - 60

52 = 157 - 105

Answer:

  3 1/2 quarts

Step-by-step explanation:

The fraction of the lemonade that is water can be determined from the ratio of water to lemon juice. That fraction of a gallon is the quantity of interest.

Of the 7+1 = 8 parts that make up the lemonade, 7 of those are water. That is, water is 7/8 of the lemonade.

Of the 4 quarts of lemonade, the quantity that is water will be ...

  (7/8)(4 quarts) = 7/2 quarts = 3 1/2 quarts . . . of water

Step-by-step explanation:

remember, the sum of all angles in a triangle is always 180°.

and the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

with a, b, c being the sides opposite of their associated angles (A, B, C).

1)

17/sin(26) = 12/sin(C)

sin(C) = 12×sin(26)/17 = 0.309438457...

C = 18.02539254...° ≈ 18°

3)

180 = 27 + 115 + C

C = 38°

19/sin(38) = AC/sin(27)

AC = 19×sin(27)/sin(38) = 14.01065332... in ≈ 14 in

In first triangle side angle m∠C is 18° and in first triangle side AC is 14 in. This can be obtained by using the law of sine.

We know the law of sine which is,

If in a triangle, Δ ABC,

[tex]\frac{sin A}{a} =\frac{sin B}{b}= \frac{sinC}{c}[/tex], where a is the side opposite to the angle m∠A, b is the side opposite to the angle m∠B and c is the side opposite to the angle m∠C.

sine of the angle scan be found using calculator.

From the question,

1) In first triangle side,

AB = 12ft, BC = 17 ft and m∠A=26°

⇒By using the law of sine,

[tex]\frac{sin A}{a} =\frac{sin B}{b}= \frac{sinC}{c}[/tex]

sin 26°/17 = sin B/AC = sin C/12

sin 26°/17 = sin C/12

12×sin 26° = 17×sin C

sin C = 5.26/17 = 0.3091

C = 18.023° ≈ 18°

3) In second triangle side,

m∠B = 27°, AB = 19 in and m∠A = 115°

m∠A + m∠B +m∠C = 180°

115° + 27° + m∠C = 180°

142° + m∠C = 180°

m∠C = 38°

⇒By using the law of sine,

[tex]\frac{sin A}{a} =\frac{sin B}{b}= \frac{sinC}{c}[/tex]

sin 115°/BC = sin 27°/AC = sin 38°/19

sin 27°/AC = sin 38°/19

sin 27° × 19 = sin 38° × AC

8.63 = 0.62 × AC

AC = 13.91 in ≈ 14 in.

Hence in first triangle side angle m∠C is 18° and in first triangle side AC is 14 in.

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The proportion cranberry juice should be mixed with 84 ounces of apple juice 1:5 that is 1 parts of cranberry juice and 5 parts of lemon juice.

According to the question,

A punch recipe calls for mixing 2 parts of cranberry juice with 5 parts of apple juice.

84/2 = 42

5*42=210

Hence, the proportion cranberry juice should be mixed with 84 ounces of apple juice 1:5 that is 1 part of cranberry juice and 5 parts of lemon juice.

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Answer:CB,CH,AE,AB

Step-by-step explanation:

The weight of A is 75kg.

Total weight of A + B + C = 84 x 3 = 252kg

Total weight of A + B + C + D = 80 x 4 =.320 kg

Weight of D = 320 - 252 = 68 kg

Given, E = D + 3 = (68 + 3) kg = 71 kg

Total weight of B + C + D + E = (79 x 4) = 316 kg

Weight of B + C = 316 kg - 71 kg - 68 kg = 177 kg

Weight of A only will be:

= 320 kg - 177 kg - 68 kg

= 75 kg

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The coefficient of t to the 4th power in the given expansion is -167403915.

Option (c) is the correct answer.

An expansion of a product of sums uses the fact that multiplication distributes across addition to represent it as a sum of products. A polynomial expression can be expanded by repeatedly substituting equivalent sum of products for subexpressions that multiply two other subexpressions, at least one of which is an addition, up until the expression becomes a sum of (repeated) products. Simplifications like grouping similar terms or canceling terms may also be used during the expansion.

Given expansion=[tex](-9t-9)^{7}[/tex]

Coefficient of the 4th power of t in the expansion,

=[tex]_{7} {C} _{7-4} (-9t)^{4}(-9)^{7-4}[/tex]

=[tex]_{7}C_{3}(-9)^{4}t^{4}(-9)^{3}[/tex]

=[tex]_{7}C_{3}(-9)^{7}t^{4}[/tex]

=[tex]35t^{4}(-9)^{7} \\[/tex]

=[tex]35t^{4}(4782969)[/tex]

= -167403915[tex]t^{4}[/tex]

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Answer:

x = 2

Step-by-step explanation:

To solve the equation, you need to set both functions equal to each other and simplify to find the value of "x".

f(x) = 2x + 1

g(x) = -x + 7

f(x) = g(x)                                              <----- Given equation

2x + 1 = -x + 7                                      <----- Insert functions

3x + 1 = 7                                             <----- Add "x" to both sides

3x = 6                                                  <----- Subtract 1 from both sides

x = 2                                                    <----- Divide both sides by 3

160 ounces is the answer

16 ounces per pound

16x10=160

First put to find the weight in ounces, *multiply* the number of pounds by the unit rate, 16 ounces per pound. Then put 10 pounds = *160 ounces.*

An ounce is the designation of several different units of mass, weight, or volume, and is largely unchanged from the ancient Roman unit of measurement, uncia. Avoirdupois ounces are 1⁄16 Avoirdupois pounds. This is a US standard and an ounce of the British Empire.

oz [Ouns] n. A unit of weight in the US customary unit, an avoirdupois unit equal to 437.5 grains or 28.35 grams. A pharmacist's weight unit is equivalent to 480 grains or 31.10 grams.

oz, equivalent to 1/16 pound (437 1/2 grain) on the Avoirdupois system and 480 grains or 1/12 pound on the Troy and pharmacist system. Avoirdupois ounces are equivalent to 28.35 grams and pharmacist ounces are equivalent to 31.103 grams.

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1 ) 6

2) 6

3) -2

4) 2

5) -2

6) 2

Answer:

200

Step-by-step explanation:

Let's call the number x :
12.5% of x = 25

Changing 12.5% into decimal would be 0.125

Now we have the equation :

0.125x = 25

Divide both sides by 0.125 to make x the subject :

x = 25 ÷ 0.125

x = 200

To check we can substitute this value into the question :

12.5% of 200 = 25

Hope this helped and have a good day

Answer:

84 square units.

Step-by-step explanation:

  [tex]\sf \boxed{\bf Area = \sqrt{s*(s-a)(s-b)*(s-c)}}[/tex]

Here, a, b and c are the sides of the triangle. s is the semi perimeter.

a = 13

b = 14

c = 15

[tex]\sf s= \dfrac{a+b+c}{2}\\\\ =\dfrac{13+14+15}{2}\\\\=\dfrac{42}{2}\\\\s = 21[/tex]

s -a = 21 - 13 = 8

s -b = 21 - 14 = 7

s - c = 21 - 15 = 6

   [tex]\sf Area = \sqrt{21*8*7*6}[/tex]

            [tex]= \sqrt{ 7* 3 * 2 * 2 * 2 * 7 * 2 * 3}\\\\=7 * 3 *2*2\\\\= 84 \ square \ units[/tex]

Answer:

B

Step-by-step explanation:

I love trig lol,

Assuming you know trig, Cos(17)=BC/42

Cos(17)*42=BC

Cos(17)~0.956

0.956*42=40.152=BC

Since this is a approximation, B is the closest to our estimate.

The probability of choosing. a green pen is 0.25

Probability is the likelihood or chance that an  event will occur. Mathematically;

Probability = Expected/Total outcome

If a bag has 3 blue pens, 6 red pens, and 3 green pens, then;

Total pen = 3+6+3

Total pen = 12

If a green pen is chosen, then

Pr(choosing a green pen) = 3/12

Pr(choosing a green pen) = 0.25

Hence the probability of choosing. a green pen is 0.25

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The angle A of the triangle ABC has a measure of approximately 34°. (Right choice: D)

To determine the missing angle of a triangle by the law of the cosine, we must know the lengths of the three sides of the figure. Please notice that angle A is opposite to the side a in accordance with the law of the cosine. Then:

[tex]\cos \theta = \frac{(10\,cm)^{2}-(17\,cm)^{2}-(11\,cm)^{2}}{-2\cdot (17\,cm)\cdot (11\,cm)}[/tex]

θ ≈ 34.016°

The angle A of the triangle ABC has a measure of approximately 34°. (Right choice: D)

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An absolute value inequality for "all numbers less than 7 and greater than -7" is given by |x| < 7.

Based on the information provided, we can logically deduce that the statement describes an intersection of set because the word "and" was used.

This ultimately implies that, we would use the less than (<) symbol to write an absolute value inequality for the given statement:

|x| < 7

Therefore, this can be translated as follows:

-7 < x < 7      or      x < 7  and    x > -7.

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A cone is a 3-dimensional shape that consists of a circular or flat surface and a curved side. Thus the volume of the given cone is 4.1 [tex]mi.^{3}[/tex]

A cone is a 3-dimensional shape that consists of a circular or flat surface and curved side. Its volume can be determined by;

The volume of a cone = [tex]\frac{1}{3}[/tex] [tex]\pi[/tex][tex]r^{2}[/tex]h

where r is the radius of its flat surface, and h is its height.

From the given question, we have to determine the value of h using the Pythagoras theorem.

Such that;

[tex]/Hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]

[tex]4^{2}[/tex] = [tex]h^{2}[/tex] + [tex]1^{2}[/tex]

16 = [tex]h^{2}[/tex] + 1

[tex]h^{2}[/tex] = 15

h = [tex]\sqrt{15}[/tex]

Thus the volume of the cone = [tex]\frac{1}{3}[/tex] [tex]\pi[/tex][tex]r^{2}[/tex]h

                             =  [tex]\frac{1}{3}[/tex]x [tex]\frac{22}{7}[/tex] x [tex]1^{2}[/tex]x    [tex]\sqrt{15}[/tex]

                             = 4.0574

Therefore the volume of the given cone is 4.1 [tex]mi.^{3}[/tex]

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Answer:

[tex]x^2+8x+8+\frac{-9}{x+4}[/tex]

Step-by-step explanation:

it would be simpler to do synthetic division by removing the variables and using the coefficients:

i hope this helped!

The equivalent value of the given expression is -21.4

Decimals are values that include decimal points. Given the expression below

-8.2 - 5−8.2

Collect like terms

-8.2 −8.2 - 5

Convert to fractions

-82/10- 82/10 -  5

-164/10 - 5

-16.4 - 5

Take the sum

-21.4

Hence the equivalent value of the given expression is -21.4

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The solution of the inequality -2(3x + 2) - 6x ≥ -4 is undefined

-2(3x + 2) - 6x ≥ -4

-6x - 4 - 6x ≥ -4

-12x ≥ - 4 + 4

-12x ≥ 0

x ≥ 0 / -12

x is undefined

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I don't think this question is complete but here's ur answer

The volume of the oblique cylinder is 6867.18 cubic units

The given parameters are:

Height = 27

Radius = 9

The volume is calculated as:

[tex]V = \pi r^2 h[/tex]

So, we have:

[tex]V = 3.14 * 9^2 * 27[/tex]

Evaluate

V = 6867.18

Hence, the volume of the oblique cylinder is 6867.18 cubic units

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The windows width in the drawing according to the task content is; 9.6inches.

According to the task content, the window's actual width on the house is given as; 48 inches.

Hence, since, the window's width on the drawing is 20% of the actual width, it follows that;

Windows drawing width = 20% × 48 = 9.6 inches.

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Answer:

5

Step-by-step explanation:

Formula for finding slope:

[tex] \frac{y1 - y2}{x1 - x2} [/tex]

Slope of line passing through (-5,5) and (-4,10)

=

[tex] \frac{5 - 10}{ - 5 - ( - 4)} \\ = \frac{ - 5}{ - 5 + 4} \\ = \frac{ - 5}{ - 1} \\ = 5[/tex]

Answer:

Slope = 5

Step-by-step explanation:

    (-5,5)   ;   x₁ = -5    & y₁ = 5

    (-4, 10)  ;   x₂ = -4  & y₂ = 10

             [tex]\sf \boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

                         [tex]\sf =\dfrac{10-5}{-4-[-5]}\\\\ =\dfrac{10-5}{-4+5}\\\\=\dfrac{5}{1}\\\\= 5[/tex]

The rational function that matches with the graph of the picture is f(x) = (2 · x + 7.2)/(x + 3).

Herein we have the graph of a rational function of the form f(x) = p(x)/q(x) . The domain of these kind of functions is all real numbers except those values of x such that q(x) = 0. Graphically speaking, there is a vertical asymptote when a discontinuity exists and an horizontal asymptote for x → ± ∞.

In accordance with the picture, there are one horizontal asymptote and one vertical asymptote. As the horizontal asymptote of the function is distinct of 0, then the grade of p(x) is the same grade of q(x). Therefore, we have a rational function of the form:

f(x) = (2 · x + k)/(x + 3)     (1)

If we know that x = 0 and y = 2.4, then the value of k is:

2.4 = (2 · 0 + k)/(0 + 3)

2.4 = k/3

k = 7.2

Therefore, the rational function that matches with the graph of the picture is f(x) = (2 · x + 7.2)/(x + 3).

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Answer:

7 hot dogs

Step-by-step explanation:

Set up an equation:

2.5x + 1.25 = 21

2.5x = 19.75

x = 7.9

You cannot buy .9 of a hot dog, so the answer is 7