can someone explain how to solve this please my midterms tomorrow! :)

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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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:

Gradient (slope) is 5.

Step-by-step explanation:

To find the gradient (slope) of a curve graph at x = x₁ can be done by steps following:

First, derive the given function which is:

[tex]\displaystyle{y = (\sqrt{x}+3)(3\sqrt{x}-5)[/tex]

Differentiation can be done two ways - go ahead and expand the expression then derive it or you can use the product rule where it states that [tex]\displaystyle{y'=u'v+uv'}[/tex]

I'll be using product rule:

[tex]\displaystyle{y' = (\sqrt{x}+3)'(3\sqrt{x}-5)+(\sqrt{x}+3)(3\sqrt{x}-5)'}[/tex]

Note that the following process will require you to have knowledge of Power Rules:

[tex]\displaystyle{y = ax^n \to y' = nax^{n-1}}[/tex]

Hence:

[tex]\displaystyle{y'=\dfrac{1}{2\sqrt{x}}(3\sqrt{x}-5) + (\sqrt{x}+3)\dfrac{3}{2\sqrt{x}}[/tex]

Now we know the derivative. Next, we find the slope at x = 1 which you substitute x = 1 in derived function:

[tex]\displaystyle{y'(1)=\dfrac{1}{2\sqrt{1}}(3\sqrt{1}-5) + (\sqrt{1}+3)\dfrac{3}{2\sqrt{1}}}\\\\\displaystyle{y'(1)=\dfrac{1}{2}(3-5) + (1+3)\dfrac{3}{2}}\\\\\displaystyle{y'(1)=\dfrac{1}{2}(-2) + (4)\dfrac{3}{2}}\\\\\displaystyle{y'(1)=-1 + 2(3)}\\\\\displaystyle{y'(1)=-1 + 6}\\\\\displaystyle{y'(1)=5}[/tex]

Finally, we have found the slope or gradient at x = 1 which is 5.

Please let me know if you have any questions!

Answer:

5 1/2

Step-by-step explanation:

Rate x Time = Distance.  If you know 2 of the parts, you can figure out the 3rd part.  You know the time and the distance, so plug those in and solve.

Let R = rate

R(1/2) = 2 3/4  Let's change  2 3/4 into a improper fraction.  

R(1/2) = 11/4 Multiply 4x2 and then add 3 that gets you 11 and the bottom number stays the same.  Next, multiply both sides of the equation by 2.

R = 22/4 or 11/2 or 5 1/2 miles per hour.

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]

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:CB,CH,AE,AB

Step-by-step explanation:

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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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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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

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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The double number line which shows the other values of fat and protein is: option B.

A number line is a type of graph with a graduated straight line which contain numerical values that are placed at equal intervals along its length.

For the fat component, we have:

Fat = 2n = 0, 2, 4, 6, 8.

For the protein component, we have:

Protein = 11n = 0, 11, 22, 33, 44.

Note: n represent integers such as 0, 1, 2, 3 and 4.

In conclusion, the double number line which represent the other values of fat and protein is shown in the image attached below.

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Complete Question:

One serving of beef je-rky contains 2 grams of fat and 11 grams of protein. Complete the double number line to show the other values of fat and protein.

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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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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Answer:

x = 19

Step-by-step explanation:

You would use vertical angles to move the 8x - 14 so that we could use the Consecutive Interior angles theorem. Which says that consecutive angles equal 180. So, you would set up your equation: 8x-14+2x+4 = 180. Add the 8 and 2 = 10. Add the -14 and 4 = -10. You get 10x-10 = 180. 180+10 = 190. 190/10 = 19. X = 19

Answer:

P = 16.4

Step-by-step explanation:

Given the equation PV = nRT and the values we know, we need to isolate P .

Thus, we have:

[tex]PV=nRT\\3P=2*0.0821*300\\P=49.26/3\\P=16.42=16.4[/tex]

Answer:

Step-by-step explanation:

Let the # of liters in both containers = y when equality is reached.

Container 1: loses 6 liters / hour

Container 2: loses 3 liters / hour

Equation

35 - 6x = 29 - 3x

Solution

35 - 6x = 29 - 3x                          Subtract 29 from both sides

35 - 29 - 6x = 29 - 29 - 3x          Combine

6 - 6x = - 3x                                  Add 6x to both sides

6 - 6x + 6x = - 3x + 6x                 Combine

6 = 3x                                           Divide both sides by 3

6/3 = 3x/3

2 = x

After 2 hours they should have the same amount of water.

35 - 6(2) = 35 - 12 = 23

29 - 3*2 = 29 - 6 = 23

Answer

After 2 hours have passed, both containers should have 23 Liters each.

i) The number of students that come to school by motorcycle only = 8

ii) The number of students that did not take all the three types of transportation = 9

iii) Number of students that did not come to school by car = 28

The total number of students = 40

The number of students that come to school by car alone = 9

The number of students that come to school by motorcycle only = 8

The number of students that come to school by car only = 11

The number of students that come to school by both car and motorcycle = 3

Number of students that did not take all the three types of transportation = 40 - (9 + 8 + 3 + 11)

= 40 - 31

Number of students that did not take all the three types of transportation = 9

Total students that come to school by car = 9+3 = 12

The total number of students that did not come to school by car = 40 - 12 = 28

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The answer is (f . g)(x) = - (34k + 17k⁷ + 17k⁵ + 40k³ + 20k² + 60).

Remember that :

(f . g)(x) = f(x) × g(x)

Hence :

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:

Domain: [0,∞)

Range: (-∞, 4]

Step-by-step explanation:

The required domain and range of the function shown in the graph are,
Domain = (0, ∞)
Range = (-∞, 4)

To calculate the domain and range of a function from its graph, you can follow these steps:

So, from the above definition, from the graph we have,
Domain = (0, ∞)
Range = (-∞, 4)

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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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The surface area of the cone is calculated to the nearest tenth as: 173.4 cm².

Surface area of a cone = πr(r + l),

Given the following:

Plug in the values

Surface area of the cone = π × 4(4 + 9.8)

Surface area of the cone = 173.4 cm²

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( 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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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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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.

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]