What is the value of (−12)4?

After 12 seconds, the equipment elevator will be 204 feet under the ground while the miner's elevator will be 235 feet under the ground.

After 12 seconds, the miner's elevator is deeper.

It is the ratio of distance and time.

We have,

Equipment elevator:

Speed = 5 feet per sec

Miner's elevator:

Speed = 17 feet per sec

Now,

The position (distance) of the equipment elevator after 31 seconds and 12 seconds:

Distance = speed x time

Distance = Distance after 31 sec + Distance after 12 sec

= (31 x 5) + (16 x 5)

= 155 + 80

= 235 feet

The position (distance) of the equipment elevator after 12 seconds:

= 17 x 12

= 204 feet

Therefore, after 12 seconds, the equipment elevator will be 204 feet under the ground while the miner's elevator will be 235 feet under the ground.

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Using the law of cosines, the measures of the angles are given as follows:

The law of cosines states that we can find one of the sides or the angle C of a triangle according to the following equation:

c² = a² + b² - 2abcos(C)

In which:

For this problem, the parameters for the triangle are given as follows:

a = b = 12, c = 3.

We want to solve for the smallest angle C, hence:

c² = a² + b² - 2abcos(C)

9 = 288 - 288cos(C)

288cos(C) = 279

cos(C) = 279/288

C = arccos(279/288)

C = 14.36º.

The other two angles are congruent, and the sum of the internal angles of a triangle is of 180º, hence:

14.36 + x + x = 180

2x = 165.64

x = 165.64/2

x = 82.82º.

Then the measures of the angles are given as follows:

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Answer:

14

83

Step-by-step explanation:

i did it on edge

Answer:

94.6 m

Step-by-step explanation:

Just put in the number in the info to the formula

formula to find distance travelled, s= 1/2 (u + v) t

U = 0

V = 43

t = 4.4

s= ??

so ,

s = 1/2 (0+43) ×4.4

s = (43× 4.4) ÷ 2

s = 189.2 ÷ 2

s = 94.6 m

yay

A line is an undefined term because it describes something that does not have width or depth. thus, option describes something that does not have width or depth is correct

If the ray lies onto the considered line segment(overlapping), then it can be said belonging to the considered line segment.

(Line segment has 2 fixed ends, whereas a ray has one end only, another end is not fixed)

A line segment is a straight line with finite length, and thus, have to endpoints (points on either ends).

A line can extend its length in both sides infinitely. It contains arrowheads indicating it can extend.

A line is an undefined term because it describes something that does not have width or depth. thus, option describes something that does not have width or depth is correct

Answer:

g = 1

Step-by-step explanation:

this is how you solve

Answer:

g = 1

Step-by-step explanation:

Add 7

[tex]-7+11g+7=9-5g+7[/tex]

Simplify it

[tex]11g=-5g+16[/tex]

Add 5g

[tex]11g+5g=-5g+16+5g[/tex]

Simplify further

[tex]16g=16\\\frac{16g}{16}=\frac{16}{16}\\= 1\\g = 1[/tex]

Answer:

Steve has to save for 4 days and Maria has to save for 3 days and they will save $36 each.

Step-by-step explanation:

S = 9 x 4 = 36

M = 12 x 3 = 36

The product of two (I) rational numbers is always a (II) real number.

A rational number is defined as any number which can be written in the form of p\q where p, q are whole numbers and co-prime.

A real number is any a number that can be indicated on the number line.

A complex number is an imaginary number which does not reside on the number line, rather can be placed in the complex plane.

The product of any two rational numbers produces a rational number and all rational numbers belong in the superset of Real numbers.

Let us consider the possibilities of the other options as given.

A) Let us consider two complex number 2+i and 2-i . When multiplied they produce 3 which is not a complex number.

B)Product of two real numbers can never produce a complex number.

D)Imaginary and complex are same kind of numbers hence they also follow the first option and is not true.

Hence the only correct option is C as we have surmised that the product of two rational numbers will always produce a real number.

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Answer:

Question 1

f(x) = 19 sin(x [tex]\pi[/tex]/38)

Question 2

f( 7) = 10.39ft

f(24) =  17.4ft

Step-by-step explanation:

f(x) = a sin(x+s)

x =  opening length

a = amplitude

s = shift

Question 1

using half of sine

x = opening = 38ft wide

s = 19

f(x) = 19 sin(x [tex]\pi[/tex]/38)

Question 2

road width =  7 + 17 + 7 = 31

height at x = 7 or at x = 7 + 17 = 24

f( 7) = 19 sin(7 π/38) = 10.39ft

f(24) = 19 sin(24 π/38) = 17.4ft

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. (x² + 2y³)⁶ is expanded as x¹² + 12x¹⁰y³ + 60x⁸y⁶ + 160x⁶y⁹ + 240x⁴y¹² + 192x²y¹⁵ + 64y¹⁸.

The Binomial theorem tells us how to expand expressions of the form (a + b)ⁿ, for example, (x + y)⁷. The larger the power is, the harder it is to expand expressions like this directly.

The total number of terms in the expansion of (x + y)ⁿ are (n+1).

The sum of exponents of x and y is always n.

nC₀, nC₁, nC₂, … .., nCₙ are called binomial coefficients and also represented by C₀, C₁, C₂, ….., Cₙ.

The binomial coefficients which are equidistant from the beginning and from the ending are equal.

i.e. nC₀ = nCₙ, nC₁ = nCₙ₋₁ , nC₂ = nCₙ₋₂ ,….. etc.

Let the function be (x² + 2y³)⁶

By using binomial expansion theorem, we get

(x² + 2y³)⁶ = x¹² + 12x¹⁰y³ + 60x⁸y⁶ + 160x⁶y⁹ + 240x⁴y¹² + 192x²y¹⁵ + 64y¹⁸

(x² + 2y³)⁶ is expanded as x¹² + 12x¹⁰y³ + 60x⁸y⁶ + 160x⁶y⁹ + 240x⁴y¹² + 192x²y¹⁵ + 64y¹⁸

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From the rules of transformation;

To get the function g, shift f upwards  by 1 unit.

Transformations simply takes the basic function and transforms it to another function.

The rules of transformation are;

Now, we want to transform f(x) = |x| into g(x) = |x| + 1

This means from the rules of transformation above, we can say that;

To get the function g, shift f upwards  by 1 unit.

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keeping in mind that a year has 12 months, thus 9 months is really 9/12 of a year.

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$960\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years\to \frac{9}{12}\dotfill &\frac{3}{4} \end{cases} \\\\\\ I = (960)(0.09)(\frac{3}{4}) \implies I=64.8[/tex]

The definition for the linear piecewise function is given as follows:

B.

A linear function is modeled by the following rule:

y = mx + b

In which:

A piecewise-defined function is a function that has different definitions, depending on the input of the function.

For x to the left of 0, we have a line with intercept of 2, hence:

y = mx + 2.

When x increases by 1, y increases by 2, hence the slope is of m = 2 and:

y = 2x + 2, x ≤ 0.

For x to the right of 0, we have a line with intercept of 4, hence:

y = mx + 4.

When x increases by 3, y decreases by 4, hence the slope is of m = -4/3 and:

y = -4/3x + 4, x > 0.

Hence the definition of the function is given by:

B.

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Answer:

1/2 is the correct answer

Step-by-step explanation:

7/8 - 3/8 = 7 -3/8 = 4/8=1/2

The total expenses of Mrs Terry is given as $3160

We have to form the equation as

2632 = 2500 + 20%(x - 2500)

We have to use the multiplicative distributive law here

Such that we would have

2632 = 2500 + 0.2x - 500

We have to rearrange the terms

2632 - 2500 + 500 = 0.2x

632 = 0.2x

Next we have to divide through by 0.2

632 / 0.2 = x

3160 = x

Hence the total expenses of Mrs Terry is given as $3160

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Following Venn diagram, the correct choice for the set is:  {2, 3, 5, 6, 8, 9}

In a Venn diagram, as used in sets, the intersect of sets refers to members that ate are common to the sets is perspective.

For the given Venn diagram, the intersect of the sets M and N is the numbers in the middle, this means the set M and N has this numbers in common.

However, the question is asking not intersect of sets M and N so knowing the intersect will help us exclude them to have {2, 3, 5, 6, 8, 9}.

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Answer:

[tex]y = \frac{3}{4}x - 8[/tex]

Step-by-step explanation:

We know that the slope of a line perpendicular to a line with a given slope is the negative reciprocal of that given slope.  We are given that we want a line perpendicular to that of 4x + 3y = 3.  To find the slope of this given line, we put it into slope intercept form y = mx + b where m is the slope:

[tex]4x + 3y = 3[/tex]

[tex]3y = 3 - 4x[/tex]

[tex]y = 1 - \frac{4}{3}x[/tex]

So we have that the slope of our given line is -4/3. The negative reciprocal of this is 3/4. We thus have that the slope of the line we are looking for is 3/4.

We then know that the equation of the line we want fits the form [tex]y=\frac{3}{4} x + b[/tex], which we know through point slope form. We are then given that (8, -2) is a point on this line. Plugging in:

[tex]-2 = \frac{3}{4}(8) + b[/tex]

[tex]-2 = 6 + b[/tex]

[tex]b = -8[/tex]

We then get the equation of the line we are looking for as [tex]y = \frac{3}{4}x - 8[/tex].

Answer:

equation: x-42=50

answer: x=8

Step-by-step explanation:

lets write the equation. We have 42 less than x is -50. 42 less than x could translate to x-42 and if it is 50, then that is what x-42 equals.

So we would have x-42=50

Now you can carry over the -42 to start solving

x-42=50

 +42    +42

(notice it is added on both sides. I add them to get rid of the -42 on the x side and whatever you do to one side you ALWAYS do to the other.)

x= 50-42

x= 8

i hope this helps :)

The value of x is 18.

3 × [tex] {(x - 2)}^{3/4} [/tex] = 24

Dividing the left hand side and right hand side of the equation by 3, we get

[tex] {(x - 2)}^{3/4} [/tex] = 8

Now, on the right hand side of the equation 8 can be written as

[tex] {(x - 2)}^{3/4} [/tex] = [tex] {(2)}^{3/4×4} [/tex]

Taking paper 4/3 on both the sides of the equation, we get

[tex] {(x - 2)}^{3 / 4 \times 4 / 3} = {2}^{3 / 4 \times 4 \times 4 / 3} [/tex]

x - 2 = 2⁴

x - 2 = 16

x = 16 + 2

x = 18

Thus, the value of x = 18.

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For the given equations 5x+8, 2x + 1, x - 4 does not form the geometric sequence as the common ratio is not equal.

For the given sequence;

The first three terms of a sequence are given by;

a = 5x+8,

ar = 2x + 1,

ar² = x - 4

Put the value of x = 11 to check if the sequence forms and GP.

a = 5x11+8 = 63

ar = 2x11 + 1 = 23

ar² = 11 - 4 = 7

Find the common ratio;

ar/ a = ar²/ar

23/ 63 = 7/ 23

But 23/ 63 ≠ 7/ 23

As, the common ratio is not same, it will not form as geometric sequence.

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Answer:

Step-by-step explanation:

Your answer is going to be x²+4x-5=0

Based on the table given, we can infer that the table shows a proportional relationship.

A proportional relationship refers to when the value of x and y increase by the same ratio for all the values in the distribution.

In the given table, Pens is increasing by 3:
= 3, 6, 9, 12

Boxes keep increasing by 1:

= 1, 2, 3, 4

This shows that the table shows a proportional relationship because both pens and boxes are increasing by the same rate.

In conclusion, the table given shows a proportional relationship.

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The translation sequence that maps angle ABC to angle A'B'C' is (x, y) ⇒ (x + 3, y + 6)

Transformation is the movement of a point around the coordinate plane. Types of transformations are rotation, translation, reflection and dilation.

Translation is a type of transformation which is either up, down, left or right in the coordinate plane.

The translation sequence that maps angle ABC to angle A'B'C' is (x, y) ⇒ (x + 3, y + 6)

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Integer -17 represents Rudy's score for 2 weeks.

Rudy's scores:

Then, add 15 and -32 as follows:

Therefore, integer -17 represents Rudy's score for 2 weeks.

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Check the picture below.

now, let's get their length of TZ and TX and thus we'll get their ratio as TX/TZ or TX : TZ

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ T(\stackrel{x_1}{-8}~,~\stackrel{y_1}{-5})\qquad X(\stackrel{x_2}{4}~,~\stackrel{y_2}{-1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ TX=\sqrt{(~~4 - (-8)~~)^2 + (~~-1 - (-5)~~)^2} \implies TX=\sqrt{(4 +8)^2 + (-1 +5)^2} \\\\\\ TX=\sqrt{( 12 )^2 + ( 4 )^2} \implies TX=\sqrt{ 144 + 16 } \implies TX=\sqrt{ 160 } \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ T(\stackrel{x_1}{-8}~,~\stackrel{y_1}{-5})\qquad Z(\stackrel{x_2}{7}~,~\stackrel{y_2}{0})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ TZ=\sqrt{(~~7 - (-8)~~)^2 + (~~0 - (-5)~~)^2} \implies TZ=\sqrt{(7 +8)^2 + (0 +5)^2} \\\\\\ TZ=\sqrt{( 15 )^2 + ( 5 )^2} \implies TZ=\sqrt{ 225 + 25 } \implies TZ=\sqrt{ 250 }[/tex]

[tex]~\dotfill\\\\ TX~~ : ~~TZ\implies \cfrac{TX}{TZ}\implies \cfrac{\stackrel{TX}{\sqrt{160}}}{\underset{TZ}{\sqrt{250}}}\implies \cfrac{\sqrt{4^2\cdot 10}}{\sqrt{5^2\cdot 10}}\implies \cfrac{4~~\begin{matrix} \sqrt{10} \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{5~~\begin{matrix} \sqrt{10} \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \implies {\LARGE \begin{array}{llll} \cfrac{4}{5} \end{array}}[/tex]

Answer:

900 kilometers

Step-by-step explanation:

Convert the percentage into a decimal.

90 ÷ 100 = 0.9

Multiply 1000 by 0.9

1000 * 0.9 = 900

After solving, the factors of the equation x²-13x-30=0 are:

So,

Given equation: x²-13x-30=0

Then,

Factors are: (x-15) and (x+2)

Therefore, after solving, the factors of the equation x²-13x-30=0 are:

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The area of the rectangular fenced area for dog run is given by:

A = 4x² + 34x + 18.

Considering a rectangle of length l and width w, we have that:

For this problem, the section enclosed by the fence is divided into two triangles, as follows:

Hence the total area is:

A = 8(2x) + (6 + 2x)(2x + 3)

A = 16x + 4x² + 18x + 18

A = 4x² + 34x + 18.

Hence the area of the rectangular fenced area for dog run is given by:

A = 4x² + 34x + 18.

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