can anyone tell me what goes with what?

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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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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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]

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

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

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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If a and b are rational numbers, then the product of (a+√b) and its conjugate is always a rational number.

The conjugate of ( a + [tex]\sqrt{b}[/tex] ) is ( a - [tex]\sqrt{b}[/tex] ) .

Product of  ( a + [tex]\sqrt{b}[/tex] ) and ( a - [tex]\sqrt{b}[/tex] )  =  ( a + [tex]\sqrt{b}[/tex] ) * ( a - [tex]\sqrt{b}[/tex] )

                                                         = ( [tex]a^{2}[/tex] ) - a[tex]\sqrt{b}[/tex] + a[tex]\sqrt{b}[/tex] - [ [tex]\sqrt{b} ^{2}[/tex] ]

                                            = ( [tex]a^{2}[/tex]) - b .

The expression ( [tex]a^{2}[/tex]) - b is rational .

Hence , if a and b are rational numbers, then the product of (a+√b) and its conjugate is always a rational number.

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Exponential Form

We've all heard the term "exponential." What does that word mean? Exponential means growing faster and faster. However, in mathematics, it represents a formula with one or more exponents. So, we know it as exponential form. I would say that things can grow exponentially as the items being talked about get bigger and faster and faster.

So, we use the following method to write the given expression in exponential.

Expression 1 = ⁴√x³

Expression 2 = ⁵√y⁴

Use n*sqrt{a}x=a^(x/n) to rewrite 4*sqrt{x}3 as x^ (3/4)

similarly, we can write the second equation as

Use n*sqrt{a}x=a^(x/n) to rewrite 5*sqrt{y}4 as y^ (4/5)

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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]

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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The value of the expression sec (-π) is equal to -1 if the given expression is undefined.

As given in the question,

Given expression: sec (-π)

Standard position of unit circle: -π is representing semicircle with terminal point on negative x-axis with coordinates (-1, 0)

Hypotenuse = √ (-1)² + 0²

                     = 1

Value of the expression is given by

sec α = Hypotenuse / Base (x-coordinate)

⇒sec(-π) = 1 / -1

⇒sec(-π) = -1

Therefore, the value of the expression sec (-π) is equal to -1.

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Answer: C, 21

Step-by-step explanation:

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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Solution of exponential equation is ,  x = 10

In, mathematics a exponential equation or exponential function is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the logarithm function can be written as  [tex]a^x[/tex] .

where, a is the base of function

           x defines  expression

Mathematically, if  [tex]log_aN = x[/tex] is an logarithmic function then, this can be converted to exponential function as  [tex]a^x = N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.

Some important formulas of exponential :

According to given statement,

5.2³ x =400

=> 5.8 x =400

=> 40x = 400

=> x =10

Thus solution for this equation is x =10.

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The complete question is :

What is the solution of each exponential equation? Check your answer.

a. 7⁻⁴x=800

b. 5.2³x=400

Answer:

1/2 is the correct answer

Step-by-step explanation:

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

Answer:

Step-by-step explanation:

Your answer is going to be x²+4x-5=0

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 :)

After approximately 16 years, the principal amount of $500 double.

So, to find out how many years will a principal of $ 500 double:

The formula for calculating compound interest is as follows:

The value of r is 0.0462. In the equation, substitute this and x:

Therefore, after approximately 16 years, the principal amount of $500 double.

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In [tex]e^{2x} =10[/tex] , x = 1., by the properties of logarithm.

Now,

In [tex]e^{2x} =10[/tex] , taking natural logarithm on both side.

=>  [tex]log_e(e^{2x})=log_e(10)[/tex]

By properties of logarithm, we know that: [tex]log_b(a)^m = m(log_b(a))[/tex]

=> [tex]2x(log_e(e))=ln(10)[/tex]

Also, as [tex]log_e(e)[/tex] = 1,

=> 2x (1) = ln(10)

=> 2x = 2.302 (approx)

=> x = 1.151

Hence, In [tex]e^{2x} =10[/tex] , x = 1.151, by the properties of logarithm.

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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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a. 3.5 x 4.1 (3.5 ×2.8) = -0.7

b.  2.5+ (-4.1) + [(−2.3) × (-1.1)] = 4.29

c. [-5.5 (-6.5) ÷ 2.4]+ (-1.1) = -0.5

Hence the required parentheses are added to make the statement true.

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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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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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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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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