If 41 and 42 are complementary angles and if the measure of 41 is 50° more than the measure of 42, determine the measures of 41 and 42

Answer:

y = 3.8x

Step-by-step explanation:

Let y = the cost of the cherries

Let x = pounds of cherries

We can find the unit rate by either:

[tex]\frac{7.98}{2.1}[/tex] =  $3.80 per pound

or

[tex]\frac{10.64}{2.8}[/tex] = $3.80 per pound

Now we can write the equation

hy = 3.8x

Answer:

(a) There are 20 ways for her to distribute the books if they are all the same and no child gets more than one. Each of the 20 children can receive one of the five books.

(b) There are 100 ways for her to distribute the books if they are different and no child gets more than one. Each of the 20 children can receive one of the five different books, so there are 5x4x3x2x1 = 100 possible ways for her to distribute the books.

(c) There are 3,628,800 ways for her to distribute the books if they are all the same and there is no restriction on the number of books that can be given to any child. This is because each child can receive any number of books from 0 to 5. Therefore, there are 6x6x6x6x6 = 6^5 = 3,628,800 possible ways for her to distribute the books.

Step-by-step explanation:

The value of b in x²+ bx + 16/49 is 8/7 and the squared binomial is (x + 4/7)²

From the question, we have the following parameters that can be used in our computation:

X^2+bx+16/49

Rewrite properly

So, we have the following representation

x²+ bx + 16/49

When represented as a square, we have

x²+ bx + 16/49 = (x + a)²

Expand the bracket

So, we have the following representation

x²+ bx + 16/49 = x² + 2ax + a²

By comparison, we have

bx = 2ax

a² = 16/49

Take the square root of both sides

a = 4/7

Substitute a = 4/7 in bx = 2ax

bx = 2 * 4/7x

So, we have

b = 2 * 4/7

Evaluate

b = 8/7

In (a), we have

x²+ bx + 16/49 = (x + a)²

Where

a = 4/7

So, we have

x²+ bx + 16/49 = (x + 4/7)²

Hence, the binomial is (x + 4/7)²

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Answer:

[tex]\textsf{1)} \quad b = \dfrac{8}{7}[/tex]

[tex]\textsf{2)} \quad \left(x+\dfrac{4}{7}\right)^2[/tex]

Step-by-step explanation:

Perfect Square Trinomial

A trinomial that can be written as the square of a binomial.

For example the perfect trinomial  x²+2dx+d² can be written  as (x+d)².

Given trinomial:

[tex]x^2+bx+\dfrac{16}{49}[/tex]

To express the given trinomial as a perfect square trinomial, determine the value of b.

As the coefficient of the x² term is one, b equals twice the square root of the constant of the trinomial:

[tex]\implies b = 2 \sqrt{\dfrac{16}{49}}[/tex]

[tex]\implies b = 2 \cdot \dfrac{4}{7}[/tex]

[tex]\implies b = \dfrac{8}{7}[/tex]

Therefore, the perfect square trinomial is:

[tex]x^2+\dfrac{8}{7}x+\dfrac{16}{49}[/tex]

To factor in the form of a squared binomial (x + d)², d is half the value of b:

[tex]\implies d = \dfrac{1}{2}b[/tex]

[tex]\implies d = \dfrac{1}{2} \cdot \dfrac{8}{7}[/tex]

[tex]\implies d=\dfrac{8}{14}[/tex]

[tex]\implies d=\dfrac{4}{7}[/tex]

Therefore, the perfect square trinomial as a squared binomial is:[tex]\implies \left(x+\dfrac{4}{7}\right)^2[/tex]

Eva takes 51 errands (mins) to return home.

What do you mean by errands and give example ?

A short trip either to take a message or to take or collect something.

For example , I'll meet you at six, I have some errands to do/run first.

Given that :

Eva left the house at 11.28 am

Returned house at 12.19 pm

From the given information, we can conclude that how long was

she running errands

 11.28 am - 12.00 pm = 32 mins

 12.00 pm - 12.19 pm = 19 mins

                       Totally = 51 mins

Therefore, Eva takes 51 errands to return home.

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Answer: d -3

Step-by-step explanation:

The answer I got was 11 = 21, which does not make sense

–2x + 11 = x + 21 + (-3)x

+3x                         +3x

x + 11 = x + 21

-x        -x

11 = 21

Answer:

-3

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(x) =-2 (x+4)

f(x)=2

x+4

Answer:a

Step-by-step explanation:

The amount you will have $6,500 with 5% in six years using continuous compounding is of:

$8,774.

The amount you will need to have the entire $32000 in the 6 years is of:

$18,890.46.

The balance of an account after t years, using continuous compounding, is given as follows:

[tex]B(t) = Pe^{kt}[/tex]

In which the parameters are given as follows:

Putting the $6,500 into the account, the values of the parameters are given as follows:

P = 6500, k = 0.05, t = 6.

Hence the balance will be of:

B(6) = 6500 x e^(0.05 x 6) = $8,774.

The balance to have the entire $32,000, considering what you already have, will be of:

32000 - 6500 = 25500

Hence the principal is obtained as follows:

Pe^(0.05 x 6) = 25500

P = 25500/e^(0.3)

P = $18,890.46.

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The minimum volume of the box =  11220 cubic centimeters

What is volume?

In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.

One notebook:

length, l= 29 cm

width = 21.5 cm

height = 1.5 cm

Volume of 1 notebook =  l*w*h

                                     =  29*21.5*1.5

                                     =  935.25

                                     ≈  935 cubic centimeters ( nearest whole number )

Volume of 12 notebooks = 935 * 12 = 11220 cubic centimeters

So, the minimum volume of the box =  11220 cubic centimeters

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Answer:

11,223

Step-by-step explanation:

Answer:

D)The space heater, because it has the greater unit rate for electricity cost.

Step-by-step explanation:

I DID IT AND GOT IT RIGHT!

The maximum width and area of rectangle are 475 feet and 225625 sq. feet respectively.

Any given rectangle  has ONE region - there is no base or most extreme, simply a region. To find the region of a rectangle  shape, increase the length times the width. For instance, a rectangle  shape 4′ long by 5′ wide will have an area of 20 square feet.

We have

l×w = area of rectangle-------------------------(1)

2w + l = 950

l = 950 - 2w

Put the value if l in equation (1)

(950 - 2w) × w = area

This is a quadratic equation for maximum value of w we have of it one zeros is zero

so,

950 - 2w = 0

w = 950/2

W =475 feet

Te

Then length = 950 - 475 =475

Area of rectangle = 475 × 475 = 225625 sq. feet

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Answer:

Step-by-step explanation:

You have a piecewise defined function f(x) and you want the values of f(-5), f(-2), and f(1).

The first step in finding the value of a piecewise defined function is to determine the function definition on the domain containing the x-value of interest.

The value x=-5 is in the interval x < -2, so the first part of the function definition applies: f(x) = 3.

  f(-5) = 3

The value x = -2 is in the interval -2 ≤ x ≤ 2, so the second part of the function definition applies: f(x) = -(x -1)².

  f(-2) = -(-2 -1)² = -(-3)²

  f(-2) = -9

The value x = 1 is in the interval -2 ≤ x ≤ 2, so the second part of the function definition applies: f(x) = -(x -1)².

  f(1) = -(1 -1)² = -(0)²

  f(1) = 0

Answer:

y = 31

Step-by-step explanation:

2y-5+123=180

123 - 5 = 118

2y+118=180

subtract 118 from both sides

2y+118 - 118 = 180 - 118

180 - 118  = 62

2y = 62

divide 2 by both sides

2y/2 = 62/2

y = 31

Answer:

Step-by-step explanation:

2y+−5+123=180

Step 1: (Combine Like Terms)

(2y)+(−5+123)=180

Step 2:  (Subtract 118 from both sides)

2y+118−118=180−118

2y=62

Step 3: Divide both sides by 2

2y/2= 62/2

y=31

Answer:

[tex]\textsf{a)} \quad y=3\left(\dfrac{5}{3}\right)^x[/tex]

[tex]\textsf{b)} \quad y=40\left(\dfrac{1}{3}\right)^x[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

From inspection of the diagram, two points on the graph are:

The y-intercept is the y-value when x = 0.

As a is the y-intercept, and the y-intercept is 3:

[tex]\implies y=3 \cdot b^x[/tex]

Substitute point (1, 5) into the equation and solve for b:

[tex]\begin{aligned}(1,5) \implies 5&=3 \cdot b^1\\5&=3b\\b&=\dfrac{5}{3}\end{aligned}[/tex]

Therefore, the equation of the exponential function is:

[tex]y=3\left(\dfrac{5}{3}\right)^x[/tex]

From inspection of the diagram, two points on the graph are:

The y-intercept is the y-value when x = 0.

As a is the y-intercept, and the y-intercept is 40:

[tex]\implies y=40 \cdot b^x[/tex]

Substitute point (-1, 120) into the equation and solve for b:

[tex]\begin{aligned}(-1,120) \implies 120&=40 \cdot b^{-1}\\\dfrac{120}{40}&=\dfrac{1}{b}\\b&=\dfrac{40}{120}\\ b&=\dfrac{1}{3}\end{aligned}[/tex]

Therefore, the equation of the exponential function is:

[tex]y=40\left(\dfrac{1}{3}\right)^x[/tex]

[tex]\textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)\cos(C)\implies c = \sqrt{a^2+b^2-(2ab)\cos(C)} \\\\[-0.35em] ~\dotfill\\\\ c = \sqrt{100^2+60^2~-~2(100)(60)\cos(60^o)} \implies c = \sqrt{ 13600 - 12000 \cos(60^o) } \\\\\\ c = \sqrt{ 13600 - 12000 \cdot \frac{1}{2} }\implies c=\sqrt{7600}\implies c=20\sqrt{19}\implies c\approx 87.18[/tex]

Answer: It is B

Step-by-step explanation:

If you put leg a (3) and leg b (4) into a Pythagorean equation it will turn out like this

3^2+4^2=x^2

9+16=x^2

25=x^2

√25=√x

5=x

5 is the missing side length, which corresponds to option b

Answer: the percent decrease is 9%

Step-by-step explanation:

Formula :12500/14000x100% and this formula can use in any of question likes this

The value of angle RPQ in the circle is 115°.

The products of the measurements of the segments of two chords are equal if they intersect in a circle.

When two chords intersect inside a circle, the resulting angle's measure is equal to the product of the lengths of the arcs it intercepts and its vertical angle, divided by two.

Therefore,

∠RPQ = 1  / 2 (arc angle RQ + arc angle SA)

arc angle RQ = 175°

arc angle SA = 55°

Hence,

∠RPQ  = 1 / 2 (175 + 55)

∠RPQ  = 1 / 2 (230)

∠RPQ  = 115°.

Therefore, the angle is 115°.

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The required value of f(5) would be 81.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

We have been given the function below as:

f(n) = f(n-1) - 3   ....(i)

f(1) = 3

To determine the value of f(5)

Substitute the value of n = 2 in the equation (i);

f(2) = - 3f(1) = - 3;

n = 3,

f(3) = - 3f(2) = 9;

n = 4,

f(4) = - 3f(3) = - 27,

n = 5,

f(5) = - 3f(4) = 81

Thus, the required value of f(5) would be 81.

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The linear functions in this problem are given as follows:

First we define the horizontal line l, given as follows:

l: y = 4.

(as no matter the value of x, the output variable assumes a value of 4).

Then the vertical line p is defined as follows:

p: x = -4.

(as no matter the value of the output y, the input variable x assumes a value of -4).

For the remaining two lines, they are defined in the slope-intercept format, as follows:

y = mx + b.

In which the coefficients are given as follows:

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The value of 3¾ft in yards would be = 1 6/25 yard

A mixed number is the type of number that is made up of three parts such as the whole number, a numerator and a denominator.

To convert to yards;

1 ft = 0.33 yard

3¾ = X yards

make x yards the subject of formula;

X yards = 3¾ × 0.33

X yards = 3.75×0.33

X yards = 1.24 yards

X yards in mixed number= 124/100 = 31/25 = 1 6/25 yard.

Note that the final value which is 124/100 is reduce to the lower figure by dividing through with 4 to arrive at the mixed number 1⁶/25

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The probability that a comfortable chair in the store is blue is 4%

From the question, we have the following parameters that can be used in our computation:

Proportion of blue chairs = 20%

Proportion of orange chairs = 50%

Proportion of black chairs = 30%

Comfortable Blue chairs = 20%

Comfortable non-blue chairs = 5%

The required probability is then calculated as

Probability = Proportion of blue chairs x Comfortable Blue chairs

Substitute the known values in the above equation, so, we have the following representation

Probability = 20% * 20%

Evaluate

Probability = 4%

Hence, the probability is 4%

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Answer:

[tex]C. \; \dfrac{x+2}{x+1}[/tex]

Step-by-step explanation:

Since the vertical asymptotes are at x = -1

This means the denominator must have x + 1 in it

The only expression is the one in choice C

Answer:

The man's monthly rental rate is $1600.

Step-by-step explanation:

To figure out the answer to your question, it says to find how much is monthly rental is. So, we can do this by simply dividing the two numbers:

4800 ÷ 3 = $1600

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Answer:

1/4

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

(6/9) × (3/8)

Cross simplify:

(3/3) × (1/4)

3/12

1/4

Answer: x =4

Step-by-step explanation: The solution of the given equation 24 + 0.44x = 19 + 1.69x will be x = 4 thus option (A) will be correct.

What is the equation?

There are many different ways to define an equation.

More than one variable may be present inside a linear equation.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

As per the given equation,

24 + 0.44x = 19 + 1.69x

24 - 19 = 1.69x - 0.44x

5 = 1.25x

x = 4

Hence "The solution of the given equation 24 + 0.44x = 19 + 1.69x will be x = 4".

Decrease in the price is $1887, the price of the next model car is $35,113.

Percentage is a measurement to find value of the given number out of hundred.

Given that,

Price of current model = $37,000

The price of next model car is 5.1% less than the current model.

The price of the next model car = 94.9% of price of current model car

                                                     = 94.9 x 37,000/100

                                                      = 35,113

The decrease in the price = 37,000 - 35,113 = 1887

The price of the next model car is $35,113 and decrease in the price is $1887.

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Answer:

14 base 10

Step-by-step explanation:

Remember what the digits mean in the base 10 system we use.

For example, the number 539 (base 10) means:

The 5 in the hundreds place means 5 × 100 = 500.

The 3 in the tens place means 3 × 10 = 30.

The 9 in the ones place means 9 × 1 = 9.

The number 539 means

5 × 100 + 3 × 10 + 9 × 1 = 500 + 30 + 9 = 539

Also keep in mind one more thing. The ones digit means the number of ones. 1 = 10^0. The number in the ones digit means the number if 10^0 you have.

The ten digits is the digit of 10^1.

The hundreds digit is the digit of 10^2 since 10^2 = 100.

In other words, the ones digit is the number of 10^0 you have.

The tens digit is the number of 10^1 you have.

The hundreds digit is the number of 10^2 you have.

Now let's look at base 5.

Here, each place to the left is a successively higher power of 5 instead of a power of 10.

Think of the number 432 base 5.

The 2 is in the units place. it represents the number of 5^0 or ones you have. In this case, it is 2 × 5^0 = 2 × 1 = 2

The 3 is in the 5^1 place. It represents the number of fives you have.

3 × 5 = 15

The 4 is in the 5^2 place. It represents the number of 25's you have.

4 × 25 = 100

The number 432 base 5 means:

4 × 5^2 + 3 × 5^1 + 2 × 5^0

= 4 × 25 + 3 × 5 + 2 × 1

= 100 + 15 + 2

= 117 base 10

In other words, 432 base 5 = 117 base 10.

Now we do the same with your number, 24 base 5.

24 base 5 =

= 2 × 5^1 + 4 × 5^0

= 2 × 5 + 4 × 1

= 10 + 4

= 14