If DAB = 80°, then DAC =

Answer:

the ansqer is g(x) = 4^x-4 + 2

Answer:

D. 5/72

Step-by-step explanation:

The non-zero digits are 1 through 9.

There are 9 different non-zero digits.

p(A) = 1/9

There are 5 odd digits.

p(B) = 5/8

p(A and B) = p(A) × p(B) = 1/9 × 5/8 = 5/72

I think the answer is

A: 1/18

The metallurgist would need 46.875 lb of an alloy containing 30 % copper and 3.125 lb of an alloy containing 62 % copper to produce 50 lb of a third alloy.

In this question we must prepare a third alloy by using correct quantity of two alloys with different copper concentrations. Required weights can be determined by applying concept of weighted average:

(32/100) · (50 lb) = (30/100) · x + (62/100) · (50 - x)

32 · 50 = 30 · x + 62 · (50 - x)

32 · 50 = 30 · x + 62 · 50 - 62 · x

32 · x = 30 · 50

x = 46.875

The metallurgist would need 46.875 lb of an alloy containing 30 % copper and 3.125 lb of an alloy containing 62 % copper to produce 50 lb of a third alloy.

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Answer:

1/4

Step-by-step explanation:

Chances of getting tails out of all the numbers (including heads)

Totals numbers (including heads & tails): 12

Tails & Even Number: 3

3/12 simplified to 1/4

The equation of the line that is perpendicular to y = 1/6 is: B. x = -8.

Perpendicular lines have slope values that equals -1 when multiplied together, that is, they are negative reciprocals.

Given the equation, y = 1/6, the slope is 0. This means it is a vertical line, therefore, the line that is perpendicular to it would automatically be a vertical line with an undefined slope which passes through (,8, -2).

The line therefore, would intercept the x-axis at -8. The equation would be: x = -8.

Equation of the perpendicular line is therefore: B. x = -8.

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Step-by-step explanation:

x = hotel charge before tax in 1st city

y = hotel charge before tax in 2nd city

y = x + 1500

x×0.08 + y×0.05 = 692.5

why ?

a% of b = b×a/100

why ?

b = 100%

1% = 100%/100 = b/100

a% = a×1% = a×b/100 = b×a/100

so, e.g. 8% of something is that something multiplied by 8/100 or 0.08

now, we are using the first equation in the second equation :

x×0.08 + (x + 1500)×0.05 = 692.5

x×0.08 + x×0.05 + 1500×0.05 = 692.5

x×0.13 + 75 = 692.5

x×0.13 = 617.5

x = 617.5 / 0.13 = $4,750

y = x + 1500 = 4750 + 1500 = $6,250

the hotel charge before tax in the first city : $4,750

the hotel charge before tax in the second city : $6,250

Answer:

2

Step-by-step explanation:

Select two points that the red line goes through like (0,-10) and (2,-6).  If I start at the bottom left of the red line, I can see that I am moving to the right and up.  That means that the slope will be positive.  As my x is increasing so is my y.  Starting at point (0,-10) 2 space, but each space counts as 2, so I really move up 4.  Then I check to see how much I moved right.  It is only one space, but again, I am counting by 2s, so I really moved 2 units to the right.  

The fraction would be 4/2 which just equals 2/1  or 2.  

This is an exercise on Thermometric scales.

We have as data:

We apply the following formula:

[tex]\large\displaystyle\text{$\begin{gathered}\sf ^{\circ}F=\frac{9}{5}\ ^{\circ}C+32 \end{gathered}$}[/tex]

We substitute data in the formula:

[tex]\large\displaystyle\text{$\begin{gathered}\sf ^{\circ}F=\frac{9}{5}\times220+32 \end{gathered}$}[/tex]

First multiply 9 x 220, then the result of this division is divided by 5.

[tex]\large\displaystyle\text{$\begin{gathered}\sf =396+32 \ \ \to \ \ [Add] \end{gathered}$}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf =428 \ ^{\circ}F \end{gathered}$}}[/tex]

Therefore the cake recipe that should be baked at 220 °C for 45 minutes, on the Fahrenteir scale is 428 °F. Which indicates that it will be very hot.

Answer:

You must graph the two equations and find the point of intersection (x,y)

Point of intersection: (-4, -3)

Step-by-step explanation:

I can not provide a picture, but if you know how to graph these linear functions on the graph properly, you will find a point where the linear functions intersect at (x,y).

Answer:

12

Step-by-step explanation:

3x^2

because the information provided states that x = -2, that is what we are going to replace x with.

3(-2)^2

the next step is to evaluate the power because that is next in PEMDAS.

(-2)^2 = 4

that leaves us with:

3 * 4 = 12      ( the " * " represents the multiplication sign)

hope this helps!

Answer:

[tex]15x^3 +10x^2 - 15x[/tex]

Step-by-step explanation:

Hello!

Use the distributive property and multiply like terms.

The simplified form is [tex]15x^3 +10x^2 - 15x[/tex].

After rounding to the nearest tenth, we get:

[tex]\frac{2.1}{1.488} = 1.5[/tex]

We have the quotient:

[tex]\frac{2.1}{1.488}[/tex]

If you multiply the numerator and denominator by 1000, you will get the simpler quotient:

[tex]\frac{2100}{1488}[/tex]

It gives:

[tex]\frac{2100}{1488} = 1.45[/tex]

Now we want to round it to the nearest tenth, which is the first digit after the decimal point.

To do so, we need to look at the number at the right of it.

In this case, we can see a 5, so we should round up, then we have:

[tex]\frac{2100}{1488} = 1.5[/tex]

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Answer:

Median is 83

Range: 61

Step-by-step explanation:

The median is the number in the middle.  The range is the max. number subtracted from the min number.

Paul's rent budget is $750, given that his food budget of $225, is 30 percent of his rent budget.

Fractions are representation of quantities as a part of a certain quantity.

Written as a/b, read as a by b, and functions as a divided by b, represents a fraction showing a parts of b equal parts.

a is called the numerator, and b is called the denominator.

Percentages are modified fractions where the whole quantity is represented by 100.

To convert a fraction into percentages we multiply it by 100, while to convert percentages to fraction divided by 100.

In the question, we are given that Paul's budget for food is 30% of the budget he has for rent.

We are asked if his budget for food is $225, what is his budget for rent.

We assume Paul's budget for rent to be $x.

We know that Paul's food's budget is 30 percent of his rent.

Hence, Paul's food budget = 30% of x.

or, Paul's budget for food = 30/100 * x {To convert percentages to fraction divided by 100}

But, we know that Paul's food budget is $225. Thus, we can show that:

225 = 30/100 * x,

or, x = (225*100)/30 = 750.

Thus, Paul's rent budget is $750, given that his food budget of $225, is 30 percent of his rent budget.

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When the coordinate satisfies the original inequality, if a stays the same, b must be greater than its previous value to satisfy the new inequality.

It should be noted that inequality provides an interval to the solution.

This is illustrated graphically. Let's illustrate this with an example, suppose a =1, b = 3

a - b < 0.

1 - 3 < 0

-2 < 0

If a stays the same value, b will be greater than 1.

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Answer:

0.2

Step-by-step explanation:

y = mx + b  The slope is the number before the x.

Use the slope-intercept form to estimate the slope and y-intercept.

Slope: 0.2

y-intercept: (0,−6.9)

The slope intercept form in math exists as one of the forms utilized to estimate the equation of a straight line, given the slope of the line and intercept it forms with the y-axis.

The slope-intercept form exists y = mx + b, where m exists the slope and b exists the y-intercept.

y = mx + b

Use the slope-intercept form to estimate the slope and y-intercept.

Slope: 0.2

y-intercept: (0,−6.9)

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The graph of the parabola g(x) is (x+2)^2 + 3

Given the following parent function of the parabola expressed as;

f(x) = x^2

The function g(x) shows a horizontal translation to the left by 2 units and vertical translation up by 3 units to have the equation;

g(x)  = (x+2)^2 + 3

Hence the graph of the parabola g(x) is (x+2)^2 + 3

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The expression x²-10x-21 is wrong since the product of two negative signs is equal to positive.

Quadratic equations are equations that has a leading degree of 2. The standard quadratic equation is given as;

f(x) = ax^2+bx+c

Given the product of the expression below;

f(x) = (x-3)(x-7)

Expand

f(x) = x(x) - 7x - 3x -3(-7)

f(x) = x^2 - 7x - 3x + 21

f(x) = x^2 - 10x + 21

Hence the expression x²-10x-21 is wrong since the product of two negative signs is equal to positive.

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Answer:

Step-by-step explanation:

(0,2)

Answer:

Step-by-step explanation

So, the graph goes through the points, (-3,0) and (2,0). 3 points on the graph can be (-3,0), (2,0), and (4,3)

The monthly payments for each add-on interest loan is $29.7.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

According to the question,

Principal (P) = $1150

Rate of Interest(R) = 6%

Time (T) = 4 years

The interest is calculated as follows:

SI = (P × R × T)/100

SI = (1150 × 6 × 4)/100

SI=$ 276

Amount (A) = P + SI

A = $(1150 +276)

A = $1426

Monthly payment with interest = A/(4×12)

= $ 1426/48

= $29.7

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They don't need to be pure real or imaginary. Any "mixed" complex number works so long as [tex]z=z'[/tex].

Let [tex]z=z'=a+bi[/tex]. Then

[tex]|z+z'| = |2a+2bi| = 2 \sqrt{a^2+b^2}[/tex]

[tex]|z| + |z'| = 2|a+bi| = 2 \sqrt{a^2+b^2}[/tex]

so [tex]|z+z'|=|z|+|z'|[/tex].

The geometric interpretation is essentially identical. [tex]|z+z'|=2|z|[/tex] is a complex number twice the distance away from the origin in the complex plane as [tex]z[/tex], which is exactly [tex]|z|+|z|[/tex].

The area of QOR from the given diagram is 2π square centimeters

A sector is said to be a part of a circle made of the arc of the circle along with its two radii.

The formula for calculating the area of a sector is expressed as;

A = r²β/2

where

r is the radius of the circle

β is the angle subtended

Given the following parameters

<QOR = 180 - <POQ

<QOR = 180 - 135

<QOR = 45 degrees

Determine the radius

L = rβ

π = r(π/4)

1 = r/4

r =  4

Determine the area of QOR

Area = 4²(π)/8

Area = 2π

Hence the area of QOR from the given diagram is 2π square centimeters

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Answer:

1.5 is the slope and 2 is the intercept

Step-by-step explanation:

I am assuming that the equation is y = 1.5x + 2.

Answer:

6.2 rounds

Step-by-step explanation:

since 1 kilometer is 0.62 miles

10 kilometers is 6.2 miles

so about 6 and 1/5 rounds

The net number of yards lost by the cowboys football team is; 8 yards.

It follows from the task content that the number of yards gained or lost by the football team during each of the three plays is; gained 7 yards, lost 8 yards and then lost 7 more yard.

Hence, by polarising yard gain as positive and yard loss as negative; we have;

Net total = 7 - 8 -7 = -8

Hence, the team lost 8 yards in the total game.

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[tex]\large\displaystyle\text{$\begin{gathered}\sf 9|x-8| < 36 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Divide \ both \ sides \ by \ 9. \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Solve \ Absolute \ Value. \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf We \ know \ x-8 < 4 \ and \ x-8 > -4 \end{gathered}$}[/tex]

         [tex]\large\displaystyle\text{$\begin{gathered}\sf x-8 < 4 \ (Condition \ 1) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x-8+8 < 4+8 \ (Add \ 8 \ to \ both \ sides) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x < 12 \end{gathered}$}[/tex]

           [tex]\large\displaystyle\text{$\begin{gathered}\sf x-8 > -4 \ (Condition \ 2) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x-8+8 > -4+8 \ (Add \ 8 \ to \ both \ \ sides) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x > 4 \end{gathered}$}[/tex]

[tex]\underline{\boldsymbol{\sf{Answer}}}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf x < 12 \ and \ x > 4 \end{gathered}$} }[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Therefore,\bf{\underline{the \ correct \ option}} \ \end{gathered}$}\large\displaystyle\text{$\begin{gathered}\sf is \ \bf{\underline{"A"}}. \end{gathered}$}[/tex]

Given the diameter of the circular garden, the area of the garden is 28.36 yd².

The area of a circle is expressed as; A = πr²

Given that;

A = πr²

A = 3.14 × (3yd)²

A = 3.14 × 9yd²

A = 28.36 yd²

Given the diameter of the circular garden, the area of the garden is 28.36 yd².

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