What is the perimeter of AYXZ?
3.5 in.
5.3 in.
6.4 in.
7.8 in.

The expression 2a−4b+7c is a trinomial and a first-degree polynomial.

The expression 2a−4b+7c is a linear polynomial because each term has a variable (a, b, c) with an exponent of one.

It is also a first-degree polynomial since the highest power of any variable is 1.

[tex]\bf \begin{array}{ccll} vinegar&oil\\ \cline{1-2} 2&5\\ 9&x \end{array}\implies \cfrac{2}{9}=\cfrac{5}{x}\implies 2x=45\implies x=\cfrac{45}{2}\implies x=22\frac{1}{2}[/tex]

22.5 ounces of oil should be mixed with 9 ounces of vinegar

An equation is an expression that shows the relationship between two or more variables and numbers.

Given that:

2 part vinegar 5 part oil.

Let y represent the amount of oil to be mixed with 9 ounces of vinegar.

y = (5/2) * 9 = 22.5 ounces

22.5 ounces of oil should be mixed with 9 ounces of vinegar

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I'm going to assume that you meant to write: The square of a number exceeds that number by 12. What are the two possible solutions.

In other words x² = x + 12

4² is 16.

4 + 12 = 16

(-3)² is 9

-3 + 12 = 9

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: Multiply (60 − 2x) and (2 + 0.25x) to create the equation y = -0.5x2 + 11x + 120

We know that David wants to increase the price per cup to increase his revenue. He found out that for every $0.25 grows( increase), x, in the price for each cup.

In the event of a price increase, 2 cups remain unsold, and doubling the cups is still not sold. Then the numbers are sold (60-2x). Depending on the choice:

Revenue= (60 -2x)(2 +0.25x)

60·2 +60·0.25x -2x·2 -2x·0.25x

= -0.5x² +11x +120

Answer:

Multiply (60 − 2x) and (2 + 0.25x) to create the equation y = -0.5x2 + 11x + 120

Step-by-step explanation:

Here, x represents the times at which the price is increased,

Since, the original price of one cup = $ 2,

So, after increasing x times of $ 0.25, the new price of each cup = 2 + 0.25x,

Also, the original number of mochas = 60,

Given,

With increasing the price $ 0.25, x times, the number of cup is decreased by 2 times of x,

That is, the new number of mochas = 60 - 2x

Hence, the total revenue would be,

y = new price of each cup × new number of mochas

⇒ y = (2 + 0.25x)(60 - 2x)

⇒ y = 120 - 4x + 15x - 0.5x²

⇒ y = -0.5x² + 11x + 120

He can find find the equation which represents his daily revenue, by Multiplying (60 − 2x) and (2 + 0.25x) to create the equation y = -0.5x² + 11x + 120

Answer:

754 inches

Step-by-step explanation:

you have to convert the 62 feet into inches which will be 62*12=744. You then add 10 to it to get 754 as your answer.

Answer:

Shorter sides: 270 feet.

Larger side: 540 feet.

Greatest possible area: 145800 square feet.

Step-by-step explanation:

So we need fencing around the garden except along the river.

The opposite sides of a rectangular are congruent.

So the sides perpendicular to the river in the picture are both of the same length, let's call it x.  The length opposite the river is y.  

So the perimeter excluding the side along the river is

x+x+y or 2x+y or 1080 is how much fencing we want.

So we have the equation:

2x+y=1080

The area of rectangle can be found by multiplying it's dimensions:

xy=A

We want to find the dimensions that provide us with the maximum area.

This is our area function so for:

A=xy

We need the area to be in terms of one variable.

Let's use our condition that 2x+y=1080.

2x+y=1080

Subtract 2x on both sides:

y=1080-2x

or

y=-2x+1080

We are going to plug this into:

[tex]A=xy[/tex]

[tex]A=x(-2x+1080)[/tex]   :  I replaced y with -2x+1080 since y=-2x+1080.

[tex]A=-2x^2+1080x[/tex] :  I distribute.

Let's find the x-coordinate of the vertex.

To do this we need to determine [tex]a[/tex] and [tex]b[/tex] in the comparison of

[tex]A=ax^2+bx+c[/tex].

[tex]a=-2[/tex]

[tex]b=1080[/tex]

[tex]c=0[/tex]

The formula for the x-coordinate of the vertex is [tex]\frac{-b}{2a}[/tex].

[tex]\frac{-b}{2a}=\frac{-1080}{2(-2)}=\frac{1080}{4}=270[/tex]

We could plug this into our area Area function in terms of to find maximum area.

We could also wait til later.  I think I will do both for a later check.

[tex]A=-2x^2+1080x[/tex] with [tex]x=270[/tex]

[tex]A=-2(270)^2+1080(270)[/tex]

[tex]A=145800[/tex]

So we one dimension of the rectangle so for which is 270 feet.

We have the maximum area which is 145800 square feet.

Now recall y=-2x+1080.

y=-2x+1080 with x=270

y=-2(270)+1080

y=540

So we have one dimension of the rectangle is 270 feet.

Another dimension is 540 feet.

And the area of the rectangle is 145800 square feet.

Does 270(540) equal 145800? 270(540)=145800 so yes.

Let's check to see if we have 1080 feet of fencing.

So we have 2 small sides of 270 and 270 feet.

We have a larger side which is 540 feet.

270+270+540=10180 so everything checks out.

Answer:

Step-by-step explanation:

[tex](g\circ f)(x)=g\bigg(f(x)\bigg)\\\\f(x)=2x+1,\ g(x)=x+14\\\\\text{Exchange}\ x\ \text{in}\ g(x)\ \text{to}\ (2x+1):\\\\(g\circ f)(x)=g\bigg(f(x)\bigg)=g(2x+1)=(2x+1)+14=2x+15[/tex]

Answer:

Step-by-step explanation:

The image is blurred.

The given frequency is showing only 4 intervals, that means there should be only 4 bars in the right histogram, that lead us only to the first or second choice as right answers.

Now, according to the frequency table the first interval is larger than the second interval and the third interval is larger than the fourth interval. This means the first bar must be taller than the second bar, and the third bar must be taller than the fourth bar, and the second histogram is showing this.

Therefore, the right histogram is the second one.

Answer:

Step-by-step explanation:

Dividing one number by another yields a quotient. The quotient of 9 divided by 15 can be expressed as a decimal or a fraction. Any time you divide a number by a larger number, the answer will always be less than one.

Answer:

C

Step-by-step explanation:

1/9

Answer:

32760

Step-by-step explanation:

There are 4 positions on the board.  There are 15 possible candidates for the first position.  That leaves 14 candidates for the second position.  Which leaves 13 for the third position, and 12 for the fourth position.

15 × 14 × 13 × 12 = 32760

Answer: There are 32,760 ways that research board can be chosen.

Step-by-step explanation:

Since we have given that

Number of research doctors participating in the study = 15

the research board requires to be established with offices of director, Assistant director, Quality control analyst, and Correspondent.

Since there are 15 choices for the Offices of director,

There are 14 choices for the Assistant director,

There are 13 choices for Quality control analyst,

There are 12 choices for Correspondent.

So, by applying "Fundamental theorem of counting", we get that

Number of ways that research board can be chosen is given by

[tex]15\times 14\times 13\times 12\\\\=32,760[/tex]

Hence, there are 32,760 ways that research board can be chosen.

Answer:

$30

Step-by-step explanation:

because we know that "1 liter cost(s) $12" we can multiply 12 by 2.5 (the amount we need to know) to get $30

Answer:

$30.0

Step-by-step explanation:

What you'll need to do is multiply 12 by 2.5.

[tex]12.5x2.5=300\\\\$30.0[/tex]

2 because everything is multiplied by 2 so the scale factor is two

Answer:

1020000

Step-by-step explanation:

Step 1 : Use BODMAS (Bracket Open Divide Multiply Add Subtract)

Step 2 : Take the common term

7.8*10^5+2.4*10^5

10^5(7.8 + 2.4)

Step 3 : Solve

10^5(7.8 + 2.4)

100,000(10.2)

=1020000

!!

Answer:

1.02 × 106

Step-by-step explanation:

1.02 × 106

Answer:

g(x + 8) = 10x + 105 wherever you see it among your answers.

Step-by-step explanation:

I think I have enough here that I can answer the question, but you should always put in your givens.

f(x) = 10x + 25                      Put g(x) where you see x in f(x)

f(g(x)) = 10(g(x) + 25             Put the value for g(x) where you see g(x)

f(x+8) = 10(x + 8) + 25         This might be the answer

From here it is a guess.

f(x+8) = 10x + 80 + 25         Combine the like terms

f(x+8) = 10x + 105

Answer:

on flvs its option C

Step-by-step explanation:

Answer:

1. so the total people including the teacher is 24. 12 and 8 are both factors of 24. 12x2 equals 24 and 8x3 equals 24 so if they get 2 packs of hot dogs and 3 pack of buns everyone can get 1 hot dog and 1 bun

Step-by-step explanation:

24 factors: 1, 2, 3,4 ,6,8,12 ,24

8×3=24

12×2=24

get 2 packs of sausages and 3 packs of buns

each person gets 1 hotdog and 1 bun

Answer:

Prasant needs more than 4.5 bags of candy to hand out during Halloween.

Step-by-step explanation:

The correct method to write a statement that matches the inequality [tex]\( h > 4.5 \)[/tex] is to express that the value of [tex]\( h \)[/tex] is greater than 4.5. This can be done by stating that [tex]\( h \)[/tex] must be some quantity more than 4.5, without specifying the exact amount by which [tex]\( h \)[/tex]exceeds 4.5.

For example, one could write the statement as:

The value of [tex]\( h \)[/tex] is more than 4.5 units.

This statement correctly conveys that [tex]\( h \)[/tex] is not equal to 4.5 and is somewhere on the number line to the right of 4.5, with no upper limit specified. It is important to note that the inequality [tex]\( h > 4.5 \)[/tex] does not include the value 4.5 itself; [tex]\( h \)[/tex] must be strictly greater than 4.5.

In summary, the statement should indicate that \( h \) is any number that is greater than 4.5, and the value of [tex]\( h \)[/tex] can be infinitely close to 4.5 but never equal to or less than it.

Answer:

0

Step-by-step explanation:

use the slope formula y^2-y^1

                                     x^2-x^1

Answer:

No

Step-by-step explanation:

In a triangle, sum of any two sides is always grater than the third side.

Here,

[tex]3 + 2 = 5 \ngtr \: 5 \\ [/tex]

Hence, 3,2,5 can no tbe the lengths of a triangle

Answer:

Advantage: If a car is losing value at a constant rate, then the linear function represents accurately the depreciation of the car.

Disadvantage: If the car is not losing value at a constante rate, then when we calculate the value of the car 'x' years after it was sold, we won't get  an accurate result.

If the minivan is purchased for $29,248 and the first year it depreciates $3000. Then, the linear function that represents the value of the car is:

y = $29,248 - $3000x

Where 'y' represents the value of the car, and 'x' represents the number of years.

Let us explain this with an example. After 6 years, the price will be:

y = $29,248 - $3000(6) =  $11,248

The advantages of using a linear function to represent the depreciation of a car are simplicity and ease of calculation, but it assumes constant depreciation rate. On the other hand, an exponential function can account for varying depreciation rates, but can be more complex. The linear function to represent the value of the minivan after x years is V(x) = 29,248 - 3,000x.

When representing the depreciation of a car over time, using a linear function has advantages and disadvantages. The advantages are that it provides a simple and straightforward representation of the depreciation, and it is easy to calculate and understand. However, a linear function assumes that the car depreciates at a constant rate over time, which may not always be accurate.

On the other hand, using an exponential function to represent the depreciation of the car has advantages and disadvantages as well. The advantage is that it can account for different rates of depreciation over time, which may be more realistic. However, exponential functions can be more complex to calculate and understand.

In the case of the minivan that depreciates $3,000 in the first year, a linear function can be used to represent the value of the car x years after it was sold. The linear function would be V(x) = 29,248 - 3,000x, where V(x) is the value of the car x years after it was sold.

Answer:

False

Step-by-step explanation:

XY is the diameter of the circle with the centre of this circle being O.

But O on it's own is just a coordinate, and not the circle.

Answer:

False, XY is not a diameter

Step-by-step explanation:

To be a diameter, it must go through the center of the circle, which is point O

The chord XY does not pass through the point O, so XY cannot be a diameter

Answer:

Step-by-step explanation:

This is direct variation, and the pertinent equation is y = -2.5x, where -2.5 is the constant of variation.

Answer:

the price is $160000

Step-by-step explanation:

0.22x = 35200

x=160000

Answer:

Choice B

Step-by-step explanation:

A dilation factor of three means you multiply each side bye three. The order of the letters of the triangle also matter. Since it is triangle LMN and ABC this means that A corresponds with L, B corresponds with M and C corresponds with N.

Answer:

x+5

Step-by-step explanation:

Given:

Dividend= x4 + 5x3 – 3x – 15

Quotient=(x3-3)

As per the rule of division of polynomial:

Dividend = Divisor × Quotient + Remainder

Divisor= required polynomial p(x)

remainder=0

x4 + 5x3 – 3x – 15= p(x) *(x3-3) + 0

p(x)=x4 + 5x3 – 3x – 15/x3-3

By long division we get

p(x)= x+5 !

Answer:

The polynomial is x+5.

Step-by-step explanation:

Here we need to recall the algorithm of the division for polynomials, which is very similar to the one for integers. Given polynomials P(x) and Q(x), there always exist polynomials S(x) and R(x) such that

P(x) = Q(x)S(x) + R(x)

where

In this particular case,  

Then, x⁴+5x³-3x-15 = (x³-3)Q(x). In order to find Q(x) we must complete the division x⁴+5x³-3x-15/x³-3. This gives us that Q(x)=x+5.

For this case we must convert the given expression to degrees:

[tex]\frac {3 \pi} {8}[/tex]

By definition we have that [tex]\pi = 180[/tex] degrees, then:

[tex]\frac {3 \pi} {8} * \frac {180} {\pi} = \frac {180 * 3} {8} = \frac {540} {8} = 67.5[/tex]

Thus, we have [tex]\frac {3 \pi} {8}[/tex] is equal to 67.5 degrees.

Answer:

67.5 degrees

Answer:

156.654

Step-by-step explanation:

162*.967=156.654

To multiply 162 by 0.967, use a calculator or perform the multiplication manually to get approximately 156.654.

The product of 162 and 0.967, you can multiply these two numbers together. When you multiply a whole number by a decimal, you're essentially combining that many groups of the decimal number. In this case, you are combining 162 groups of 0.967.

Here is the step-by-step calculation:

Write down the numbers: 162 and 0.967.

Multiply the whole number by the decimal: 162 * 0.967.

Use a calculator or long multiplication to find the product.

If you use a calculator, the answer you would get is approximately 156.654.

Using the formula for compound interest, you can calculate the future value of an investment for different compounding methods. These values turned out to be $66299.84 for annual compounding, $66933.56 for semi-annual compounding, $67183.56 for monthly compounding and $67239.46 for daily compounding.

To solve this problem, you need to understand the compound interest formula: A = P(1 + r/n)^(nt).

Where:

(a) For annual compounding (n=1): A = 47400*(1 + 0.07/1)^(1*5) = $66299.84

(b) For semi-annual compounding (n=2): A = 47400*(1 + 0.07/2)^(2*5) = $66933.56

(c) For monthly compounding (n=12): A = 47400*(1 + 0.07/12)^(12*5) = $67183.56

(d) For daily compounding (n=365): A = 47400*(1 + 0.07/365)^(365*5) = $67239.46

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Final answer:

Calculate the value of the investment after 5 years using different compounding methods.

Explanation:

The value of the investment at the end of 5 years:

Annual: $61,571.76

Semiannual: $62,041.46

Monthly: $62,263.11

Daily: $62,334.74

Answer:

I prefer to express solutions to inequalities using interval notation. Both formats are are important but I think interval notation is easier to understand and represents better the solutions.

For example, if you have the following inequation:

x-2> 1

x>3

Therefore, the solution could be written either x>3 OR (3, +inf). But what happens if the solution to the system of equation is x>3 or x<-3? The solution can be easily written as: (-inf, -3) U  (3, inf) instead of 'x>3 or x<-3' which is more confusing.