When using distributive property is it important to include the sign in front of the number?

Answer:

they all add one

and...

the position is multiplied by different numbers

Based on the total budget of Mr. Bell for the incentive and the cost of a pizza box, the equation that matches the word problem is 60 ≥ 9.25x

The amount that Mr. Bell will spend at the most is the budget for the incentive of $60.

He will not spend more than this amount but will spend a maximum of it. This amount of $60 is therefore equal to or greater than the cost of the pizzas:

60 ≥ cost of the pizza

The cost of the pizza is:

= Cost per pizza box x number of boxes

= 9 × x

= 9x

The equation is therefore:

60 ≥ 9.25x

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The distance formula to get the distance of the fly from the corner of the room in meters is 1.985 meter.

Distance formula -

The distance formula is given by the equation -

\(d=\sqrt{ (x2-x1)^{2} +(y2-y1)^{2} \\\)

\(where , (x_1, x_2)\) and \((y_1,y_2)\)  are two given points.

Apply the distance formula to get the distance of the fly from the corner of the room in meters.

Now,

\(x_1 ,y_1\) are form the origin,

Given:

\((x_2,y_2) =(1.5,1.3)\)

By using the equation ,

\(d=\sqrt{ (x2-x1)^{2} +(y2-y1)^{2} \\\)

\(\\d = \sqrt[2]{(1.5^{2} -0^{2})+ (1.3^{2}-0^{2} ) }\)

\(d=\sqrt{(2.25+1.69)\\\\d=\sqrt{\frac{225}{100} +\frac{169}{100} } \\d=\sqrt{\frac{394}{100} } \\d=\frac{\sqrt{394} }{10} \\\\\)

Root value of 394,

\(\sqrt{394}\) = 19.85

\(d= \frac{19.85}{10} \\\\d=1.985\) metre.

Therefore, the distance formula to get the distance of the fly from the corner of the room in meters is 1.985

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The common factor that is missing from both sets of parentheses is:

\(6x^2+11,\\\)

A polynomial that divides evenly and completely into another polynomial is said to be a factor. Finding all of a polynomial's factors, which are multiplied to create the original polynomial, is known as factoring. A component that appears in every term of the polynomial is known as a common factor.

We are given a polynomial of degree 3 as:

\(24x^3-54x^2+44x-99,\)

Now we have to factor the given polynomial using grouping.

We proceed in the following steps:

\(24x^3-54x^2+44x-99\\\\24x^3+44x-54x^2-99\\\\4x(6x^2+11)-9(6x^2+11)\)

( Since we take out the common terms in each of the following groups and obtain a common factor in both the groupings)

Hence, the common factor that is missing is:

\(6x^2+11\),

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Answer:c

Step-by-step explanation:just did the test

Answer:

Step-by-step explanation:

1. Write the question.

17 - 2x = -11

2. Subtract 17 from both sides

-17          -17

    - 2x = -28

3. Negatives cancel

      2x = 28

4. Divide both sides by 2

        /2     /2

        x = 14

5. Check the answer, write the equation.

17 - 2x = -11

6. Substitute x with the value

17 - 2(14) = -11

17 - 28 = -11

-11 = -11

The answer is correct!

Hope this helped,

Kavitha

Answer:

c = -5

Step-by-step explanation:

6c + 14 = -5c + 4 + 9c

1) We want to first combine the c values on the right side. This would give us 6c + 14 = 4c + 4.

2) Next, we want to move the c value to one side of the equation. This means we would subtract 4c from the right side. This gives us 2c + 14 = 4.

3) We can then subtract 14 from the left side to isolate the c value. This gives us 2c = -10.

3) We can then divide both sides by 2 and get the answer for c.

This gives us c = -5.

Using the law of indices the equivalent expression of \(144^{\frac{3}{2} }\) is 1728

The equivalent expression of \(144^{\frac{3}{2} }\) can be express as follows:

Using the law of indices,

\((a^{b} )^{c} = a^{bc}\)

Applying this laws,

\(144^{\frac{3}{2} }=(12^{2} )^{\frac{3}{2} }\)

Hence,

\(144^{\frac{3}{2} }=(12^{2} )^{\frac{3}{2} } = 12^{3}\)

Finally,

12³ = 1728

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The expression that is equivalent to 144 superscript three-halves (\(144^{\frac{3}{2} }\) ) is 1728

From the question, we are to determine the expression which is equivalent to 144 superscript three-halves

The given expression is

\(144^{\frac{3}{2} }\)

This can be simplified as shown below

\(144^{\frac{3}{2} }\)

\((12^{2} )^{\frac{3}{2} }\)

This becomes

\(12^{2 \times \frac{3}{2} }\)

\(12^{3}\)

= 1728

Hence, the expression that is equivalent to 144 superscript three-halves (\(144^{\frac{3}{2} }\) ) is 1728.

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Answer:

$468.16

Step-by-step explanation:

answer key

Answer: 20:3

Step-by-step explanation:

=) 2 cm = 20 mm

therefore, 20:3

The given expression is 4(8x + 5). This is a product of a coefficient and a binomial expression. In mathematics, a binomial is a polynomial with two terms.

They are represented as ax + b or a + bx or (a + b) etc. Given expression is 4(8x + 5). We can simplify this by applying the distributive property. It is given as follows; The distributive property of multiplication states that a(b + c) = ab + ac To simplify the given expression, we need to multiply the coefficient 4 with each term in the parentheses.

It can be done as follows; 4(8x + 5) = 4*8x + 4*5 We multiply 4 with 8x and 4 with 5 to obtain; 32x + 20 This is the main answer. Therefore, the simplified form of 4(8x + 5) is 32x + 20. To simplify the given expression 4(8x + 5), we can use the distributive property. According to this property, the product of a number with the sum of two or more terms is equal to the sum of the products of that number with each term of the sum. In other words, a(b + c + …) = ab + ac + … In the given expression, 4 is multiplied with the binomial (8x + 5). Hence,

4(8x + 5) = 4*8x + 4*5

= 32x + 20

Hence, the simplified form of 4(8x + 5) is 32x + 20.

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Answer:

A

Step-by-step explanation:

To multiply powers of a variable, add the exponents:

\(x^m\cdot x^n = x^{m+n}\)

This rule works for all exponents, positive, negative, or zero.  Also, remember that \(x^0=1\).

Also, remember the definition of negative exponent:  \(x^{-n} = \frac{1}{x^n}\)

To multiply the two monomials, start by multiplying the coefficients, 14 and 4.  That gives 56, so your answer begins with 56.

Now for the powers of x,  \((x^3)(x^{-5}) = x^{3+(-5)} =x^{-2} = \frac{1}{x^2}\)

For the powers of y,  \((y^{-4})(y^4)=y^{4+(-4)} = y^0 = 1\)\((y^{-4})(y^4) = y^{-4+4} = y^0 =1\)

Your answer is

\(56 \cdot \frac{1}{x^2} \cdot 1 =\frac{56}{x^2}\)

The value  of  x the subject of the formula is 2c(4+a)

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.

Equation with Lines

More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.

Given ,

X/2c = a+4 by simplifying ,

x=2c(4+a)

Therefore the value of x the subject of the formula is 2c(4+a)

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Answer:

They started the morning shift with 80 cups of coffee

3 hours into the shift the chef made 40 more cups of coffee

45 minutes into the shift 60 cups of coffee were sold

Explanation:

The graph says that:

1. They started the shift with 80 cups of coffee in stock (point A)

2. 25 minutes later, they had 60 cups of coffee (point B)

3. at 45 minutes, they had 20 cups of coffee (point C)

4. at 2 hours they had 0 cups of coffee. (point D)

5. After 3 hours they had 40 cups of coffee (point E)

6. At the end of the morning they had 10 cups of coffee. (point F)

Therefore, the true statement are:

They started the morning shift with 80 cups of coffee because that is the information showed by point A.

3 hours into the shift the chef made 40 more cups of coffee because at point D there was no cups of coffee, then at point E which is 3 hours into the shift there were 40 cups of coffee.

45 minutes into the shift 60 cups of coffee were sold because they started with 80 cups and 45 minutes later they had 20 cups. It means that they sell 80 - 20 = 60 cups of coffee.

So, the answers are:

They started the morning shift with 80 cups of coffee

3 hours into the shift the chef made 40 more cups of coffee

45 minutes into the shift 60 cups of coffee were sold

Answer:

y=8

Step-by-step explanation:

The two triangles are similar, but scaled to a ratio.

Given the ratio of two corresponding sides AC and NL, the scale is 10:5 which is 2. So, the side MN when scaled to the same ratio, the corresponding side's length y = 4*2 = 8 ft

Answer:

Step-by-step explanation:

gradient = 5 = [k-(-1)]/[6-2]

[k+1]/4 = 5

k+1=20

k=19

The value of k in the line that passes through the points A(2, -1) and (6, k) with a gradient of 5 is found to be 19 by using the formula for gradient and solving the resulting equation for k.

To find the value of k in the line that passes through the points A(2, -1) and (6, k) with a gradient of 5, we'll use the formula for gradient, which is (y2 - y1) / (x2 - x1).

The given points can be substituted into the formula as follows: The gradient (m) is 5. The point A(2, -1) will be x1 and y1, and point B(6, k) will be x2 and y2. Now, we set up the formula as follows: 5 = (k - (-1)) / (6 - 2).

By simplifying, the equation becomes 5 = (k + 1) / 4. To find the value of k, we just need to solve this equation for k, which is done by multiplying both sides of the equation by 4 (to get rid of the denominator on the right side) and then subtracting 1 from both sides to isolate k. So, the equation becomes: k = 5 * 4 - 1. After carrying out the multiplication and subtraction, we find that k = 20 - 1 = 19.

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Answer:

Explained in detail below

Step-by-step explanation:

4/28 = 1/7 = 1:7

The relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean is (b) The 95% C.I. is more precise in estimating a mean than the 90% C.I.

You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval.

The upper and lower numbers of a range with a 95% confidence interval (CI) of the mean are determined from a sample. This range describes potential possibilities for the mean because the actual population mean is unknown. Hence, the 95% C.I. is more precise in estimating a mean than the 90% C.I.

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Answer: zero, hope it helps!! tell if there’s an error

Answer:

No

Step-by-step explanation:

4*3 = 12

5*1 = 5

12 + 5 = 17

17 = 19 <-- doesn't make sense

Answer:

eh..you probaly shouldnt trust me

Step-by-step explanation:

8, and (8+2) = 10 Therefore the second term is 10. Another arithmetic sequence of common difference-5 and first term 15. The firs two terms of this sequence are: 15, and (15 - 5) = 10. Therefore again a 10 as second term.

9.5 or 9 1/2 inches per second in miles per hour is 0.5 .

What is conversion of units?
The process of translating measurements of a given quantity between different units, frequently using multiplicative conversion factors that change the value of the measured quantity without changing its effects, is known as unit conversion. The specific circumstances and the desired result dictate the conversion process. This may be governed by a regulation, contract, set of technical requirements, or other publicly available standards.

What is the conversion factor for inch to mile?
A value in inch when divided by 63360 gives a value in mile.

What is the conversion factor for second to hour?
A value in second when divided by 3600 gives a value in hour.

Given, the speed of Caroline in inches per second = 9 1/2 = 9.5/1 - (i)
Therefore following above literature and dividing numerator by 63360 and denominator by 3600, we get the speed in miles per second.
Thus, required speed = [9.5/63360]/[1/3600) = 0.539 = 0.5

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The 95% confidence interval for the given population proportion is between 0.1716 to 0.2884.

The confidence interval for a population proportion is calculated by the formula,

\(C.I = \bar{p}\pm z_{\alpha/2}\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }\)

Where \(\bar{p}\) is the sample proportion and α is the level of significance.

It is given that,

The statistics reported on CNBC projects, a surprising number of motor vehicles are not covered by insurance. The sample results are

The sample size n = 200;

The number of successes = 46

So, the sample proportion \(\bar{p}\) = 46/200 = 0.23

For a 95% confidence interval, the level of significance is

α = 1 - 95/100 = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

Then, the z-score for the value 0.025 is

\(z_{\alpha/2}\) = 1.96 (from the table)

Thus, the confidence interval is

\(C.I = \bar{p}\pm z_{\alpha/2}\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }\)

⇒ C.I = 0.23 ± (1.96) × \(\sqrt{\frac{0.23(1-0.23)}{200} }\)

⇒ C.I = 0.23 ± 1.96 × 0.0298

⇒ C.I = 0.23 ± 0.0584

So, the upper limit is 0.23 + 0.0584 = 0.2884 and the lower limit is 0.23 - 0.0584 = 0.1716.

Therefore, the 95% confidence interval for the given population proportion lies between 0.1716 to 0.2884.

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The equation of the parabola with focus (2,5) and directrix x=18 is (x - 18)² + (y - 5)² = (y - (5 + (18 - 2) / 2))².

A parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating

straight line of that surface.

The focus of a parabola is a fixed point on the interior of a parabola used in the formal definition of the curve.

The directrix is a straight line perpendicular to the axis of symmetry and placed symmetrically with respect to the focus.

The axis of symmetry is the line through the focus and perpendicular to the directrix.

The vertex of a parabola is the point where its axis of symmetry intersects the curve. It is the point where the parabola changes direction or "opens

up" or "opens down.

The directrix is a fixed straight line used in the definition of a

parabola. It is placed such that it is perpendicular to the axis of symmetry and at a distance from the vertex equal to the

distance between the vertex and focus. It is the line that is equidistant to the focus and every point on the curve.Here's

the solution to the given problem:

The distance between the directrix and the focus is equal to p = 16 (since the directrix is x = 18, the parabola opens to the left, so the distance is measured horizontally)

The vertex is (h,k) = ((18+2)/2,5) = (10,5)

Then we can use the following formula: (x - h)² = 4p(y - k)

Substitute the vertex and the value of p. (x - 10)² = 64(y - 5)

Expand and simplify. (x - 10)² + (y - 5)² = 64(y - 5)

The equation of the parabola is (x - 10)² + (y - 5)² = 64(y - 5).

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Answer:

.50 = equally likely as unlikely

1 = certain

.25 = unlikely

0 = impossible

.75 = likely

Step-by-step explanation:

Think of these as percentages, it'll help you figure out.

.50 is 50%

1 is 100%

.25 = 25%

0 is 0%

.75 = 75%

Answer:  Corresponding Parts of Congruent Triangles are Congruent

Step-by-step explanation: So you use it when two triangles are congruent to each other (which means the same) so like ASA angle side angle will tell you if the triangle is congruent to each others.

The Formula for h(x) is 7.5cos(51.4x - 154.3)-1.5.

What is trigonometric function ?

Trigonometric functions are referred to as Circular Functions will be merely outlined because the functions of associate degree angle of a triangle.

The difference in y values from max to min = 15. 15/2 = a
max cosine = 1, min cosine =-1
7.5 x 1 - 1.5 = 6
7.5x -1 -1.5 = -7.5-1.5= -9
h(x) = 7.5cos(bx+c) -1.5
now just get a period or frequency that matches the x coordinates 3 and 6.5 to get b and c
at (3,6) cosine = 1 to get a maximum value. cosine is at a max when cos(bx+c) = 1 and bx+c=0, 360, 720...
if x=3, then 3b +c=0 and c=-3b
for (6.5,-9) to be a minimum h value, then cos(6.5b+c) =-1 that happens when the angle = 180. +n360 for any integer n. 6.5b+c = 180
c= 180-6.5b
c=-3b
180-6.5b =-3b
add 6.5b to both sides to get
180= 3.5b
b = 180/3.5 = 51 1/7
c=-3b = -153 3/7
h(x) = 7.5cos(51.4x - 154.3)-1.5
hence , Formula for h(x) is 7.5cos(51.4x - 154.3)-1.5

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If two coplanar lines are cut by a transversal so that a pair of alternate interior angles are equal then the two lines are parallel.

The four sets of opposing angles that each have their own vertex point, are on different sides of the transversal and are both either internal or exterior are called alternate angles.

In geometry, a transversal line is one that cuts across the plane in two places. It does so at two spots where two lines meet. Many right angles are produced when two transverse lines meet. There are four types of similar angles: matching, alternative interior, alternate exterior, and co-interior.

In geometry, two lines are considered parallel if and only if all pairs of alternative interior angles in any transversal are equal.

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Answer: 7.2

Step-by-step explanation: 2.4(3) is really just 2.4 * 3 so 2.4 times 3 is 7.2.

Answer:

13.824

Step-by-step explanation:

Raise 2.4 to the power of 3.