2. Find four consecutive integers such that six times the sum of the first and third is 12
greater than 9 times the fourth.

Answer:

3

[tex]3 {y}^{0} [/tex]

[tex] = 3 \times 1[/tex]

[tex] = 3[/tex]

If any numbers or constant power is zero then it will be 1

Answer:

3

Step-by-step explanation:

So anything to the power of zero is equal to 1. So you have the equation: [tex]3y^0=3(1)=3[/tex]

If this doesn't make much sense, I sometimes like to use identities to show why this is. So since you're most likely learning exponents, you likely know the identity: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex] well you can use this identity to express the equation: [tex]\frac{x^a}{x^a}=x^{a-a}=x^0[/tex]. and since x^a should equal x^a, and it's being divided by it self, this is equal to 1.

Btw if you didn't understand the identity: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex] I'll try to briefly explain it. The reason this is true, is because you can cancel stuff out if it's being multiplied in the denominator and numerator. For example: [tex]\frac{3a}{3}[/tex]. I can cancel out the 3, because if I multiply 3 by a, and then divide by 3, I'm going to be left with a, because they're inverse to each other. This should hold true for exponents. So you can think of the identity more like: [tex]\frac{x*x*x...\text{a amount of times}}{x*x*x\text{b amount of times}}[/tex] seeing it like this might help understand why you subtract, since you're just cancelling out the x's.

I'll give you a more definitive example to help you grasp it in an example so: [tex]\frac{2^4}{2^2}=\frac{2*2*2*2}{2*2}=\frac{2*2}{1}=2^2[/tex]. See how I canceled out 2 of the 2's, well all I was really doing was subtracting 2 from the degree of the numerator, or in other words I was subtracting the degree of the denominator from the numerator since the bases were the same which is exactly what the identity is doing.

Answer:

=============

Let the pizza was shared between x people.

Set up equation and solve for x:

If we exclude Lemo, the number of friends is 4.

The probability that the mean clock life would differ from the population mean by greater than 12.5 years is 98.30%.

Given mean of 14 years, variance of 25 and sample size is 50.

We have to calculate the probability that the mean clock life would differ from the population mean by greater than 1.5 years.

μ=14,

σ=[tex]\sqrt{25}[/tex]=5

n=50

s orσ =5/[tex]\sqrt{50}[/tex]=0.7071.

This is 1 subtracted by the  p value of z when X=12.5.

So,

z=X-μ/σ

=12.5-14/0.7071

=-2.12

P value=0.0170

1-0.0170=0.9830

=98.30%

Hence the probability that the mean clock life would differ from the population mean by greater than 1.5 years is 98.30%.

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There is a mistake in question and correct question is as under:

What is the probability that the mean clock life would differ from the population mean by greater than 12.5 years?

Answer:

463/50 or 9 13/50

Answer:

9.26=9 13/50

Step-by-step explanation:

Rewrite the decimal number as a fraction with 1 in the denominator

9.26=9.26/1

Multiply to remove 2 decimal places. Here, you multiply top and bottom by 10^2 = 100

9.26/1×100/100=926/100

Find the Greatest Common Factor (GCF) of 926 and 100, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 2,

926÷2/100÷2=463/50

Simplify the improper fraction,

=9 13/50

In conclusion,

9.26=9 13/50

Answer:

C. Decreasing

Step-by-step explanation:

The graph is decreasing because the graphed line read from left to right is slanting down.

Hope this helps!

If not, I am sorry.

Answer:

Step-by-step explanation:

Hello

If a graph is constant, it doesn't have any change at all.

If a graph is increasing, it looks like this-:

[tex]\Huge\nearrow[/tex]

If a graph is decreasing, it looks like this-:

[tex]\searrow[/tex]

Since the given graph is most similar to [tex]\searrow[/tex], it's decreasing.

[tex]\pmb{\tt{done~!!}}[/tex]

[tex]\orange\hspace{300pt}\above2[/tex]

Answer:

Infinitely Many Solutions

Step-by-step explanation:

[tex]10x-6y=-8\\-10x+6y=8\\\0 = 0\\[/tex]

The value of x based on the information given in the triangle is D. x = 1.

From the information given, it stated that the triangles are similar.

In this case, both triangles have side 4 and 5. Therefore, we are to find the last side. This will be:

4x - 1 = x + 2

Collect like terms

4x - x = 2 + 1

3x = 3

x = 3/3

x = 1

Therefore, the correct option is D.

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Answer:

x=1

Step-by-step explanation:

Answer:

6 units

Step-by-step explanation:

5--1=6

[tex]\bf{-5x^{2} +10x-25 }[/tex]

[tex]\bf{Rewrite \ 10 \ as:5\cdot2.}[/tex]

[tex]\bf{Rewrite \ 25 \ as:5\cdot5.}[/tex]

[tex]\bf{=-5x^2+5\cdot \:2x-5\cdot \:5}[/tex]

[tex]\bf{Factor \ the \ common \ term \ 5.}[/tex]

[tex]\bf{=5(-x^{2} +2x-5) \ \ \to \ \ \ Answer }[/tex]

The length of the piece should be 17.716 inches.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

length = 45 m

one inch = 2.54 cm

So, length of strip would be

=45/2.54

=17.716

Hence, the length of the piece should be 17.716 inches.

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Answer:The answers are 0.084 or -1.184

Step-by-step explanation:

The solution is in the attached file

Answer:Liam started a weight-loss program when Luke did. The first week, he lost 1 pound less than 3/2 times the pounds Luke lost the first week. The second week, he lost 4 pounds less than 5/2 times the pounds Luke lost the first week. The third week, he lost 1/2 pound more than 5/4 times the pounds Luke lost the first week.Assuming they both lost the same number of pounds over the three weeks, complete the following sentences.Step-by-step explanation:

Step-by-step explanation:

[tex] = \frac{14\pi}{6} [/tex]

[tex] = \frac{ \cancel{14}\pi}{ \cancel6} [/tex]

[tex] = \frac{7\pi}{3} [/tex]

[tex] = \frac{6\pi + \pi}{3} [/tex]

[tex] = \frac{6\pi}{3} + \frac{\pi}{3} [/tex]

[tex] = 2\pi + \frac{\pi}{3} [/tex]

[tex] = 0 + \frac{\pi}{3} [/tex]

[tex] = \frac{\pi}{3} \: \text{where} \: \frac{\pi}{3} < 2\pi[/tex]

The answer is B.

Answer:

The simplified form of [tex]12 q-(-6 q) \text { is } 18 q[/tex].

Step-by-step explanation:

[tex]- Given: $12 q-(-6 q)$\\ - Simplify.\\ - The simplified form of $12 q-(-6 q)=(12+6) q$ i.e., $18 q$.[/tex]

Using translation concepts, the equation of the graph F(x) is given as follows:

F(x) = -x² - 3.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Researching this problem on the internet, the graph of G(x) = x² was reflected over the axis(multiplied by -1), and shifted down 3 units(F(x) -> G(-x) - 3), hence the equation for F(x) is:

F(x) = -x² - 3.

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Answer:

The product is the difference of squares is [tex]$$\left(m-7\right)\left(m+7\right)={{m}^2}-49$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{aligned}&(m-7)(m+7)=(m)^{2}-(7)^{2} \\&(m-7)(m+7)=m^{2}-49\end{aligned}$$[/tex]

Answer:528 apple trees

Step-by-step explanation:Listen 198/6=33 so then just multiply 33x16 that equals 528 hope this helps

Hello !

Answer :

100% of x ⇒ 100/100 × x = 1 × x = x

200% of y ⇒ 200/100 × y = 2 × y = 2y

The rate of change of the linear function represented by the table is 3

The rate of change of a function is also known as the slope of a function. The equation for calculating the slope is expressed as:

Slope = y2-y1/x2-x1

using the coordinates from the table (-2, -13) and (-1, -10)

Substitute

Slope = -10-(-13)/-1-(-2)

Slope = -10+13/-1+2

Slope =3

Hence the rate of change of the linear function represented by the table is 3

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The expression that is a prime polynomial is:

B. [tex]x^3 - 27y^2[/tex].

A prime polynomial is a polynomial that cannot be factored.

In this problem, item b gives a prime polynomial, as:

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Step-by-step explanation:

[tex]f(x) = 4x[/tex]

[tex] \: [/tex]

[tex]y = 4x[/tex]

[tex]4y = x[/tex]

[tex]y = \frac{x}{4} [/tex]

[tex] {f}^{ - 1} (x) = \frac{ x}{4} [/tex]

[tex]h(x) = \frac{x}{4} [/tex]

The answer is D.

To have solution for f(x)=log3(x-2)-2. x must be x >2 or x ( 2, ∞) .

f(x)=log3(x-2)-2

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.

Since,
f(x)=log3(x-2)-2
The above function will goes to infinity when we put x = 2.
So the given function has solution for x > 2.

Thus, the To have solution for f(x)=log3(x-2)-2. x must be x >2 or x ( 2, ∞) .

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[tex]\huge\boxed{11\ \text{units}}[/tex]

To solve this, we need to find the distance between points C and D.

The distance formula is:

[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute the values from points [tex]C(x_1, y_1)[/tex] and [tex]D(x_2, y_2)[/tex].

[tex]\sqrt{(-4-(-4))^2+(-5-6)^2}[/tex]

Subtract.

[tex]\sqrt{0^2+(-11)^2}[/tex]

Evaluate the powers.

[tex]\sqrt{0+121}[/tex]

Solve for the final answer.

[tex]\sqrt{121}\\\boxed{11}[/tex]

Answer:

your answer please mark me as brainlist

The solution to the system of equation is (-0.6, 1.6)

Given the system of linear equations as shown:

y = 2/3x+ 2 .................. 1

6x - 4y = -10................ 2

Substitute equation 1 into 2 to have:

6x - 4(2/3x + 2) = -10
6x - 8/3 x - 8 = -10
10/3 x = -2

10x = -6

x =-0.6

Determine the value of y

y = 2/3x + 2

y = 2/3 (-0.6) + 2

y = -0.4 + 2

y = 1.6

Hence the solution to the system of equation is (-0.6, 1.6)

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Hello,

check for x = 2, we can see h(x) = 0

h(x) = √(x - 2) ⇒ h(2) = √(2 - 2) = √0 = 0 ⇒ ok

h(x) = √x - 2 ⇒ h(2) = √2 - 2 ≠ 0 ⇒ not this answer

h(x) = √x + 2 ⇒ h(2) = √2 + 2 ≠ 0 ⇒ not this answer

h(x) = √(x + 2) ⇒ h(2) = √(2 + 2) = √4  ≠ 0 ⇒ not this answer

So the answer is  h(x) = √(x - 2)

A geometric sequence goes from one term to the next by always multiplying or dividing by the constant value except 0. The constant number multiplied (or divided) at each stage of a geometric sequence is called the common ratio (r).

A geometric series is the sum of an infinite number of terms of a geometric sequence.

A geometric series is convergers if |r| < 1.

A geometric series is diveres if |r| > 1.

Calculate the common ratio:

[tex]r=\dfrac{18}{27}=\dfrac{18:9}{27:9}=\dfrac{2}{3}\\\\r=\dfrac{12}{18}=\dfrac{12:6}{18:6}=\dfrac{2}{3}\\\\r=\dfrac{8}{12}=\dfrac{8:24}{12:4}=\dfrac{2}{3}[/tex]

[tex]\left|\dfrac{2}{3}\right| < 1[/tex]

Therefore exist the sum.

Formula of a sum of a geometric series:

[tex]S=\dfrac{a_1}{1-r},\qquad|r| < 1[/tex]

Substitute:

[tex]a_1=27,\ r=\dfrac{2}{3}[/tex]

[tex]S=\dfrac{27}{1-\frac{2}{3}}=\dfrac{27}{\frac{1}{3}}=27\cdot\dfrac{3}{1}=81[/tex]

[tex]\huge\boxed{S=81}[/tex]

The total area of the given right trapezoidal prism is gotten as; A = 2592 sq.units

The formula to find the Surface Area of a Trapezoidal Prism is;

A = h(b + d) +l(a + b + c + d) unit square.

Where;

h = height

b and d are the lengths of the base

a + b + c + d is the perimeter

l is length

Thus;

A = 12(25 + 15) + 32(13 + 25 + 13 + 15)

A = 480 + 2112

A = 2592 units square

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