A garden table and a bench cost $793 combined. The garden table costs $43 more than the bench. What is the cost of the bench?​

Answer: (2, -25)

Step-by-step explanation:

The x coordinate of the vertex is [tex]x=-\frac{-4}{2(1)}=2[/tex].

When x=2, [tex]h(2)=2^2 - 4(2)-21=-25[/tex].

So, the vertex is (2, -25).

Hello,

[tex]y = ax + b[/tex]

We know the slope is 2 so :

[tex]y = 2x + b[/tex]

The equation of the line that passes through the point (5,4) so :

[tex]4 = 2 \times 5 + b[/tex]

[tex]4 = 10 + b[/tex]

[tex]b = 4 - 10[/tex]

[tex]b = - 6[/tex]

The equation of the line that passes through the point (5,4) and has a slope of 2 is :

[tex]y = 2x - 6[/tex]

y = 2x - 6

Most lines are written in slope-intercept form, but we can use slope-point form in situations like this.

Slope-Point Form

The formula for slope-point form is [tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]. So, we can plug in the information we have, the point and slope.

This is an equation for the line given to us. However, this form can be simplified further.

Slope-Intercept Form

Slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept. To find the most simplified form of the equation we need to use the properties of equality.

First, distribute the 2

Next, add 4 to both sides

Now, we have the equation for the line in slope-intercept form. Both of the equations technically meet the requirements for the question, but slope-intercept is more common to use.

The parabola vertex is (1,5), the focus of the parabola is (1,6), and the directrix y = 4.

The graph of a parabolic equation is a U-shape curve graph that is established from a quadratic equation.

From the given information:

[tex]\mathbf{y=\dfrac{1}{4}(x-1)^2+5}[/tex]

The vertex of an up-down facing parabolic equation takes the form:

y = ax² + bx + c  is [tex]\mathbf{x_v = -\dfrac{b}{2a}}[/tex]

Rewriting the given equation:

[tex]\mathbf{y = \dfrac{x^2}{4}-\dfrac{x}{2}+\dfrac{21}{4}}[/tex]

[tex]\mathbf{x_v = -\dfrac{b}{2a}}[/tex]

[tex]\mathbf{x_v = -\dfrac{(-\dfrac{1}{2})}{2(\dfrac{1}{4})}}[/tex]

[tex]\mathbf{x_v =1}[/tex]

Replacing the value of x into the equation, y becomes:

[tex]\mathbf{y_v = 5}[/tex]

Thus, the parabola vertex is (1,5)

From the vertex, the focus of the parabola is (1,6), and the directrix y = 4.

The graphical representation of the parabola is seen in the image attached below.

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12,480 es par y la suma de sus digitos da un multiplo de 3, por ello concluimos que es divisible por 6.

Para que un número sea divisible por 6 debe cumplir dos condiciones.

En este caso tenemos 12,480, que sabemos que es par.

La suma de sus digitos da:

1 + 2 + 4 + 8 + 0 = 15

15 es multiplo de 3.

Entonces este número cumple ambas condiciones, por lo que concluimos que 12,480 es divisible por 6.

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Answer:

$21.15

Step-by-step explanation:

(235)(.045)(2)

The value of y  / 3 in the equation is x / 4.

Therefore,

x + 4 / 4 = y + 3 / 3

then y / 3 can be found as follows,

x + 4 / 4  = x / 4 + 4 / 4 = x  / 4 + 1

y + 3 / 3  = y / 3 + 3 / 3  = y / 3 + 1

x  / 4 + 1 = y / 3 + 1

subtract 1 from both sides of the equation

x  / 4 + 1 - 1 = y / 3 + 1 - 1

x / 4 = y / 3

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The measure of x in the right angled triangle shown is 4.09

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

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

From the diagram shown:

sin(17) = x / 14

x = 4.09

The measure of x in the right angled triangle shown is 4.09

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After conversion 98.2 °F=119.2°C

96.6 °F=116.3°C

100.1 °F==122.6°C

How can we convert temperature from Fahrenheit to Celsius?

We will convert using this formula

C= (F-32) *5/9

We will convert temperature from Fahrenheit to Celsius as shown below:

C= (F-32) *5/9

For Oral

Temperature=98.2°F

C= (98.2-32) *5/9

=119.16°C

Rounding to nearest tenth

=119.2°C

For Axillary

Temperature=96.6 °F

C= (96.6-32) *5/9

=116.28°C

Rounding to nearest tenth

=116.3°C

For Rectal

Temperature=100.1 °F

C= (100.1-32) *5/9

=122.58

Rounding to nearest tenth

=122.6°C

Hence, after conversion 98.2 °F=119.2°C

96.6 °F=116.3°C

100.1 °F=122.6°C

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Answer:

BA + BC = AC

Step-by-step explanation:

B is the midpoint of AC

Then

BA = AC/2 and BC = AC/2

Then

BA + BC = AC/2 + AC/2 = AC

Answer:a

Step-by-step explanation:

Answer: The center of the circle will be (1,2) and the radius will be 2.5

Step-by-step explanation: Basically since its (x-1) it would become x=1 so that's ur first value same thign with y but that would be ur second value. And since in your equation it is 6.25 that would be 2.5 because 6.25 is r^2 and you are looking for r.

Answer:

Yes because putting value of x and y as 1 and -1 in equation :

y=3x-4

-1 = 3 * 1 - 4

-1 = -1 (True)

Answer: The transverse axis of the hyperbola lies on the line y=–3 and has length 6; the conjugate axis lies on the line x=2 and has length 8.

Step-by-step explanation:

Answer: H. Parallel lines may intersect.

Step-by-step explanation:

By definition, parallel lines never intersect.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{8,903 = e^{5x}}}[/tex]

[tex]\huge\textbf{Simplify:}[/tex]

[tex]\mathsf{8,903 = e^{5x}}}[/tex]

[tex]\mathsf{e^{5x} = 8,903}}[/tex]

[tex]\huge\textbf{Solve for the exponent:}[/tex]

[tex]\large\textsf{We get: }\downarrow\\\\\mathsf{2.718282^{5x}=8903}[/tex]

[tex]\huge\textbf{Take the logarithm from both sides:}[/tex]

[tex]\mathsf{log(2.718282^{5x}) = log(8,903x)}[/tex]

[tex]\large\textsf{We get:}\\\\\mathsf{5x \times log(2.718282)=log(8903)}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{5x = \dfrac{log(8903)}{log(2.718282)}}[/tex]

[tex]\large\textsf{We get: }\\\\\mathsf{5x = 9.094143}[/tex]

[tex]\huge\textbf{Divide 5 to both sides:}[/tex]

[tex]\mathsf{\dfrac{5x}{5} = \dfrac{9.094143}{5}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{x= \dfrac{9.094143}{5}}[/tex]

[tex]\mathsf{x = 1.818829}[/tex]

[tex]\mathsf{x \approx 2}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x =}\frak{\ 1.818829}}\huge\checkmark[/tex]

[tex]\large\textbf{Or if you're estimating your answer}\downarrow[/tex]

[tex]\huge\boxed{\mathsf{x \approx }\frak{\ 2}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

  (f∘g)(x) = 27x² -90x +77

Step-by-step explanation:

The composition of functions (f∘g)(x) is interpreted to mean f(g(x)). The value is found the way any function value is found. The argument is substituted for the variable in the function definition.

After substituting g(x) for the argument of f(x), the resulting expression can be simplified.

  [tex](f\circ g)(x) =f(g(x))=f(3x-5)\\\\=3(3x-5)^2+2=3(9x^2-30x+25)+2\\\\\boxed{(f\circ g)(x)=27x^2-90x+77}[/tex]

Answer:

$73915.40

Step-by-step explanation:

→ Find the multiplier

( 3 + 100 ) ÷ 100 = 1.03

→ Multiply by principal amount and raise it to the power of years

55000 × 1.03¹⁰ = 73915.40

Answer: $630,513.36

Step-by-step explanation:

Let's make a table of values to see how much he earns every year after graduation.

1 year -> $55,000

2 years -> 55,000 * 103% = $56,650

3 years -> 56,650 * 103% = 55000 * 103% * 103% = $58,349.50

4 years ->  58349.50 * 103% = 55,000 * 103% * 103% * 103% = 55000(1.03)³

Here, we see that every year, he gets 103% of what he got the previous year, which is also 1.03 times his previous salary.

We also see that we multiply 55000 by 1.03 three times in the fourth year, and two times in the third year. This means that we multiply 55000 by 1.03 n-1 times.

Using this, let's generalize this for n.

n years -> [tex]55000(1.03)^{n-1}[/tex]

We are trying to find his total income after ten years, or the sum of his salary from year 1 to year 10. We can represent this in sigma notation like this

[tex]% Adjusted limits of summation$\displaystyle\sum_{n=1} ^{10} 55000(1.03)^{n-1}$[/tex]

This essentially translates to the sum of the first ten terms in the sequence [tex]55000(1.03)^{n-1}[/tex], starting at n=1.

Since this is a geometric sequence, or a sequence where we need to multiply by the same number to get to the next term, we can find the sum using the sum of geometric series formula. This formula is as follows:

[tex]S_n=a_1\frac{1-r^n}{1-r}[/tex]

where [tex]S_n[/tex] is the sum of the first n terms, [tex]a_1[/tex] is the first term, r is the common ratio, and n is the number of terms. In this question, [tex]S_n[/tex] is the total income after n years, [tex]a_1[/tex] is his salary after the first year, r is how much his salary increases by each year, and n is the number of years we are calculating the sum for.

[tex]a_1[/tex] -> 55000

r -> 1.03

n -> 10

Now that we have the values for each variable, let's plug them in and solve

[tex]S_{10}=55000(\frac{1-1.03^{10}}{1-1.03})\\S_{10}=630513.36[/tex]

The total income he will have received after ten years is $630,513.36.

hi

I cannot figure the number  2.16 thousand has it does not mean anything to me.

But the only thing you need to do is to add  15 times 220

so = 3300

Answer:

5,460 people

Step-by-step explanation:

2,160 + 220x is the expression. Now, we plug in 15 for x.

2,160 + 220(15)

2,160 + 3,300 = 5,460

Brainliest, please :)

Answer:

[tex]6 + ( \frac{4}{3} + ( \frac{5}{6} - \frac{1}{3} ))[/tex]

[tex] = 6 + ( \frac{4}{3} + ( \frac{5 - 2}{6})) [/tex]

[tex] = 6 + ( \frac{4}{3} + \frac{3}{6})[/tex]

[tex] = 6 + ( \frac{8 + 3}{6})[/tex]

[tex] = 6 + \frac{11}{6} [/tex]

[tex] = \frac{6}{1 } + \frac{11}{6} [/tex]

[tex] = \frac{36 + 11}{6} [/tex]

[tex] = \frac{47}{6} [/tex]

[tex] = 7 \frac{5}{6} [/tex]

The function with the greatest average rate of change is the function k(x)

The average rate of change is calculated as

[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]

The interval is [0,2].

So, we have

[tex]m = \frac{y_2 - y_1}{2 -0}[/tex]

[tex]m = \frac{y_2 - y_1}{2}[/tex]

For function j(x), we have

j(2) = 3 * 1.6^2 = 7.68

j(2) = 3 * 1.6^0 = 3

So, we have

[tex]m_j = \frac{7.68 - 3}{2}[/tex]

[tex]m_j = 2.34[/tex]

For function g(x), we have

g(2) = 25/2

g(0) = 8

So, we have

[tex]m_g = \frac{25/2 - 8}{2}[/tex]

[tex]m_g = 2.25[/tex]

For function k(x), we have

k(2) = 9

k(0) = 4

So, we have

[tex]m_k = \frac{9 - 4}{2}[/tex]

[tex]m_k = 2.5[/tex]

For function f(x), we have

f(2) = 1.5 * 2^2 = 6

f(0) = 1.5

So, we have

[tex]m_f = \frac{6 - 1.5}{2}[/tex]

[tex]m_f = 2.25[/tex]

The function with the greatest average rate of change is the function k(x) with a rate of 2.5

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Answer:

Step-by-step explanation:

volume of the triangular prism height times base times length so 10 times 8 times 12 = 960.

The value of x to the nearest hundredth is 4.14

The given diagram is a right triangle with the following parameters

Opposite side to 16 degrees = x

Hypotenuse = 15

Using the expression below

sin theta = x/15

sin16 = x/15

x = 15sin16

x = 4.135

Hence the value of x to the nearest hundredth is 4.14

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The value of x is 0.5

The equation is given as:

(x -2)(x + 3) = (x - 2)(4 - x)

Divide both sides by x - 2

x + 3 = 4 - x

Evaluate the like terms

2x = 1

Divide by 2

x = 0.5

Hence, the value of x is 0.5

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Answer:

one pound of chocolate chips = $2.75

one pound of walnuts = $3.75

Step-by-step explanation:

we can solve this by first making an equation

let's write the number of chocolate chips in c

and the number of walnuts in w

5c  + 3w = 25

7c + 9w = 53

let's first solve for c by multiplying the top equation by 3 and subtracting the bottom equation from it

(15c + 9w = 75) - (7c + 9w = 53)

8c = 22

c = $2.75

Let's now start to solve for w by inputting c into one of the equations.

(2.75)7 + 9w = 53

19.25 + 9w = 53

9w = 53 - 19.25

9w = 33.75

w = $3.75

a pound of chocolate chips  = 2.75

a pound of walnuts = 3.75

give me brainliest, please!

Hope this helps :)

Answer:

each pound of chocolate chips costs $2.75

each pound of walnuts costs $3.75

Step-by-step explanation:

let c be the cost of a pound of chocolate chips

and w be the cost of a pound of chocolate chips

For 5 pounds of chocolate chips and 3 pounds of walnuts,

the total cost is $25  means  5c + 3w = 25

For 7 pounds of chocolate chips and 9 pounds of walnuts,

the total cost is $53  means  7c + 9w = 53

Now we have to solve the system:

[tex]\begin{cases}5c+3w=25&\\ 7c+9w=53&\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}15c+9w=75&\\ 7c+9w=53&\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}15c+9w=75&\\ 8c=22&\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}15c+9w=75&\\ c=\frac{11}{4} &\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}9w=75-15 \times \frac{11}{4} &\\ c=\frac{11}{4} &\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}9w=\frac{135}{4} &\\ c=\frac{11}{4} &\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}w= \frac{15}{4} &\\ c=\frac{11}{4} &\end{cases}[/tex]

The two characteristics that makes the median a better choice are: A. The data are skewed and there are outliers.

In a data distribution, the median is a better choice to use to describe the data over the mean when an outlier exist and the data is skewed.

IN the dot plot given below, the data has an outlier of 10 while the data distribution is also screwed, this makes the median a better choice.

Therefore, the answer is: A. The data are skewed and there are outliers.

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Answer: 23.1

Step-by-step explanation:

[tex]\frac{x}{14}=\frac{33}{20}\\\\x=\frac{(33)(14)}{20}\\\\x=23.1[/tex]

The place value in the thousands for the 0 in 10,000 is three (3).

A place value refers to a numerical value which denotes a digit based on its position in a given number and it includes:

In this scenario, the place value in the thousands for the 0 in 10,000 is three (3).

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Answer:

Six Serving Men is a team exercise that examines an issue from twelve different viewpoints. It is based on the words of the poem by Rudyard Kipling: I keep six honest serving men, they taught me all I knew. Their names are What and Why and When and How and Where and Who. To use this technique in a meeting, provide 12 areas for answering questions related to the central topic

Step-by-step explanation:

1) This is a Two tailed Test.

2) Decision rule is; If the p-value is greater than 4% fail to reject H₀.

3) P-value = 0.00968764 and so we reject H₀

We are given the hypothesis as;

Null Hypothesis; H₀: m₁ = m₂

Alternative Hypothesis; H₁: m₁ ≠ m₂

1) Since the alternative hypothesis has "not equal to sign", then it is a two tailed test.

2) Since we are told to use significance level as 0.04, then we can say that the decision rule is;

If the p-value is greater than 4% fail to reject H₀.

3) Using a 2-Sample Z-Test online TI calculator gives the test statistic as;

z = 2.5868

4) From z-score calculator, p-value equals 0.00968764. This is less than 0.04 and as such the decision regarding H₀ is to reject H₀.

5) P-value = 0.00968764

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The pressure of the submarine at a depth of 23000 meters is 2.3575 * 10⁸ N/m²

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

Pressure = density * acceleration due to gravity (g) * depth

g = 10 m/s², hence:

Pressure = 1025 * 10 * 23000 = 2.3575 * 10⁸ N/m²

The pressure of the submarine at a depth of 23000 meters is 2.3575 * 10⁸ N/m²

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