Which
Charles factors the expression 9 x + gx using a factor of 5 x. He writes the factored expression as 3 «(4x+1).
best describes the accuracy of Charles's solution?
His solution is accurate,
His solution is inaccurate. The factor does not divide evenly into both terms.
O His solution is inaccurate. The factoring of g xy using the given GCF is incorrect.
His solution is inaccurate. The factoring of 3 using the given GCF is incorrect.

Answer:

6 times

Step-by-step explanation:

y = −3.5x + 20 ; x = 4

y = -3.5(4) + 20

y = -14 + 20

y = 6

Answer:

[tex]BA = 6.0[/tex]

[tex]BC = 13.4[/tex]

Step-by-step explanation:

Given

The attached triangle

Solving (a) BA

Considering the tangent of angle C, we have:

[tex]tan\ C = \frac{BA}{AC}\\[/tex]

This gives:

[tex]tan\ 25 = \frac{BA}{12}[/tex]

Make BA the subject

[tex]BA = 12 * tan\ 25[/tex]

[tex]BA = 12 * 0.4663[/tex]

[tex]BA = 6.0[/tex] --- approximated

Solving (a) BC

Using Pythagoras theorem

[tex]BC^2 = BA^2 + AC^2[/tex]

[tex]BC^2 = 6.0^2 + 12^2[/tex]

[tex]BC^2 = 180[/tex]

Square root of both sides

[tex]BC = \sqrt{180[/tex]

[tex]BC = 13.4[/tex]

Answer:

16x^10+16x^8+4x^6

The expanded and simplified form of [tex](2x^3 + 4x^5)^2[/tex] is  [tex]4x^6 + 16x^8 + 16x^10[/tex].

when we combine all the like terms.

To expand and combine like terms for the expression [tex](2x^3 + 4x^5)^2,[/tex] we need to square each term inside the parentheses and then combine like terms.

Using the FOIL method (First, Outer, Inner, Last) to multiply the terms, we have:

[tex](2x^3 + 4x^5)^2 = (2x^3)^2 + 2(2x^3)(4x^5) + (4x^5)^2[/tex]

Simplifying each term:

[tex](2x^3)^2 = 4x^6\\2(2x^3)(4x^5) = 16x^8\\(4x^5)^2 = 16x^10[/tex]

Combining like terms, we have:

[tex](2x^3 + 4x^5)^2 = 4x^6 + 16x^8 + 16x^10[/tex]

Therefore, the expanded and simplified form of [tex](2x^3 + 4x^5)^2[/tex] is [tex]4x^6 + 16x^8 + 16x^10.[/tex]

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Full Question

Expand and combine like terms: (2x^3+4x^5)^2 by simplication.

(No graph needed)

Answer:

c) 135

Step-by-step explanation:

dog ratio is 3

45 ÷ 3 = 15

therefore ratio 1 is 15

ratio 9

9×15 = 135

Answer:

(i) The derivative of the function is [tex]f' = \frac{1}{10}[/tex].

(ii) The domain of all first order polynomials (linear functions) is the set of all real numbers. That is:

[tex]Dom\{f(x)\} = \mathbb{R}[/tex]

The domain of all zero order polynomials (constant functions) is the set of all real numbers. That is:

[tex]Dom\{f'\} = \mathbb{R}[/tex]

Step-by-step explanation:

(i) Find the derivative of the function using the definition of derivative:

The derivative is defined by the following limit:

[tex]f' = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex] (1)

If we know that [tex]f(x) = \frac{1}{10}\cdot x - \frac{1}{3}[/tex], then the definition of derivative is expanded:

[tex]f' = \lim_{h \to 0} \frac{\frac{1}{10}\cdot (x+h) - \frac{1}{3}-\frac{1}{10}\cdot x +\frac{1}{3}}{h}[/tex]

[tex]f' = \lim_{h \to 0} \frac{\frac{1}{10}\cdot h }{h}[/tex]

[tex]f' = \lim_{h \to 0} \frac{1}{10}[/tex]

[tex]f' = \frac{1}{10}[/tex]

The derivative of the function is [tex]f' = \frac{1}{10}[/tex].

(ii) State the domain of the function and the domain of its derivative:

The domain of all first order polynomials (linear functions) is the set of all real numbers. That is:

[tex]Dom\{f(x)\} = \mathbb{R}[/tex]

The domain of all zero order polynomials (constant functions) is the set of all real numbers. That is:

[tex]Dom\{f'\} = \mathbb{R}[/tex]

Answer:   y = 2x - 3/4

Step-by-step explanation:

y = mx + b where m is the slope, and b is the y-intercept.

y = 2x - 3/4

Answer:

x = 16.1 in

Step-by-step explanation:

Using sin law

sin44 / x = sin98/ 23in

x = 16.1 in (nearest tenth)

Answer:

4

Step-by-step explanation:

Answer:

The appropriate alternative hypothesis if he wanted to substantiate his suspicion would be [tex]H_{a}: \mu > 238[/tex]

Step-by-step explanation:

At the null hypothesis, we test that the mean is equal to a certain value.

At the alternate hypothesis, we test that the mean is different, less than or more than the mean value tested at the null hypothesis.

The historical U.S. mean unemployment insurance benefit was reported to be $238 per week.

This means that the null hypothesis is:

[tex]H_{0}: \mu = 238[/tex]

A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was above the national level.

This means that the alternate hypothesis is:

[tex]H_{a}: \mu > 238[/tex]

Answer:

It can be concluded that at 5% significance level that there is no difference in the amount paid by chain A and chain B for the job under consideration

Step by Step Solution:

The given data are;

Chain A 4.25, 4.75, 3.80, 4.50, 3.90, 5.00, 4.00, 3.80

Chain B 4.60, 4.65, 3.85, 4.00, 4.80, 4.00, 4.50, 3.65

Using the functions of Microsoft Excel, we get;

The mean hourly rate for fast-food Chain A, [tex]\overline x_1[/tex] = 4.25

The standard deviation hourly rate for fast-food Chain A, s₁ = 0.457478

The mean hourly rate for fast-food Chain B, [tex]\overline x_2[/tex] = 4.25625

The standard deviation hourly rate for fast-food Chain B, s₂ = 0.429649

The significance level, α = 5%

The null hypothesis, H₀:  [tex]\overline x_1[/tex] = [tex]\overline x_2[/tex]

The alternative hypothesis, Hₐ:  [tex]\overline x_1[/tex] ≠ [tex]\overline x_2[/tex]

The pooled variance, [tex]S_p^2[/tex], is given as follows;

[tex]S_p^2 = \dfrac{s_1^2 \cdot (n_1 - 1) + s_2^2\cdot (n_2-1)}{(n_1 - 1)+ (n_2 -1)}[/tex]

Therefore, we have;

[tex]S_p^2 = \dfrac{0.457478^2 \cdot (8 - 1) + 0.429649^2\cdot (8-1)}{(8 - 1)+ (8 -1)} \approx 0.19682[/tex]

The test statistic is given as follows;

[tex]t=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{S_{p}^{2} \cdot \left(\dfrac{1 }{n_{1}}+\dfrac{1}{n_{2}}\right)}}[/tex]

Therefore, we have;

[tex]t=\dfrac{(4.25-4.25625)}{\sqrt{0.19682 \times \left(\dfrac{1 }{8}+\dfrac{1}{8}\right)}} \approx -0.028176[/tex]

The degrees of freedom, df = n₁ + n₂ - 2 = 8 + 8 - 2 = 14

At 5% significance level, the critical t = 2.145

Therefore, given that the absolute value of the test statistic is less than the critical 't', we fail to reject the null hypothesis and it can be concluded that at 5% significance level that chain A pays the same as chain B for the job under consideration

Answer is in the photo. I can't attach it here, but I uploaded it to a file hosting. link below! Good Luck!

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Answer:

2400

Step-by-step explanation:

x+y+z=147

x+(x+1)+(x+2)=147

3x+3=147

3x=144

x=48

The three consecutive positive numbers are 48, 49, and 50.

48 • 50 = 2400

Answer:

2400 just believe me I’m correct

Answer:  $1.50 per ticket

Step-by-step explanation:

Divide 7.50 by 5 (You can do any of them. Like, 10.50/7 or 13.50/9 but you'll get the same answer.)

Once you divide them, you'll get 1.5.

$1.50 per ticket.

Not that bad

Answer:

58 units

Step-by-step explanation:

I decided that one side is 37 units and another is 2 units, since that would make the area 37 units. (you can also use 74 units and 1 unit)

Then I multiplied 37 by 5/4, which equals a new length of 46.25 units, and I also multiplied 2 by 5/4, which equals a new length of 2.5 units.

Finally, I solve for the area of the triangle:

1/2(46.25 x 2.5) ≈ 58 units (rounded to the nearest whole number)

Answer: v-(kx8)

Step-by-step explanation: plz mark me brainliest

Answer:

hello! As I think it is 2p coin but not sure

Answer:

21 is 84% to 25, so there would be 25 total questions on the test

Answer:

-11

Step-by-step explanation:

[tex]3( - 2) + 5( - 1)[/tex]

[tex] - 6 + ( - 5)[/tex]

[tex] - 11[/tex]

Answer: 1 is not in the domain of f g.

Step-by-step explanation:

Pen is 3 x 2 = 6

Pencils s 4 x 3 = 12

Answer:

C

Step-by-step explanation:

Answer:\A) x > 10

Step-by-step explanation:

Hope this helps!!

Answer:

Total Depth: 64.28m

Step-by-step explanation:

Assuming that the submarine is travelling at a constant rate, then we can use the information provided and apply a Rule of Three since it is basically a ratio problem. In this rule, you simply need to multiply the diagonal values of the ratio and divide by the last value to get the variable, which would be the depth after 110m

70min  <=======>  25 m

110min  <=======>  x m

(110 * 25) / 70 = x

2750 / 70 = x

39.28 = x

We can see that at 110min the depth would be 39.28 m but since this is an additional period of time that the submarine travelled we need to add this distance to the initial 25 m to get the total depth of the submarine.

39.28m + 25m = 64.28m

Answer:

The quartile 3 is 0.3

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

X~Exp (0.2)

This means that [tex]m= 0.2, \mu = \frac{1}{0.2} = 5[/tex]

Find the quartile 3.

The 3rd quartile is the 75th percentile, for which [tex]P(X \leq x) = 0.75[/tex], or [tex]P(X > x) = 1 - 0.75 = 0.25[/tex]

Since

[tex]P(X > x) = e^{-\mu x}[/tex]

[tex]e^{-5x} = 0.25[/tex]

[tex]\ln{e^{-5x}} = \ln{0.25}[/tex]

[tex]-5x = \ln{0.25}[/tex]

[tex]x = -\frac{\ln{0.25}}{5}[/tex]

[tex]x = 0.277[/tex]

Rounding to the nearest tenth, the quartile 3 is 0.3.

Answer:

$51.63

Step-by-step explanation:

Joe spent 5 days on the trip and spent $258.14 total on food. To find the cost for each day, divide 258.14 by 5.

258.14 / 5 ≈ 51.63

Answer:

a) The axis of symmetry is the line, y = 2

b)  The vertex  of a parabola is (-3, 2)

c) The focus of the parabola is (0, 2)

d) The directrix of a parabola is, x = -6

e) Please find attached the graph of the parabola

Step-by-step explanation:

a) The function for the parabola can be expressed as follows;

12·(x + 3) = (y - 2)²

The general form of the equation of the parabola is x = a·(y - k)² + h

The axis of symmetry is the line, y = k

By comparison, with the given equation of the parabola, we have;

12·(x + 3) = (y - 2)²

x = (1/12)·(y - 2)² - 3

Therefore;

a = (1/12), k = 2, h = -3

The axis of symmetry is y = k

∴ The axis of symmetry is the line, y = 2

b) The vertex  of a parabola = (h, k)

∴ The vertex  of a parabola = (-3, 2)

c) The focus of a parabola is [tex]\left(h + \dfrac{1}{4\cdot a} , \ k\right)[/tex]

Therefore, the focus of the parabola is [tex]\left(-3 + \dfrac{1}{4\cdot \dfrac{1}{12} } , \ 2\right)[/tex] = (0, 2)

The focus of the parabola = (0, 2)

d) The directrix of a parabola is [tex]h - \dfrac{1}{4\cdot a}[/tex]

[tex]\therefore h - \dfrac{1}{4\cdot a} = -3 - \dfrac{1}{4\cdot \dfrac{1}{12} } = -3 - 3 } = -6[/tex]

The directrix of a parabola is, x = -6

e) Please find attached the graph of the parabola, showing the vertex, focus, directrix, and axis of symmetry, created with Microsoft Excel

The axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6

It is given that the parabola equation is  [tex]\rm 12(x+3)=(y-2)^2[/tex]

It is defined as the graph of a quadratic function that has something bowl-shaped.

We know the standard form of a parabola is:

[tex]\rm x= a(y-k)^2+h[/tex]  .........(1)

We have the equation of parabola:

[tex]\rm 12(x+3)=(y-2)^2\\\\\rm x+3 =\frac{1}{12} [(y-2)^2]\\\\\rm x =\frac{1}{12} [(y-2)^2]-3\\[/tex]........(2)

a) Axis of symmetry: the axis of symmetry is a straight line that divides the parabola into two identical parts.

By comparing the equation (1) and (2), we get:

Axis of symmetry ⇒ (y - k) = 0 ⇒ (y - 2) = 0 ⇒ y = 2.

b) Vertex of the parabola = (h,k): (-3, 2)

c) The focus of the parabola is [tex]\rm (h+\frac{1}{4a} ,k)[/tex],

[tex]\rm h = -3, a = \frac{1}{12} , k= 2[/tex]

∴ [tex]\rm (-3+\frac{1}{4\times(\frac{1}{12}) } ,2)\\\\\rm (0,2)[/tex]

The focus of the parabola is (0, 2)

d) The directrix of a parabola is [tex]\rm x = h-\frac{1}{4a}[/tex]

[tex]\rm x = -3-\frac{1}{4\times\frac{1}{12} }\\\\\rm x= -3-3\\\rm x= -6[/tex]

The directrix of a is x = -6

e) Shown in the below picture: graph of the parabola and vertex, focus, directrix, and axis of symmetry

Thus, the axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6

Know more about the parabola here:

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Answer:

y = 4

Step-by-step explanation:

use the distributive property

9y - 36 = 0

     +36  +36

9y = 36

divide by 9

y = 4

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-XxDeathshotxX

Step-by-step explanation:

...hope it help u.... ..

Answer:

The maximum value is (2,9) I can't really see the question well btw