Solve for x. 4x − 3/ 3 =7 Enter your answer in the box. x =

Answer:

[tex]\large\boxed{x=\dfrac{5\pm3\sqrt3}{2}}[/tex]

Step-by-step explanation:

[tex]Domain:\ x-5\neq0\to x\neq5\\\\\dfrac{2}{x-5}=4x\\\\\dfrac{2}{x-5}=\dfrac{4x}{1}\qquad\text{cross multiply}\\\\(4x)(x-5)=(2)(1)\qquad\text{use the distributive property}\\\\(4x)(x)+(4x)(-5)=2\\\\4x^2-20x=2\\\\2^2x^2-20x=2\\\\(2x)^2-2(2x)(5)=2\qquad\text{add}\ 5^2\ \text{to both sides}\\\\(2x)^2-2(2x)(5)+5^2=2+5^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(2x-5)^2=2+25\\\\(2x-5)^2=27\to2x-5=\pm\sqrt{27}\qquad\text{add 5 to both sides}[/tex]

[tex]2x=5\pm\sqrt{9\cdot3}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\2x=5\pm\sqrt9\cdot\sqrt3\\\\2x=5\pm3\sqrt3\qquad\text{divide both sides by 2}\\\\x=\dfrac{5\pm3\sqrt3}{2}[/tex]

To graph the function f(x) = -15x + 4, plot the points (0,4) and (1,-11) on the graph. The slope of the line is -15 and the y-intercept is 4.

To graph the equation f(x) = -15x + 4, you need to plot two points on a graph then draw a line through those points. First, plug in value x = 0 into the equation, you get f(0) = -15*(0) + 4 = 4. So, one point is (0,4). Second, let's plug another x value, for example, x = 1, into the function. Hence, f(1) = -15*(1) + 4 = -11, giving you the second point (1,-11).

Also remember that this is a linear function and you'll see that it forms a straight line when graphed. The slope of the line is -15, which means the line will fall to the right. The y-intercept of the line is 4, which is the point where the line crosses the y-axis.

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The graph of f(x) = -15x + 4 is a line with a slope of -15 and a y-intercept of 4. Connecting points (0, 4) and (1, -11) depicts the downward-sloping trend.

To graph the linear function f(x) = -15x + 4, we can use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope (m) is -15, and the y-intercept (b) is 4.

To create the graph, we choose two points and connect them with a line. Let's select x = 0 and x = 1 to find the corresponding y-values.

For x = 0: y = -15(0) + 4 = 4. So, the point (0, 4) is on the graph.

For x = 1: y = -15(1) + 4 = -11. The point (1, -11) is on the graph.

Now, we can use these two points to draw the line on the coordinate plane. The line will have a negative slope, indicating a downward trend, and it intersects the y-axis at 4.

In summary, the graph of f(x) = -15x + 4 is a downward-sloping line that passes through the point (0, 4) and (1, -11).

For more such information on: slope

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Answer:

Always.

Step-by-step explanation:

I can think of no example that makes always false.

Replacing the minimum value in a dataset with a smaller number can sometimes change the mean. Hence, the correct answer is B.

Sometimes, replacing only the minimum value in a dataset with a smaller number may change the mean.

For example, if the dataset is {1, 3, 4, 5} and you replace the minimum value 1 with 0, the mean changes from 3.25 to 3.

Step-by-step explanation:

To find the y-coordinate points we need to evaluate the function for all the [tex]x[/tex] values in the table. In other words, we need to replace [tex]x[/tex] with each value in our given function and simplify.

- For x = 0

[tex]f(x)=(x-2)^2-5[/tex]

[tex]f(0)=(0-2)^2-5[/tex]

[tex]f(0)=(-2)^2-5[/tex]

[tex]f(0)=4-5[/tex]

[tex]f(x)=-1[/tex]

Since [tex]x=0[/tex] and [tex]y=-1[/tex], our first point is (0, -1)

- For x = 1

[tex]f(x)=(x-2)^2-5[/tex]

[tex]f(1)=(1-2)^2-5[/tex]

[tex]f(1)=(-1)^2-5[/tex]

[tex]f(1)=1-5[/tex]

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

Our second point is (1, -4)

- For x = 2

[tex]f(x)=(x-2)^2-5[/tex]

[tex]f(2)=(2-2)^2-5[/tex]

[tex]f(2)=(0)^2-5[/tex]

[tex]f(x)=-5[/tex]

Our third point is (2, -5)

- For x = 3

[tex]f(x)=(x-2)^2-5[/tex]

[tex]f(3)=(3-2)^2-5[/tex]

[tex]f(3)=(1)^2-5[/tex]

[tex]f(3)=1-5[/tex]

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

Our fourth point is (3, -4)

- For x = 4

[tex]f(x)=(x-2)^2-5[/tex]

[tex]f(4)=(4-2)^2-5[/tex]

[tex]f(4)=(2)^2-5[/tex]

[tex]f(4)=4-5[/tex]

[tex]f(x)=-1[/tex]

Our fifth point is (4, -1)

Now we just need to plot each point in our coordinate plane and join them with the parabola as you can see in the attached picture.

Final answer:

The total cost of renting the instrument is represented by the expression 65 + 30x, which accounts for the initial rental fee and the additional cost per subsequent month.

Explanation:

The expression that represents the total cost of renting the instrument is C = 65 + 30x, which is option C. To understand this, consider that there is a flat rental fee of $65 for the first month and an additional cost of $30 for each subsequent month an instrument is rented. The variable x represents the number of additional months the instrument is rented. Therefore, the total cost is given by the initial cost plus the cost for additional months, which in algebraic terms is 65 + 30x.

Add/subtract common factors.

3 - 11 + 4x = -32

-8 + 4x = -32

4x = -32 + 8

4x = -24

Then, isolate the x by using division/multiplication. But for this problem, use division.

x = -24 / 4

x = -6

Answer:

Inscribed angle

Step-by-step explanation:

Answer: X= -3/4, -1/2

Step-by-step explanation:

Divide the new price by 1 + percent of increase:

325 / 1.30 = 250

The original price was £250

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

• 1 + tan²x = sec²x

• cot x = [tex]\frac{1}{tanx}[/tex]

Given

secΘ = [tex]\frac{4}{3}[/tex], then

tan²Θ = sec²Θ - 1 = ([tex]\frac{4}{3}[/tex] )² - 1 = [tex]\frac{16}{9}[/tex] - 1 = [tex]\frac{7}{9}[/tex], hence

tanΘ = ± [tex]\sqrt{\frac{7}{9} }[/tex] = ± [tex]\frac{\sqrt{7} }{3}[/tex]

Since 270° < Θ < 360° ← fourth quadrant where tanΘ < 0

Hence tanΘ = - [tex]\frac{\sqrt{7} }{3}[/tex]

and

cotΘ = [tex]\frac{1}{-\frac{\sqrt{7} }{3} }[/tex] = - [tex]\frac{3}{\sqrt{7} }[/tex] = - [tex]\frac{3\sqrt{7} }{7}[/tex]

Set the function equal to 0 and solve for

x=0,2,-6

Answer:

The solutions are:

[tex]x= 0[/tex]  and [tex]x= 2[/tex]  and [tex]x = -6[/tex]

Step-by-step explanation:

1) Make the function equal to zero

[tex]f(x)=x^3+4x^2-12x = 0[/tex]

2) Take x as a common factor

[tex]x(x^2+4x-12) = 0[/tex]

3) Factor the expression [tex]x^2+4x-12[/tex]

The sought-after factors are such numbers that when multiplying them obtain as result -12 and when adding both numbers obtain as result 4.

The numbers that meet this condition are

6 and -2

Because

[tex]6*(-2) = -12\\\\6 -2 = 4[/tex]

Then the factors are

[tex]x^2+4x-12=(x-2)(x+6)[/tex]

4) Solve the equation for x

[tex]x(x-2)(x+6) = 0[/tex]

The solutions are:

[tex]x= 0[/tex]  and [tex]x= 2[/tex]  and [tex]x = -6[/tex]

Answer:

Y = 2

Step-by-step explanation:

Solve for Y:

(3 + 5)×2 Y = 5×8 - 2×4

3 + 5 = 8:

8×2 Y = 5×8 - 2×4

5×8 = 40:

8×2 Y = 40 - 2×4

-2×4 = -8:

8×2 Y = -8 + 40

8×2 = 16:

16 Y = 40 - 8

40 - 8 = 32:

16 Y = 32

Divide both sides of 16 Y = 32 by 16:

(16 Y)/16 = 32/16

16/16 = 1:

Y = 32/16

The gcd of 32 and 16 is 16, so 32/16 = (16×2)/(16×1) = 16/16×2 = 2:

Answer: Y = 2

Without more information on the shape, it's not possible to provide the area of the figure from just the provided dimensions. Assuming it's a rectangle and using significant figures, the example calculation yields an area of 4.1 cm² when multiplying 0.6238 cm by 6.6 cm and rounding to two significant figures.

To find the area of a figure with given dimensions, one would typically multiply the length by the width. However, the question provided seems to be missing specific details about the shape of the figure. Given the figure's dimensions, if we assume it is a rectangle, the calculation would be straightforward: multiply the length by the width. Unfortunately, without additional information about the exact shape or context provided by equations or a figure reference, it is not possible to provide an accurate answer. It's essential to verify the shape and relevant equations before proceeding with the area calculation.

However, based on the examples given, to calculate the area with significant figures, one must consider the number of significant figures in the given dimensions. For example, if we multiply 0.6238 cm by 6.6 cm, the result is 4.11708 cm², which we round to 4.1 cm² (to two significant figures) because we are multiplying a number with four significant figures by a number with two significant figures.

The top right graph has a slope of 1/3

Answer:

top right

Step-by-step explanation:

Answer:

+- 5 and +- 3

Step-by-step explanation:

qn 2:

4r² = 91 + 9

4r² = 100

r² = 25

r = +- 5

qn 3:

4r² = 29 + 7

4r² = 36

r² = 9

r = +- 3

Answer:

Step-by-step explanation:

[tex]\bold{Q2.}\\\\4r^2-9=91\qquad\text{add 9 to both sides}\\\\4r^2-9+9=91+9\\\\4r^2=100\qquad\text{divide both sides by 4}\\\\\dfrac{4r^2}{4}=\dfrac{100}{4}\\\\r^2=25\to r=\pm\sqrt{25}\\\\\boxed{r=\pm5}[/tex]

[tex]\bold{Q3.}\\\\4r^2-7=29\qquad\text{add 7 to both sides}\\\\4r^2-7+7=29+7\\\\4r^2=36\qquad\text{divide both sides by 4}\\\\\dfrac{4r^2}{4}=\dfrac{36}{4}\\\\r^2=9\to r=\pm\sqrt9\\\\\boxed{r=\pm3}[/tex]

for this case we must write a proportion that shows the earnings obtained from Mrs. Miller for the sale of the house.

By making a rule of three we have:

179000 ------------> 100%

x -----------------------> 6%

Where "x" represents the gains obtained.

So:

[tex]x = \frac {6 * 179000} {100}[/tex]

Writing the proportion:

[tex]\frac {x} {179000} = \frac {6} {100}[/tex]

The earns were:

[tex]x = 10740[/tex]

ANswer:

[tex]\frac {x} {179000} = \frac {6} {100}\\x = 10740[/tex]

Answer:

$10,740

Step-by-step explanation:

You know that Mrs. Miller sells a house for $179,000. Then the cost of the house will be the 100%.

Knowing that she earns 6% of comission, you can set up the following proportion (Let be "x" the amount of money she earns), then:

[tex]\frac{\$179,000}{100}=\frac{x}{6}[/tex]

Now you need to solve for "x". Therefore, you get:

 [tex](6)(\frac{\$179,000}{100})=x[/tex]

 [tex]x=\$10,740[/tex]

Answer:

The area of the figure is [tex]56\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of the figure is equal to the area of two triangles plus the area of rectangle

so

[tex]A=2[\frac{1}{2}(b)(h)]+(L)(W)[/tex]

we have

[tex]b=1+4+1=6\ cm[/tex] ----> the base of triangle

[tex]h=2\ cm[/tex] ---> the height of triangle

[tex]L=11\ cm[/tex] ----> the length of rectangle

[tex]W=4\ cm[/tex] ----> the width of rectangle

substitute

[tex]A=2[\frac{1}{2}(6)(2)]+(11)(4)[/tex]

[tex]A=56\ cm^{2}[/tex]

Answer:

It's the first option.

Step-by-step explanation:

(x + 2)^2 gives a duplicate (multiplicity 2) root. (because (x + 2)^2 = 0 so x = -2 multplicity 2)

(x - 4) gives one root of 4.

(x + 1)^3  gives x = -1 with multiplicity 3.

Answer:

-2 with multiplicity 2, 4 with multiplicity 1, and -1 with multiplicity 3.

Step-by-step explanation:

The given polynomial function is: [tex]f(x)=(x+2)^2(x-4)(x+1)^3[/tex].

To find the roots of this polynomial, we equate each factor to zero.

This implies that;

i. [tex](x+2)^2=0[/tex], [tex]\implies x=-2[/tex], the multiplicity of this root is 2, because the factor repeats twice

ii.  [tex]x-4=0[/tex], [tex]\implies x=4[/tex], the multiplicity of this root is 1, because the factor repeats once.

ii.  [tex](x+1)^3=0[/tex], [tex]\implies x=-1[/tex], the multiplicity of this root is 3, because the factor repeats three times.

Answer:

The solutions of the equation are √3 - 1/2 and -√3 - 1/2

Step-by-step explanation:

* Lets revise how to make the completing square

- The form of the completing square is (x - h)² + k, where h , k

 are constant

- The general form of the quadratic is x² + bx + c, where b , c

 are constant

- To change the general form to the completing square form equate  

 them and find the constant h , k

* Now lets solve the problem

∵ x² + x = 11/4 ⇒ subtract 11/4 from both sides

∴ x² + x - 11/4 = 0

- Put the equation equal the form of the completing square

∵ x² + x - 11/4 = (x - h)² + k ⇒ solve the bracket power 2

∴ x² + x - 11/4 = x² - 2hx + h² + k

- Equate the like terms

∵ x = -2hx ⇒ divide both sides by x

∴ 1 = -2h ⇒ divide both sides by -2

∴ -1/2 = h

∴ the value of h = -1/2

∵ -11/4 = h² + k

- Substitute the value of h

∴ -11/4 = (-1/2)² + k

∴ -11/4 = 1/4 + k ⇒ subtract 1/4 from both sides

∴ -12/4 = k

∴ k = -3

∴ The value of k is -3

- Substitute the value of h and k in the completing square form

∴ (x - -1/2)² + (-3) = 0

∴ (x + 1/2)² - 3 = 0 ⇒ add 3 to both sides

∴ (x + 1/2)² = 3 ⇒ take square root for both sides

∴ x + 1/2 = √3 OR x + 1/2 = -√3

∵ x + 1/2 = √3 ⇒ subtract 1/2 from both sides

∴ x = √3 - 1/2

OR

∵ x + 1/2 = -√3 ⇒ subtract 1/2 from both sides

∴ x = -√3 - 1/2

* The solutions of the equation are √3 - 1/2 and -√3 - 1/2

Answer:

Diane purchased 7 pens

Step-by-step explanation:

Let

x----> the number of pens

y----> the number of pencils

we know that

x+y=17

y=17-x -----> equation A

0.60x+0.40y=8.20 -----> equation B

Solve the system of equations by substitution

Substitute equation A in equation B and solve for x

0.60x+0.40(17-x)=8.20

0.60x+6.8-0.40x=8.20

0.20x=8.20 -6.8

x=1.4/0.2=7 pens

Answer:  The number of pen purchased by Diane is 7.

Step-by-step explanation:  Given that Joe’s department store sells pens for 60 cents each and pencils for 40 cents each.

Diane purchased a total of 17 items for $8.20.

We are to find the number of pen that Diane purchased.

We know that

1 cent = $ 0.01.

Let x and y represents the number of pen and pencils that Diane purchased.

Then, according to the given information, we have

[tex]60\times0.01x+40\times 0.01y=8.20\\\\\Rightarrow 0.6x+0.4y=8.20\\\\\Rightarrow 6x+4y=82~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

and

[tex]x+y=17\\\\\Rightarrow y=17-x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Substituting the value of y from equation (ii) in equation (i), we get

[tex]6x+4y=82\\\\\Rightarrow 6x+4(17-x)=82\\\\\Rightarrow 6x+68-4x=82\\\\\Rightarrow 2x=82-68\\\\\Rightarrow 2x=14\\\\\Rightarrow x=\dfrac{14}{2}\\\\\Rightarrow x=7.[/tex]

Thus, the number of pen purchased by Diane is 7.

The answer would be 17n+6.

Answer:

17n+6

Step-by-step explanation:

you add 5n and 12n and get 17n and you can't add 6 to 17n so your answer is 17n+6

A horizontal shift happens when you add or subtract a value from the input value of x.

To shift left the number would be added to the x.

The answers are:

h(x) = 3 ln(x + 3) + 1

r(x) = −3 ln(x + 1) + 3

p(x) = ln(x + 2) − 2

Answer:

h(x) = 3 ln(x + 3) + 1

r(x) = −3 ln(x + 1) + 3

p(x) = ln(x + 2) − 2

Step-by-step explanation:

The parent function given to us is: [tex]f(x)=\ln x[/tex].

A horizontal translation to the left k units is of the form [tex]y=\ln (x+k)[/tex].

This implies that;

h(x) = 3 ln(x + 3) + 1, is a horizontal translation to the left by 3 units.

r(x) = −3 ln(x + 1) + 3, is a horizontal translation to the left by 1 unit.

p(x) = ln(x + 2) − 2, is a horizontal translation to the left by 2 unit.

Answer:

  1500(1.0115)^(2t)

Step-by-step explanation:

The formula for the balance in an account earning compound interest is ...

  A = P(1 +r/n)^(nt)

where P is the principal invested, r is the annual rate, n is the number of times per year interest is compounded, and t is the number of years.

__

Using the given values in the formula, we have ...

  A = 1500(1 +0.023/2)^(2t)

Simplifying a bit, this is ...

  A = 1500(1.0115)^(2t) . . . . . CD value after t years

Your answer is 5! (:

Answer:

5

Step-by-step explanation:

A square root of a number n is a number r such that r2=n. in the case 25 we find that 52=25 , so 5 is a square root of 25. sorry if this is confusing. found this from google.

Answer:

The solutions are the points (1,3) and (4,0)

Step-by-step explanation:

we have

[tex]y=x^{2} -6x+8[/tex] ----> equation A

[tex]y=-x+4[/tex] ----> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations are the intersection points both graphs

using a graphing tool

The graph has two intersection points

therefore

the system of equations has two solutions

The solutions are the points (1,3) and (4,0)

see the attached figure

Answer:

its c on edge

Step-by-step explanation:

cause um if you look at c on edge it looks like the bestes answer

Answer:

C) (6x6x6x6)x(6x6x6)

Step-by-step explanation:

an exponent is the base multiplied by itself that many times, and another way to write 2 exponents multiplied by each other (and have the same base) is by simply adding the exponents, for example, 6^4x6^3 is 6^7 :D Hope this helps!

Answer:

The answer is C :)

Step-by-step explanation:

Final answer:

The projectile reaches its maximum height after 22 seconds, which is determined by the vertex formula t = -b/(2a) applied to the given quadratic function representing the height over time.

Explanation:

To determine after how many seconds the projectile reaches its maximum height, we need to analyze the function h(t) = -16t2 + 704t. This is a quadratic function, and the maximum height will be reached at the vertex of the parabola represented by this function.

The vertex of a parabola given by ax2 + bx + c can be found using the formula t = -b/(2a), where a, b, and c are coefficients from the quadratic equation. In this case, a = -16 and b = 704.

Using the formula to find the time t when the projectile reaches its maximum height, we calculate: t = -704/(2 × -16) = 704/32 = 22. Therefore, the projectile reaches its maximum height after 22 seconds.

Answer:

The answer should be D. It is -2 on the inside because it is backwards of what you may think and because it is inside the square root. The -3 represents a down shift of 3

Answer: Last option.

Step-by-step explanation:

Below are shown some transformation for a function f(x):

[tex]f(x) + k[/tex] shifts the function k units upward.

[tex]f(x) - k[/tex] shifts the function k units downward.

[tex]f(x+k)[/tex] shifts the function k units to the left.

[tex]f(x-k)[/tex] shifts the function k units to the right.

Then, knowing that the graph of the function [tex]y=\sqrt{x}[/tex] is shifted 3 units down and 2 units rights, the function that represents the new graph is:

[tex]y=\sqrt{x-2}-3[/tex]

Which is the last option.

Answer:

8:12, which reduces to 2:3

Step-by-step explanation:

The tennis team played 12 total matches if they won 8 and lost 4. (8+4=12). They're asking for ratio of wins to total matches. They won 8 and played twelve in total so: 8:12. Ratios are like fractions and must be reduced. So it's 2:3.

Answer:

The ratio of wins of the total number of matches played is 2/3

Step-by-step explanation:

A tennis team won 8 matches and lost 4 which means that the tennis team have played 12 matches in total.

So, the ratio of wins to the total numbers of matches played is:

Ratio of wins = won matches/total matches

Ratio of wins =  8/12 = 2/3

The angels are ADJACENT ANGELS

Answer:

21

(Side Note: I solved this for anyone who needs the answer.)

Definitions:

Adjacent: Congruent meaning same measure.

Vertical: Two angles that have a common side.

Explanation:

This equation is adjacent.

If we look at this problem and look to the bottom and see that tiny square, that means it is a right angle, right angles equal to 90 degrees.

Step-By-Step:

To solve for x, we need to put 25 degrees and x into a formula.

x + 35 = 90

Next and the last step is to subtract 90 and 35:

90 - 35 = 21

Our final answer is 21.

            Hope this helps!

      ~Hocus Pocus