Eduardo’s average speed on his commute to work was 55 miles per hour. On the way home, he hit traffic and only averaged 40 miles per hour. If the round trip took him 1.25 hours, which expression represents the distance, in miles, for his trip home that is missing from the table?



t – 1.25
1.25 – t
40(1.25 – t)
40(t – 1.25)

Answer:

AB or x =6sqrt(3) (which is what the pic ask for)

but you ask for AC which is 9

Step-by-step explanation:

The hypotenuse is twice the length of the short leg.

The short leg is 3sqrt(3) (because I see it is opposite the smallest angle which is 30 in this case).

So the hypotenuse is twice 3sqrt(3) which is 6sqrt(3)

You are also asking for AC though... That is the short leg times sqrt(3) so that measurement is 3sqrt(3)*sqrt(3)=3(sqrt(3*3))=3(3)=9

Answer:

I believe it's C.

Step-by-step explanation:

Hope my answer has helped you!

Answer:

D

Step-by-step explanation:

From the graph we can see:

Given the information extract, we can rule out A, B, and C immediately. Answer choice D is right.

Answer:

The mistake is he said"The equation has infinitely many solutions."

But based on what he was solving for, this equation does not have any solutions, so that's his mistake.

The other answer is correct, but the answer is D if you just want the answer.

Answer:

2 sets of possible solutions:

x=3, y = 5

and

x=-1, y = -3

Step-by-step explanation:

Using the graphical method, (see attached)

you can graph both equations and find their intersection points.

From the attached plot, you can see that the graphs intersect at (3,5) and (-1,-3)

Alternatively, you can solve this numerically by solving the following system of equations. You will get the same answer.

y = 2x + 1 ------------------- eq. (1)

y = x² - 4 ------------------- eq. (2)

Answer:

2.5

Step-by-step explanation:

because half of 5 is 2.5

Answer:

[tex]\large\boxed{\log_2\dfrac{x^3}{\left(\dfrac{3}{x+4}\right)}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\\\\\log_ab^n=n\log_ab\\\\\log_a\left(\dfrac{c}{d}\right)=\log_ac-\log_ad\\\\==============================[/tex]

[tex]\text{We have:}\\\\3\log_2x-(\log_23-\log_2(x+4))\\\\=\log_2x^3-\log_2\dfrac{3}{x+4}\\\\=\log_2\dfrac{x^3}{\frac{3}{x+4}}[/tex]

The expression 3log(2)3 - log(2)(x+4) can be simplified by using the logarithmic laws, resulting in the final single logarithm of log2(39 / (x+4)).

The original expression, 3log(2)3 - log(2)(x+4), can be simplified using a few laws of logarithms. Firstly, using the rule that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number, we can simplify. We find that the expression becomes log(2)33 - log(2)(x+4). Secondly, by applying the rule that the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers, we can further simplify. The final expression is now log2(39 / (x+4)). This is the expression written as a single logarithm.

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Answer:

Step-by-step explanation:

Answer:

The Answer IS: 2480 I just did the question

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

3/2 = 3/2x - 6/5x

Get a common denominator of 10 for the fractions with x

3/2 = 3/2 *5/5 x - 6/5 *2/2 x

3/2 = 15/10x - 12/10x

3/2 = 3/10 x

Multiply each side by 10/3 to isolate x

10/3 * 3/2 = 10/3 * 3/10 x

10/2 = x

5 =x

Answer:

Mykel you should have 2 rows of -5

Step-by-step explanation:

so the first row should have 5 red blocks and the second row should also have 5 red blocks. The reason it should be red is because red stands for negative.

Answer:

280 mL

Step-by-step explanation:

If x is the amount of 35% solution and y is the amount of pure water, then:

0.15 = (0.35x + 0y) / (x + y)

0.15 = (0.35x) / (x + y)

Given that x = 210 mL:

0.15 = (0.35×210) / (210 + y)

210 + y = 490

y = 280

The third angle would have to be either an obtuse angle or a right angle.

The third angle can either be an acute angle or obtuse angle

The sum of an interior angle of a triangle is 180 degrees

Acute angles are angles that are less than 90 degrees. If the two angles of a triangle are acute, the two angles can be 30 and 45 degrees

If the third angle is m<C

m<C = 180 - (30 + 45)

m<C = 180  - 75

m<C = 105 degrees

Since the angle is greater than 90 and less than 180, hence it is an Obtuse angle.

Similarly, if the two angles of a triangle are acute, the two angles can be 30 and 89 degrees

If the third angle is m<D

m<D = 180 - (30 + 90)

m<D = 180  - 119

m<D = 61 degrees

Since the angle is less than 90degrees, hence it is an acute angle.

This shows that the third angle can either be an acute angle or obtuse angle

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Note that perimeter of rectangle [tex]P=2l+2w[/tex]

So we have to solve for width or w.

[tex]P=2l+2w[/tex]

[tex]30=2\times10+2w[/tex]

[tex]w=5[/tex]

Width of a rectangle is 5 units.

Hope this helps.

r3t40

Answer:

So, the inverse of function

[tex]f(x) = \frac{-1}{2} \sqrt{x+3}[/tex] is [tex]f^{-1}(x)= 4x^2-3[/tex]

Step-by-step explanation:

We need to find the inverse of the given function

[tex]f(x) = \frac{-1}{2} \sqrt{x+3}[/tex]

To find the inverse we replace f(x) with y

[tex]y = \frac{-1}{2} \sqrt{x+3}[/tex]

Now, replacing x with y and y with x

[tex]x = \frac{-1}{2} \sqrt{y+3}[/tex]

Now, we will find the value of y in the above equation

Multiplying both sides by -2

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

Taking square on both sides

[tex](-2x)^2 = (\sqrt{y+3})^2[/tex]

[tex]4x^2 = y+3[/tex]  

Finding value of y

[tex]y = 4x^2-3[/tex]

Replacing y with f⁻¹(x)

[tex]f⁻¹(x)= 4x^2-3[/tex]

So, the inverse of function

[tex]f(x) = \frac{-1}{2} \sqrt{x+3}[/tex] is [tex]f^{-1}(x)= 4x^2-3[/tex]

ANSWER

[tex]f^{ - 1} (x) =4 {x}^{2}- 3[/tex]

EXPLANATION

A function will have an inverse if and only if it is a one-to-one function.

The given function is

[tex]f(x) = - \frac{1}{2} \sqrt{x + 3} \: \: where \: \: x \geqslant - 3 [/tex]

To find the inverse of this function, we let

[tex]y=- \frac{1}{2} \sqrt{x + 3}[/tex]

Next, we interchange x and y to get,

[tex]x=- \frac{1}{2} \sqrt{y+ 3}[/tex]

We now solve for y.

We must clear the fraction by multiplying through with -2 to get;

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

Square both sides of the equation to get:

[tex](- 2x)^{2} = (\sqrt{y+ 3}) ^{2} [/tex]

[tex]4x^{2} = y + 3[/tex]

Add -3 to both sides

[tex]4 {x}^{2} - 3 = y[/tex]

Or

[tex]y = 4 {x}^{2}- 3[/tex]

This implies that,

[tex]f^{ - 1} (x) =4 {x}^{2}- 3[/tex]

This is valid if and only if

[tex]x \geqslant - 3[/tex]

For this case we must find an expression equivalent to:

[tex]\frac {10x ^ 6y ^ {12}} {- 5x ^ {- 2} y^ {- 6}}[/tex]

We have to:

[tex]\frac {10} {- 5} = - 2[/tex]

Now, by definition of division of powers of equal base, we put the same base and subtract the exponents. Rewriting the expression we have:

[tex]-2x ^ {6 - (- 2)} y^ {12 - (- 6)} =\\-2x ^ {6 + 2} y ^ {12 + 6} =\\-2x ^ 8y ^ {18}[/tex]

Answer:

Option B

Answer:

Yes there is GCF > 1 ⇒ (GCF = 4)

The completely factored form is 4(x - 2)(x² + 2x + 4)

Step-by-step explanation:

* Lets find the greatest common factor of the two terms

- The binomial is 4x³ - 32

- The terms of the binomial are 4x³ and 32

- The greatest common factor of 4 and 32 is 4 because both of them

  can divided by 4

∵ 4x³ ÷ 4 = x³

∵ 32 ÷ 4 = 8

∴ The greatest common factor GCF is 4

∴ 4x³ - 32 = 4(x³ - 8)

* Yes there is GCF > 1

# x³ - 8 is the difference of two cubs, it can factorize it into two

  brackets

- The first bracket has cube root of x³ and cube root of 8

- The second bracket comes from the first bracket it has three terms

# The 1st term is square the 1st term in the first bracket

# The 2nd term is the product of the 1st term and the 2nd term of the

  1st bracket with opposite sign of the 2nd term in the 1st bracket

# The 3rd term is the square of the 2nd term in the 1st bracket

* Lets do these steps with x³ - 8

∵ The first bracket = (∛x³ - ∛8)

∵ ∛x³ = x and ∛8 = 2

∴ The first bracket = (∛x³ - ∛8) = (x - 2)

- Lets make the 2nd bracket from the 1st bracket

∴ The second bracket = (x² + (x)(2) + 2²)

∴ The second bracket = (x² + 2x + 4)

∴ The factorization of x³ - 8 = (x - 2)(x² + 2x + 4)

* The completely factored form is 4(x - 2)(x² + 2x + 4)

Answer:

....Yes it is 4                                                                                                                       ....4(x-2)

Step-by-step explanation:

the screenshot shows proof :))

Answer:

42

Step-by-step explanation:

This means 0.84 divided by 0.02

which equals to 42

the points mean that there is a zero

if a number has been written in that format of  "point" then "number" without any number before the point, it means there is  a zero there

if you need anything else clarified please do so in the comment section i would like to help more

           Hope this helps and if it does mark as branliest answer thx

The value of the rational expression when x is -2 or -1 is 0 and 3, respectively.

To find the value of the rational expression when x is -2 or -1, we substitute these values into the expression. Plugging in -2, we have (-2)^2 - 4/((-2)+2)((-2)+1) = 0.

Next, plugging in -1, we have (-1)^2 - 4/((-1)+2)((-1)+1) = 3.

Therefore, the value of the rational expression when x is -2 or -1 is 0 and 3, respectively.

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Answer:

[tex]18g + 7 - 12g - 3 = 6g + 4[/tex]

Step-by-step explanation:

[tex]18g+7-12g-3\\=18g-12g+7-3\\=6g+7-3\\=6g+4[/tex]

Answer:

[tex]\large\boxed{(g\circ f)(2)=1296}[/tex]

Step-by-step explanation:

[tex]f(x)=-x+8,\ g(x)=x^4\\\\(g\circ f)(x)=g\bigg(f(x)\bigg)\\\\(g\circ f)(x)=\bigg(-x+8\bigg)^4\\\\(g\circ f)(2)\to\text{put x - 0 to the equation of the function:}\\\\(g\circ f)(2)=(-2+8)^4=(6)^4=1296[/tex]

Answer:

B

Step-by-step explanation:

x is the number of years of experience.

In the graph, the point (y) is not shown for 5 years of experience but we can easly figure this out by plugging in 5 into x of the equation of best fit given.

Hence

[tex]y= 1.3x +5.5\\y= 1.3(5) +5.5\\y=12[/tex]

So, the best estimate is $12 per hour, the correct answer is B

Answer:

its b

hope its right

[tex]\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{3}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-4}{-5-6}\implies \cfrac{-1}{-11}\implies \cfrac{1}{11}[/tex]

Answer:

1/11

Step-by-step explanation:

Answer: OPTION A.

Step-by-step explanation:

Find the length scale factor by dividing the known length of the larger triangle by the known length of the smaller triangle:

[tex]lenght\ scale\ factor=\frac{35}{25}=\frac{7}{5}[/tex]

Then, the  area scale factor is:

[tex]area\ scale\ factor=(\frac{7}{5})^2=\frac{49}{25}[/tex]

To find the area of the the larger triangle, multiply the area of the smaller triangle by the area scale factor. Then:

[tex]A_{(larger)}=(270ft^2)(\frac{49}{25})=529.2ft^2[/tex]

So, the option that shows an approximation of the area of the larger triangle is the option A:

[tex]A_{(larger)}[/tex]≈[tex]530ft^2[/tex]

Answer:

D:Spring A is 3 m longer than spring B because 15 – 12 = 3.

Step-by-step explanation:

In this question, you should remember the Hooke's Law in physics.

The Hooke's Law simply explains that the extension that occurs on a spring is directly proportional to the load applied on it.

The mathematical expression for this law is

[tex]F=-kx[/tex]

where;

F= force applied on the spring

x = the extension on the spring

k= the spring constant which varies in spring.

The question will need you to calculate the extension on the springs A and B then compare the values obtained.

In spring A

Force, F=60N and spring constant ,k=4 N/m

To find the extension x apply the expression;

[tex]F=-kx\\\\60=-4*x\\\\60=-4x\\\\\frac{60}{-4} =\frac{-4x}{-4} \\\\\\-15=x[/tex]

Here the spring extension is 15 m

In spring B

Force, F=60N and spring constant , k=5N/m

To find the extension x apply the same expression

[tex]F=-kx\\\\60=-5*x\\\\60=-5x\\\\\\\frac{60}{-5} =\frac{-5x}{-5} \\\\\\-12=x[/tex]

Here the extension on the spring is 12 m

Compare

The extension on spring A is 3 m longer than that in spring B because when you subtract the value of spring B from that in spring A you get 3m

[tex]=15m-12m=3m[/tex]

Answer:

D)Spring A is 3 m longer than spring B because 15 – 12 = 3.

trust

Answer:

x^3(2x+1)(2x-1)

Step-by-step explanation:

first take common then use formula of a^2-b^2

Answer:

The factor of the provided expression are: [tex]x^3(4x-1)(4x+1)[/tex]

Step-by-step explanation:

Consider the provided expression.

[tex]16x^5-x^3[/tex]

Here the Greatest common factor in the above expression is x³.

The above expression can be written as:

[tex]x^3(16x^2-1)[/tex]

[tex]x^3((4x)^2-1^2)[/tex]

Now use the difference of the square property: [tex]a^2-b^2=(a+b)(a-b)[/tex]

By using the above property we can rewrite the provided expression as shown:

[tex]x^3(4x-1)(4x+1)[/tex]

Hence, the factor of the provided expression are: [tex]x^3(4x-1)(4x+1)[/tex]

Answer:

7

Step-by-step explanation:

Replace a with 5 and b with 3.

5+3-1=7

Answer:

7.

Step-by-step explanation:

Substitute for a and b in the given identity:

5 * 3 = 5 + 3 - 1

= 8 - 1

= 7.

Answer:

D   sin 85         sin 31

    ---------- =     ----------

      b                  9.3

Step-by-step explanation:

We can use the law of sins

sin B        sin A         sin C

---------- = ----------- = ----------

b                   a            c

We do not know angle C, but we can calculate it

The angles of a triangle add to 180

A + B + C = 180

64+ 85 + C = 180

149 + C = 180

C = 180-149

C =31

sin B         sin C

---------- = ----------

b                  c

We know B =  85, C = 31, b = unknown and c = 9.3

sin 85         sin 31

---------- = ----------

b                  9.3

the correct answer would be D

Answer:

Step-by-step explanation:

[tex]\text{The formula of a perimeter of a rectangle:}\\\\P=2(l+w)\\\\l-length\\w-width\\\\\text{We have}\ l=(w+24)\ in,\ P=128\ in\\\\\text{Substitute:}\\\\128=2(w+24+w)\qquad\text{divide both sides by 2}\\\\64=2w+24\qquad\text{subtract 24 from both sides}\\\\40=2w\qquad\text{divide both sides by 2}\\\\20=w\to w=20\ in\\\\l=20+24=44\ in[/tex]

Answer:

The quotient is 2x^2 - x + 1.

Step-by-step explanation:

If x + 1 is the divisor in long division, then -1 is the divisor in synthetic division:

-1   /   2    1    0    1

              -2    1    -1

    ----------------------

       2      -1     1    0

The quotient is 2x^2 - x + 1.  The coefficients were obtained through synthetic division.