Select the correct answer.
Which is the simplified form of the expression ?

Answer:

The answer is a

Step-by-step explanation:

Answer:

Graph 2 which has both solid and dashed line

Step-by-step explanation:

Given the linear inequalities :

y>2/3x+3 - - - (1)

y ≤ -1/3x+2 - - - (2)

One quick observation that can be made from the two graphs is the type of line used to plot the two linear inequalities;

Inequalities that uses either the < or > sign are plotted using a dashed line while inequalities with makes use of ≤ or ≥ are plotted using the solid line. Therefore we can conclude that the graph which uses both the solid line and the dashed line to represent the linear inequality conditions is the correct choice.

Answer:

Step-by-step B represents the $14 John earned in the 2 hours he worked.

explanation:

Answer:

1000

Step-by-step explanation:

Answer:

f(4) = 31

f(0) = 7

f(-1) = 1

Step-by-step explanation:

f(x) = 6x + 7

f(4) = 6(4) + 7

f(4) = 24 + 7

f(4) = 31

f(0) = 6(0) + 7

f(0) = 0 + 7

f(0) = 7

f(-1) = 6(-1) + 7

f(-1) = -6 + 7

f(-1) = 1

Answer:

g(x) = x^3 - 2

Step-by-step explanation:

As you can see on the graph, the line has been translated down 2 units.

If the graph of f has the same shape as the graph of g, then the slope remains the same. The y intercept (k) changes by -2 units, so the k value is -2

g(x) = x^3 - 2

Hope this helps!!

Answer:

7x+y=-3

Step-by-step explanation:

if m is the slope of a line, then the slope of its parallel line will have the same slope m,

in the given equation, y=-7x-8, the slope is -7

among the options, 1st option has a slope of -7, since,

7x+y=-3

or, y=-7x-3

Answered by GAUTHMATH

Answer:

[tex]67.5\text{ [square units]}[/tex]

Step-by-step explanation:

The composite figure consists of one rectangle and two triangles. We can add up the area of these individual shapes to find the total area of the irregular figure.

Formulas:

By definition, the base and height must intersect at a 90 degree angle.

The rectangle has a base of 10 and a height of 5. Therefore, its area is [tex]A=10\cdot 5=50[/tex].

The smaller triangle to the left of the rectangle has a base of 2 and a height of 5. Therefore, its area is [tex]A=\frac{1}{2}\cdot 2\cdot 5=5[/tex].

Finally, the larger triangle on top of the rectangle has a base of 5 and a height of 5. Therefore, its area is [tex]A=\frac{1}{2}\cdot 5\cdot 5=12.5[/tex].

Thus, the area of the total irregular figure is:

[tex]50+5+12.5=\boxed{67.5\text{ [square units]}}[/tex]

Answer:

P=8(h)

Step-by-step explanation:

P is her total pay. You find that by multiplying what she makes an hour (8) by the total number of hours she has worked (h).

Answer:

p=8h

Step-by-step explanation:

Pay equals $8 per the number of hours

Answer:

3z+3x=2

Step-by-step explanation:

3z+8=12+3x-2

collecting like terms

3z-3x=12-2-8

3z-3x=2

3z=2+3x

divide through by three

z= ⅔+x

Answer:

slope is 2÷3 of giving line points

Answer:

the anwer is B ( i mean second option)

And you can try it

you will find ;

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

HAVE A NİCE DAY

Step-by-step explanation:

GREETİNGS FROM TURKEY ツ

Answer:

-36m^3-21n^3+85mn^2+36m^2n

Step-by-step explanation:

That's what the calculator says:).

Answer:

Step-by-step explanation:

B

Answer:

Step-by-step explanation:

-2

Answer:

15 / 4

Step-by-step explanation:

1 kg = 1000 g

3 kg

= 3 x 1000

= 3000 g

3kg to 800g

= 3kg : 800g

= 3000 : 800

= 30 : 8

= 30 / 8

= 15 / 4

15/4 is the fraction representing the ratio of 3 kilograms to 800 grams.

To express the ratio of 3 kilograms to 800 grams as a fraction in its lowest terms.

we need to convert both the quantities to the same units. Since 1 kg is equal to 1000 g, we can convert 3 kg to grams as follows:

3 kg = 3 * 1000 g = 3000 g

Now, we have the quantities in the same unit, and the ratio becomes:

3000 g to 800 g

To express this ratio as a fraction, we place the quantities over each other:

3000 g

-------

800 g

Now, to simplify the fraction to its lowest terms, we find the greatest common divisor (GCD) of the two numbers (3000 and 800) and divide both the numerator and denominator by this GCD.

The GCD of 3000 and 800 is 200, so dividing both by 200 gives us:

3000 ÷ 200 = 15

800 ÷ 200 = 4

Therefore, the ratio 3 kg to 800 g expressed as a fraction in its lowest terms is 15/4.

In summary, we first converted the units to the same (grams) to make the ratio easier to handle. Then, we represented the ratio as a fraction and simplified it to its lowest terms using the GCD method. The final answer, 15/4, is the fraction representing the ratio of 3 kilograms to 800 grams.

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[tex]{\color{red}{\huge{\underbrace{\overbrace{\mathfrak{\:\:\:\:\:\:\:꧁"Answer"꧂\:\:\: }}}}}}[/tex]

[tex]\small\color{blak}{{\underline{\bold{ Find \:a X } } } }[/tex]

[tex]\small\color{black}{{\underline{\bold{173°=15z+10x-2 } } } } \\ = 173 = 25x - 2 \\ = - 25x = - 2 - 173 \\ = - 25x - 175 \\ = \small\color{blue}{{{\boxed{\tt\red{} \:\:\:\:\:\:\:\:\:\: x=7\:\:\:\: }}}}[/tex]

[tex]\small\color{blak}{{\underline{\bold{ Find\:a\:m<QSR } } } }[/tex]

[tex]\small\color{blak}{{\underline{\bold{ 10(7)-2 } } } }\\=70-2\\=\small\color{red}{{{\boxed{\tt\red{} \:\:\:\:\:\:\:\:\:\: m<QSR=68°\:\:\:\: }}}}[/tex]

[tex]\Large\color{red}{{\underline{\mathfrak {{꧁"Carry\:on\: learning"꧂ }}}}}[/tex]

The measure of angle QSR is 68 degrees.

Substitution means putting numbers in place of letters to calculate the value of an expression.

According to the given question.

m ∠TSQ = 15x

m ∠TSR = 173 degrees

m ∠QSR = 10x -2

Since,

m ∠TSR = m ∠TSQ + ∠QSR

Substitute the value of m ∠TSR, m ∠TSQ and m ∠QSR in the above expression.

⇒ [tex]173 = 15x + 10x - 2[/tex]

⇒ [tex]173 = 25x - 2[/tex]

⇒ [tex]175 = 25x[/tex]

⇒ [tex]x = \frac{175}{25}[/tex]

⇒ [tex]x = 7[/tex]

Again, for finding the value of angle QSR substitute the value of x in 10x - 2.

Therefore,

m ∠QSR = 10(7) - 2

⇒ m ∠QSR = 70 - 2

⇒ m ∠QSR = 68 degrees

Hence, the measure of angle QSR is 68 degrees.

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9514 1404 393

Answer:

  y = 7√2

Step-by-step explanation:

We are given the side opposite the angle, and we want to find the hypotenuse. The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

  sin(45°) = 7/y

  y = 7/sin(45°) = 7/(1/√2)

  y = 7√2

__

Additional comment

In this 45°-45°-90° "special" right triangle, the two legs are the same length. Thus, ...

  x = 7

Answer:

Tommy's age is 9 years old.

Timmy's age is 14 years old.

Step-by-step explanation:

Take Tommy's age to be x and Timmy's age to be x+5

x+x+5=23

2x+5=23

2x=23-5=18

x=18÷2=9

x+5=9+5=14

Answer:

36 (maybe...)

Step-by-step explanation:

Technically there is no way to answer this question, it says that 120 ADULTS were surveyed and then asks how many STUDENTS rank themselves as introverts.  But if we a supposed to assume that all adults are students:

The ratio of 3:7 means that for every 3 introverts, there are 7 extroverts.

In other words for every 10 people (total introvert+extrovert) there are 3 introverts.

So to find the number of introverts in the group of 120, just multiply by 3/10 or 0.3

The answer would be 36

Answer:

The right answer is "0.3193".

Step-by-step explanation:

According to the question,

Mean,

[tex]\frac{1}{\lambda} = 13[/tex]

[tex]\lambda = \frac{1}{13}[/tex]

As we know,

The cumulative distributive function will be:

⇒ [tex]1-e^{-\lambda x}[/tex]

hence,

In the first 5 years, the probability of failure will be:

⇒ [tex]P(X<5)=1-e^{-\lambda\times 5}[/tex]

                    [tex]=1-e^{-(\frac{1}{13} )\times 5}[/tex]

                    [tex]=1-e^(-\frac{5}{13})[/tex]

                    [tex]=1-0.6807[/tex]

                    [tex]=0.3193[/tex]

Answer:

[tex]f(h(xc)) = 2xc-4[/tex]

Step-by-step explanation:

Given

[tex]f(x) = x - 7[/tex]

[tex]h(x) = 2x + 3[/tex]

Required

[tex]f(h(xc))[/tex]

First, calculate h(xc)

If [tex]h(x) = 2x + 3[/tex]

Then

[tex]h(xc) = 2xc + 3[/tex]

Solving further:

[tex]f(x) = x - 7[/tex]

Substitute h(xc) for x

[tex]f(h(xc)) = h(xc) - 7[/tex]

Substitute [tex]h(xc) = 2xc + 3[/tex]

[tex]f(h(xc)) = 2xc + 3 - 7[/tex]

[tex]f(h(xc)) = 2xc-4[/tex]

This is one single number that's slightly smaller than 400 thousand.

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

Explanation:

There are 26 letters in the english alphabet. We don't use letters i or o, so we have 26-2 = 24 choices for that first slot.

Then we have 10 choices for the second slot because there are 10 single digits 0 (zero) through 9.

After making the selection for the second slot, we have 10-1 = 9 choices left for the third slot. The fourth slot has 10-2 = 8 digits to pick from. The subtraction occurs because we cannot reuse the digits.

Finally, the last slot will be a letter. We have 24-1 = 23 letters left to pick from.

Overall, we have 24*10*9*8*23 = 397,440 different license plates possible.

--------------------

Extra info (optional section)

You may be wondering "why do we multiply those values?". Well consider a simple example of having only 2 slots instead of 5.

Let's say the first slot is a letter A to Z, excluding letters i and o. The second slot will be the digit from 0 through 9.

If you make a table with 24 rows and 10 columns, then you'll have 24*10 = 240 cells overall. Notice the multiplication here. The 24 rows represent each letter, and the 10 columns are the digit numeric digits.

Each inner cell is a different two character license plate. For example A5 is one such plate. This idea can be extended to have 5 characters.

Answer:

729π ft³

Step-by-step explanation:

Applying,

Volume of a cone

V = πr²h/3.............. Equation 1

Where r = radius of the base, h = height, π = pie

From the question,

Given: r = 9 ft, h = 27 ft

Substitite these values into equation 1

V = π(9²)(27)/3

V = 729π ft³

Hence the volume of the figure in terms of π is 729π ft³

(3.1) … … …

[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{2x-y}{x-2y}[/tex]

Multiply the right side by x/x :

[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{2-\dfrac yx}{1-\dfrac{2y}x}[/tex]

Substitute y(x) = x v(x), so that dy/dx = x dv/dx + v :

[tex]x\dfrac{\mathrm dv}{\mathrm dx} + v = \dfrac{2-v}{1-2v}[/tex]

This DE is now separable. With some simplification, you get

[tex]x\dfrac{\mathrm dv}{\mathrm dx} = \dfrac{2-2v+2v^2}{1-2v}[/tex]

[tex]\dfrac{1-2v}{2-2v+2v^2}\,\mathrm dv = \dfrac{\mathrm dx}x[/tex]

Now you're ready to integrate both sides (on the left, the denominator makes for a smooth substitution), which gives

[tex]-\dfrac12\ln\left|2v^2-2v+2\right| = \ln|x| + C[/tex]

Solve for v, then for y (or leave the solution in implicit form):

[tex]\ln\left|2v^2-2v+2\right| = -2\ln|x| + C[/tex]

[tex]\ln(2) + \ln\left|v^2-v+1\right| = \ln\left(\dfrac1{x^2}\right) + C[/tex]

[tex]\ln\left|v^2-v+1\right| = \ln\left(\dfrac1{x^2}\right) + C[/tex]

[tex]v^2-v+1 = e^{\ln\left(1/x^2\right)+C}[/tex]

[tex]v^2-v+1 = \dfrac C{x^2}[/tex]

[tex]\boxed{\left(\dfrac yx\right)^2 - \dfrac yx+1 = \dfrac C{x^2}}[/tex]

(3.2) … … …

[tex]y' + \dfrac yx = \dfrac{y^{-3/4}}{x^4}[/tex]

It may help to recognize this as a Bernoulli equation. Multiply both sides by [tex]y^{\frac34}[/tex] :

[tex]y^{3/4}y' + \dfrac{y^{7/4}}x = \dfrac1{x^4}[/tex]

Substitute [tex]z(x)=y(x)^{\frac74}[/tex], so that [tex]z' = \frac74 y^{3/4}y'[/tex]. Then you get a linear equation in z, which I write here in standard form:

[tex]\dfrac47 z' + \dfrac zx = \dfrac1{x^4} \implies z' + \dfrac7{4x}z=\dfrac7{4x^4}[/tex]

Multiply both sides by an integrating factor, [tex]x^{\frac74}[/tex], which gives

[tex]x^{7/4}z'+\dfrac74 x^{3/4}z = \dfrac74 x^{-9/4}[/tex]

and lets us condense the left side into the derivative of a product,

[tex]\left(x^{7/4}z\right)' = \dfrac74 x^{-9/4}[/tex]

Integrate both sides:

[tex]x^{7/4}z=\dfrac74\left(-\dfrac45\right) x^{-5/4}+C[/tex]

[tex]z=-\dfrac75 x^{-3} + Cx^{-7/4}[/tex]

Solve in terms of y :

[tex]y^{4/7}=-\dfrac7{5x^3} + \dfrac C{x^{7/4}}[/tex]

[tex]\boxed{y=\left(\dfrac C{x^{7/4}} - \dfrac7{5x^3}\right)^{7/4}}[/tex]

(3.3) … … …

[tex](\cos(x) - 2xy)\,\mathrm dx + \left(e^y-x^2\right)\,\mathrm dy = 0[/tex]

This DE is exact, since

[tex]\dfrac{\partial(-2xy)}{\partial y} = -2x[/tex]

[tex]\dfrac{\partial\left(e^y-x^2\right)}{\partial x} = -2x[/tex]

are the same. Then the general solution is a function f(x, y) = C, such that

[tex]\dfrac{\partial f}{\partial x}=\cos(x)-2xy[/tex]

[tex]\dfrac{\partial f}{\partial y} = e^y-x^2[/tex]

Integrating both sides of the first equation with respect to x gives

[tex]f(x,y) = \sin(x) - x^2y + g(y)[/tex]

Differentiating this result with respect to y then gives

[tex]-x^2 + \dfrac{\mathrm dg}{\mathrm dy} = e^y - x^2[/tex]

[tex]\implies\dfrac{\mathrm dg}{\mathrm dy} = e^y \implies g(y) = e^y + C[/tex]

Then the general solution is

[tex]\sin(x) - x^2y + e^y = C[/tex]

Given that y (1) = 4, we find

[tex]C = \sin(1) - 4 + e^4[/tex]

so that the particular solution is

[tex]\boxed{\sin(x) - x^2y + e^y = \sin(1) - 4 + e^4}[/tex]

Answer:

C

Step-by-step explanation:

In ∆DEG, we are given that all the three angles are congruent.

This means that all the three angles have equal measure. Thus,

<D = <E = <F

An equilateral triangle has equal angle measure. ∆DEF is an equilateral triangle.

Since the sum of a triangle is 180°, therefore, each angle in ∆DEF = 60°

m<D = 60°

Answer:

7.07 (3 significant figures)

Step-by-step explanation:

the distance between the two points on the x axis is 5 and the distance between the two point son the y axis is 5. thus by using pythagerous theorem you are able to get the hypotenuse which is the distance between the two points which in this case is 7.07 when rounded to 3 significant figures. not sure if im correct but i hope it helps

Answer:

Step-by-step explanation:

circumference = πd ≅ 250 ft

d ≅ 250/π ≅80 ft

Answer:

[tex]\mu = 5.2[/tex]

[tex]\sigma = 2.257[/tex]

Step-by-step explanation:

Given

[tex]n = 260[/tex] -- samples

[tex]p = \frac{1}{50}[/tex] --- one in 50

Solving (a): The mean

This is calculated as:

[tex]\mu = np[/tex]

[tex]\mu = 260 * \frac{1}{50}[/tex]

[tex]\mu = 5.2[/tex]

Solving (b): The standard deviation

This is calculated as:

[tex]\sigma = \sqrt{\mu * (1-p)}[/tex]

[tex]\sigma = \sqrt{5.2 * (1-1/50)}[/tex]

[tex]\sigma = \sqrt{5.2 * 0.98}[/tex]

[tex]\sigma = \sqrt{5.096}[/tex]

[tex]\sigma = 2.257[/tex]