Consider the given function. Which statement about the functions is true?

Answer:

x = 8/9

Step-by-step explanation:

5x + 2(x - 3) = -2(x - 1)

Distribute on both sides.

5x + 2x - 6 = -2x + 2

Combine like terms on the left side.

7x - 6 = -2x + 2

Add 2x to both sides.

9x - 6 = 2

Add 6 to both sides.

9x = 8

Divide both sides by 9.

x = 8/9

Dotted linear inequality shaded below passes through (0, 4) & (4,3). Dotted parabolic inequality shaded above passes through points (negative 6,4), (negative 4, 0) & (negative 2, 4).

Hello! Let me help you to find the correct option to this problem. First of all, we have the following system of inequalities:

[tex]\left\{ \begin{array}{c}y< -\frac{1}{4}x+4\\y>(x+4)^{2}\end{array}\right.[/tex]

To solve this, let's write the following equations:

[tex]y=-\frac{1}{4}x+4[/tex]

This is a linear function written in slope-intercept form as [tex]y=mx+b[/tex]. So, the slope [tex]m=-\frac{1}{4}[/tex] and the y-intercept is [tex]b=4[/tex]. Since in the inequality we have the symbol < then the graph of the line must be dotted. To get the shaded region, let's take a point, say, [tex](0, 0)[/tex] and let's test whether the region is above or below the graph. So:

[tex]y< -\frac{1}{4}x+4 \\ \\ Let \ x=y=0 \\ \\ 0<-\frac{1}{4}(0)+4 \\ \\ 0<4 \ True![/tex]

Since the expression is true, then the region is the one including point [tex](0, 0)[/tex], that is, it's shaded below.

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

This is a parabola that opens upward and whose vertex is [tex](-4,0)[/tex]. Since in the inequality we have the symbol > then the graph of the parabola must be dotted. Let's take the same point [tex](0, 0)[/tex] to test whether the region is above or below the graph. So:

[tex]y>(x+4)^{2} \\ \\ Let \ x=y=0 \\ \\ 0>(0+4)^2\\ \\ 0>16 \ False![/tex]

Since the expression is false, then the region is the one that doesn't include point [tex](0, 0)[/tex], that is, it's shaded above

____________________

[tex]y=-\frac{1}{4}x+4 \\ \\ \\ \bullet \ (0,4): \\ \\ y=-\frac{1}{4}(0)+4 \therefore y=4 \\ \\ \\ \bullet \ (4,3): \\ \\ y=-\frac{1}{4}(4)+4 \therefore y=3[/tex]

So the line passes through these two points.

[tex]y=(x+4)^2 \\ \\ \\ \bullet \ (-6,4): \\ \\ y=(-6+4)^2 \therefore y=(-2)^2 \therefore y=4 \\ \\ \\ \bullet \ (-4,0): \\ \\ y=(-4+4)^2 \therefore y=0 \\ \\ \\ \bullet \ (-2,4): \\ \\ y=(-2+4)^2 \therefore y=(2)^2 \therefore y=4[/tex]

So the line passes through these three points.

Finally, the shaded region is shown below.

Answer:

-55/4

Step-by-step explanation:

-4 1/4 - (9 1/2)

Both the terms are given in whole fraction:

Change the terms into improper fraction

4*-4+1 = -17/4

2*9 + 1=19/2

Now,

-17/4 - 19/2

Now take the L.C.M of the denominator.

L.C.M of 4 and 2 is 4

Solve for numerator:

L.C.M (4) divided by denominator of first term will give quotient 1. Then 1 multiply by the numerator -17 will give us 1* -17 = -17

Then 4 divided by denominator of 2nd term will give us 2 as a quotient. Then quotient multiplied by numerator of 2nd term will give us 19*2 = 38

Therefore,

-17 - 38/4

= -55/4

The answer is -55/4....

The expression -4 1/4 - (9 1/2), is simplified to be expressed as -53/4

To simplify the expression -4 1/4 - (9 1/2), we need to convert the mixed numbers to improper fractions and perform the subtraction.

First, let's convert the mixed numbers to improper fractions:

-4 1/4 = -4 + 1/4 = -4 * 4/4 + 1/4 = -16/4 + 1/4 = -15/4

9 1/2 = 9 + 1/2 = 9 * 2/2 + 1/2 = 18/2 + 1/2 = 19/2

Now we can substitute these values back into the original expression:

-15/4 - 19/2

To subtract fractions, we need a common denominator. The least common multiple (LCM) of 4 and 2 is 4, so we can rewrite the fractions with a common denominator of 4:

-15/4 - 19/2 = -15/4 - 38/4

Now we can subtract the fractions:

-15/4 - 38/4 = (-15 - 38)/4 = -53/4

Therefore, the expression -4 1/4 - (9 1/2) simplifies to -53/4.

Read more about how to simplify here: https://brainly.com/question/6979644

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Answer:

12

Step-by-step explanation:

Given expression is:

[tex](x^16)^\frac{3}{4}[/tex]

By the rues of exponents, when there is exponent on exponent then the exponents are multiplied.

So,

[tex]= x^{16*\frac{3}{4}}\\ = x^{4*3}\\=x^{12}[/tex]

The exponent of x will be 12 after the simplification ..

Answer: Second Option

[tex]P (-1.17 <z <1.17) = 0.7580[/tex]

Step-by-step explanation:

The shaded area corresponds to the interval

[tex]-1.17 <z <1.17.[/tex]

By definition, for a standard normal distribution the area under the curve in the interval (b <z <h) is equal to:

[tex]P (b <z <h)[/tex]

So in this case we look for:

[tex]P (-1.17 <z <1.17)[/tex]

This is:

[tex]P (-1.17 <z <1.17) = P (z <1.17) - P (z <-1.17)[/tex]

Looking at the standard normal table we have to:

[tex]P (z <1.17) = 0.8790\\P (z <-1.17) = 0.1210[/tex]

So:

[tex]P (-1.17 <z <1.17) = 0.8790- 0.1210\\\\P (-1.17 <z <1.17) = 0.7580[/tex]

Answer:

B

Step-by-step explanation:

Using the Sine Rule in ΔABC

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]

∠C = 180° - (82 + 58)° = 180° - 140° = 40°

Completing values in the above formula gives

[tex]\frac{a}{sin58}[/tex] = [tex]\frac{b}{sin82}[/tex] = [tex]\frac{8.4}{sin40}[/tex]

We require a pair of ratios which contain b and 3 known quantities, that is

[tex]\frac{b}{sin82}[/tex] = [tex]\frac{8.4}{sin40}[/tex]

OR

[tex]\frac{sin40}{8.4}[/tex] = [tex]\frac{sin82}{b}[/tex] → B

Answer:

B

Step-by-step explanation:

Check the picture below.

notice, on the first 2 lines, we used the quadrilateral conjecture.

on the lines 3 and 4 we used the inscribed angle theorem.

line 5, if we add those 3 arcs, we end up with 427°, mind you that the surplus is arcYW or "b", since it's added twice by XW and YZ.

line 6, if we subtract a full circle from it, we have the surplus.

line 7, we simply subtract YW from XW, leaving the leftover of arc "a".

Answer:

The correct answer would be option A, Don't you agree that the financial crisis is essentially over.

Step-by-step explanation:

A survey questionnaire is a series of question which is set formally to be asked from a specific sample of a population to gather, analyze and interpret the data obtained from the sample population. So the questions in the survey must be structured, to the point, clear, short and straight. Survey questions are desirably closed ones and the ones which do not need much explanation by the person who is doing the survey. So the first question in this question require an explanation, and also the question is not structured, clear and to the point and thus is not a good survey question. Comparatively, the second question is more structured, clear and to the point and such questions are normally desirable in the surveys.  

Answer:

See image

Step-by-step explanation:

Plato

Answer:

x= 3

y= 2

Step-by-step explanation:

The given equations are :

2x-5y = -4    equation 1

x +6y = 15    equation 2

We will multiply the equation:2 by 2

2(x+6y=15)

2x+12y=30   equation 3

Lets call this equation:3

Now we will use the elimination method:

Subtract equation 3 from equation 1:

2x-5y = -4

2x+12y=30

_________

   -17y = -34

y= -34/-17

y = 2

Now put the value of y in any equation:

We will use equation 1

2x-5y = -4

2x-5(2)= -4

2x-10= -4

Move the constant to the R.H.S

2x= -4+10

2x=6

Divide both the terms by 2

x= 3

Therefore the solution set is (x,y){(3,2)}....

Answer:

Step-by-step explanation:

[tex]\text{The distributive property:}\ a(b+c)=ab+ac\\\\15=3\cdot5\\21=3\cdot7\\\\15+17=3\cdot5+3\cdot7=3\cdot(5+7)[/tex]

Answer:

The basic answer to your question is that we have to start somewhere.

The essence of mathematics (in the sense the Greeks introduced to the  

world) is to take a small set of fundamental "facts," called  

postulates or axioms, and build up from them a full understanding of  

the objects you are dealing with (whether numbers, shapes, or  

something else entirely) using only logical reasoning such that if  

anyone accepts the postulates, then they must agree with you on the  

rest.

It can sometimes be proven.

Answer:

No

Step-by-step explanation:

Given a function f(x)

For the function to be odd then f(- x) = - f(x)

f(- x) = 3(- x)² + (- x) = 3x² - x

- f(x) = - (3x² + x) = - 3x² - x

Since f(- x) ≠ - f(x) then f(x) is not an odd function

Answer: Third Option

[tex]Q_1=3[/tex]

[tex]Q_3=6[/tex]

Step-by-step explanation:

Notice that we already have the data sorted from least to greatest.

Now to find Q1 and Q3 we can use the following formulas

For a set of data ordered from least to greatest of the form [tex]X_1, X_2, ..., X_n[/tex]

Where n is the total number of data

[tex]Q_1=X_{\frac{1}{4}(n+1)}[/tex]

In this case [tex]n=10[/tex]

So:

[tex]Q_1=X_{\frac{1}{4}(10+1)}[/tex]

[tex]Q_1=X_{2.75}[/tex]

Round the nearest whole and get:

[tex]Q_1=X_{3}[/tex]

[tex]Q_1=3[/tex]

For [tex]Q_3[/tex] we have:

[tex]Q_3=X_{\frac{3}{4}(n+1)}[/tex]

[tex]Q_3=X_{\frac{3}{4}(10+1)}[/tex]

[tex]Q_3=X_{8.25}[/tex]

Round the nearest whole and get:

[tex]Q_3=X_{8}[/tex]

[tex]Q_3=6[/tex]

For this case we have a function of the form[tex]y = g (x)[/tex]

Where:

[tex]g (x) = 2 (x-4)[/tex]

We must find the value of "x" when the function has a value of 20, that is, [tex]g (x) = 20[/tex]:

[tex]2 (x-4) = 20[/tex]

We apply distributive property:

[tex]2x-8 = 20[/tex]

We add 8 to both sides of the equation:

[tex]2x = 20 + 8\\2x = 28[/tex]

We divide between 2 on both sides of the equation:

[tex]x = \frac {28} {2}\\x = 14[/tex]

Answer:

Option C

Answer:

option c 14

Step-by-step explanation:

did the test

Answer:

So 67 degrees is one value that we can take the sine of such that is equal to cos(23 degrees).

(There are more values since we can go around the circle from 67 degrees numerous times.)

Step-by-step explanation:

You can use a co-function identity.

The co-function of sine is cosine just like the co-function of cosine is sine.

Notice that cosine is co-(sine).

Anyways co-functions have this identity:

[tex]\cos(90^\circ-x)=\sin(x)[/tex]

or

[tex]\sin(90^\circ-x)=\cos(x)[/tex]

You can prove those drawing a right triangle.

I drew a triangle in my picture just so I can have something to reference proving both of the identities I just wrote:

The sum of the angles is 180.

So 90+x+(missing angle)=180.

Let's solve for the missing angle.

Subtract 90 on both sides:

x+(missing angle)=90

Subtract x on both sides:

(missing angle)=90-x.

So the missing angle has measurement (90-x).

So cos(90-x)=a/c

and sin(x)=a/c.

Since cos(90-x) and sin(x) have the same value of a/c, then one can conclude that cos(90-x)=sin(x).

We can do this also for cos(x) and sin(90-x).

cos(x)=b/c

sin(90-x)=b/c

This means sin(90-x)=cos(x).

So back to the problem:

cos(23)=sin(90-23)

cos(23)=sin(67)

So 67 degrees is one value that we can take the sine of such that is equal to cos(23 degrees).

Answer:

7 friends multiply $2

Its product is: $14

Step-by-step explanation:

[tex]\huge{\boxed{c+148}}[/tex]

We need to find the number of pies baked in years 1 and 2.

There were 148 pies baked in year 1. [tex]148[/tex]

There were [tex]c[/tex] pies baked in year 2. [tex]148+c[/tex]

Rearrange the terms so the variable is first. [tex]c+148[/tex]

Answer:

since we know that there were 148 pies sold the first year, and c number of pies sold this year. You would add these two to find the total amount of both years.

148+c

Answer:

The officer saves $91.45 per month

~Step-by-step explanation~

Ok this is how I do fractions and its not very good, but it works.

First I divided 6400 by 5, 6, and 7, (I didn't do 3 because you can just multiply the answer to 6 by 2.) the reason I divided these is to see how much 1 part of their fraction is worth. So in total I got  1066.66 (irrational number) for insurance which means I got 2133.32 for his monthly living ( had to multiply by 2). For his car payment I got 1828.57 (I divided and then multiplied by 2) and for his rent I got 1280. I added these all together to get the total he spends each month which was 6308.55, and I subtracted that from 6400 to figure out that he puts $91.45 in his savings account

Answer:

The answer is R91.43.

Step-by-step explanation:

Monthly salary of the worker = R6400

The monthly expenses are 1/5 for rent that is [tex]\frac{1}{5}\times6400= 1280[/tex]

The car payment is 2/7 that is [tex]\frac{2}{7}\times6400= 1828.57[/tex]

The insurance is 1/6 that is [tex]\frac{1}{6}\times6400= 1066.67[/tex]

Few other monthly living expenses are 1/3 that is [tex]\frac{1}{3}\times6400= 2133.33[/tex]

We will total these values:

[tex]1280+1828.57+1066.67+2133.33=6308.57[/tex]

So, the amount that is saved per month = [tex]6400-6308.57=91.43[/tex]

The answer is R91.43.

Answer:

19/24

Step-by-step explanation:

Since you are looking for the fraction he spend, you have to add 3/8 and 5/12 with one another. To do this you have to change those fractions to have the same denominators. so you multiply 3/8 by 3/3 to get 9/24 and you multiply 5/12 by 2/2 to get 10/24. You then add 9/24 with 10/24 to get 19/24. Since you cannot simplify this further, 19/24 is your answer.

Bob spent [tex]\frac{19}{24}[/tex] of his birthday money

For given question,

Bob spent 3/8 of his birthday money at a baseball game and 5/12 on a new bat and glove.

We need to find the fraction of his birthday money he spent.

so we add given two fractions.

[tex]\frac{3}{8}+ \frac{5}{12}\\\\ =\frac{3\times 3}{8\times 3}+ \frac{5\times 2}{12\times 2}\\\\=\frac{9}{24}+ \frac{10}{24}\\\\=\frac{9+10}{24}\\\\ =\frac{19}{24}[/tex]

Therefore, Bob spent [tex]\frac{19}{24}[/tex] of his birthday money.

Learn more about the fraction here:

https://brainly.com/question/12151403

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Answer:

y = - 2

Step-by-step explanation:

The equation of a horizontal line parallel to the x- axis is

y = c

where c is the value of the y- coordinates the line passes through.

The points (2, - 2) and (0, - 2) have the same y- coordinate and therefore lie on a horizontal line with equation

y = - 2

Answer:

[tex]\large\boxed{V=\pi r^3}[/tex]

Step-by-step explanation:

The formula of a volume of a pyramid:

[tex]V=\dfrac{1}{3}BH[/tex]

B - base area

H - height

Let r - radius of the cone.

We have H = 3r.

The base of the cone: [tex]B=\pi r^2[/tex].

Substitute:

[tex]V=\dfrac{1}{3}\pi(r^2)(3r)[/tex]           cancel 3

[tex]V=\pi r^3[/tex]

Answer:

For plato users is option A

Step-by-step explanation:

A. V =[tex]\pi[/tex]r3

Answer:
it’s a circle graph

Answer:

=60 the second option.

Step-by-step explanation:

Given the trigonometric ratio, we can find the value of the angle by simply finding the inverse of the given ratio.

If for example Cos ∅= a, then ∅=Cos⁻¹a

If Cos (x)= 0.5, then x= Cos⁻¹ 0.5

Cos⁻1 0.5=60°

The angle whose sine is 0.5 is ∅=60°

Answer: second option.

Step-by-step explanation:

You have that:

[tex]cos(x)=0.5[/tex]

Then, to find the value of "x", you need to apply Arccosine ( This is the inverse function of the cosine).

Therefore, applying this in the procedure, you get that the value of "x" is the following:

[tex]cos(x)=0.5\\\\x=Arccos(0.5)\\\\x=60\°[/tex]

You can observe that this matches with the second option.

Answer: The outlier in this scatter plot is Point D.

Step-by-step explanation:

The reason its Point D because its the only one that is the farest away from the rest of the points on the plot.

The reason why "Point D" would be the correct answer because the point is no where near the "trend" of the scatter plot.

When you look at the scatter plot, you would notice that there following a "trend" when the graph increases.

However, you would notice that point D is not really near there, therefore making it an outlier.

An outlier is pretty much something that is left out, and in this case, point D would be the outlier since it's left out of the typical growth of the scatter plot.

Answer:

The answer is def. A.

Answer: OPTION A.

Step-by-step explanation:

By definition:

A number is Rational when it can be written as a simple fraction.

A number is Irrational when it cannot be written as a simple fraction.

Notice that:

[tex]\frac{2}{5}[/tex] is a Rational number.

[tex]\sqrt{88}=2\sqrt{2}[/tex] It is an irrational number.

Therefore, the sum of these numbers is an Irrational number:

[tex]\frac{2}{5} + \sqrt{88}=\frac{2}{5} + 2\sqrt{22}=9.78083151...[/tex]

Answer:

Step-by-step explanation:

[tex]B=(\frac{-9-1}{2},\frac{-4+6}{2} ) (midpoint formula)\\B=(-5,1)\\\\Then using midpoint formula again,\\E=(-4,3)=(\frac{-5+x}{2} =-4,\frac{1+y}{2} =3)\\so \\x=-3\\y=5\\\\D=(-3,5)[/tex]:

Answer:

Please read explanation below.

Step-by-step explanation:

Let's go over what some of the symbols of inequalities represent:

[tex]>[/tex]: greater than

[tex]<[/tex]: less than

[tex]\ge[/tex]: greater than or equal to

[tex]\le[/tex]: less than or equal to

The symbol in the equation that is given to you is [tex]\ge[/tex]. It seems as though each of the answer choices have everything written as the same thing except for the description of the inequalities. Check the one that applies.

Answer:

The equation of the line is y = -x + 1

Step-by-step explanation:

* Lets explain how to solve the problem

- The slope-intercept form of the equation is y = mx + c, where m is

 the slope of the line and c is the y-intercept

- To make this equation you need slope (m) and a point on the line to

 find the value of c

- The parallel lines have same slopes

* Lets solve the problem

- The line is parallel to the line y = -x - 5

∵ y = mx + c

∵ The slope of the line y = -x - 5 is the coefficient of x

∴ m = -1

∵ Parallel lines have same slopes

∴ The slope of the line is -1

∴ the equation of the line is y = -x + c

- To find c substitute x and y in the equation by the coordinates of

  any point lies on the line

∵ The line passes through point (3 , -2)

∵ y = -x + c

∴ -2 = -(3) + c

∴ -2 = -3 + c ⇒ add 3 for both sides

∴ c = 1

∴ The equation of the line is y = -x + 1

Answer:

A

Step-by-step explanation:

Given

5(x - 7) = 55, then using the distributive property, that is

a(b - c) = ab - ac, then

5x - 35 = 55

The property that was used to write the equation in step 2 is option A) distributive property

Given that,

So here we have to use the distributive property i.e.

So,  

5x - 35 = 55

Therefore we can conclude that The property that was used to write the equation in step 2 is option A) distributive property

Learn more: brainly.com/question/6201432

Answer:

B.

Step-by-step explanation:

So [tex]2x^2+5x+3[/tex] will have two factors if one factor in the form [tex](ax+b)[/tex] is given.

The other factor will also be in the form of [tex](cx+d)[/tex].

So we have

[tex](x+1)(cx+d)[/tex]:

Let's use foil.

First:  x(cx)=cx^2

Outer: x(d)=dx

Inner: 1(cx)=cx

Last: 1(d)=d

---------------------Adding like terms:

cx^2+(d+c)x+d

We are comparing this to:

2x^2+     5x+3

So we see that c=2 and d=3 where the other factor is cx+d=2x+3.

Also this works since c+d=5 (we know this because 2+3=5).

Answer:

B

Step-by-step explanation: