Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Consider the equation below.

ANSWER

C. [tex]g(x) = {(x + 3)}^{2} - 2[/tex]

EXPLANATION

The blue graph is obtained by shifting the red to the left by 3 units and down 2 units.

The vertex is now at (-3,-2).

The base function has equation:

[tex]f(x) = {x}^{2} [/tex]

This implies that,

[tex]g(x) = f(x + 3) - 2[/tex]

[tex]g(x) = {(x + 3)}^{2} - 2[/tex]

The correct answer is C

Answer:

The prime factors of 60 are 2, 3, and 5.

Answer:

36 minutes

Step-by-step explanation:

In order to find how many minutes it takes to fill 675 bottles, we need to find how many bottles the machine produces in one minute.

To do so, we can divide 150 by 8, which would give us the total amount of bottles produced in one minute.

150/8 = 18.75

So, 18.75 bottles are produced in one minute

To find the total number of minutes it takes to fill 675 bottles, we can divide 675 by the number of bottles produced in one minute, which is 18.75

675/18.75 = 36

Therefore, it takes the machine 36 minutes to fill 675 bottles.

Given : Machine fills 150 bottles of water every 8 minutes

[tex]\mathsf{\implies Machine\;fills\;1\;bottle\;of\;water\;in\;\left(\dfrac{8}{150}\right)\;minutes}[/tex]

[tex]\mathsf{\implies Machine\;fills\;(675 \times 1)\;bottles\;of\;water\;in\;\left(675 \times \dfrac{8}{150}\right)\;minutes}[/tex]

[tex]\mathsf{\implies Machine\;fills\;675\;bottles\;of\;water\;in\;\left(675 \times \dfrac{4}{75}\right)\;minutes}[/tex]

[tex]\mathsf{\implies Machine\;fills\;675\;bottles\;of\;water\;in\;\left(135 \times \dfrac{4}{15}\right)\;minutes}[/tex]

[tex]\mathsf{\implies Machine\;fills\;675\;bottles\;of\;water\;in\;\left(9 \times 4}\right)\;minutes}[/tex]

[tex]\mathsf{\implies Machine\;fills\;675\;bottles\;of\;water\;in\;\boxed{\mathsf{36}}\;minutes}[/tex]

Answer:

(x-3)(4x+5)

Step-by-step explanation:

4x2−12x+5x−15

=4x(x−3)+5(x−3)

=(x−3)(4x+5)

Answer:

B

Step-by-step explanation:

Given

4x² - 7x - 15

To factorise the quadratic

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 4 × - 15 = - 60 and sum = - 7

The factors are - 12 and + 5

Use these factors to split the x- term

4x² - 12x + 5x - 15 ( factor the first/second and third/fourth terms )

= 4x(x - 3) + 5(x - 3) ← factor out (x - 3) from each term

= (x - 3)(4x + 5) ← in factored form

Hence 4x + 5 is a factor of the trinomial → B

Hi!

Let's take a look at the equation:

F = C + 32

What do we notice?

C and F are both variables.

Variables are unknown numbers represented by a letter.

In this case, C and F are the variables.

Hope this helps!

- Melanie

slope is [tex]\frac{rise}{run}[/tex] or [tex]\frac{vertical}{horizontal}[/tex]

Look at the image below:

The red (4) is the rise and the blue (1) is the run

this means the slope is...

[tex]\frac{4}{1}[/tex]

4

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

D. x = 8

Step-by-step explanation:

MNOP is a trapezoid with a meadian QR

So

QR = 1/2(NO + MP)

2(QR) = NO + MP

2(16) = 8 + 2x + 8

32 = 2x + 16

2x = 16

 x = 8

Answer:

The correct answer option is D. x = 8.

Step-by-step explanation:

We are given a trapezoid MNOP with the median QR and we are to find the value of x.

If we observe the figure, we can see that the length QR is the double of NO which means 8 units are added to NO. So the ratio for NO and MP would be 1:3.

NO = 8

QR = 8 + 8 = 16

MP = 8 + 8 + 8 = 24

Finding x:

2x + 8 = 24

2x = 24 - 8

2x = 16

x = 8

Answer:

B

Step-by-step explanation:

You are given that a valid point on g(x) is (4,1) or y=1 when x=4

Substitute this point into each of the choices and see which one is valid.

A : g(x) = [tex]\frac{1}{4}[/tex]x² = (1/4) (4²) = 4 ≠ 1 (not valid)

B: g(x) = [(1/4) x]² = [(1/4) 4]² = 1² = 1 (valid)

C: g(x) = 4x² = 4 (4²) = 64 ≠ 1 (not valid)

D: if you expand it out, you'll find that this is identical to option A which we determined earlier to be not valid.

Hence the only valid choice is B

Answer:

The other 2 sides have lengths 24 and 25.

Step-by-step explanation:

h^2 = x^2 + 7^2 where x is the other leg and h is the hypotenuse.

h^2 - x^2 = 49

(h + x) (h - x) = 49

The factors of 49 are 1 , 7 , and 49.

h + x could be 49 and h - x could be 1:

(25 + 24)(25 - 24) = 49.

So h = 25 and x = 24.

recall your d = rt, distance = rate * time.

j = jet's rate

w = wind's rate

so with the wind the actual speed of the Jet is really j + w, because the wind is adding speed to it, and against it is j - w, since the wind is eroding speed from it.

[tex]\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{against the wind}&8730&j-w&9\\ \textit{with the wind}&7260&j+w&6 \end{array}~\hfill \begin{cases} 8730=(j-w)(9)\\ 7260=(j+w)(6) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{\cfrac{8730}{9}=j-w\implies }970=j-w\implies 970+w=j \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{using the 2nd equation}}{\cfrac{7260}{6}=j+w}\implies 1210=j+w\implies \stackrel{\textit{doing some substitution on \underline{j}}}{1210=(970+w)+w} \\\\\\ 1210=970+2w\implies 240=2w\implies \cfrac{240}{2}=w\implies \boxed{120=w} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{we know that}}{970+w=j}\implies 970+120=j\implies \boxed{1090=j}[/tex]

Check the picture below.

let's recall that a circle has a total of 360°, so the arcDCF is 360 - 266 = 94, and is the intercepted arc by the inscribed ∡DEF.

Hola! My name is Zalgo and I am here to help you out today. So, let's observer everyone's ratio and if it can be simplified, we can simplify ti to make it easier. Jasmine has 12:10, Aaron has 3:2, Lucian has 10:10 and Gretchen has 14:2. If we simplify Jasmines, for every 6 blue, she has 5 red (6:5). Lucian has an equal ration if we simplify it (1:1) and Gretchen would have 7 blue for every 1 red (7:1). So, the person with the lowest ration would be Lucian.

I hope that this helps! :3

"Stay Brainly and stay proud!" - Zalgo

(By the way, can you mark me as Brainliest? I'd greatly appreciate it! Gracias! XT)

Lucian has the lowest ratio of blue to red marbles which is 1:1 option third "Lucian" is the correct choice.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We have data shown in the table:

For Jasmine, the ratio of blue to red marbles:

12:10

6:5

For Aaron, the ratio of blue to red marbles:

3:2

For Lucian, the ratio of blue to red marbles:

10:10

1:1

For Gretchen, the ratio of blue to red marbles:

14:2

7:1

Thus, Lucian has the lowest ratio of blue to red marbles which is 1:1 option third "Lucian" is the correct choice.

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Answer:

A   12+6i

    ----------

     5

Step-by-step explanation:

6

-----------

2-i

Multiply by the complex conjugate

6               2+i

----------- *------------

2-i               2+i

12 +6i

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

4 -2i +2i -i^2

12+6i

----------

4 - (-1)

12+6i

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

5

Answer:

Step-by-step explanation:

[tex]\text{The equation of a horizontal line:}\ y=a.\\\\\text{The equation of a vertical  line:}\ x=a\\\\a-any\ real\ number\\\\\text{We have}\ x=-5.\ \text{It's a vertical line.}\ \text{The line that is perpendicular}\\\text{to the vertical line is a horizontal line.}\\\\\text{The line passes through the point}\ (1,\ \pi)\to x=1,\ y=\pi.\\\\\text{Therefore the equation is}\ y=\pi[/tex]

Answer:

8/9

Step-by-step explanation:

This is already in slope-intercept form.

Compare to y=mx+b where m is slope and b is y-intercept and you should see that 8/9 is in place of m and is therefore your slope

The figures that are reflections of ABCD are KLMN, PQRS and WXYZ

The given parameters are

ABCD ≅ KLMN ≅ PQRS ≅ WXYZ

The above parameter can be rewritten as

ABCD ≅ KLMN

ABCD ≅ PQRS

ABCD  ≅ WXYZ

The above parameters mean that:

Using that as a guide, we understand that:

Congruent shapes can be reflections of one another

This means that the figures that are reflections of ABCD are the figures that are congruent to ABCD

Hence, the figures that are reflections of ABCD are KLMN, PQRS and WXYZ

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Answer: b,d

Step-by-step explanation: im smart

The ratio of the number of mops to the number of brooms is,

⇒ Ratio = 3 : 4

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

There are 8 brooms and 6 mops in a janitor's closet.

Hence, The ratio of the number of mops to the number of brooms is,

⇒ Ratio = number of mops / number of brooms

⇒ Ratio = 6 / 8

⇒ Ratio = 3 / 4

⇒ Ratio = 3 : 4

Thus, The ratio of the number of mops to the number of brooms is,

⇒ Ratio = 3 : 4

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C

It's a reflection over the y-axis.

The trigonometric expressions sin(π/6) is equivalent to the y coordinate of the terminal point (√3/2, 1/2) option (B) is correct.

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

We have:

y coordinate of the terminal point (√3/2, 1/2)

Terminal point = (√3/2, 1/2)

sin(a) = 1/2

a = sin⁻¹(1/2)

a = π/6

a is the angle.

y coordinate is sin(π/6)

Thus, the trigonometric expressions sin(π/6) is equivalent to the y coordinate of the terminal point (√3/2, 1/2) option (B) is correct.

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Final answer:

The trigonometric expression equivalent to the y-coordinate (1/2) of the given terminal point (√3/2, 1/2) is sin(30°) or sin(π/6).

Explanation:

The student is asking for the trigonometric expression equivalent to the y-coordinate of the terminal point (√3/2, 1/2). In trigonometry, the y-coordinate of a point on the unit circle corresponds to the sin of the angle from the positive x-axis to the radius that ends at the point. Since the terminal point given is in the first quadrant and matches the coordinates for a 30° (or π/6 radians) angle in standard position on the unit circle, the y-coordinate is equal to sin(30°) which is 1/2. Therefore, the trigonometric expression equivalent to the y-coordinate 1/2 is sin(30°) or sin(π/6).

Answer:

y=mx+b

(6,6)    (3,8)

6m+b=6

3m+b=8

6m+b-3m-b=-2

3m=-2

m = -2/3

-2+b=8

b=10

y = -2/3x+10

I choose 12.

-2/3(12)+10

=2

so put x as 12; y as 2.

Answer:

We want to add an x value we have not used before. A function has EVERY X IN A DOMAIN going to ONLY ONE Y value.

6,3,9,7 are already used for x.

so you can put in x = 8 and y = 12 as an answer. That will work and show a function. There are also other answers.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

We are given that there are two line segments, red and blue, that stretch from the center of the circle to a point on the circle.

Given that the length of the blue segment is 5, we are to determine the length of the red segment.

Since both the line segments stretch from the center of the circle to its circumference so they must be equal.

Therefore, length of the red line segment is 5.

Answer:

the answer is 5

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

First add 3 to both sides (what you do on one side you must do to the other). Since 3 is being subtracted, addition (the opposite of subtraction) will cancel it out (make it zero) from the right side and bring it over to the left side.

2 < u - 3

2 + 3 < u - 3 + 3

5 < u - 0

5 < u

For the graph will you have a empty or colored in circle?

If the symbol is ≥ or ≤ then the circle will be colored in. This represents that the number the circle is on is included.

If the symbol is > or < then the circle will be empty. This represents that the number the circle is on is NOT included.

Which direction will the ray go?

If the variable is LESS then the number then the arrow will go to the left of the circle.

If the variable is MORE then the number then the arrow will go to the right of the circle.

In this case your inequality is:

5 < u OR u > 5

aka 5 is less then u OR u is greater then 5

This means that the graph will have an empty circle and the arrow will go to the right of 5. Look at image below.

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Part 1) The measure of x is 23°

Part 2) The value of y is [tex]y=5\ units[/tex]

Part 3) The value of z is [tex]z=12\ units[/tex]

Step-by-step explanation:

step 1

Find the value of x

we know that

[tex]x+67\°=90\°[/tex] ------> by complementary angles

[tex]x=90\°-67\°=23\°[/tex]

step 2

Find the value of y

In the right triangle of the figure

[tex]cos(67\°)=\frac{y}{13}[/tex] -----> adjacent side angle of 67 degrees divided by the hypotenuse

[tex]y=(13)cos(67\°)=5\ units[/tex]

step 3

Find the value of z

In the right triangle of the figure

[tex]sin(67\°)=\frac{z}{13}[/tex] -----> opposite side angle of 67 degrees divided by the hypotenuse

[tex]z=(13)sin(67\°)=12\ units[/tex]

Answer:

Step-by-step explanation:

Here you estimate the proportion of people in the population that said did not have children under 18 living at home.It can also be given as a percentage.

The general expression to apply here is;

[tex]C.I=p+-z*\sqrt{\frac{p(1-p)}{n} }[/tex]

where ;

p=sample proportion

n=sample size

z*=value of z* from the standard normal distribution for 95% confidence level

Given;

n=5000

Find p

From the question 54% of people chosen said they did not have children under 18 living at home

[tex]\frac{54}{100} *5000 = 2700\\\\p=\frac{2700}{5000} =0.54[/tex]

To calculate the 95% confidence interval, follow the steps below;

The value of z* from the table is 1.96

The value of p=0.54 as calculated above

[tex]0.54(1-0.54)=0.2484[/tex]

Divide the value of p(1-p) with the sample size, n

[tex]\frac{0.2448}{5000} =0.00004968[/tex]

[tex]=\sqrt{0.00004968} =0.007048[/tex]

Here multiply the square-root of p(1-p)/n by the z*

[tex]=0.007048*1.96=0.0138[/tex]

The 95% confidence interval for the lower end value is p-margin of error

[tex]=0.54-0.0138=0.5262[/tex]

The 95% confidence interval for the upper end value is p+margin of error

[tex]0.54+0.0138=0.5538[/tex]

Answer: 0.5262 - 0.5538

Step-by-step explanation:

1) Find the standard deviation with the given information:

n=5000

p=54% ⇒ 0.54

1-p = 1 - 0.54 = 0.46

[tex]\sigma =\sqrt{\dfrac{p(1-p)}{n}}\\\\\\.\ =\sqrt{\dfrac{0.54(0.46)}{5000}}\\\\\\.\ =\sqrt{\dfrac{0.2484}{5000}}\\\\\\.\ =\sqrt{0.00004968}\\\\\\.\ =0.007048[/tex]

2) Find the margin of error (ME) with the given information:

C=95% ⇒ Z = 1.960

σ=0.007048

ME = Z × σ

     = 1.96 (0.007048)

     = 0.01381

3) Find the confidence interval with the given information:

p = 0.54

ME = 0.01381

C = p ± ME

    = 0.54 ± 0.01381

    = (0.5262, 0.5538)

Answer:

1/9

Step-by-step explanation:

1/3*1/3=1/9

Answer: An opposite definition would be "A shape with a set of points that DOES NOT have the same distance from a given point."

Step-by-step explanation: No need for step-by-step explanations.

The opposite of a circle might be considered an ellipse, as its geometric properties contrast with those of a circle. Ellipses have two focal points with a constant sum of distances to any point on the ellipse, unlike circles which have one central point with a constant distance to any point on the circle.

The opposite of a circle in geometric terms could be considered an ellipse. While a circle has a constant distance from the center to any point on its boundary, known as its radius, an ellipse does not.

In an ellipse, instead of one point being equidistant from all points on the shape (as in a circle), there are two points inside the ellipse known as the foci. The sum of the distances from these two foci to any point on the ellipse remains constant. This differs from the property of a circle where the distance from its center to any point on the circle is always the same.

Another potential 'opposite' of a circle might be a straight line or a polygon, since these shapes do not have the same properties of symmetry and constancy of distance from a single central point that a circle does.

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Answer:

(x^2-8x+7)  +      (-8x+9)/(4x^2+3x-2)

Step-by-step explanation:

Answer:

no because you have division by a variable

Step-by-step explanation:

If you have y   +   2/y as an expression, this expression is not a polynomial expression because you have division by variable.

You are looking for an expression with only positive or 0 integer exponents.  

Here are some examples of a polynomial:

5

5x+1

5x^2+x+1

-x

-x+1

3x^3+5x+1

4x^4+7x^2+x+1

and so on...

Here are some examples of expressions that aren't polynomials:

5+sqrt(x)

5+|x|

|x|-5

x^2+5|x|

5/x^3

6x^(-2)

and son on....

Answer:

Both!

Step-by-step explanation:

By both!

You have all 3 corresponding sides are proportional so you have SSS.  That is

24/8=15/5=18/6

You also have SAS because 15/5=18/6 and you have the angle between the sides that I'm referring to in that proportion.

The SSS (Side-Side-Side) theorem can prove triangle similarity if all sides of two triangles are proportional, whereas the SAS (Side-Angle-Side) can prove similarity if two sides and the included angle of one triangle are proportional to those of another triangle. However, these theorems are only applicable if these conditions are met.

In mathematics, particularly in geometry, we often deal with proving the similarity or congruence of shapes, especially triangles. The SSS (Side-Side-Side) and SAS (Side-Angle-Side) theorems are two of those methods used to establish similarity between triangles. However, these theorems need specific conditions to be applicable.

The SSS Similarity theorem states that if the three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar. In other words, if you can match up the sides of one triangle to the sides of the other in such a way that every pair of corresponding sides has the same ratio, then the triangles are similar.

On the other hand, the SAS Similarity theorem states that if an angle of one triangle is congruent to an angle of a second triangle, and the sides including these angles are in proportion, then the triangles are similar.

Given the exact measures of the sides and angles of the triangles, it's possible to use either the SSS or SAS theorem to establish similarity. If, however, these specifics are not available or do not meet the conditions required for SSS or SAS, we cannot use these theorems to prove similarity.

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