Square ABCD has side length 4. Determine the
area of the shaded region (use pi as 3).

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

There are 4 steps to complete to go from 0 to 1. Hence each step is:

1 out of 4, or simply  [tex]\frac{1}{4}[/tex]

F is located at the 3rd mark, which will be  [tex]\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=\frac{3}{4}[/tex]

Hence, F is located at  [tex]\frac{3}{4}[/tex]

Answer:

F is on [tex]\frac{3}{4}[/tex] on the number line

Step-by-step explanation:

Notice in the image that between 0 and 1 there are 4 subdivisions.

Then divide.

[tex]\frac{1}{4} = 0.25[/tex].

Each subdivision is equal to 0.25 units.

Point F is in the third subdivision.

This means that the distance between 0 and F is:

[tex]\frac{1}{4}*3 = \frac{3}{4} = 0.75[/tex].

Finally F is on [tex]\frac{3}{4}[/tex] on the number line

Answer:

B

Step-by-step explanation:

let's recall that

1² = 1

1⁴ = 1

1¹⁰⁰⁰⁰⁰⁰⁰⁰⁰ = 1

[tex]\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) \\\\ a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^{12}y^{18}+1\implies x^{4\cdot 3}y^{6\cdot 3}+1^3\implies (x^4)^3(y^6)^3+1^3\implies (x^4y^6)^3+1^3 \\[2em] [x^4y^6+1][(x^4y^6)^2-(x^4y^6)(1)+1^2]\implies (x^4y^6+1)(x^8y^{12}-x^4y^6+1)[/tex]

Angle 6, an acute angle, measures below 90 degrees, reflecting a sharp inclination. Angle 4, a right angle at precisely 90 degrees.

In the geometric configuration, Angle 6 is characterized as an acute angle, signifying that its measure falls between 0 and 90 degrees. Acute angles are typically associated with sharp inclinations, emphasizing a compact angular span. On the other hand, Angle 4 is identified as a right angle, precisely measuring 90 degrees.

Right angles are distinctive for their perpendicular alignment, forming the cornerstone of rectangular shapes and providing structural stability. The significance of Angle 4 lies in its pivotal role in defining perpendicularity within geometric constructs.

This geometric interplay showcases the diversity of angles, with acute angles like Angle 6 emphasizing sharpness and right angles like Angle 4 embodying orthogonality, contributing to the intricacies and precision inherent in geometric relationships.

Answer:

The exact distance is √(29) or 29^(1/2)

Step-by-step explanation:

Find the answer using the distance formula (aka the Pythagorean theorem)

d=√(x1+x2)^2+(y1+y2)^2)

d=√(-1+6)^2+(4+-2)^2), Solve for d:

d= √((25)+(4))

d=√(29)

Answer:

[tex]\sqrt{35}[/tex]

Step-by-step explanation:

To calculate the distance (d) use the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (6, - 2)

d = [tex]\sqrt{(6+1)^2+(-2-4)^2}[/tex]

  = [tex]\sqrt{7^2+(-6)^2}[/tex]

  = [tex]\sqrt{49+36}[/tex] = [tex]\sqrt{85}[/tex] ← exact value

Answer:

4x^5\sqrt[3]{3x}

Step-by-step explanation:

Given

[tex]\sqrt[3]{16x^7}\left(\sqrt[3]{12x^9}\right)\\\sqrt[3]{4^{2} x^7}\sqrt[3]{4(3)x^9}\\  4^\frac{2}{3} . x^\frac{7}{3} . 4^\frac{1}{3} . 3^\frac{1}{3} . x^\frac{9}{3}\\  4^\frac{2+1}{3} .  3^\frac{1}{3}. x^\frac{9+7}{3} \\4^\frac{3}{3} . 3^\frac{1}{3}. x^\frac{16}{3}\\ 4\sqrt[3]{3x^16}[/tex]

[tex]4\sqrt[3]{3} . x^\frac{16}{3} \\4\sqrt[3]{3} . x^\frac{15}{3} .x^\frac{1}{3} \\4\sqrt[3]{3} . x^5 .x^\frac{1}{3} \\4x^5\sqrt[3]{3x}[/tex] !

Answer:

The expression [tex]\sqrt[3]{16x^{7} } * \sqrt[3]{12x^{9} }[/tex] = [tex]4x^{5}} (\sqrt[3]{3x})[/tex]

Step-by-step explanation:

Given

[tex]\sqrt[3]{16x^{7} } * \sqrt[3]{12x^{9} }[/tex]

Required

Products of both

To do this, we have to apply the laws of indices,

Follow the highlighted steps

Step 1: Multiply both parameters directly

Since they both have the same roots, they can be multiplied directly according to the law of indices

[tex]\sqrt[3]{16x^{7} } * \sqrt[3]{12x^{9} }[/tex] becomes

[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex]

Step 2: Apply the 1st law of indices

First law of indices states that

[tex]x^{a} * x^{b} = x^{a + b}[/tex]

So, [tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] becomes

[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] = [tex]\sqrt[3]{16 * 12 * x^{7} * x^{9} }[/tex]

[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] = [tex]\sqrt[3]{16 * 12 * x^{7+9} }[/tex]

[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] = [tex]\sqrt[3]{16 * 12 * x^{16} }[/tex]

[tex]\sqrt[3]{16x^{7} * 12x^{9} }[/tex] = [tex]\sqrt[3]{192 * x^{16} }[/tex]

Step 3: Rewrite the expression

[tex]\sqrt[3]{192 * x^{16} }[/tex] = [tex]({192 * x^{16} })^{\frac{1}{3} }[/tex]

Step 4: Expand the Expression in bracket

[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]({64 * 3* x^{15} * x^{1} })^{\frac{1}{3} }[/tex]

Break down into bits

[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]64^\frac{1}{3} * 3^\frac{1}{3} * (x^{15})^\frac{1}{3} * (x^{1})\frac{1}{3}[/tex]

[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex](4^{3}) ^\frac{1}{3} * 3^\frac{1}{3} * (x^{15})^\frac{1}{3} * (x^{1})\frac{1}{3}[/tex]

[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex](4^{3*\frac{1}{3}}) * 3^\frac{1}{3} * (x^{15}*^\frac{1}{3}) * (x^{\frac{1}{3}})[/tex]

[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4 * 3^\frac{1}{3} * (x^{5}}) * (x^{\frac{1}{3}})[/tex]

[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4 (x^{5}})* 3^\frac{1}{3} * (x^{\frac{1}{3}})[/tex]

[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4x^{5}} * (3^\frac{1}{3} * x^{\frac{1}{3}})[/tex]

[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4x^{5}} * (3x)^\frac{1}{3}[/tex]

[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4x^{5}} * \sqrt[3]{3x}[/tex]

[tex]({192 * x^{16} })^{\frac{1}{3} }[/tex] = [tex]4x^{5}} (\sqrt[3]{3x})[/tex]

Hence, the expression [tex]\sqrt[3]{16x^{7} } * \sqrt[3]{12x^{9} }[/tex] = [tex]4x^{5}} (\sqrt[3]{3x})[/tex]

B im pretty sure its B

Answer:

Step-by-step explanation:

Notice that the paragraph is describing some results they got of a recent survey. That is, they are giving specific statistical data about what people prefer.

So, this is an example of descriptive statistics. Remember that descriptive statistics is about using means, medians, standard deviation, percentages or any other stats that help to describe a phenomenom.

Therefore, the right answer is D.

Answer:

The equation is y= 2x+5

Step-by-step explanation:

Lets find the slope of the line through the points (-2,1) and (-4,-3).

where x1 = -2,  y1= 1,  x2= -4,  y2 = -3.

Now apply slope formula:

m= y2-y1/ x2-x1

m= -3-1/-4-(-2)

m = -4/-4+2

m= -4/-2

Divide the term by 2:

m = 2

Now we will apply point slope formula:

y-y1 = m (x-x1)

Now substitute the values in the formula:

y-1=2(x-(-2))

y-1 =2(x+2)

y-1=2x+4

Now combine the constants:

y= 2x+4+1

y=2x+5

So the equation is y= 2x+5 ....

Answer:

7.5 ft

Step-by-step explanation:

Volume of a prism is V = L*W*H.

In this case, the volume is V = 300 ft^3 (not 300 ft).  Therefore,

300 ft^3 = L*W*H = (8 ft)(5 ft)(height)

Solving for the height, H, we get:

       300 ft^3

H = --------------- = 7.5 ft

         40 ft^2

Answer:

7.5 ft

Step-by-step explanation:

Vole is the length time the width times the height

V = l*w*h

Substituting what we know

300 = 5*8*h

300 = 40h

Divide each side by 40

300/40 =40h/40

7.5 =h

A. [tex]\sqrt{3}[/tex]

In the  Geometry, the triangle is a 3-sided polygon that consists of 3 edges and 3 vertices. The most important property of the triangle is that the sum of the internal angles of the triangle is = to 180 degrees. its property is known as angle sum property of triangle.

We have been given the image of the right triangle and we are asked to find the value of the tan(60) for our given triangle

from we know that tangent represents the relation between opposite or adjacent of the right triangle.

[tex]tan = \frac{opposite}{adjacent}[/tex]

We can see that our adjacent side is not given, but corresponding angle to adjacent side is given that is 30 degrees. So we could conclude that our given triangle is 30-60-90 triangle.

from the sides corresponding to 30-60-90 triangle equals to[tex]x,x\sqrt{3}[/tex] and [tex]2x[/tex] , so the adjacent side for our given triangle will be,

[tex]x\sqrt{3} =8 \sqrt{3\\\\\\[/tex]

[tex]\frac{x \sqrt{3} }{\sqrt{3} } =\frac{8\sqrt{3} }{\sqrt{3} }[/tex]

[tex]x=8[/tex]

Upon substituting these values on above formula we will get,

[tex]tan( 60^{0} ) = \frac{8\sqrt{3} }{8} \\tan( 60^{0})=\sqrt{3}[/tex]

hence, the value of tan(60) is  [tex]\sqrt{3}[/tex]and option B is the correct choice.

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Answer:

Step-by-step explanation:

This is a way of asking you what the highest common factor is. So factor into primes and find the highest that is between them.

48: 2 * 2 * 2 * 2 * 3

60: 2 * 2 * 3 * 5

The answer is Bolded and underlined.

HCF: 2 * 2 * 3

HCF: 12

The greatest number that could be in a pack is 12

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut point with the y axis.

By definition, if two straight lines are parallel then their slopes are equal. Thus, the slope of the line sought will be [tex]m = 2.[/tex]

[tex]y = 2x + b[/tex]

We substitute the given point to find b:

[tex]2 = 2 (-1) + b\\2 = -2 + b\\2 + 2 = b\\b = 4[/tex]

Finally the line is:

[tex]y = 2x + 4[/tex]

Answer:

[tex]y = 2x + 4[/tex]

Answer:

y = 2x + 4.

Step-by-step explanation:

The slope = the slope of y = 2x - 3 which is 2.

Using the point-slope form:

y - y1 = 2(x - x1)

Using the point (-1, 2):

y - 2 = 2(x - -1)

y =  2x + 2 + 2

y = 2x + 4  is the answer.

Answer:

False

Step-by-step explanation:

This statement states that If opposite angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram.

This is a false statement.

Lets recall the properties of a parallelogram to understand the concept. The definition says that a quadrilateral is said to be a parallelogram if its opposite angles are congruent and two consecutive angles are supplementary.

Therefore the statement is false....

Answer:

The correct answer option is B. (x - 1).

Step-by-step explanation:

We are to determine the factor of the polynomial function [tex]f(x)[/tex] which is graphed on the given coordinate plane.

We know that if the zeros (or intercepts) of an equation are [tex] r _ 1 [/tex] and [tex] r _ 2 [/tex] then the factors for this equation will be [tex] ( x - r _ 1 ) [/tex] and [tex]( x - r _ 2 ) [/tex].

From the graph, we can see that it intercepts the x axis at [tex]1[/tex] and [tex]6[/tex]. So the roots will be [tex](x-1)[/tex] and [tex](x-6)[/tex].

Therefore, the correct answer option is B. (x - 1).

Answer: SECOND OPTION.

Step-by-step explanation:

We can verify each option by making eac equal to zero and solving for "x":

First option

[tex]x-3=0\\x=0+3\\x=3[/tex]

The first option is not a factor of the polynomial function, because the parabola does not intersect the x-axis at [tex]x=3[/tex].

Second option

[tex]x-1=0\\x=0+1\\x=1[/tex]

The second option is a factor of the polynomial function, because the parabola intersects the x-axis at [tex]x=1[/tex].

Third option

[tex]x+1=0\\x=0-1\\x=-1[/tex]

The third option is not a factor of the polynomial function, because the parabola does not intersect the x-axis at [tex]x=-1[/tex].

Fourth option

[tex]x+3=0\\x=0-3\\x=-3[/tex]

The fourth option is not a factor of the polynomial function, because the parabola does not intersect the x-axis at [tex]x=-3[/tex].

Answer:

168°

Step-by-step explanation:

∠QRS is an angle formed by 2 chords of the circle and is half the measure of its intercepted arc QS, that is

m QS = 2 × 84° = 168°

Applying the inscribed angle theorem, the measure of arc QS is: 168°.

According to the inscribed angle theorem, the measure of an inscribed angle in a circle equals half of the measure of the intercepted arc.

Based on the inscribed angle theorem,

arc QS = 2(m∠QRS)

arc QS = 2(84)

arc QS = 168°

Therefore, applying the inscribed angle theorem, the measure of arc QS is: 168°.

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Answer:

3

Step-by-step explanation:

12 times table= 12,24,36..

if we have 24 books then not everyone can get a book.

it's best to get the 3 boxes of 36 as everyone can get one. As my teacher always said, the more the better.

Answer:

True options: 1, 2 and 5

Step-by-step explanation:

From the given diagram, you can see that the center of the hyperbola is placed at the origin, so first option is true (see attached diagram for definition of center, vertices, foci, i.e.)

There are two vertices of the hyperbola, they are placed at (-6,0) and (6,0), so second option is true.

The transverse axis is the segment connecting vertices, this segment is horizontal, so option 3 is false.

The foci are not placed within the rectangular reference box, so this option is false.

The directrices are vertical lines with equations [tex]x=\pm \dfrac{a}{e}[/tex], so this option is true.

Answer:1 2 5

Step-by-step explanation:

Answer:

4/20

Step-by-step explanation:

20 %

Percent means out of 100

20/100

Divide top and bottom by 10

2/10

We want the denominator to be 20 so multiply the top and bottom by 2

4/20

For this case we must find a fraction equivalent to 20%

We have to:

[tex]\frac {1} {20} =[/tex] 0.05 * 100% = 5%

[tex]\frac {2} {20} =[/tex] 0.1 * 100% = 10%

[tex]\frac {4} {20} =[/tex] 0.2 * 100% = 20%

[tex]\frac {5} {20} =[/tex] 0.25 * 100% = 25%

Answer:

[tex]\frac {4} {20}[/tex]

Option C

Answer:

13

Step-by-step explanation:

Using pythag the. , we see the rule a2+b2=c2 (Square)

so, a2=25, b2= 144,

25+144=c2

c2=169

sqrt=13

Answer:

y = -x - 3

Step-by-step explanation:

Plug in -1 for x and your result will come out to 1 because of that double negative [-(-1) = 1]. Next, deduct 3 from 1 to get -2.

I am joyous to assist you anytime.

let's firstly convert the mixed fractions to improper fractions and then divide.

[tex]\bf \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}}~\hfill \stackrel{mixed}{3\frac{4}{5}}\implies \cfrac{3\cdot 5+4}{5}\implies \stackrel{improper}{\cfrac{19}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{4}\div\cfrac{19}{5}\implies \cfrac{5}{4}\cdot \cfrac{5}{19}\implies \cfrac{25}{76}[/tex]

Answer:

1/3

Step-by-step explanation:

covert the mixed number to an improper fraction

1x4+1 / 4

any expression multiplied by 1 remains the same

4+1 / 4

Add the numbers

5 / 4

Dividing is equivalent to multiplying with the reciprocal value

5 / 4 x 1 / 3 x 4 / 5

reduce the numbers with greatest common divisor 5

1 / 4 x 1 / 3 x 4

reduce the numbers with greatest common divisor 4

1 /3

Answer: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225.

Step-by-step explanation:

1 x 1 = 1

2 x 2 = 4

3 x 3 = 9

4 x 4 = 16

5 x 5 = 25

6 x 6 = 36

7 x 7 =49

8 x 8 = 64

9 x 9 = 81

10 x 10 = 100

11 x 11 = 121

12 x 12 = 144

13 x 13 = 169

14 x 14 = 196

15 x 15 = 225

Answer:

hello : answer: A

Step-by-step explanation:

a(1) = –10 and a(n) = 4a(n– 1) + 7, if n ≥ 2.

n=2 : a(2)=4a(1)+7        a(2) =4(-10)+7 = -33

n=3 : a(2)=4a(2)+7        a(3) =4(-33)+7 = -125

n=4 : a(2)=4a(3)+7        a(4) =4(-125)+7 = -493

n=5 : a(2)=4a(4)+7        a(5) =4(-493)+7 = -1965

n=6 : a(2)=4a(5)+7        a(6) =4(-1965)+7 = -7853

[tex]\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+6}x\stackrel{\stackrel{c}{\downarrow }}{+9}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{\underline{one solution}}~~\textit{\Large \checkmark}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ 6^2-4(1)(9)\implies 36-36\implies 0[/tex]

Answer:

0

Step-by-step explanation:

Descriminator is calculated by the following formula:

b*b - 4 * a * c, where a,b,c are the numbers in equitation.

slope of DE would be [tex]\( m_{DE} = \frac{(2c - b)}{(0 - (-a))} = \frac{(2c - b)}{a} \).[/tex]

slope of FG would be[tex]\( m_{FG} = \frac{(0 - c)}{(0 - (a+b))} = \frac{-c}{-(a+b)} = \frac{c}{a+b} \).[/tex]

To find the slope of line segments DE and FG from a trapezoid on a coordinate plane, we can follow these steps:

1. Identify the Coordinates of Endpoints:

  - For DE, identify coordinates D and E.

  - For FG, identify coordinates F and G.

2. Use the Slope Formula:

  - The slope  m  of a line passing through two points [tex]\( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m = \frac{(y_2 - y_1)}{(x_2 - x_1)} \).[/tex]

3. Calculate the Slope for DE:

  - Plug the coordinates of D and E into the slope formula.

4. Calculate the Slope for FG:

  - Plug the coordinates of F and G into the slope formula.

Given the coordinates in the image, let's calculate the slopes for DE and FG:

For DE:

- Let's say D has coordinates  (-a, b)  and E has coordinates (0, 2c)

- The slope of DE would be [tex]\( m_{DE} = \frac{(2c - b)}{(0 - (-a))} = \frac{(2c - b)}{a} \).[/tex]

For FG:

- Let's say F has coordinates[tex]\( (a+b, c) \)[/tex] and G has coordinates  (0, 0) .

- The slope of FG would be[tex]\( m_{FG} = \frac{(0 - c)}{(0 - (a+b))} = \frac{-c}{-(a+b)} = \frac{c}{a+b} \).[/tex]

Answer:

C. 3x

Step-by-step explanation:

The first two choices give 1 solution each.

The last choice gives an infinite number of solutions.

Choice C. gives no solution.

3x + 9 = 3x

Subtract 3x from both sides.

9 = 0

Since 9 = 0 is false, equation 3x + 9 = 3x has no solution.

The expression can be written in the box on the other side of the equation as C. 3x.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The given expression is

3x + 9 = _

Subtract 3x from both sides;

9 = 0

Since 9 = 0 is false,

The equation 3x + 9 = 3x has no solution.

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Answer:

Correct answer is figure D.

Step-by-step explanation:

According to the attached image Figure  D is correct option.

In a reflection transformation, all the points of an object are reflected or flipped. It is a type of transformation where the new image is the mirror image of the original and x-coordinates and y-coordinates changes the place.

Figure A is rotation and translation and Figure B and C are translation

Thus the correct option is Figure D....

Answer:

a = 44 degrees

Step-by-step explanation:

angle 0 + angle a + angle b = 180 degrees

angle b = angle a

92 + a + b = 180 degrees

92 + 2a = 180 degrees

a = 44 degrees

!!

Answer:

This is the zero product rule.

Step-by-step explanation:

a: b = 0, then a = 0, b = 0, or both a = 0 and b = 0.

This is the zero product rule.

It shows that for the product to be zero,  at least  one factor must be zero

If a*b= 0: It shows that one of the factor is zero or may be both the factors are zero that is why their resultant product is 0....

Answer:

This is an odd question...

The couple should find out the following:

1.) is the agency legitimate?

2.) Will they be doing a hard inquiry on our credit history? if so, this could affect our current credit score

3.) Will they charge me to review my current credit reports?

Three things that should be considered about a credit agency are : Credibility and Reliability, Financial Efficiency, Accreditation and Acclamation

Given - The couple are facing debt issues. They need a credit counselling agency.

While choosing an agency, they should be careful about the following aspects of respective agency.

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Answer:

Step-by-step explanation:

Answer:

Answer is 1.98

You're welcome.