What is the area and perimeter of a square that has side lengths that are all 8 inches long?

Answer:

[tex]\Huge \boxed{\textbf{F. One solution}}[/tex]

Step-by-step explanation:

To find the number of solutions for the given equation, we can start by simplifying and solving the equation.

First, distribute the 7 on the left side of the equation:

Now, subtract 5x from both sides:

Next, subtract 14 from both sides:

Finally, divide by 30:

Simplifying the fraction, we get:

Since we found a unique value for x, the equation has only one solution.

Therefore, the correct answer is option F.

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Equation graphed along with the parent function is, g(x) = ∛(x-3) + 4

The correct option is B.

The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x).

Given that;

Graph of a parent function.

And, Equation is graphed along with the parent function.

Here, The Parent function is,

f(x) = ∛x

Hence, By the graph,

There is 3 unit horizontal shift to positive side, and 4 unit vertical shift to upwards in parent function

Thus, The function drawn along with it is;

g(x) = ∛(x-3) + 4

Hence, g(x) = ∛(x-3) + 4 is the equation, graphed along with the parent function.

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The complete question is this,

Which equation is graphed along with the parent function?

g(x)= ^3 √x+3 +4

g(x)= ^3 √x-3 +4

g(x)= ^3 √x-4 +3

g(x)= ^3 √x+4 +3

Answer:

4 in

Step-by-step explanation:

Surface area = 1/2 ( 5x12) *2   + 5 x h  + 13 * h +  12 x h

                                 60 + 30h = 180

                                          h = 4 in

just a quick addition to "jsimpson11000" posting above

keeping in mind that for a triangular prism, the base is always the triangular face.

Check the picture below.

[tex]5h~~ + ~~12h~~ + ~~\stackrel{\textit{two triangles}}{2\left[\cfrac{1}{2}(12)(5) \right]}~~ + ~~13h~~ = ~~180 \\\\\\ 60+30h=180\implies 30(2+h)=180\implies 2+h=\cfrac{180}{30} \\\\\\ 2+h=6\implies \boxed{h=4}[/tex]

im stuck on the same thing

The answer to your question is true

Answer:

true, the square root of 361 is 19

Step-by-step explanation:

(  ﾟｰﾟ)ﾉ

The infinite series, [tex]ln(6)/6 + ln(7)/7 + ln(8)/8 + ln(9)/9 + ln(10)/10 + ... = \int_{1}^{ \infty } \frac{ln(x + 5)}{ (x + 5 )}dx\\ [/tex] is diverges as the integral diverges.

We know that the Integral test : Suppose that f(x) is a continuous, positive and decreasing function on the interval [ k,∞) and that f(n)= a, then

If [tex] \int_{k}^{ \infty } f(x)dx[/tex] is convergent then the series, [tex] \sum_{n = 1}^{ \infty } a_{n}[/tex]

If [tex] \int_{k}^{ \infty } f(x)dx[/tex] is divergent so is [tex]\sum_{n = 1}^{ \infty } a_{n}[/tex].

We have an integral equals to an infinite series [tex] \frac{ln(6)}{6} + \frac{ln(7)}{7} + \frac{ln(8)}{8} + \frac{ln(9)}{9} + \frac{ln(10)}{10} + ... = \int_{1}^{ \infty } \frac{ln(x + 5)}{ (x + 5 )}dx \\ [/tex]

[tex]\int_{1}^{ \infty } \frac{ln(x + 5)}{ (x + 5 )}dx = {\lim_{k-> \infty } \\}\int_{1}^{k} \frac{ln(x + 5)}{ (x + 5 )}dx [/tex]

[tex]= {\lim_{k-> \infty } \\}[ \frac{ {(ln(x+5))}^{2} }{2} ]_{1}^{k}\\ [/tex]

[tex] = \infty [/tex]

This implies that the integral diverges, so by integral test the series also diverges.

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Answer:

three times

Step-by-step explanation:

Please find the attachment for detail

The plan cost same for 800 minutes.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Plan A costs $12 plus an additional $0.14 for each minute of calls.

Plan B costs $28 plus an additional $0.12 for each minute of calls.

let the number of minutes for which two plans are equal be x.

so, 12 + 0.14x = 28 + 0.12 x

12 - 28 = 0.12x - 0.14x

-16 = -0.02x

x= 800 minutes

and, the plan cost

y = 12 + 0.14x

y = 12 + 0.14(800)

y = $124

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Answer:

-2 <n>5 I believe? that's all I know

Answer:

below

Step-by-step explanation:

For the LEFT part

n < -2      or     -2 > n

for the RIGHT part

n>5  

combine these two to get       -2 > n > 5

The Cartesian, or rectangular, coordinate system is composed of an x-axis that runs horizontally and a y-axis that goes vertically.

The rectangular coordinate system of the Cartesian plane, which bears Rene Descartes' (1596–1650) name, assigns each point in the plane a pair of integers.

An x-axis that runs horizontally and a y-axis that runs vertically make up the Cartesian, or rectangular, coordinate system. The origin is the place where the two axes meet. Any point can be characterized by its distance from the origin along the x-axis and along the y-axis, and this distance is represented by the symbol (x, y).

A two-dimensional coordinate plane produced by the intersection of the x- and y-axes is known as the cartesian plane in mathematics. At the location known as the origin, the x- and y-axes cross perpendicularly.

Therefore, the correct answer is option D. A graph used in mathematics to plot points.

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The equation of the sphere with center coordinates  (4, −12, 8) and radius 10 is x² -8x + y² + 24y + z² -16z + 124 =0 .

And different plane equations are :

Intersection with xy-plane : ( x - 4 )² + ( y + 12 )² = 6²

Intersection with yz plane :( y + 12 )² + ( z - 8 )² = (√84)²

Intersection with zx plane :( x - 4 )² +  ( z - 8 )² = -44

Equation of the sphere with center coordinates (4, −12, 8) and radius 'r' = 10 is :

( x - 4 )² + ( y + 12 )² + ( z - 8 )² = 10²

⇒ x² -8x + y² + 24y + z² -16z + 224 = 100

⇒x² -8x + y² + 24y + z² -16z + 124 =0

Intersection with xy-plane

z = 0

( x - 4 )² + ( y + 12 )² + ( 0 - 8 )² = 10²

⇒( x - 4 )² + ( y + 12 )² = 6²

Circle with center ( 4,-12) and radius 6.

Intersection with yz-plane

x = 0

( 0 - 4 )² + ( y + 12 )² + ( z - 8 )² = 10²

⇒( y + 12 )² + ( z - 8 )² = (√84)²

Circle with center ( -12, 8) and radius √84.

Intersection with zx-plane

y = 0

( x - 4 )² + ( 0 + 12 )² + ( z - 8 )² = 10²

⇒( x - 4 )² +  ( z - 8 )² = -44

Not possible as radius cannot be negative.

Therefore, the equation of the sphere with the given center and radius is equal to x² -8x + y² + 24y + z² -16z + 124 =0 and equation of the intersection of different planes are:

xy-plane : ( x - 4 )² + ( y + 12 )² = 6²

yz plane :( y + 12 )² + ( z - 8 )² = (√84)²

zx plane :( x - 4 )² +  ( z - 8 )² = -44

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a) The data is not symmetric

b) The complete table:

  Class interval         Frequency         Relative Frequency

c) Proportion of subdivisions has total length less than 2000 is 0.49

Proportion of the subdivisions has total length between 2000 and 4000 is 0.36

a) To draw the stem and leaf plot we take the thousandth place digit as stem and the leaf is obtained by remaining digits.

       Stem     Leaf

The data is not symmetric

b) To draw the histogram first we form the frequency distribution and the relative frequency using the formula

Relative Frequencies are given by

Relative frequency = Frequency / Total frequency

     Class interval         Frequency         Relative Frequency

                                       = 47

Histogram attached at end of solution

The histogram is approximately positively skewed.

c) Proportion of lengths less than 2000 = sum of relative frequency from 0 to 2000

= 0.26 + 0.23

Proportion of subdivisions has total length less than 2000 = 0.49

Proportion of length between 2000 and 4000 = sum of relative frequency between 2000 and 4000

= 0.21 + 0.15

Proportion of the subdivisions has total length between 2000 and 4000 = 0.36

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The method to calculate the reference angle is discussed below.

Reference Angle is the acute angle between the terminal side and the

x - axis.

Given is reference angle.

You determine a reference angle by looking at the terminal side of the angle you're working with and its relation with the positive or negative x-axis (depending on which quadrant the terminal side is in).

Therefore, the method to calculate the reference angle is discussed above.

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{Question in english -

How is a reference angle calculated?}

If there is no solution to the system of equations, it signifies that the equations describe two parallel lines in the two-dimensional plane. This indicates that the lines will never meet because they have the same slope but separate y-intercepts. This signifies that the two lines are geometrically distinct and will never intersect.

A geometric significance is a geometric aspect or quality of a form or item. This encompasses the object's size and orientation, as well as its symmetry and proportions. Several areas, including architecture, engineering, graphic design, and mathematics, rely on geometric importance. In architecture, for example, the size and direction of a structure may be utilised to decide how much light it receives and how much shade it casts. The geometry of an item can be used to determine its strength, stiffness, and durability in engineering. The symmetry and dimensions of an object may be employed in graphic design to produce an appealing and balanced design.

The given question states that when there are no solutions to a system of K equations in two variables, it means that the lines associated with those equations are either parallel or coincident. Geometrically, this means that the lines are not intersecting, which implies that the two variables cannot simultaneously satisfy all of the equations.

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Answer:

a) 4

b) 2

Step-by-step explanation:

I use this sentence to remember quadrants:

All Students Take Coffe

- All trigs are positive in 1 Quadrant

- Sin and (cosine) is positive in 2 quadrant

-Tan and (Cotan) are positive in 3 quadrant

- Cos and (Sec) are positive in 4 quadrant

all other trigs other than those are negative.

a) cos is positive in 1 and 4 quadrant. Csc is reciprocal of Sin and is negative in 3 and 4 quadrant. 4th quadrant satisfies both conditions.

b) csc  is reciprocal of Sin and is positive in 1 and 2 quadrants. Sec is reciprocal of Cos and is negative in 2 and 3 quadrant. 2nd quadrant fulfills both conditions.

If my bowl of easter candy has colorful foil-wrapped chocolate eggs. there are 5 gold, 7 blue, and 10 pink. The probability that she reaches in without looking and gets a chocolate candy wrapped in pink foil is 0.45.

Total color = 5 gold + 7 blue + 10 pink

Total color = 22

Now let find the probability that she reaches in without looking and gets a chocolate candy wrapped in pink foil

Probability (pink) = 10/22

Probability (pink) = 0.45

Therefore the  probability of Callie Brooke getting a pink foil-wrapped chocolate egg is 10/22, or approximately 0.45.

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C is equidistant to the following points:  CL=CM=CN

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

One of the triangle's centers where the bisectors of the inner angles converge is known as the incline

The circumcenter of a triangle, which is equal distances from all the vertices, is where the perpendicular bisectors of the triangle meet.

so, C is equidistant to the following points:  CL=CM=CN

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A sales presentation aims to attract and compel the audience to whom the presentation is made.

Creating a sales presentation involves several steps:

Define the goal and audience of the presentation: Before creating the presentation, it is important to understand the goal of the presentation, and the target audience it is meant for. This will help you tailor the content of the presentation to the specific needs and interests of the audience.

Research the product or service: Understand the product or service you are selling inside and out. This will help you answer any questions that may come up during the presentation and show that you are an expert on the subject.

Create an outline: Once you have a clear understanding of your audience and the product or service, create an outline for the presentation. This will help you organize your thoughts and stay on track during the presentation.

Create compelling content: Use persuasive language and storytelling to create content that is engaging and easy to understand. Use statistics, testimonials, and visual aids to support your points.

Design the visual aids: Use charts, graphs, images, and other visual aids to supplement the text of your presentation. Make sure that the visual aids are clear and easy to understand, and that they support the points you are making.

Rehearsal: Practice the presentation several times before delivering it. This will help you build confidence and ensure that the presentation flows smoothly.

Delivery: During the presentation, engage with the audience and be responsive to their questions and feedback. Make sure that you are well-prepared and that you stay on track.

Follow-up: After the presentation, make sure to follow up with the audience and address any remaining questions or concerns they may have.

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Answer:

The model shows that there are 9 pieces that are each ft long.​. The model shows that there are 9 pieces that are - 1.

The amount of money that is compounded monthly for 30 years will be $17,153.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

If $10,000 is deposited into a savings account that pays 1.8% annual interest.

Then the rate is given as,

r = 1.8% / 1200

r = 0.0015

Then the number of years is given as,

n = 30 x 12

n = 360

Then the amount of money that is compounded monthly for 30 years is given as,

A = $10,000 × (1 + 0.0015)³⁶⁰

A = $10,000 × (1.0015)³⁶⁰

A = $10,000 × 1.715

A = $17,153

The amount of money that is compounded monthly for 30 years will be $17,153.

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The axis of symmetry for the function f(x) is x = 8 , and h(x) is x = 3

The axis of symmetry is a hypothetical straight line that splits a form into two identical halves, making one half the mirror image of the other. Both pieces are overlaid when folded along the axis of symmetry.

A straight line called the axis of symmetry is what gives an object its symmetrical form and exactly the same reflections are produced on each side of the axis of symmetry on the graph.

From the given information:

f(x) = -4(x - 8)² + 3

Use the vertex form, y = a ( x − h )² + k, to determine the values of a, h, and k.

Since the value of a is negative, the parabola opens down, and the vertex (h, k) is (8, 3).

The distance (p) from the vertex and the focus of the quadratic equation can be calculated by using the formula:

P = 1/4a

Replacing the value of a from above:
P = 1/4(-4)

P = -1/16

The focus of a parabola can be determined by adding the p to the y-coordinate k if the parabola opens up or down. Thus, (h, k + p) = (8, 47/16).

Thus, the axis of symmetry is finally estimated by finding the line that passes through the vertex and the focus;

Axis of symmetry x = 8

For the graphical function of h(x); we use the following points on the graph to determine the equation of the parabola: (1,-2), (3,2), (5,-2)

Thus, h(x) = -x² + 6x - 7

Rewriting the function in its vertex form, we have:

y = - (x - 3)² + 2

Using the vertex form;

The vertex (h,k) = (3,2). The axis of symmetry (x) is the line that passes through the vertex and the focus, x = 3.

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Answer: 400 ft

Step-by-step explanation:

Since the triangles are Congruent Triangles (similar)

x/40  =  50/5

Cross multiply

5x = 2000

divide both sides by 5

5x/5 = 2000/5

x = 400 ft

Yes, b(-6, 9, 2) is in the span of the other given vectors [tex]a_1[/tex] = (-1, 3, -1), [tex]a_2[/tex] = (-2, -3, 6).

b as a linear combination of the other vectors [tex]a_1[/tex] and [tex]a_2[/tex]

b = c [tex]a_1[/tex] + d [tex]a_2[/tex]

A vector is a quantity that has magnitude and direction.

We say that a vector u spans vectors v, w if u = av + bw where a and b are scalars.

As per the given data:

[tex]a_1[/tex] = (-1, 3, -1), [tex]a_2[/tex] = (-2, -3, 6), b = (-6, 9, 2)

We need to write vector b as a linear combination of vectors [tex]$a_1[/tex] and  [tex]a_2$[/tex].

Let c and d be scalars.

b = c [tex]a_1[/tex] + d [tex]a_2[/tex]

(-6, 9, 2) = c(-1, 3, -1) + d(-2, -3, 6)

(-6, 9, 2) = (-c - 2d, 3c - 3 d, -c + 6d)

-6 = -c - 2d........(i),

9 = 3c - 3d ...... (ii),

2 = -c + 6d .......(iii)

b = c [tex]a_1[/tex] + d [tex]a_2[/tex]

On solving equations (i) and (ii), we get c = 4, d = 1

Now, we will check if c = 4, and d = 1 satisfy equation (iii).

= - c + 6d

= -4 + 6(1)

= -4 + 6

= 2

As it satisfies this equation, so b is a linear combination of [tex]$a_1[/tex] and [tex]a_2[/tex]

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Determine if b is in the span of the other given vectors. If so, write b as a linear combination of the other vectors.  (if b cannot be written as a linear combination of the other two vectors, enter done in both answer blanks.) a1=[-1 3 -1],a2=[-2 -3 6],b=[-6 9 2]

Answer:

x=4 and x=3

Step-by-step explanation:

Ian would have $16 left in his checking account.

Here is the working:

$28 (starting amount) - $12 (check written)

= $16 (remaining amount)

Answer: To convert cubic meters (m³) to gallons, we can use the conversion factor 1 m³ = 264.172 gallons.

First, we need to find the amount of water needed to fill the pool to 94% of its capacity. We can do this by multiplying the volume of the pool (60 m³) by 94% (0.94).

60 m³ * 0.94 = 56.4 m³

Now we can use the conversion factor to convert the volume in cubic meters to gallons:

56.4 m³ * 264.172 gallons/m³ = 14,958.2 gallons

So the number of gallons of water that will be needed to fill the empty swimming pool to 94% of its capacity is 14,958.2 gallons.

Rounded to 3 decimal values is 14,958.2 gallons.

Step-by-step explanation:

The correct answer is option A. 110 snacks have between 100 and 120 mg of sugar.

A bar in a histogram represents a range of values and the height of the bar represents the frequency of the values in that range. In this case, the bar represents the range of values between 100 and 120 mg of sugar and the height of the bar represents the frequency of snacks with that amount of sugar. So, the statement that best describes the meaning of one of the bars in the histogram is: 110 snacks have between 100 and 120 mg of sugar.

In summary, the bar in the histogram represents a range of values and the height of the bar represents the frequency of the values in that range. In this case, the bar represents the range of values between 100 and 120 mg of sugar and the height of the bar represents the frequency of snacks with that amount of sugar.

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