Determine the coordinates of the preimage given the image below and the composition of a rotation 180 about the origin and a translation 3
units up.

Answer:

a = 5 cm

Step-by-step explanation:

Formula we use,

→ (AC)² = (BC)² + (AB)²

Now the value of a will be,

→ (13)² = a² + (12)²

→ 169 = a² + 144

→ a² = 169 - 144

→ a = √25

→ [ a = 5 cm ]

Hence, value of a is 5 cm.

The values of the three integers are:

x= -9, y=66, z= -25

In French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.

In order to solve an equation with variables, you must first determine which variables' values make the equality true. Unknowns are the variables for which the equation must be solved, and equation solutions are the values of the unknowns that satisfy the equality..

Given,

Sum of three integers= 32

x+ y+ z=32  →1

And also given that,

x+ y= z+82 →2

z+16=x →3

By solving equation 1, we get

z+16+y+z=32

2z+y=16 →4

By solving equation 2, we get

z+16+y= z+82

y=82-16

y=66

By solving equation 4, we get

2z+66=16

2z=-50

z=-25

By solving equation 3, we get

x=z+16

x=-25+16

x=-9

Therefore, the three integers are x=-9, y=66, z=-25

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From the coefficients of the quadratic equation and the vertex of the parabola, it was found that the graph again crosses the x-axis  in x=7.

The standard form for a quadratic equation is ax²+ bx + c=0, where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

For solving the quadratic function, you should find the discriminant: Δ=b²-4ac and then use this variable in the formula: [tex]\frac{-b \pm \sqrt{\Delta} }{2a}[/tex] .

The given equation is a quadratic function because have a degree equal to 2. Therefore, the graph is represented by a parabola. The vertex of the parabola is given by the coordinates(xv= -b/2a, yv= -Δ/4a).

From the given figure, it is possible to see that:

For x= -1, you have y=0, then:

ax²+bx+c=0 -> x=-1

a (-1)²-b+c=0

a*1-b+c=0

a-b+c=0 (1)

For y= 2, you have x=0, then:

ax²+bx+c=0

a*0²+b*0+c=2

0+0+c=2

c=2 (2)

As, a-b+c=0 (1) and c=2 (2), you have:

a-b+c=0

a-b+2=0

a-b=-2 (3)

Now, you should use the information about the xv.

[tex]x_v=\frac{-b}{2a} =3[/tex]

-b=6a

b=-6a

From equation 3, you will find the coefficient a .

a-b=-2 (3)

a-(-6a)= -2

a +6a =-2

7a= -2

a=-2/7

If a= -2/7, from equation 3 you can find the coefficient b.

b=-6a = -6* (-2/7)=12/7

Thus, the quadratic equation of the plot is: ax²+bx+c

[tex]f(x)=-\frac{2}{7}\cdot \:x^2+\frac{12}{7}\cdot \:x+2[/tex]

Now, you should find the roots for the found equation :[tex]f(x)=-\frac{2}{7}\cdot \:x^2+\frac{12}{7}\cdot \:x+2[/tex].

[tex]x_{1,\:2}=\frac{-12\pm \sqrt{12^2-4\left(-2\right)\cdot \:14}}{2\left(-2\right)}[/tex]

[tex]x_1=\frac{-12+16}{2\left(-2\right)}=-1,\:x_2=\frac{-12-16}{2\left(-2\right)}=7[/tex]

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The identification of the missing angles and their congruency names are;

a. ∠4 and ∠7 = Consecutive interior

b. ∠2 and ∠11 = alternate exterior angles

c. ∠12 and ∠16 = corresponding angles

d. ∠8 and ∠13 = alternate interior angles

e. ∠11 and ∠15 = corresponding angles

f. ∠7 and∠10 = none

g. ∠1 and ∠14 = alternate exterior angles

h. ∠12 and ∠15 = Consecutive interior

i. ∠6 and ∠7 = none

j. ∠1 and ∠3 = corresponding angles

k. ∠12 and ∠16 = corresponding angles

l. ∠6 and ∠15 = alternate exterior angles

m. ∠5 and ∠10 = alternate interior angles

n. ∠8 and ∠14 = corresponding angles

Corresponding angles are defined as the angles which are formed in corresponding corners with the transversal in a case where two parallel lines are intersected by any other line.

Alternate interior angles are defined as the angles formed when a transversal intersects two coplanar lines.

Alternate exterior angles are defined as the pair of angles that are formed on the outer side of the parallel lines but on the opposite side of the transversal.

Therefore, the angles given can be classified similarly using the image as:

a. <4 and <7 are Consecutive interior angles

b. <2 and <11 are alternate exterior angles

c. <12 and <16 are corresponding angles

d. <8 and <13 are alternate interior angles

e. <11 and <15 are corresponding angles

f. <7 and <10 are none

g. <1 and <14 are alternate exterior angles

h. <12 and <15 are Consecutive interior

i. < 6 and <7 are none

j. <1 and <3 are corresponding angles

k. <12 and <16 are corresponding angles

l. <6 and <15 are alternate exterior angles

m. <5 and <10 are alternate interior angles

n. <8 and <14 are corresponding angles

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With the help of sets we can conclude our answer.

acc to our qusetion-

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The expression -9(1/2x-3) is -9/2x + 27.

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:

-9(1/2x-3)

Now, solving the above expression as

-9 x 1/2x= -9/2x

-9(-3)= +27

So,  -9(1/2x-3) = -9/2x + 27

Hence, the expression is -9/2x + 27.

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The width of the rectangle is 4 inches and length of the rectangle is 8 inches.

Given,

The width of the rectangle = x inches

The length of the rectangle = x + 4 inches

Perimeter of the rectangle = 24 inches

We have to find the dimensions of the rectangle;

Here,

Perimeter of rectangle = 2(length + width)

So,

24 = 2(x + 4 + x)

24/2 = 2x + 4

12 - 4 = 2x

x = 8/2

x = 4.

That is,

Width of the rectangle = 4 inches

Length of the rectangle = 4 + 4 = 8 inches.

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Answer: C

Step-by-step explanation:

All i used was a desmos graphing calculator

Answer:

[tex]=45[/tex]

Step-by-step explanation:

1 ) Simplify

[tex]\frac{(18^7)(20^7)}{(25^3)(2^2^1)(27^4)}[/tex]

[tex]= \frac{612220032(20^7)}{(25^3)(2^2^1)(27^4)}[/tex]

[tex]= \frac{(612220032)(1280000000)}{(25^3)(2^2^1)(27^4)}[/tex]

[tex]= \frac{783641640960000000}{(25^3)(2^2^1)(27^4)}[/tex]

[tex]= \frac{783641640960000000}{15625(2^2^1)(27^4)}[/tex]

[tex]= \frac{783641640960000000}{(15625)(2097152)(27^4)}[/tex]

[tex]= \frac{783641640960000000}{32768000000(27^4)}[/tex]

[tex]= \frac{783641640960000000}{(32768000000)(531441)}[/tex]

[tex]= \frac{783641640960000000}{17414258688000000}[/tex]

[tex]=45[/tex]

Hope this helps! :)

The ratio sinC is given by 4/5 and in decimal form is given by sinC = 0.8.

The trigonometric functions are real functions in mathematics that connect the angle of a right-angled triangle to the ratios of its two side lengths. They are also known as circular functions, angle functions, or goniometric functions. They are extensively employed in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more. As some of the most basic periodic functions, they are frequently employed in Fourier analysis to examine periodic events.

The sine, cosine, and tangent are the trigonometric functions that are most commonly utilized in contemporary mathematics. The cotangent, secant, and their less common reciprocals, the cosecant, are each of their reciprocals. These six trigonometric functions each have an analog in the hyperbolic functions, as well as an equivalent inverse function.

The value of sin C is given by

sinC = perpendicular/ hypotenuse

sinC = AB/AC

sinC = 4/5

In decimal form, it is written as

sinC = 0.8

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110 additional miles he will have to drive .

To calculate : additional miles qiang will have to drive

Let the additional no. of miles he has to drive be x .

⇒ Total Distance = 15 + x

    Total Time ( in hrs ) = ( 15 / 30 ) + ( x / 55 ) = ( 1 / 2 ) + ( x / 55 )

The equation becomes ,

[ ( 15 + x ) ] / [ ( 1 / 2 ) + ( x / 55 ) ] = 50

On simplification we get ,

15 + x = 25 + ( 10x / 11 )

x = 110

Therefore , 110 additional miles he will have to drive .

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The product in simplest form is [tex]-250\sqrt[3]{50}[/tex] .

In the question,

It is given that,

[tex]5*\sqrt[3]{5} * (-10\sqrt[3]{50})[/tex]

By radical laws, [tex]\sqrt{a} * \sqrt{b} = \sqrt{ab}[/tex]

So,

The given question becomes:

[tex]-50*\sqrt[3]{50*5} = -50*\sqrt[3]{250} = -250\sqrt[3]{5} }[/tex]

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It is false, that the sum of the numbers of dots that show up when we roll three dice simultaneously does not follow a discrete uniform distribution.

The Discrete uniform distribution is a symmetric probability distribution used in probability theory and statistics. It contains a finite number of values that are equally likely to be observed; each value has an equal chance of 1/n. "A known, finite number of outcomes equally likely to occur" is another approach to describe the discrete uniform distribution.

The perfect example of Discrete uniform distribution is throwing a die. Tossing a fair dice is an easy illustration of the discrete uniform distribution. The possible results are 1, 2, 3, 4, 5, and 6, and the likelihood of a certain result is 1/6 each time the die is thrown. Because not all sums have an equal chance, the distribution that results when two dice are thrown and their values are summed is no longer uniform.  

From the above observation, we can say that the sum of the number of dots that show up when we roll three dice simultaneously will follow a discrete uniform distribution.

It is false, that the sum of the numbers of dots that show up when we roll three dice simultaneously does not follow a discrete uniform distribution.

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In linear equation, 22.5 kilometer  is Shaq from his original starting point.

What is linear equation?

Shaq is he climbs up on the side of a mountain = 4 1/2 = 9/2

  then he climbs down = 5 kilometer

Shaq from his original starting point = 9/2 * 5

                                                          = 45/2 = 22.5 kilometer

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a. Timothy is correct, as each vertex of triangle KLM was multiplied by 1.5.

b. The two triangles are similar, as they have the same angle measures, since a dilation does not change the angle measures.

A dilation occurs when each of the vertices of a image is multiplied by a constant, which is called scale factor.

The vertices of triangle KLM and given as follows:

K(-1,3), L(8,4) and M(10,-3).

The vertices of the triangle K'L'M', obtained after the dilation, are given as follows:

K'(-1.5, 4.5), L'(12, 6) and M'(15, -4.5).

Hence the scale factor is given by the multiplication of one the equivalent coordinates of the equivalent vertices, as follows:

-1.5/-1 = 1.5.

Meaning that Timothy is correct.

The two triangles are similar, as the dilation changes the side lengths but keep the angle measures constant, keeping the similarity of the triangles.

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If the Jackson family just bought 15 pack of Lacroix at Costco and the family drinks about eight cans a week, then after 1.25 weeks

Total number of packs they bought = 15 pack

The average cans they finish each week = 8

Number of cans left = 5 cans

Number of cans used = Total number of packs they bought - Number of cans left =

= 15 - 5

= 10 cans

After how many weeks will there be only five cans left = Number of cans used ÷ The average cans they finish each week

Here we have to use the division

Substitute the values in the equation

After how many weeks will there be only five cans left = 10 /8

= 1.25 weeks

Hence, if the Jackson family just bought 15 pack of Lacroix at Costco and the family drinks about eight cans a week, then after 1.25 weeks

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Answer:

A relationship is proportional if each pair of data values are related in the same way, by multiplying by a factor. You can recognize a proportional relationship by looking at data, an equation, or a graph.

Step-by-step explanation:

Answer:
simply just divide!

Step-by-step explanation:

okay, here is one example:

in 3 hours, you went 126 miles

In 4 hours, you went 168 miles

In 5 hours, you went 210 miles

So what is the unit rate of the miles(x) per hour(y).

The smallest number would be easier to divide. So you divide 126 and 3 and would be 42 miles.

Then find the quotient for the other ones.
168 divide 4 = 42

210 divide 5 = 42.

What is the same of all of them? 42 is the factor to all of the problems. So the proportional relationship (k) is 42. In a equation it would be y=42x (y=Kx)

To find the next number in the sequence you just multiply (x) with the factor.

When an aabbccddeeff individual is crossed with an individual with the genotype aabbccddeeff, the probability that their offspring will have the genotype aabbccddeeff would be 1/64.

The genotype of an organism refers to the complete set of genetic material. An offspring's genotype is the result of the combination of genes from their parents.  In order to obtain the overall probability, individual probabilities for each locus will be multiplied. The Parent cross would be AABbccDdEeFF x AaBBCCDdEeff and offspring would be AaBbCcddEEFf.

Multiplying all the probability:

½ * ½ * 1 * ¼ * ¼ * 1 = 1/64

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We will use the  distributive property to take a common factor in the next step:

(1/5)*x - (1/10)*x = (1/5 - 1/10)*x

Using that we will see that the solution is x = 10.

The distributive property can be written as:

A*(B + C) = A*B + A*C

Now we have the equation:

(1/5)*x + 8 = (1/10)*x + 9

If we group like terms we get:

(1/5)*x - (1/10)*x = 9 - 8

Here we apply the property, we can rewrite the left side as:

(1/5)*x - (1/10)*x = (1/5 - 1/10)*x

Then we can write:

(1/5)*x - (1/10)*x = 9 - 8

(1/5 - 1/10)*x = 1

(1/10)*x = 1

x = 10*1

x = 10

And that is the solution.

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If the receiver is placed at the focus, it is 4 inches from the bottom of the dish. The result is obtained by using the equation of parabola with the vertex is at (0,0).

With the vertex at (0,0), the equation of a parabola can be expressed as

x² = 4ay

Where

Given

How far is the receiver from the bottom of the dish if it is placed at the focus?

Suppose that the vertex is at (0,0).

x = 1/2 × diameter

x = 1/2 × 48

x = 24

Now, we got two points (-24, 36) and (24,36). See the picture in the attachment!

By using the x and y value, the value of a is

x² = 4ay

24² = 4a(36)

576 = 144a

a = 576/144

a = 4 inches

Hence, the receiver is placed at 4 inches from the bottom of the dish.

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Answer:

Vertex: (2, -1)

Axis of Symmetry: x=2

Parabola: Downwards

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

(3*2)^2

3*2=6

6^2=36

Answer:

36

Step-by-step explanation:

(3x2)^2
6^2

36

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The statement about That by increasing the sample size, the amount of sampling error will be decreased is true.

Given that,

That by increasing the sample size, the amount of sampling error will be decreased

Sampling error is inversely related to sample size. Therefore, if we expand the size of our sample, the likelihood of sampling error is reduced and the results are more trustworthy. The standard error is the term used to describe the sampling error that is most frequently utilized (SE). A measurement of the range of estimations around the "actual value" is the standard error. You get a lower return by increasing the sample size beyond what you already have because the added accuracy won't make much of a difference.

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Deep foundations are recommended for larger or hillside developments , or those on poor soil .

Foundation Systems in Building

There are two classifications of foundations in building shallow foundations and deep foundations . These categories refer to the depth of soil in which the foundation is formed .

Shallow Foundations : Shallow foundations are usually located less than six feet below the lowest finished floor of a structure.

Deep Foundations : Deep foundations are structural elements that are used to transfer loads from weak and compressible soils to a stronger layer, usually located at a significant depth below the ground.

Recommendation

A shallow foundation can be constructed in as little as a one-foot depth , whereas a deep foundation is formed at a depth of 10 - 300 feet . Deep foundations are recommended for larger or hillside developments , or those on poor soil .

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Answer:

Step-by-step explanation: A shallow foundation distributes loads from the building into the upper layers of the ground.

Shallow foundations perform very well on sites with strong soils, sufficiently thick natural gravel rafts overlying weaker soils or where robust, engineered ground improvement is carried out.

Deep foundations can provide a good foundation for houses on sites with poor soil conditions near the surface,

The Answers is 90

Step-by-step explanation: Imagion taking 4 DE and make a square out of it. All sides of a square is 90 degress so De is 90 degress

Answer:

B, E

Step-by-step explanation:

3 meters is 300 centimeters so that eliminates A and D since they are lower and we know E is higher than 300

Now to find if B and C are higher since they both are 2 meters is we make 3 meters look like this it will be

2 meter 100 centimeters and b is the only one greater

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The dimensions of the box that minimize total cost are height h =3.17m, width, w and length, l=9.52m  are equal to  .

Let h is the height of the box.

Given Volume of the box is 216 m³  with no top.

And the cost of the bottom is 40USD/m².

For the sides, it is 30USD/m².

The bottom of the box is square, so l = w.

So Volume

[tex]V=hl^{2}[/tex]

[tex]216=hl^{2}[/tex]

[tex]h=\frac{216}{l^{2} }[/tex]

Now Surface Area of the box without a top is

S = 4hl + l²

So,

cost = 4 × 30hl +40l²

cost = 120 hl + 40 l²

Putting h ,

cost = 120 × [tex](\frac{216}{l^{2} })l + 40l^{2}[/tex]

cost = [tex]\frac{25960}{l^{2} }+40l^{2}[/tex]

To find minimum cost, derivate the  by using the calculator at

[tex]l=3\sqrt[3]{4}[/tex]

l=4.762203 m

[tex]h=\frac{216}{4.762203^{2} }[/tex]

h = 9.5244069354 m

Hence the dimensions of the box are

l=w

 =9.52 m

and height ,h=3.17 m  

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The correct option A, 266. 9 cm²;  total surface area of the cone given in figure is found as 266.9 sq cm.

For the given question.

Put values -

Total surface area = πr (h + r)

Total surface area = 3.14 x 5 (12 + 5)

Total surface area = 3.14 x 5 x 17

Total surface area = 266.9 sq cm.

Thus, total surface area of the cone given in figure is found as 266.9 sq cm.

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