Question 1 of 10
Which of the following is the solution to | x1-2 ≤-3?
O A. All values are solutions
OB. xs-1 and x 25
OC. xs-1
OD. No solution

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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Answer:

Vertex: (2, -1)

Axis of Symmetry: x=2

Parabola: Downwards

Step-by-step explanation:

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 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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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 area of the shaded portion of the parallelogram is 35.43  centimeter square

The base of the parallelogram = 8 centimeter

The height of the parallelogram = 6 centimeter

The area of the parallelogram = Base × Height

= 8 × 6

= 48 centimeter square

The radius of the circle = 2 centimeter

The area of the circle = π × [tex]r^2[/tex]

= π × [tex]2^2[/tex]

= 12.57 centimeter square

The area of the shaded region = The area of the parallelogram - The area of the circle

Substitute the values in the equation

= 48 - 12.57

= 35.43 centimeter square

Hence, the area of the shaded portion of the parallelogram is 35.43  centimeter square

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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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The word problem including the given equation is mentioned below.

Given, a system of equations

x + y = 0

2x - y = 6

We have to make a word problem using the given system of equations.

Ram and Rahul are two friends and both attempt a test of 10 marks. Now, Ram prepared for the test whereas Rahul didn't prepared for the test and marked the wrong answers in the test. If negative marking is allowed in the test and it is given that, sum of the marks of both the students is zero. Also, twice the marks of Ram is 6 less than the marks of Rahul.

Find the marks of both the students.

Hence, the word problem including the given equation is mentioned above.

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Answer:

b

Step-by-step explanation:

In the given equation  4 - 2y + 3 = - 9, y is equal to 8.

The equation is a statement in which the values of two mathematical expressions are equal (indicated by the sign =).

To find the value of y from the given equation

∴  4 - 2y + 3 = - 9

=> 4+3 -2y = -9

=> 7 - 2y = -9

=> 7 + 9 = 2y

=> 16 = 2y

=> 16/2 = y

=> 8 = y

=> y = 8

So, the value of y in the above equation 4 - 2y + 3 = -9 is 8.

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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

Hopes this helps please mark brainliest

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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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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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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The net yardage the team had after those 4 plays is -32.

From the information, the football team averaged a loss of 8 yards in each of 4 plays.

In a situation where they did not gain any yards, the net yardage the team had after those 4 plays will be:

= Yards loss × Number of matches

= -8 × 4

= -32

This illustrates the concept of multiplication that was used to calculate the net yardage.

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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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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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Answer:

3.24759526401

Step-by-step explanation:

divide that

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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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,

i gotchu what do u want

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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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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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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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: D

Step-by-step explanation:

-7(-4-(4)(-6))

-7(-4-(4)(-6))

=140

To make 21 gallons of 3% disinfectant solution, 7 gallons of 5% solution are used, and 14 gallons of 2% solution are used.

21 gallons of the 3% solution is required.

Therefore, the amount of disinfectant in the solution

= 3/100  X  21 gallons

= 0.63 gallons

Let the amount of 5% disinfectant solution used be x

Therefore,

the amount of 2% disinfectant solution used is (21 - x)

Now, the amount of disinfectant added through these solutions must be equal to the amount of disinfectant in the solution.

Hence,

5/100 X x  +  2/100 X (21 - x) =  0.63

or, 5x/100 + (42 - 2x) / 100 = 0.63

or, 0.05x + 0.42 - 0.02x = 0.63

or, 0.03x = 0.63 - 0.42

or, 0.03x = 0.21

or, x = 0.21 / 0.03

or, x = 7

Therefore 21 - x = 14

Hence 7 gallons of 5% solution is used and 14 gallons of 2% solution is used.

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Answer:

7/65

Step-by-step explanation: