The number of students at Bedrock Middle School decreased to 90 % last year's number. Last year, there were 1,500 students. How many students are there this year?​

To solve 3x^2(9x)^0, simplify the expression inside the parentheses first, then multiply by 3x^2.

To solve the equation 3x2(9x)0, we can simplify the expression inside the parentheses first. Any number raised to the power of 0 is equal to 1. So, (9x)0 becomes 1. Now we have 3x2 * 1. Multiplying any number by 1 doesn't change its value, so the equation simplifies to 3x2.

Answer:

C and E repr. constant functions.

Step-by-step explanation:

C and E represent constant functions.  One can tell immediately by the fact that y remains the same even when x changes.

Answer:

The correct option is C and E.

Step-by-step explanation:

Constant functions is the function those output value(y) remains same for any input values(x).

Now consider the provided options.

Option A, B and D has different output value(y) for different the different input values(x)

Now consider the option C and E.

Option C and E has same output value(y) for different the different input values(x).

Therefore, the correct option is C and E.

Answer:

2.5

Step-by-step explanation:

if the distance to ET is 5 and l is closer to e it only makes sense for 2.5\

The given expression x - (-x) + y simplifies to 2x + y. None of the provided options are equivalent to the original expression, hence the answer is 'None of the above'.

The expression you're trying to simplify is x - (-x) + y. In mathematics, subtracting a negative number is the same as adding its positive counterpart. Therefore, the given expression simplifies to x + x + y, which is 2x + y.

It seems the original question was looking for an expression equivalent to x - (-x) + y from the given choices. Based on the simplification we just did, none of the provided choices (0 + y, y, none of the above) are equivalent to the original expression, 2x + y. Therefore, the correct answer is 'None of the above'.

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Answer:

Step-by-step explanation:

Total Number of animals = 23 + 27 = 50

Number of Dogs = 27

Percentage of dogs = [tex]\frac{27}{50}[/tex] × 100 = 54%

The percentage of dogs will be 54%.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Number of cats = 23

Number of dogs = 27

Now,

Total number of animals = 23 + 27

                                      = 50

And, Number of dogs = 27

Hence, The percentage of dogs = (27/50) × 100

                                                  = 54%

Thus, The percentage of dogs will be 54%.

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100% - 25% = 75%

$35 x 75/100 = $26.25

The sale price should be $26.25.

a shirt was original $35 and is now 25% off.

Since it is 25% off

So, it should be

= 100% - 25%

= 75%

Now the 75% of $35 should be $26.25.

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Answer:

D

Step-by-step explanation:

Since the triangle is right use the sine trig ratio to solve for x

noting that sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] ← exact value

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{8}{x}[/tex]

Multiply both sides by x

x × sin45° = 8 ( divide both sides by sin45° )

x = [tex]\frac{8}{sin45}[/tex] = [tex]\frac{8}{\frac{1}{\sqrt{2} } }[/tex] = 8[tex]\sqrt{2}[/tex]

Answer:

[tex]\sqrt{5}[/tex]

Step-by-step explanation:

Given

5 ÷ [tex]\sqrt{5}[/tex] = [tex]\frac{5}{\sqrt{5} }[/tex]

To simplify multiply the numerator/ denominator by [tex]\sqrt{5}[/tex]

= [tex]\frac{5}{\sqrt{5} }[/tex] × [tex]\frac{\sqrt{5} }{\sqrt{5} }[/tex]

= [tex]\frac{5\sqrt{5} }{5}[/tex] = [tex]\sqrt{5}[/tex]

Answer:  √5

Step-by-step explanation:

[tex]\dfrac{5}{\sqrt5}\bigg(\dfrac{\sqrt5}{\sqrt5}\bigg)=\dfrac{5\sqrt5}{5}=\large{\boxed{\sqrt5}}[/tex]

Answer:

8/27 yd³

Step-by-step explanation:

The equation for the volume of a cube of edge length s is V = s³.

If the edge length, s, is 2/3 yard, then the volume of this cube is:

V = (2/3 yd)³ = 8/27 yd³ (which corresponds to Answer C)

Answer:

208⅓ ft²

Step-by-step explanation:

The dimensions of Rachel's living room are 80 times the measurements on the scale drawing.

Calculate the width:

                                                                                     w = 80 × 1⅞

Convert the mixed number to an improper fraction     = 80 × 15/8

Cancel the 8s                                                                  = 10 × 15

                                                                                        = 150 in

Convert inches to feet                                                   = 150/12  

Convert the improper fraction to a mixed number      = (144 + 6)/12

                                                                                        = 12⁶/₁₂

Reduce the fraction to lowest terms                             = 12½ ft

Calculate the length

l = 80 × 2½  = 80 × 5/2 = 40 × 5 = 200 in = 200/12 = (192 + 8)/12

l = 16⁸/₁₂ = 16⅔ ft

Calculate the area

A = lw

A = 16⅔ × 12½

Convert the mixed numbers to improper fractions

A = 50/3× 25/2

Cancel the 2s

= 25/3 × 25

Multiply numerators and denominators                        

= 625/3

Convert the improper fraction to a mixed number    

= (624 + 1)/3

= 208⅓ ft²

The area of Rachel's living room is 208⅓ ft².

Answer:

x=-1/2

Step-by-step explanation:

4x-6=10x-3

Subtract 4x from each side

4x-4x-6=10x-4x-3

-6 =6x-3

Add 3 to each side

-6+3 =6x-3+3

-3 = 6x

Divide each side by 6

-3/6 = 6x/6

-1/2 =x

➷ 4x - 6 = 10x - 3

Add 3 to both sides:

4x - 3 = 10x

Subtract 4x from both sides:

- 3 = 6x

Divide both sides by 6:

x = -1/2

The correct answer would be B. x = -1/2

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Answer:

Step-by-step explanation:

[tex]2(x+2)+2=2(x+3)+1\qquad\text{use the distributive property}\\2x+4+2=2x+6+1\qquad\text{subtract 2x from both sides}\\6=7\qquad\boxed{FALSE}\to\text{no solution}\\===============================\\2x+3(x+5)=5(x-3)\qquad\text{use the distributive property}\\2x+3x+15=5x-15\\5x+15=5x-15\qquad\text{subtract 5x from both sides}\\15=-15\qquad\boxed{FALSE}\to\text{no solution}\\===============================\\46x+3=x+12\qquad\text{subtract x from both sides}\\45x+3=12\qquad\text{subtract 3 from both sides}\\45x=9\qquad\text{divide both sides by 45}\\x=\dfrac{9}{45}\to x=\dfrac{1}{5}\to\text{one solution}\\===============================\\4-(2x+5)=2(4x-2)\qquad\text{use the distributive property}\\4-2x-5=8x-4\\-2x-1=8x-4\qquad\text{subtract 8x from both sides}\\-10x-1=-4\qquad\text{add 1 to both sides}\\-10x=-3\qquad\text{divide both sides by (-10)}\\x=0.3\to\text{one solution}\\===============================\\5(x+4)-x=4(x+5)-1\qquad\text{use the distributive property}\\5x+20-x=4x+20-1\\4x+20=4x+19\qquad\text{subtract 4x from both sides}\\20=19\qquad\boxed{FALSE}\to\text{no solution}[/tex]

Answer:

A, B, E

Step-by-step explanation:

Answer:

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Step-by-step explanation:

Answer:

The simplified form of n to the -6th power times p to the 3rd power is p^3/n^6.

Step-by-step explanation:

For this case we have that by definition of properties of powers, it is fulfilled that:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

We have the following expression:

[tex]n ^ {- 6} * p ^ 3[/tex]

We can rewrite it as:

[tex]\frac {p ^ 3} {n ^ 6}[/tex]

Finally:

[tex]n ^ {- 6} * p ^ 3 = \frac {p ^ 3} {n ^ 6}[/tex]

Answer:

Option C

The length is 13 and width is 8

Let the length is L

Width will be L-5

Area of rectangle = Length x Width

Putting the values

104 = L x L-5

104=l(l−5)

Simplify both sides of the equation.

104=l²−5l

Subtract l²-5l from both sides.

104−(l²−5l)=l²−5l−(l²−5l)

−l²+5l+104=0

Factor left side of equation.

(−l−8)(l−13)=0

Set factors equal to 0.

−l−8=0 or l−13=0

l=−8 or l=13

We will take l = 13 because length cannot be negative

Now for width we know that w = l -5

So width is 13 -5 = 8

Answer:

4( \sqrt[3]{7x} )  is a like radical to  \sqrt[3]{7x}

Step-by-step explanation:

Answer:

The correct answer option is: Isabella should have divided the product of [tex]12\pi[/tex] and 9 by 3 to get [tex]V=\frac{12\pi (9)}{3}[/tex]

Step-by-step explanation:

We are given a diagram of a cone with height [tex] 9 cm [/tex] and area of the base (circle) [tex] 12 \pi   cm^ 2 [/tex].

Isabella uses the equation [tex] V = \frac { 1 } { 3 } ( 12 ) ^ 2 ( 9 ) \pi [/tex] and we are to find the error that she is making in finding the volume of this cone.

The volume of a cone is given by: [tex]\pi r^2\frac{h}{3}[/tex] out of which [tex]\pi r^2[/tex] represents the area of the base (circle).

Therefore, Isabella should have divided the product of [tex]12\pi[/tex] and 9 by 3 to get [tex]V=\frac{12\pi (9)}{3}[/tex].

The answer is in fact D or Isabella should have divided the product of 12 Pie and 9 by 3 to get V=  12 Pie (9)/3

Answer:

1) The picture whose width = x and Length = (x + 8) feet

2) Width = 4 feet

   Length = 12 feet

Step-by-step explanation:

A rectangle has one side longer than the other.

Area of a rectangle = product of its sides.

                                  = length × width

Width = x feet

Length = (x + 8) feet

Area = 48

∴ x × (x + 8) = 48

   x² + 8x = 48

  x² + 8x + 4² = 48 + 4²

  (x + 4)² = 64

 x + 4 = √64

x = ±8 - 4

x = - 12        or x = 4

     Since length can not be negative, x = 4

∴ Width = 4 feet

   Length =4 + 8 = 12 feet

The dimensions of the rectangle where its area is 48 square feet and length is 8 feet more than width is 4 feet (width) and 12 feet (length). The question is set on algebra, calculation of area and understanding of shapes.

This problem falls under the category of algebra and involves understanding the concept of shapes, particularly rectangles, and calculation of their area.

We know, the area of a rectangle is calculated as the product of its length and width. Given that the area is 48 square feet and the length is 8 feet more than the width. Let's denote the width as 'w' and the length as 'w + 8'.

So, we can set up the equation as: w * (w + 8) = 48. Solving this quadratic equation will give us the values for 'w' and 'w + 8' or the dimensions of the rectangle.

If you factor the quadratic equation, you get (w - 4)(w + 12) = 0. Setting these factors to zero, we find that w = 4 or w = -12. Since width cannot be negative, the width is 4 feet. And the length, which is 8 feet more than the width, will be 4 + 8 = 12 feet.

For the picture representation, simply imagine or draw a rectangle. Label the shorter side as 4 feet (width) and longer side (length) as 12 feet.

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Answer:

Your answer would be the first option.

A right angle is 90 degrees

An obtuse angle is more than 90 degrees and that angle is more that 90 degrees

Answer:

x = 60°

Step-by-step explanation:

This is an equilateral triangle. All angles of this triangle are congruent and have a measure of 60°.

Other method.

We know: the sum of the measures of the angles of the triangle is equal to 180 °.

Therefore we have the equation:

x + x + x = 180°

3x = 180°           divide both sides by 3

x = 60°

Answer:

Answer (a): Area of garden [tex]= 4x^2+12x+9[/tex]

Answer (b): Area of the square garden and the walkway =  [tex]16x^2+24x+9[/tex]

Step-by-step explanation:

Answer (a):

From given picture we see that Length of the garden = 2x+3

Width of the garden = 2x+3

Then area of the square garden = (Length)(Width)

[tex]= (2x+3)(2x+3)[/tex]

[tex]= 4x^2+6x+6x+9[/tex]

[tex]= 4x^2+12x+9[/tex]

Answer (b):

From given picture we see that width of the walkway = x

Then length of the garden including walkway =x + (2x+3) +x=4x+3

Similarly width of the garden = 4x+3

Then area of the square garden and the walkway = (Length)(Width)

[tex]= (4x+3)(4x+3)[/tex]

[tex]= 16x^2+12x+12x+9[/tex]

[tex]= 16x^2+24x+9[/tex]

Answer:

m∠1 = (a + b) you will also need to divide the sum by 2

Step-by-step explanation:

The measures of angles formed by intersecting chord can be found by adding their arc measures and dividing in 2.

In this case, m< 1 = 1/2 ( a + b).

Based on the angle of intersecting chords theorem, the equation of that can be used to solve m∠1 is: m∠1 = 1/2(a + b).

The angle of intersecting chords theorem states that the measure of any of the vertical angles formed when two chords intersect equals half of the sum of the two intercepted arcs.

Therefore, based on the angle of intersecting chords theorem, the equation of that can be used to solve m∠1 is: m∠1 = 1/2(a + b).

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Answer:

B option. AB is larger than FD

Step-by-step explanation:

The rule which must be remembered here is:

The side opposite to the larger angle will be larger in measure. We have to compare two sides that are opposite to two angles 72 and 65.

So using the above rule we can say that side opposite to angle 72 will be greater in measure than the side opposite to 65.

The side opposite to 72 is AB and side opposite to 65 is FD.

Therefore, we can conclude that AB is larger in measure than FD, which makes option B as the correct answer,

Answer:

The correct answer option is AB is longer than FD.

Step-by-step explanation:

We are given two triangles, ΔABC and ΔDEF, where AC ≅ FE and BC ≅ DE.

One out of three angles is known for each triangle: ∠ACB = 72° and ∠DEF = 65° and we are to determine which of the statements is correct about AB and FD.

We know that the side opposite to the bigger angle is longer. Since ∠C = 72° is greater than ∠E, therefore side AB is longer than FD.

Answer:

option C

Step-by-step explanation:

Given table is a linear function when the change in y to change is x is a constant.

From the tables, difference of x is a constant 1

Lets look at the difference of y values

First table

We find the change in y values

[tex]-6+2=-4[/tex]

[tex]-2+6=+4[/tex]

the difference is not a constant. So it is not a linear

Second table

[tex]-5+2=3[/tex]

[tex]-9+5= 4[/tex]

the difference is not a constant. So it is not a linear

Third table

[tex]-10+2= -8[/tex]

[tex]-18+10=-8[/tex]

[tex]-26+18= -8[/tex]

the difference is a constant. So it is a linear function.

Answer:

False

Step-by-step explanation:

The measures of a right-angle are;

A right triangle has a 90° angle and two acute angles and the sum of angles should add up to 180°. The leg angles could be  45 to form an  °isosceles triangle.

Answer the anser is 3

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Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

-1 2/7 x 1/6 = -0.21

Final Answer:

The population is the total number of students in the school.

Explanation:

The gym teacher's inquiry regarding the number of students playing a sport pertains to a subset of the larger student body. In statistical terms, the 20 students she questioned represent a sample.

The population, in this context, encapsulates the entirety of students attending the school, irrespective of whether they were asked about their sports participation or not.

When the gym teacher approached 20 students throughout the day, she was essentially drawing information from a limited group within the school. The population, however, extends beyond these 20 individuals to encompass every student enrolled in the institution.

This broader set includes students who might not have been present that day or were not approached by the teacher for their input. Determining the population aids in understanding the context and scale of the sampled data.

For instance, if the gym teacher's goal is to ascertain the percentage of students engaged in sports activities, the population figure (total number of students) becomes crucial for accurate statistical inference.

Consequently, the teacher can use this information to make informed decisions or implement strategies that cater to the entire student body, considering the interests and involvement in sports across the school.

Answer:

30m^2

Step-by-step explanation:

Formula for the area of a triangle is b * h / 2.

Plug in the values for each variable.

6 * 10 / 2 = 30.

Answer:

A=30m^2

Step-by-step explanation:

area of a triangle equals Length*Height divided by 2

length equals 6 height equals 10

6*10=60    60/2=30    A=30m^2