There are 56 students going on a field trip to the science center. The students tour the center in groups of 8 how many groups of students are there

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:

fog functions are basically saying f(g(x)).

So (f o g)(x) = f(g(x)).

This is also true for gof functions.

(g o f)(x) = g(f(x)).

All we do for these problems is plug in g(x) into the x value in the f(x) equation.

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:

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:

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

Answer: The correct answer is 3.

Step-by-step explanation:

You need to write an equation to solve this problem, using x as the number of personal training sessions.

The equation to solve this problem is

35 + 25 x = 65 + 15x

First, subtract 35 from both sides:

25x = 30 + 15x

Subtract 15x from both sides:

10x = 30

The last step is to divide both sides by 10:

x = 3

You can then double check your work to make sure that the answer is correct:

35 + (25 x 3) = 110

65 + (15 x 3) = 110

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:

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

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:

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:

[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 the anser is 3

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Step-by-step explanation:

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]

➷ Error: When he divided both sides by the length, he didn't subtract the exponents. Instead on subtracting the exponents, he added them - which is incorrect.

Correct solution: 54x^9 y^8 / 6x^3 y^4 = 9x^6 y^4

The width is 9x^6 y^4

(This is based on the rule that when you divide values with exponents, you have to subtract the exponents)

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Answer:

Error: He added the exponents of the variables. The exponents must be subtracted.

Correct solution: [tex]w=9x^6y^4[/tex]

Step-by-step explanation:

According the quotient property of exponents, when you divide two powers with equal base, you must subtract the exponents.

Therefore, keeping the property above on mind, you have:

[tex]w=\frac{54x^9y^8}{6x^3 y^4}\\\\w=9x^{(9-3)}y^{(8-4)}[/tex]

Therefore, you have that the width of the rectangle is the shown below:

[tex]w=9x^6y^4[/tex]

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:

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:

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:

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

Answer:

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

Step-by-step explanation:

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°

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:

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:

5 dozen hot dogs

Step-by-step explanation:

Erica started with 80 dozen hot dogs.

At the end of the day on Wed, she had 75 dozen hot dogs (from the graph)

To determine what she sold, take what she started with and subtract what she ended with

80-75 = 5

She sold 5 dozen hot dogs

Answer: D) All of these are correct

Answer:

D. All of these are correct

Step-by-step explanation:

She needs four inches of ribbon and each spool has 24 inches, so we can write this equation like:

384/24 = s

where s is the number of spools.

If we divide 384 inches by the 24 inches each spool has she will get how many spools she needs.

Now having the equation: 384/24 = s, we can change it and it will mean the same.

384/24 = s  is the same as 24s = 384; just sending the 24 to multiply on the other side.

And it is the same as 384/s = 24 just sending the s to the other side dividing.

So all of the answers are correct they are just in different orders.

Answer:

(D) [tex]8.46\cdot 3.51^x[/tex]

Step-by-step explanation:

One could run this on a computer and verify the best fit through brute force. The more elegant way is, as usual, to think: What are special values of x for an exponential function? Zero, for starters - anything to the power of zero is 1. The function value for x=0 in the table is 10. Which choices A through D are close to 10 for x=0? Well, (C) and (D), the rest is too far. Next, what is the function value for the next easy one, x=1? The table says 30. Which of (C) and (D) is close to 30 for x = 1. It turns out we can safely exclude (C) because 10.84*1.77 is about 19 and that's way too far from 30. Let's check (D): 8.46*3.51=29.7 - that's quite close. Since there is no other candidate left, I bet my money on (D). Feel free to verify closeness for the other values of x if you are unconvinced yet.  

Answer:

[tex]\text{D. }y = 8.46(3.51)^{x}[/tex]

Step-by-step explanation:

The quickest way is probably to do some direct substitution.

First, let's try f(0).

The values of y predicted by the four equations are, respectively, 3.14, 5.32. 10.84, and 8.46.

It looks like C and D are the closest to the observed data.

Now, let's try f(4) on C and D.

C: 10.84(1.77)⁴ = 10.84 × 9.815 = 106.4

D:  8.46(3.51)⁴ =    8.46 × 151.4 = 1284

The best curve is [tex]y = 8.46(3.51)^{x}.[/tex]

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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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:

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:

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\