5. In Jaden's town, the middle school has 443 more students than
the high school. If the middle school has 817 students, how
many students are at the high school?

Answer:

49/10

Step-by-step explanation:

when you plug in 490% into your calculator, it shlukd be 49/10.

Answer:

Step-by-step explanation:

49/10 divide the numerator and denominator by gif.490/100=2x5x7 with the power of two=2x5x7with the power of two /2x5 both with th power of two divided 2x5=7 with the power of two/2x5=49/10

Answer:

  f(3) = g(3)

Step-by-step explanation:

The graph shows f(3) = 6, and it shows g(3) = 6. Then ...

  f(3) = g(3)

To determine if two functions f and g are equal at certain points, one must refer to their definitions or graphs. If f(x) and g(x) are defined as x², they are the same function as they produce identical outputs for any numerical input.

The student's question pertains to function comparison and the evaluation of these functions at specific points. The statement "f(6) = g(3)" implies that the value of the function f when x is 6 is equal to the value of function g when x is 3.

The answer to the question will rely on the specific definitions or graphical representations of the functions f and g, provided in the original question or accompanying materials.

For the functions defined by f(x) = x² and g(s) = s², f and g are indeed the same function since they both return the square of their input, regardless of the variable used to represent that input.

Since both function names are simply placeholders for the operation being performed (squaring), f and g yield the same output for any identical numeric input.

Based on the examples in the reference information, we can see that two different functions could have the same graph if they result in the same set of points on a Cartesian plane. This would make them the same function in the context of their graphical representation.

Answer:

Step-by-step explanation:

y + 31 = 19....subtract 31 from both sides

y = 19 - 31

y = - 12 <===

Answer:

Actual mean: 223 pages

Predicted mean / estimate: 225 pages

Explanation below

Step-by-step explanation:

Mean = total amount ÷ # of numbers

155 + 214 + 312 + 198  + 200 + 170 + 250 + 260 + 215 + 256

Add

2,230

# of numbers = 10

2,230 ÷ 10 = 223

The exact mean is 223

If I were to predict the mean, I would say that a good estimation would be around 225, because I see that the highest number in the data set is 312, and the lowest is 155. If 312 is rounded down to 300, and 155 is rounded down to 150, the number exactly in the middle of 300 and 150 is 225.

Actual mean: 223 pages

Predicted mean: 225 pages

Hope this helps :)

The simplified expression is:

[tex]g(x)-f(x) = x^2-6x-1[/tex]

Solution:

Given that the expression is:

[tex]g(x) - f(x) = (x^2-x+3)-(5x+4)[/tex]

We have to simplify the expression

The expression can be simplified by combining the like terms

Like terms are terms that have the same variables and powers. The coefficients do not need to match

From given,

[tex]g(x) - f(x) = (x^2-x+3)-(5x+4)\\\\Remove\ the\ paranthesis\ and\ solve\\\\g(x) - f(x) = x^2-x+3-5x-4\\\\Combine\ the\ like\ terms\\\\g(x)-f(x) = x^2-x-5x+3-4\\\\Add\ the\ like\ terms\\\\g(x)-f(x) = x^2 -6x + 3 - 4\\\\Add\ the\ constants\\\\g(x)-f(x) = x^2 -6x -1[/tex]

Thus the expression is simplified

Option C:  ∠2 and ∠8

Option E: ∠3 and ∠5

Solution:

Two parallel lines cut by a transversal.

Option A: ∠5 and ∠4

∠4 is not interior of parallel lines.

Hence it is not true.

Option B: ∠6 and ∠5

∠6 is not interior of parallel lines.

Hence it is not true.

Option C: ∠2 and ∠8

∠2 and ∠8 lies in the interior of the parallel lines.

∠2 and ∠8 lies in alternate of the transversal line.

Therefore, ∠2 and ∠8 are alternate interior angles.

Hence it is true.

Option D: ∠8 and ∠1

∠1 is not interior of parallel lines.

Hence it is not true.

Option E: ∠3 and ∠5

∠3 and ∠5 lies in the interior of the parallel lines.

∠3 and ∠5 lies in alternate of the transversal line.

Therefore, ∠3 and ∠5 are alternate interior angles.

Hence it is true.

Therefore ∠2 and ∠8, ∠3 and ∠5 are alternate interior angles.

Alternate Interior angles are on the opposite side. The Pair of angles that are alternate interior angles are ∠2 and ∠8, ∠3 and ∠5.

When two parallel lines are cut by a transverse. the angles formed on the interior of the parallel lines, on the opposite sides of the transverse are known as the Alternate Interior Angle.

In the given figures, the angles that are formed on the inner side of the two parallel lines are ∠2, ∠3, ∠8, and ∠5. Since, for a pair of angles to be alternate interior angles, they must be on the opposite side of the transverse. Therefore, ∠2 and ∠8, ∠3 and ∠5 are the two pairs of alternate interior angles.

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Step-by-step explanation:

In parallelogram RECT is a rectangle,

EC = x + y , RT = 2x - y, RE = 2x + y and TC = 3x - 3

To find, the values of the variable = ?

∵ The opposite sides are equal.

∴ RE = TC and RT = EC

2x + y = 3x - 3

⇒ x - y = 3                   .......... (1)

Also,

2x - y = x + y

⇒ x - 2y = 0               .......... (2)      

Subtracting (1) from (2), we get

∴ x - y - (x - 2y ) = 3 - 0

⇒ x - y - x + 2y = 3

⇒ y = 3

Put y = 3 in equation (1), we get

x - 3 = 3  

⇒ x = 3 + 3 = 6

∴ x = 6 and y = 3

Thus, the values of the variable are 3 and 6.

Final answer:

The sum of 8/15 and 2/5 is 14/15, which is closer to 1 than to 0 or 1/2 after finding a common denominator and adding the fractions.

Explanation:

To determine whether 8/15 + 2/5 is closer to 0, 1/2, or 1, you need to first find a common denominator for the fractions. The least common denominator for 15 and 5 is 15. You can then rewrite the second fraction, 2/5, with 15 as the denominator by multiplying both the numerator and denominator by 3, which gives you 6/15.

Now add the two fractions:

8/15 + 6/15 = 14/15

This sum is very close to 1, but still less than 1. Therefore, 14/15 is closest to 1.

To conceptualize this, you can think about the fractions in terms of division: 8 divided by 15 is a bit more than half, and 2 divided by 5 is exactly 0.4, which is also slightly less than half. Their sum is thus nearly a whole but not quite there, clearly indicating it's closer to 1 than to 0 or 1/2.

Answer:

13.1mi

Step-by-step explanation:

Length(l) = 4.1mi

Breadth(b) = 2.5 mi

Perimeter of a rectangle = addition of all sides that is = l + l + b + b as a rectangle has 2 opposite equal length and also breadth.

Therefore perimeter = 4.1 + 4.1 + 2.5 + 2.5

= 8.1 + 5

=13.1 mi

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Answer:

13.2 mi

Step-by-step explanation:

Perimeter of a rectangle

= 2 (L + W)

From the question

L = 4.1

W = 2.5

Using the above formula , we have P = 2 (4.1 + 2.5)

Using the distributive property

2x4.1 + 2x2.5

8.2 + 5

13.2mi

Answer:

The cup can hold 235.5 cubic cm of popcorn.

Step-by-step explanation:

Given:

A cone shaped popcorn cup has a radius of 5 cm and a height of 9cm.

Use 3.14 as an approximation for pi.

Now, to find cubic cm of popcorn the cup can hold.

Radius ( r ) = 5 cm.

Height ( h ) = 9 cm.

π = 3.14 ( as per question ).

So, to get the cubic cm of popcorn the cup can hold we put formula of volume:

[tex]Volume = \pi r^2\frac{h}{3}[/tex]

[tex]Volume=3.14\times 5^2\times \frac{9}{3}[/tex]

[tex]Volume=3.14\times 25\times 3[/tex]

[tex]Volume=235.5\ cubic\ cm.[/tex]

Therefore, the cup can hold 235.5 cubic cm of popcorn.

Answer:

There would be 20 jars of creamy peanut butter.

Step-by-step explanation:

You have 100 jars of peanut butter divide that by 100. That would give you the amount for 1%. Multiply that by 20 for the 20% which will give you your answer of 20.

100/100=1

1*20=20

Number of creamy peanut butter jars is 20.

Final answer:

The factory made 20 jars of creamy peanut butter, which is calculated by finding 20% of the total 100 jars produced.

Explanation:

The student has asked how many jars of creamy peanut butter were made if a factory produced 100 jars and 20% of them contained creamy peanut butter. To find the answer, we simply need to calculate 20% of 100 jars.

Here is the calculation:

First, we convert the percentage to a decimal: 20% = 0.20.

Next, we multiply the total number of jars by this decimal: 100 jars × 0.20 = 20 jars.

Therefore, the factory made 20 jars of creamy peanut butter.

Answer:

55 square feet

Step-by-step explanation:

We can represent the area as a sum of two rectangles.

A = 8 * 5 + 5 * 3 = 40 + 15 = 55 square feet

Answer:

Step-by-step explanation:

Area of rectangle at top

length =5ft; breadth = 3 ft

Area = 5*3 = 15 sq.ft

Area of rectangle at bottom

length = 8ft ; breadth =8-3 = 5 feet

Area = 8*5 = 40 sq.ft

Area of the figure = 15 + 40 = 55 sq.ft

Answer:

x = - 1, x = 5

Step-by-step explanation:

Given

(x + 1)(x - 5) = 0

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 5 = 0 ⇒ x = 5

Answer:

Step-by-step explanation:

x+1*x-5=0

Since we know the answer to the equation is 0, that means that it doesn't matter if we multiply x, add to it, or subtract from it, it will all eventually become 0.

So:

            X=0

Answer:

Don't forget to include a ± sign in your equation once you have taken the square root. Next, if the coefficient of the squared term is 1 and the coefficient of the linear (middle) term is even, completing the square is a good method to use. Finally, the quadratic formula will work on any quadratic equation.

Step-by-step explanation:

x² + 4x = 15 can be solved best using the completing the square method.

2x(x−3)=0 can be best solved using the zero product property.

Answer:

i) Therefore option A is Correct.   Δ ECD   [tex]\sim[/tex] Δ ACB by the SAS ( Side Angle Side) Similarity Theorem.

ii) Yes it can be proven that ED || AB after proving that Δ ECD   [tex]\sim[/tex] Δ ACB

Step-by-step explanation:

i) CE = [tex]\frac{1}{2}[/tex] AC ..... given

ii)  CD =  [tex]\frac{1}{2}[/tex] CB .... given

iii)  Therefore [tex]\frac{CE}{AC} = \frac{CD}{CB} = \frac{1}{2}[/tex]

iv)  Angle ACB or ∠C is common to Δ ACB and Δ CED.

v) Therefore from the above 4 equations we can say that by

   SAS theorem the two triangles are similar , that is ,  Δ ECD   [tex]\sim[/tex] Δ ACB .

 Therefore option A is Correct.

 vi)  Yes it can be proven that ED || AB after proving that Δ ECD   [tex]\sim[/tex] Δ ACB.

Since Δ ECD   [tex]\sim[/tex] Δ ACB , therefore ∠CED = ∠CAB  and ∠CDE = ∠CBA.

Therefore we can say that ED is parallel to AB or that ED || AB.

Answer:

1. 8n + 4

2. 5x +13

3. X + 3

4. X - 6

5. 4x + 1

Step-by-step explanation:

1.

2n + 6 and 6n -2 so simply addition will be

2n +6 +6n -2

8n +4

2.

3x + 9 + 2x + 4

5x + 13

3.

3x + 5 - 2x -2

X +3

4.

4x + 3 - 3x -9

X -6

5.

6x + 2 - 2x -1

4x + 1

The value of x in the equation  2.14x - 12.18 = 5.76 is  8.38.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Given, we have to solve for x or find the value of x in the equation

2.14x - 12.18 = 5.76.

2,14x = 5.76 + 12.18.

2.14x = 17.94.

x = (17.94/2.14).

x = 8.38.

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Answer:

32,753

Step-by-step explanation:

If you multiply 7 x 7 you get 49

If you multiply 8 x 8 x 8 x 8 x 8 you get 32,768

If you multiply 8 x 8 you get 64

Next you add 49 and 32,768; you get 32,817

Then you subtract 32,817 - 64; you get 32,753

Hope this helped!

~Oreo!!

[tex] {7}^{2} + {8}^{5} - {8}^{2} = 49 + {8}^{5} - 64 \\ = {8}^{5} - 15 \\ = 32768 - 15 \\ = 32753[/tex]

Answer:

B

Step-by-step explanation:

Could be wrong

The length of KM is,

⇒ KM = 80 units

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

Line a is the perpendicular bisector of KM.

Now, We can formulate;

Two sides are isosceles triangle are equal.

Hence we get;

9x - 5 = 7x + 7

9x - 7x = 12

2x = 12

x = 6

Thus, The length of KL is,

KL = 6x + 4

KL = 6 x 6 + 4

KL = 40

So, The length of KM is,

⇒ KM = 2 KL

⇒ KM = 2 × 40

⇒ KM = 80 units

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Final answer:

In the expression 5x – 8(3y + 13) – 1: 5 is the coefficient of the first term, (3y+13) is a binomial, and –1 is the constant term.

Explanation:

The expression provided is 5x– 8(3y + 13) – 1, and we need to identify the roles of specific parts of each term:

In the first term, 5 is a coefficient.

In the second term, (3y+13) is a binomial.

In the third term, -1 is a constant.

To complete the statements for the given expression 5x – 8(3y + 13) – 1, we need to identify the components of each term:

1. In the first term:

Here, 5 is a coefficient because it is the numerical factor that multiplies the variable x. Coefficients indicate the quantity by which a variable is multiplied.

2. In the second term:

In this term, (3y+13) is enclosed within parentheses, making it a binomial. A binomial is an algebraic expression consisting of two terms separated by either a plus or a minus sign.

3. In the third term:

This term is a constant because it is a fixed numerical value that does not change. Constants can exist independently and do not involve any variables.

Complete question:

Use the given expression to complete the statements.

5x– 8(3y + 13) – 1

In the first term, 5 is a ____.

In the second term, (3y+ 13) is a ___.

In the third term, -1 is a ____.

Answer:17

Step-by-step explanation:trust me use mathaway;)  mathaway dot com

Answer:

x=-41/3, y=6 (-41/3, 6).

Step-by-step explanation:

3x+4y=-17

y=-6*-1

-------------------

3x+4y=-17

y=6

3x+4(6)=-17

3x+24=-17

3x=-17-24

3x=-41

x=-41/3

The arrangement with the lowest probability of occurrence to the event with the highest probability of occurrence is 0.2, 0.25, 0.7 and 0.87

Probability is the likelihood or chance that an event will occur. Mathematically;

Probability = expected outcome/total outcome

The probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles is 3/12 = 0.25

The probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples is 7/10 = 0.7

The probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens is 4/20 = 0.2

The probability of picking a golf ball from a box containing 2 tennis balls

and 13 golf balls is 13/15 = 0.87

From the probabilites above, the arrangement with the lowest probability of occurrence to the event with the highest probability of occurrence is 0.2, 0.25, 0.7 and 0.87

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It is a function

A function is a relation between two sets that associates to every element of a first, called set A, one and only one element of the second set, called set B. In other words, we can't have any element of the set A assigned to more than one element in the set B. Put another way, we can't have repeated elements of the first set. In this problem we have a relation given by the table:

[tex]\begin{array}{cc}x & y\\5 & -2\\7 & -2\\9 & -2\end{array}[/tex]

So the assignation is as follows:

[tex]5 \rightarrow -2 \\ \\ 7 \rightarrow -2 \\ \\ 9 \rightarrow-2[/tex]

As you can see every element of the set A (set x) is assigned to the same element in the set B (set y) but we have no repeated element in the first set, so this is a function.

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Answer:

1

Step-by-step explanation:

3(4x-2)=-6+12

12x-6=6

12x=6+6

12x=12

x=12/12

x=1

Answer:

False because -6+12= just 6 but the other expression is 10x

Step-by-step explanation:

HOPE it helps

Answer:

2(x+4)=6+x

Step-by-step explanation:

Let x be our variable.

We want to write about equation using x that gives us -2 as solution.

We can write many of such equation.

An example is:

[tex]2( x + 4) = 6 + x[/tex]We cross check.

Let us expand:

[tex]2x + 8 = 6 + x[/tex]

Group similar terms:

[tex]2x - x = 6 - 8[/tex]

Combine similar terms:

[tex]x = - 2[/tex]

Answer:

jufhjgcfhjcfjgjghfj

Answer: 4.5

Step-by-step explanation: because, 3x4=12 then you have 1.5 left and 1.5 is half of three so you would have .5 and you then add 4+.5 to get 4.5

Answer:

the answer is 4.5 h

Step-by-step explanation:

The transformer is 27.5 ft above the ground.

Solution:

The given image is like a triangle.

Angle 'L' represents the triangle is right triangle.

Use Pythagoras theorem to find the answer.

Base of the triangle = 12 ft

Hypotenuse of the triangle = 30 ft

Height of the triangle = x

Using Pythagoras theorem,

[tex]\text{Base} $^{2}+$ Height $^{2}=$ Hypotenuse $^{2}$[/tex]

[tex]12^2+x^2=30^2[/tex]

[tex]144+x^2=900[/tex]

Subtract 144  on both sides of the equation.

[tex]x^2=900-144[/tex]

[tex]x^2=756[/tex]

Taking square root on both sides.

[tex]x=27.5[/tex]

Hence the transformer is 27.5 ft above the ground.

Answer:

110.1

Step-by-step explanation:

So, we just need to figure out 734% of 15.

734% can be written as 734/100.

734*15=11010.

11010/100 = 110.1

In the photo, the beetle is 110.1 millimeters

Answer:

10 boxes in the top row.

192 boxes in entire display.

Step-by-step explanation:

Let n be the number of rows.

Given:

Total number of rows = 8

Boxes in bottom row = 38

And each row has four fewer boxes than the row below it.

Solution:

Part A:

We know that the bottom row has 38 boxes and each row has four fewer boxes than the row below it.

Using below function for determining the number of boxes in each rows.

[tex]f(n)=38-(8-n)4[/tex]

Where:

n = Number of row.

We need to find the boxes in the first row.

So, substitute n = 1 in above function.

[tex]f(1)=38-(8-1)4[/tex]

[tex]f(1)=38-7\times 4[/tex]

[tex]f(1)=38-28[/tex]

[tex]f(1)=10[/tex]

Therefore, 10 boxes in the top row.

Part B:

Total boxes in the entire display.

Using formula as given below to determine the sum of the boxes in entire display.

[tex]S_{n} = \frac{n}{2}(f(1)+f(n))[/tex]

Substitute n = 8, f(1) = 10 and f(8) = 38 in the above equation.

[tex]S_{8} = \frac{8}{2}(10+38)[/tex]

[tex]S_{8} = 4(48)[/tex]

[tex]S_{8} = 4\times 48[/tex]

[tex]S_{8} = 192\ boxes[/tex]

Therefore, 192 boxes in the entire display.