Jada was helping her cousin with his math homework. He was supposed to solve the equation 8 + x = 5. He said, "If I subtract
8 from both sides, I get x = 5-8. This doesn't make sense. You can't subtract a bigger number from a smaller number. If I have
5 grapes, I can't eat 8 of them!"
What do you think Jada could say to her cousin to help him understand why 5-8 actually does make sense?

The nth term of this quadratic sequence 3, 8, 15, 24, 35, … is 2n

An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.

Confirm if the sequence is quadratic and this is done by finding the second difference

Sequence = 3, 8, 15, 24, 35, …

1st difference = 5, 7, 9, 11

2nd difference = 2, 2, 2

Divide the second difference by 2, and let the value be a

2 ÷ 2 = 1

So the first term of the terms is [tex]n^{2}[/tex]

subtract [tex]n^{2}[/tex] from the sequence gives 2, 4, 6 , 8, 10

the nth term is 2n

Therefore, the nth term is 2n

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The expression that represents the amount of sodium per serving in the new soup is 0.67x milligrams.

The new soup recipe contains 33%, percent less sodium per serving than the old soup recipe. The old soup recipe contained x milligrams of sodium per serving.

The expression that can be used to represent the amount of sodium per serving in milligrams in the new soup can be computed as follows;

Old soup amount of sodium = x milligram

The new soup contains 33% less sodium per serving than the old soup recipe.

Therefore,

amount of sodium per serving in the new soup = x - 33% of x

amount of sodium per serving in the new soup = x - 33 / 100 x

amount of sodium per serving in the new soup = x - 0.33x

Therefore,

amount of sodium per serving in the new soup = x(1 - 0.33)

amount of sodium per serving in the new soup = x(0.67)

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The rate that Jacob would require to be able to end up with $17, 000 from $15, 000 after 6 years is  0.52%

To find the rate, you can use a spreadsheet. The relevant function would be the rate function.

Nper = Number of periods = 6 years x 4 quarters per year = 24 quarters

Pv = $15, 000

Fv = $17, 000

The interest rate required by Jacob would be given as:

= 0.005228753

= 0.52%

In conclusion, Jacob would require a periodic interest rate of 0.52%.

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In a school, 2/5 of the students participated in an organized outing. The students participated in the outing is 144 students.

Let X be the total number of student, then

Total number of students in the school = 380

X = 380

number of the students participated in an organized outing = 2/5

so, the number of the students are calculated as :

= X x (2/5)

= 380 x (2/5)

= 72 x 2

= 144 students

Participated student = 144

In a school, 2/5 of the students participated in an organized outing. The students participated in the outing is 144 students.

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Answer:

280 miles

Step-by-step explanation:

You drive your car for 4 hours at an average speed of 70 miles per hour. How far did you go?

70 * 4 = 280 miles

Answer:

length = 13 cm and width = 14 cm

Step-by-step explanation:

let n be the length then n + 1 is the width

the perimeter (P) of a rectangle is calculated as

P 2(l + w) ← l is length and w is width

given P = 54 , then

2(n + n + 1) = 54 ( divide both sides by 2 )

2n + 1 = 27 ( subtract 1 from both sides )

2n = 26 ( divide both sides by 2 )

n = 13

n + 1 = 13 + 1 = 14

length = 13 cm and width = 14 cm

The coordinates of the point will be (5 , 5).

Section formula is used to find coordinates of a point when a point divides the line segment externally or internally.

For a line segment A ([tex]x_{1} , y_{1}[/tex]) and B ([tex]x_{2} , y_{2}[/tex]) getting divided by point C (x , y) in ratio m : n the formula is given as

x = [tex]\frac{mx_{2} + nx_{1} }{m + n}[/tex]             y = [tex]\frac{my_{2} + ny_{1} }{m + n}[/tex]

Now in the question it is given that C from point A is twice the distance from point B which means ratio of A:B IS 2:1

A = (1 , 3)

B = (7 , 6)

by applying the formula

x = (2*7 + 1*1) / 2+1

x = 15/3

x = 5

y = (2*6 + 1*3) / 2+1

y = 15/3

y = 5

Therefore the coordinates of C will be (5 , 5)

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The value in dollars of a $3,000 investment after n years is given by f(n) = 3,000(1.05)n.

The value of the investment after 4 years is $12600.

A simple definition of an equation is a mathematical statement that depicts the relationship between two values. In an equation, the equal sign often equates the two values.

From this question we can assume that n = 4.

In the given equation,

F(n)= 3000(1.05)n

After putting the value of n which is 4, it will be:

F(4)= 3000(1.05) × 4 = 12600

Hence, the value of the investment after 4 years in $12600.

There are many different kinds of equations:

• Linear equation

o Equation with one variable

o Equation with two variables

o Equation with three variables

• Polynomial equation

o Monomial equation

o Binomial equation

o Polynomial equation

• Quadratic equation

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Step-by-step explanation:

both roots are square roots.

if we write the 2 or leave the base of the root blank, it both means square root.

so, we have

sqrt(15) / sqrt(3)

we can combine them into

sqrt(15/3) = sqrt(5) = 2.236067977...

The pair of triangles that can be used to show that the slope of line a is same everywhere is upper half triangles

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees

The total area that is bounded by a triangle's three sides is referred to as the triangle's area. In essence, it is equal to 1/2 of the height times the base, or A = 1/2 b h.

The pair of triangles in choice C (shown in the figure below) demonstrates that line a has a constant slope throughout.

Let's investigate:

Rise/run = slope

Regarding the initial lower triangle:

Rise = 3.5

Run = 4.5

Slope = 3.5/4.5 ≈ 0.8

For the upper second traingle:

Rise = 4

Run = 5

Slope = 4/5 = 0.8

As a result, it demonstrates that the graph's line's slope is constant throughout.

The pair of triangles that can be used to show that the slope of line a is same everywhere is upper half triangles

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Answer: 44 feets

Step-by-step explanation:

657-613= 44

as for the last question, i don't quite understand what it is asking but id say that grade 7 won since jill's friend jumped more than 6.5 feets

Drawing is Given There:

hence,Although two or more fields may be next to each other, they shouldn't have the same boundary (e.g., a sideline or a fence.)

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Answer:

Soccer field B was translated to the left and down. Soccer field C was rotated and translated down. D building was translated to the right and down. E building was translated to the right and down. Baseball field F was translated to the right and down. Baseball field G was rotated and then translated to the right and down. Baseball field H was rotated and then translated to the right and down. Baseball field I was rotated and then translated to the right. 

Step-by-step explanation:

Answer:

a number x times by 3

Step-by-step explanation:

yw I hope that helps

For the figure 7, the measure of each angle is:

a) m ∠1=131°

b) m ∠2=49°

c) m ∠3=92°

d) m ∠4=88°

e) m ∠5=92°

f) m ∠6=88°

g)  m ∠8=49°

h) m∠9=92°

i) m ∠10=88°

j) m ∠11=131°

k) m ∠12=49°

l) m ∠13=131°

m) m ∠14=49°

n) m ∠15=92°

For the figure 8,

a) m ∠1=12°

b) m ∠3=105°

c) m ∠4=12°

d) m ∠5= 63°

e) m ∠6=105°

f) m∠7=105°

g) m ∠8=105°

h) m ∠11=12°

i) m ∠12=168°

j) m ∠13=12°

k) m ∠14=168°

An angle in Euclidean geometry is the figure produced by two rays, called the sides of the angle, that have a common termination, called the vertex of the angle. Angles formed by two rays lie in the plane containing the rays. Angles are also generated by the intersection of two planes. These are referred to as dihedral angles. Two intersecting curves can also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection.

7) From the figure,

m ∠7=131°

m ∠7=m ∠1

m ∠1=131°

m ∠1+m ∠7+m ∠2+m ∠8=360°

131°+131°+ m ∠2+m ∠8=360°

m ∠2+m ∠8=360°-262°

m ∠2+m ∠8=98°

m ∠2=m ∠8

2m ∠2=98°

m ∠2=49°

m ∠8=49°

And also given that,

m ∠16= 88°

m ∠10=88°

m ∠10+m ∠16+m ∠9+m ∠15=360°

m ∠9+m ∠15=360°-176°

=184°

m ∠9=92°

m ∠15= 92°

m ∠11=m ∠7

m ∠11=131°

m ∠11=m ∠13

m ∠12= m ∠14=m ∠2= m ∠8=49°

m ∠10= m ∠16= m ∠6=m ∠4=88°

m ∠3=m ∠5= m∠9=m ∠15=92°

a) m ∠1=131°

b) m ∠2=49°

c) m ∠3=92°

d) m ∠4=88°

e) m ∠5=92°

f) m ∠6=88°

g)  m ∠8=49°

h) m∠9=92°

i) m ∠10=88°

j) m ∠11=131°

k) m ∠12=49°

l) m ∠13=131°

m) m ∠14=49°

n) m ∠15=92°

8) From the figure,

m ∠2=63°, m ∠9=105°

m ∠2=m ∠5= 63°

m ∠6+ m ∠5+m ∠4=180°

m ∠9= m∠7=m ∠6=m ∠3=105°

m ∠4=180°-63°-105°

m ∠4=12°

m ∠4=m ∠1= m ∠13=m ∠11=12°

m ∠11+m ∠13+m ∠12+m ∠14=360°

m ∠12=m ∠14

2m ∠12=360°-24°=336°

m ∠12=168°

m ∠12=m ∠14=168°

m ∠3=m ∠10=m ∠8=105°

a) m ∠1=12°

b) m ∠3=105°

c) m ∠4=12°

d) m ∠5= 63°

e) m ∠6=105°

f) m∠7=105°

g) m ∠8=105°

h) m ∠11=12°

i) m ∠12=168°

j) m ∠13=12°

k) m ∠14=168°

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Answer:  I checked all four of these equations using factoring and I get all of the SAME answers, except for #2 which is x=4 or -6. It looks like you had -4.

Good Job!

1) x=5 or x=−5

2) x=4 or x=−6

3) x=3 or x=−3

4) x=1/2 or x=−3

Step-by-step explanation:

The cost of materials for the least expensive such container is $327.081  .

In the question ,

it is given that

the volume of the container = 10 m³ .

let the width of the container = x

so , the length of the container = 2x

So , base area = 2x*x = 2x²

cost for base = $20

cost for the sides = $12

Since the volume is 10 m³

Volume = base area *  height

10 = 2x² * h

h = 10/2x²

h = 5/x²

The cost of making the container

cost of base = 2x² * (20) = 40x²

cost of sides = [2*2x*(5/x²) + 2*x*(5/x²)](12)

= 360/x

the total cost of the container [tex]=[/tex] cost of base [tex]+[/tex] cost of sides

= 40x² + 360/x

= 40( x² + 9/x)

to get the minimum cost , we differentiate with respect to x and equate to 0

= 40 ( 2x - 9/x²)

2x - 9/x² = 0

2x³ = 9

x³ = 9/2

x³ = 4.5

x = 1.651

Substituting x in the cost equation ,

we get

Cost = 40x² + 360/x

= 40(1.651)² + 360/(1.651)

= 109.032 + 218.049

= 327.081

Therefore , The cost of materials for the least expensive such container is $327.081  .

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Answer:

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

It has a variable x and its coefficient (-1), the 3 is the constant.

[tex]\Large \boxed{\sf -1}\\\\\\\displaystyle \sf A\ coefficient\ in\ an\ expression\ is\ the\ integer\\ value\ multiplied\ by\ the\ variable.\\\\(-1) \times x + 3[/tex]

Answer: B

Step-by-step explanation:

The slope of the line that passes through (3,4) and (2,-1) is 5/1 as a fraction

From the question, the points are given as

(3,4) and (2,-1)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (3,4) and (2,-1)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (3,4) and (2,-1)

Substitute the known values in the above equation

So, we have the following equation

Slope = (-1 - 4)/(2 - 3)

Evaluate the difference in the above equation

So, we have the following representation

Slope = -5/-1

Lastly, we evaluate the quotient

So, we have

Slope = 5

The solution is to be in fraction form

So, we have

Slope = 5/1

Hence, the slope of the line is 5/1

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Possible question

Calculate the slope of (3,4) and (2,-1) as a fraction

The equation which can be used to represent each situation, in terms of x, is;

A = 80 + 2x

B = 45 + 3x

The interval of miles driven, x, for which Company A is cheaper than Company B is when x = 35 miles

Let

Company A:

A = 80 + 2x

Company B:

B = 45 + 3x

Company B > Company A:

45 + 3x > 80 + 2x

collect like terms

3x - 2x > 80 - 45

x > 35

In conclusion, the interval of miles driven, x, for which Company A is cheaper than Company B is 35 miles.

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a) The bearing of Wellington from Gisborne is 232°

b) The bearing of Wellington from Auckland is  175.37°

We are given that AW = 410 km and GW = 400 km.

a) AG  is a transversal intersecting two parallel lines N₁A and N₂B and ∠N₁AG = 115°.

Thus;

∠AGN₂ = 180 − 115 = 65°  

since the sum of the interior angles on the same sides of the transversal intersecting two parallel lines are supplementary.

Thus;

∠N₂GW = 65 + 63 = 128°.

The reflex angle;

∠N₂GWW = 360 − 128° = 232°

b) In  △AGW, we can say that by the sine rule;

(sin∠WAG)/WG = (sin∠AGW)/AG  

Plugging in the relevant values;

(sin∠WAG)/400 = (sin∠63°)/410

Solving for ∠WAG gives; ∠WAG = 60.37°

Then;

∠N₁AW = 115 + 60.37

∠N₁AW = 175.37°

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Answer: The integral of the rate of change of a function is equal to the total change in the function.

Step-by-step explanation:

The rate of change of the volume of a sphere with the radius is. DV.

Answer:

1.90°

2.30°

3.60°

Step-by-step explanation:

calculate it using the distance and angle

which is division

Answer: 7

Step-by-step explanation: 2.9x - 12.3 = 8

2.9x= 8+12.3

2.9x=20.3

x=20.3/2.9

x=7

If a washer and dryer cost $750 and the cost of the washer is two times the cost of the dryer, then the cost of the dryer $250

The total cost of a washer and dryer combined = $750

The cost of the dryer = x

The cost of the washer is two times the cost of the dryer.

The cost of the washer = 2x

Then the equation will be

x + 2x = 750

Add the like terms of the equation

3x = 750

Move 3 to the right hand side of the equation

x = 750/3

x = $250

Hence, if a washer and dryer cost $750 and the cost of the washer is two times the cost of the dryer, then the cost of the dryer $250

The complete question is:

A washer and dryer cost $750 combined the cost of the washer is two times the cost of the dryer what is the cost of the dryer?

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A matrix is a form of writing items in rows and columns.

The value of [tex]c_{11}[/tex] is -3

The value of [tex]c_{12}[/tex] is 12

The value of [tex]c_{21}[/tex] is -36

The value of [tex]c_{22}[/tex] is 69

A matrix is a form of writing items in rows and columns.

[tex]C=\left[\begin{array}{ccc}c_{11}{&c_{12}\\c_{21}&c_{22}\end{array}\right][/tex]

We have,

[tex]A=\left[\begin{array}{ccc}0&-2\\4&7\end{array}\right][/tex]

[tex]B=\left[\begin{array}{ccc}3&-2\\6&-9\end{array}\right][/tex]

[tex]AB=\left[\begin{array}{ccc}3&-2\\6&-9\end{array}\right]\left[\begin{array}{ccc}3&-2\\6&-9\end{array}\right][/tex]

[tex]AB=\left[\begin{array}{ccc}(9-12)&(-6+18)\\(18-54)&(-12 + 81)\end{array}\right][/tex]

[tex]AB=\left[\begin{array}{ccc}-3&12\\-36&69\end{array}\right][/tex]

AB = C

[tex]C=\left[\begin{array}{ccc}-3&12\\-36&69\end{array}\right][/tex]

Now,

[tex]C=\left[\begin{array}{ccc}c_{11}{&c_{12}\\c_{21}&c_{22}\end{array}\right][/tex]

Thus,

The value of [tex]c_{11}[/tex] is -3

The value of [tex]c_{12}[/tex] is 12

The value of [tex]c_{21}[/tex] is -36

The value of [tex]c_{22}[/tex] is 69

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Expression equivalent to log 9⁵ is 5 log9.

Equivalent is not the same as equal in mathematics. While equivalent indicates similar but not the same, equal means the same in all respects. For instance, 1 + 1 is equivalent to 2, even if 2 is said to be equal to 2. Equivalent value or dated value refers to the value of an original sum at any given moment. The original amount and interest accrued up to the dated value date are combined to create the comparable payment. Money amounts are not directly comparable if they are payable or due at separate times.

Given,

Expression equivalent to log 9⁵

a) 5 log9

Expression equivalent to log 9⁵ is 5 log9.

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Number which produces an irrational number when multiplied by 1/2 is 2/3.

Any real number that cannot be written as the quotient of two integers, p/q, where p and q are both integers, is referred to as an irrational number. For instance, the square root of 2 cannot be expressed as an integer or a fraction. Additionally, if the value of the square root of 7 yields a value after the decimal point that neither terminates nor repeats, it will be an irrational number. The number 7 is an irrational number because its value, 2.64575131106, is non-terminating and non-repeating.

Given,

Number which produces an irrational number when multiplied by 1/2

We multiply 2/3 by 1/2

2/3 × 1/2

1/3

0.3333

which is an irrational number.

Number which produces an irrational number when multiplied by 1/2 is 2/3.

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The exponential generating function for the sequence of factorials is x! = Γ(x+1) = [tex]\int\limits^{infinity}_0 {t}^{x}{e}^{-t} \, dt[/tex].

We are given a sequence. A sequence in mathematics is an enumerated collection of items in which repetitions are permitted and order is important. It has members, just like a set. The length of the sequence is defined by the number of elements. The given sequence consists of factorials. The product of all positive integers less than or equal to n, denoted by n!, is the factorial of a non-negative integer n. We need to find the exponential generating function for the given sequence. The sequence is 0!, 1!, 2!, …, n!. The exponential generating function for the sequence of factorials is given below.

x! = Γ(x+1) = [tex]\int\limits^{infinity}_0 {t}^{x}{e}^{-t} \, dt[/tex]

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