On a particular airline, bags checked in must weigh less than 50 pounds. Betty packed 32 pounds of clothes and five gifts that weigh the same amount. Which inequality can be used to find the possible weight, w, of each gift.
(A) x + 32 < 50
(B) 5x + 32 < 50
(C) 5 + x + 32 < 50
(D) x/5 + 32 < 50

Answer:

12.87%

Step-by-step explanation:

To identify the % of their monthly income is spent on entertainment we use following formula

Total Budget of Entertainment / Total Net Income

$399/$3,100*100

12.87%

Answer:

Area of Trapezoid is 39 unit²

Step-by-step explanation:

Given as :

For A Trapezoid

The measure of base side 1 = [tex]b_1[/tex] = 10 unit

The measure of base side 2 = [tex]b_2[/tex] = 16 unit

The height of the Trapezoid = h = 3 unit

Let  The Area of Trapezoid = A square unit

Now, From Formula

Area of Trapezoid = [tex]\dfrac{1}{2}[/tex] × (sum of opposite base) × height

I.e A =  [tex]\dfrac{1}{2}[/tex] × ([tex]b_1[/tex] + [tex]b_2[/tex]) × h

Or, A =  [tex]\dfrac{1}{2}[/tex] × (10 unit + 16 unit) × 3 unit

Or, A =  [tex]\dfrac{1}{2}[/tex] × (26 unit) × 3 unit

Or, A =  [tex]\dfrac{1}{2}[/tex] × 78 unit²

Or, A = [tex]\dfrac{78}{2}[/tex] unit²

I.e A = 39 unit²

So, The Area of Trapezoid = A = 39 unit²

Hence, The Area of Trapezoid is 39 unit² . Answer

Answer:

The slope of AB is [tex]\frac{4}{3}[/tex], the slope of BC is [tex]- \frac{2}{7}[/tex], the slope of CD is [tex]\frac{4}{3}[/tex], and the slope of AD is [tex]- \frac{2}{7}[/tex], Quadrilateral ABCD is a parallelogram because both pair of opposite sides are parallel.

Step-by-step explanation:

The quadrilateral ABCD has vertices A(-5,1), B(-2,5), C(5,3) and D(2,-1).

Now, slope of line AB = [tex]\frac{5 - 1}{- 2 - ( - 5)} = \frac{4}{3}[/tex]

Slope of line BC = [tex]\frac{3 - 5}{5 - (- 2)} = - \frac{2}{7}[/tex]

Slope of line CD = [tex]\frac{- 1 - 3}{2 - 5} = \frac{4}{3}[/tex]

And slope of DA = [tex]\frac{1 - ( - 1)}{- 5 - 2} = -\frac{2}{7}[/tex]

Therefore, the slope of AB is [tex]\frac{4}{3}[/tex], the slope of BC is [tex]- \frac{2}{7}[/tex], the slope of CD is [tex]\frac{4}{3}[/tex], and the slope of AD is [tex]- \frac{2}{7}[/tex], Quadrilateral ABCD is a parallelogram because both pair of opposite sides are parallel. (Answer)

Answer:

The slope of AB is 4/3, the slope of BC is -2/7, the slope of CD is 4/3, and the slope of AD is -2/7. Quadrilateral ABCD is a parallelogram because both pairs of opposite sides are parallel.

Step-by-step explanation:

Answer:

C : 40%

Step-by-step explanation:

20 ÷ 50 = 0.40 also to solve just divide the smaller number from the greater number in order to be able to get the correct percentage.

Answer:

Step-by-step explanation

is / of = % / 100.....proportion formula

20 is what percent of 50...

20 / 50 = x / 100

cross multiply

50x = 2000

x = 2000/50

x = 40.......so 20 is 40% of 50

Answer:

y+1=5(x+2)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-1)=5(x-(-2))

y+1=5(x+2)

Answer:

Step-by-step explanation:

1 - 25 (a+b)^2 = 1 - 5² (a+b)²

= 1 - (5*[a + b) ]²                    { [tex]a^{m} *a^{n}  = a^{m+n}[/tex] }

= 1 - (5a +5b)²

= (1 + 5a +5b) (1 - [5a + 5b])      { a² - b² = (a + b)(a - b)   }

=(1 + 5a +5b) (1- 5a - 5b)

Answer:

The equation of the line is 2 x +3 y = 15.

Step-by-step explanation:

Here the given points are ( -3, 7) & ( 3, 3) -

Equation of a line whose points are given such that

[tex]x_{1}, y_{1}[/tex] ) & ( [tex]x_{2}, y_{2}[/tex] )-

 y - [tex]y_{1}[/tex]   =  [tex]\frac{ y_{2} - y_{1} }{ x_{2} - x_{1} }[/tex]   ( x - [tex]x_{1}[/tex]  )

i.e.  y - 7= [tex]\frac{3 - 7}{3 - (-3)}[/tex]  ( x- (-3))

      y - 7 =  [tex]\frac{-4}{3 + 3}[/tex] ( x + 3 )

      y - 7= [tex]- \frac{2}{3}[/tex]  ( x + 3 )

      3 ( y - 7)  =  - 2 ( x + 3)

      3 y -21 = -2 x - 6

      2 x + 3 y = 21 - 6

      2 x + 3 y = 15

Hence the equation of the required line whose passes trough the points ( - 3, 7) & ( 3, 3)  is 2 x + 3 y = 15.

Answer:The reasonable time for the base ball to land on the ground is 5 seconds

Step-by-step explanation:

To get the time we will differentiate

h(t) = -16t2 + 80t + 224, w.r.t t

dh(t)/dt= 0

-32t +80=0

32t=80

t=80/32

t= 2.5 seconds This is the time the base ball has been in the air

The reasonable time for it to take the baseball to land on the ground is T= 2×t

T= 2×2.5

T=5 seconds

Answer: 37

Step-by-step explanation:

if n=24

n+13 becomes 24+13

24+13 = 37

The value of the expression is 37.

An expression in mathematics is a set of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

Given the expression n+13

Substitute the value of n the given expression.

24+13 = 37

Hence the value is 37.

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Answer:

The sum of any two supplementary angles is 180⁰. If you have been given a task to that one angle measures 120⁰ and have to find its supplement, you will compute as ⇒ 180⁰ - 120⁰ = 60⁰. So, the missing will be 60⁰.

Step-by-step explanation:

Let us consider the m∠MON = 45⁰, as shown in figure a. As straight line measure 180⁰, and the sum of any two supplementary angles is 180⁰. So, 180⁰ - 45⁰ = 135⁰ ⇒ m∠MOL = 135⁰.

So, the supplement of m∠MON = 45⁰ is m∠MOL = 135⁰.

Keywords: supplementary angle, angle measure

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Answer:

The 10th term from the end of the AP is 39 th term

[tex]\therefore a_{39} =114[/tex]

Step-by-step explanation:

Given:

Arithmetic Sequence as

7 , 10 , 13........154,157

∴ First term = a₁ = 7

Second term = a₂ = 10

∴ Common Difference = d = a₂ - a₁ = 10 - 7 = 3

∴ d = 3

[tex]a_{n} = 157[/tex]

To Find:

[tex]a_{10} = ?[/tex]

Solution:

An equation for the nth term of the arithmetic sequence is given by

[tex]a_{n} =a_{1} + (n-1)\times d[/tex]

Substituting  a₁  and d  and we get

[tex]157=7+(n-1)\times 3\\150=3n-3\\\\3n=147\\n=\frac{147}{3}\\\\n=49\\[/tex]

There are 49 terms in given AP

Therefore the 10th term from the end will be 39th term

[tex]a_{39} =a_{1} + (39-1)\times 3=7+38\times 3=114[/tex]

[tex]\therefore a_{39} =114[/tex]

Answer:

2(x-8) < -20

Step-by-step explanation:

Answer:

x = a number

2(x - 8) < -20

When a triangle is translated, the resulting triangle will be congruent to the original triangle.

The congruency statement is ABCD = ZYXW

From the complete question, corresponding points are:

This means that:

Hence, the congruency statement is ABCD = ZYXW

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Answer:

The measure of the third angle is a 90 degrees

Step-by-step explanation:

Let

A and B ----> two complementary angles in a triangle

C ---> the measure of the third angle in a triangle

we know that

If two angles are complementary, then their sum is equal to 90 degrees

so

[tex]A+B=90^o[/tex] ---> equation A

Remember that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

[tex]A+B+C=180^o[/tex] ----> equation B

substitute equation A in equation B

[tex](90^o)+C=180^o[/tex]

solve for C

subtract 90 degrees both sides

[tex]C=180^o-90^o[/tex]

[tex]C=90^o[/tex]

therefore

we have a right triangle

The rate at which the vehicle can travel is 6 miles per gallon

Solution:

Given that experimental vehicle is able to travel [tex]\frac{3}{8}[/tex] mile on [tex]\frac{1}{16}[/tex] gallon of water

To find: Rate at which the vehicle can travel, in miles per gallon of water

distance traveled in miles = [tex]\frac{3}{8} \text{ miles }[/tex]

gallon of water = [tex]\frac{1}{16} \text{ gallons }[/tex]

Miles per gallon is given as:

[tex]\text{ miles per gallon }=\frac{\text{ distance traveled in miles}}{\text{gallon of water }}[/tex]

Substituting the given value we get,

[tex]\rightarrow \frac{\frac{3}{8}}{\frac{1}{16}}\\\\\rightarrow \frac{3}{8} \times \frac{16}{1}\\\\\rightarrow 3 \times 2 = 6[/tex]

So the rate at which the vehicle can travel, in miles per gallon of water is 6 miles per gallon

Answer: The answer is 5.2 (rounded to the nearest tenth)

Actual Answer: 5.19615242

Hope this helps!

Answer:

its the square root of 27 to the power of 2

Step-by-step explanation: hope this helps

Well, when your rounding by ones, if the ones place is lower than 5,  round lower. Like for example, 4 is lower than 5. So if you have 5,784, you have to round that 4 down to a 0. So it would be 5,780.

if it's higher that 5, like 7, you round up. Like for example, 507, you round it to 10, so 510.

Rounding up numbers involves looking at the digit to be dropped: if it's 5 or above, round up the last retained digit. Several examples like 31.57 up to 32 and 8.1649 down to 8.16 illustrate this process.

Rounding up a number involves several steps. Let's take a few examples:

(a) The number 31.57 rounds up to 32. Here, the dropped digit is 5, and the digit we keep or retain is even. Since our dropped digit is 5 or higher, we add one to the retained digit, thus getting 32.

(b) The number 8.1649 rounds down to 8.16. The dropped digit is 4, which is less than 5, so we do not add any to our retained number, getting 8.16.

These examples demonstrate that we are rounding to the nearest whole number or to certain decimal places depending on the precision needed in the problem. When the digit we are dropping is 5 or above, we round up the previous digit. If it is less than 5, we leave the previous digit as it is.

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We know that we can use y for "how much the job pays" and x for "hours of work."

Let's find how much the job pays in 1 hour by dividing.

25 / 2 = $12.5 per hour

We can mulitply x to 12.5 because this shows how much he earned.

An equation will look like 12.5x = y

Best of Luck!

The job pays $12.50 per hour. The equation to represent the pay, y, for x hours of work is 'y = 12.5x', which depicts direct proportionality.

To solve this question, you must first understand that the job pays $25 for every 2 hours worked. Therefore, to find out how much the job pays for x hours of work, you'd simply multiply the rate per hour ($12.50, since $25 divided by 2 is $12.50) by x hours.

The equation that represents how much the job pays, y, for x hours of work is: y = 12.5x.

Here, 'y' denotes the total payment received and 'x' is the number of hours worked. This format is commonly used in equations representing direct proportionality, where one variable (in this case, pay) changes directly as the other (hours worked).

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Answer:

all work is shown and pictured

Answer:

OPTION A

Step-by-step explanation:

Roots of a function can be determined from the graph by the point which cuts the x - axis.

Here, (-4, 0) and (2, 0) are the points that cut the x - axis.

That means, the roots should have been x = -4, 2.

So, from the options, we see that OPTION A has roots f(x) = (x + 4)(x - 2)².

Since, it is a parabola, we have (x - 2)².

Note that f(-4) = 0 and

f(2) = 0.

Hence, OPTION A is the answer.

I am not sure if i understand that 3600 is the cost of all the bikes they have bought in total, but they would have to sell 31 bikes to break even.

Answer:

1/36

Step-by-step explanation:

3(1/3)=3/3=1

2*3=6

(1/6)^2=(1/6)(1/6)=1/36

Answer:

The maximum value of C is 14

Step-by-step explanation:

we have the following constraints

[tex]x\geq 0[/tex] ----> constraint A

[tex]y\geq 0[/tex] ---> constraint B

[tex]2x+2y\leq 10[/tex] ---> constraint C        

[tex]3x+y\leq 9[/tex] ---> constraint D

Determine the area of the feasible region using a graphing tool

see the attached figure

The vertices of the feasible region are

[tex](0,0),(0,5),(2,3),(3,0)[/tex]

To find out the maximum value of the objective function C, substitute the value of x and the value of y of each vertices in the objective function an then compare the results

we have

[tex]C=4x+2y[/tex]

For (0,0) ----> [tex]C=4(0)+2(0)=0[/tex]

For (0,5) ----> [tex]C=4(0)+2(5)=10[/tex]

For (2,3) ----> [tex]C=4(2)+2(3)=14[/tex]

For (3,0) ----> [tex]C=4(3)+2(0)=12[/tex]

therefore

The maximum value of C is 14

Answer:

I think its 500 each or its Love seat=500. Sofa=1000

Step-by-step explanation:

For 500 you would do 1500/3 because sofa is double+love seat. So each would cost 500 if you divide it by 3. So the sofa would be 1000. The love seat would be 500. 1000+500=1500.

Hope this helps!!

Final answer:

To determine the cost of the sofa and love seat, we create an equation from the given information. Solving for x, we find that the love seat costs $500 and the sofa, costing double, is $1000.

Explanation:

To solve the problem in question, let's call the cost of the love seat x. According to the information given, the sofa costs double the love seat, so the sofa's cost will be 2x. Together, the sofa and love seat cost $1500, which gives us the equation:

x + 2x = $1500

Combining like terms, we get:

3x = $1500

To find the value of x, we divide both sides of the equation by 3:

x = $1500 / 3

x = $500

This means the love seat costs $500. To find the cost of the sofa, we multiply the cost of the love seat by 2:

2x = 2 * $500

2x = $1000

Therefore, the sofa costs $1000, and the love seat costs $500.

============================================

How I got that answer:

The vertex is the lowest point of parabolas that open upward.

(h,k) = vertex

(h,k) = (-3,-1)

h = -3

k = -1

For each of the answer choices, a = 1.

The general template of a quadratic in vertex form is

y = a(x-h)^2 + k

Plug a = 1, h = -3, k = -1 into that equation. Simplify.

y = a(x-h)^2 + k

y = 1(x-(-3))^2 + (-1)

y = (x+3)^2 - 1

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h,k) is the vertex of the parabola. The provided equations have vertices at different points. You must match the vertex of your graph with the correct equation.

In order to find the equation of the graph in vertex form, we need to locate the vertex on the graph. The vertex form of a quadratic equation is y = a(x - h)² + k, where (h,k) is the vertex of the parabola.

Considering the options provided:

However, without a graph or specific vertex provided, we won't be able to define the equation of the graph precisely in vertex form. You need to match the vertex of your graph to one of the above options.

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The fir trees are 9 meters tall and the pine trees are 12 meters tall

Solution:

Let f be the height of one fir tree

Let p be the height of one pine tree

Given that combined height of one fir tree and one pine tree is 21 meters

So we get,

height of one fir tree + height of one pine tree = 21

f + p = 21 ----- eqn 1

Also given that height of 4 fir trees stacked on top of each other is 24 meters taller than one pine tree

height of 4 fir trees stacked on top of each other  = 24 + height of one pine tree

4f = 24 + p ---- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "f and "p"

From eqn 1,

f = 21 - p ----- eqn 3

Substitute eqn 3 in eqn 2

4(21 - p) = 24 + p

84 - 4p = 24 + p

-4p - p = 24 - 84

-5p = - 60

Substitute p = 12 in eqn 3

f = 21 - 12 = 9

Summarizing the results:

height of one fir tree = 9 meters

height of one pine tree = 12 meters

Answer:

4.0

Step-by-step explanation:

AB / AC = AE / AD

1 / 4.5 = AE / 18

4.5 AE = 18

AE = 4.0

Since BE and CD are parallel, triangles ABE and ACD are similar, meaning their side lengths are proportional.

AC = AB + BC = 1 + 3.5 = 4.5

The proportion of AB to AC (corresponding sides of two similar triangles) is 1 / 4.5

Let x be the variable that represents the unknown length of AE

The proportion of AE to AD (another set of corresponding sides of two similar triangles) is x / 18

Since the triangles are similar, these two proportions must be equal.

1 / 4.5 = x / 18

Cross multiply

4.5x = 18

Divide both side by 4.5

x = 4

The length of AE is 4, no need to round since the answer is already a whole number.

Let me know if you need any clarifications, thanks!

Final answer:

To find the length of line segment GF in a right triangle EFG, you can use the Pythagorean theorem. Plug in the given values of the lengths of the legs EF and EG, and solve the equation to find the length of GF.

Explanation:

To find the length of line segment GF in a right triangle EFG, you can use the Pythagorean theorem. According to the Pythagorean theorem, the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In this case, the hypotenuse is line segment GF. Let's label the length of EF as x, and the length of EG as y.

Using the Pythagorean theorem, we can set up the following equation: x^2 + y^2 = GF^2.

Plugging in the given values, x = 9.4 and y = 6.8, we get: 9.4^2 + 6.8^2 = GF^2. Solving this equation will give us the length of line segment GF.

Answers:

1220 dollars invested at 5% interest rate.

2120 dollars invested at 10% interest rate.

===============================================

Explanation:

Label the two accounts A and B.

Account A earns 5% interest

Account B earns 10% interest

Brian invests x dollars in account A and x+900 dollars in account B.

Using the formula, i = P*r*t, we can compute the simple interest for both accounts

----------

Start with account A over the course of t = 1 year.

i = P*r*t

i = x*0.05*1

i = 0.05x

then compute the interest for account B (use t = 1 also).

i = P*r*t

i = (x+900)*0.10*1

i = 0.10x + 90

---------

Over the course of 1 year, Brian earns 0.05x dollars in interest with account A and also 0.10x+90 dollars in interest with account B.

In total he earns 0.05x+0.10x+90 = 0.15x+90 dollars in interest.

We're told this amount of interest he earns is $273, so,

0.15x+90 = 273

0.15x+90-90 = 273-90

0.15x = 183

0.15x/0.15 = 183/0.15

x = 1220

This means $1220 was invested at 5% interest.

x+900 = 1220+900 = 2120

and $2120 was invested at 10% interest.

---------

Check:

If you invested $1220 in account A, then you earn

i = P*r*t

i = 1220*0.05*1

i = 61 dollars in interest

If you invest $2120 in account B, then you earn

i = P*r*t

i = 2120*0.10*1

i = 212 dollars in interest

So you get a total of 61+212 = 273 dollars in interest from both accounts. This confirms the two answers.

Final answer:

The question involves setting up a system of equations to find out how much Brian has invested in each of his savings accounts — one with a 5% interest rate and the other with a 10% rate, given that the total interest earned is $273 and the difference in the amount in each account is $900.

Explanation:

Brian has money in two different savings accounts, one with a 5% interest rate and the other with a 10% interest rate. He has $900 more in the account with the higher interest rate, and the total interest earned from both accounts is $273. To solve the problem, we need to set up a system of equations.

Let x be the amount in the 5% account, therefore x + $900 will be the amount in the 10% account. Using the formula Interest = Principal × Rate × Time, and assuming the time is 1 year, we get two equations:

The sum of these two interests is $273, so we have:

Solving the equation, we find that x = $1,220 and x + $900 = $2,120. Therefore, Brian has $1,220 in the account with a 5% interest rate and $2,120 in the account with a 10% interest rate.