Lashonda bought a desk on sale for $159.60. This price was 62% less than the original price. What was the original price?

Answer:

The segment GT is a median of triangle GFH

Step-by-step explanation:

we know that

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.

The angle bisector of a triangle is a line segment that bisects one of the vertex angles of a triangle.

In this problem

SH represent a line segment that bisects the vertex angle H of triangle GFH, so represent an angle bisector.

GT represent a median of triangle GFH, because the point T is the midpoint  of segment FH (FT=TH)

therefore

The segment GT is a median of triangle GFH

Answer:

The amount invested in the mutual fund that earned 5% was $1,000

The amount invested in the mutual fund that earned 3% was $1,800

Step-by-step explanation:

Let

x ----> the amount invested in the mutual fund that earned 5%

y ----> the amount invested in the mutual fund that earned 3%

we know that

[tex]x+y=2,800[/tex] ----> [tex]y=2,800-x[/tex] ----> equation A

[tex]5\%=5/100=0.05[/tex]

[tex]3\%=3/100=0.03[/tex]

[tex]0.05x+0.03y=104[/tex] ----> equation B

Solve the system by substitution

substitute equation A in equation B

[tex]0.05x+0.03(2,800-x)=104[/tex]

Solve for x

[tex]0.05x+84-0.03x=104[/tex]

[tex]0.05x-0.03x=104-84[/tex]

[tex]0.02x=20[/tex]

[tex]x=\$1,000[/tex]

Find the value of y

[tex]y=2,800-x[/tex]

[tex]y=2,800-1,000=\$1,800[/tex]

therefore

The amount invested in the mutual fund that earned 5% was $1,000 and the amount invested in the mutual fund that earned 3% was $1,800

Answer:

y = -9x + 4 ?

Step-by-step explanation:

y-4 I=I -(x+9)

y-4 I=I -9x

+4 I I +4

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

y = -9x+4

Answer:

4.5 miles.

Explanation:

24 x 1,000 = 24,000

24,000 ÷ 5380 = 4.5

Answer:

The answers are 31, 46, 52

Step-by-step explanation:

The sequence is 4+6=10, 10+15= 25, 25+6=31, 31+15=46, 46+6=52

Answer:

I didn't really understand but I hope this helps sorry if it doesn't!!

Step-by-step explanation:

r = number of rides

1.50r

1.50×12=18

1.50×19=28.50

12 rides = $18

19 rides = $28.50

and if you need the entrance fee:

30-18=12

so it would probably be $12.

and for the total ig fo the last one it would be:

28.50+12=40.50

so $40.50

Again I didn't really understand the question but I hope this helps!!

Answer:

154,791

Step-by-step explanation:

Answer:

39 times 49 times 81 = 154791

Answer:

$66.00

Step-by-step explanation:

first we need multiply :D I will use the formula I =prt

principal= $500

rate=3.3%

time= 4 years

but we need to convert the percent, 3.3%, to a decimal

3.3%=0.033 or .033

now we multiply !

500 × 0.033 × 4 = 66 = $66.00

:D

Answer:$66.00

Step-by-step explanation:

first we need multiply :D I will use the formula I =prt

principal= $500

rate=3.3%

time= 4 years

but we need to convert the percent, 3.3%, to a decimal

3.3%=0.033 or .033

now we multiply !

500 × 0.033 × 4 = 66 = $66.00

Answer:

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

Step-by-step explanation:

7x-5y=26

2x+4y=2

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

simplify 2x+4y=2 into x+2y=1

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

7x-5y=26

x+2y=1

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

x=1-2y

7(1-2y)-5y=26

7-14y-5y=26

7-19y=26

19y=7-26

19y=-19

y=-19/19

y=-1

x+2(-1)=1

x-2=1

x=1+2

x=3

Answer: x=-1,y=0

Step-by-step explanation:

7x - 5y = 26 multiplied by factor of 2 becoming 14x-10y=52

2x+4y= 2 multiplied by factor of 7 becoming 14x+28y=14

now solve by elimination

 14x+28y=14

-(14x-10y=52)

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

38x=-38

x=-1

to find y plug in x to an equation

2(1)+4y= 2

y=0

Answer:

The number is 6.

Step-by-step explanation:

(78/x+10)*8=184

8(78/x+10)=184

78/x+10=184/8

78/x+10=23

78/x=23-10

78/x=13

x=78/13

x=6

Answer:The unknown number can be calculated by the following formula;

Step-by-step explanation:

Answer:

82g

Step-by-step explanation:

You multiply 9×8 to find the answer as each pencil is 9g and there is 8 pencils in a box.

72g because 8*9g is 72

Answer:

a)

[tex]\left\{\begin{matrix}g=525-s\\ g=s+25\end{matrix}\right.[/tex]

c)

Gavin earned $275

Seiji earned $250

Step-by-step explanation:

a) Denoting s as the earning of Seiji and g the earnings of Gavin, we know they together earned $525. This forms the equation

s+g=525, or equivalently

[tex]g=525-s[/tex]

We also know that Gavin earned $25 more than Seiji. It can be written as

[tex]g=s+25[/tex]

Combining both equations we get the system

[tex]\left\{\begin{matrix}g=525-s\\ g=s+25\end{matrix}\right.[/tex]

b)  The graph is shown below

c) Both functions have one point in common. It's the solution of the system. We can conclude that

Gavin earned $275

Seiji earned $250

Answer:

x = 15

Step-by-step explanation:

If ZABC = 130º

ZABC = (6x+40)°​ = 130º

This equation can be rearranged to solve for x by isolating it (moving everything over to the other side).

(6x+40)°​ = 130º

Solve it without the degrees sign because it looks confusing.

6x+40 = 130

6x+40 - 40 = 130 - 40   (subtract 40 from both sides)

6x = 90

6x/6 = 90/6    (divide both sides by 6)

x = 15

Therefore x is 15. The degrees symbol is already included outside the bracket.

Answer:

61 ¹/₂₀

Step-by-step explanation:

You cannot get a proper fraction while converting 61.05 into a fraction. You will only end up with improper fractions. This is your answer as a simplified improper fraction. If you also want a mixed number answer, that is down below.

61   1/20

I hope this helps you! :)

Answer:

The length of river frontage for each lot are 96.55 ft. 98.85 ft, 101.15 ft and 103.45 ft.

Step-by-step explanation:

See the attached diagram.

The river frontage of 400 ft will be divided into 84 : 86 : 88 : 90 for each lot as AP, BQ, CR, DS and ET all are parallel.

Therefore, PQ : QR : RS : ST = 84 : 86 : 88 : 90 = 42 : 43 : 44 : 45

Let, PQ = 42x, QR = 43x, RS = 44x and ST = 45x

So, (42x + 43x + 44x + 45x) = 400

⇒ 175x = 400

⇒ x = 2.2988.

So, PQ = 42x = 96.55 ft.

QR = 43x = 98.85 ft.

RS = 44x = 101.15 ft and  

ST = 45x = 103.45 ft

(Answer)

Answer:

2.48

Step-by-step explanation:

For each gallon she got she paid $2.48. I know this by doing 34.72 divided by 14 which got me the answer of $2.48.

For this case we have that by definition, the distance between two points is given by:

[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]

We have to:

[tex](x_ {1}, y_ {1}): (4, -1)\\(x_ {2}, y_ {2}): (7,5)[/tex]

Substituting:

[tex]d = \sqrt {(7-4) ^ 2 + (5 - (- 1)) ^ 2}\\d = \sqrt {(7-4) ^ 2 + (5 + 1) ^ 2}\\d = \sqrt {(3) ^ 2 + (6) ^ 2}\\d = \sqrt {9 + 36}\\d = \sqrt {45}\\d = 6,708[/tex]

We round:

[tex]d = 6.7[/tex]

Answer:

[tex]d = 6.7[/tex]

i cant see the whole problem

Answer:

64.28 m

Step-by-step explanation:

In the attached file

Answer:

x=3

Step-by-step explanation:

one property of a trapezoid and medians is the middle line is half of the bottom and top combined. so the equation would look like this

3x+2+4x+3/2=13.

7x+5/2=13

7x+5=26

x=3

hope this helps,

Answer:

6.12

1.39

4.12

12

Step-by-step explanation:

If y ∝ x, then y = kx.

So, the constant of proportionality is given by [tex]k = \frac{y}{x}[/tex]

Case 1:

$18.36 for 3 pizzas

Therefore, the constant of proportionality is [tex]\frac{18.36}{3} = 6.12[/tex]

Case 2:

$4.17 for 3 pounds of bananas.

Hence, the constant of proportionality is [tex]\frac{4.17}{3} = 1.39[/tex]

Case 3:

$16.48 for 4 pounds of potatoes.

Hence, the constant of proportionality is [tex]\frac{16.48}{4} = 4.12[/tex]

Case 4:

2 cups of flour to make 24 cookies.

Hence, the constant of proportionality is [tex]\frac{24}{2} = 12[/tex] (Answer)

Answer:

-18/5 or - 3 3/5.

Step-by-step explanation:

-2/3 (x-3) - x = 8

-2/3x + 2 - x = 8

-2/3x - 3/3x  = 8 - 2

-5/3 x = 6

x =   6 * -3/5

x = -18/5

[tex] \frac{16 {x}^{3} {y}^{2} }{36x {y}^{2} {z}^{3} } = \frac{4 {x}^{2} }{9 {z}^{3} } \\ \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{ - a} = \frac{1}{ {x}^{a} } [/tex]

Harrison's prediction that the actual quotient for 57872 divided by 305 would be less than his estimate of 200 is correct. This is because the divisor (305) is larger than in the estimate (300), and also because the dividend (57872) is smaller than in the estimate (60000), leading to a smaller quotient.

Harrison predicted that the actual quotient for 57872 divided by 305 would be less than his estimate of 60,000 divided by 300 which equals 200. To understand Harrison's prediction, we have to look at the numbers involved. When you are dividing two numbers, the quotient decreases as the divisor (the number you are dividing by) increases, given that the dividend (the number being divided) remains the same. In this case, 305 is larger than 300, so if the dividend were the same, the quotient for our original problem would indeed be smaller. However, the dividend in our original problem (57872) is smaller than the dividend in the estimate (60000). So we have a smaller number being divided by a slightly larger one, and this will also lead to a smaller quotient. Therefore, Harrison's prediction is correct.

https://brainly.com/question/31535032

#SPJ2

Answer:

The corresponding pair of sides are in the same ratio.

Step-by-step explanation:

For two triangles to be similar, the theorem that is required is the corresponding sides of the two triangles are in the same ratio.

Now, see the diagram of two triangles given with the question.

The ratios of the corresponding sides are [tex]\frac{20}{16} = \frac{19}{\frac{76}{5} } = \frac{5}{4}[/tex]

If two pairs corresponding sides are in 5 : 4 ratio, then the third pair of corresponding sides will also be in 5 : 4 ratio.

Therefore, the two triangles are similar. (Answer)

To prove that two triangles are similar, you can use the AA (Angle-Angle) Postulate, SSS (Side-Side-Side) Similarity Theorem, or SAS (Side-Angle-Side) Similarity Theorem. These methods involve comparing the angles and sides of the triangles to see if they meet the similarity conditions.

Triangle Similarity Theorem

To determine whether two triangles are similar, you can use several different theorems or postulates. These include the AA (Angle-Angle) Postulate, the SSS (Side-Side-Side) Similarity Theorem, and the SAS (Side-Angle-Side) Similarity Theorem.

AA (Angle-Angle) Postulate: If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

SSS (Side-Side-Side) Similarity Theorem: If the three sides of one triangle are proportional to the three corresponding sides of another triangle, then the triangles are similar. For example, if triangle ABC and triangle DEF have corresponding sides such that AB/DE = BC/EF = AC/DF, then the triangles are similar.

SAS (Side-Angle-Side) Similarity Theorem: If an angle of one triangle is congruent to an angle of another triangle and the sides containing these angles are proportional, then the triangles are similar. For example, if ∠A = ∠D and AB/DE = AC/DF, then triangles ABC and DEF are similar.

By using these theorems, you can determine if two triangles are similar by comparing their angles and sides as per the given conditions.

Answer:

Range = highest value - lowest value

= 71-11

= 60

Hope this helps!

Answer:

{            } should be the answer glad i could help

Step-by-step explanation: could i get marked as brainliest on this it took up alot of my time

The solution of the given proportionality is x = 603

The given proportionality is,

2/67 = 18/x

Since we know that,

Proportion is mostly discussed using ratios and fractions. A fraction is written as a/b, whereas a ratio is expressed as a:b, and a percentage says that two ratios are equal.

In this case, a and b can be any two numbers. The ratio and proportion are important foundations for understanding numerous ideas in mathematics and science.

Now proceeding the expression,

⇒ 18/x = 2/67

Taking reciprocal both sides we get,

⇒ x/18 = 67/2

Multiply 18 both sides we get,

⇒ x = (67x18)/2

      =  67x9

      = 603

Hence,

x = 603

To learn more about proportionality visit:

https://brainly.com/question/17793140

#SPJ6

Answer: The amount of money from the previous month times 4.

Step-by-step explanation:

Answer:

a= 151.87 units

Step-by-step explanation:

Given:

Consider,a right triangle Δ ACB with Angle C as 90°,

and side a, b, and c be the sides opposites to the respective angles. Such that

c = Hypotenuse = 155

b = Shorter leg = 31

a = Longer leg  = ?

To Find:

a = Longer leg  = ?

Solution:

In Right angle Δ ACB

If we apply Pythagoras Theorem we get

[tex](\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}[/tex]

Now substituting the given above values we get,

[tex]c^{2}= b^{2} + a^{2}\\x^{2}  155^{2}= 31^{2}+ a^{2}\\ 24025=961+a^{2}\\\therefore a^{2}=24025-961\\a^{2} = 23064\\ a=\pm 151.8683\\\therefore a = 151.87 .......\textrm{Distance cannot be in negative}[/tex]

∴ a= 151.87 units......(rounded to nearest hundredth)

Answer:

x=2+i, x=2-i

Step-by-step explanation:

x^2-4x+5=0

Apply the quadratic formula.

There are are no real solutions for this equation.

An equation whose highest degree is 2, is called a quadratic equation.

We can solve a quadratic equation by two ways:

                          [tex]x=\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]

                             or

                           [tex]x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]

Comparing with the standard equation [tex]ax^{2} +bx+c=0[/tex],

∴ Discriminant = [tex]\sqrt{b^{2}-4ac }[/tex] = [tex]\sqrt{-4}[/tex]

Find out more about 'Quadratic Equation' here:  brainly.com/question/1214333

#SPJ2