The sum of two numbers is 4. Four times the larger number plus three times the smaller number is 31. Find the numbers.
The larger number is___
and the smaller number is ____

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:4/3

Step-by-step explanation:24/18

Divide both the numerator and the denominator by their highest common  factor. i.e 6

24÷6/18÷6

⇒ 4/3

The value of fraction for 24 divided by 18 is,

⇒ 4 / 3

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The expression is,

⇒ 24 divided by 18

Now, We can write as;

⇒ 24 divided by 18

⇒ 24 ÷ 18

⇒ 24 / 18

⇒ 4 / 3

Thus, The value of fraction for 24 divided by 18 is,

⇒ 4 / 3

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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]

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Answer:

[tex]\displaystyle 4 > x[/tex]

Step-by-step explanation:

3 - 2x > −5

- 3 - 3

_________

[tex]\displaystyle \frac{-2x}{-2} > \frac{-8}{-2} \\ \\ x < 4[/tex]

Whenever you divide\multiply by a negative, you reverse the inequality symbol.

** The above answer is written in reverse, which is the exact same result.

I am joyous to assist you anytime.

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:

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

Step-by-step explanation:

Answer:

[tex]\theta =2\pi k,\ \ k\in Z\ \\\text{or}\ \\\theta=-\dfrac{2\pi}{3}+2\pi k,\ \ k\in Z[/tex]

Step-by-step explanation:

Given:

[tex]\cos \theta-\sqrt{3}\sin \theta=1[/tex]

Divide this equation by 2:

[tex]\dfrac{1}{2}\cos \theta-\dfrac{\sqrt{3}}{2}\sin \theta=\dfrac{1}{2}[/tex]

Note that

[tex]\cos \dfrac{\pi }{3}=\dfrac{1}{2}\\ \\\sin \dfrac{\pi }{3}=\dfrac{\sqrt{3}}{2}[/tex]

So, the previous equation is

[tex]\cos \dfrac{\pi}{3}\cdot \cos \theta-\sin \dfrac{\pi}{3}\cdot \sin \theta=\dfrac{1}{2}[/tex]

Remind that

[tex]\cos x\cos y-\sin x\sin y=\cos (x+y),[/tex]

then

[tex]\cos \left(\dfrac{\pi}{3}+\theta\right)=\dfrac{1}{2}[/tex]

The solution of this equation is

[tex]\dfrac{\pi}{3}+\theta=\pm \arccos \dfrac{1}{2}+2\pi k,\ \ k\in Z\\ \\\dfrac{\pi}{3}+\theta=\pm \dfrac{\pi}{3}+2\pi k,\ \ k\in Z\\ \\\theta =2\pi k,\ \ k\in Z\ \text{or}\ \theta=-\dfrac{2\pi}{3}+2\pi k,\ \ k\in Z[/tex]

Answer:

4.5 miles.

Explanation:

24 x 1,000 = 24,000

24,000 ÷ 5380 = 4.5

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:

Range = highest value - lowest value

= 71-11

= 60

Hope this helps!

i cant see the whole problem

Answer:

64.28 m

Step-by-step explanation:

In the attached file

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:

-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

Answer:

154,791

Step-by-step explanation:

Answer:

39 times 49 times 81 = 154791

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:

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:

$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:

The next two terms for the geometric sequence are 250 and - 1,250

Step-by-step explanation:

1. Let's find the next two terms for the geometric sequence which first three terms are as follows:

- 2, 10, - 50.....

Aₓ = Aₓ₋₁ * - 5 ; A₁ = - 2

A₁ = - 2

A₂ = A₁ * - 5 = -2 * - 5 = 10

A₃ = A₂ * - 5 = 10 * - 5 = - 50

A₄ = A₃ * - 5 = - 50 * - 5 = 250

A₅ = A₄ * - 5 = 250 * - 5 = - 1,250

The next two terms for the geometric sequence are 250 and - 1,250

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

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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:

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:

D)99 degrees

Step-by-step explanation:

The answer is D. All the angles in any quadrilateral add up to 360 degrees. And since the figure is a paralledlogram, for each angle there is another angle with the same measurement. So 81 + 81 + x + x = 360 which gives us 162 + 2x = 360. If you solve for x you get 99 degrees.

Raise 2 to the 4th power:

√(16*9)

Multiply:

√144

Find square root:

Answer = 12

Answer:

1/12

Step-by-step explanation:

1/2-[-1/4+2/3]

1/2-[-3/12+8/12]

1/2-[5/12]

1/2-5/12

6/12-5/12

1/12

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

x = 50 mph (level rate)

x-30 = 20 mph (mountain rate)

Explain:

time = time

160/(x-30) = 400/x

160x = 400(x-30)

160x = 400x - 12000

-240x = -12000

[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]

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,