The ratio of three numbers is 4 : 1 : 7. The sum of the numbers is 24. What are the three numbers?

Answer:

Amy has 12 5¢ coins

Step-by-step explanation:

Let x represent 20¢ coins and y represent 5¢ coins.

Amy has four more 20¢ coins than 5¢ coins. Hence:

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

And the total value of all her coins is $3.80. Thus:

[tex]0.2x+0.05y=3.8[/tex]

This yields a system of equations:

[tex]\displaystyle \begin{cases} x=y+4 \\ 0.2x+0.05y=3.8\end{cases}[/tex]

We can solve by substitution. Substitute the first equation into the first:

[tex]\displaystyle 0.2(y+4)+0.05y=3.8[/tex]

Distribute:

[tex]\displaystyle 0.2y+0.8+0.05y=3.8[/tex]

Combine like terms:

[tex]\displaystyle 0.25y = 3[/tex]

And divide both sides by 0.25. Hence:

[tex]y=12[/tex]

Thus, Amy has 12 5¢ coins.

Using the first equation:

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

Substitute:

[tex]x=(12)+4=16[/tex]

Thus, Amy has 16 20¢ coins.

In conclusion, Amy has 12 5¢ coins and 16 20¢ coins.

Step-by-step explanation:

+ Both equations

You will get : 5x=13 ; x=13/5

and put x to the first equation

2*13/5-y=4

y=6/5

(13/5;6/5)

Answer is C

Answer:

If the triangle is similar by any axiom then the ratio of their sides will be equal then you can easily find the side of the triangle

OR

You can also find it by congurency.

Hope this helps

Answer:

Minimum Possible Temperature: 55° F

Maximum Possible Temperature: 71° F

Step-by-step explanation:

Beginning temperature: 63° F

Change in temperature: 8° F

If the temperature decreased: 63° F - 8 °F = 55° F

If the temperature increased: 63° F + 8° F = 71° F

Minimum Possible Temperature: 55° F

Maximum Possible Temperature: 71° F

Answer:

13

Step-by-step explanation:

(4+√3)(4-√3) = (4)^2-(√3)^2 =16-3 = 13

Answer:

Step-by-step explanation:

(a + b)(a -b) =a² - b²

a = 4 and  b = √3

(4 + √3)(4 - √3)= 4² - (√3)²

                        = 16 - √3*√3

                        = 16 - 3

                        =  13

Answer:

hope found the answers bye.

Step-by-step explanation:

9x + 4y - 4  =  0     

Putting in the x-value of -1, we get:

9(-1) + 4y - 4  =  0

Simplifying:

-9 + 4y - 4  =  0

Combining the -9 and the -4:

4y - 13  =  0

Getting rid of the -13 by adding 13 to both sides:

4y - 13 + 13  =  0 + 13

4y  = 13

Dividing both sides by 4:

y = 13/4

Checking:  Is 9(-1) +4(13/4) -4  really zero?    Yes!

Answer:

1/2×2×12=12 feet

Step-by-step explanation:

1/2× base area × height

f(x) = -2x

-2x = 0

x = 0/-2

x = 0

Now putting 0 as x in g(x)

g(x) = 8x^2 - 5x + 7

g(0) = 8(0)^2-5(0)+7

= 0 - 0 + 7

= 7

Answered by Gauthmath must click thanks and mark brainliest

Answer:

Step-by-step explanation:

If these were similar, then the ratio 35/18 (the top and bottom measures from each of the polygons) would have to equal the ratio 63/10 (the side measures from each of the polygons).

35/18 = 1.944444

63/10 = 6.3

They are not similar because the simplified ratios are not the same.

Answer:

k=-1/2

Step-by-step explanation:

u have to change line 4x + ky=11 to this form:

y=11/k-4x/k

then, if 2 lines are parallel, their slopes have to equal

so: 8=-4/k -> k=-1/2

Answer:

x = constant ( other than 5)

Step-by-step explanation:

The slope of a line x=5 is  undefined

Parallel lines have the same slope

So any line that is vertical ( slope undefined) will be parallel

Using Pythagoras Theorem

[tex]\\ \sf\longmapsto B^2=H^2-P^2[/tex]

[tex]\\ \sf\longmapsto B=\sqrt{H^2-P^2}[/tex]

[tex]\\ \sf\longmapsto B=\sqrt{29^2-21^2}[/tex]

[tex]\\ \sf\longmapsto B=\sqrt{841-441}[/tex]

[tex]\\ \sf\longmapsto B=\sqrt{400}[/tex]

[tex]\\ \sf\longmapsto B=20[/tex]

Answer:

91

Step-by-step explanation:

P>J and P>M

269 -> split into 3 parts

Approx is 90

IF Peter's score is 90, then the other 2 scores could be 90 and 89

+ 1 to Peter's score

Hence Peter's least possible score could be 91.

Step-by-step explanation:

here's the answer to your question

Answer:

[tex]=\frac{81m^2n^5}{8}[/tex]

Step-by-step explanation:

One is given the following expression:

[tex]\frac{(3m^-^1n^2)^4}{(2m^-^2n)^3}[/tex]

Simplify, distribute the exponent outside of the parenthesis by the terms inside of it. Remember, when a value that already has an exponent is raised to another exponent, the equivalent of these two values is multiplying the exponents together. Use this property here:

[tex]=\frac{(3m^-^1n^2)^4}{(2m^-^2n)^3}[/tex]

[tex]=\frac{3^4m^(^-^1^)^(^4^)n^(^2^)^(^4^)}{2^3m^(^-^2^)^(^3^)n^3}[/tex]

[tex]=\frac{81m^-^4n^8}{8m^-^6n^3}[/tex]

Now simplify this fraction. Keep in mind that a fraction is another way of representing the operation of division. When one wants to divide terms raised to an exponent, one must make sure that these terms have a like base. Then one will subtract the exponents from each other. Do this step with terms that have a variable base:

[tex]=\frac{81m^-^4n^8}{8m^-^6n^3}[/tex]

[tex]=\frac{81m^(^-^4^)^-^(^-^6^)n^(^8^)^-^(^3^)}{8}[/tex]

[tex]=\frac{81m^-^4^+^6n^8^-^3}{8}[/tex]

[tex]=\frac{81m^2n^5}{8}[/tex]

Answer:

b. vertical angles

Step-by-step explanation:

<2 and <5 are vertical angles

They are formed by the same lines, are opposite each other and share a vertex.  Vertical angles are equal

Answer:

x=1

Step-by-step explanation:

log_4(x + 3) + log_4x = 1

We know that loga(b) + loga(c) = loga(bc)

log_4(x + 3)x = 1

Raise each side to the base of 4

4^log_4(x + 3)x = 4^1

(x+3)x = 4

x^2 +3x = 4

Subtract 4 from each side

x^2 +3x -4 = 0

Factor

(x+4) (x-1) =0

Using the zero product property

x= -4  x=1

But x cannot be negative since logs cannot be negative

x=1

Answer:

A..  x = 1.

Step-by-step explanation:

log_4(x + 3) + log_4x = 1

log_4 x(x + 3) = log_4 4

Removing the logs:

x(x + 3) = 4

x^2 + 3x - 4 = 0

(x + 4)(x - 1) = 0

x = 1, -4.

We can ignore the -4 as there is no log of a negative.

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

Explanation:

The two equations given to us are

Divide the second equation over the first equation and that would lead to b = 6

Notice how the 'a' terms divide to 1 and go away, i.e. cancel out.

The b terms divide to (b^2)/b = b

The right hand side values divide to 18/3 = 6

So that's how we end up with b = 6

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

Now if b = 6, then we can say,

ab = 3

a*6 = 3

a = 3/6

a = 1/2

Or we could say

ab^2 = 18

a*6^2 = 18

a*36 = 18

a = 18/36

a = 1/2

Answer:

b, c, d

Step-by-step explanation:

Answer:

39.401

Step-by-step explanation:

Answer:

Question #1

Set up an equation to find x:

[tex]x+x+10=26\\2x=26-10\\2x=16\\x=8[/tex]

The length of the side marked x is 8.0 m.

Question #2

Set up an equation to find x

[tex]11+11+x+x=34\\2x=34-22\\2x=12\\x=6[/tex]

The new width is 6 cm.

Answer:

D

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers

12 = 2x + 4y , that is

2x + 4y = 12 ← is in standard form

Step-by-step explanation:

The total of the number of computers he sold in 2015 is 67.

The total of the number of computers he sold in 2016 is 61.

The total of the number of computers he sold in 2017 is 71.

He sold 35 computers in Quarter 1, 24 in Quarter 2, 61 in Quarter 3, and 79 in Quarter 4.

He sold the most computers in 2017 and the least in Quarter 2.

Therefore, to find the total number of computers he sold all time, we add 67, 61, and 71 together to get 199.

Hope this helped!

Answer with Step-by-step explanation:

From the given table

(a)

In quarter 1

Computer sold in 2015=12

Computer sold in 2016=15

Computer sold in 2017=8

Total computer sold in quarter 1=12+15+8=35

In quarter 2

Computer sold in 2015=9

Computer sold in 2016=10

Computer sold in 2017=5

Total computer sold in quarter 2=9+10+5=24

In quarter 3

Computer sold in 2015=21

Computer sold in 2016=17

Computer sold in 2017=23

Total computer sold in quarter 3=21+17+23=61

In quarter 4

Computer sold in 2015=25

Computer sold in 2016=19

Computer sold in 2017=35

Total computer sold in quarter 4=25+19+35=79

In 2015

Total number of computer sold=12+9+21+25=67

In 2016

Total number of computer sold=15+10+17+19=61

In 2017

Total number of computer sold=8+5+23+35=71

(b)He sold the most computers in 2017

(c) He sold the least computers in quarter 2.

Answer:

The 27th term is 73.5.

Step-by-step explanation:

We want to find the 27th term of the arithmetic sequence:

15, 17.25, 19.5, 21.75, ...

We can write a direct formula. Recall that the direct formula for an arithmetic sequence is given by:

[tex]x_n=a+d(n-1)[/tex]

Where a is the initial term and d is the common difference.

From the sequence, we can see that our initial term a is 15.

To find the common difference, subtract a term and its previous term. Thus, the common difference will be:

[tex]d=17.25 - 15 = 2.25[/tex]

Thus, our direct formula is:

[tex]x_n=15+2.25(n-1)[/tex]

To find the 27th term, let n = 27. Substitute and evaluate:

[tex]\displaystyle \begin{aligned} x_{27} &=15+2.25((27)-1) \\ &= 15+2.25(26) \\&= 15+58.5 \\ &= 73.5\end{aligned}[/tex]

Thus, the 27th term is 73.5.

Answer:

D. (7×10) + (3×3) + (2×1)

Step-by-step explanation:

(7×10)=70 + (3×3)=9 + (2×1)=2

=70+9+2

=792

(| 5 - 3x | - 1) - (1 - 3x) = 0

|5 - 3x| - 1 - 1 + 3x = 0

|5 - 3x| - 2 + 3x = 0

1) (5 - 3x) - 2 + 3x = 0, if 5 - 3x >= 0

3 = 0. has no solutions

2) -(5 - 3x) - 2 + 3x = 0, if 5 - 3x < 0

-5 + 3x - 2 + 3x = 0

6x = 7

x = 7/6

5 - 3x < 0

-3x < -5

x > 5/3.

has no solutions

Answer:

MATH

Step-by-step explanation:

Answer:

simultaneous equations

Step-by-step explanation:

phils age =7x

Peter age=x

scenario 2

phils age = 4(7x)

Peter age= 2x-2

[tex]7x + x = 4(7x) + 2x - 2[/tex]

Answer:

10 levels

Step-by-step explanation:

Ralph is on level 7

Mike level 5

Don level 10 and is playing the last one of game

The game has 10 levels

Leo is playing the first level and Ralph is sex levels above Leo. This means that Ralph is playing level:

= 1 + 6

= 7

Mike is two levels below Ralph which means that Mike is playing level:

= 7 - 2

= 5

Don is playing the last level and is five levels above Mike which means that Don is playing level:

= 5 + 5

= 10

Don is playing level 10 which is the last level so the game has 10 levels.

Find out more at https://brainly.com/question/23623247.

Answer:

x is 30 degrees

Step-by-step explanation: