Use the quadratic formula to write a quadratic equation that has the solutions x=-4 ± 2/6.

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.

Answer:

1/2×2×12=12 feet

Step-by-step explanation:

1/2× base area × height

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:

8 hours

Step-by-step explanation:

y = 30x + 45

Assuming x is the hours and y is the cost

300 = 30x +45

Subtract 45 from each side

300-45 = 30x+45-45

225 = 30x

Divide by 30

225/30 = 30x/30

17/2 = x

8.5 =x

The largest number of hours without going over means round down

8 hours

Answer:

b, c, d

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:

x=30/tan(22)

x= 74.2526056

Step-by-step explanation:

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

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: 14 hours

Step-by-step explanation:

Let the number of hours of TV that Jamie watched be represented by x.

Since Roberto watched 5 more hours of tv than Jamie last week, therefore the number of hours of TV that Roberto watched will be: x + 5

Together, they watched a total of 23 hours of tv last week. Therefore,

x + (x + 5) = 23

2x + 5 = 23

2x = 23 - 5

2x = 18

x = 18/2

x = 9

Jamie watched 9 hours of TV

Therefore, Roberto watched x+ 5 = 9 + 5 = 14 hours

Answer:

6.8=6 8/5

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hope it help

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:

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.

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!

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:

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

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

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

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:

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:

A

Giải thích:

f(1)=f(x)

f(-1) và f(-2)= f(-x)

=> f(1)=f(-1) =A. f(x)=f(-x)

Question is slightly wrong .We have to find BD

we know

[tex]\boxed{\sf BD^2=AD\times DC}[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow BD^2=4\times 2[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow BD^2=8[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow BD=\sqrt{8}[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow BD=2√2[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow BD=2(1.4)[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow BD=2.8[/tex]

Answer:

39.401

Step-by-step explanation:

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.

Answer:

MATH

Step-by-step explanation:

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:

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.

Step-by-step explanation:

here's the answer to your question

Answer:

acute angle.

Step-by-step explanation:

because it is 60 degree

Nếu AOB là một đường thẳng thì góc BOC =90°