Part of the proceeds from a garage sale was $540 worth of $5 and $20 bills If there were 3 more bills $5 bills than $20 bills, find the number of each denomination.

Answer:

x = 10

Step-by-step explanation:

4x + 3(x - 1) = 67 ← distribute parenthesis and simplify left side

4x + 3x - 3 = 67

7x - 3 = 67 ( add 3 to both sides )

7x = 70 ( divide both sides by 7 )

x = 10

Hi. . .

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[tex]\boxed{\fbox{\huge{x = 10}}}[/tex]

Let's solve your equation step-by-step ~

[tex]\sf{4x \: + \: 3(x \: - \: 1) = 67}[/tex]

[tex]\sf{4x \: + \: (3)(x) \: + \: (3)(-1) = 67} \: (Distribute)[/tex]

[tex]\sf{4x \: + \: 3x \: + \: -3 = 67}[/tex]

[tex]\sf{(4x \: + \: 3x) \: + \: (-3) = 67} \: (Combine \: like \: terms)[/tex]

[tex]\sf{7x \: + \: 7 \: -3 = 67}[/tex]

[tex]\sf{7x \: - \: 3 = 67}[/tex]

[tex]\sf{7x \: - \: 3 \: + \: 3 = 67 \: + 3}[/tex]

[tex]\sf{7x = 70}[/tex]

[tex]\sf{\frac{7x}{7} = \frac{70}{7}[/tex]

[tex]\boxed{\fbox{\huge{x = 10}}}[/tex]

Hope It Helps...

Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

pythagorus theorem

a² + b² = c²

c² - b² = a²

26² - 24² = a²

676 - 576 = a²

a² = 100

a = 10

Answer:

No solution

Step-by-step explanation:

The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

a) Yes it does, because the graph of their relationship is a Straight line

b) Independent variables are variables whose variation does not depend on another. Number of works does not depend on followers. Therefore, it is independent

C)number of followers depend on the number of locks passing. It is dependent.

D) Slope = (Y₂- Y₁)/(x₂-x₁) = (100-82)/ (3-0) =  18/3 = 6

It represents the increase in number of followers per week,

E) y-intercept is value of y when x=0

y-intercept = 82. It means his initial number of followers

F) Slope-intercept form → y = mx + c m = slope горе C = y-intercept y = no of followers x= weeks.

Y=6x+82

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Answer:

0.93

Step-by-step explanation:

Answer:

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

Given equation and steps to solve it:

All steps given above including the missing one. As we can see, we divided both sides by 4, so the justification for this step is Division Property of Equality.

Hence, the correct choice is C.

Answer:

Four times x over four equals four over four; Division Property of Equality

Step-by-step explanation:

See on antepenultimate step

Now for getting x we have to divide each side by 4

We get.

The given statement is An integer is divisible by 100 if and only if its last two digits are zeros.

The two conditional statements that can be made are:

1) If an integer is divisible by 100 its last two digits are zeros.

This is a true statement. If a number is divisible by 100, it means 100 must be a factor of that number. When 100 will be multiplied by the remaining factors, the number will have the last two digits zeros.

2) If the last two digits of an integer are zeros, it is divisible by 100.

This is also true. If the last two digits are zeros, this means 100 is a factor of the integer. So the number will be divisible by 100.

Therefore, the two conditional statements that are formed are both true.

So, option A is the correct answer.

Yes, it is. When the definition is separated into two conditional statements, both of the statements are true.

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The given statement is An integer is divisible by 100 if and only if its last two digits are zeros.

An integer is a number with no decimal or fractional part, from the set of negative and positive numbers, including zero.

The two conditional statements that can be made are:

1) If an integer is divisible by 100 its last two digits are zeros.

This is a true statement. If a number is divisible by 100, it means 100 must be a factor of that number. When 100 will be multiplied by the remaining factors, the number will have the last two digits zeros.

2) If the last two digits of an integer are zeros, it is divisible by 100.

This is also true. If the last two digits are zeros, this means 100 is a factor of the integer. So the number will be divisible by 100.

Therefore, the two conditional statements that are formed are both true.

So, option A is the correct answer.

Yes, it is. When the definition is separated into two conditional statements, both of the statements are true.

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Answer:

16

Step-by-step explanation:

consider X  = Damon's age

3x + 8 = 2x

x = 8

so Damon will be 16 in 8 years ( 8+8)

Answer:

16

Step-by-step explanation:

24/3 8

24+8=32

8+8=16

16/32=1/2

Answer:

T = 15 + 0.75c

T = $19.5

Step-by-step explanation:

Assume that T stands for total cost and c stands for number of single cookies purchased, the equation would be:

T = 15 + 0.75c

Therefore, a dozen cookies plus six single cookies would cost:

T = 15 + 0.75(6)

T = 15 + 4.5

T = $19.5

The graph goes upwards on the left side and downwards on the right side, so the correct option is the first one.

We have the function:

[tex]y = -9*x^3 + 5*x^2 -2x[/tex]

This is a cubic polynomial with a negative leading coefficient.

So, when x takes large negative values, because the leading coefficient is negative, y will take large positive values.

And when x takes large positive values, because the leading coefficient is negative, y will take large negative values.

So the nature is:

The graph goes upwards on the left side and downwards on the right side. The correct option is the first one.

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Answer:

6 + (7 + 8) = 21

Step-by-step explanation:

the associative property of addition is: (a + b) + c = a + (b + c)

So the equivalent addition sentence would be:

(6 + 7) + 8 = 6 + (7 + 8) as they both equal 21

Answer:

2 1/4

Step-by-step explanation:

Half of 4 is 2 and half of 1/2 is 1/4 so half of 4 1/2 is 2 1/4

The length of BC as shown in the diagram is 6.32units

The formula for calculating the distance between two points is expressed as:

D = √(x2-x1)²+(y2-y1)²

Given the following coordinate points (3, 6) and (5, 0)

Substitute

BC = √(0-6)²+(5-3)²

BC = √(36+4)

BC = √40

BC = 6.32 units

Hence the length of BC as shown in the diagram is 6.32units

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Answer:

D. y = (x + 8) (x + 1)

Explanation:

[tex]\sf y = x^2 + 9x + 8[/tex]

[tex]\rightarrow \sf y = x^2 + 9x + 8[/tex]

middle term split

[tex]\rightarrow \sf y = x^2 + 8x +x + 8[/tex]

factor the common terms

[tex]\rightarrow \sf y = x(x + 8) + 1(x + 8)[/tex]

collect into groups

[tex]\rightarrow \sf y = (x + 1)(x + 8)[/tex]

Option D

The range:
[tex]{x|70\leq x\leq 82[/tex]

Answer:

5.32⋅10−6

Step-by-step explanation:

Answer:

5320000

Step-by-step explanation:

standard notation form : 5320000

Answer: six ways

Step-by-step explanation: The pairs when the cube is rolled that are less than five would be; (1,1), (1,2), (1,3), (2,1), (2,2), (3,1) since each cube is out of six.

Answer:

88

Step-by-step explanation:

Answer:

16.5 meters

Step-by-step explanation:

The length of an arc of a circle = 2πr(C/360°) ;where:

C is the central angle of the arc,

R is the radius of the arc

Length of the arc = 2π(7)(135/360)

= 16.493

= 16.5 metres (approx.)

Answer:

Arc Length: 5.25π or [tex]\frac{21}{4} \pi[/tex]

Explanation:

An arc is the part of the circumference of a circle.

Formula:

[tex]\sf Arc \ Length = \dfrac{\theta}{360} \ \times \ 2\pi \ \times radius[/tex]

If applied:

[tex]\sf Arc \ Length = \dfrac{135}{360} \ \times \ 2\pi \ \times 7[/tex]

[tex]\sf Arc \ Length = \dfrac{3}{8} \ \times \ 14\pi[/tex]

[tex]\sf Arc \ Length = \dfrac{21}{4} \pi[/tex]

[tex]\sf Arc \ Length = 5.25 \pi[/tex]

Answer: Read attachment.

Step-by-step explanation: Attached below is my work. Hope it helps!

#Step1

It will result -2x-2y=-8

#2

#3

add

Find x

Answer: 40/21

Step-by-step explanation:

[tex]3 \times 105=315\\\\6 \times 10^{2}=600\\\\\implies \frac{6 \times 10^{2}}{3 \times 105}=\frac{600}{305}=\boxed{\frac{40}{21}}[/tex]

Answer: B

Step-by-step explanation:

[tex]P(x) Q(x)=R(x) \implies Q(x)=\frac{R(x)}{P(x)}\\\\Q(x)=\frac{2x^{3}+2x^{2}+3x+3}{x+1}={2x^{2}(x+1)+3(x+1)}{x+1}=\boxed{2x^{2}+3}[/tex]

350 tickets sold of children and 425 tickets sold for adult.

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.

Let x be the number of adult tickets that were sold and y be the number of children's tickets that were sold.

Total 775 tickets were sold for the game.

So,

x + y = 775

If adults tickets sold for 2.50 and children's tickets sold for 1.50 and all the tickets were sold for a total of 1587.5, it means that

2.5x + 1.5y = 1587.5

put x = 775 - y

2.5(775 - y) + 1.5y = 1587.5

1937.5 - 2.5y + 1.5y = 1587.5

-y = 1587.5- 1937.5

y = 350

and, x = 775 - y = 775 - 350

x = 425

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Answer:

Step-by-step explanation:

Two possible patters of sitting:

⇒ [tex]I) M W M W M W[/tex]

⇒ [tex]II) W M W M W M[/tex]

⇒ Three ways can be used to seat each set of three people, for a total of six.

⇒ There are two groups

2 × 3 = 6 (ways in six groups.)

*The two options can be distributed in two groups.

⇒ Total methods are equal to 6 * 6 * 2 = 72 ways.

Any wave's speed is equal to its frequency times wavelength. Now, the question doesn't specifically state what kind of wave it is. Thus, there might be two distinct scenarios: If the wave is elastic (sound is an example), you can't calculate its speed unless you also know its frequency and wavelength. However, the speed in vacuum is constant (3*108 m/s) if the wave is electromagnetic (for instance, light). In order to maintain constant velocity, frequency must shift in response to variations in wavelength. The frequency of light rays is constant in all other optical media (apart from vacuum and air), although their velocity and wavelength change correspondingly. However, that is not the case here since if it must be an EM wave with a wavelength of 10 m, then it must be a radio wave that travels uniformly through all medium at a speed of 3*108 m/s.

Answer:

[tex]x=\dfrac{11}{4}[/tex]

Step-by-step explanation:

Given:

[tex]9^{-\frac{1}{2}}=\dfrac{27^{\frac{1}{4}}}{3^{(x-1)}}[/tex]

Rewrite 9 as 3² and 27 as 3³:

[tex]\implies (3^2)^{-\frac{1}{2}}=\dfrac{(3^3)^{\frac{1}{4}}}{3^{(x-1)}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 3^{-1}=\dfrac{3^{\frac{3}{4}}}{3^{(x-1)}}[/tex]

Multiply both sides by [tex]3^{(x-1)}[/tex] :

[tex]\implies 3^{-1} \cdot 3^{(x-1)}=3^{\frac{3}{4}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies 3^{(-1+x-1)}=3^{\frac{3}{4}}[/tex]

[tex]\implies 3^{(x-2)}=3^{\frac{3}{4}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]\implies x-2=\dfrac{3}{4}[/tex]

[tex]\implies 4(x-2)=3[/tex]

[tex]\implies 4x-8=3[/tex]

[tex]\implies 4x=11[/tex]

[tex]\implies x=\dfrac{11}{4}[/tex]