Renata wins a $20 gift card to an online music site. After Renata purchases 16 songs, the gift card has a remaining
balance of $0. Which equation represents the relationship between y, the remaining balance on Renata's gift card,
and x, the number of songs purchased?

Answer:

6

Step-by-step explanation:

The given expression is,

[tex]\frac{5^{x+2}-5^x }{5^x\times4}[/tex]

Now, we know that,

[tex]a^{m+n} = a^m . a^n[/tex]

Then,

[tex]5^{x+2}=5^x . 5^2[/tex]

So,

[tex]\frac{5^{x+2}-5^x}{5^x\times4}=\frac{5^x.5^2-5^x}{5^x\times4}[/tex]

Now, taking [tex]5^{x}[/tex] common from the numerator of the given expression, then

[tex]\frac{5^{x+2}-5^x}{5^x\times4}=\frac{5^x(5^2-1)}{5^x\times4}[/tex]

[tex]\implies\frac{5^{x+2}-5^x }{5^x\times4}=\frac{5^2-1}{4}[/tex]

[tex]\implies\frac{5^{x+2}-5^x}{5^x\times4}=\frac{5\times5-1}{4}=\frac{25-1}{4}[/tex]

[tex]\implies\frac{5^{x+2}-5^x}{5^x\times4}=\frac{24}{4}=6[/tex]

So, the simplified form of the given expression gives the result 6.

Answer:

-22.25

Step-by-step explanation:

-31.7+4.5(2.1)

-31.7+9.45

-22.25

Answer:

The value of x will be an interger above or equal to 0. The value of y will be a interger equal or above 0.

Step-by-step explanation:

You can never buy a negative amount of books (x). You can only spend a positive amount of money. So even if she did not buy a book it would be 0, never under it.

Answer: it's the 2nd one

Step-by-step explanation: The value of x can be any real number greater than or equal to 0, and y will be a real number greater than or equal to 0

Answer:

There are 126 $1 bills and 21 $5 bills.

Step-by-step explanation:

Given,

Total cash Amount = $231

Solution,

Let the number of $1 bill be 'x'.

And  the number of $5 bill be 'y'.

Now according to question, one-dollar bills is six times of five-dollar bills.

So, we can frame it in equation form as;

[tex]x=6y[/tex]   ⇒ equation 1

Again according to question, there is only one-dollar bills and five-dollar bills, and no change.

That means the total cash amount is in the form of $1 and $5.

So, we can frame the above sentence in equation form as;

[tex]1\times x+5\times y=231\\\\x+5y=231[/tex]⇒ equation 2

Now substituting the value of x in equation 2, we get;

[tex]6y+5y=231\\\\11y=231\\\\y=\frac{231}{11}=21[/tex]

So, [tex]x=6y=6\times 21=126[/tex]

Hence There are 126 $1 bills and 21 $5 bills.

For this case we have that by definition, the equation of a line in its standard form is given by:

[tex]ax + by = c[/tex]

We have the following equation in the slope-intersection form:

[tex]y = -3x + 2[/tex]

Where:

-3: It's the slope

2: It is the cut-off point with the y axis.

We manipulate algebraically:

Adding 3x to both sides of the equation we have:

[tex]y + 3x = 2\\3x + y = 2[/tex]

Thus, the correct option is option B.

Answer:

Option B

Answer:

Part 1: 100

Part 2: 29.19 (Rounded)

Part 3: 20.96 (Rounded)

Step-by-step explanation:

Part 1: Triangle Sum Theorem (All angles of a triangle add up to 180 degrees)

45 + 35 + A = 180

80 + A = 180

Move the constant to the other side

80 + A = 180

-80          -80

A = 80°

Part 2: Law of sines

[tex]\frac{a}{sin(100)} = \frac{17}{sin(35)}[/tex]

Cross multiplication

sin(35)a = 16.7417318

Divide both sides by sin(35)

a = 29.18831866

Part 3: Law of cosines

[tex]b=29.19^{2}+17^{2}-2*29.19*17*cos(45)[/tex] = 439.2809039

Square root the answer

[tex]\sqrt{439.2809039}[/tex] =20.95902917

The value of angle A is 100 degrees and the measure of side a is 29.2 and b is 20.96.

A triangle is a polygon with three sides, angles, and vertices.

The triangle ABC, has AB = 17, angle ABC = 45 degree, angle ACB = 35 degree.

The measure of angle A can be determined by using the angle sum property.

45 + 35 + A = 180

80 + A = 180

A = 180-80

A = 100 degree.

Using the law of sines to find the length of side a,

a/ sin A = b/ sin B = c/sin C

a/ sin100 = 17/ sin 35

a = 17 * sin 100 / sin35

a = 29.2

Use the law of cosines to find the length of side b.

b² = c² +a² -2ac cos B

b² = (17)² + (29.2)² - 2* 17* 29.2 cos 45

b² = 439.23

b = 20.96

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Answer:

-81

Step-by-step explanation:

Answer:

1/81

Step-by-step explanation:

Answer:

0.56

Step-by-step explanation:

First, we need to look at the size of the image as a whole. It is 10x10, so it has 100 squares within it.

When counted, there are 56 shaded squares.

This gives us [tex]\frac{56}{100} =0.56[/tex]

the answer is 0.56, because there’s 56 shades squares.

Explanation: there’s 100 squares, 56 are shaded 56/100.

For every 7 boys there are 5 girls.

Divide the number of boys by the ratio for boys: 28 / 7 = 4

Now multiply that by the ratio for girls:

4 x 5 = 20

There are 20 girls.

Answer:

D) Implement better procedures at the security gate.

Step-by-step explanation:

Answer:

[tex]\large\boxed{A=6y+24}[/tex]

Step-by-step explanation:

[tex]\text{The formula of an area of a rectangle:}\\\\A=l\times w\\\\l-\text{length}\\w-\text{width}\\\\\text{We have:}\\\\l=6,\ w=y+4\\\\\text{Substitute:}\\\\A=6\times(y+4)\\\\\text{use the distributive property}:\ a(b+c)=ab+ac\\\\A=(6)(y)+(6)(4)\\\\A=6y+24[/tex]

Final answer:

To find the expression that represents the area of the rectangle, use the distributive property. The expression is 6y + 24.

Explanation:

To find the expression that represents the area of the rectangle, we can use the distributive property. The area of a rectangle is given by the formula A = length  imes width. So, for this rectangle, the length is 6 and the width is y + 4. To distribute the 6, we multiply it by both terms inside the parentheses: A = 6(y) + 6(4). This simplifies to A = 6y + 24, which is the expression that represents the area of the rectangle.

Answer:

2

Explanation:

Another way to write this is:

20 ÷ 10

2 whole tens go into 20.

20 ÷ 10 = 2

Answer: 2

This question is asking you to divide 20 by 10. This means:

20 ÷ 10=2

If 10 can go into a number 2 times, it means that 10•2=20. So, since we dont know how many times 10 goes into 20, we divide 20 by 10.

Below I have attached an image of the long division in case you need to do that as well.

Hope this helps comment below for more questions :)

The area calculated by them is 21.

Step-by-step explanation:

The given points are (-4,-2),(-3,-5),(3,-2) and (2,3).

The area of the quadrilateral:

A= [tex]\frac{(x1 y2+x2y3+x3y4+x4y1)-(x2y1+x3y2+x4y3+x1y4) }{2}[/tex].

From the given points,

A=[tex]\frac{(20+6+9-4)-(6-1-4-12) }{2}[/tex]

A=[tex]\frac{(31)-(-11) }{2}[/tex]

A= [tex]\frac{42}{2}[/tex]

The area of the quadrilateral = 21.

Answer:

The are is 28

Step-by-step explanation:

Given:

Point 1:  (– 4, – 2)

Point 2: (– 3, – 5)

Point 3: (3, – 2)  

Point 4: (2, 3)

then, the coordinates of the first point are x1 = -4, y1 = -2; of the second point x2 = -3, y2 = -5; and so on.

We can compute the area of the quadrilateral with the  shoelace formula as follows:

area = 1/2 * |x1*y2 + x2*y3 + x3*y4 + x4*y1 - x2*y1 - x3*y2 - x4*y3 - x1*y4 |

area = 1/2 * |(-4)*(-5) + (-3)*(-2) + 3*3 + 2*(-2) - (-3)*(-2) - 3*(-5) - 2*(-2) - (-4)*3 |

area = 1/2 * 56 = 28

Answer:

Rank 1 - plane.

Rank 2- line.

Rank 3- point.

Step-by-step explanation:

Here,  I have given the ranks based on what includes what.

Rank 1 is given to plane because infinite lines together makes a planes

and infinite points together makes a line.

so, Rank 1 includes both Rank 2 and Rank 3.

Now, Rank 2 is line because it consists of infinite number of points together

and is used to form a plane.

Rank 3 is point as it is the basic thing for any line or plane

See, it is simple, group of points make a line and group of lines make a plane.

visualize it this way,

When you zoom too in a plane, you see a line and when you zoom too in a line, you see a point.

Answer:

Total number of milkshakes sold on Monday = 300

Number of milkshakes without whipped cream = 90

Step-by-step explanation:

Given:

Adrienne adds whipped cream to 210 milk shakes which is 70% of the total milk shakes sold.

To find the total milkshakes sold.

Solution:

Let the total number of milkshakes sold on Monday be = [tex]x[/tex]

Percentage of milkshakes with whipped cream added to them = 70%

Number of milk shakes with added whipped cream can be given as:

⇒ [tex]70\% \textrm{ of the total number of milkshakes}[/tex]

⇒ [tex]70\% x[/tex]

⇒ [tex]\frac{70}{100}x[/tex]  [Representing percent in fraction form]

⇒ [tex]0.7x[/tex]  [evaluating in decimals]

We know that the number of milkshakes with whipped cream added to them = 210.

So, we have:

[tex]0.7x=210[/tex]

Solving for [tex]x[/tex]

Dividing both sides by  0.7

[tex]\frac{0.7x}{0.7}=\frac{210}{0.7}[/tex]

∴ [tex]x=300[/tex]

Thus, total number of milkshakes sold on Monday = 300

Number of milkshakes without whipped cream = [tex]300-210[/tex]= 90

Answer: 2x6x3=36 divided by 4=9+1=10.

The expression (2x6x3) ÷ 4 + 1 Grinch's plus two is solved using the order of operations, giving a result of 10 plus two Grinch's, symbolized as 10 + 2G.

The question is a basic arithmetic problem that involves both multiplication and addition within parentheses, followed by division and then more addition.

The order of operations, often abbreviated as PEMDAS - which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right) - must be followed to solve the expression correctly.

Let's solve the expression step by step:

The final answer is 10 plus two Grinch's, which we write as 10 + 2G.

Okay I will just keep it in terms of pi to make it more pretty.

area = 1/4π(8²) = 16π

answer: 16π

Answer : The area of the shape is, 50.24 unit square.

Step-by-step explanation :

To calculate the the area of shaded sector in the circle in degree, the formula used as:

[tex]A=\frac{\theta}{360}\times \pi r^2[/tex]

where,

A = area of sector

[tex]\theta[/tex] = angle = 90°

r = radius of circle = 8 unit

Now put all the given values in the above formula, we get:

[tex]A=\frac{90}{360}\times 3.14\times (8)^2[/tex]

[tex]A=50.24[/tex]

Therefore, the area of the shape is, 50.24 unit square.

Answer:

2x + 45 = 6

Step-by-step explanation:

(2/9)x + 5 = 2/3                        Subtract 5 from both sides

(2/9)x +5-5=2/3-5

(2/9)x = - 4 1/3                          Multiply by 9

2x = -13/3 * 9

2x = -39

x = -19.5

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

I see. You don't want it solved. Multiply by 9 to clear the fractions.

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

2x + 45 = 6

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

Solve it now. It should be easier.

2x = 6 - 45

2x = - 39

x = -19.5

Ahmed could have gained 61 rupees more, if had given had given in compound interest.

Solution:

Given that Ahmed lent amir Rs8000 at simple interest for 3 years at the rate of 5% per annum

Simple Interest calculation:

Principal = 8000

Rate of interest = 5%

Time = 3

Formula:

[tex]S.I=\frac{p\times n\times r}{100}[/tex]

Where , "p" is the principal and "n" is the number of years and "r" is the rate of interest

Substituting the values in formula,

[tex]S.I = \frac{8000 \times 3 \times 5}{100}\\\\S.I = 80 \times 3 \times 5 = 240 \times 5\\\\S.I = 1200[/tex]

Compound Interest calculation:

Principal = 8000

Rate of interest = 5% compounded annually

Time = 3

Formula:

[tex]C.I=P(1+\frac{R}{100})^n-P[/tex]

Substituting the values in formula,

[tex]\Rightarrow C.I=8000(1+\frac{5}{100})^3-8000\\\\\Rightarrow C.I=9261-8000\\\\\Rightarrow C.I=1261[/tex]

Therefore, the difference between the interests:

1261 - 1200 = 61

Thus he could have gained 61 rupees more, if had given had given in compound interest.

Answer:

[tex]3\frac{3}{4}\ \frac{yd^2}{h}[/tex]

or

[tex]3.75\ \frac{yd^2}{h}[/tex]

Step-by-step explanation:

we know that

To find out the unit rate, divide the total square yards by the total time in hours

so

[tex]\frac{(5/4)}{(1/3)}=\frac{15}{4}\ \frac{yd^2}{h}[/tex]

Convert to mixed number

[tex]\frac{15}{4}\ \frac{yd^2}{h}=\frac{12}{4}+\frac{3}{4}=3\frac{3}{4}\ \frac{yd^2}{h}[/tex]

or

[tex]3.75\ \frac{yd^2}{h}[/tex]

Answers:

x = 6

y = 6*sqrt(2)

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

Explanation:

To find these values, you can use the general template of a 45-45-90 triangle or you can use trig ratios

tan(45) = 1

tan(angle) = opposite/adjacent

tan(45) = x/6

1 = x/6

6*1 = x

x = 6

-------

sin(45) = 1/sqrt(2)

sin(angle) = opposite/hypotenuse

sin(45) = 6/y

1/sqrt(2) = 6/y

1*y = sqrt(2)*6

y = 6*sqrt(2)

Answer:

Jaime drove for 6.127 miles.

Step-by-step explanation:

See the attached diagram.

The length from All Groceries Food store to Get Rich Savings bank along Flower street is x miles (say) and the length from Get Rich Savings bank to AAA hardware along the Broad street is 4 miles.

Since, the Flower street and Broad street are perpendicular to each other, hence,  

[tex]\tan 28 = \frac{x}{4}[/tex]

⇒ x = 4 tan 28 = 2.127 miles.

Therefore, Jaime drove for (4 + 2.127) = 6.127 miles ≈ 6.1 miles. (Answer)

Answer:

-2x+8

Step-by-step explanation:

Answer:

For the given equations the values of x and y by using substitution method are  [tex]x=1[/tex]  and [tex]y=\frac{13}{2}[/tex]

Step-by-step explanation:

Given system of equations are

[tex]-3x+2y=16\hfill (1)[/tex]

[tex]x-2y=-12\hfill (2)[/tex]

Solve the given equations by substitution method:

Now (2) implies

[tex]x-2y=-12[/tex]

[tex]x=-12+2y\hfill (3)[/tex]

Now substitute the x value in equation (1)

[tex]-3x+2y=16[/tex]

[tex]-3(-12+2y)+2y=16[/tex]

[tex]36-6y+2y=16[/tex]

[tex]36-4y=16[/tex]

[tex]-4y=16-36[/tex]

[tex]y=-(\frac{-26}{4})[/tex]

[tex]y=\frac{26}{4}[/tex]

Therefore  [tex]y=\frac{13}{2}[/tex]

Now substitute the y value in equation (3)

[tex]x=-12+2y[/tex]

[tex]x=-12+2\times \frac{13}{2}[/tex]

[tex]x=-12+13[/tex]

[tex]x=1[/tex]

Therefore [tex]x=1[/tex]  and [tex]y=\frac{13}{2}[/tex]

Answer:

$32.50

Step-by-step explanation:

Just divide $65 by 2 and you get $32.5(0).

Juan spent $32.50 on the 2 tires.

You are very welcome!

The cost of two tires = 65 - cots of tuned up.

And we need the cost of two tires.

Subtraction is a mathematic operation. Which is used to remove terms or objects in an expression.

Given:

Juan bought two new tires for his bike.

He also had the bike tuned up.

The total bill was $65.

To find the cost of two tires:

The cost of two tires = 65 - cots of tuned up.

Therefore, we need the value of missing information.

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The complete question:

Draw a Conclusion: Juan bought two new tires for his bike. He also had the bikec tuned up. The total bill was $65. How much did Juan spend on the 2 tires?

Answer:

4.80 rounded

Step-by-step explanation:

Answer:

The value of x in terms of b is (-3/b)

The value of x when b is 3 is -1

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

Step-by-step explanation:

The given function is :

-2 (bx - 5) = 16

Divide both sides by 2

bx - 5 = 16/(-2) = -8

Add 5 to both sides

bx = -8 + 5 = -3

Divide both sides by (b)

∴ x = -3/b

∴ The value of x in terms of b is (-3/b)

When b = 3 ⇒ ∴ x = -3/b = -3/3 = -1

Answer:

Two intersecting lines that form right angles (90 degree angles). All perpendicular line intersections will form .

Step-by-step explanation:

Answer: 90° angle

Step-by-step explanation: In the image provided, you can see that the 2 lines cross at a point so they're intersecting lines. However, notice the box that is used at the point where the lines meet. This box means that the lines meet at a 90° angle or a right angle and 2 lines that intersect at a right angle are called perpendicular lines which means that the lines are perpendicular.

Answer:

See explanation

Step-by-step explanation:

Consider triangles ABC and DEC. In these triangles,

Thus, by AAS postulate, triangles ABC and DEC are congruent. Congruent triangles have congeruent corresponding sides.

So,

[tex]BC\cong EC[/tex]

The Angle Angle Side postulate (AAS) states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.