Estimate the side length of a square that has a 9cm long diagonal

The sales tax would be $42.00, making the total cost $112.00.

To calculate the sales tax on an item, one must first convert the sales tax rate from a percentage to a decimal. Converting 60% to a decimal by dividing by 100 gives us 0.60.

Then, multiply this decimal by the selling price to find the amount of sales tax.

Amount of sales tax = price x rate of sales tax

So for a selling price of $70.00, the sales tax would be calculated as follows:

= $70.00 x 0.60 = $42.00

The sales tax on a $70.00 item at a rate of 60% is $42.00.

To find the total cost, one must add this tax to the original selling price.

Total cost = selling price + sales tax

Total cost = $70.00 + $42.00

Total cost = $112.00

Thus, the total amount paid including sales tax would be $112.00.

Answer:

C

Step-by-step explanation:

To find whether it is a arithmetic or geometric sequence it is easiest to try to subtract term a2 from a1, seeing if d or r is positive. If that does not heed an answer try dividing a2 by a1 to see if it is a geometric sequence.

The terms go as follows just in case (They would normally be in subscripts)-

a1= -12

a2= -7

a3= -2

a4= 3

Answer: Yes; 5 (choice A)

We add 5 to each term to get the next

-12+5 = -7

-7+5 = -2

-2+5 = 3

and so on. The nth term formula is

an = -12 + 5(n-1)

If you were to plug in n = 1, 2, 3, ... then it should generate the terms shown

Answer:

x=-1, y=4

Step-by-step explanation:

When we solve by elimination, we are getting rid of one variable, in this case y.  We will add the two equations together.

5x-4y=-21

-2x+4y=18

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

3x  = -3

Divide each side by 3

3x/3 =-3/3

x =-1

Now we need to calculate y

-2x +4y = 18

Substitute x=-1

-2(-1)+4y = 18

2+4y =18

Subtract 2 from each side

4y = 18-2

4y=16

Divide each side by 4

4y=16/4

y =4

The point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (3, 0) and (6, -3). Substitute:

[tex]m=\dfrac{-3-0}{6-3}=\dfrac{-3}{3}=-1[/tex]

The point-slope form:

[tex]y-(-3)=-1(x-6)\\\\\boxed{y+3=-(x-6)}[/tex]

or

[tex]y-0=-1(x-3)\\\\\boxed{y=-(x-3)}[/tex]

The slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

From the second point-slope form we have slope-intercept form:

[tex]y=-(x-3)\\\\y=-x-(-3)\\\\\boxed{y=-x+3}[/tex]

Answer:

$16.32

Step-by-step explanation:

1. Ms. Blankenship bought 32 glue sticks each for  $1.40, then she spent

[tex]\$1.40\cdot 32=\$44.80[/tex]

for all sticks.

2. Ms. Blankenship bought 32 boxes each for  $0.59, then she spent

[tex]\$0.59\cdot 32=\$18.88[/tex]

for all boxes.

3. Together 32 glue sticks and 32 boxes cost

[tex]\$44.80+\$18.88=\$63.68.[/tex]

4. If Ms. Blankenship had $80, then she had left

[tex]\$80-\$63.68=\$16.32.[/tex]

As x increases, x^3 grows faster than 3x.

As x increases, the growth rate of x^3 (x cubed) is faster than that of 3x. This can be explained by comparing their respective derivatives.

The derivative of x^3 with respect to x is 3x^2, while the derivative of 3x is simply 3.

The derivative represents the rate of change, or the slope of the function at a given point. In the case of x^3, its derivative 3x^2 grows at a faster rate than the derivative of 3x, which is a constant (3).

This means that as x increases, the rate of change of x^3 (3x^2) increases faster compared to the rate of change of 3x (which is constant at 3). In other words, x^3 exhibits exponential growth, while 3x exhibits linear growth. So, as x increases, x^3 grows faster than 3x.

for such more question on growth rate

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Answer:

53028.064 I think

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

To find the x- intercepts set y = 0, that is

- 2x² - 9x + 5 = 0

To factorise the quadratic consider the factors of the product of the coefficient of the x² term and the constant term that sum to give the coefficient of the x- term.

product = - 2 × 5 = - 10 and sum = - 9

The factors are - 10 and + 1

Use these factors to split the middle term

- 2x² - 10x + x + 5 = 0 ( factor the first/second and third/fourth terms )

- 2x(x + 5) + 1(x + 5) ( factor out (x + 5) )

(x + 5)(- 2x + 1) = 0

equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

- 2x + 1 = 0 ⇒ x = [tex]\frac{1}{2}[/tex]

x-intercepts are x = - 5 and x = [tex]\frac{1}{2}[/tex]

Answer:

What drop down menues??????????????????????

Step-by-step explanation:

Answer:

options?

Step-by-step explanation:

Answer:

Car D will have a different measurement because the 60.35 would round up to be 60.31 where all the other would round down and remain at 60.30

Step-by-step explanation:

The point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

We have the line

[tex]y-3=-\dfrac{1}{5}(x+2)\to m=-\dfrac{1}{5}[/tex]

If m₁ and m₂ are the slopes of the perpendicular lines, then

[tex]m_1m_2=-1\to m_2=-\dfrac{1}{m_1}[/tex]

Therefore the slope of ouer line is

[tex]m=-\dfrac{1}{-\frac{1}{5}}=5[/tex]

We have the point (-2, 7). Put the coordinates to the equation of a line in the point-slope form:

[tex]y-7=5(x-(-2))[/tex]

[tex]y-7=5(x+2)[/tex]      use the distributive property

[tex]y-7=(5)(x)+(5)(2)[/tex]

[tex]y-7=5x+10[/tex]       add 7 to both sides

[tex]\boxed{y=5x+17}[/tex]

If an image is being enlarged by 15% you would take the base number multiply it by the percent in decimal form and add the result to the base number.

4.25*0.15=0.6275

0.6375+4.25=4.8875

Answer: 4.8875

To find out the height of the photocopied drawing, we first calculate 15% of the original height (4.25 inches) and add this to the original height. The photocopied drawing is approximately 4.89 inches tall.

The student photocopied a drawing with the copier set to enlarge the image by 15%. If the original drawing is 4.25 inches tall, the enlarged photocopied drawing would be larger by 15% of 4.25 inches.

Firstly, to find 15% of 4.25 inches, you multiply 4.25 by 0.15 (the decimal equivalent of 15%), which equals 0.6375 inches.

Adding this to the original height of the drawing, we get 4.25 inches + 0.6375 inches = 4.8875 inches, which is approximately 4.89 inches when rounded to two decimal places.

So, the photocopied drawing is approximately 4.89 inches tall.

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Answer:think as it as coordinates on a graph. Time=x Amount=y. So if the time is 0 and the amount is 60 you would graph a point on (0,60)

Step-by-step explanation:

Answer: the two numbers is 35 and 18

Step-by-step explanation: 35+18=53 35-18=17

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Final answer:

The two numbers are 35 and 18. We found these by solving the simultaneous equations x + y = 53 and x - y = 17, representing their sum and difference.

Explanation:

Finding Two Numbers Given Their Sum and Difference

Let's denote the two unknown numbers as x and y. According to the conditions given:

x + y = 53 (Equation 1: The sum of the two numbers)

x - y = 17 (Equation 2: The difference of the two numbers)

We can solve these two simultaneous equations to find the values of x and y.

Add the two equations:

(x + y) + (x - y) = 53 + 17

2x = 70

x = 35

Substitute x in Equation 1:

35 + y = 53

y = 53 - 35

y = 18

Therefore, the two numbers are 35 and 18.

Answer: you need to get a common denominator.. once you have a common denominator, you can compare numerators to see what is larger..

Step-by-step explanation:

to get the common denominator, you would first see what this would be.. in this case 18, as that's the lowest.  then, you would multiply each fraction by 2/2 for first and 3/3 for second, which are just funky looking ones.  therefore, D is the correct answer.

Answer:It is C

Step-by-step explanation:In the question it says to COMPARE the fraction.

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Answer:

4:2 is the same as:

2:1

8:4

or anything that is proportional to 4:2

Step-by-step explanation:

A proportion is anything that corresponds in size or amount to something else.

Answer:

2:1

Step-by-step explanation:

just reduce the ratio b and divivd bith sides by 2

Answer:

The mystery number is -3

Step-by-step explanation:

five more then -8 times a number is 29.

-8n +5 = 29

Subtract 5 from both sides

-8n +5-5 = 29-5

-8n = 24

Divide by -8 on each side

-8n/-8 = 24/-8

n= -3

The mystery number is -3

The mystery number in the equation is -3, determined by solving the algebraic equation 5 + (-8 × n) = 29.

The equation given in the problem statement translates to the mathematical expression 5 + (-8 × n) = 29, where n is the mystery number. To find the value of n, we can perform the following steps:

Subtract 5 from both sides to get -8n = 24.

Divide both sides by -8 to isolate n, giving us n = 24 / -8.

Calculate the result to find that n = -3.

Therefore, the mystery number is -3.

Answer:

The equation of this line would be 4x + y = 13

Step-by-step explanation:

In order to find this equation we must first find the slope of the original line. To do this, we solve the original equation for y.

4x + y - 2 = 0

4x + y = 2

y = -4x + 2

The original slope (the coefficient of x) is -4, which means the new slope will also be -4 because parallel lines have the same slope. Now, we can use this slope along with the point in point-slope form to find the equation of the line. Just plug in the numbers and solve for the coefficient.

y - y1 = m(x - x1)

y + 3 = -4(x - 4)

y + 3 = -4x + 16

4x + y + 3 = 16

4x + y = 13

Answer:

[tex]-\frac{1}{2\pi}[/tex] cm³/min  

Step-by-step explanation:

Let h = height of water and r = radius of its surface  

[tex]V = \frac{ 1}{ 3}\pi r^{2}h[/tex]

At all times,  

[tex]\frac{r }{h } = \frac{4 }{16 } = \frac{ 1}{4 }[/tex]

So, [tex]r = \frac{h }{4 }[/tex]  

[tex]V = \frac{ 1}{ 3}\pi (\frac{h }{ 4})^{2}h[/tex]

[tex]V = \frac{ 1}{ 48}\pi h^{3}[/tex]

[tex]\frac{\text{d}V}{\text{d}h} = \frac{ 1}{ 16}\pi h^{2}[/tex]

We want [tex]\frac{\text{d}h}{\text{d}t}[/tex]

[tex]\frac{\text{d}V}{\text{d}t} = \frac{\text{d}V}{\text{d}h} \frac{\text{d}h}{\text{d}t}[/tex]

[tex]\frac{\text{d}V}{\text{d}t}[/tex] = -2 cm³/min  

[tex]-2 = \frac{ 1}{ 16}\pi h^{2} \frac{\text{d}h}{\text{d}t}[/tex]

[tex]\frac{\text{d}h}{\text{d}t} = -\frac{2}{\frac{ 1}{ 16}\pi h^{2} }[/tex]

[tex]\frac{\text{d}h}{\text{d}t} = -\frac{32}{\pi h^{2}}[/tex]

When h = 8  cm

[tex]\frac{\text{d}h}{\text{d}t} = -\frac{32}{\pi\times8^{2}}[/tex]

[tex]\frac{\text{d}h}{\text{d}t} = -\frac{32}{64\pi}[/tex]

[tex]\frac{\text{d}h}{\text{d}t} = -\frac{1}{2\pi}[/tex] cm³/min

The depth of the water is decreasing at a rate of [tex]\frac{1}{2\pi}[/tex] cm³/min

.

Answer:

25%  

Step-by-step explanation:

Change = Final - initial

% Change =(Final - Initial)/Initial × 100%

% Change = (50 - 40)/40 × 100%

% Change = 10/40 × 100%

% Change = 25%

Answer:

25%

Step-by-step explanation:

1) Find the difference of the two numbers, do (Largest Number)-(Smallest Number).

2) Use your difference as a fraction. Use the difference over the initial value.

3) Create a proportion

10/40 = x/100

4) Cross multiply, 10*100 = 200, 40*p = 40p

5) Simplify expression 1,000=40p

6) Solve, 1,000/40 = 25

7) Put it as a fraction, 25/100

8) Make it a percent 25%

Answer:

The 8th term is 23

Step-by-step explanation:

If we are given the formula for the sequence

an=2n+7,

then to find the 8th term we substitute n=8 into the formula.

a8 = 2(8) +7

a8 = 16+7

a8 = 23

The 8th term is 23

Answer:

a (5,2)

Step-by-step explanation:

To get to the smiley face, we move 5 units in the x direction from the origin, then we move 2 units up in the y direction  (x,y)  so the point is at (5,

If the points P (7, 12), Q (-3, -12) and R (14, 5) lie on a circle with the center C (0, 2), then the distance OP, OQ and OR are the same.

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute:

[tex]OP=\sqrt{(2-7)^2+(0-12)^2}=\sqrt{(-5)^2+(-12)^2}=\sqrt{25+144}=\sqrt{169}\\\\\boxed{OP=13}\\\\OQ=\sqrt{(2-(-3))^2+(0-(-12))^2}=\sqrt{5^2+12^2}=\sqrt{25+144}=\sqrt{169}\\\\\boxed{OQ=13}\\\\OR=\sqrt{(2-14)^2+(0-5)^2}=\sqrt{(-12)^2+(-5)^2}=\sqrt{144+25}=\sqrt{169}\\\\\boxed{OR=13}[/tex]

OP = OQ = OR, therefore the points P, Q and R lie on one circle.

There are 0 unique triangles that can be drawn with the side lengths 4 cm, 5 cm, and 10 cm

How to determine the total number of unique triangles that can be drawn

From the question, we have the following parameters that can be used in our computation:

Side lengths = 4 cm, 5 cm, and 10 cm

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

So, we have

4 + 5 > 10 --- false

4 + 10 > 5 --- true

5 + 10 > 4 --- true

Since one of the conditions is false, no triangles can be formed using the side lengths

Answer: The new price is $3350.

Answer:

$3350; $30 150  

Step-by-step explanation:

Original price = $33 500

Discount = 33 500 × 10 %

Discount = 33 500 × 0.10

Discount = $3350

New price = Original price - Discount

New price = 33 500 - 3350

New price = $30 150

Answer:

B. 12,17,23

Step-by-step explanation:

2,3,5,8, _,_,_

2,3 is increased by 1

3,5 is increased by 2

5,8 is increased by 3.  theres our pattern, each time it increases it follows the next number so the next 3 numbers it would be increased by is. 4,5,6.

Now knowing it is 4,5,6 we need to add, start adding.

8+4=12. Which answers have 12 in them? B and C.

We know 12 is the next number, now we add 5 to that.

12+5=17.

B has 17 but C doesn't, so that tells you its most likely going to be B. To make sure add 6 to 17.

17+6=23. Its true that it is B, as B is 12.17.23.

The next three terms in the sequence are 13, 21, and 34.

The given sequence is 2, 3, 5, 8.

To find the next three terms in the sequence, we need to determine the pattern.

By observing the sequence, we can see that each term is obtained by adding the two previous terms.

For example,

3 = 2 + 1,

5 = 3 + 2, and

8 = 5 + 3.

Using this pattern, the next term would be obtained by adding 8 + 5, -

8 + 5 = 13

The two terms after that would be

13 + 8 = 21 and

21 + 13 = 34.

Therefore, the next three terms in the sequence are 13, 21, and 34.

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Answer: [tex]\bold{\pm \{1, 2, 3, 4, 6, 12, \dfrac{1}{2}, \dfrac{3}{2}\}}[/tex]

Step-by-step explanation:

        Q                       P

f(x) = 2x³ - bx² + cx + 12

Possible rational roots are all of the factors of P divided by all of the factors of Q, including both positive and negative signs.

[tex]\quad \pm \dfrac{\text{factors of P}}{\text{factors of Q}}\\\\=\pm \dfrac{\text{factors of 12}}{\text{factors of 2}}\\\\=\pm \dfrac{1,2,3,4,6,12}{1,2}\\\\=\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm \dfrac{1}{2}, \pm \dfrac{3}{2}\\[/tex]

The proportional relationship:

y = ax for a > 0.

Therefore your answer is:

Answer:4/52=1/13

Step-by-step explanation:

The deck has 52 cards and contains 4 aces. When you draw a card, the probability of drawing an ace is 4/52=1/13

Answer:

you divide the top number by the bottom number

Step-by-step explanation:

2/5 = 0.4