1. Julia used square tiles to make
a design. She laid the tiles in a
square, 8 tiles wide by 8 tiles
long. Each tile has an area of 1
square inch. What is the area of
Julia's tile design?

Answer:

[tex]\textsf{a)} \quad y=1.8(3.2)^x[/tex]

[tex]\textsf{b)} \quad y=5(7)^x[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

Given ordered pairs:

The y-intercept is the y-value when x = 0.

Therefore, as the y-intercept is 1.8, a = 1.8.

[tex]\implies y=1.8b^x[/tex]

Substitute point (1, 5.76) into the equation and solve for b:

[tex]\begin{aligned} y&=1.8b^x\\\implies 5.76&=1.8 \cdot b^1\\5.76&=1.8b\\b&=\dfrac{5.76}{1.8}\\b&=3.2\end{aligned}[/tex]

Therefore, the exponential equation is:

[tex]\boxed{y=1.8(3.2)^x}[/tex]

To complete the given table, simply substitute the values of x into the found equation:

[tex]\begin{array}{c|l}x&\phantom{189}y\\\cline{1-2} \vphantom{\dfrac12}}0&\phantom{18}1.8\\\vphantom{\dfrac12}}1&\phantom{18}5.76\\\vphantom{\dfrac12}}2&\phantom{1}18.432\\\vphantom{\dfrac12}}3&\phantom{1}58.9824\\\vphantom{\dfrac12}}4&188.74368\end{array}[/tex]

Given ordered pairs:

The y-intercept is the y-value when x = 0.

Therefore, as the y-intercept is 5, a = 5.

[tex]\implies y=5b^x[/tex]

Substitute point (2, 245) into the equation and solve for b:

[tex]\begin{aligned} y&=5b^x\\\implies 245&=5 \cdot b^2\\49&=b^2\\b&=\sqrt{49}\\b&=7\end{aligned}[/tex]

Therefore, the exponential equation is:

[tex]\boxed{y=5(7)^x}[/tex]

To complete the given table, simply substitute the values of x into the found equation:

[tex]\begin{array}{c|l}x&\phantom{11}y\\\cline{1-2} \vphantom{\dfrac12}}0&\phantom{1111}5\\\vphantom{\dfrac12}}1&\phantom{111}35\\\vphantom{\dfrac12}}2&\phantom{11}245\\\vphantom{\dfrac12}}3&\phantom{1}1715\\\vphantom{\dfrac12}}4&12005\end{array}[/tex]

Answer:7

Step-by-step explanation:

78.9 kg.

To convert 78,900 grams to kilograms, we can divide the number of grams by 1,000. Since 1 kilogram is equal to 1,000 grams, dividing the number of grams by 1,000 will give us the equivalent number of kilograms.

Therefore, 78,900 grams is equivalent to 78,900 / 1,000 = 78.9 kilograms.

The required investment return on the fund is $6300 which is 16.8% of the investment.

Given that,
purchased 5,000 shares of a mutual fund at a price of $7.50 per share. Later sell those shares for $8.35 per share. During the time you owned the shares, the fund paid a dividend of $0.41 per share.

When someone applies for their money on something so that he can get a higher value in returns of his money.

Here,
Profit = 5000[8.35 + 0.41-7.50]
profit = $6300
Profit percentage = 6300 / [7.5 × 5000] × 100%
Profit percentage = 16.8%

Thus, the required investment return on the fund is $6300 which is 16.8% of the investment.

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Answer: 48 3/4 miles/hour.

Step-by-step explanation: To find Daniel's speed in miles per hour, we need to first convert the time he rollerbladed to hours. We can do this by dividing the number of minutes he rollerbladed by 60 minutes per hour, as follows:

time in hours = 4 minutes / 60 minutes/hour = 1/15 hours

We can then use the formula for speed, which is distance divided by time, to find Daniel's speed in miles per hour as follows:

speed in miles per hour = distance in miles / time in hours

speed in miles per hour = 3 1/4 miles / 1/15 hours

speed in miles per hour = 3 1/4 miles * 15 hours/1

speed in miles per hour = 48 3/4 miles/hour

Therefore, Daniel's speed in miles per hour was 48 3/4 miles/hour.

Answer:

Check explanation!

Step-by-step explanation:

Daniel  rollerbladed at 15 mph, we know this because 60 divided by 4 = 15 (number of minutes in an hour divided by his time = answer)

so daniel rollerbladed at 15 mph

Answer:

21.64 % probability of rain at a random year

Step-by-step explanation:

79/365 * 100

21.64 %

The answer is x = -70.

To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.

Multiply all terms by the same value to eliminate fraction denominators

/7 = −10

7⋅/7 = 7(−10)

Cancel multiplied terms that are in the denominator

7⋅/7 = 7 (−10)

x =7(-10)

Multiply the numbers

=7(−10)

=−70.

Hence The answer is x = -70.

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Answer:

Part A: The bill is $27.32

Part B: The percentage is 19%

My work:

Part A

   ?                   8

---------     =    ---------

25.30             100

equals 2.02400

then round to get the tax amount which is $2.02

to find the bill cost we need to add the tax and the cost of the meal:

2.02 + 25.30 = 27.32

Part B

to find the tip we need to subtract the bill from the total lunch cost:

27.32 + t = 4.92                              (t = tip)

32.24 - 27.32 = 4.92

So now that we know the tip we can figure out how much percentage that is of the cost of the meal:

4.92              ?

--------    =   --------

25.30         100

which equals 19.4466403/100

the percentage is 19%

Answer:

HL

Step-by-step explanation:

the two triangles are right and have the same hypotenuse (the diagonal side) and one congruent leg (the horizontal side)

The rate that best represents the relationship between the number of square feet and the number of gallons of paint is 156 square feet per gallon of paint.

Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that a contractor has 18 gallons of paint that will cover 2,808 square feet. Therefore, the relationship between the number of square feet and the number of gallons of paint can be written as,

Number of square feet per gallon of paint

= Total area painted by 18 gallons / Total area of the paint

= 2,808 square feet / 18 gallons

= 156 square feet per gallon of paint

Hence, the correct option is C.

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The complete question is:

A contractor has 18 gallons of paint which will cover 2,808 square feet. Which of the following rates best represents the relationship between the number of square feet and the number of gallons of paint?

1 point

A. 182 gallons of paint per square foot

B. 2,912 gallons of paint per square foot

C. 156 square feet per gallon of paint

D. 16 square feet per gallon of paint

Answer:

Step-by-step explanation:

4.2 miles

Answer:

Step-by-step explanation:

option 2 since it equals 14/4

Answer:

-8/3

Step-by-step explanation:

Answer:500 I hope this helpful

Step-by-step explanation:

3000 divided by 48 times 8

To make the calculation easier, first multiply the numbers that result in multiples of 10

24000 divided by 48

Divide the numbers
=500

Answer:

250

Step-by-step explanation:

If we follow the rules of PEMDAS, we go from left to right. Therefore, first, do 3,000 divided by 48.

3,000/48=62.5

Now, multiply 62.5 by 4.

62.5x4= 250

250 is your answer :D

Hope this helps and have a wonderful day!

Sarah spends reading 30 min + [tex]0.05 min^{2}[/tex].

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. To assist identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.

However, in modern mathematics, and particularly in computer algebra, formulae are considered expressions that may be evaluated as true or false based on the values assigned to the variables in the expressions.

The problem is in a mathematical expression.

30 min+3s min did Sarah spend reading

Convert s to min

.30min+3s min× 1min/60s

Cancel the common units and simplify.

Cross-cancel units.

30 min + [tex]0.05 min^{2}[/tex]

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Answer: C

Step-by-step explanation:

38520 *.12 = $4,622.40

When the figure passed through the transformations the image formed is similar to the image at B as attached

The figure is in the second quadrant

clockwise rotation 90degrees about the origin will being the figure to the first quadrant

Translation 9 units down will bring an image to the -6 of the y direction in the fourth quadrant

reflection over the y axis will create a mirror image of the figure and make the image at the third quadrant

The option B correctly shows the final image

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The figure that should be the next, following the pattern is option (b)

The missing information that completes this question is added as an attachment

From the attached figure, we have the following pattern:

When the pattern is studied carefully, we can see that the next figure is the figure in option (b)

This is so because the figure in option (b) is gotten by rotating the last figure in the pattern by 45 degrees to the right

Hence, the conclusion about the figure that should be the next figure is that the next figure should be figure (b)

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With the help of similar triangles the height of Flagpole is 15.13 feet

what is similar triangle?

Triangles that are similar in shape but differ in size are known as similar triangles. Examples of related objects are all equilateral triangles and squares with any side length. To put it another way, if two triangles are comparable, then their corresponding angles and sides are congruent and equal in size.

solution:

let C is the point of reflection in triangle ABC and EDC

∠ ABC = ∠ EDC ( 90 Degree)

∠ ACD = ∠ ECD ( Reflective angle )

By symmetry,

AB/ED = BC/CD

5.6/ x  = 7.4 / 20

       x  =  15.13 feet

Hence the height of flagpole is 15.13 feet

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The zeros of the quadratic equation: h(x) = x^2 - 2x - 35

are -5 and 7, thus the correct option is B.

Here we have the quadratic equation:

h(x) = x^2 - 2x - 35

Using the quadratic formula we will get the two solutions:

[tex]x = \frac{2 \pm \sqrt{(-2)^2 - 4*1*-35} }{2*1} \\\\x = \frac{2 \pm 12 }{2} \\\\[/tex]

The solutions are:

x = (2 + 12)/2 = 7

x = (2 - 12)/2 = -5

Then the factors of the quadratic are (x - 7) and (x + 5), the correct option is B.

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Answer: D

Step-by-step explanation:

Yes, human can distinguish pixels on a same-sized HDTV with 2 times 10 to the 6th power pixels.

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

In the scientific form, we write a number in the form of base×10ⁿ.

Where 0 ≤ base < 10 and n can be any rational number.

Given,

Humans can distinguish up to 18,400,000 individual dots called pixels on a typical computer display

We need to check whether human distinguish pixels on a same sized HDTV with 2 x 10 to the 6th power pixels

2×10⁶ pixels.

= 2000000 pixels.

As  2000000 < 18400000

Hence, human can distinguish pixels on a same-sized HDTV with 2 times 10 to the 6th power pixels.

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Answer:x=-9

Step-by-step explanation:-12/4=-3 then do 3*-3=-9

The value of numerical expression 4(16)³ / 10³ will be 16.384.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ 4(16)³ / 10³

Simplify the expression, then we have

⇒ 4(16)³ / 10³

⇒ 4 x 4096 / 1000

⇒ 16384 / 1000

⇒ 16.384

The value of numerical expression 4(16)³ / 10³ will be 16.384.

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Answer:

C

Step-by-step explanation:

(√2) can be interpreted as 2^(1/2) and the second term can be interpreted as 2^(1/3). The law of exponents tells us that we must add the exponents when multiplying two numbers with the same base. 1/2 + 1/3 is 3/6+2/6 = 5/6 so the final answer would be 2^(5/6)

x=-4, y=-5

You can substitute equation 2 into equation 1 since it's easier. After that, just substitute x=-4 back into equation 2.

The triangle ΔBAE is congruent to the triangle ΔCDE by ASA postulate.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

If two lines intersects, then the opposite angle of the line will be congruent to each other.

In ΔBAE and ΔCDE,

AB = DC, (Given)

∠BAE = ∠CDE, (Right angle)

∠BEA = ∠DEC, (Opposite angle)

The triangle ΔBAE is congruent to the triangle ΔCDE by ASA postulate.

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The cost of one square inch of the cookie cake is $5.

What is area of circle?

The area encircled by a circle with radius r is known as πr^2 in geometry. Here, the Greek letter π stands for the constant proportion of a circle's circumference to its diameter, which is roughly equal to 3.14159.

Given:

A circular cookie cake costs $15.70.

The diameter of the cookie cake is 10 inches.

We have to find the cost of one square inch of the cookie cake.

Let the diameter is 10 inches.

So, the radius is 10/2 = 5 inches.

Area of circle = πr^2

                      = 3.14 x (5)^2

                       = 3.14 x 25

Area of circle  = 78.5 square inches.

So, the cost of one square inch cookie cake is,

78.5 / 15.70 = 5

Hence, the cost of one square inch of the cookie cake is $5.

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Answer: The answer is $0.20.

Step-by-step explanation: Hope this helps! :)

Answer:  3.46

Step-by-step explanation:

5[tex]u^{2}[/tex] = 60

 [tex]u^{2}[/tex] = 12

 u = [tex]\sqrt{12}[/tex]

 u = 3.46