The human heart circulates from 770,000 to 1,600,000 gallons of blood through a person's body every year. Write a compound inequality to represent the number of gallons of blood that the heart circulates through the body in one day. x

By trigonometric formulas and algebra properties, the equivalence between the trigonometric expression (sin x - cos x)² and the trigonometric expression 1 - 2 · sin x · cos x.

In this problem we need to prove if the trigonometric expression (sin x - cos x)² is equivalent to the trigonometric expression 1 - 2 · sin x · cos x, this can be proved by trigonometric formulas and algebra properties. First, write the initial expression:

(sin x - cos x)²

Second, expand the binomial:

sin² x - 2 · sin x · cos x + cos² x

Third, use the fundamental trigonometric expression:

1 - 2 · sin x · cos x

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Answer: x= (2)/5 & x= (-2)/5

Step-by-step explanation:

Factor Form:

1. Use the sum product patturn

25x^2-4=0 → 25x^2+10-10-4=0

2. Common factors from each pair

25x^2+10-10-4=0 → 5x(5x+2)-2(5x+2)=0

3. Rewrite the factored form

5x(5x+2)-2(5x+2)=0 → (5x+2)(5x-2)=0

4. Create separate equations

(5x+2)(5x-2)=0 → 5x+2=0  5x-2=0

5. Solve

5x+2=0  5x-2=0 → x=(2)/5   x=(-2)/5

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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Answer: x=-2

Step-by-step explanation:

they’re corresponding angles meaning they’re congruent or equal to each other then solve like any other problem

The number is -136.

Two or more expressions with an equal sign are defined as an equation.

Let the number be x.

Given that, two more than the number, x, is 15 less than the product of 7/8 and the number, therefore:

x + 2 = (7/8)x - 15

x - (7/8)x = -15 -2

x/8 = -17

x = -136

Hence, the number is -136.

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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:

[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]

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.

Answer: 32

Step-by-step explanation:

4 ÷ 1/8
You can reduce the expression by cancelling out common factors;
4/1 ÷ 1/8
Cross cancel the ones, and then multiply 4 and 8
4 x 8 = 32

Answer:1/8

Step-by-step explanation:

The reciprocal of a number is what you multiply by a number to give 1. Therefore

8x = 1

x = 1/8

Min-Seo and Orlando have the same ratio of responses but Jian and Leona do have not the same ratio of responses.

The ratio notion is used in mathematics when evaluating two or more numbers. It works as a comparison tool to demonstrate how big or small a particular number is. A ratio divides two quantities in order to compare them.

As per the given information in the question,

The ratios given in the question are,

2.

The ratio obtained by Min-SEO = 4/5 and,

The ratio obtained by Orlando = 8/10

The ratio in the simplest form will be: 4/5

This means that Nin-SEO and Orlando have the same ratio of responses.

3.

The ratio obtained by Jian = 3/4 and,

The ratio obtained by Leona = 10/12

The simplest form of ratio = 5/6

This means that Jian and Leona do have not the same ratio of responses.

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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:

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:

Step-by-step explanation:

4.2 miles

The slope is 0.003

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

the coordinates are (12000, 20) and (18000, 2)

so, slope= 18 / 6000

              = 0.003

The 3 in the thousandths place rounds down to 3, or stays the same, because the digit to the right in the ten thousandths place is 0.003.

Hence, the slope is 0.003.

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The weight of the bicycle is 19.375 pounds.

In physics and engineering, the weight of an object refers to the gravitational force that pulls on it. Weight is frequently described as a scalar quantity that measures the gravitational force's strength.

The weight of the frame of the bicycle= 16 pounds

1 pound= 16 ounces

Therefore, 16 pounds= 16 x 16 = 256 ounces

The weight of one tire= 9 ounces

Therefore, the weight of two tires= 9 x 2 = 18 ounces

The weight of the seat= 12 ounces

The weight of handlebars= 24 ounces

Therefore, the total weight of the bicycle = 256 + 18 + 12 + 24                                                                              

                                                                     = 310 ounces

Therefore, the bicycle weighs 310 ounces

That is 310/ 16 = 19.375 pounds

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Let p be the amount of sales (in dollars) of phones.

Let c be the amount of sales (in dollars) of computers.

Equation 1: sales

    p + c = 2100

the amount of all sales is 2100

Equation 2: commission

   0.05p + 0.07c = 119

5% commission on phones plus 7% commission on computers totals to 119

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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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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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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The similarity is that Sunni and Shia Muslims agree on the fundamental tenets of Islam, such as worshiping Allah as God, acknowledging Muhammad (Peace Be Upon Him) as the Prophet, and adhering to the Quran's teachings.

The difference is that Shia place a greater emphasis on Muhammad's family ancestry through a succession of Imams than Sunnis do on imitating the Prophet and his example.

All Shia and Sunni Muslims recognize the importance of the Quran; contrary to popular belief, Shi'a does not use a corrupted version of the Quran.

Shi'a and Sunni Muslims both use the Hadith, though they often prefer different collections of sayings.

They have different perspectives on imams. Imams are considered saints in Sunni Islam and must have a strong commitment to the Quran and Sunnah in order to be nominated. In Shia Islam, however, only God has the authority to name an imam. Only imams in Shia Islam have the authority to translate the Quran.

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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

Answer:

A = 3

B = -1

C = 5

Step-by-step explanation:

y - 7 = 3(x - 4)    Distribute the 3

y - 7 = 3x -12  subtract y from both sides

-7 = 3x -y -12  Add 12 to both sides

5 =3x -y  Flip the equation around the equal sign

3x -y = 5

The 3 is the A, -1 is the B and 5 is the C.

Answer:

3cm,4cm,5cm

Step-by-step explanation:

5 is the longest side ( the hypotenuse)

and by Pythagoras theorem x=√(3²+4²)

= √(9+16)

=√(25)

= 5

so 3cm,4cm,5cm is a right angle triangle.

x=√(27²+36²)

=√(729+ 1296)

=√2025

=45

so 27cm,36cm,45cm is a right angle triangle

The length of the hypotenuse side of the right triangle ΔXYZ, found using Pythagorean Theorem is b·√(10)

Pythagorean Theorem  indicates that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the square of the legs of the right triangle.

The specified parameters of triangle are;

The hypotenuse of the triangle, ΔXYZ = [tex]\overline{YZ}[/tex]

The length of the legs of the right triangle are;

[tex]\overline{XY}[/tex] = b, and [tex]\overline{XZ}[/tex] = 3 × [tex]\overline{XY}[/tex]

Therefore;

[tex]\overline{XZ}[/tex] = 3 × b (substitution property of equality)

The length of the hypotenuse side can be calculated as follows;

Therefore;, according to Pythagorean theorem, we get;

[tex]\overline{YZ}[/tex]² = [tex]\overline{XY}[/tex]²  +  [tex]\overline{XY}[/tex]²

[tex]\overline{YZ}[/tex]² = b²  +  (3·b)² = b² + 9·b² = 10·b²

[tex]\overline{YZ}[/tex] = [tex]\sqrt{10\cdot b^2} = b \cdot \sqrt{10}[/tex]

The  length of the  hypotenuse side , [tex]\overline{YZ}[/tex] = b·√(10)

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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 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: 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

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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