Write the equation's of the lines using the given information m=1/4, (4, 3)

Answer:2x+1

Step-by-step explanation:

Answer: r=11

Step-by-step explanation:

A=πr^2

A=121π

121π=πr^2

r^2=121

r=11

Answer:6(x+7= 42

Step-by-step explanation:

The restaurant freezer is 43 degrees colder than the restaurant

Answer:

11/2 times 1/3 is 11/6

Step-by-step explanation:

11/2 times 1/3,

We have to multiply the numerators and denominators,

\((11/2)(1/3) = (11*1)/(2*3) = 11/6\\11/6\)

hence we get 11/6

The measure of the side MN is 19.1.

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

The different trigonometric identities are expressed as:

From the information given, we have that:

Using the tangent identity:

\(\text{tan} \ \theta = \dfrac{\text{opposite}}{\text{adjacent}}\)

Substitute the values

\(\text{tan}(60) =\dfrac{\text{MN}}{11}\)

Cross multiply the values, we have:

\(\text{MN} = \sf 1.73(11)\)

\(\text{MN} = 19. 05 \thickapprox\bold{\underline{19.1 \ ft}}\)

Hence, the measure of the side MN is 19.1.

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Let a=\(4x^{4} -20x^{2} -3x^{2} +15\) . So the resulting polynomial after factorization is a= \((4x^{2} -3)(x^{2} -5)\).

A polynomial is an expression that only uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are also known as indeterminates.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

Let

\(a=4x^{4}-20x^{2} -3x^{2} +15\\=4x^{4} -3x^{2} -20x^{2} +15\\=x^{2} (4x^{2} -3)-5(4x^{2} -3)\\=(4x^{2} -3)(x^{2} -5)\)

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Answer:

26ft

Step-by-step explanation:

This would form a triangle so you would use Pythagorean theorem to find the hypotenuse ( the longest side )

Answer: b. 50

Step-by-step explanation:

Hence the employee made an error for 50 serving size.

Answer:

Hello there hope you are having a wonderful day. your answer would most likely be B. which is 50

Step-by-step explanation:

I took the test and got a 100%

Happy to help :)

\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi\)

Answer:

From the information given, you can write the following system of equations:

x+y+z=16 (1)

5x+4.5y+5.5z=82 (2)

z=x+y (3)

You can replace (3) in (1) and (2):

x+y+x+y=16

2x+2y=16 (4)

5x+4.5y+5.5(x+y)=82

5x+4.5y+5.5x+5.5y=82

10.5x+10y=82 (5)

Now, you have the following equations:

2x+2y=16 (4)

10.5x+10y=82 (5)

You can isolate x in (4):

2x=16-2y

x=8-y (6)

Then, you have to replace (6) in (5):

10.5(8-y)+10y=82

84-10.5y+10y=82

84-82=10.5y-10y

2=0.5y

y=2/0.5

y=4

Now, you can replace the value of y in (6) to find x:

x=8-4

x=4

Finally, you can replace the vaue of x and y in (3) to find z:

z=4+4

z=8

According to this, she should buy 4 apple pies, 4 banana pies and 8 chocolate pies.

The function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

To complete the square for the function g(x) = 4x² - 28x + 49, we follow these steps:

Step 1: Divide the coefficient of x by 2 and square the result.

  (Coefficient of x) / 2 = -28/2 = -14

  (-14)² = 196

Step 2: Add and subtract the value obtained in Step 1 inside the parentheses.

  g(x) = 4x² - 28x + 49

  = 4x² - 28x + 196 - 196 + 49

Step 3: Rearrange the terms and factor the perfect square trinomial.

  g(x) = (4x² - 28x + 196) - 196 + 49

  = 4(x² - 7x + 49) - 147

  = 4(x² - 7x + 49) - 147

Step 4: Write the perfect square trinomial as the square of a binomial.

  g(x) = 4(x - 7/2)² - 147

Therefore, the function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

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The probable question may be:

Rewrite the function by completing the square.

g(x)=4x²-28x +49

g(x)= ____  (x+___ )²+____.

The product and the quotient of the functions are as follows:

(rs)(4) =8

(r / s)(3) = 2

A function relates input and output. It relates an independent variable with a dependent variable.

Therefore, let's solve the function as follows:

r(x) = 2√x

s(x) = √x

Therefore, let's find

(rs)(4) = r(4) × s(4) = 2√4 × √4 = 4 × 2 = 8

Let's find

(r / s)(3) = r(3) / s(3) = 2√3 / √3 = 2

Therefore,

(rs)(4) =8

(r / s)(3) = 2

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The ranking from the lowest to highest APR for the given companies is A, B, D, C.

The correct option is b.

To rank the companies from the lowest to highest Annual Percentage Rate (APR) based on a $600 loan amount, we need to calculate the APR for each company. The formula to calculate APR is APR = (Fees / Loan Amount) * (365 / Terms of Loan).

Let's calculate the APR for each company:

For Company A:

APR_A = ($60 / $600) x (365 / 18) = 0.1 x 20.28 = 2.028%

For Company B:

APR_B = ($80 / $600) x (365 / 12) = 0.1333 x 30.42 = 4.054%

For Company C:

APR_C = ($90 / $600) x (365 / 10) = 0.15 x 36.5 = 5.475%

For Company D:

APR_D = ($110 / $600) x (365 / 14) = 0.1833 x 26.07 = 4.79%

Now, we can rank the companies from the lowest to highest APR:

Company A - APR: 2.028%

Company B - APR: 4.054%

Company D - APR: 4.79%

Company C - APR: 5.475%

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Answer:

$8.96

Step-by-step explanation:

3.5 x 2.56 = 8.96

The total surface area is 28 square units.

Each of the 6 faces in the original cube has an area of 2* 2 = 4 square units. Thus, the original figure's surface area as a whole was 24 square units.

The new figure has the same surface area as the old one, plus six new faces that each have an area of one dollar per square unit, for a total surface area increase of six dollars. However, the 1 square unit of the bigger cube's top and the 1 square unit of the smaller cube's bottom are not surfaces and do not contribute to the surface area.

This results in a total surface area of 24 + 6 - 1 - 1 = 28 square units.

Therefore, The total surface area is 28 square units.

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Answer:

Option A is correct.

Step-by-step explanation:

1. solve the inequalities

2. find the intersection :)

The trigonometric ratios used to find the lengths of the sides of the given right triangles are;

\(\displaystyle sin(30^{\circ}) = \mathbf{\frac{1}{2}}\)

\(\displaystyle cos(30^{\circ}) = \mathbf{\frac{\sqrt{3} }{2}}\)

\(\displaystyle sin(60^{\circ}) = \mathbf{\frac{\sqrt{3} }{2}}\)

\(\displaystyle cos(30^{\circ}) = \mathbf{\frac{\sqrt{3} }{2}}\)

1. The given triangle is a right triangle, and one of the interior angles is 45°, we have that the length of the legs are equal

Therefore, x = 13

By Pythagorean theorem, we have;

y = √(13² + 13²) = 13·√2

2. x = y

30² = x² + y² = 2·x²

x = √(30² ÷ 2) = 15·√2 = y

\(3. {} \hspace {0.3 cm}\displaystyle cos(60^{\circ}) = \frac{1}{2} = \mathbf{\frac{3}{x}}\)

x = 3 × 2 = 6

y = √(6² - 3²) = 3·√3

\(4. \ \displaystyle sin(30^{\circ}) = \frac{1}{2} = \mathbf{\frac{y}{34}}\)

34 = 2·y

y = 17

x = √(34² - 17²) = 17·√3

5. x = y

10·√2 = √(x² + y²) = √(x² + x²) = x·√2

Therefore; x = 10 = y

\(6. {} \hspace{0.75cm} \displaystyle \frac{25 \cdot \sqrt{3} }{x} = \mathbf{\frac{\sqrt{3} }{2}}\)

2 × 25·√3 = x·√3

x = 50

\(\displaystyle \frac{y}{50} = \frac{1}{2}\)

y = 25

7. x = y

x·√2 = 2·√14

x = √2·√14 = √28 =  2·√7 = y

\(8. {} \hspace{0.75cm} \displaystyle \frac{24 }{x} = \frac{\sqrt{3} }{2}\)

48 = x·√3

x = 16·√3

y = 8·√3

9. x = 22·√3 ÷ 2 = 11·√3

y × 2 = √3 × 22·√3 = 66

y = 66 ÷ 2 = 33

10. y = 2  × √6 = 2·√6

2·x = √3 × 2·√6

x = √3 × √6 = 3·√2

11. x = √10

y = √(10 + 10) = 2·√10

12. 4·√(21) × 2 = y·√3

y = 8·√7

x = 4·√7

13. √3 × 34 = x × 2

x = 17·√3

z = 34

y = 34·√2

14. x × √3 = 27 × 2

x = 3 × 9 × 2 ÷ √3 = 18·√3

y·√3 = 9·√3 × 2

y = 18

z = 9

15. x = 14·√2

y = 7

z × 2 = 14 ×√3

z = 7·√3

16. x = 8·√3

16·√3 × √3 = a × 2

a = 24 (The length of the side common to both triangles)

z = y

Therefore;

y·√2 = 24

y = 24 ÷ √2 = 12·√2 = z

17. z = 39·√2

x·√3 = 39 × 2

x = 26·√3

y = 13·√3

18. z·√2 = 20

z = 10·√2

x × √3 = 10 × 2

x = 20 ÷ √3

\(\displaystyle x = \frac{20}{\sqrt{3} } = \underline{\frac{20 \cdot \sqrt{3} }{3}}\)

y = 10 ÷ √3

\(\displaystyle \underline{ y = \frac{10 \cdot \sqrt{3} }{3}}\)

19. x = 6

y = 12

z = 12·√2

20. z·√2 = 10·√6

z = 5·√12

x = 10·√12

y = 10·√12 × √3 ÷ 2 = 30

21. 4·√15 × 2 = s×√3

s = 8·√5

s = The length of one side of the equilateral triangle (all angles are 60°)

The perimeter of the equilateral triangle = 3 × s = 3 × 8·√5 = 24·√5

22. s·√2 = 28

s = The length of a side of the square

s = 14·√2

The perimeter = 4 × 14·√2 = 56·√2

23. The length of the ramp = 2 × 37.5 inches = 75 inches

75 inches = 75 inches ÷ 12 inches/feet = 6.25 feet

24. The length of the sides of the infield of the baseball field = 90 feet

The distance from third to first base = The diagonal of the infield = 90·√2 ft.

The horizontal speed of the ball, v = 90·√2 ft. ÷ 1.2 s =  75·√2 ft./s

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Answer:

Below!.

Step-by-step explanation:

There are 5 test in total.

5x90=450

79+94+91+92

= 356

356<450

subtract 356 from both sides.

The lowest score sherman can get is 94.

Answer:

1,3,4

Step-by-step explanation:

Answer:

1 3 4 / a b d

Step-by-step explanation:

Its the pythagorean theorum in reverse. :)

Answer:

C) Experiment

Step-by-step explanation:

With a controlled experiment, a researcher can use a student batch that studied the old curriculum as a control group, and the new batch of students as the 'test' group. To measure student achievement, the researcher would need to either:

1. compare test results for the 2 groups

2. do a longitudinal study - follow the 2 groups of students across several years, and track their 'achievements' (university admissions, jobs, income, etc)

With the other 3 options, the results wouldn't necessarily be accurate or relevant.  

Answer:

Step-by-step explanation:

Puedo ayudarte con tu cálculo. (√7) 2 es lo mismo que √(7^2), que es igual a 7. Por lo tanto, el valor de (√7) 2 es 7.

The algorithm/abstract strategy to justify the fraction 3/5 involves interpreting it as a division, performing the division, and obtaining the decimal representation as the results.

To justify the fraction 3/5, we can use the concept of division and understand it as a ratio or proportion.

Algorithm/Abstract Strategy:

Start with the numerator, which is 3.

Identify the denominator, which is 5.

Interpret the fraction as a ratio or comparison between the numerator and denominator.

Understand that 3/5 represents a division where the numerator (3) is divided by the denominator (5).

Perform the division: 3 ÷ 5.

Simplify the division to its simplest form, if necessary.

The result of the division, in this case, is the decimal representation of the fraction.

If required, convert the decimal representation to a percentage or any other desired form.

For example, if we perform the division 3 ÷ 5, the result is 0.6.

So, 3/5 can be justified as the ratio or proportion where the numerator (3) is divided by the denominator (5) resulting in 0.6.

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To calculate the GPA score, you have to follow these steps:

1. Calculate the point value of the letter grade by the number of credit hours for the course, the result will be the quality points (qp) per course.

2. Add the quality points for each to determine the total quality points (QP)

3. Add the credit hours of each course to determine the total credit hours (CH)

4. The GPA score is equal to the quotient between the total quality points and the total credit hours.

You know that Joe has a GPA score of 0.5 with 36 credit hours, and you need to determine the number of credit hours needed for a GPA of 2.0, assuming he will obtain A in all his future courses.

First, let's determine his total quality points (QP) so far:

So far he has a total of 18 quality points.

Next, the point value for grade A is 4, if "x" represents the number of additional credit hours he must take, then the quality points for these extra courses can be calculated as follows:

Add this value to the quality points he has earned so far to determine the tota

h(x) = f(x)g(x) represents the product of two functions, combining their behaviors into a new function.

In mathematics, the expression h(x) = f(x)g(x) represents the product of two functions, f(x) and g(x). When evaluating h(x) for a given value of x, it involves multiplying the corresponding values of f(x) and g(x).

The product of two functions allows for the combination of their individual behaviors and characteristics. The resulting function, h(x), inherits properties from both f(x) and g(x). The behavior of h(x) will depend on the specific functions involved.

For example, if f(x) represents a linear function and g(x) represents an exponential function, their product h(x) = f(x)g(x) will exhibit a combined behavior reflecting both linearity and exponential growth. The specific form of the functions will determine the precise behavior of h(x) and its graph.

It is important to note that the product of two functions assumes that the functions are defined for the given values of x and that the multiplication operation is valid for the corresponding function values.

h(x) = f(x)g(x) represents the product of two functions, combining their behaviors to form a new function. The specific nature of h(x) depends on the characteristics of f(x) and g(x).

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The volume of the composite solids that consists of rectangular prisms is: A. 190 m³.

Note that the formula for finding the volume of a rectangular prism is given as:

Volume of rectangular prism = length * width * height.

Find the volume of each rectangular prism and add them together:

Volume of prism 1:

length = 10 m

width = 4 m

height = 3 m

Volume = 10 * 4 * 3 = 120 m³

Volume of prism 2:

length = 10 m

width = 1 m

height = 7 m

Volume = 10 * 1 * 7 = 70 m³

Total Volume = 120 + 70 = 190 m³.

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