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Answer:

∠1 = 110

Step-by-step explanation:

Vertically Opposite angles, means that when you have two parrallel lines,  The angles opposite of each other are equal. So 4 = 2 on the bottom line.

This means angle 1 is equal to it's opposite angle, 110'.

Answer:

110 degrees

Step-by-step explanation:

Since completing the known angle is 70 degrees, angle 1 must be 70 degrees. It is also adjacent to 110, which means it equals the same.

Answer:

its c 98

Step-by-step explanation:

multiply hight by width so 14x7 and thats 98 but idrk

Answer:

3,047.092 =

 3,000  

+ 0  

+ 40  

+ 7  

+   0.0

+   0.09

+   0.002

Step-by-step explanation:

Answer: 3 x 5 x 13

Step-by-step explanation:

195 / 5 = 39

39/3 = 13

So...

3 x 5 x 13

Answer:

5*3*13

Step-by-step explanation:

195

5*39

5*3*13

Answer:

\(\dfrac{5e^2}{2}\)

Step-by-step explanation:

Differentiation is an algebraic process that finds the slope of a curve. At a point, the slope of a curve is the same as the slope of the tangent line to the curve at that point. Therefore, to find the slope of the line tangent to the given function, differentiate the given function.

Given function:

\(y=x^2\ln(2x)\)

Differentiate the given function using the product rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let\;$u=x^2}\)\(\textsf{Let\;$u=x^2$}\implies \dfrac{\text{d}u}{\text{d}x}=2x\)

\(\textsf{Let\;$v=\ln(2x)$}\implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{2}{2x}=\dfrac{1}{x}\)

Input the values into the product rule to differentiate the function:

\(\begin{aligned}\dfrac{\text{d}y}{\text{d}x}&=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}\\\\&=x^2 \cdot \dfrac{1}{x}+\ln(2x) \cdot 2x\\\\&=x+2x\ln(2x)\end{aligned}\)

To find the slope of the tangent line at x = e²/2, substitute x = e²/2 into the differentiated function:

\(\begin{aligned}x=\dfrac{e^2}{2}\implies \dfrac{\text{d}y}{\text{d}x}&=\dfrac{e^2}{2}+2\left(\dfrac{e^2}{2}\right)\ln\left(2 \cdot \dfrac{e^2}{2}\right)\\\\&=\dfrac{e^2}{2}+e^2\ln\left(e^2\right)\\\\&=\dfrac{e^2}{2}+2e^2\\\\&=\dfrac{5e^2}{2}\end{aligned}\)

Therefore, the slope of the line tangent to the graph of y = x²ln(2x) at the point where x = e²/2 is:

\(\boxed{\dfrac{5e^2}{2}}\)

⇒Parallel line have the same gradient if the gradient of the given equation is m=-6  it means that the gradient of the new equation is also m=-6

The general equation of a straight line is y=mx+c

⇒plug in the points and find the value of the unknown c

\(6=-6(9)+c\\6=-54+c\\c=6+54\\c=60\)

⇒This means that the new equation parallel to the given equation is⇒

\(y=-6x+60\)

Remember that

If two figures are similar, then the ratio of their volumes is equal to the scale factor elevated to the cubic

so

we have

the scale factor is 4/7

so

the volume ratio is equal to

therefore

Answer:

y = (x + 4)²

Step-by-step explanation:

Given equation is,

y = x²+ 8x + 16

By using identity (a + b)² = a² + 2ab + b²

y = x² + 2(4)(x) + 4²

Here a = x and b = 4

y = (x + 4)²  

Therefore, factored form of the given equation is y = (x + 4)²

21 inches

it could be an isosceles

The calculation of this can be done by first determining the future value of the monthly payments of $327.50

The future value of an annuity can be determined using a financial calculator, mathematical formula, or spreadsheet software. The future value of an annuity is calculated by multiplying the periodic payment amount by the future value factor,

which is based on the number of payments and the interest rate.For example, suppose we want to know the future value of a $500 end-of-month deposit into an annuity that pays 6% interest compounded monthly for five years.

The future value factor for 60 periods at 0.5 percent per month is 80.9747, which can be multiplied by the monthly deposit amount to find the future value of the annuity.500 × 80.9747 = 40,487.35

This means that a $500 end-of-month deposit into an annuity paying 6% interest compounded monthly for five years will have a future value of $40,487.35.

Therefore, to accumulate a $20,000 down payment for a home in five years, you would need to deposit $327.50 per month into the annuity.

 for 60 months using the formula and then solving for the monthly payment amount where FV = $20,000 and n = 60, r = 0.5%.FV = PMT [(1 + r)n – 1] / r$20,000 = PMT [(1 + 0.005)60 – 1] / 0.005PMT = $327.50 (rounded to the nearest cent).

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 409/99

 4  13/99

Hi there !

4.131313.. = 4.(13) = 4  13/99 = (4*99+13)/99 = 409/99

Good luck !

Answer:

Step-by-step explanation:

3x = 90 + 46 - 14

3x = 122

x=\(\frac{122}{3}\)≈40,7

Answer: 40.6 repeated

Step-by-step explanation: combine -46 and 14 which is -32. then add 32 to 90. then divide 3 on both sides. 122/3 is 40.6 repeated

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Answer:

Step-by-step explanation:

To find the common roots between two functions, we need to find the roots (or solutions) of each function individually and then identify the shared solutions.

For the function f(x) = x^2 + x - 6, we can find the roots by setting the function equal to zero and solving for x:

x^2 + x - 6 = 0

To factorize this quadratic equation, we need to find two numbers that multiply to -6 and add up to 1 (the coefficient of x). The numbers that satisfy these conditions are 3 and -2:

(x + 3)(x - 2) = 0

Setting each factor equal to zero:

x + 3 = 0 or x - 2 = 0

Solving for x in each equation:

x = -3 or x = 2

Therefore, the function f(x) = x^2 + x - 6 has two roots: x = -3 and x = 2.

To find the common roots between this function and another function, we would need to know the second function. If you provide the second function, I can help determine if there are any shared roots.

Answer:

  see the attachment

Step-by-step explanation:

When you have a number of function evaluations to do, it is convenient to let a graphing calculator or spreadsheet do them. That avoids the tedium and the mistakes in arithmetic.

Here's your completed table.

Answer:

8 dollars and 67 cents...8.67

Step-by-step explanation:

5 dollar bill

3 one dollar bills

2 quarters

1 dime

1 nickel

2 pennies

Answer:

16 and 25

Step-by-step explanation:

list perfect square numbers from 1 to 10

1, 4,9,16,25,36,49,64,81,100

looking at the list, 2 numbers he could be thinking of are 16 and 25

Answer:

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

Simplify in below steps:

Step-by-step explanation:

x²-4x+3x-12

x²-x-12.

2s²+4s-4s-8

2s²-8

Answer:

x = the number of kg of cement

3x = number of kg of sand

4x = number of kg of gravel

x + 3x + 4x = 480

8x = 480, so x = 60

60 kg of cement

3(60) = 180 kg of sand

4(60) = 240 kg of gravel

Bob will need 180 kg of sand.

Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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Total earnings for selling the same number of each type of sandwiches are $7.10x. This is a simple sum.

Here, the number of each type of sandwiches sold is x.

Pretzel ham sandwich cost $2.25. so, the earnings for selling Pretzel ham sandwich is $2.25x.

Similarly, earnings for selling pretzel turkey sandwich is $1.55x, earnings for selling bagel ham sandwich is $2.00x and earnings for selling bagel turkey sandwich is $1.30x. The total earning can be found by a simple sum of all individual earning of each type of sandwiches.

Therefore, Total earnings for selling the same number of each type of sandwiches are = $2.25x + $1.55x + $2.00x + $1.30x = $7.10x

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Answer:

5<x<29

Step-by-step explanation:

One theorem tells us that if a triangle has two congruent sides and one of the included angle is bigger than the other, the triangle with the included angle that is bigger. has a bigger side than the other.

This is the opposite in this case. The triangles share two sides and we know that the triangle with the side length 18 has a bigger angle than the triangle with the side length 15. So this means that

\(48 > 2x - 10\)

Let find the range of x values.

An angle cannot be negative or zero so this means that

\(2x - 10 > 0\)

Solve for x.

\(2x > 10\)

\(x > 5\)

The angle cannot be bigger than 48 so

\(48 > 2x - 10\)

Solve for x.

\(58 > 2x\)

\(29 > x\)

So x must be greater than 5 but less than 29.

Answer:

d

Step-by-step explanation:

Answer:

b i think

Step-by-step explanation:

Answer:

82 degrees

Step-by-step explanation:

due to the resemblance of 90 degrees

Answer: \(g(-2)=2a\)

Step-by-step explanation:

\((f \cdot g)(-2)=f(-2)g(-2)\\\\\therefore a \cdot g(-2)=2a^2 \implies g(-2)=2a\)

The function g(-2) from the given functions is 2a.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are f(-2)=a and (f·g)(-2)=2a².

Here, (f·g)(-2)=2a²

f(-2)·g(-2)=2a²

a·g(-2)=2a²

g(-2)=2a²/a

g(-2)=2a

Therefore, the function g(-2) is 2a.

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