Find the slope of the line.

Therefore, the equation of the line passing through the point (1,5) with a slope of 7 is y = 7x - 2.

The equation of a line in the point-slope form is given by the following equation:

y-y_1 = m(x-x_1)

where m is the slope of the line and (x1, y1) is any point on the line.

Therefore, we can write the equation of the line passing through the point (1,5) with a slope of 7 as follows:

y-5 = 7(x-1)

Expanding the right-hand side of the equation gives:

y-5 = 7x-7

Adding 5 to both sides of the equation gives:

y = 7x-2

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Therefore, the value of m = 1/ 3, b = -11/6. equation in the form \(y = mx+b\).

"Slope-intercept" refers to a method of expressing a linear equation in the form y = mx + b, where "m" is the slope of the line and "b" is the y-intercept.

The "slope" of a line refers to how steeply it rises or falls as it moves from left to right. It is calculated by dividing the change in y by the change in x between any two points on the line.

The "y-intercept" is the point where the line intersects the y-axis. It is the value of y when x equals zero.

By expressing a linear equation in slope-intercept form, you can easily identify the slope and y-intercept, which can provide useful information about the line's behavior.

To write the equation in the form y = mx + b, we need to solve for y:

\(-2x + 6y = -11\)

\(6y = 2x - 11\)

\(y = (2/6)x - (11/6)\)

\(y = (1/3)x - (11/6)\)

So, the equation in slope-intercept form is. \(y = (1/3)x - (11/6)\), where the slope m is 1/3 and the y-intercept b is -11/6.

Therefore,

m = 1/3

b = -11/6

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The area of the figure in this problem is given as follows:

A. 30 in².

The area of a triangle is given by half the multiplication of the base length by the height of the triangle.

Applying the Pythagorean Theorem, we can obtain the missing side length, as follows:

4² + x² = 6²

x² = 36 - 16

x² = 20

x = square root of 20

x = 4.47.

For a right triangle, one side is considered the height of the other, hence the sides are:

Hence the area of the triangle is then obtained as follows:

Area = 0.5 x 4 x 12.47

Area = 25 in².

Which is closest to 30 in².

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Answer: a part of the circumference of a circle or other curve

Step-by-step explanation:

In general, an arc is any smooth curve joining two points. The length of an arc is known as its arc length

Answer:

Step-by-step explanation:

Answer:

384.61

Step-by-step explanation:

ok the 3000 does NOW MATTER  they ask about the norm. so 2500 ÷ 6.50$

=384.61 :)

Answer:

when the doubled the pair of sandals manufactured=3000-2500

=500

the amount spend on manufacturing running shoes=,2500-500

=2000

number of sandals made=500//2.50

(without doubling) =200

number of running shoes =2000/4

=500

The composition of transformation shown in the image attached is

In mathematics, a transformation refers to a change in the position, size, shape, or orientation of a geometric figure or mathematical function. Geometric transformations can be applied to shapes, such as

In the figure the first transformation is rotation about the origin 90 degrees clockwise

The second transformation, is reflection across the x axis

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The value of x in the triangle is determined as 45.

The value of x in the triangle is calculated by applying the following formula,.

The measure of angle ABD = 0.2x + 52

The measure of angle CBD = 0.2x + 42

From the diagram, we can set-up the following equations;

x + 16 = 0.2x + 52

Simplify the equation above, by collecting similar terms;

x - 0.2x = 52 - 16

0.8x = 36

Divide both sides of the equation by " 0.8 "

0.8x / 0.8 = 36/0.8

x = 45

Thus, the value of x in the triangle is calculated by equating the appropriate values to each other.

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Answer:

The square root of 50 is approximately 7.07.

Answer:

7.07106781187...

Step-by-step explanation:

its an irrational number

The answer is A.

An indefinite integral is a function that, when differentiated, equals the original function. It is denoted by ∫f(x)dx, where f(x) is the function to be integrated. An indefinite integral always has an arbitrary constant of integration, which is denoted by C. This is because the derivative of any constant is zero, so the derivative of ∫f(x)dx+C is still equal to f(x).

A definite integral is the limit of a Riemann sum as the number of terms tends to infinity. It is denoted by ∫

a

b

​

f(x)dx, where a and b are the limits of integration. A definite integral does not have an arbitrary constant of integration, because the limits of integration specify a unique value for the integral.

In other words, an indefinite integral is a family of functions that share the same derivative, while a definite integral is a single number.

Answer:

it is the first one and the last one

Step-by-step explanation:

Answer: The two lines intersect at (-4,3)

Step-by-step explanation:

So our first step would be to turn both of these into standard slope-intercept form.

1.)

4y + 3x = 0

4y = -3x

y = -3/4x

2.)

4y - x = 16

4y = x + 16

y = 1/4x + 4

Now that we have our 2 equations, y = -3/4x and y = 1/4x + 4 we can graph them to get an intersection at (-4,3)

Answer:

Step-by-step explanation:

even function are symmetrical about the y axis or f(-x)=f(x)

odd function are symmetrical about the origin -f(-x)=f(x)

f(x)=x^6 + 10x^4-11x^2+19

f(-x)=(-x)^6+10(-x)^4+11(-x)^2+19=x^6 + 10x^4-11x^2+19

the function is even

Answer:

y = 8.66

Step-by-step explanation:

tan 60° = y/5

1.7321= y/5

y = 8.66

Answer: (960.80,1039.20)

Step-by-step explanation:

Let X denotes a random variable that represents the life of the light bulbs produced at the factory.

As per given,

\(\sigma=80\\\\ n=16\\\\ \overline{x}=1000\)

Critical z-value for 95% confidence interval : z* = 1.96

Confidence interval for population mean:

\(\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}\\\\ =1000\pm (1.96)\dfrac{80}{\sqrt{16}}\\\\=1000\pm 1.96\times\dfrac{80}{4}\\\\=1000\pm 1.96\times20\\\\=1000\pm39.2\\\\=(1000-39.2,\ 1000+39.2)\\\\=(960.80,1039.20)\)

So, a 95% confidence interval estimate (CIE) of the true mean life (m) of light bulbs produced in this factory = (960.80,1039.20)

Incomplete question. The full question read;

Decide whether the following statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). Explain your reasoning.

​I'm putting all my savings into stocks because stocks always outperform other types of investments over the long term.

Choose the correct answer below.

A.  The statement does make sense because stocks historically outperform bonds and cash over the long term and investing in stocks is​ high-risk, which offers higher returns.

B.  The statement does not make sense because although stocks historically outperform bonds and cash over the long​ term, investing in stocks is​ high-risk and there is no guarantee that the investment will yield a high return.

C.  The statement does make sense because stocks are a​ low-risk investment, offering predictable low returns.

D.  The statement does not make sense because stocks never outperform bonds and cash over the long term.

Answer:

B.  The statement does not make sense because although stocks historically outperform bonds and cash over the long​ term, investing in stocks is​ high-risk and there is no guarantee that the investment will yield a high return.

Step-by-step explanation:

Of course, the statement does not make sense because it does clearly say the reality about stocks. By saying "stocks always outperform" other investment types it hides the possibility of losses from stock investments.

For example, a company's stock may be negatively affected as a result of employee layoffs or unexpected company scandals. Hence, there is no guarantee that the investment will yield a high return.

Answer:

\(\displaystyle \frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Step-by-step explanation:

This can be solved with either the washer (easier) or the shell method (harder). For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution.  I'll show how to do it with both:

Shell Method (Horizontal Axis)

\(\displaystyle V=2\pi\int^d_cr(y)h(y)\,dy\)

Radius: \(r(y)=2-y\) (distance from y=2 to x-axis)

Height: \(h(y)=2-(-\ln y)=2+\ln y\) (\(y=e^{-x}\) is the same as \(x=-\ln y\))

Bounds: \([c,d]=[e^{-2},1]\) (plugging x-bounds in gets you this)

Plugging in our integral, we get:

\(\displaystyle V=2\pi\int^1_{e^{-2}}(2-y)(2+\ln y)\,dy=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Washer Method (Parallel to x-axis)

\(\displaystyle V=\pi\int^b_a\biggr(R(x)^2-r(x)^2\biggr)\,dx\)

Outer Radius: \(R(x)=2-e^{-x}\) (distance between \(y=2\) and \(y=e^{-x}\))

Inner Radius: \(r(x)=2-1=1\) (distance between \(y=2\) and \(y=1\))

Bounds: \([a,b]=[0,2]\)

Plugging in our integral, we get:

\(\displaystyle V=\pi\int^2_0\biggr((2-e^{-x})^2-1^2\biggr)\,dx\\\\V=\pi\int^2_0\biggr((4-4e^{-x}+e^{-2x})-1\biggr)\,dx\\\\V=\pi\int^2_0(3-4e^{-x}+e^{-2x})\,dx\\\\V=\pi\biggr(3x+4e^{-x}-\frac{1}{2}e^{-2x}\biggr)\biggr|^2_0\\\\V=\pi\biggr[\biggr(3(2)+4e^{-2}-\frac{1}{2}e^{-2(2)}\biggr)-\biggr(3(0)+4e^{-0}-\frac{1}{2}e^{-2(0)}\biggr)\biggr]\\\\V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\biggr(4-\frac{1}{2}\biggr)\biggr]\)

\(\displaystyle V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\frac{7}{2}\biggr]\\\\V=\pi\biggr(\frac{5}{2}+4e^{-2}-\frac{1}{2}e^{-4}\biggr)\\\\V=\pi\biggr(\frac{5}{2}+\frac{4}{e^2}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4}{2e^4}+\frac{8e^2}{2e^4}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4+8e^2-1}{2e^4}\biggr)\\\\V=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Use your best judgment when deciding on what method you use when visualizing the solid, but I hope this helped!

Answer:

1. 5.65

2.

3. d ; F ; c; a

4.

5. d

Answer:

1. 25.1 - 19.33 = 5.77

2. 2 1/6

3. A,C,D,F

4. 6/8 + 7/8 = 13/8 = 1 5/8

5. A

Step-by-step explanation:

Hope this helps.

Answer:

1/24

Step-by-step explanation;

Answer:

See below for explanation

Step-by-step explanation:

The area of an isosceles triangle is \(A=\frac{1}{2}bh\), so let's write the base as an equation of y:

\(\displaystyle 9x^2+4y^2=36\\\\4y^2=36-9x^2\\\\y^2=9-\frac{9}{4}x^2\\\\y=\pm\sqrt{9-\frac{9}{4}x^2\)

As you can see, our ellipse consists of two parts, so the hypotenuse of each cross-section will be \(\displaystyle 2\sqrt{9-\frac{9}{4}x^2\), and each height will be \(\displaystyle \sqrt{9-\frac{9}{4}x^2}\).

Hence, the area function for our cross-sections are:

\(\displaystyle A(x)=\frac{1}{2}bh=\frac{1}{2}\cdot2\sqrt{9-\frac{9}{4}x^2}\cdot\sqrt{9-\frac{9}{4}x^2}=9-\frac{9}{4}x^2\)

Since we'll be integrating with respect to x because the cross-sections are perpendicular to the x-axis, then our bounds will be from -2 to 2 to find the volume:

\(\displaystyle V=\int^2_{-2}\biggr(9-\frac{9}{4}x^2\biggr)\,dx\\\\V=9x-\frac{3}{4}x^3\biggr|^2_{-2}\\\\V=\biggr(9(2)-\frac{3}{4}(2)^3\biggr)-\biggr(9(-2)-\frac{3}{4}(-2)^3\biggr)\\\\V=\biggr(18-\frac{3}{4}(8)\biggr)-\biggr(-18-\frac{3}{4}(-8)\biggr)\\\\V=(18-6)-(-18+6)\\\\V=12-(-12)\\\\V=12+12\\\\V=24\)

Therefore, this explanation confirms that the correct volume is 24!

Answer:

0.89

Step-by-step explanation:

The probability that a randomly selected male's systolic blood pressure will be less than 108 is 0.25.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Here, mean  = 110, standard deviation = 8

P = \(\frac{x_{mean}-x }{SD}\)

P = (110 - 108)/8

P = 2/8 = 0.25

P(Z<0.25) = 0.5 - 0.25 = 0.25

Thus, The probability that a randomly selected male's systolic blood pressure will be less than 108 is 0.25.

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Answer:

See below

Step-by-step explanation:

The dimensions that will minimize the cost of constructing this box is length = 56in , depth = 0.13in and height = 46.6inch

According to the question,

Volume of Rectangular box = 350 in³

Let Area of base of box = l × b

Let height of box be h

So , V = lbh

=> 350 = lbh

=> h = 350/lb ------------(1)

To Minimize the cost,

Total Area = base area + front lateral Area

Front lateral Area = lh + (2b + l) h

So, Total area =  lb + lh + (2b + l) h

Substituting value of h from equation (1)

=> TA =  lb + l( 350/lb) + (2b + l) (350/lb)

Cost function =>

C = 5lb + 10(350/ b) + 3(2b + l)(350/lb)

Solving,

C = 5lb + 3500/b + 2100/l + 1050/b

=> C =  5lb + 4550/b + 2100/l is required cost function

Now, To minimize the cost

We will differentiate Cost function w.r.t a and b

C' = 5b - 2100/l² = 0 ----------(2)

C' = 5a - 4550/b² =0 -----------(3)

Solving both using substitution method

=> b = 420/l²

=> 5lb² = 4550

=> lb² = 910

=>176400/l³ = 910

=> l³ = 176400/910

=> l = 56 in

putting value of a,

b = 0.13 in

Therefore ,

height =  350 / 7.5

=> h = 46.67 in

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Answer:

See Explanation

Step-by-step explanation:

The question required attachment; however, follow the following steps to answer your question.

See Attachment

Considering the horizontal plane of the gird.

Count the number of the squares in that plane;

This gives 4

Multiply 4 by length of each side of a square;

\(Perimeter = 8mm * 4\)

\(Perimeter = 32mm\)

Answer:

(x - 11)(x + 2)

Step-by-step explanation:

You have to find factors that add up to -9 and multiply up to -22. First numbers to pop up should be 11 and 2. Now you simply figure out which signs go where, and to produce -9, 11 has to be subtracted and 2 has to be added to x.

The rate of interest that Ariana should get in order to end up with a final amount of $233,000 is 0.07%.

What is compound interest and how is it calculated?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Mathematically, A = P (1 + (R/f))ⁿ ;
where A = amount that the depositor will receive
P = initial amount that the depositor has invested
R = rate of interest offered to the depositor
f = frequency of compounding offered per year
n = number of years.

Given, Amount that Ariana wants to end up receiving = A = $233,00
Principal amount that Ariana can invest = P = $62,000
Frequency of compounding offered per year = f = 1
Number of years = 20
Let the rate of interest offered to the depositor be = R
Following the formula established in the literature, we have:
233000 = 62000(1 + R)²⁰ ⇒ 3.76 = (1 + R)²⁰ ⇒ 1.07 = 1 + R ⇒ R = 0.07%
Thus, the rate of interest that Ariana should get in order to end up with a final amount of $233,000 is 0.07%.

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Answer:

d. (-6, 0)

Step-by-step explanation:

no explanation bc u need this quick