Determine the slope & y intercept for the line shown. Then write the equation of the line. If you hurry I’ll mark you brainliest

The equation of the line through \((1,2)\) which make equal intercepts on the axis \(x+y=3\)

The equation of the line through (1,2) makes an equal intercept on the axis

The formula of the intercept form is

\(\frac{x}{a} +\frac{y}{b} =1\)

If they make an equal intercept

\(a=b\\\frac{x}{a} +\frac{y}{a} =1\\x+y=a\)

Put the value of the point in the axis, and we get.

\(1+2=a\\a=3\)

Put the value in the equation, and we get.

\(x+y=3\)

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Step-by-step explanation:

there is a (V.O.A) which is vertically opposite angle

and in the given part he himself said that there is two = angles

so there for the two third angles are equal

so we can say they are similar

If f (x) < g(x) for all real 1; The expression that must be true is I f'(x)sg'(x) for all real x II. f'(x)≤g'(x) for all real x III. f(x)dx ≤ [8(x)dx is option D. I and II only

I. f(x) and g(x) have continuous first and second derivatives everywhere, so by the mean value theorem, there exists a point c in the interval (a, b) such that f'(c) = (f(b) - f(a)) / (b - a) and g'(c) = (g(b) - g(a)) / (b - a). Since f(x) < g(x) for all x, we have f(b) - f(a) < g(b) - g(a), so f'(c) < g'(c), and thus, f'(x) < g'(x) for all x.

II. f(x) and g(x) have continuous first and second derivatives everywhere, so by the mean value theorem, there exists a point c in the interval (a, b) such that f''(c) = (f'(b) - f'(a)) / (b - a) and g''(c) = (g'(b) - g'(a)) / (b - a). Since f'(x) < g'(x) for all x, we have f'(b) - f'(a) < g'(b) - g'(a), so f''(c) < g''(c), and thus, f''(x) < g''(x) for all x.

III. This statement is not necessarily true. The definite integral of f(x)dx is equal to the area between the curve and the x-axis, and the definite integral of g(x)dx is equal to the area between the curve and the x-axis. The definite integral of a function does not depend on the value of the function at each point, but on the overall shape of the curve, so it is not guaranteed that f(x)dx ≤ g(x)dx just because f(x) < g(x) for all x.

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The complete question goes thus:

Let f and g have continuous first and second derivatives everywhere. If f (x) < g(x) for all real 1; which of the following must be true? I f'(x)sg'(x) for all real x II. f'(x)≤g'(x) for all real x

III. f(x)dx ≤ [8(x)dx

(A) None

(B) I only

(C) III only

(D) I and II only

(E) I, II, and III

Answer:

$31.53

Step-by-step explanation:

I used a calculator

The number of green marbles removed from the bag is 3.

We will use the Formula of Probability:

In mathematics, the probability is defined as the ratio between the number of favorable outcomes and the total number of outcomes.

p(A) = n(A) / n(S)

p(A) is the probability of event A.

n(A) is the number of outcomes with respect to A.

n(S) is the total number of possible outcomes.

Given in the Question:

A bag contains 14 blue, 6 red, 12 green, and 8 purple marbles.

So the total number of marbles in the bag = 40

It is given that 25 marble are removed from the bag randomly

thus, the remaining marbles in the bag = 40 - 25 = 15

It is given that the probability of drawing a green marble from the bag after removing 25 marbles is 3/5.

So, for finding the number of green marbles in the bag after removing we can write,

n(A) = p(A) × n(S)

here, A is the event of drawing the number of green marbles and p(A) = 3/5 and  n(s) = 15 (after removing)

Thus, the number of green marbles in the bag after removing = 3/5 × 15

So, the number of green marbles left in the bag = 9

then, the green marbles removed from the bag = 12 - 9 = 3.

Therefore, only 3 green marbles are removed from the bag.

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Answer:

9 and 40investment is costing 542

Answer:

5x + 8 = -27 :)

Step-by-step explanation:

let the number be x.

"more than" means +

"5 times a number" means 5x

"is" means =

put this information together:

5x + 8 = -27

hope this helped! xoxo

1. For Joshua's triangle; the distance of the green side of the triangle d₃ is 5.

2. For Murney's triangle, the perimeter of the triangle is 12.

3. For Grace, Abby and Chris's triangle, the perimeter of the triangle is 5 + √17 +  4√2.

4. For Chloe's triangle, the perimeter of the triangle is 11 + √65.

The distance of the triangles is calculated as follows;

For Joshua's triangle;

The length of d₁, d₂, and d₃ is calculated as follows;

d₁ = √ [(3 - 2)² + (2 - 0)²] = √5

d₂ = √ [(-1 - 3)² + (4 - 2)²] = 2√5

d₃ = √ [(-1 - 2)² + (4 - 0)²] = 5

The distance of the green side of the triangle d₃ = 5

For Murney's triangle, the perimeter of the triangle is calculated as;

BC = √ [(4 - 4)² + (6 - 2)²] = 4

AC = √ [(1 - 4)² + (2 - 2)²] = 3

AB = √ [(4 - 1)² + (6 - 2)²] = 5

Perimeter = 4 + 3 + 5 = 12

For Grace, Abby and Chris's triangle, the perimeter of the triangle is calculated as;

AC = √ [(-3 - 2)² + (2-2)²] = 5

BC = √ [(1 - 2)² + (2 + 2)²] = √17

AB = √ [(1 + 3)² + (2 + 2)²] = 4√2

Perimeter = 5 + √17 +  4√2

For Chloe's triangle, the perimeter of the triangle is calculated as;

AC =  √ [(-3 - 4)² + (2-2)²] = 7

BC =  √ [(4 - 4)² + (6-2)²] = 4

AB =  √ [(4 + 3)² + (6-2)²] = √65

Perimeter = 7 + 4 + √65 = 11 + √65

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The equation Σ_{n=0}{∞} n!(x-6)n represents an infinite series and does not yield a finite set of values.

The given equation is a summation notation (Σ) representing the sum of terms in an infinite series. In this series, each term is given by n!(x-6)^n, where n ranges from 0 to infinity. The term n! represents the factorial of n, which is the product of all positive integers from 1 to n.

Since the exponent n ranges from 0 to infinity, the series continues indefinitely, and there is no finite set of values that satisfies this equation. It represents a mathematical concept known as a power series, which converges or diverges based on the values of x within a certain interval.

Therefore, we cannot provide a finite set of values that satisfy this equation.

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The complete question is

What is the finite set of values that satisfies the equation: Σ_{n=0}{∞} n!(x-6)n?

The income you need to afford a $425,000 house is largely dependent on your debt-to-income ratio, credit score, and down payment. However, a general rule of thumb is to have an annual income that is at least three times the purchase price of the home, which in this case would be $1,275,000.

To more accurately determine the income needed to afford a $425,000 house, consider factors such as the interest rate on the mortgage, property taxes, homeowners insurance, and any homeowner association fees.

These additional expenses can significantly impact your monthly mortgage payment and thus your income requirements.
It's important to keep in mind that lenders have varying criteria when determining mortgage eligibility and income requirements, so it's best to speak with a mortgage professional to get a more accurate estimate based on your individual circumstances.

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Explicit formula for the given scenario of Miguel running where he runs 1 mile in the first week and 2 miles farther than the distance of the previous week is given by y = 2x -1.

As given in the question,

Distance covered by Miguel in the first week = 1 mile

Goal decided by Miguel = 2 miles farther than the distance of the previous week

Here First term ,a₁ = 1

Difference  'd' = 2

Nth term to represent the explicit formula is given by :

aₙ = a₁ + ( n - 1 ) d

⇒ aₙ = 1 + ( n - 1 )2

⇒ aₙ = 1 + 2n - 2

⇒ aₙ = 2n -1

Replace aₙ by 'y' and n by x we get ,

y = 2x - 1

Therefore, explicit formula for the given scenario of Miguel running where he runs 1 mile in the first week and 2 miles farther than the distance of the previous week is given by y = 2x -1.

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Answer:

1/2x + 18 = 11 - 3x

Step-by-step explanation:

x = -2

The volume of the blue triangular prism is 216 cubic centimeters.

We assume that the two figures are similar, if the scale factor between the two is K, then the volume of the blue prism will be K³ times the volume of the green one.

To find the value of K, we can compare the two known sides:

4cm*K = 6cm

K = 6cm/4cm = 3/2

Then the volume of the blue prism is:

(3/2)³*64cm³ = 216 cm³

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Answer:

0.995 +0.005 will get you to 1. so the awnser is 0.995

Answer:

i think it is 50ft but i'm not too sure

Step-by-step explanation:

if you take the 100ft and than use the 20 degrees and divide them you get 50 ? so maybe, just 100 divided by 20

The steps for using a compass and straightedge to construct a square is:

Given:

Let AB the length of one side given.

Steps:

a. Using your straightedge, draw a reference line, if one is not provided.

b. Copy the side of the square onto the reference line, starting at a point labeled A'.

c. Construct a perpendicular at point B' to the line through \(AB\).

d. Place your compass point at B', and copy the side of the square onto the perpendicular B'G. Label the end of the segment copy as point C.

e. With your compass still set at a span representing AB, place the compass point at C and swing an arc to the left.

f. Holding this same span, place the compass point at A' and swing an arc intersecting with the previous arc. Label the point of intersection as D.

g. Connect points A' to D, D to C, and C to B' to form a square.

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Answer:

The height of the pile is increasing at a rate of 16.72 feet per minute. To solve this problem, we need to use the volume formula for a right circular cone: V=pi/3 r²h. We know that the volume is 20 cubic feet per minute, the height is 14 feet and the radius of the base is 14 feet. So we can calculate the rate of change of the height by rearranging the formula to give v/(pi/3r²). So for our example, v/(pi/3*14²)=20/(pi/3*14²)=20/(3.14*196)=20/613.44=16.72 feet per minute.

       Rate at which the car is moving is 27 miles per gallon.

   If we plot gallons of gas remaining in the tank at x-axis and miles driven on y-axis, points will form a linear graph.

After driving 45 miles, 15 gallons of the gas remaining in the tank will  represent a point (15, 45).

Similarly, after 153 miles gas,11 gallons of the gas remaining in the tank will form a point (11, 153).

Slope of the line joining these points will represent the rate.

Therefore, slope of the line = \(\frac{y_2-y_1}{x_2-x_1}\)

                                              = \(\frac{153-45}{15-11}\)

                                              = 27 miles per gallon

    Hence, rate at which the car is moving is 27 miles per gallon.

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Answer:

63

Step-by-step explanation:

Step-by-step explanation:

there are 91 2-digit numbers : 10 ..99

and there are 9 2-digit numbers with identical first and second digit : 11, 22, 33, 44, 55, 66, 77, 88, 99

99 has to be excluded, because there are no 2 2- digit numbers that I can subtract from each other and get 99.

so, e are dealing with 8 possibilities.

88 = 99-11

98-10

77 = 99-22

98-21

97-20

...

78-1

66 = 99-33

98-32

...

67-1

...

11 = 99-88

98-87

...

12-1

all the double- digit numbers are 11 apart. so, by picking 12 numbers, I have to have at least one that I can combine with one of the other 11 to get a double-digit number.

The simplified form of the given exponential notation is 2¹² = 4096.

Exponential notation is used to express any large number or very small number into a small form by using powers.

An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation. This maths operation can be addition, subtraction, multiplication, or division.

For examples, - 2³, a², -9ⁿ are some kind of exponential notations.

Given is an exponential notation, (2⁻⁴)⁻³

Using exponential identity, (aⁿ)ᵇ = aⁿᵇ

(2⁻⁴)⁻³ = 2⁻⁴⁽⁻³⁾

= 2⁴⁽³⁾

= 2¹²

= 4096

Hence, the simplified form is (2⁻⁴)⁻³ = 2¹² = 4096

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Answer:

39 games

Step-by-step explanation:

Since the ratio is 3 to 2, there are total of 5 units:

65 / 5 = 13 games per unit

win has 3 units:

13 x 3 = 39 games

Answer:

I think the answer is 54.2, but it may not be correct.

Step-by-step explanation:

To find the mean of something, you're supposed to find the sum of all the numbers and the divide it by how many numbers are in the set. Hope this helped!

Answer:

tan x = c/b

cos x = b/a

sin x = c/a

Step-by-step explanation:

an easy way to memorize it would be SOH CAH TOA

SOH = sin, opposite, hypotunese

-- you find the angle and you divide it's opposite and hypotunese when it asks for sin

CAH = cos, adjacent, hypotunese

-- you find the angle's adjacent side and hypotunese, then divide

TOA = tan, opposite, adjacent

-- you find the angle's opposite side and divide it by the adjacent side

Using the z-distribution, it is found that since the test statistic is less than the critical value for the right-tailed test, it is found that it can be concluded that the proportion of the population in favor of candidate A is not significantly greater than 0.75.

At the null hypothesis, it is tested if the proportion is not significantly more than 75%, that is:

\(H_0: p \leq 0.75\)

At the alternative hypothesis, it is tested if the proportion is significantly more than 75%, that is:

\(H_1: p > 0.75\)

The test statistic is given by:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

In which:

In the sample, 80 out of 100 people favored candidate A, hence, the parameters are:

\(n = 100, \overline{p} = \frac{80}{100} = 0.8, p = 0.75\)

Hence:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

\(z = \frac{0.8 - 0.75}{\sqrt{\frac{0.75(0.25)}{100}}}\)

\(z = 1.15\)

The critical value for a right-tailed test, as we are testing if the proportion is greater than a value, is \(z^{\ast} = 1.645\).

Since the test statistic is less than the critical value for the right-tailed test, it is found that it can be concluded that the proportion of the population in favor of candidate A is not significantly greater than 0.75.

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Answer:

x = 2y/3

y = 3x/2

Answer:

Step-by-step explanation:

The external angle of the triangle is equals to the sum of the 2 opposite angles. Therefore,