5x-20
x² - 4x + 18
X-4 니
y2-4+18

The correct point-slope equation for the line that passes through the point (-4,-2) and is parallel to the line given by y = 5x + 44 is: A. y + 2 = 5(x + 4)

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

Since the line is parallel to y = 5x + 44, the slope is equal to 5.

At data point (-4, -2) and a slope of 5, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-2) = 5(x - (-4))  

y + 2 = 5(x + 4)

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Within sample variance occurs within a single sample or group.

Within sample variance refers to the variation or dispersion of values within a single sample or group. It measures how much the individual data points deviate from the mean or central tendency within that specific sample. This variance is calculated by taking the average of the squared differences between each data point and the sample mean.

For example, let's say we have a sample of test scores for a group of students. Within sample variance would help us understand how much the individual test scores vary within that particular group. If the test scores are tightly clustered around the mean, the within sample variance would be low, indicating a high level of similarity among the scores. Conversely, if the test scores are widely spread out, the within sample variance would be high, suggesting a greater diversity or variability among the scores.

In summary, within sample variance occurs within a single sample or group and quantifies the dispersion of values around the mean within that sample. It helps assess the level of variation or homogeneity within the data set.

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1. The particular solution that satisfies the first differential equation and the initial condition is f(x) = 4x^2 + 7

2. The particular solution that satisfies the second differential equation and the initial condition is f(s) = 7s^2 - 3s^4 + 19

1. To find the particular solution that satisfies the differential equation and the initial condition, we need to integrate the given differential equation and apply the initial condition.

Let's solve each problem step by step:

Given: f'(x) = 8x, f(0) = 7

First, we integrate the differential equation by applying the power rule of integration:

∫f'(x) dx = ∫8x dx

Integrating both sides, we get:

f(x) = 4x^2 + C

To find the value of C, we apply the initial condition f(0) = 7:

f(0) = 4(0)^2 + C

7 = C

Therefore, the particular solution that satisfies the differential equation and the initial condition is:

f(x) = 4x^2 + 7

2.  f'(s) = 14s - 12s^3, f(3) = 1

Similarly, we integrate the differential equation:

∫f'(s) ds = ∫(14s - 12s^3) ds

Integrating both sides:

f(s) = 7s^2 - 3s^4 + C

Applying the initial condition f(3) = 1:

f(3) = 7(3)^2 - 3(3)^4 + C

1 = 63 - 81 + C

1 = -18 + C

C = 19

Hence, the particular solution that satisfies the differential equation and the initial condition is:

f(s) = 7s^2 - 3s^4 + 19

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Answer:

4:6 I think sorry if wrong

Step-by-step explanation:

Answer:

2 to 3. Or 2:3

Step-by-step explanation:

There are 4 triangles to every 6 squares

Their GCF is 2 so divide by 2 to get 2:3

The answer resulted in x = 5 after the operation as the picture suggests, hope this helps

Answer:

13 in

Step-by-step explanation:

add them all because its says perimeter

Answer: 13 in.

Step-by-step explanation: 1+1+3+5+3 = 13

The distance bewteen the points (-3,5) and (3,1) in a simple radical form is 2√13.

The distance formula used in finding the distance between two points is expressed as;

d = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

From the graph;

Point A: (-3,5)

x₁ = -3

y₁ = 5

Point B: (3,1)

x₂ = 3

y₂ = 1

Plug the given values into the distance formula and simplify.

\(d = \sqrt{( x_2 - x_1)^2 + (y_2 -y_1 )^2} \\\\d = \sqrt{( 3-(-3))^2 + (1 -5)^2} \\\\d = \sqrt{( 3+ 3)^2 + (1 -5)^2} \\\\d = \sqrt{( 6)^2 + (-4)^2} \\\\d = \sqrt{36 + 16} \\\\d = \sqrt{52}\\\\d = 2\sqrt{13}\)

Therefore, the distance between the points is 2√13.

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Salut/Hello!

Step-by-step explanation:
/ - fraction line
Ben's probability to pass is 0,8
to make it simpler for you to understand I'm going to use percentages.

We can transform 0,8 in a fraction so 8/10 and amplify it by 10 so 80/100
so the percentage showing that Ben will pass is 80% to find out the percentage that Ben will fail we subtract 80% from 100% which results in 20%

so the probability that Ben will fail is 0,2
and Tom's probability to fail is 0,3


To find out the answer to b) we need to understand how we calculate it.

Take as an example a dice. A dice has 6 faces and you need 1 side to get out of jail (let's say you need a 6). Your probability to get that side is 1/6

But what if you have two dice and you need both to be 6? Well in that case it'll be 1/6 x 1/6 which is 1/36

So, to find out the probability of both passing, we have to do 8/10 x 7/10 which is 56/100 and it's equal to 0,56. And you might wonder why the probability both will pass seems bigger than their probability to pass. Well 0,8 actually can mean 0,800000... and so on but it's easier to just let it as 0,8

For c) the probability that only one will pass is: 0.12

We first need to find the probability both fail
100% - 56% = 44%

and we subtract 44% from 56% which is equal to 12% or 0.12


I hope it was helpful! :]

Answer:

259.5

Step-by-step explanation:

8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5

An initial amount of $725,000, an APR of 6.25%, and a desired time frame of 22 years, the monthly withdrawal amount would be approximately $4,491.95.

To calculate the monthly withdrawal amount that would completely exhaust your savings in 22 years, we can use the present value of an ordinary annuity formula. The present value (PV) represents the initial amount you have, the interest rate per period (i) is the monthly interest rate, and the number of periods (n) is the total number of months.

Here's the step-by-step calculation:

Convert the APR to a monthly interest rate:

Monthly interest rate (i) = Annual interest rate / Number of compounding periods per year

i = 6.25% / 12 = 0.0625 / 12 = 0.00521 (rounded to 5 decimal places)

Determine the total number of periods:

Total number of periods (n) = Number of years * Number of compounding periods per year

n = 22 * 12 = 264

Use the present value of an ordinary annuity formula to calculate the monthly withdrawal amount (PMT):

PMT = PV / [(1 - (1 + i)^(-n)) / i]

In this case, PV = $725,000

PMT = $725,000 / [(1 - (1 + 0.00521)^(-264)) / 0.00521]

Calculate the monthly withdrawal amount using a financial calculator or spreadsheet software:

PMT ≈ $4,491.95 (rounded to the nearest cent)

Therefore, you can withdraw approximately $4,491.95 per month to completely exhaust your savings in 22 years assuming monthly compounding.

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Answer:

Step-by-step explanation:

it surprises me  you can't do these  yourself  :/  do you not understand percent's?  what makes this tough for you ?

1) y = 0.12x

2) y = 0.25x

3) y = 0.6x   ( repeating so the 6 has the line over it )

4) y = 0.833 ( repeating so the 3s has the line over them )

The rule for continuity that is violated at x = -4 is "lim f(x) exists as x approaches a."

The function f(x) is defined as different expressions for different intervals of x. For x less than -4, f(x) is given by 0.1x + 15.4, while for x greater than -4, f(x) is given by √x + 13. At x = -4, the two expressions meet, but they do not agree on the limit as x approaches -4 from both sides. Therefore, the function violates the continuity rule that requires the limit of f(x) to exist as x approaches -4. In this case, the function f(x) is not continuous at x = -4.

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Therefore , the solution of the given problem of expression comes out to be the multiplication is done first using the sequence of operations: 57=35 and 51/5=1. 35 is then reduced by 1 to yield 34.

Mathematical processes such as multiplying, dividing, adding, and even deleting are necessary. If they were combined, the following statement would result: An equation, some statistics, and a mathematical formula Values, components, and mathematical processes like additions, subtractions, algebraic expressions, and divisions make up a statement of truth. Words and sentences can be analysed and ranked.

Here,

a. Accurate. The commutative property of addition says that the sum remains constant regardless of the addends' order. As a result, -19+7 is equivalent to 7-19, which is equivalent to -12+19.

b. True. Any integer is itself when multiplied by 1. As a result, 4/5 + 1 equals 4/5.

c. Accurate. One is obtained by multiplying two reciprocals. As a result, 3/2 2/3 equals 32 23, which is reduced to 1.

d. Correct. The multiplication is done first using the sequence of operations: 57=35 and 51/5=1. 35 is then reduced by 1 to yield 34.

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Step-by-step explanation:

Remember that :

1 m = 100 cm

6¾ m = 27/4m

now, result times 100, then :

27/4 . 100 = 675 cm

Subject : Mathematics

Level : ES

Chapter : Measurement

To check which point is lying on the given graph, we can just put the values in the equation in input x, and see if y comes out same as that specified y ordinate of the given point.

The points that lie on the graph of y = 1. 5 ⌈x⌉ are:

(–4. 5, –2. 5), (7. 9, 9. 5) and (1. 3, 3. 5)

The graph is of y = 1. 5 + ⌈x⌉

Putting x = -4.5, we get:

\(y = 1.5 + \lceil{x}\rceil\\y = 1.5 + \lceil -4.5 \rceil\\y = 1.5 + -4 = -2.5\)

The specified point too has y ordinate as -2.5, thus, this point lies on the graph of given function.

Putting x = 0.8, we get:

\(y = 1.5 + \lceil{x}\rceil\\y = 1.5 + \lceil 0.8 \rceil\\y = 1.5 + 1 = 2.5\)

But specified point's y ordinate is 0.5, thus, this point doesn't lie on the graph of given function.

Putting x = 7.9, we get:

\(y = 1.5 + \lceil{x}\rceil\\y = 1.5 + \lceil 7.9 \rceil\\y = 1.5 + 8 = 9.5\)

The specified point too has y ordinate as 9.5, thus, this point lies on the graph of given function.

Putting x = 4.5, we get:

\(y = 1.5 + \lceil{x}\rceil\\y = 1.5 + \lceil 4.5 \rceil\\y = 1.5 + 5 = 6.5\)

But specified point's y ordinate is 6, thus, this point doesn't lie on the graph of given function.

Putting x = 1.3, we get:

\(y = 1.5 + \lceil{x}\rceil\\y = 1.5 + \lceil 1.3 \rceil\\y = 1.5 + 2 = 3.5\)

The y ordinate of given point too is 3.5, thus, this point lies on the graph of given function.

Thus, the points (–4. 5, –2. 5), (7. 9, 9. 5), (1. 3, 3. 5) lie on the given graph.

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Answer:

4 it's na answer the answer is 4

Answer:

what? better explanation

Answer:

x=12

Step-by-step explanation:

4:6

10:x

1. 6-4=2

2. 10+2=12

or

1. 10-4=6

2. 6+6=12

Answer:

(B) has the closest values.

Step-by-step explanation:

Solve the triangle: A = 51°, b = 14, c = 6

A. a ≈ 14.9, C ≈ 28.1, B ≈ 100.9

B. a ≈ 11.2, C ≈ 24.1, B ≈ 104.9

C. a ≈ 14.9, C ≈ 24.1, B ≈ 104.9

Using the cosine rule,

a^2 = b^2+c^2-2bc (cos(A))

= 196+36 - 2(14)(6)cos(51)

=  196+36 - 105.72

= 126.27

a = sqrt(126.27)

= 11.24

using sine rule,

sin(C)/sin(A) = 6/11.24

sin(C) = 6/11.24*sin(51)= 0.41495

C = arcsin(0.41495 = 24.5 degrees, reasonably close to the given value, probably due to the answer used the rounded value of a.

B = 180-51-24.5 =104.5

Out of the given options, only (B) has the correct value of a and C

The absolute value is:

Work/explanation:

First, we will evaluate 2-7.

It evaluates to -5.

Now, let's find the absolute value of -5 by using these rules:

\(\sf{\mid a\mid=a}\)

\(\sf{\mid-a \mid=a}\)

Similarly, the absolute value of -5 is:

\(\sf{\mid-5\mid=5}\)

Answer:

18

Step-by-step explanation:

hope this helps! :D

have a miraculous day!! <3

The product of 0.6 and 0.35 is 21/100.

To find the product of 0.6 and 0.35, we can multiply the whole numbers and then multiply the decimals separately.

Whole numbers:

0.6 can be expressed as 6/10

0.35 can be expressed as 35/100

Decimals:

0.6 × 0.35 = 6/10 × 35/100

Now let's calculate the product:

Whole numbers:

6 × 35 = 210

Decimals:

10 × 100 = 1000

The product of 0.6 and 0.35 is:

210/1000

Simplifying the fraction by dividing both numerator and denominator by their greatest common divisor (which is 10):

21/100

Therefore, the product of 0.6 and 0.35 is 21/100.

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The value of the function (f/g)(x) is (x+5)/(3x+5) if f(x) = 3x² + 10x - 25

g(x) = 9x²-25.

The earliest known attempt to the concept of function may be traced back to the works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. The concept of a function was codified in terms of set theory at the end of the nineteenth century, which substantially expanded its realms of applicability.

Given,

f(x) = 3x² + 10x - 25

g(x) = 9x² - 25

To find (f/g)(x) divide f(x) by g(x)

(f/g)(x)=(3x²+ 10x-25)/(9x²-25)

We have to factorize both the numerator and denominator

For the numerator

3x²+10x-25

3x²+15x-5x-25

3x(x+5)-5(x +5)

(3x-5 )(x+5)

For the denominator

9x² - 25

(3x)² - 5²

We have to use the formula,

a²- b² = (a+b)(a-b)

(3x)²-5² = (3x+5)(3x-5)

Therefore,

(f/g)(x)=(3x-5)(x+5)/(3x+5)(3x-5)

By simplifying we get,

(f/g)(x)=(x+5)/(3x+5)

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Answer:

-1

Step-by-step explanation:

slope = y2-y1/x2-x1

(5,5) (7,3)

slope = 5-3/5-7 = 2/-2 = -1

Answer:

La opción correcta es;

C) 30, 80

Step-by-step explanation:

Deje que el número de preguntas buenas sea X y el número de preguntas malas sea Y,

Se nos da que X = 3Y ............... (1)

y X + Y = 40 .................................. (2)

Por lo tanto;

Poniendo X = 3Y en la ecuación (2), tenemos;

3Y + Y = 40

4Y = 40

Y = 40/4 = 10

X = 3Y = 3 × 10 = 30

Por lo tanto, la buena pregunta respondida = 30

Dado que las buenas preguntas reciben 3 puntos y las malas preguntas reciben -1 punto, tenemos;

Puntaje total = Preguntas buenas × Punto otorgado + Preguntas malas × Puntos otorgados

Puntuación total = 30 × 3 + 10 × - 1 = 90 - 10 = 80

Answer:

\(\frac{3x-6}{x(x-3)}\)

Step-by-step explanation:

We require the denominators of the fractions to be common.

Multiply numerator/denominator of first fraction by x - 3

Multiply numerator/denominator of second fraction by x

Then

= \(\frac{2(x-3)}{x(x-3)}\) + \(\frac{x}{x(x-3)}\) ( simplify numerators, leaving the common denominator

= \(\frac{2x-6+x}{x(x-3)}\)

= \(\frac{3x-6}{x(x-3)\\}\)

Answer:

I believe it b

Step-by-step explanation:

could be wrong

Answer:

0.5

Step-by-step explanation:

2x + 5 = 6

2x = 6 - 5

x = 6-5 / 2

x = 1/2

x = 0.5