What is the equation of the line that passes
through the point (-3, 4) and has a slope of
2/3?

Required equation of the parabola with origin as its vertex and directrix  

y = 1/2 is equal to x² = -2y.

As given in the question,

Let vertex of the parabola be ( h, k )

Vertex of the given parabola be at origin

⇒ ( h , k ) = ( 0 , 0 )

Directrix is y =1/2 above the vertex.

Focus is ( 0, -1/2)

Equation of the parabola is given by

Distance between focus to the vertex = distance between vertex to the directrix

( y - (1/2) )² = ( x - 0)² +  ( y - (-1/2) )²

⇒ y² - y + 1/4 = x² + y² + y + 1/4

⇒ -y = x² + y

⇒x² = -y - y

⇒ x² = -2y

Therefore, the equation of the parabola with vertex at origin and directrix y =1/2 is equal to x² = -2y .

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The value of the given expression 6 3/5-2 7/10 is 39/10.

What is an expression?

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

Here, we have

Given: 6 3/5-2 7/10

We have to solve this expression and find the value of the given expression.

6 3/5-2 7/10 = 33/5 - 27/10

6 3/5-2 7/10 = (66-27)/10

6 3/5-2 7/10 = 39/10

Hence, the value of the given expression is 39/10.

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Answer:

13

Step-by-step explanation:

w = -8 -5 =-13=13

The compound inequality solved are:

x ≤ 2 and x > -5

x > 4 or x < -5.3

The graph of the number line is given above.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

-2 x ≤ 4 and 10 > -2x

x ≤ 4/-2 and 10/2 > -x

x ≤ -2 and 5 > -x

x ≤ 2 and x > -5

This means.

-5 < x ≤ 2

The number line can be graphed as,

<----__-5__-4__-3__-2__-1__0__1__2__3__4__5----->

             o---------------------------------------- o

10 < 3x - 2 or -3x - 2 > 14

10 + 2 < 3x or -3x > 14 + 2

12 < 3x or -3x > 16

x > 4 or -x > 16/3

x > 4 or x < -16/3

x > 4 or x < -5.3

x > 4 can be represented on a line graph as,

__-1__0__1__2__3__4__5__6__7--------->

                                     o----------------------->

x < -5.3 can be represented on a number graph as,

<---------8__-7__-6__-5__-4__-3__-2__-1__0__1__2__3__4---------->

<--------------------------o

Thus,

The compound inequality solved are:

x ≤ 2 and x > -5

x > 4 or x < -5.3

The graph of the number line is given above.

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Using translation concepts, the equation for the graph is b.

y = cos(x + π/2) + 1

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Suppose that we've got:

f(x) = a cos (bx - c) + d

Then, this function has:

Amplitude (the maximum distance of the graph from the middle line) = a

Period =[tex]\dfrac{2\pi}{b}[/tex]

Phase shift = [tex]\dfrac{c}{b}[/tex]

Maximum value: a + d

Minimum value: -a + d

In this problem, we have a cosine function

(zero at π/2, this is zero at the origin), shifted π/2 units to the right and 1 unit up.

Since the standard amplitude is between -1 and 1, here is between 0 and 2).

Hence the rule is given as follows:

b. y = cos(x + π/2) + 1

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Answer: 13

Step-by-step explanation:

Minus 29 from 42 to get 13

Answer:

13

Step-by-step explanation:

If you subtract 20 from 42, you will get your answer. Then you plug it into the equation to make sure it's correct.

42-29=13

29+13=42

42-13=29.

-Hope this helped

The function f(x) = 14(0.87) has is a constant function has no growth or decay.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given a function f(x) = 14(0.87) Now it is a constant function as for every different values of x the function f(x) has same value and has no growth or decay.

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Answer:

16.13

Step-by-step explanation:

multiply 10.75 and 1.5 which equals 16.125 so you would round up to 16.13 so your final answer would be $16.13 per hour

Answer:88 i think

Step-by-step explanation:

The Cramer rule can be applied to solve the system of equations and the value of x₂ is x₂ = 12.

For a given system of equations ax + by = c ; px + qy =r, if the determinant of the coefficient matrix [tex]A = \begin{bmatrix}a&b\\p&q\end{bmatrix}[/tex] is non-zero, then as per the Cramer rule, the solution to the system of equations is:

[tex]x=\frac{ \begin{vmatrix}c&b\\r&q\end{vmatrix}}{\begin{vmatrix}a&b\\p&q\end{vmatrix}}\quad\text{and}\quad y=\frac{ \begin{vmatrix}a&c\\p&r\end{vmatrix}}{\begin{vmatrix}a&b\\p&q\end{vmatrix}}[/tex]

The given system of equations is:

-2x₁ - x₂ = 2

-3x₁ - 2x₂ = -3

The coefficient matrix of the system of equations is:

[tex]A = \begin{bmatrix}-2&-1\\-3&-2\end{bmatrix}[/tex]

Now, find the determinant of the coefficient matrix:
[tex]A = \begin{vmatrix}-2&-1\\-3&-2\end{vmatrix}\\A = 4-3\\A =1[/tex]

Since the determinant of the coefficient matrix is non-zero, the Cramer rule can be applied.

According to the Cramer rule, it follows:

[tex]x_2=\frac{\begin{vmatrix}-2&2\\-3&-3\end{vmatrix}}{\begin{vmatrix}-2&-1\\-3&-2\end{vmatrix}}\\\\x_2=\frac{6-(-6)}{1}\\\\x_{2}=12[/tex]

Hence, the Cramer rule can be applied to solve the system of equations and the value of x₂ is x₂ = 12.

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The equivalent expression to (36 - y²) is (6 - y) (6 + y).

The correct answer option is option C

(36 - y²)

Check all options

A. (36 + 12y + y²)

No

B. (36 - 12y + y²)

No

C. (6 - y) (6 + y)

open parenthesis

= 36 + 6y - 6y - y²

= 36 - y²

Yes

D. (6 - y) (6 - y)

= 36 - 6y - 6y + y²

= 36 - 12y + y²

No

In conclusion, the expression (6 - y) (6 + y) is equivalent to (36 - y²)

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Answer: Sonya's heart rate increased by 75% after running a mile on the treadmill.

Step-by-step explanation:

To find the percent increase in Sonya's heart rate, we can use the following formula:

Percent increase = (New value - Old value) / Old value * 100

Substituting the given values into the formula, we get:

Percent increase = (133 beats per minute - 76 beats per minute) / 76 beats per minute * 100

Calculating the result, we get:

Percent increase = 57 beats per minute / 76 beats per minute * 100

= 0.75 * 100

= 75%

Therefore, Sonya's heart rate increased by 75% after running a mile on the treadmill.

Answer:

  C.  4² +8² ≠ 10²

Step-by-step explanation:

You want to know why it is not possible for the lengths 4, 8, and 10 to form a right triangle.

The side lengths of a right triangle must satisfy the Pythagorean relation:

  a² +b² = c²

These numbers do not:

  4² +8² = 16 +64 = 80 ≠ 10² = 100

A right triangle is not formed because ...

  4² +8² ≠ 10²

__

Additional comment

The smallest Pythagorean Triple is {3, 4, 5}. Doubling these numbers gives {6, 8, 10}. If the two longest sides are 8 and 10, the shortest must be 6 for a right triangle to be formed.

When the side lengths are reduced to a mutually prime set of numbers, their sum must be even.

   4:8:10 reduces to 2:4:5 which has an odd sum.

Answer:

w-10

Step-by-step explanation:

(3w-6)-(2w+4)

Take out the brackets:

3w-6-2w-4

Group the like terms:

3w-2w-6-4

Simplify:

w-10

The value of a number in the number line is always positive thus, the value of -8 will be 8 and it will be the largest among all.

In mathematics, a number line is a straight line containing numbers arranged at equal segments or periods throughout its duration.

In another word, a number line is basically a line in which infinite numbers have been written in ascending order or increasing order.

As per the given numbers in the number line has been drawn below,

The value of a number in the number line is the absolute value without considering the sign.

For example value of -2 is the distance from zero to -2 so it will be 2.

The largest value is 8 among all numbers.

Hence "The value of a number in the number line is always positive thus, the value of -8 will be 8 and it will be the largest among all".

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Answer:

Center: (2,-1)

Radius: 4

Step-by-step explanation:

Circle equation: (x-h)^2 + (y-k)^2 = r^2

Finding the center:

Set to equaling 0 and solve for x and y

(x - 2)^2=0

(y + 1)^2=0

Finding the radius:

In the equation, because it's set to r^2, you would undo the square.

[tex]\sqrt{16}[/tex]=4

Answer:

second option or B

And to mark brainliest on answers when 2 people answer a crown button will appear on the bottom right and you click that

Step-by-step explanation:

-7+4x>-3

+7.     +7

4x>4
/4.  /4

x>1
So second option is correct

Hopes this helps sorry for late response I was eating

The required monthly payment is given as follows:

$644.22.

The monthly payment is defined by the equation presented as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

The parameters are listed as follows:

For this problem, the values of these parameters are given as follows:

P = 120000, r = 0.05, n = 30 x 12 = 360.

Then:

r/12 = 0.05/12 = 0.004167.

Hence the monthly payment is obtained as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 120000\frac{0.004167(1.004167)^{360}}{(1.004167)^{360} - 1}[/tex]

A = $644.22.

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On solving the question, we that when focus is (0,4) and a directrix y is -4 coordinate is (0,0).

Parabola is the name of the graph of the quadratic function. Another way to think of this is the collection of all points whose distance from the focal point is equal to the distance from the line.

Focus (0,4) ,

the directrix y is (-4)

The vertex (h ,k) - halfway between the,

directrix and focus.

y = [y coordinate of focus + directrix] / 2.

The x coordinate will be the same as the x coordinate of the focus.

[tex]\frac{(0, 4-4)}{2} \\(0,0)[/tex]

Focus of (3,0),

a directrix of x = -3

The vertex (h , k) is halfway

between the directrix

and focus.

x = [x coordinate of focus + directrix] / 2.

The x coordinate will be the same as the y coordinate of the focus.

[tex]\frac{3-3,0}{3} \\(0,0)[/tex]

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if 40 is the least frequent multiple of two whole numbers. The higher number to lesser number ratio is 4:5. The two digits after that are 8 and 10.

Least Common Multiple is the meaning of the abbreviation LCM.

The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers.

It can also be computed using two or more numbers.

Finding the LCM of a given collection of numbers can be done in a variety of ways.

Utilizing the prime factorization of each number and then calculating the product of the greatest powers of the shared prime factors is one of the quickest techniques to determine the LCM of two numbers.

In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple.

The smallest number among all numbers is called the least common multiple of two or more numbers.

According to our question-

The number LCM is equal to 40.

4 × 5 × x = 40

20 × x = 40

20x=40

x=2

The larger number is equal to 4 x=4(2)=8.

The smaller value is =5x=5(2)=10.

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Complete question-

The least common multiple of two whole numbers is 40. The ratio of the greater number to the lesser number is 4:5. What are the two numbers?

The answers are ; a) -5/9, 6/10, -7/11, 8/12, b) f(n) = n/(n+4) and c) f(56) is positive.

A sequence is defined as an arrangement of numbers in a particular order.

A sequence is given ; -1/5, 2/6, -3/7, 4/8.....

Part A

From inspection of the sequence, the pattern is:

i) Add 1 to the numerator of the previous term.

ii) Add 1 to the denominator of the previous term.

iii) Make every other term negative.

Therefore, The next four terms are -5/9, 6/10, -7/11, 8/12

Part B

From inspection of the sequence, we can see that the numerator is the position of the term (n) in the sequence.  So when n = 1 the numerator is 1, when n = 2 the numerator is 2, etc.

The denominator is 5 more than the position of the term in the sequence.  So when n = 2 the denominator is 2 + 4 = 6, and when n = 4 the denominator is 4 + 4= 8.

Hence, the rule can be,

f(n) = n/(n+4)

If n is even, then f(n) is positive.

If n is odd, then f(n) is negative.

Part C

56 is an even number.

As the function f(n) is positive when n is even, the sign of f(56) is positive.

Therefore, the answers are ; a) -5/9, 6/10, -7/11, 8/12, b) f(n) = n/(n+4) and c) f(56) is positive.

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the percent of change in the average cost of a gallon from year one to year two is 5.8%

The term "average cost" refers to the production cost per unit, which is determined by dividing the overall production cost by the overall number of units produced.

The overall cost of production can also be divided into fixed and variable costs. Since total fixed costs often remain constant, changes in total variable costs are the main cause of changes in average costs.

The average cost of a gallon of gas in year one was $2.95

The average cost of a gallon of gas in year two was $2.78

The change in the average cost of a gallon from year one to year two is

$2.95 - $ 2.78

⇒$0.17

So percent of change in the average cost of a gallon from year one to year two is

($0.17/$2.95) * 100%

⇒ 0.0576 * 100%

⇒ 5.76%

⇒ 5.8%

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Jenny needs to score 79 on final exam.

Total marks divide by total number subjects=Average

100+88+96+84+98+x=90*6

461+x=540

x=79

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Answer: 28 inches

Hope this helps!!! :)

Answer:

√64 = 8

8i

Step-by-step explanation:

i = √-1

but √64 is a positive number which will produce 8i

Answer:

x= 1/3rd and 5/3rds

Step-by-step explanation:

9x^2 + 5 = 18x

9x^2-18x+5=0

a=9 b=-18 c=6

x=-b+- the Square root of b^2-4ac all over 2a

so x= 18+- the Square root of -18^2 -4x9x5 all divided by 18

x= 18+- the square root of 144 all over 18

so 18+12 over 18 and 18-12 over 18

this simplifies down to x= 5/3 and 1/3

Answer: y-3 = -4/5(x+0)

Step-by-step explanation:

formula

y-y1=m(x-x1)

y = y coordinate of the second point

y1 = y coordinate of point one

m = slope

x = x coordinate of the second point

x1 = x coordinate of point one

slope formula

y2-y1/x2-x1

-1-3/5-0

slope = -4/5

the 2 points on the graph are (0,3) (5,-1)

substitute and solve

y-3 = -4/5(x+0)

y-3=-4/5x

Answer: Gwen's breakfast in total was $8. Max's Breakfast in total is $8 as well. so their breakfast together is $16 in total

Answer:

their breakfast cost 16 dollars

Step-by-step explanation:

because you would do 2 times 2 which is 4 and 1 times 4 which is also 4 add those two together to get 8 and the double it because max got the same thing

The value of the given fraction in mixed numbers is 6, or 36/6.

A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. In mathematics, a fraction is used to represent a piece or part of a whole. It symbolizes the equal pieces of the whole. A fraction is made up of two parts: the numerator and the denominator. The top number is known as the numerator, while the bottom number is known as the denominator.

Here,

=81/6-45/6

=(81-45)/6

=36/6

=6

The value for given fraction in mixed number will be 6 that is 36/6.

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