A line passes through the point (10,-1) and has a slope of 3/2. Write an equation in point-slope form for this line.

Answer: 1 1/3

Step-by-step explanation: 0.33 repeating and in general is equal to 1/3

In this question, you're solving by adding the two expressions together.

(f+g)(x) is the same as:

3x - 1 + x + 2

Solve:

3x - 1 + x + 2

combine like terms:

4x - 1 + 2

4x + 1

Answer:

4x + 1

Answer:

4/9 or 0.444...

Step-by-step explanation:

[tex] \frac{7}{9} - \frac{1 \times 3}{3 \times 3} [/tex]

[tex] \frac{7}{9} - \frac{3}{9} [/tex]

[tex] \frac{4}{9} [/tex]

Answer: 4/9

Step-by-step explanation: Since our denominators in this problem are 9 and 3, and 9 factors as 3 x 3, they have a common factor of 3 so we find their least common denominator by multiplying the 3 that comes from the 3's that match up times the 3 that doesn't match up so we have 3 x 3 or 9.

In order to get a common denominator of 9 for both our fractions, we multiply top and bottom of the the second fraction by 3 and we have 7/9 - 3/9 which simplifies to 4/9. So 7/9 - 1/3 is 4/9.

I have also attached my work in the image provided.

Answer:

9076

Step-by-step explanation:

Answer:

Contour lines. Hope this helps!

Maricel's code will adjust the shot by 12º

Answer:

The correct angle will be 12.5 degrees.

Answer:

0.00144

Step-by-step explanation:

(13/1)(4/3)(12/1)(4/2)/(52/5)=(13)(4)(12)(6)/2598960=3744/2598960≈0.00144

Answer:

The final simplification is (32p^-15).

Step-by-step explanation:

Given:

(2p^-3)^5 we have to simplify.

Property to be used:(Power rule)

Power rule states that: [tex](a^x)^y=a^x^y[/tex] ...the exponents were multiplied.

Using power rule.

We have,

⇒[tex](2p^-3)^5[/tex]          

⇒[tex](2^5)(p^-3^*5)[/tex]     ...taking exponents individually.

⇒[tex]32(p^-^1^5)[/tex]         ...[tex]2^5=2*2*2*2*2=32[/tex]

⇒[tex]32p^-^1^5[/tex]

So our final values are 32p^-15

Answer:

(6 + 2) + 7 = 6 + (2 + 7)

Explanation:

(6 + 2) + 7

6 + 2 = 8

8 + 7 = 15

6 + (2 + 7)

2 + 7 = 9

9 + 6 = 15

15 = 15

You will be adding 6, 2 and 7 no matter what. The parenthesis do not make a difference. 6 + 2 + 7 is the same thing as 6 + 2 + 7. 15 = 15.

Answer:

A.

Step-by-step explanation:

A. 15 = 15 (true)

B. -3 = 11 (false)

C. 11 = -3 (false)

Answer:

No

Step-by-step explanation:

The vertical line test can be used to determine whether a graph represents a function. A vertical line includes all points with a particular X value. The Y value of a point where a vertical line intersects a graph represents an output for that input X value. If we can draw any vertical line (left to right) that intersects a graph more than once, then the graph does not define a function because that X value has more than one output. A function has only one output (X) value for each input value.

EXAMPLES:

(3,-7), (2,4), (-3,-7), (3,0), (0,2)  

The first numberin each set is th X value or output.

The 3 has two Y values, -7 and 0, it can only have one Y value.

Only one X can have a one Y vale to make it a function.

The relation given by the set (3,-7), (2,4), (-3,-7), (3,0), (0,2) is not a function, since the x-value 3 corresponds to two different y-values (-7 and 0).

In mathematics, a relation is a set of ordered pairs. For that set to be a function, each input (x-value) should correspond to only one output (y-value). That means no two ordered pairs should have the same x-value but different y-values.

Looking at your given set (3,-7), (2,4), (-3,-7), (3,0), (0,2), we can see that the x-value 3 corresponds to two y-values: -7 and 0. Therefore, this relation is NOT a function.

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Answer:

Step-by-step explanation:

0.4 × 3.2

Convert to fraction

0.4 = 4/10 = 2/5 & 3.2 = 32/10 = 16/5

0.4 × 3.2 = 2/5 × 16/5 = 32/25 = 1.28

Without conversion you press ur calculator and you get 1.28

Answer:2492

Step-by-step explanation:

4Log4(x+8)=4^2

Divide both sides by 4 we get

Log4(x+8)=4^2/4

Log4(x+8)=4

4(x+8)=10^4

4(x+8)=10000

Open brackets

4x+32=10000

Subtract 32 from both sides

4x+32-32=10000-32

4x=9968

Divide both sides by 4

4x/4=9968/4

X=2492

Answer:

B is the answer

Frank will plant a total of 5y + 9 vegetable seeds across his two gardens.

Frank has two gardens where he plans to plant vegetable seeds. In one garden, he will plant y vegetable seeds. In the other garden, he will plant 4y+9 seeds. To find the total number of seeds Frank is going to plant, we need to add together the number of seeds for each garden.

The total number of seeds is:

Total seeds = y + (4y + 9)

Combine like terms:

Total seeds = y + 4y + 9

Total seeds = 5y + 9

Thus, Frank will plant a total of 5y + 9 vegetable seeds across both gardens.

Answer:

Step-by-step explanation:

11kx + 13kx = 6.......for x

24kx = 6.....divide both sides by 24k

x = 6 / (24k)

x = 1/4k OR k/4

Answer: 5/11,5

Step-by-step explanation:

Multiply equation one by -4

Multiply equation two by 2

Then, it becomes

-8x - 28y = 28

-8x - 6y = 38

Subtract equation two from equation one .

It becomes -22y = -10

Divide both sides by 22, you have y= 5/11

NOW substitute y=5/11 into equation two to get X.

-4x -3(5/11) =19

-4x = 19 + 15/11

-4x = 20

Divide both sides by -4

X = -5

To solve the system of equations, the elimination method was used, resulting in the solution of the equations as an ordered pair (-6 16/77, 5/11).

To solve the system of equations 2x + 7y = -7 and -4x - 3y = 19, one can use the elimination method. This involves manipulating the two equations to eliminate one of the variables, allowing the other variable to be found. We can multiply the first equation by 2 to align the coefficients of the 'x' terms and then add the equations to cancel out the 'x' terms.

Multiply the first equation by 2: 4x + 14y = -14.

Add this to the second equation: (4x + 14y) + (-4x - 3y) = -14 + 19.

This simplifies to 11y = 5, and solving for 'y' gives y = 5/11.

Substitute 'y' back into the first original equation: 2x + 7(5/11) = -7.

Solve for 'x', which gives x = -6 16/77.

So, the solution to the system of equations, expressed as an ordered pair, is (-6 16/77, 5/11).

Answer:

y = - [tex]\frac{5}{6}[/tex] x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (6, - 3) and (x₂, y₂ ) = (0, 2)

m = [tex]\frac{2+3}{0-6}[/tex]= [tex]\frac{5}{-6}[/tex] = - [tex]\frac{5}{6}[/tex], thus

y = - [tex]\frac{5}{6}[/tex] x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (6, - 3), then

- 3 = - 5 + c ⇒ c = - 3 + 5 = 2

y = - [tex]\frac{5}{6}[/tex] x + 2 ← equation of line

The equation of the line in slope-intercept form that passes through the points (6,-3) and (0, 2) is y = -5/6x + 2, where -5/6 is the slope and 2 is the y-intercept.

To write an equation in slope-intercept form (y = mx + b) of the line that passes through two points (6,-3) and (0, 2), first, we need to calculate the slope (m).

The formula to calculate the slope is (y2 - y1) / (x2 - x1). Plugging in the values from the given points, we get the slope as (2 - (-3)) / (0 - 6) = 5 / -6 = -5/6.

Next, substitute one of the points and the slope into the equation to find the y-intercept (b). If we use (0, 2), we get 2 = -5/6 * 0 + b, hence, b=2.

Therefore, the equation of the line in slope-intercept form that passes through these points is y = -5/6x + 2.

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Answer:

see attached picture please

To solve the mixture problem, we set up an equation based on the total weight and another based on the total cost, then solve the system of equations algebraically to find out how many pounds of peanuts and raisins are needed.

The question involves creating a cost-based blend of two items, peanuts and raisins, to produce a mixture with a target cost per pound. This is a typical algebraic mixture problem, commonly encountered in high school math. To solve this problem, we want to find out how many pounds of peanuts and raisins are needed to make a 50-pound mixture that costs $1.47 per pound when peanuts cost $1.20 per pound and raisins cost $2.10 per pound.

Let's denote the weight of peanuts as P pounds and the weight of raisins as R pounds. The total weight of the mixture is given as 50 pounds, which gives us the equation:

P + R = 50

Next, we need to consider the total cost of the mixture. The cost of the peanuts is P times $1.20, and the cost of the raisins is R times $2.10. Since the mixture should have an overall cost of $1.47 per pound, our cost equation becomes:

1.20P + 2.10R = 1.47 × 50

From our first equation, we can express R as 50 - P, and substitute it into our second equation to find the value of P. After solving these linear equations, we will obtain the exact quantities of peanuts and raisins required to make the desire mixture.

Answer:

1 4/12

Step-by-step explanation: What you need to do first is make them improper fractions with the same denominator.

1 1/6 = 7/6       1 4/12 = 16/12.       Now you can make them have the same denominator. 7/6 = 14/12 and 16/12. So 1 and 4/12 is bigger.

The width of rectangle is [tex]2\frac{1}{4}[/tex] cm and length is [tex]5\frac{5}{12}[/tex] cm.

Step-by-step explanation:

Let,

Width of rectangle = w

Length of rectangle = [tex]w+3\frac{1}{6}=w+\frac{19}{6}[/tex]

Perimeter of rectangle = [tex]15\frac{1}{3}=\frac{46}{3}[/tex] cm

Perimeter = 2(Length + Width)

[tex]\frac{46}{3}=2(w+\frac{19}{6}+w)\\\\\frac{46}{3}=2(2w+\frac{19}{6})\\\\\frac{46}{3}=4w+\frac{19}{3}\\\\4w+\frac{19}{3}=\frac{46}{3}\\\\4w=\frac{46}{3}-\frac{19}{3}\\\\\ 4w=\frac{46-19}{3}\\\\4w=\frac{27}{3}\\\\4w=9[/tex]

Dividing both sides by 4

[tex]\frac{4w}{4}=\frac{9}{4}\\\\w=\frac{9}{4}[/tex]

Width of rectangle = [tex]\frac{9}{4}=2\frac{1}{4}\ cm[/tex]

[tex]Length = w+\frac{19}{6}=\frac{9}{4}+\frac{19}{6}\\\\Length = \frac{27+38}{12}=\frac{65}{12}\\\\Length=5\frac{5}{12}\ cm[/tex]

The width of rectangle is [tex]2\frac{1}{4}[/tex] cm and length is [tex]5\frac{5}{12}[/tex] cm.

Keywords: rectangle, perimeter

Learn more about perimeter at:

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Final answer:

The width of the rectangle is 9.92 cm (approx.) and the length is 13.09 cm, calculated using the given perimeter and the relationship between the width and length, both rounded to three significant figures.

Explanation:

The question asks to find the width and length of a rectangle given that the length is 3 1/6 cm longer than the width and the perimeter is 15 1/3 cm. To solve this, first express the perimeter as an equation involving width (w) and length (l):

Perimeter (P) = 2l + 2w

Since the length is 3 1/6 cm longer than the width, we can express the length as:

l = w + 3 1/6

Substitute the value of l in the perimeter equation:

15 1/3 = 2(w + 3 1/6) + 2w

Convert mixed numbers into improper fractions for easier computation:

46/3 = 2(w + 19/6) + 2w

Expand and solve for w:

46/3 = (4w + 19/3)

3(46) = 4w(3) + 19

138 = 12w + 19

119 = 12w

w = 119/12

w = 9.916666...

To match our significant figures requirement, we report the width of the rectangle as 9.92 cm to three significant figures. Now calculate the length:

l = w + 3 1/6

l = 9.92 + 3.1666...

l = 13.0866...

Again, matching our significant figures requirement, the length is reported as 13.09 cm to three significant figures.

Answer:

I=60

Step-by-step explanation:

So

P=$250

R=6%

T=4

So to get the answer we would need to multiply everything to get the interest so the answer would be 60 because 250 times 6% equals to 15 then we would multiply 15 by 4 and then get out answer of $60 interest.

Answer: x=13

Step-by-step explanation:

Replace u wit y = 3x+14

6x-6(3x+14)=-24

6x-18-84 = -24

6x-102=-24

Add -102 on both sides

6x=78

Divide 6 on both side and have your answer

Answer:

Step-by-step explanation:

I've already answered this question.

Answer:

A. 4x² - 2x + 11

Step-by-step explanation:

(4x² + 6) - (2x - 5) =

Drop the first set of parentheses since it is unnecessary.

= 4x² + 6 - (2x - 5)

To drop the second set of parentheses, you must change every sign inside the parentheses.

= 4x² + 6 - 2x + 5

Now combine like terms.

= 4x² - 2x + 11

Answer:

45h=d

Step-by-step explanation:

If d represents the distance in miles, then the equation would be 45h=d because when you multiply 45 by the amount of hours h, then you would get the total distance in miles. For example, Oliver drives 45 miles per hour for 3 hours. When we substitute h, the number of hours, for 3, then we get:

45(3)=d

And all we need to do is to multiply them together to get d, which in this case, it is 135 miles.

Answer: $ 360

Step-by-step explanation:

since the monthly payment is 3% of the price , this means that the monthly payment is 3% of 12000

= 0.03 x 12000

= $ 360

[tex]m=-\frac{1}{3}[/tex] is the slope of a perpendicular line.

Step-by-step explanation:

For two lines to be perpendicular to each other, their slope must be mutually negative reciprocal (to check if the numbers are multiplied, they should be -1).

Given equation:

          y = 3 x – 1

We know the standard slope equation, as y = m x + b. When comparing this with the given equation, we get slope value,

           m = 3

But in question, they asked to find slope of a line perpendicular to the line. So, apply this ‘the perpendicular slope will be the opposite (negative) reciprocal of the original slope’

Therefore, the slope of a perpendicular line is

          [tex]m=-\frac{1}{3}[/tex]