Compare the slope-intercept and point-slope forms of a linear equation.​

Answer:

1. y=2x+4

2. y=x

3. y=-1/2x+1

4. y=-x+1

Step-by-step explanation:

the formula for these are y=mx+b. Your slope would be m and y intercept would be b. so y=2x+4 would mean that the slope is 2 and y intercept is 4. you can find the points by checking what points are on the blue line.

The solutions of the equation x^2 - 6x + d = 0 are both integers and d is a prime number is 5.

From the information, the solution of the equation x^2-6x+d=0 are integers

To find d, the numbers which can be added or subtracted to get -6 is needed which when multiplied will give a prime number

In this case - 5- 1 = -6

And when multiplied (-5×-1) will give +5 which is a prime number.

Therefore, x^2-6x+5=0

This illustrates that d is 5.

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Answer:

51.3

Step-by-step explanation:

Since it's telling us that (x=7) then that means 8.2x is going to be multiplied

8.2(7) or 8.2 x 7.

Then you end up getting an answer of 57.4

But you are not finished yet and need to subtract 6.1

so 57.4 - 6.1 = 51.3

And your result will be (51.3)

I hope this helps you understand this problem!

x-intercept

The x-intercept is where y=0.

[tex]-7x+10(0)=35\\\\-7x=35\\\\x=\boxed{-5}[/tex]

y-intercept

The y-intercept is where x=0.

[tex]-7(0)+10y=35\\ \\ 10y=35\\\\y=\boxed{7/2}[/tex]

The value of the correlation coefficient is 0.60.

There is a 0.6 correlation coefficient between two variables, which measures the strength of the relationship.

R² is the coefficient of determination, which measures how much variation can be explained by the regression line.

This means that, the R² value of the data is 36%

R² = 36% = 0.36

Correlation coefficients measure the strength of relationships between variables in the form of square roots.

That is ; R = √R²

R = √0.36

Hence, the correlation Coefficient, R is 0.60

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The equation formation is the form of a real word problem for some of them, thus the cost of candy for the given condition is $6.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

As per the given,

Let's say the cost per pound of strawberry taffy is "s" and the cost per pound of banana taffy is "b".

Then, the cost of 8 pounds of strawberry taffy and 3 pounds of banana taffy will be,

8s + 3b = 66

And,

The cost of 10 pounds of strawberry taffy and 3 pounds of banana taffy will be,

10s + 3b = 78

By solving both above equations,

2s = 12

s = $6

3b = 78 - 10(6)

b = $6

Hence, "The equation formation is the form of a real word problem for some of them, thus the cost of candy for the given condition is $6".

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Using the concepts of co-ordinate geometry, we got that (1.14,3.17) is best set of co-ordinates for the equipment staging if art contractors must locate an equipment staging area to serve the three construction sites, located at (x,y) coordinates (0,3), (1,4) and (5,5).

So, for x co-ordinates how we can find the output, for this we need to find that co-ordinate in which stagging area is maximum.

So that co-ordinate is given = [x-coordinate of point A + x-co-ordinate of point y)/2.0]-1.36

=>the best x-co-ordinate is =[(0+5)/2.0]-1.36

=>the best x-co-ordinate is =1.14,

Similarly, for the y-co-ordinate

the best y-co-ordinate is given by =[[y-co-ordinate of point A+ y-co-ordinate of point B]/2.0] +0.67

=>the best y-co-ordinate is given by =[(0+5)/2/0]+0.67=2.5+0.67

=>the best y-co-ordinate is given by=(

Therefore, the best x and y co-ordinate is (1.14,3.17)

Hence, when art contractors  locate an equipment staging area to serve three construction sites, located at (x,y) coordinates (0,3), (1,4) and (5,5). traffic between the staging area and each of the sites is 30 trips a week, except for the site located at (5,5), which is only 10 trips a week. the best set of co-ordinates for the equipment staging area is (1.14,3.17).

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Inconclusion the amount she invested in each account is $1,000 invested at interest rate 12% .

What is interest rate?

Let x represent the amount invested at 3%.

. 12x +.03(2000-x)= 150

.09x+ 60 = 150

Collect like terms

.09x = 90

Divide both side by .09x

x  = 90/.09

x=$1000

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Answer:2.86

Step-by-step explanation:

3.5(x +2) = 17

3.5x + 7 = 17

3.5x =17 - 7

3.5x =10

x = 10/3.5

x = 2.86

The point slope form of the equation is  y - 1 = [tex]\frac{1}{5}[/tex] ( x-5)

What is equation of line ?

  A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system. The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

Here the given point ,

=> [tex](x_1,y_1)=(5,1)[/tex]

Slope m = [tex]\frac{1}{5}[/tex]

Here using equation formula

=> [tex]y-y_1 = m ( x- x_1)[/tex]

=> y - 1 = [tex]\frac{1}{5}[/tex] ( x-5)

Hence the point slope form of the equation is  y - 1 = [tex]\frac{1}{5}[/tex] ( x-5)

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7.82 % is probability that all reservation holders who show will be accommodated.

What is probability in math?

If 236 are booked.

and there is only room of 213.

if 214 or 215 or 216 ............  etc

all the way to 236

there won't be enough seats.

P( X = 214 ) = ²³⁶C₂₁₄ * ( 0.9005 ) ²¹⁴   * ( 0.995 )²²

P( X = 214 ) = 0.08439109

                   = 8.44 %

P( X = 215 ) =  ²³⁶C₂₁₅ *  ( 0.9005 ) ²¹⁵   * ( 0.995 )²¹

                    = 0.0781522

                     = 7.82 %

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Answer:

======================

Let the sides be t for triangle and s for square.

Answer:

14 inches

Step-by-step explanation:

The side lengths of an equilateral triangle are the congruent.

The side lengths of a square are the congruent.

Let x be the length of one side of the equilateral triangle.

⇒ Perimeter of triangle = 3x

Let y be the length of one side of the square.

⇒ Perimeter square = 4y

Given:

Create a system of equations with the given information and defined variables:

[tex]\begin{cases}3x = 4y + 10\\x = y + 6\end{cases}[/tex]

Substitute the second equation into the first equation and solve for y:

[tex]\implies 3(y+6)=4y+10[/tex]

[tex]\implies 3y+18=4y+10[/tex]

[tex]\implies 18=y+10[/tex]

[tex]\implies y=8[/tex]

Therefore, the side length of the square is 8 inches.

Substitute the found value of y into the second equation and solve for x:

[tex]\implies x=8+6[/tex]

[tex]\implies x=14[/tex]

Therefore, the side length of the triangle is 14 inches.

The inequality that represents the bid for the artwork is A. b ≥ 25,000.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this case, the famous piece of artwork was up for bid at a museum auction and the minimum bid was $25,000.

Let the minimum bid be b. This will be b ≥ 25,000.

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Answer: angle 1 and 4

Step-by-step explanation:

Answer: x=3

Step-by-step explanation:

5x+2=7x-4
-5x +4    -5x +4
2x=6
divide both sides by 2
x=3

Answer: 4

Step-by-step explanation: in average, they drink 12/3 = 4 milk jugs per day.  

The solution of the inequality that determines how far Dev can travel over the weekend is -

x ≤ 400 miles.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Dave who is planning a car trip for weekend.

Assume that [x] represents the number of miles Dev can travel.

We can write the inequality as -

18 - 0.04x ≤ 2

0.04x ≤ 16

x ≤ 400 miles

Therefore, the solution of the inequality that determines how far Dev can travel over the weekend is -

x ≤ 400 miles.

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The largest area that can be enclose in straight wall is 2450 m².

Let 'x' be the length of rectangle.

Let 'y' be the width rectangle.

Perimeter =  140 meters

2x + y = 140      

y = 140 - 2x

Area = xy

Put the value of y in area.

Area = x(-2x + 140)

Area = -2x² + 140x

Differentiating the area with respect to x.

dA/dx = -4x + 140

Put dA/dx = 0 to get the critical point.

-4x + 140 = 0

x = 140/4

x = 35

Largest area at x = 35.

y = 140 - 2x

y = 140 - 2×35

y = 70

Area = xy

Area = 70×35

Area = 2450 m²

Thus, the largest area that can be enclose in straight wall is 2450 m².

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The average rate of change of function [tex]g(x)=5(2)^{x}[/tex] from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.

The correct option is (A).

What is the average rate of change of a function?

The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function.

Using function notation, we can define the Average Rate of Change of a function f from a to b as:

                                     [tex]rate(m) = \frac{f(b)-f(a)}{b-a}[/tex]

The given function is  [tex]g(x) = 5(2)^{x}[/tex],

Now calculating the average rate of change of function from x = 1 to x = 2.

                               [tex]m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(2)-g(1)}{2-1}\\\\m=\frac{5(2)^{2}-5(2)^1}{2-1}\\ m=\frac{10}{1} \\m=10[/tex]

Now, calculate the average rate of change of function from x = 3 to x = 4.

                                 [tex]m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(4)-g(3)}{4-3}\\\\m=\frac{5(2)^{4}-5(2)^3}{4-3}\\ m=\frac{40}{1} \\m=40[/tex]

The jump from m = 10 to m = 40 is "times 4".

So option (A) is correct.

Hence, The average rate of change of function [tex]g(x)=5(2)^{x}[/tex] from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.

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Answer:1

Step-by-step explanation:

The answer is one because the graph starts at 12$ and Wallace only needs $8.

180 students do not take lunch to school.

From the question, we have

Number of students do not take lunch to school= 200-20

=180 students

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.

The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

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Answer:

The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all four sides. x is in this case the length of the rectangle while y is the width of the rectangle. The area is a measurement of the surface of a shape. for example

You are able to find the perimeter of the rectangle by adding length and width and multiplying by two because the opposite sides of a rectangle are equal in length. Both lengths of the rectangle are the same, and both widths are the same. For example, P = 2 * (14 + 8) = 2 * (22) = 44 centimeter (17.3 in).

Step-by-step explanation:

Answer:

70%

Explan your answer :

200-130=70 and 70% of 100 = 30% so

Answer: 65

Step-by-step explanation:

0.65

×

100

=

0.65×100=

65

%

65%

The difference between the distance between the two cities if of 14.842 latitudes.

The earth has one latitude running right in the center called the equator. On either side of the equator, there are 90 more latitudes each.

Therefore, the earth has 181 latitudes.

Now if we see the image we can see that all these latitudes fall on the vertical diameter of the Earth.

Hence the distance covered by all 181 latitudes = 2 X radius of the Earth

= 2 X 6378 km

= 12756

Assuming that all the latitudes are equidistant, we get the distance between 2 latitudes to be

12756/181

= 70.475 km

Let the two cities be A and B. It is given that the distance between the two cities is 1046 km and one is due north of the other.

Therefore the difference in latitudes between the two cities is

1046/70.475

= 14.842 latitudes

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Answer:

3*3*3 or 3^3

Step-by-step explanation:

27/3=9/3=3

so 3*3*3 or 3^3

The modified r squared tells us more about the relationship among sales, price, as well as advertising by explaining approximately 60% of a variance in sales.

R-squared (R2) would be a statistical measure that quantifies the proportion of the variation explained from an independent variable other variables within a regression model for a dependent variable.

Thus, the modified r squared tells us more about the relationship among sales, price, as well as advertising by explaining approximately 60% of a variance in sales.

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Answer:

16(2z-3) or GCF: 16

Step-by-step explanation:

32z-48 has a GFC of 16

16(2z-3)

Answer:

$16(2z-3)

Step-by-step explanation:

Prime factorization:

32: 2*2*2*2*2

48: 2*2*2*2*3

Notice any similarities:

2*2*2*2=16

$32z-$48 = $16(2z-3)