Standard form of y=(X+3)^2-10

The equation of the line that passes through the point (0,0) and is perpendicular to the line y=-2x+10 is .

We will be using the concept of slope and equation of straight line for this question. Here it has been said that the line passes through (0,0) which is the origin, so we know the point ([tex]x_{1},y_{1}[/tex]) is (0,0).This point will be required while solving the equation for the straight line. The line is said to be perpendicular to another line given by y=-2x+10. When two lines are parallel their slopes are equal and when two lines are perpendicular the product of their slopes is equal to -1. The slope of a line can be found from the equation of the line by dividing the coeeficient of x by the coefficient of y.

Slope of y=-2x+10 is -2

mx-2=-1⇒m=1/2

equation of a straight line,

[tex](y-y_{1} )=m(x-x_{1} )\\[/tex]

⇒y-0=[tex]\frac{1}{2}[/tex](x-0)

⇒y=[tex]\frac{x}{2}[/tex]

⇒2y=x

⇒2y-x=0

Thus the equation of the line that passes through (0,0) and is perpendicular to y=-2x+10 is 2y-x=0.

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The scale drawing which is equal to 9 yards in real time is 12 cm.

Given that 4cm on the scale, drawing is equal to 3 yards in real-time

we have to find the scale drawing which is equal to 9 yards in real-time.

Let the scale drawing be 'x'

Now it can be written as

4 cm ------ 3 yards

x cm ------- 9 yards

Now we can divide this as

4/x = 3/9

By cross multiplication, we get

4 * 9 = 3 * x

x = 4 * 9 / 3

x = 12

Therefore, the scale drawing which is equal to 9 yards in real time is 12 cm.

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Solution:

A.) [tex](-4-\sqrt{13},-4+\sqrt{13})[/tex]

Hope this helps!

Answer:

h(10) = -25

Step-by-step explanation:

h(x) = -3x + 5

h(10) = -3(10) + 5

        = -30 + 5

        = -25

I hope this helps!

Trent writes 10×6=60, then in multiplication equation 10 represents the number of muffin boxes, 6 represents the numbers of muffins in each box and 60 represents the total numbers of muffins.

Given,

Trent writes 10×6=60,

Here,

10 represents the number of muffin boxes

6 represents the numbers of muffins in each box

60 represents the total numbers of muffins

Hence, Trent writes 10×6=60, then in the multiplication equation 10 represents the number of muffin boxes, 6 represents the numbers of muffins in each box and 60 represents the total numbers of muffins.

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Answer:

Let

x--------> the number

we know that

solve for x

Adds  both sides

Multiply by  both sides

therefore

the answer is

the number is 12

Step-by-step explanation:

The value of x and y by using the given expressions is x = -5/2 and y = -15/2.

What is an expression?

An expression can be defined as the combination of variables and constants with two or more operations applied to it. The operation can be addition, subtraction, multiplication and division.

Simplifying the expressions for x and y

The given expressions are:

x - y = 5           —--- 1

x + y = -10             —---- 2

Adding the expression 1 and 2, we get,

2x = -5

x = -5/2

Subtracting the expression 1 and 2, we get,

-2y = 15

y = -15/2

Hence, the value of x and y by using the given expressions is x = -5/2 and y = -15/2.

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Th elastic potential energy of two decimal places is    k=60×1^2 N/M

Given that,

Spring has a potential energy of =30 J

we know that,

Energy of a spring=1/2 kx^2

here, x=1cm

x^2=0.01m

30=1/2 kx^2

30=1/2 k(0.01)^2

60=k(0.01)^2

k=60/(0.01)^2

k=60×1^2N/M

Hence the potential energy of two decimal places is k= 60×1^2 N/M

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Answer:

570

Step-by-step explanation:

570

The absolute difference that is between the loans paid as 570

We have the following details:

Po = $15000

loan a 5 year loan, interest = 8 percent and repayments = 304.15 dollars

Loan b

3 year loan, interest = 11 percent repayments = $491.08

Total number of repayments = 5 x 12 = 60

Total repayments = 304.15 dollars x 60

= $18249

The total interest that is paid for A would be

$18249 - $15000

= $3249

For the second loan

Total number of repayments = 3 x 12 months = 36

Total repayment = 36 x 491.08 = $17678.88

The total interest for the loan B would be: $17678.88 - $15,000

= $2678.88

Then the absolute difference between the paid loan would be

$3249 -  $2678.88 = 570.12

Hence we would have the absolute difference that is between the loans paid as 570.

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Answer:

[tex]\frac{341}{10} =34\frac{1}{10}[/tex]

Step-by-step explanation:

[tex]7\frac{3}{4} *4\frac{2}{5}[/tex]

→ Convert both fractions into improper

[tex]\frac{31}{4} *\frac{22}{5}[/tex]

→ Simplify

[tex]\frac{31}{2} *\frac{11}{5}[/tex]

→ Calculate

[tex]\frac{341}{10} =34\frac{1}{10}[/tex]

2/5 get dumps out of the box from 4 and 7/10 pounds of candy then weight of the candy left in the box  is 2 and [tex]\frac{41}{50}[/tex] pounds.

As given,

Total weight of the candy =  4 and 7/10 pounds =  [tex]\frac{47}{10\\}[/tex] pounds

pound is the  imperial unit of weight generally written as lb.

one pound = 0.4535 kilograms = 453.5 gm.

[tex]\frac{2}{5}[/tex] th of candy is dumps out of the box.

1- [tex]\frac{2}{5}[/tex] = [tex]\frac{3}{5}[/tex] th of the total candy is left in the box.

weight of the candy left in the box = [tex]\frac{3}{5}[/tex] * [tex]\frac{47}{10}[/tex] = [tex]\frac{141}{50}[/tex] pounds.

now 141= 50*2 + 41

[tex]\frac{141}{50}[/tex] pound = 2 and [tex]\frac{41}{50}[/tex] pounds

Hence, weight of the candy left in the box= 2 and [tex]\frac{41}{50}[/tex] pounds.

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Answer:

4 + -1 = 3, 3 - 5 = -2.

Step-by-step explanation:

Hope this helps!!

Using the expected value of a discrete distribution, it is found that:

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

For the probabilities, we consider that it is given by the number of desired outcomes divided by the number of total outcomes.

For one bet, the distribution is given as follows:

Hence the expected value is given by:

E(X) = 578 x 5/6 - 300 x 1/6 = $431.67.

For two bets, the distribution is given as follows:

Hence the expected value is given by:

E(X) = 682 x 2/3 - 300 x 1/3 = $354.67.

For three bets, the distribution is given as follows:

Hence the expected value is given by:

E(X) = 945 x 1/2 - 300 x 1/2 = $322.5.

For four bets, the distribution is given as follows:

Hence the expected value is given by:

E(X) = 1312 x 1/3 - 300 x 2/3 = $237.33.

Hence, considering the greatest and the smallest expected values, we have that:

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Answer:

Step-by-step explanation:

The Perimeter of rectangle 3cm 5cm is 16 cm.

In geometry, a rectangle is a plane figure of four sides having four angles of 90 degree. A rectangle has different length and breadth.

Some important formulas for rectangle :

Perimeter is define as the distance around all the edges of a shape. In case of rectangle perimeter is the distance of all 4 edges i.e. 2 lengths and 2 breadth .

Thus , perimeter of rectangle = ( 2 × length ) + (2 × breadth)

                                                 = 2 ( length + breadth )

In the given question,

length of rectangle =  3cm

breadth of rectangle = 5cm

therefore, perimeter of rectangle = 2(3+5) = 16cm

Hence, The Perimeter of rectangle is 16 cm.

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Answer:

[tex] \large \sf \: x=30[/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

5/9 = x/54

Step 1: Cross-multiply.

5/9 = x/54

(5)*(54)=x*(9)

270=9x

Step 2: Flip the equation.

9x=270

Step 3: Divide both sides by 9.

9x/9 = 270/9

x=30

Answer:

36.3 seconds per lap

Step-by-step explanation:

200m in 2.42  if each lap = 50m

50m = 36.3 seconds

Since the pairs of y values have singular and unique x values, the following set of points are a function.

Since an increase in one unit in the x value, yields an increase in one unit in the the y value, there exists a relation between these set of points.

[tex]y (x)= x + 3 \\ D_{f} ∈ [1,3][/tex]

Option: C

Answer:

Subscribe to itsIceboiiYT

Answer:  The answer is -1

Step-by-step explanation:

-28/-4+-48/6

7-8

-1

Answer: -1

Step-by-step explanation:

-28 divided by -4 is 7

-48 divided by 6 is -8

7 - 8 would be a total of -1

Dots sold 65 T-shirts and 13 shorts

let the x represent the number of T-shirts and y and shorts

7x + 9y= 572.......equation 1

x= 5y........equation 2

substitute 4y for x in the equation

7(5y) + 9y = 572

35y  + 9y= 572

44y= 572
y= 572/44

y= 13

substitute 13 for y in equation 2

x= 5(13)

x= 65

Hence there 65 T-shirts and 13 shorts

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Answer:

1.5 pounds

Step-by-step explanation:

3/2 = 1.5

Answer:

Area = 192.5 ft.²

Step-by-step explanation:

By splitting the shape in 2, we can find the area much simpler.

Starting with the parallelogram (on the left), the area formula is A = b × h.

b (base) = 11 ft.

h (height) = 7 ft.

A (area) = (11 ft.)(7 ft.)

A = 77 ft.² (save this for later)

Then, the trapezoid's (on the right) area formula is A = [(a + b) ÷ 2] × h.

a (first base) = 8 ft.

b (second base) = (20 - 7) = 13 ft.

h (height) = 11 ft.

A = [(8 ft. + 13 ft.) ÷ 2] × 11 ft.

A = [(21 ft.) ÷ 2] × 11 ft.

A = (10.5 ft.) × 11 ft.

A = 115.5 ft.²

Now, bringing back the first area, we can add them together to find the total:

A = 77 ft.² + 115.5 ft.²

A = 192.5 ft.²

Hope this helps! I'd appreciate Brainliest but if not it's totally fine!

Answer:

see attached

Step-by-step explanation:

The vector difference u -v can be represented on a vector diagram by the sum u +(-v), where -v is a vector the same length as v, but in the opposite direction.

__

The equation when solved for t gives d/r

Subject of formula can be defined as a variable or element expressed in terms of other variables in an equation.

Iris also known as the variable that is being worked out in equation.

From the information given, we have the equation as;

d = rt

Where;

Now, let's make 't' the subject

Divide both sides by the coefficient of t

d/r = rt/r

t = d/r

Thus, the equation when solved for t gives d/r

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The complete question:

The formula below relates distance, rate, and time. Solve this formula for t.

d = rt

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

For the given function :

[tex]\qquad \sf  \dashrightarrow \: f(x) = \dfrac{7}{x - 10} - 7[/tex]

f(x) is defined for all real values of x, except the value of x for which the denominator becomes 0, because if denominator is 0, the function at that instant will be undefined.

that is : f(x) is not defined when :

[tex]\qquad \sf  \dashrightarrow \: x - 10 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 10[/tex]

Hence, f (x) is defined for all real values of x except 10

It can be represented as :

[tex]\qquad \sf  \dashrightarrow \: f(x) : x \in R \sim \{10 \}[/tex]

Answer:

Step-by-step explanation:

Based on the fact that the widow got an exemption on homestead tax, the amount that the owner would pay in property taxes is $3,471.20.

The widow received a homestead tax exemption of $25,000 on the property.

The amount to be paid in property tax is:

= (8.8 + 9.3 + 6.5) / 1,000 x (185,000 - 25,000)

= 21.7/1,000 x 160,000

= $3,471.20

In conclusion, the property tax to be paid is $3,471.20.

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