A triangle has vertices at A(-7, 6), B(4,9), C(-2, -3). What are the coordinates of each vertex if the triangle is translated 4 units right and 6 units down?

Answer:

-3/7

Step-by-step explanation:

You can add 1350 additional watts without overloading the circuit.

Step-by-step explanation:

Given,

Circuit overloads at 2400 watts

Electricity used by heater = 1050 watts

Let,

x be the number of additional watts.

Electricity used by heater + Additional watts ≤ Circuit's capacity

[tex]1050+x\leq 2400[/tex]

Subtracting 1050 from both sides

[tex]1050-1050+x\leq 2400\\x\leq 1350[/tex]

You can add 1350 additional watts without overloading the circuit.

Keywords: inequality, subtraction

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If a circuit can handle up to 2400 watts, and a heater using 1050 watts is already plugged in, an additional 1350 watts of electrical devices can be plugged in without overloading the circuit.

The subject at hand is related to electrical power and circuits. In electrical circuits, overloading occurs when more electrical power is drawn than the circuit can safely handle. This limit in your scenario is represented as 2400 watts of electricity. If a portable heater using 1050 watts of electricity is already plugged into the circuit, you subtract the wattage of the heater from the maximum wattage to find out how much more you can add without overloading the circuit.

So, we calculate 2400 watts (total wattage that the circuit can handle) - 1050 watts (wattage used by the heater) = 1350 watts. Therefore, you can plug in additional items up to 1350 watts without overloading the circuit.

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Answer:

length iof opposite sides are equal

Step-by-step explanation:

Final answer:

To prove ABCD is a parallelogram, we showed that the given pairs of opposite sides are parallel and the slopes of opposite sides are equal, confirming the definition of a parallelogram.

Explanation:

To complete the proof that ABCD is a parallelogram, we must show that both pairs of opposite sides are parallel and that the lengths of opposite sides are equal or that the slopes of opposite sides are equal. Since it's given that BC is parallel to AD and CD is parallel to AB, the condition for parallel sides is satisfied. To fulfill the second condition, we calculate the slopes of the sides.

The slope of BC is calculated using the coordinates of B(-3,4) and C(2,2):

Slope of BC = (4 - 2) / (-3 - 2) = 2 / -5

The slope of AD, using the coordinates A(-2,-2) and D(3, -4), is:

Slope of AD = (-4 - (-2)) / (3 - (-2)) = (-2) / 5

Because the slopes of BC and AD are negative reciprocals, BC and AD are parallel. A similar calculation can be made for AB and CD, using their corresponding coordinates, to confirm that their slopes are equal. Thus, because both pairs of opposite sides are parallel, ABCD is a parallelogram.

Answer:

63.1∅∅

Step-by-step explanation:

Answer:

63.1

Step-by-step explanation:

If you are rounding anything, look at the number before. If its 5 or above, move the next number up. If its 4 or below, just keep the number the same. In this case the number is .094. The 4 is irrelevant because we are rounding in the tenths not the hundreths. So we look at the next one. Its a 9 there for round it up so you have 63.1

Answer: [tex]a=\frac{b(zd-c)}{d}[/tex]

Step-by-step explanation:

Having the following equation given in the exercise:

[tex]z=\frac{a}{b}+\frac{c}{d}[/tex]

You can solve for "a" following this procedure:

1. You can apply the Subtraction property of equality and subtract [tex]\frac{c}{d}[/tex] from both sides of the equation:

[tex]z-(\frac{c}{d})=\frac{a}{b}+\frac{c}{d}-(\frac{c}{d})\\\\z-\frac{c}{d}=\frac{a}{b}[/tex]

2. Now you must subtract the terms on the left side of the equation. Notice that the Least Common Denominator is "d". Then:

[tex]\frac{zd-c}{d}=\frac{a}{b}[/tex]

3. Finally, you can apply the Multiplication property of equality and multiply both sides of the equation by "b". So, you get:

[tex](b)(\frac{zd-c}{d})=(\frac{a}{b})(b)\\\\a=\frac{b(zd-c)}{d}[/tex]

Question:

One dollar is worth 3 1/2 kruneros. What is the value of 43 3/4 kruneros?

Answer:

The value of [tex]43\frac{3}{4}[/tex] kruneros is 12.5 dollars

Solution:

Given that,

Dollar is worth three and 3 1/2 kruneros

Which means,

[tex]1 \text{ dollar } = 3\frac{1}{2} \text{ kruneros }\\\\1 \text{ dollar } = 3.5 \text{ kruneros }[/tex]

We have to find the value of [tex]43\frac{3}{4}[/tex] kruneros

Let us convert the mixed fractions to improper fractions

Multiply the whole number part by the fraction's denominator.

Add that to the numerator.

Then write the result on top of the denominator.

[tex]43\frac{3}{4} = \frac{43 \times 4 + 3}{4} = \frac{175}{4} = 43.75[/tex]

So we have to find the value of 43.75 kruneros

Let "x" be the value of 43.75 kruneros

Then,

1 dollar = 3.5 kruneros

x dollar = 43.75 kruneros

This forms a proportion and we can solve the sum by cross multiply

[tex]1 \times 43.75 = x \times 3.5\\\\x = \frac{43.75}{3.5}\\\\x = 12.5[/tex]

Thus value of [tex]43\frac{3}{4}[/tex] kruneros is 12.5 dollars

Answer:

12w+15

Step-by-step explanation:

Distribute 3 to whats inside of parentheses

3*4w=12w

3*5=15

12w+15

Answer:

12w + 15

Explanation:

3(4w + 5)

= (3)(4w + 5)

= (3)(4w) + (3)(5)

= 12w + 15

Answer:

Step-by-step explanation:

a) r = 10/2 = 5 feet

Area of floor =πr² =3.14*5*5 = 78.5 feet²

B) h = 3 foot

Volume of cylinder = πr²h = 3.14*5*5*3 = 235.5 cubic feet

Volume of hemisphere =2/3πr³= 2*3.14*5*5*5/3=261.67 cubic feet

Volume of space inside the observatory = 497.17 cubic feet

Answer:

c=13 its the square root :)

Step-by-step explanation:

Answer:

1 , -7

Step-by-step explanation:

(x+3)² = 16

then

(x+3)² = 4²

then

|x+3| = 4

then

x+3=4 or x+3= -4

then

x=4-3=1  or  x= -4-3= -7

Answer:

175

Step-by-step explanation:

The circle has to = 360 degrees. 360-10=350

350/2=175

The x is halfway that's why you divide by 2.

Answer:

1 Quarter + 1 Nickel , 3 Dimes , 30 Pennies , 15 Pennies + 1 Nickel + 1 Dime ,    10 Pennies +  2 Nickels + 1 Dime ...

Step-by-step explanation:

1 Dollar = 100 cents

30% of 100 = 30 cents

There are many different ways to make 30 cents with certain coin combinations.

Using the different available coins, a combination of 3 different coins can be combined to give a total value of 30 cents.

30% of a dollar = (30/100) = $0.30 = 30 cents

1 Quarter + 1 Nickel , 5 Pennies = 25 + 5 + 5 = 30 cents

1 dime + 2 Nickels + 10 Pennies = 10 + 10 + 10 = 30 cents

3 Nickels + 1 dime + 5 Pennies = 15 + 10 + 5 = 30 cents

Therefore, the listed are 3 possible combinations of obtaining 30 cents.

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Answer:

y = 14

Step-by-step explanation:

The triangle in the figure is an isoceles triangle meaning the two sides of the triangle are equal. This I know because of that short lines on line AC and CB of the triangle.

Now, the base angles of an isoceles triangle are equal and applying this theorem to this problem, we have:

50 = 2x

solving for x,

x = 25

Now the sum of angles in a triangle is 180 degrees

=> 50 + 50 + 5y + 10 = 180

5y = 180 - 110

5y = 70

y = 14

Answer:

11 and 23

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

5(1/5)+(1/5)15

1+3

4

Answer:

4

Step-by-step explanation:

when c = 1/5 and d =15

5c + cd = c×(5 + d) = (1/5)×(5+15) = 1/5×(20) = 20/5 = 4

Answer:

Let's look again at the amount of money spent. They bought $15 game tokens and 3 admission tickets. If t is the cost of one admission ticket, as given, then the total money they spent can be written as:

$15 + 3 • t

making the statement a) false.

If the admission ticket costs $2.50, then, using the expression above, they spent:

$15 + 3 • $2.50

$15 + $7.50

$22.50

making the statement b) true.

From the table, we see that number of feet is always three times the number of yards.

So, if we label the number of yards with y and number of feet with f, we get:

f = 3y

which means that the number of feet in y yards is 3y.

When using decimal numbers we should know that the digit before the decimal point is integer and the digits after the point are decimals.

When adding two numbers, one of which isn't decimal number, sometimes it's helpful to write it in that manner. In this case, we could write 7 as 7.0.

Now, adding these two numbers should be easier:

7.0 + 0.8 = 7.8

Note that we simply add up decimal numbers and integers independently.

Here, it's important to remember one of the key features of multiplication; any number multiplied with one equals to that same number. It doesn't matter whether that number is integer, decimal number, a fraction or an expression.

So, in this case, we have:

8.3 • 1 = 8.3

We can write expressions for both girls. Samantha ran five miles each day for seven days, so her distance is:

S = 5 • 7 = 35

Mariska, on the other hand, ran seven miles each day for five days, meaning that her distance is:

M = 7 • 5 = 35

So, this means that they ran the same distance, but let us explain why. Another important feature of multiplication is that if you change the order of the numbers multiplied, you still get the same value. So, if we write:

a • b = c

then:

b • a = c

which was the case in this question (5 • 7 = 7 • 5).

Let's define the number of balls on the playground as b. Then, one more ball than that would be b+1.

Let's define the number of cookies in the jar as c. Then, three more cookies than that would be c+3.

Let's define the number of the questions on the first test as q. Then, twelve fewer then this would be q-12.

Let's define the cost of the shirt as s. Then, eight dollars more then this would be s+8.

Let's define number of drinks on the tray as d. Then, eight times as much would be 8•d.

Let's define Yumi's pay as y. Then, five dollars less would be y-5.

Let's define the number of students in math class as m. Then, half as many would be m • 1/2 = m/2

Let's define Emily's age as e. Then, third of her age would be e • 1/3 = e/3.

Let's define minutes spent exercising as x. Then, ten times this would be 10•x.

So, Spencer bought three books of stamps and spent $4.50 on mailing a package. The total amount Spencer spent at the post office is the amount spent on the books plus mailing of the package. If we mark the price of one book as b, since he bought three books, he spent 3•b. So, the total amount he spent in the post office is:

3•b + $4.50.

The three even integers are 66, 68 and 70

Solution:

Let the three consecutive even integers be x, x + 2, x + 4

Let the first integer be x

Let the second integer be x + 2

Let the third integer be x + 4

Given that, sum of the first and third of three consecutive integers is 136

Sum of first and third integer = 136

x + x + 4 = 136

2x + 4 = 136

2x = 136 - 4

2x = 132

x = 66

Thus the consecutive integers are:

first even integer = x = 66

second even integer = x + 2 = 66 + 2 = 68

third even integer = x + 4 = 66 + 4 = 70

Thus the three even integers are 66, 68 and 70

Answer:

The top angle of the triangle is, X = 68°.

Step-by-step explanation:

Let there is a triangle named PQR with bottom corner angles ∠ P and ∠ Q and the ∠ R is the angle at the top.

Now, given that ∠ P = 31° and ∠ Q = 81° and we have to find out ∠ R i.e. X.

In Δ PQR, we know, ∠ P + ∠ Q + ∠ R = 180°

⇒ 31° + 81° + X = 180°

⇒ X = 68°

Therefore, the top angle of the triangle is 68°. (Answer)

Answer:

x=29/8

Step-by-step explanation:

3 5/8=29/8

7 1/4=29/4

---------------

x+29/8=29/4

x=29/4-29/8

x=58/8-29/8

x=29/8

Answer:

I just had this question and i believe the answer was infinitely

Step-by-step explanation:

Answer:

its 2/9

Step-by-step explanation:

I remember this from a long time ago but any number repeating that is less than nine is just put over 9, but as it goes up you put it over 99 and so on.

Marco has ( d + 14.55 ) $

Step-by-step explanation:

Marco's mom gave him d dollars for his allowance one week.

Allowance of one week = d $

He also earned $ 1 4 . 5 5 for his newspaper route that week.

Earning of Marco by selling newspaper route that week = 14.55 $

Total earning = Allowance of one week + Earning of Marco by selling newspaper route that week

Total earning = ( d + 14.55 ) $

So Marco has ( d + 14.55 ) $

Answer:

Step-by-step explanation:

Answer:

4 im not 100% but i think so

Step-by-step explanation:

Answer:

Step-by-step explanation:

4(x + 8) + 5(y + 3) =

4x + 32 + 5y + 15 =

4x + 5y + 47

total of 3 terms : 4x, 5y, and 47

Answer:

10

Step-by-step explanation:

because

Answer:

I put it into a calculator and got this: 7/125

Step-by-step explanation:

It is equal to 8 x 7 x 1 / 100 x 1 / 10

And multiplying something by 1 doesn't change it. So we can get rid of that:

8 x 7 / 100 / 10

8 x 7 is 56, so we can simplify it to

56 / 100 / 10

56 / 100 is 0.56, and 0.56 / 10 is 0.056. So the final answer is 0.056.

The first step in solving the inequality is to distribute –4 to get -8x + 4 > 5 - 3x

Solution:

Given inequality is:

[tex]-4(2x - 1) > 5 - 3x[/tex]

The first step in solving the inequality is to distribute -4 to terms inside the bracket in left side of equation

This is done according to BODMAS rule

According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right

Thus in given inequality, brackets has to solved first

This is done by using distributive property

a(b + c) = ab + bc

Therefore,

[tex]-4(2x - 1) = (-4 \times 2x) +(-4 \times -1) = -8x + 4[/tex]

Thus, the inequality becomes,

[tex]-4(2x - 1) > 5 - 3x\\\\-8x + 4>5-3x\\\\-5x>1\\\\x<\frac{1}{5}[/tex]

Thus solution to given inequality is found

Answer:

The coordinates of the Pizza Hut is (6,-11)

Step-by-step explanation:

Gym is equidistant and collinear from Target and Pizza Hut.

T (-17, 17) :  [tex](x_1,y_1)[/tex]

G (-5.5, 3) : (x,y)

P : [tex](x_2,y_2)[/tex]

Mid point formula ; (x,y) is on mid point on line formed by joining points [tex](x_1,y_1)[/tex]and [tex](x_2,y_2)[/tex]

m = 1, n = 1

[tex]x=\frac{x_1+x_2}{2}[/tex]

[tex]-5.5=\frac{-17+x_2}{2}[/tex]

[tex]-11=-17+x_2[/tex]

[tex]x_2=17-11 = 6[/tex]

[tex]y=\frac{y_1+y_2}{2}[/tex]

[tex]3=\frac{17+y_2}{2}[/tex]

[tex]6=17+y_2[/tex]

[tex]y_2=-17+6 = -11[/tex]

The coordinates of the Pizza Hut is (6,-11)

To find the coordinates of Pizza Hut, use the midpoint formula with the given coordinates of You Fit Gym and Target.

To find the coordinates of Pizza Hut, we can use the fact that You Fit Gym is equidistant and collinear from Target and Pizza Hut. Since Target is located at (-17, 17) and You Fit Gym is at (-5.5, 3), we can use the midpoint formula to find the coordinates of the Pizza Hut. The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) are [(x1 + x2)/2, (y1 + y2)/2].

Using this formula, we can find the coordinates of the Pizza Hut:

x-coordinate: (-17 + (-5.5))/2 = -11.25

y-coordinate: (17 + 3)/2 = 10

Therefore, the coordinates of the Pizza Hut are (-11.25, 10).

Answer:

17.3

Step-by-step explanation:

241.5 divided by 14 is 17.25 rounded up its 17.3