Simplify square root of five times the quantity six minus four square root of three.

Answer:

[tex]\large\boxed{(x+2)(3x-1)-(x+4)(x-7)=2x^2+8x+26}[/tex]

Step-by-step explanation:

[tex](x+2)(3x-1)-(x+4)(x-7)\\\\\text{Use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(x+2)(3x-1)=(x)(3x)+(x)(-1)+(2)(3x)+(2)(-1)\\\\=3x^2-x+6x-2=3x^2+(-x+6x)-2=3x^2+5x-2\\\\(x+4)(x-7)=(x)(x)+(x)(-7)+(4)(x)+(4)(-7)\\\\=x^2-7x+4x-28=x^2+(-7x+4x)-28=x^2-3x-28\\\\(x+2)(3x-1)-(x+4)(x-7)=(3x^2+5x-2)-(x^2-3x-28)\\\\=3x^2+5x-2-x^2-(-3x)-(-28)=3x^2+5x-2-x^2+3x+28\\\\=(3x^2-x^2)+(5x+3x)+(-2+28)\\\\=2x^2+8x+26[/tex]

Answer:

2x^2 +8x +26

Step-by-step explanation:

I think you're supposed to simplify this:

So what you do is: you must have learmt about FOIL

which means First, Outside, Inside, Last.

So, this is how to do it using FOIL:

(3x^2 -x+6x-2) - ( x^2-7x+4x-28)

Now simplify, combine like terms wherever you can,

(3x^2 +5x -2) - ( x^2 -3x -28)

Note: multiply the subtraction sign otherwise you will end up making a mistake,

3x^2 +5x -2 - x^2 +3x+28

3x^2 -x^2 +5x+3x-2+28

2x^2 +8x +26 Answer

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Note: Some of these steps can be eliminated, i showed everything for the purpose of making things clear for you!

Answer:

MOP = DAB

Step-by-step explanation:

the sides have to be matched up as well. the side with only one dash (MO) has to correspond with the side with one dash from the other triangle (DA). Thus, the letters in the sequence (MOP) have to match up in the same order (DAB)

The correct congruency statement with regards to the congruence of the triangles is the fourth statement

The details of the steps by which the congruence statement can be found can be presented as follows;

The marks on the segment indicates;

PO is congruent to BA

MO is congruent to DA

PM is congruent to BD

Therefore, the triangle MOP is congruent to the triangle DAB

The order in which the markings on the triangles are located can also be used to find the correct congruence statement

The name of the triangle MOP indicates that the vertice of the triangle between the segment with three marklings, III, and the segment with one marking, I, is considered first, which is the vertice M and D on each triangle

The next mentioned vertice is the vertice between the segment with one marking and the segment with two markings, which is the vertice O and A on each triangle

The third considered vertice is the third vertice on both triangles, which corresponds to the vertice P and B on each triangle

The congruency statement is therefore ΔMOP ≅ ΔDAB

Answer:

fifteen

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

1/4(60)=60/4=15

Answer:

HL

Step-by-step explanation:

HL- If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

The theorem which verifies that ΔGHI is congruent to ΔUVW is LL.

Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.

Given are two triangles.

ΔGHI and ΔUVW.

Given that ∠G = ∠U = 90°.

So the triangles are right angled triangles.

The hypotenuse of the triangles are HI and VW.

Also given that, the legs of the triangles are equal.

Leg - Leg (LL) congruence theorem states that if the legs of a right triangles are equal to the legs of another right triangles, then the triangles are congruent.

Hence the theorem used is LL theorem.

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The expression to determine the total amount Joe spent on gasoline and oil is 2.85 * g + 3.15 * c. If Joe bought 8.4 gallons of gasoline and 6 cans of oil, he will have spent 42.84 dollars in total.

Part A: To determine the total amount Joe spent on gasoline and oil, we need to calculate the cost of gasoline and the cost of oil separately, and then add them together.

The expression to calculate the cost of gasoline is: 2.85 * g, where 'g' represents the number of gallons of gasoline Joe bought.

The expression to calculate the cost of oil is: 3.15 * c, where 'c' represents the number of cans of oil Joe bought.

Therefore, the expression to determine the total amount Joe spent is: 2.85 * g + 3.15 * c.

Part B: If Joe bought 8.4 gallons of gasoline and 6 cans of oil, we can substitute these values into the expression we derived in Part A.

The total amount Joe spent can be calculated as follows:

Total amount spent = 2.85 * 8.4 + 3.15 * 6

Simplifying the expression:

Total amount spent = 23.94 + 18.90

Total amount spent = 42.84 dollars

Answer:

2y-1

Step-by-step explanation:

1/2(4y-2)=2y-1

Answer: 1 30000000000001/40000000000000

Step-by-step explanation:

fun

A car is worth $300

Step-by-step explanation:

A board game allows players to trade and sell game pieces of equal value

We need to find how much the car is worth

Assume that the car is worth $x and the house is worth $y

∵ Player 1 traded three cars plus $100 for a house

∴ 3 x + 100 = y

- Subtract 100 from both sides

∴ 3 x = y - 100

- Subtract y from both sides

∴ 3 x - y = - 100 ⇒ (1)

∵ Player 2 sold two houses and a car for $2300

∴ x + 2 y = 2300 ⇒ (2)

Now we have system of equation to solve it

Multiply equation (1) by 2 to eliminate y

∵ 6 x - 2 y = - 200 ⇒ (3)

- Add equations (2) and (3)

∴ 7 x = 2100

- Divide both sides by 7

∴ x = 300

A car is worth $300

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Answer:

32000 sh.

Step-by-step explanation:

100%+6%=106%

106%=33920

100%=?

100×33920=3392000

3392000÷106

32000 sh.

Answer:

the answer is A)

Step-by-step explanation:

-11 + 15 = 4

4 - 8 = -4

-4 + 4 = 0

Answer:

Step-by-step explanation:

Hello

The temperature rises 15 degrees Fahrenheit (ﾟF) and then drops by 8ﾟF. If the temperature started at -11ﾟF, what temperature change would be required to bring the temperature to 0ﾟF?

A) an Incase of 4ﾟF

B) a decreased of 4ﾟF

C) a decreased of 19ﾟF

D) an increase of 19ﾟF

-11 + 15 - 8 = -19 + 15 = -4° F

A) An increase of 4° F

Answer:

She read 3/4 of a book each month.

Step-by-step explanation:

In order to find this, you divide the amount of books read by the amount of months. When doing this, you get 3/4. If you wanted to check, you can multiply this number of 4 to find the number of books she read. When you do this, you get three, which is correct.

Answer:

213

Step-by-step explanation:

Let

The relationship between x and y can be represented through a linear equation.

y = a . x + b

where,

a is the slope

b is the y-intercept

The slope refers to the price per print, that is, a = $0.15/p.

Then,

y = $0.15/p . x + b

Even if x = 0, there is a fixed cost of $3.00 (y = $3.00). We can replace these values in the expression above.

$3.00 = $0.15/p . 0 + b

b = $3.00

The final equation is:

y = $0.15/p . x + $3.00

If MaryAnn has $35,

$35 = $0.15/p . x + $3.00

$32 = $0.15/p . x

x = 213 p

She can order 213 prints.

Answer:

(8,-3)

Step-by-step explanation:

(x1+x2/2), (y1+y2/2)

7+9/2=16/2=8           x=8

-5-1/2=-6/2=-3          y=-3

Answer:

Step-by-step explanation:

The formula of a midpoint of AB

[tex]A(x_A,\ y_A),\ B(x_B,\ y_B)\\\\M_{AB}\left(\dfrac{x_A+x_B}{2};\ \dfrac{y_A+y_B}{2}\right)[/tex]

We have the points X(7, -5) and Y(9, -1).

Substitute:

[tex]M_{XY}\left(\dfrac{7+9}{2};\ \dfrac{-5+(-1)}{2}\right)\\\\M_{XY}\left(\dfrac{16}{2};\ \dfrac{-6}{2}\right)\\\\M_{XY}(8,\ -3)[/tex]

Option C: y = 80x is the right answer

Step-by-step explanation:

Varying directly means that the increase/decrease in one quantity will cause increase/decrease in other quantity.

If y varies directly with x it is given by::

y ∝ x

When the proportionality symbol is removed, a proportionality constant is introduced

y = kx

If x = 1/2 and y = 40

then

[tex]40 = k * \frac{1}{2}\\k = 40*2\\k = 80[/tex]

Putting the value of k, we get

y = 80x

Hence,

Option C: y = 80x is the right answer

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Answer:

3069

Step-by-step explanation:

q=6/3=2

s10=3(2^10-1)÷(2-1)=3×(1024-1)=

3069

Answer:

Biker will catch the cyclist after 2 hr and 40 min.

Step-by-step explanation:

Given:

Speed of Bicyclist = 20 km/h

Travelling time = 4 hrs

∴ Distance = Speed × Time = [tex]20\times4=80 \ km[/tex]

Also he rest for 1 hr.

So we can say that, after 5 hrs Bicyclist is 80 km ahead when the biker Started.

Now Biker rate is given 50 km/h

And Bicyclist rate is 20 km/h

So, for each hour, biker advances 50 - 20 = 30 kilometers

now bicyclist distance is 80 km

and biker advances 30 per hour.

Therefore to catch up bicyclist at 80 km i.e time taken to reach 80 km with 30 km rate per hour.

Time = [tex]\frac{80}{30}=2 \frac{2}{3} h[/tex]

Hence, Biker will catch the cyclist after 2 hr and 40 min.

Answer:

2 hours

Step-by-step explanation:

the biker leaves when the first biker stops not after the break is over

The value of the expression 5w - (w/x) when w=6 and x=2 is 27.

The original expression given with the variables w and x is: 5w - (w/x). The question asks us to evaluate this expression when w=6 and x=2. So, we simply substitute w with 6 and x with 2 into the expression:

5*6 - (6/2) = 30 - 3 = 27

Therefore, the value of the expression 5w - (w/x) when w=6 and x=2 is 27.

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Answer:

The sell price of the truck rental after applying the coupon of 20 % is       $ 120  .

Step-by-step explanation:

Given as :

The regular rented price for the truck = $ 150

The discount as off coupon = 20 %

Let The sell price for truck after discount = x

So , Discount % = [tex]\dfrac{\textrm market price - \textrm Selling price}{\textrm market price}[/tex]

Or, 20 % = [tex]\dfrac{\textrm 150 - \textrm x}{\textrm 150}[/tex]

Or, [tex]\dfrac{x}{150}[/tex] = 1 -  [tex]\dfrac{20}{100}[/tex]

Or,  [tex]\dfrac{x}{150}[/tex] = [tex]\dfrac{100 - 20}{100}[/tex]

or,  [tex]\dfrac{x}{150}[/tex] = [tex]\dfrac{80}{100}[/tex]

∴ x = [tex]\frac{80\times 150}{100}[/tex]

I.e x = 8 × 15

Or, x = 120

Hence the sell price of the truck rental after applying the coupon of 20 % is $ 120  . Answer

Answer:

the % is 80% and the price $120

Step-by-step explanation:

The total cost y of a corporate team-building event can be expressed by the equation y = 1 + 1x, where x represents the number of attendees. This equation includes both the fixed and variable costs.

To determine the cost y of a corporate team-building event based on the number of attendees x, we need to include both the initial fixed cost and the variable cost per attendee.

The fixed cost of the event is $1, and the variable cost per attendee is also $1. The total cost can be expressed using the following equation:

y = 1 + 1x

Here:

For example, if there are 5 attendees, the total cost would be calculated as:

y = 1 + 1(5) = 1 + 5 = 6 dollars

Helen uses 0.3 kg of nuts for 2.5 kg of granola.

Multiplication is an operation that represents the basic idea of repeated addition of the same number.

Given that, Helen uses 0.12 kilogram of nuts in each batch of granola

that she makes, and she makes 2.5 batches,

For 1 batch she uses .12 kg of nuts, so for 2.5 kg she will use = 2.5*0.12 = 0.3 kg

Hence, Helen uses 0.3 kg of nuts for 2.5 kg of granola.

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Answer

y=-\frac{11}{13}x+\frac{8}{13}

Step-by-step explanation:

Answer:

y = -(11/13)x + (8/13)  

Step-by-step explanation:

recall slope intercept form of a linear equation takes the general form:

y = mx + b

In this case, simply rearrange the given equation such that it looks like the general equation above.

11x+13y=8  (subtract 11x from both sides)

13y = -11x + 8  (divide both sides by 13)

y = -(11/13)x + (8/13)    (answer)

The real is B.) f(x) = -x + 11

A.) f(x) = -y + 11 is the wrong answer.

I have pictures to prove that they are the same in the graph as x + y = 11.

Hope this will help a lot more than the other answer.

Answer:

B.) f(x) = -x + 11

Step-by-step explanation:

Answer:

Step-by-step explanation:

450000000000

Answer:

125,000

47,829,690,000,000‬

Step-by-step explanation:

Step-by-step explanation:

When you divide fractions, you multiply by the reciprocal.

The new equation would be:

[tex] \frac{5}{\frac{3}{8} \times \frac{8}{7} } [/tex]

[tex] \frac{5}{1} \times \frac{7}{3} = \frac{35}{3} [/tex]

Answer:

200/21

Step-by-step explanation:

5/(3/5) divided by 7/8

First divide 5 by 3/5. To do this you must write 5 as 5/1, and multiply 5/1 by the reciprocal of 3/5 (5/3).

5/1 (5/3)

numerator: 5*5=25

denominator: 1*3=3

25/3

Then divide 25/3 by 7/8 by multiplying 25/3 by the reciprocal of 7/8 (8/7).

25/3 (8/7)

numerator: 25*8= 200

denominator: 3*7= 21

200/21 or 9 11/21

Answer:

Total number of students= 7+ 9+4+5= 25

Tennis: total= 5:25= 1:5 (simplify by dividing both sides by 5

Answer:

1:5

Step-by-step explanation:

First We Add The Number Of Students.

7+9+4+5=25

the students were divided into 5 kind of sports so it will be 5/25

5/25 means 1/5 and

1/5 means 1:5

Answer:

x = 4 ± [tex]\sqrt{19}[/tex]

Step-by-step explanation:

Given

x² - 8x = 3

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 4)x + 16 = 3 + 16

(x - 4)² = 19 ( take the square root of both sides )

x - 4 = ± [tex]\sqrt{19}[/tex] ( add 4 to both sides )

x = 4 ± [tex]\sqrt{19}[/tex], that is

x = 4 - [tex]\sqrt{19}[/tex], 4 + [tex]\sqrt{19}[/tex]

Final answer:

The solution set for the quadratic equation x² - 8x = 3 is found by completing the square, resulting in (4 - √19, 4 + √19).

Explanation:

To solve the quadratic equation by completing the square, we start with x² – 8x = 3. First, we move the constant term to the other side of the equation:

x² – 8x + ____ = 3 + ____

Now we need to find a number to fill in the blanks that makes the left side a perfect square trinomial. To do this, take half of the coefficient of x, which is -8/2 = -4, and then square it, which gives us 16. Add 16 to both sides:

x² – 8x + 16 = 3 + 16

x² – 8x + 16 = 19

The left side is now a perfect square, (x – 4)² = 19. Taking the square root of both sides gives us:

x – 4 = ±√19

Add 4 to both sides to solve for x:

x = 4 ±√19

Therefore, the solution set for the equation x² – 8x = 3 is (4 – √19, 4 + √19).

Answer:

k = 5 and (6,2).

Step-by-step explanation:

Since (1,-1) is a solution of the equation 3x - ky = 8, so the point (1,-1) will satisfy the equation above.

Hence, putting x = 1 and y = -1 in the equation will give left-hand side = right-hand side.

So, 3(1) - k(-1) = 8

⇒ 3 + k = 8

⇒ k = 5 (Answer)

Therefore, the equation of the straight line is 3x - 5y = 8 ....... (1)

Now, putting x = 6 , then from equation (1) we get y = 2

Therefore, (6,2) is also a point on the graph of equation (1). (Answer)

Answer:

The value of product is 7.

Step-by-step explanation:

Since we have given that

4 square 7x4 square root 7x4 square root 7x4 square root 7

We need to find the product of the following terms:

We will apply the "law of exponents":

i.e.

(a^m)^n=a^{mn}

4 square 7x4 square root 7x4 square root 7x4 square root 7

=7 ^(1/4)4=7

Hence, the value of product is 7.

The value of product is 7.

The term "product" refers to the result of one or more multiplications. For example, the mathematical statement would be read " times equals ," where is called the multiplier, the multiplicand and is their product.

Given is an expression, 4 square 7 • 4 square root 7• 4 square root 7 •4 square root 7

Converting into mathematical notation,

= [tex]\sqrt[4]{7} . \sqrt[4]{7} . \sqrt[4]{7} . \sqrt[4]{7} .[/tex]

We need to find the product of the following terms:

We will apply the "law of exponents":

(xᵃ)ᵇ = xᵃᵇ

[tex](\sqrt[4]{7})^4\\\\= (7^\frac{1}{4})^4\\\\= 7[/tex]

Hence, the value of product is 7.

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Answer:

The answer would be Option 3: 43.25

Step-by-step explanation:

Triangles angles all added together add up to 180 degrees.

So first we subtract 93.5 from 180. This gives us 86.5. The we divide this by 2 to get 43.25.

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