Rewrite 9(10+11+12) using the distributive property of multiplication over addition

[tex]\text{Hey there!}[/tex]

[tex]\text{Is 6(6 + x) equivalent to 6x + 3?}[/tex]

[tex]\text{Kind of yes, and kind of no}[/tex]

[tex]\text{But in order for you to solve for this equation you have to use the distribute}\\\text{ property}[/tex]

[tex]\text{The distributive property formula is}\rightarrow\text{a(b + c) = a(b) + a(c) = ab + ac}[/tex]

[tex]\text{Let's solve for the equation, shall we?}[/tex]

[tex]\text{6(6 + x)}\\\text{6(6) + 6(x)}\\\text{6(6) = 36}\\\text{36 + 6(x)}\\\text{6(x) = 6x}\\\boxed{\text{\underline{36+6x}}}[/tex]

[tex]\text{36 + 6x}\neq \text{6x+ 36}[/tex]

[tex]\text{So, thus your answer has to be NO}[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

B: 3.844x10^5

E: 3.844x10^6

Step-by-step explanation:

Answer:

y=0

Step-by-step explanation:

Parallel lines never intersect therefore you need to find what y=-5 would look like on a graph (look at the image for reference, it is the blue line). Because it is a straight line then you just need to find what would make a straight line across the origin, therefore you would have to do y=0 (the red line on the image.)

The reason for putting y=0 or y=-5 is because the y value will ALWAYS stay the same and the x value will continue going on and on, without intersecting.

Answer:

w = I /2 - 4

Step-by-step explanation:

half the length : I /2

4 less than half the length : I /2 - 4

To match the requirements : w= I /2 - 4

Answer:

5+4w=7

Step-by-step explanation:

Answer:

[tex]k=-5[/tex]

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]6x^{2} +7x+k=0[/tex] 

so

[tex]a=6\\b=7\\c=k[/tex]

substitute in the formula

[tex]x=\frac{-7\pm\sqrt{7^{2}-4(6)(k)}} {2(6)}\\\\x=\frac{-7\pm\sqrt{49-24k}} {12}[/tex]

so

[tex]x_1=\frac{-7+\sqrt{49-24k}} {12}\\\\x_2=\frac{-7-\sqrt{49-24k}} {12}[/tex]

Remember that

[tex]2x_1+3x_2=-4[/tex]

substitute

[tex]2(\frac{-7+\sqrt{49-24k}} {12})+3(\frac{-7-\sqrt{49-24k}} {12})=-4\\\\(\frac{-14+2\sqrt{49-24k}} {12})+(\frac{-21-3\sqrt{49-24k}} {12})=-4[/tex]

Multiply by 12 both sides

[tex](-14+2\sqrt{49-24k})+(-21-3\sqrt{49-24k})=-48\\\\-35-\sqrt{49-24k}=-48\\\\\sqrt{49-24k}=48-35\\\\\sqrt{49-24k}=13[/tex]

squared both sides

[tex]49-24k=169\\24k=49-169\\24k=-120\\k=-5[/tex]

therefore

The equation is

[tex]6x^{2} +7x-5=0[/tex]

The roots are

[tex]x=\frac{-7\pm\sqrt{49-24(-5)}} {12}\\\\x=\frac{-7\pm\sqrt{169}} {12}\\\\x=\frac{-7\pm13} {12}\\\\x_1=\frac{-7+13} {12}=\frac{1} {2}\\\\x_2=\frac{-7-13} {12}=-\frac{5} {3}[/tex]

Speed of boat in still water is 12 km/hr and speed of current is 9 km/hr

Solution:

From given,

Downstream distance = 213 km

Time taken for downstream = 11 hours

Thus, speed is given as:

[tex]\text{Downstream speed} = \frac{\text{Downstream distance}}{\text{time taken}}[/tex]

[tex]\text{Downstream speed} = \frac{231}{11} = 21[/tex]

Thus downstream speed is 21 km/hr

Also,

Upstream distance = 213 km

Time taken for upstream = 77 hours

Thus, speed is given as:

[tex]\text{Upstream speed} = \frac{\text{Upstream distance}}{\text{time taken}}\\\\\text{Upstream speed} = \frac{231}{77} = 3[/tex]

Thus upstream speed is 3 km/hr

If the speed downstream is "a" km/hr and the speed upstream is "b" km/hr , then:

[tex]\text{Speed in still water } = \frac{1}{2}(a+b)\\\\\text{Speed of current } = \frac{1}{2}(a-b)[/tex]

Here, a = 21 and b = 3

Therefore,

[tex]\text{Speed in still water } = \frac{1}{2}(21+3) = \frac{24}{2} = 12\\\\\text{Speed of current } = \frac{1}{2}(21-3) = \frac{18}{2} = 9[/tex]

Thus speed of boat in still water is 12 km/hr and speed of current is 9 km/hr

The speed of boat in still water is 12 km/hr as:

Let speed of Boat be 'b' and speed of Current be 'c'.

Distance given is 210 miles.

Therefore speed for downstream = 210 ÷ 10=21 mph

speed for upstream =3mph

Now we can form the two equations as :

i) b+c = 21 ......(i) For downstream

ii) b-c = 3.........(ii) For Upstream

Solving by substitution method :

From equation (ii) c = b - 3 Substitute this value of c in equation

(i) we get b + b - 3 = 21

Therefore b = 12. Now substitute the value of b in any of the equations above (i) or (ii) and get c= 9

b= 12 and c = 9.

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Answer:

Look at the picture.

x < 0 and y < 0

Answer:

Step-by-step explanation:

x^2 + 2x + 1 = 17

x^2 + 2x = 17 - 1

x^2 + 2x = 16

x^2 + 2x + 1 = 16 + 1

(x + 1)(x + 1) = 17

(x + 1)^2 = 17

x + 1 = sqrt 17

x = -1 (+ - ) sqrt 17

x = -1 + sqrt 17 or x = -1 - sqrt 17 <===

Answer:

x = -1 + square root 17

Step-by-step explanation:

I took the test

Answer:

2. The company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r + t = 20 and 5 r + 5 t = 150.

Step-by-step explanation:

The total lunch budget of the company  =  $150

Total number of employees  = 20

The cost of 1 roast beef sandwich = $5

The cost of 1 tuna sandwich = $5

r represents the number of roast beef sandwiches provided.

t represents the number of tuna sandwiches provided.

Now, consider the given statements:

Here, total number of sandwiches purchased  = Total number of employees

⇒ r +  t = 20   .... (1)

Also, as each type of sandwich costs $5.

So, the cost of r roast beef sandwiches = r x ( Cost of  1  beef sandwich)

= r x ( $5) = 5 r

And, the cost of t tuna sandwiches = t x ( Cost of  1  tuna sandwich)

= t x ( $5) = 5 t

Total cost of (r +t) sandwiches = Total Lunch Budget

⇒ 5 r +  5 t = 150   .... (2)

Hence, from (1) and (2) the above situation can be represented as:

r +  t = 20  

5 r +  5 t = 150

Hence, the company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r + t = 20 and 5 r + 5 t = 150.

We can ise Pythagorean triplet which is ( 12 , 16 , 20 )

Therefore the answer is 16.

Step-by-step explanation:

Or we can use Pythagoras theorem , stated as ;

( hyp )^2 = ( adj )^2 + ( opp )^2

hyp ( hypotenuse ) = 20

We can assume the adj ( adjacent ) = 12

By substituting the values ,

20^2 = 12^2 + ( adj )^2

400 = 144 + ( adj )^2

400 - 144 = ( adj )^2

256 = ( adj )^2

Take the square root of both sides

✓256 = adj

16 = adj

Therefore the length of the other leg which is the adjacent( adj ) side is 16.

The length of the other leg is 16

To find the length of the other leg of a right triangle, given one leg is 12 and the hypotenuse is 20, we use the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the lengths of the legs (a and b) is equal to the square of the length of the hypotenuse (c).

This relationship is given by:

a² + b² = c²

1.  Here, one leg (a) is 12 and the hypotenuse (c) is 20. So we can write:

12² + b² = 20²

2.  Calculating the squares gives:

144 + b² = 400

3. Subtract 144 from both sides to find b²:

b² = 256

4. Finally, take the square root of both sides to find b:

b = √256 = 16

Thus, the length of the other leg is 16.

Answer:

x = 18.5

Step-by-step explanation:

Multiply 5 and 3.7.

Which equals 18.5.

Check: 18.5 / 3.7 = 5.√

Answer:

The length of the intercepted arc for circle S is  (1/2)π ft

Answer:

The sum of the roots of a polynomial is 5/3, the product of the same polynomial is -11. Write the polynomial function in standard form.n:

Answer:

f(x) = x³ - 7x - 6

Step-by-step explanation:

Given that the zeros are x = - 1, x = - 2 and x = 3 then the corresponding factors are

(x + 1), (x +2) and (x - 3)

The polynomial is then the product of the factors, that is

f(x) = (x + 1)(x + 2)(x - 3) ← expand the first pair using FOIL

     = (x² + 3x + 2)(x - 3) ← distribute

     = x³ - 3x² + 3x² - 9x + 2x - 6 ← collect like terms

     = x³ - 7x - 6

Answer:

Step-by-step explanation:

Let, it will take x years to be of same height for these trees.

We know that 1 ft = 12 inches.

8 ft = [tex]12\times8 = 96 inch[/tex]. 2 ft = 24 inch.

After x years, the height of type A will be (96 + 6x) inch and the height of type B will be (24 + 15x) inch.

We need find the value of x, for which 96 + 6x = 24 + 15x or, 9x = 72 or, x = 8.

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]x+2y > 4[/tex]

Isolate the variable y

subtract x both sides

[tex]2y > -x+4[/tex]

Divide by 2 both sides

[tex]y > -\frac{1}{2}x+2[/tex]

The solution of the inequality is the shaded area above the dashed line

[tex]y=-\frac{1}{2}x+2[/tex]

The slope of the dashed line is negative

The y-intercept of the dashed line is (0,2)

The x-intercept of the dashed line is (4,0)

therefore

The graph in the attached figure

Answer:

-95/36

Step-by-step explanation: I think that's right.

Answer:

product

Step-by-step explanation:

Answer:

The Correct Answer is product of powers

Step-by-step explanation:

Answer:

[tex]10\frac{1}{2}\ \frac{acres}{hour}[/tex]

Step-by-step explanation:

The correct question is:

Darcy harvests 8 3/4 ​ acres of corn every 5/6​  of an hour. Darcy harvests corn at a constant rate. How many acres does she harvest per hour?

we know that

To find out the corn rate harvested per hour or the unit rate, divide the number of acres of corn harvested by the total time it takes

so

[tex]8\frac{3}{4} :\frac{5}{6}[/tex]

Convert mixed number to an improper fraction

[tex]8\frac{3}{4}=8+\frac{3}{4}=\frac{8*4+3}{4}=\frac{35}{4}[/tex]

substitute

[tex]\frac{35}{4} :\frac{5}{6}=\frac{210}{20}=\frac{21}{2}\ \frac{acres}{hour}[/tex]

Convert to mixed number

[tex]\frac{21}{2}\ \frac{acres}{hour}=\frac{20}{2}+\frac{1}{2}=10\frac{1}{2}\ \frac{acres}{hour}[/tex]

Answer:

[tex]10\frac{1}{2}[/tex] or [tex]\frac{21}{2}[/tex]

Answer:

a

Step-by-step explanation:

Hey!

~Set up the equation: -5(x-1)=40

~ Divide 5 on both sides: 40/-5

~ Simplify: x-1=-8

~ We want to get x by itself, so subtract +1 to both sides.

~ Simplify: x = -7

~ Therefore, x = -7.

Answer:

x = - 7

Step-by-step explanation:

-5(x - 1) = 40

-5x + 5 = 40

- 5x = 40 - 5

- 5x = 35  | x(-)

5x = - 35

x = - 35 : 5

x = - 7

The diagonal of square is 9.90 units long.

Step-by-step explanation:

Given,

Length of each side of square= s = 7 units

Diagonal of square = s√2

Putting s = 7

Diagonal of square = [tex]7*\sqrt{2}[/tex]

Diagonal of square = 7 * 1.414

Diagonal of square = 9.898

Rounding off to nearest hundredth

Diagonal of square = 9.90 units

The diagonal of square is 9.90 units long.

Keywords: square, diagonal

Learn more about diagonals at:

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Answer:

d = 9.9 units

Step-by-step explanation:

The step by step explanation is in the picture below

Answer:

Function 1.

Step-by-step explanation:

The rate of change of Function 2 = (18.75 - 14.25)/ (5 - (-1))

=  4.5 / 6

= 3/4 or 0.75.

For Function 1 it is  5/6 or 0.83

So Function 1 has greatest rate of change.

Answer:

Hypotenuse = 20

Step-by-step explanation:

As we know that in 30 60 90 triangle

Short leg = X

Hypotenuse = 2X

Perpendicular = X[tex]\sqrt{3}[/tex]

Short leg = X = 10

Hypotenuse = 2X = 10*2 = 20

Final answer:

In a 30-60-90 triangle, the hypotenuse is twice the length of the shortest leg. Therefore, with a shortest leg of 10, the hypotenuse is 20.

Explanation:

The student has asked about the length of the hypotenuse in a 30-60-90 triangle where the shortest leg is given as 10. In a 30-60-90 triangle, the ratios of the sides are 1:√3:2. Since the shortest leg (the one opposite the 30° angle) is known to be 10, we can find the hypotenuse by multiplying the length of the shortest leg by 2.

Thus, the hypotenuse is 20.

To summarize the process, if the shortest leg a is known, then the hypotenuse c is calculated using the formula: c = 2a. Given that a = 10, the calculation would be c = 2 × 10 = 20.

Answer:

(y + 2)(y + 3)

Step-by-step explanation:

Volume is length x width x height.

A cube has the same length, width and height.

The volume of the cube is 2 x 2 x 2 = 8cm

Answer: 8 cm

Happy to help!

Answer: the answer is 8

Step-by-step explanation: The answer is 8 because the equation LxHxW and since It is a cube it is 2x2x2

Answer:

E

Step-by-step explanation:

7+8+4=19

4/6 + 3/6 + 1/6 = 1 2/6

19 + 1 1/3

20 1/3

Answer:

Let's write this out in an equation.

y = 4 + 7x

The mathematical equation 'Y is 4 more than the product of 7 and x' can be written as 'Y = 7x + 4' where Y is the dependent variable and x is the independent variable. This is a standard form linear equation.

The subject of this question is Mathematics, and it appears to be targeted at a Middle School level. The statement 'Y is 4 more than the product of 7 and x' is a mathematical equation that can be written as Y = 7x + 4. Here, '7x' refers to the product of 7 and x, and the '+ 4' indicates that Y is 4 more than this product. It is a linear equation in variable x.

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Answer:

All that you would have to do is add 10 more blocks to show that its 10 more than 43

Answer:

more than 16 squares