Rewrite the expression as a sum of terms, where each term is in the form k\cdot a^nk⋅a
n
k, dot, a, start superscript, n, end superscript.
\sqrt a\left(2a^2-\dfrac4a\right)=
a
​ (2a
2
−
a
4
​ )=

1st one is 0

2nd one is -3

3rd one is -2

4th one is 5

Combine like terms, isolate the variable, and make the slope of the variable 1 to find all the answers.

Answer:

Part 1) The length of DC is [tex]13\ units[/tex]

Part 2) The measures of the angles in the isosceles triangle are

The base angles are 67.4° and the vertex angle is 45.2°

Step-by-step explanation:

step 1

In the right triangle BDC Find the length of DC

Applying the Pythagoras Theorem

[tex]DC^{2}=BC^{2} +BD^{2}[/tex]

we have

[tex]BC=AB=10/2=5\ units[/tex]

[tex]BD=12\ units[/tex]

substitute

[tex]DC^{2}=5^{2} +12^{2}[/tex]

[tex]DC^{2}=169[/tex]

[tex]DC=13\ units[/tex]

step 2

Find the measures of internal angles in the isosceles triangle ABC

we know that

∠DAC=∠DCA ------> base angles

∠ADC ------> vertex angle

Find the measure of angle DCA

In the right triangle BDC

sin(∠DCA)=BD/DC

substitute the values

sin(∠DCA)=12/13

∠DCA=arcsin(12/13)=67.4°

so

∠DAC=∠DCA=67.4°

Find the measure of angle ∠ADC

Remember that the sum of the internal angles of a triangle must be equal to 180 degrees

so

∠DAC+∠DCA+∠ADC=180°

substitute

67.4°+67.4°+∠ADC=180°

∠ADC=180°-134.8°=45.2°

Answer:

Two more people.

Step-by-step explanation:

If 4 people can mow a lawn in 6 hours, then 4 people can mow 1/6 of a lawn in 1 hour.

If 4 people can mow 1/6 of a lawn in 1 hour, then 1 person can mow 1/24 of a lawn in 1 hour.

If 1 person can mow 1/24 of a lawn in 1 hour, then 6 people can mow 1/4 of a lawn in 1 hour.

If 6 people can mow 1/4 of a lawn in 1 hour, then 6 people can mow a lawn in 4 hours.

6 people minus 4 people is 2 people.

There are two more people will be needed to mow the lawn in 4 hours, It is assuming that each person mows at the same rate

The rate of work is defined as the number of units of work completed per unit time.

Let the number of the person are x,

Condition 1;

4 people in 6 hours complete the work, work done in one hour;

1 hour =(1/6) of the total work

Condition 2;

If four individuals can do one-sixth of the total work, one person can do one-quarter of the work in an hour.

1 person do = (1/4) of the total work;

Condition 3;

If one person can do 1/24 of total work

Six persons can do 1/4 of total work in the same amount of time.

If six individuals can mow a quarter of a lawn in an hour, The number of  people will be needed to mow the lawn in 4 hours;

n=6-4

n=2

Hence, there are two more people will be needed to mow the lawn in 4 hours,

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So you work for 2 hours and each hour you get 7.50

So you do 2*7.50 = 15$

Then you do the windows

3 hours and every hour you earn 6.25

3*6.25=18.75$

Now you add them

15+18.75= 33.75$ but if you want an average then around 34$

Answer:

That number is 0.45

Step-by-step explanation:

3/5x = 2x - 63/100

0.63 = 2x - 3/5x

0.63 = 10/5x - 3/5x

0.63 = 7/5x

7x = 0.63*5 = 3.15

x = 3.15/7

Answer:

0.63Google

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Given x < - 6

Since less than, then looking for an open circle at - 6 on the number line

If ≤ then closed circle at - 6

Also since less than - 6 we are looking for the arrow pointing to the left indicating values less than - 6 , arrow right indicates greater than - 6

The option is therefore A

feet will be the best way to measure the high jump

Answer:

median, mean , and mode

Step-by-step explanation:

Answer:

It's ÷ (divide)

Step-by-step explanation:

Because 48+27 is 75, and 750÷10 is also 75.

Hope I helped :)

ANSWER

(1,-3)

EXPLANATION

The given equations are:

y = 5x - 8

y = 4x - 7

We equate the two equations to get:

5x - 8=4x - 7

Group similar terms:

5x - 4x=-7+8

Simplify bottom sides

x=1

Put x=-15 into the first equation:

y=5(1)-8

y=-3

(1,-3)

The solution is (1,-3)

Answer:

option C

x = 6

y = 4

z = 1

Step-by-step explanation:

Given in the question a matrix in the row echelon form of the augmented matrix.

[tex]\left[\begin{array}{ccc}1&0&+4=-1\\0&1&-1=+3\\0&0&+1=+1\end{array}\right][/tex]

First Equation

x0 + y0 + z(1) = 1

0 + 0 + z = 1

Second Equation

x0 + y(1) + z(-1) = 3

0 + y - z = 3

y -1 = 3

Third Equation

x(1) + y0 + z(4) = -1

x + 0 + 4z = -1

x + 4 = -1

Answer:

Step 2, he didn't add the values he completed the square with to both sides.

Step-by-step explanation:

When you complete the square, you need to add the values to both sides, not just one.

So when Homer added 49 + 1 or 50 to the left side of the equation, he should've also added 50 to the right side of the equation.

Hence, the equation would now be :

(x-7)^2 + (y+1)^2 = 75

Answer:

Step-by-step explanation:

Pythagoream theorem applies.

The long wires are [tex]\sqrt{45^2+30^2}m[/tex] long, or about 54m long.

The short ones are [tex]\sqrt{20^2+30^2}m[/tex], or about 36m long. You will need 4 of each, so it's [tex]4* 54m + 4*36m = 540m[/tex] of wire

Answer:

[tex]x<-2[/tex]

Step-by-step explanation:

Isolate the variable to find the solution set.

[tex]5>x+7 \\ \\ x<-2[/tex]

Answer:

see explanation

Step-by-step explanation:

Solve the inequality

5 > x + 7 ( subtract 7 from both sides )

- 2 > x ⇒ x < - 2

solution set {x | x ∈ R, x < - 2 }

Answer:

4,1,2,3

Step-by-step explanation:

1.8+7=15

2.10/5=2

3.8+10=18

4.2(5)=10

Answer:

(x - 2)(x² + 2x + 4)

Step-by-step explanation:

A difference of cubes factors in general as

• a³ - b³ = (a - b)(a² + ab + b² )

note 8 = 2³ = 8 ⇒ b = 2 , with a = x

Hence

x³ - 8

= x³ - 2³

= (x - 2)(x² + 2x + 2²) = (x - 2)(x² + 2x + 4)

Answer: The rewritten expression would be [tex](x-2)(x^2+2x+4)[/tex]

Step-by-step explanation:

Since we have given that

[tex]x^3-8[/tex]

We need to use the difference of cubes:

As we know the formula of "Difference of cubes":

[tex]a^3-b^3=(a-b)(a^2+b^2+ab)[/tex]

So, it can be written as

[tex](x)^3-(2)^3=(x-2)(x^2+2x+4)[/tex]

Hence, the rewritten expression would be [tex](x-2)(x^2+2x+4)[/tex]

Answer:

the answer is d

Step-by-step explanation:

To solve 2y - x = 3/4 (-y + 1) for y, distribute 3/4, combine like terms, and isolate y. The solution is y = (4x - 3)/11, which is answer D.

The student has asked to solve for y in the equation: 2y - x = 3/4 (-y + 1). To solve for y, we can follow these steps:

First, distribute the 3/4 across the parentheses: 2y - x = 3/4 (-y) + 3/4 (1).

This simplifies to: 2y - x = -3/4y + 3/4.

Add 3/4y to both sides to get: 2y + 3/4y - x = 3/4.

Combine like terms on the left: (2 + 3/4)y - x = 3/4. This is equivalent to (11/4)y - x = 3/4.

Add x to both sides: (11/4)y = x + 3/4.

Finally, multiply both sides by 4/11 to solve for y: y = (4/11)x + 3/11.

Therefore, the correct answer is D) y = (4x - 3)/11.

The first one is three

The second one is twelve

The last one is 2

Answer:

it would be a rectangle

Step-by-step explanation:

it would be a rectangle because when you cut it in the cross section there will be four parell sides, so therefore it would have to make a rectangle because the side lengths would not be even.

Answer: it would be a rectangle

ANSWERS

A.

[tex] \frac{19}{20} [/tex]

EXPLANATION

It was given that triangle LMN is a right triangle and angle L and M are complementary.

This implies that:

[tex] \sin(L) = \cos(M) [/tex]

It was given in the question that:

[tex] \cos(M) = \frac{19}{20} [/tex]

This implies that:

[tex] \sin(L) = \frac{19}{20} [/tex]

Answer:

They distort differences between values.

Step-by-step explanation:

Non-zero axes distort differences between values, but they are not always misleading.

It depends on who is looking at them.

Consider the bar graphs below, showing the change in interest rates over time.

A naïve reader might conclude that interest rates had risen sharply (the zero-axis shows that they have remained steady).

However, a professional who specializes in interest rates might find the information in the left-hand graph quite useful.

A professional who specializes in interest rates might find the information in the left-hand graph quite useful.

They distort differences between values.

We have given that, a graph

They distort differences between values,

Non-zero axes distort differences between values, but they are not always misleading.

It depends on who is looking at them.

Consider the bar graphs below, showing the change in interest rates over time.

A naïve reader might conclude that interest rates had risen sharply (the zero-axis shows that they have remained steady).

However, a professional who specializes in interest rates might find the information in the left-hand graph quite useful.

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Answer: 5 units down, 3 units up.

Step-by-step explanation: at the translation, the line is at 5, -3, putting the translation at 5 units right, 3 units up.

Answer:

(x-3)^2

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

a/(1-r)

Use the infinite geometric series formula.

ANSWER

[tex]S_{\infty} = 16 [/tex]

EXPLANATION

Given the series:

8 + 4 + 2 + . . .

The first term of the series is

[tex]a_1 = 8[/tex]

The common ratio is

[tex]r = \frac{4}{8} = \frac{1}{2} [/tex]

The sum of this series is given by

[tex]S_{\infty} = \frac{a_1}{1 - r} [/tex]

[tex]S_{\infty} = \frac{8}{1 - \frac{1}{2} } [/tex]

Simplify:

[tex]S_{\infty} = \frac{8}{\frac{1}{2} } = 8 \times 2 = 16 [/tex]

I think it's width= 3 times length

So the 1. length is 18/3=6

The 2. Width is 8*3=24

The 4. width is 12*3=36

The reason is because your mutliplying by 3

Answer:

28

Step-by-step explanation:

We start by doing 28 - 14 which equals 14.

We do this because we want to find out the amount of books before he bought 14. We have 14 which is after he sold half of his comics. A half is 1/2, that means you multiply 14 by 2. You get 28.

Final answer:

Julio initially had 28 comic books, sold half, then purchased 14 more, which resulted in him having a total of 28 comic books. We used a simple algebraic equation to determine the original amount.

Explanation:

Let's denote the original number of comic books that Julio had as x. According to the problem, Julio sold half of his comic books (x/2) and then bought 14 more. Consequently, he now has 28 comic books in total.

To express this situation mathematically, we can create the following equation to represent the changes in the number of comic books Julio has:

x/2 + 14 = 28

If we simplify this equation by subtracting 14 from both sides, we get:

x/2 = 28 - 14

x/2 = 14

By multiplying both sides of the equation by 2, we can find the original number of comic books Julio had:

x = 14 * 2

x = 28

Therefore, Julio began with 28 comic books before he sold half and bought 14 more.

Answer:63Minutes

Step-by-step explanation:

Answer: 63.

Step-by-step explanation: In order to find how fast she runs 6 miles, it'd be convenient to know how fast she runs in 1 mile. So:

8 miles = 84 minutes.

8/8 = 1

84 / 8 = 10.5

6 x 1 = 6

10.5 x 6= 63.

Hello,

First we work out the equations:

x + y =62 will be the first equation.

2x= y +13 is the second equation.

We can first rewrite the second equation as 2x – y =13.

So we have:

x + y = 62

2x –y =13

KEEP IN MIND: With y being positive in one of the equations and negative in the other, we can combine the equations to quickly eliminate y and solve for x.

x + y = 62

+2x –y =13

3x = 75 divide both sides by 3 to get x.

x = 25

Now that we have x we can substitute the value for x, 25.

25 + y = 62 we can subtract 25 from both sides to get y.

y = 62- 25

y = 37

2(25) = 37 + 13

Therefore,

50 = 50

Have a amazing day.

The two numbers your friend has are 25 and 37. This solution is found by creating a system of equations based on the clues given and solving for the two variables.

Your friend essentially gave you a system of two equations to solve where the two numbers are x and y. The first equation from your friend's statement is '2 times the first number is 13 more than the second number', which transforms to 2x = y + 13. The second equation is 'the sum of the two numbers is 62', which converts to x + y = 62.

Solving this system of equations can reveal the two numbers your friend has. We can utilize the substitution method, where we express y from the first equation as y = 2x - 13 and plug it into the second equation. This substitution gives us x + (2x - 13) = 62. This simplifies to 3x - 13 = 62, and by rearranging, we find 3x = 75. Dividing by 3 we get x = 25.

Using the value of x = 25, now we can find y = 2(25) - 13 = 37.

So, your friend's numbers are 25 and 37.

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Answer:

x + y = 5

Hope this helps you out!

Hello There! The answer is 12w - 12y + 3.

Here's a step by step on how to solve  3(2w-4y+3)+6w-6.

Step 1: Multiply the 3 by the numbers in the parenthesis.

3(2w-4y+3)+6w-6 ⇒ 6w - 12y + 9 + 6w - 6

Step 2: Rearrange the numbers so like terms are next to each other.

6w - 12y + 9 + 6w - 6 ⇒ 6w + 6w - 12y - 6 + 9.

Step 3: Combine like terms. (6w + 6w and - 6 + 9).

6w + 6w - 12y - 6 + 9 ⇒ 12w - 12y + 3

This is your final answer since you cannot simplify any further. I hope this helps and have a great day!

Answer:

12 w - 12 y + 3

Hope this helps :)

Have a great day !

5INGH

Step-by-step explanation:

3 ( 2 w - 4 y + 3 ) + 6 w - 6 =

6 w - 12 y + 9 + 6 w - 6 =

12 w - 12 y + 3