Fill in the blanks. The vertical line that contains the vertex is called the blank ?

Answer:

Step-by-step explanation:

Rewrite without absolute value for the given conditions:

1) y = |x−3|+|x+2|−|x−5|, if x > 5

  y = x-3 + x + 2 - (x-5)

  y = x + 4

2) y = |10-x|, if x<10

   y = 10 - x

In both cases, the value of x is held to values that make the absolute value notation redundant, so they can be removed.

===============

Write the absolute value equations in the form x−b=c (where b is a number and c can be either number or an expression) that have the following solution sets:

1) All numbers such that x≤5

x≤5 kinda does it for me.  X can be any number less than or equal to 5.  Ta da. (?)

2) All numbers such that x≤−14.

x ≤ -14

Same comment.  I'm not sure what is being asked.

Answer:

y = 2x - 7

Step-by-step explanation:

Step 1: Subtract 2x from both sides.

Step 2: Divide both sides by -1.

Answer:

18/x + 3

Step-by-step explanation:

This can be written algebraically as 18/x +3. This question is a little unclear, but I think it’s asking to write it as an equation

Answer:

He'll have 24 chocolates remaining.

Step-by-step explanation:

Lets make an equation to represent the problem where x = the number of days and c = chocolates remaining.

60 - 4x = c

Since he ate four chocolates everyday for 9 days, the x in this equation would be 9.

Multiply 9 by 4 to get 36, Then subtract that from 60 to get 24.

Answer:

its false

Step-by-step explanation:

Answer:

No, it's not.

Step-by-step explanation:

2b + y = 15 is not an expression because it's an equation containing an equal sign. An expression cannot include inequality signs or equal signs.

Answer:

Step-by-step explanation you do the inverse which is subtraction and you get y

2-2=0 15-2=13 y=13

Answer: He might have 1$ or 51 $ because he spent 49$ and he could have 50$ as his pocket money or he could have 100$ as his pocket money and had 51$ left

Step-by-step explanation: Hope this helps :)

Answer:

4/8

Step-by-step explanation:

Answer:

B. < 2 & < 3

Explanation:

Example of supplementary angles in the image:-

She needs to purchase a cover to protect the hot tub of an area of 38.5 square feet.

It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

Claire has a hot tub with a diameter of 7 feet. She wants to purchase a cover to protect the hot tub.

The area of the circle is given by

[tex]\rm Area = \dfrac{\pi}{4}d^2[/tex]

We have d = 7 ft, then the area of the circle will be

[tex]\rm Area = \dfrac{3.14}{4}*7^2\\\\Area = 38.5 \ ft^2[/tex]

More about the circle link is given below.

https://brainly.com/question/11833983

Answer:

30 cakes

Step-by-step explanation:

For one cake alone, find a common denominator (which is 6). So [tex]2\frac{2}{3}[/tex] ([tex]\frac{8}{3}[/tex]) is equal to [tex]\frac{16}{6}[/tex] cups. [tex]\frac{1}{2}[/tex] is [tex]\frac{3}{6}[/tex] cups.

So for one cake, it takes [tex]\frac{19}{6}[/tex] cups of flour. Henry has [tex]\frac{570}{6} = 95[/tex] cups of flour.

If you divide the 570 by 19, Henry can make 30 cakes.

Answer:

7.62

Use the Pythagorean theorem. (a^2)+(b^2)=(c^2)

(3^2)+(7^2)=58

Then the square root of 58 is 7.61577 rounding that to the hundredths gives you 7.62

7.62

To round find the hypotenuse, use the Pythagorean theorem which states that A squared plus B squared = C squared which is the answer to our problem. Then find the square root of the solution and voila.

Answer:

n = 5

Step-by-step explanation:

it is stated that the two triangles are similar so we can use the similarity ratio to find the value of n:

RQ/BA = QR/AC

n/2 = 10/4 cross multiply expressions

4n = 20 divide both sides by 4

n = 5

Using proportions, it is found that 2.04 times more pennies were minted in the year 2000 compared to the year 2013.

A proportion is a fraction of a total amount. From it, the amount of times a measure a is greater than a measure b is given by a divided by b.

In this problem:

Hence, 2.04 times more pennies were minted in the year 2000 compared to the year 2013.

Hence, applying the proportion:

[tex]\frac{1.43 \times 10^{10}}{7.07 \times 10^9} = \frac{14.3 \times 10^9}{7.07 \times 10^9} = 2.04[/tex]

More can be learned about proportions at https://brainly.com/question/14398287

Answer:

Perimeter of the triangle is 58

Step-by-step explanation:

create an equation

(x+3)2+(2x-1)2=(x-7)+(4x-8)+(3x+1)

2x+6+4x-2=x-7+4x-8+3x+1

combine like terms

6x+4=8x-14

18=2x

x=9

now we substitute in the expression to find the perimeter

9-7=2

36-8=28

27+1=28

2+28+28=30+28=58

Answer:

4 airplanes

Step-by-step explanation:

1 = 2/3

6 = x

cross multiply

x = 6 × 2/3

therefore x = 4

Answer:

4 airplanes

Step-by-step explanation:

1 =2/3

6 =×

you have to cross multiply

× =6×2/3

Therefore x=4

Answer:

y=-1/2x+2

Step-by-step explanation:

First, the slope of perpendicular line have negative reciprocal coefficients. In this case the coefficient is 2, The reciprocal of 2 is 1/2 and the negative of 1/2 is -1/2. So x will have a coefficient of -1/2.

Second, find the equation with a slope of -1/2 that passes through (-2,3). There are a few ways to do this. I like to plug the given x value into the expression -1/2x, so -1/2(-2) which equals positive 1 and for the line to pass through the point (-2,3) you need to add 2. So: y=-1/2x+2

Answer:

[B] The probability of Alex picking a red marble is 50%.

[C] They both have the same probability of picking a red marble.

Step-by-step explanation:

Given;

Alex and James both have a bag of marbles.

Alex's bag has 10 red marbles and 10 blue marbles.

James's bag has 15 red marbles, 10 blue marbles and 5 green marbles.

They each take a marble out of their bag without looking.

Solve;

Alex have 10 Blue marbles so 10 out of 20 are Blue.

James has 10 Blue Marbles so 10 out of 30 are Blue.

Hence, [A] They both have the same probability of picking a blue marble.

is False.

Alex have 10 red and 10 blue which 10 = 10

thus, [B] The probability of Alex picking a red marble is 50%.

Alex's have 10 red marbles and James's have 15 red marbles.

10 out of 20 of them are red. Thus, that 50%

15 out of 30 of them are red. Thus, that 50%

50%  = 50%

Hence, [C] They both have the same probability of picking a red marble.

is true.

James have 15 red, 10 Blue, 5 Green marbles.

15 + 10 + 5 =30 [ Total ]

5 out of 30 is Green

5/30 = 0.16666666666

Round = 16.67%

Hence, [D]  The probability of James picking a green marble is 5%.

is False.

15 out of 30 and 10 out of 20

15/30 = 50% and 10/20 = 50%

Thus, [E] James has a higher chance of picking a red marble than Alex.

is False.

~Learn with Lenvy~

Select the statements that are correct:

A - They both have the same probability of picking a blue marble. [ x ]

B - The probability of Alex picking a red marble is 50%. [✓]

C - They both have the same probability of picking a red marble. [✓]

D - The probability of James picking a green marble is 5%. [x]

E - James has a higher chance of picking a red marble than Alex. [x]

We know that ,

[tex]probability \: \% = \frac{favourable \: outcomes}{total \: outcomes} \times 100 \\ [/tex]

Alex has↷

[tex] \frac{10}{20} \times 100 = 50\% \\ [/tex]

[tex] \frac{10}{20} \times 100 = 50\% \\ [/tex]

James has ↷

[tex] \frac{15}{30} \times 100 = 50\% \\ [/tex]

[tex] \frac{10}{30} \times 100 = 33.33\% \\ [/tex]

[tex] \frac{5}{30} \times 100 = 16.66\% \\ [/tex]

Answer:

Option C(0.07) is the correct answer.

Answer:

2[tex]\sqrt{137}[/tex]

Step-by-step explanation:

Solving for the equations,

x² + 4y² = 361

4x² + y² = 324

Add both equations

5x² + 5y² = 685

Divide both sides by 5

x² + y² = 137

Multiply both sides by 4

4x² + 4y² = 548

Now take the square of both sides.

[tex]\sqrt{4x^{2} +4y^{2} } =\sqrt{548}[/tex]

= 2[tex]\sqrt{137}[/tex]

Answer: [tex]2\sqrt{137}[/tex]

Step-by-step explanation:

Trust me i'm good at geometry. Besides, if you actually paid attention in class, you'd know how to solve this

Answer: 2√10

Step-by-step explanation:

A way we can find what x equals, is to find the opposite of what ever sign is on a side, in the equation x^2=40, the opposite of squaring is to find the square root of it.

It is important that what you do to one side, you do to the other.

So we have to square root both sides so we can get rid of the ^2 on x to get x =. This would look like √x^2 = √40

The square root of x^2 would revert back to just x

To find the square root of 40, its important to first see if its a perfect square. In this scenario, it isnt. Because it isnt, we have to find the closest perfect square that we can multiply to get 40, in this equation, the closest would be 4 so we do 4*10.

Then we reduce the 4 by square root and we get 2

Then we cant do anything else with the 10, so we would right the answer as a radical, with the square root you got from the perfect square on the outside and the remainder on the inside of the square root, like x√r where x is the number obtained from square root and r is the remainder that we cant do anything else with.

After doing this, we get the answer 2√10, which can be said "two radical ten"

Answer:

X=3 hours

Step-by-step explanation:

1)     1 1/2 + 1 1/2 = x

2)     3=x

3)      x=3

Answer:1130

Step-by-step explanation:

Answer:

x+y=1

Step-by-step explanation:

y-y1=m(x-x1)

y-2=-1(x-(-1))

y-2=-(x+1)

y=-x-1+2

y=-x+1

y-(-x)=1

y+x=1

x+y=1

Answer:

40 times greater

Step-by-step explanation:

6 x 10^6 = 2.4 x 10^8

6 x 1000000 = 2.4 x 100000000

6000000  =  240000000

240000000 / 6000000

= 40

I hope this helps <3

Step-by-step explanation:

1) 320 to 180

2) 320 to 500

3) 500 to 180

4) 320 to 500