For people who have taken PreCalc/Calc:

Find the constant a such that the function is continuous on the entire real line.

(Summer Math Packet)

Answer:

D. Multiply the second equation by 3. The solution is x = 12, y = 10

Step-by-step explanation:

Given:

x + 3y = 42 (first equation)

2x - y = 14 (second equation)

To solve by elimination, starting with elimination of the y-variable, multiply the second equation by 3 to get a third equation.

2x - y = 14 (2nd eqn.) × 3

6x - 3y = 42 (3rd equation)

Add the 3rd equation and the 1st equation together.

x + 3y = 42 (first equation)

6x - 3y = 42 (3rd equation)

7x = 84

7x/7 = 84/7

x = 12

To find y, substitute x = 12 in the first equation

x + 3y = 42 (first equation)

12 + 3y = 42

12 + 3y - 12 = 42 - 12

3y = 30

3y/3 = 30/3

y = 10

Solution is x = 12, y = 10

Answer:

B.) x + (x + 16) = 90

2x+16=90

2x=90-16

x=74/2

x=37

Answer:

f(-4)= -2

Step-by-step explanation:

f(x)=x^2+5x+2 find(-4)

replace x= -4 in function

f(-4) = (-4)^2+ 5*-4+2

       = 16 -20 +2

       = 18-20

       = -2

Answer:

7833

Step-by-step explanation:

4896(on country)+2937(outside country)=7833 in total

this is all the information in the question

Answer:

12.4 feet

Step-by-step explanation:

A ladder placed against the wall forms a right angle triangle

Hypotenuse ² = opposite ² + adjacent ²

Hypotenuse = 13 feet

Opposite = 4 feet

Adjacent = x

Hypotenuse ² = opposite ² + adjacent ²

13² = 4² + x²

169 = 16 + x²

169 - 16 = x²

153 = x²

Find the square root of both sides

√153 = √x²

12.369316876852 = x

x = 12.4 feet

Adjacent = x = 12.4 feet

Answer:

[tex]x = 15.[/tex]

Step-by-step explanation:

Given

See attachment for floor space

Required

Find x

The floor can be partitioned into three space.

The dimension and the area of each space is:

Dimension: 10 by 10

[tex]A_1 = 10* 10 = 100[/tex]

Dimension: 10 by x

[tex]A_2 = 10* x = 10x[/tex]

Dimension: x by x

[tex]A_3 = x* x=x^2[/tex]

So, the total area is:

[tex]Area =100 +10x + x^2[/tex]

Given that:

[tex]Area = 475[/tex]

So, we have:

[tex]100+10x+x^2 =475[/tex]

Rewrite as:

[tex]x^2 +10x+100-475=0[/tex]

[tex]x^2 +10x-375=0[/tex]

Expand

[tex]x^2 + 25x -15x -375 = 0[/tex]

Factorize

[tex]x(x + 25) -15(x +25) = 0[/tex]

Factor out x + 25

[tex](x+25)(x-15)=0[/tex]

Solve:

[tex]x = -25\ or\ x = 15[/tex]

x cannot be negative; So:

[tex]x = 15.[/tex]

Answer:

66.6667%

Step-by-step explanation:

Answer:

7 boys

Step-by-step explanation:

We must find the median of the data given. A median is the "middle number" of a set of numbers ordered in increasing value.

Step 1, ordering the numbers:

We will start by ordering the numbers from smallest to largest. We have:

2, 2, 6, 8, 9, 12

Step 2, finding the "middle number":

Well...notice how there is an even amount of numbers in the data set. We can't exactly find one "middle number". We can however, narrow the list down to two "middle numbers."

We have 6 and 8.

Step 3, taking the average:

To find the median, we will take the average of the two "middle numbers."

[tex]\frac{6+8}{2} =\\\frac{14}{2}=\\\fbox{7}[/tex]

The median is 7 boys.

I hope this helps! Let me know if you have any questions :)

Answer:

I don't know either B or D ........

Answer:

A, y=1/4x+2

Step-by-step explanation:

All of the equations are the same except forthe slope. Look at the points where the line crosses the points, I chose (0,2) and (4,3). The line goes up one and over four from the first point to the second point. Since it’s rise over run, up and over, it’s 1/4x

Answer:1 min

Step-by-step explanation:

Try this option:

1. the required surface area consists of: A=A₁+A₂+A₃, where

2. A₁=pi*r*l - the surface of the cone:

pi=3.14; r=4/2=2 cm; l=sqrt(6²+2²)=2√10≈6.33 (cm);

A₁=3.14*2*6.33=39.74 (cm²).

3. A₂=a²-pi*r² - the surface of the top plane:

A₂=36-3.14*4=23.43 (cm²).

4. A₃=5*a² - the surface of the five planes of the given cube:

A₃=5*6²=180 (cm²).

5. the required area:

A=39.74+23.43+180=243.17 (cm²).

Answer: 243.17

Answer:

The sequence would be arithmetic. This is because an arithmetic sequence has a common number multiplying, adding, subtracting etc. The common rule for this set of numbers was x5. 9x5=45, 45x5=225 etc. We simply used this method with negative numbers, but the rule was still multiplying.

Happy learning!

--Applepi101 :)

Answer:

Arithmetic

Step-by-step explanation:

It has a constant difference between each number whilst Geometric usually has the same difference between each number

Answer:

6 × (11 - x) = -72 => x = 23

or

6 × (x - 11) = -72 => x = -1

Step-by-step explanation:

there are at least two possibilities, as the "difference between two numbers a and b can be excised as either a-b or b-a.

in any case, just following the sentence

Six times = 6 ×

difference of 11 and a number = 11 - x

is -72 = -72

so,

6 × (11 - x) = -72

and that is true for x = 23

but

the other direction is possible too

6 × (x - 11) = -72

and that is true for x = -1

Answer is the last one: Yes because ABC and GFC are similar using AA

Lemme know if you need an explanation! :]

Answer:

yup its d

Step-by-step explanation:

just took the test and it was right

Answer:

There are many answers

Step-by-step explanation:

393 + 1 = 394

392 + 2 = 394

391 + 3 = 394

And so forth...

Hope this helps :)

Answer:

B

Step-by-step explanation:

a rectangle that is not a square

The plane will be rectangular which is not a square. Then the correct option is B.

It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.

A cube is intersected by a plane from the top edge of one face to the bottom edge of the opposite face as shown.

Let a be the side length of the cube.

The length of the rectangular plane will be

L² = a² + a²

L = a√2

Then the dimension of the plane is 'a' and 'a√2' units.

The plane will be rectangular which is not a square. Then the correct option is B.

More about the rectangle link is given below.

https://brainly.com/question/10046743

#SPJ2

Answer:

Coordinate point of the image is (9, -2)

Step-by-step explanation:

In the coordinate point (4, -6);

=> x-value = 4

=> y-value = -6

We know that the translation of;

=> 5 units right would add 5 to the x-value

=> 4 units up would add 4 to the y-value

Therefore the answer; (x, y) => (9, -2)

Hope this helps!

Answer:

62.8 m^2

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h  where r is the radius and h is the height

V = (3.14) ( 2)^2 *5

V = 62.8 m^2

Answer:

V = 62.8 cm³

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Geometry

Volume of a Cylinder Formula: V = πr²h

Step-by-step explanation:

Step 1: Define

Identify variables

r = 2 cm

h = 5 cm

Step 2: Find Volume

Step-by-step explanation:

Let running speed = x.

So, cycling speed = 2x.

Total distance traveled = 20 + 25 = 45km

Time taken running = 20/x

Time taken cycling = 25/2c

Total time taken = 5 hours

So, 5 = 20/x + 25/2x

Solving this equation for x gives:

10x = 65. Thus x = 6.5

Since cycling speed = 2x, cycling speed = (6.5)(2)

So cycling speed is 13 km/h.

Hope it helps.

Answer:

x = 15

Step-by-step explanation:

(5x-3)=(3x+27)

Subtract 3x from each side

(5x-3x-3)=(3x-3x+27)

2x-3 = 27

Add 3 to each side

2x-3+3 = 27+3

2x= 30

Divide by 2

2x/2 = 30/2

x = 15

Answer:

-23

Step-by-step explanation:

Answer:

-23

Step-by-step explanation:

When you do positive-negative you subtract the 2 numbers then take the sign of the number that had the highest absolute value.

25-2=23

The absolute value of -25 is 25

(|-25| = 25)

And the absolute value of 2 is 2

(|2| = 2)

25 > 2

So it would be -23

Answer:

180m^3

Step-by-step explanation:

Given data

Height = 15m

Lenght= 4m

Width=3m

We know that the volume of a rectangular prism is expressed as

Volume= L*W*H

Substitute

Volume= 4*3*15

Volume= 180m^3

Answer:

909 and 3267

Step-by-step explanation:

There are a total of 24 possible combinations using these 4 digits. This means that any one of these combinations subtracted from 4310 would be a possible solution. Therefore, we can create the following 2 combinations (below in bold) and subtract them from 4310 to get two possible solutions...

4310 - 3401 = 909

4310 - 1043 = 3267

Finally, we have two possible solutions which would be 909 and 3267

Answer:

24

Step-by-step explanation:

15 - 3d

Let d = -3

15 - 3(-3)

Multiply

15 +9

Add

24

Answer:

24

Step-by-step explanation:

15 - 3d

* plug in -3 *

15 - 3(-3)

simplify -3(-3)

-3(-3) = + 9

add

15 + 9 = 24

Answer:

Market

Step-by-step explanation:

Market : 5 bags = $23.60

Farm : 7 apples = $32.76

Market = $23.60 ÷ 5

= $4.72 each BAG

Farm = $32.76 ÷ 7

= $4.68 each APPLE

Thus, market is the better deal because you will get 5 bags of apple for $4.72 for each bag.

Answer:

$375

Step-by-step explanation:

$13,500÷36=$375

Hope this helps! :)

Answer:

Step-by-step explanation:

13500 divided by 36