(SAT prep) Find the value of x in each case of the following exercises:

Answer:

[tex] \frac{2}{3} \bigg[ x\sqrt{ {x}} + (x - 1)\sqrt{ {(x - 1)}} \bigg] + c[/tex]

Step-by-step explanation:

[tex] \int \frac{1}{ \sqrt{x} - \sqrt{x - 1} } dx \\ \\ = \int \frac{ \sqrt{x} + \sqrt{x - 1}}{ (\sqrt{x} - \sqrt{x - 1} )( \sqrt{x} + \sqrt{x - 1} )} dx \\ \\ = \int \frac{ \sqrt{x} + \sqrt{x - 1}}{ (\sqrt{x})^{2} - (\sqrt{x - 1} )^{2}} dx \\ \\ = \int \frac{ \sqrt{x} + \sqrt{x - 1}}{ x - (x - 1 )} dx \\ \\ = \int \frac{ \sqrt{x} + \sqrt{x - 1}}{ x - x + 1} dx \\ \\ = \int \frac{ \sqrt{x} + \sqrt{x - 1}}{ 1} dx \\ \\ = \int (\sqrt{x} + \sqrt{x - 1}) dx \\ \\ = \int \sqrt{x} \: dx+ \int\sqrt{x - 1} \: dx \\ \\ = \int {x}^{ \frac{1}{2} } \: dx+ \int {(x - 1)}^{ \frac{1}{2} } \: dx \\ \\ = \frac{ {x}^{ \frac{3}{2} } }{ \frac{3}{2} } + \frac{ {(x - 1)}^{ \frac{3}{2} } }{ \frac{3}{2} } + c \\ \\ = \frac{2}{3} {x}^{ \frac{3}{2} } + \frac{2}{3} {(x - 1)}^{ \frac{3}{2} } + c \\ \\ = \frac{2}{3} \bigg[ \sqrt{ {x}^{3} } + \sqrt{ {(x - 1)}^{3} } \bigg] + c \\ \\ = \bold{\purple {\frac{2}{3} \bigg[ x\sqrt{ {x}} + (x - 1)\sqrt{ {(x - 1)}} \bigg] + c}} [/tex]

Answer:

6

Step-by-step explanation:

It is six because 6x6=36

Answer:

The mean speed of the automobiles traveling on this road is the closest to 64 miles per hour

Step-by-step explanation:

Given

[tex]\begin{array}{cc}{Speed} & {Frequency} & {45-55} & {50} & {55-65} & {325} & {65-75} & {275} & {75-85} & {25} \ \end{array}[/tex]

Required

Calculate the mean

First, calculate the midpoint (x)

For 45 - 55: [tex]x = \frac{1}{2}(45+55) = 50[/tex]

For 55 - 65: [tex]x = \frac{1}{2}(55+65) = 60[/tex]

For 65 - 75: [tex]x = \frac{1}{2}(65+75) = 70[/tex]

For 75 - 95: [tex]x = \frac{1}{2}(75+85) = 80[/tex]

So, we have:

[tex]\begin{array}{ccc}{Speed} & {Frequency} & {x} & {45-55} & {50} & {50} & {55-65} & {325} & {60} & {65-75} & {275} &{70} & {75-85} & {25} &{80}\ \end{array}[/tex]

The mean is then calculated as:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

[tex]\bar x = \frac{50*50+325*60+275*70+25*80}{50+325+275+25}[/tex]

[tex]\bar x = \frac{43250}{675}[/tex]

[tex]\bar x = 64.07[/tex]

[tex]\bar x = 64[/tex] --- approximated

Answer:

<

Step-by-step explanation:

Need points :(

Answer:

Step-by-step explanation:

x+23+x=90

2x=67

x=33.5

Answer:

2

Step-by-step explanation:

So first you would do y2-y1/x2-x1

9-(-1)/6-1

10/5=

2

Step-by-step explanation:

nasaan po ang tanong, where is the question

Answer:

y= 9 x= -42

Step-by-step explanation:

Answer:

-5<n≤2

Step-by-step explanation:

Divide 3 by -15 nad 6 since we need to find the "n" we need to divide on all sides, so -15 divided by 3 is -5 so replace -15 with -5 and 6 divided by 3 is 2 so replace 6 with 2

Answer:

Step-by-step explanation: the answer is B i think

Answer:

A

Step-by-step explanation:

[tex]V = \frac{nd^2h}{6}[/tex]

multiply both sides by 6

[tex]6V = nd^2h[/tex]

divide both sides by [tex]nd^2[/tex]

[tex]\frac{6V}{nd^2} = h[/tex]

So the answer is A.

Answer:

-3

....................

Answer:

-3

Step-by-step explanation:

Answer:

if you need it as improper then 25/12

Step-by-step explanation:

For b you had to add 25 and 35 together to make 60.

Divide 60 by 2 to get 30. 30 is the average between the two numbers. You then find the frequency of 30 using the graph. For the 12 year olds it is 40 and for the 18 year olds it is 60. Find the difference between these 2. So 60-40= 20

Step-by-step explanation:

oatmeal 12/8 = 1.5 per student

apple 27/6 = 4.5 per student

carmine gets 1.5 + 4.5 = 6 muffins

Answer:

Step-by-step explanation:

(12 oatmeal)/(8 students) = (1.5 oatmeal)/student

Each student gets 1.5 oatmeal muffins.

(27 apple)/(6 students) = (4.5 apple)/student

Each student gets 4.5 apple muffins.

Carmine gets 1.5 oatmeal plus 4.5 apple = 6 muffins

Answer:

[tex]\frac{1}{5}[/tex]

Step-by-step explanation:

Answer:

1/5

Step-by-step explanation:

6/30 can be simplified by finding the LCD (least common denominator), which is 6

divide both the top & bottom by 6

6/6 = 1

30/6 = 5

thus, your answer is 1/5

Answer:

6 dimes & 10 quarters

Step-by-step explanation:

Here are the two equations. The first one deals with the numbers of coins. The second one deals with the values of the coins.

d + q = 16

0.1d + 0.25q = 3.1

Solve the first equation for d and plug into the second equation.

d = 16 - q

0.1(16 - q) + 0.25q = 3.1

1.6 - 0.1q + 0.25q = 3.1

0.15q = 1.5

q = 10

d + q = 16

d + 10 = 16

d = 6

Answer: 6 dimes & 10 quarters

Benjamin has 6 dimes and 10 quarters.

A linear equation is  defined as an equation in which the highest power of the variable is always one.

Given that two equations,

d + q = 16

0.1d + 0.25q = 3.1

Where q represents the number of quarters in his wallet, and d represents the number of dimes.

d = 16 - q

0.1(16 - q) + 0.25q = 3.1

1.6 - 0.1q + 0.25q = 3.1

0.15q = 1.5

q = 10

d + q = 16

d + 10 = 16

d = 6

Hence Benjamin has 6 dimes and 10 quarters.

Learn more about linear equation

https://brainly.com/question/2263981

#SPJ2

Answer:

A, C, and D

Step-by-step explanation:

Answer: A - C - D  

Step-by-step explanation:

A= 21

B= 19

C= 21

D= 21

E= 20

Answer:

The answer is A 21

Step-by-step explanation:

Step-by-step explanation:

A discrete variable can be defined as a definite variable that we can get it's possible values just by counting. With this in mind.

1. The number of countries ever visited is a discrete variable

2. Shoe size is definite, it is a discrete variable.

3. Number of pets living in a household is a discrete variable.

A continuous variable is one that we can get the value through measurements.

1. Pounds of chocolate consumed in the past is continuous

2. Height in inches is continuous

Answer:

3

Step-by-step explanation:

2 plus 1 is 3

Supplementary: N and M

Supplementary angles: A pair of angles whose sum is equal to 180°.

Vertical: N and R

Vertical angles: A pair of angles that are made by two intersecting lines.

Complimentary: P and Q

Complimentary angles: A pair of angles whose sum is equal to 90°.

Hope this helps! :D

Answer:

y=1/5x+4

Step-by-step explanation:

Answer:

90 mm^2

Step-by-step explanation:

split into two rectangles.

First rectangle: 5 x 6 = 30 mm^2

Second rectangle: 10 x 6 = 60 mm^2

30 + 60 = 90 mm^2

Answer:

90 [tex]mm^{2}[/tex]

Step-by-step explanation:

Hi!

What we have over here is a composite figure.

Basically, it's made up of different shapes

We can either make a rectangle by making a horizontal line from the point in between 6 mm and 5 mm

Or we can make a rectangle by going verticle from the point in between        6 mm and 5 mm

Either way, we have two rectangles now, and we can use our formula [tex]l*w[/tex] to find the area.

For the first example, we would do:

[tex]6*5[/tex] [tex]=30[/tex]

[tex]6*10=60[/tex]

Then we add the two areas of the two rectangles:

[tex]60+30=90[/tex] [tex]mm^{2}[/tex]

For the second example, we would do:

[tex]5*6=30[/tex]

[tex]5*12=60[/tex]

[tex]60+30=90[/tex] [tex]mm^{2}[/tex]

Just cut the figure into shapes you can calculate the area of and you should be good to go!

Let me know if you have any questions

Answer:

5 must be added to both the terms to get the ratio 4:5.

Step-by-step explanation:

(3+x)/(5+x)=4/5

Therefore,

15+5x=20+4x

=5x-4x=20-15

=x=5

I hope it's helpful!

Answer:

3+y/5+y=4/5

let y be the no.to be added

5(3+y)=4(5+y)

15+5y=20+4y

-5= -y

y=5

Step-by-step explanation:

no entiendo.....aaaaa

Answer:

6b+4

Step-by-step explanation:

Answer:

x+6=10-4+6

x=6+6-6

x=6

Answer:

61k

Step-by-step explanation:

63+59=122

122/2=61

Answer:

61000

Step-by-step explanation:

First add 63K + 59K. You'll get 122K. Then divide that number by two. You'll get 61 K, which is 61000.