Answers
1) Quesion 1:
9+√2
---------
4 - √7
Answer: the third option:
36 + 9√7 + 4√2 + √14
-----------------------------
9
Explanation:
Multiply both numerator and denominator by the conjugate of the denominator.
The conjugate of 4 - √7 = 4 + √7
=>
[tex] \frac{9+ \sqrt{2} }{4- \sqrt{7} } . \frac{4+ \sqrt{7} }{4+ \sqrt{7} } = \frac{(9)(4)+9 \sqrt{7}+4 \sqrt{2} + \sqrt{2} . \sqrt{7} }{(4)^2-( \sqrt{7})^2 } =[/tex]
[tex]= \frac{36+9 \sqrt{7} +4 \sqrt{2} + \sqrt{14} }{16-7} [/tex]
2) Question 2: sum
[tex]5x (\sqrt[3]{x^2y})+2( \sqrt[3]{x^5y})[/tex]
Answer: fourth option
[tex]7x( \sqrt[3]{x^2y} )[/tex]
Explanation:
Take x^5 out of the second radical which will result in a like term of the first radical:
[tex]5x( \sqrt[3]{x^2y} )+2( \sqrt[3]{x^5y}) =5x( \sqrt[3]{x^2y} )+2x( \sqrt[3]{x^2y})=7x( \sqrt[3]{x^2y}) [/tex]
which is the fourth option
3) Question 3. Which expression is equivalent to:
[tex] \frac{ \sqrt{10} }{ \sqrt[4]{8} }[/tex]
Answer: the first option
Explanation
[tex] \frac{ \sqrt{10} }{ \sqrt[4]{8} } = \frac{ \sqrt[4]{10^2} }{ \sqrt[4]{8} } = \frac{ \sqrt[4]{100} }{ \sqrt[4]{8} } . \frac{ \sqrt[4]{8^3} }{ \sqrt[4]{8^3} } = \frac{ \sqrt[4]{(100)(512)} }{8} = \frac{ \sqrt[4]{51200} }{8} = \frac{4 \sqrt[4]{200} }{8} = \frac{ \sqrt[4]{200} }{2} [/tex]
4) Question 4 What is the simplest form?
Answer: the second option
Explanation:
[tex] \sqrt[4]{81x^8y^5}=x^2 y\sqrt[4]{3^4y} =3x^2y \sqrt[4]{y} [/tex]
5) Question 5 Product
Answer: the fourth option:
[tex]104x^4+16x^4 \sqrt{30} [/tex]
Explanation:
Use the square of a binomial product: (a + b)^2 = a^2 + 2ab + b^2
[tex](4x \sqrt{5x^2} )^2+2(4x \sqrt{5x^2})(2x^2 \sqrt{6}) +(2x^2 \sqrt{6} )^2=[/tex]
[tex]=16x^2(5x^2)+16x^4( \sqrt{30} )+4x^4(6)=80x^4+16x^4 \sqrt{30} +24x^4=[/tex]
[tex]=104x^4+16x^4 \sqrt{30} [/tex]
which is the fourth option.
6) Question 6 Product
Answer: fourth option
Explanation:
[tex] \sqrt[3]{16x^7} . \sqrt[3]{12x^9} = \sqrt[3]{2^4.2^2.3x^7x^9} = \sqrt[3]{2^6.3.x^{16}}=2^2 x^5 \sqrt[3]{3x} =4 x^5\sqrt[3]{3x} [/tex]
which is the fourth option.
7) Question 7. Simplified form of 2√18 + 3√2 + √162
Answer: 18√2
Explanation:
[tex]2 \sqrt{18}+3 \sqrt{2} + \sqrt{162}=2(3) \sqrt{2} + 3 \sqrt{2} +9 \sqrt{2} =18 \sqrt{2} [/tex]
which is the second option.
8) Question 8 which function is undefined for x = 0.
Answer: second option y = √ (x - 2)
Explanation.
The square root function is not defined for negative values.
When x = 0, x - 2 = -2, whose square root is not defined.
Therefore, the square root of x - 2 is not defined for x = 0.
Related Questions
The Running Shoe Company advertised that tbe would award a number of prizes equal to 1% of the total number of entries in a contest .They received 1,600 entries .How many prizes should they award?
Answers
The Running Shoe Company should award 16 prizes, as 1% of 1,600 entries is 16.
The student asked, "How many prizes should The Running Shoe Company award if they received 1,600 entries in a contest and they award a number of prizes equal to 1% of the total number of entries?"
To find the number of prizes, we need to calculate 1% of 1,600 entries.
Step 1: Convert the percentage to a decimal by dividing by 100. So, 1% becomes 0.01.
Step 2: Multiply the total number of entries by 0.01 to find 1% of it.
1,600 entries * 0.01 = 16 prizes
Therefore, The Running Shoe Company should award 16 prizes.
50% of babies are born female. Olive wants to find the probability that 20 or more of the 50 babies born today were female. Use the simulation data to find the probability. Round to the nearest percent.
Answers
A dairy mixes chocolate milk to sell in gallon containers. They mix 2,365 cups of skim milk with 108 cups of chocolate syrup. If each gallon container holds 16 cups of the chocolate milk, how many full containers will be filled?
Answers
Now, since each gallon is 16 cups and you are determining the amount of gallons, you take the total number of cups (2473) and divide it by the 16 cups. this then gets you the answer of 154.5635. BUT... Since it wants to know how many FULL containers... the real answer is simply 154 GALLONS
= 154.56
the quantity will fill a 16 containers
After taking core samples all over a cone-shaped mountain, you have determined that for every 1,000,000 yd3 there is about 2 lbs of gold to be mined. If the mountain has a base that is 2,000 yards wide and a height that is 3,000 yards tall, about how much gold is it expected to hold?
Answers
To find the expected amount of gold in the mountain, calculate the volume of the cone and multiply it by the gold density.
Explanation:To determine the amount of gold expected to be held in the mountain:
Calculate the volume of the cone using the formula V = (1/3)πr²h.
Convert the volume to cubic yards since the gold density is given in lbs per 1,000,000 yd³.
Multiply the volume by the gold density to find the total amount of gold expected in lbs.
please help Use the expression 8a + 16c.
Part A
Factor the expression using the GCF.
A. 2(4a + 8c)
B. 4(2a + 4c)
C. 8(a + 2c)
D. 16(12a + c)
Part B
What is the value of the expression when a = –5 and c = –1? Enter your answer in the box.
Answers
C. 8 (a + 2c)
Explanation:
The answer is c because when you have this equation (below) you have find what both numbers are divisible by:
[tex]8a + 16c[/tex]
Both of these numbers are divisible by 8 (This number would be on the outside of the parenthesis).
[tex] \frac{8a}{8} + \frac{16c}{8} [/tex]
Now that you know they're both divisible by 8 you can start to put together your equation. So far you should have this:
8 (? +?)
Now to find the other numbers you have to think... what number multiplied by 8 will make it equal to 8a? The answer would be a. 8 times a = 8a. (Another way to do this is to just divide 8a by 8 same with 16)
Now your equation should look like this:
8 (a + ?)
Now do the same thing with the 16c as you did with the 8a. (either divide 16c by 8 or think of a number times 8 that will make it equal 16c) For this one I'm going to use the division method - so what is 16c ÷ 8? 16 ÷ 8 = 2 and finally just add the c. So your answer is 2c.
Your equation should not look like this:
8 (a + 2c)
You're done!
Part B.
-56
Eplanation:
To find this just plug in the numbers into the equation. a = -5 and c = -1.
For this I used the original equation :
[tex]8a + 16c[/tex]
Plug in the numbers....
[tex]8( - 5) + 16( - 1)[/tex]
And solve!
[tex] - 40 + - 16[/tex]
And finally....
[tex] - 40 + - 16 = - 56[/tex]
So the value of the equation if a were -5 and c were -1 would be -56!
The required expression is C. 8(a + 2c) and value of the expression when a = –5 and c = –1 is -56.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given the expression is
8a + 16c.
To find the Factor form of the given expression by using GCF.
We have,
8a + 16c.
Factors of each term:
8a = 2 x 2 x 2 x a
16c = 2 x 2 x 2 x 2 x c
The common factors are 2, 2 and 2. then Taking out the greater common factor (GCF) in the given expression;
GCF = 8
The answer is C. 8(a + 2c)
when a = –5 and c = –1
Then;
8(a + 2c)
8(-5 + 2(-1)) = 8 (-7) = -56
To know more about an expression follow;
brainly.com/question/19876186
#SPJ3
What is the solution of the equation y=5x+50
Answers
X=0
Y= 50
Hope this help
Malik drinks 1\2 liter of water and 1\3 liter of liter of juice.did malik drink more water or juice?
Answers
find the measure of the missing angle in the triangle shown 49° 57°
Answers
So the equation would have to be 270-106= 164. The missing angle that you are missing is 164 degrees
Could u help me with 8 and 10
Answers
I don’t know how to find the missing angles
Answers
Rubin is 5 years older than one third Terry’s age. Sheldon is three years younger than 2 times Rubin’s age. Define a variable and write an expression to represent Rubin’s age. Then find Rubin age and Sheldon age if Terry is 6 years old.
Answers
Terry = x
Rubin is 5 years older than one third Terry’s age
Rubin = 5 + 1/3x
Sheldon is three years younger than 2 times Rubin’s age.
Sheldon = 2(5 + 1/3x) - 3
If Terry is 6,
Rubin = 5 + 1/3(6) = 5 + 2 = 7
Sheldon = 2( 5 + 1/3 (6)) - 3 = 11
Ans: Rubin is 7 and Sheldon is 11
You sell lemonade for $2 per cup and orange juice for $3 per cup. You sell a total of 100 cups for $ 240. How many cups of lemonade and orange juice were sold ?
Answers
240/3 = 80 cups of orange juice
From the given information,you can write an linear equation like this:
$2x + $3(100 - x) = 240
First, you have to distribute them = 2x + 300 - 3x
Then, you have to add like terms = 1x + 300=240
Next, you have to transpose 300 to the left = -1x = 300 - 240
So, you have to subtract = -1x = -60
And, you solve = -60 = -60 So x = 60
60 cups of lemonade sold
Orange:
100 - x = 100 - 60 = 40 cups of orange juice sold
So you can check our answer by using the original linear equation
2x + 3( 100 - x) = 240 2(60) + 3 (100 - 60) = 240 120 + 3(40) = 240 120 + 120 = 240 240 = 240
Hope this helps! ;)
The diameter was of four half circles are sides of a square with a side length of 7 cm.
Find the exact area of the shaded region in terms of pi. (Please show work)
Answers
Answer:
shaded area = 24.5π -49
Step-by-step explanation:
The area of a segment of a circle is given by the formula ...
A = 1/2r²(θ -sin(θ))
Here, the radius of the circle is (7 cm)/2 = 3.5 cm, and the angle of interest is π/2 radians.
There are 8 segments of this size in the shaded area, so we have ...
shaded area = 8(1/2)(3.5 cm)²(π/2 -sin(π/2))
shaded area = 24.5π -49
How do you solve 9x+2=8x+9
Answers
Hope this helps and have a wonderful day :)
A building engineer analyzes a concrete column with a circular cross section. The circumference of the column is 18π meters. What is the area of the cross section?
Answers
--------------------------------------------------------
Work Shown
C = 18pi is the given circumference
d = diameter which is unknown
C = pi*d
18pi = pi*d
18 = d
d = 18
The diameter is 18 meters.
Half of this is the radius r = d/2 = 18/2 = 9
The radius is 9 meters
Use the value of r to find the area of the circle
A = pi*r^2
A = pi*9^2
A = pi*81
A = 81pi
The area of the circular cross section is 81pi square meters
find the value of this pronumeral
Answers
A triangle's interior angles also measure 180º.
The angle measuring 130º is complementary to the corresponding interior angle, so that interior angle plus 130 has to equal exactly 180º.
180 - 130 = 50º
45 + 50 = 95º, so subtract that from 180 to find the measure of the last interior angle of the triangle.
180 - 95 = 85º
That angle of 85º is complementary to the other outside angle, n, and to find that subtract 85 from 180.
180 - 85 = 95º
n = 95
Hope this helps!
A mini-cube measures 1.5 in. wide. A mega-cube is 5 times as wide. What is the volume of the mega-cube, rounded to the nearest tenth?
Answers
Answer:
the answer is 421.9 in³
2a - 1 = 19
Solve the equation and show all work please show steps!!
Answers
The answer is "x=10".
Reason:
First write the equation:
2a-1=19
Add one on both sides:
19+1=20
2a=19
Now divide 2 by 20:
20/2=10
a=10
If you need anymore help feel free to ask me!
Hope this helps!
~Nonportrit
A parallelogram is symmetric with respect to either diagonal. true or false?
Answers
Not all parallelogram is symmetric with respect to either diagonal, therefore the answer is False.
A parallelogram is known as a quadrilateral (having four sides) with two pairs of parallel-lateral lines. A parallelogram has no line of symmetry but there are some exceptions to specific types of parallelograms. For example:
Rhombus is a special type of parallelogram and it has two lines of symmetry along its diagonals.A rectangle has two lines of symmetry going through the mid-point of the opposite sides.A square has four lines of symmetry with two lines going through the diagonal and two lines going through the opposite sides.Therefore, we can conclude that not all parallelogram is symmetric with respect to either diagonal.
Learn more about parallelogram here:
https://brainly.com/question/9680084?referrer=searchResults
Justin drank 1 liter of water during soccer practice. He drank 2000 milliliters of water during the soccer game. How many milliliters of water did he drink during the practice and the game?
Answers
2000 + 1000 = 3000 mL
He drank 3000 mL during practice and the game.
Deyonne made 25% more cookies than Cameron. They sold the cookies for $0.50 each. Let x represent the number of cookies Cameron made. Which of the following expressions represent possible revenue from the sales. Select all that apply.
.50[x+(x+.25x)]
.50(x+.25x)
.50(x+1.25x)
.50(.75x+x)
.50(1.75x)
.50(2.25x)
Answers
.50(x+1.25x)
.50(2.25x)
graph the quadratic function f(x)=−1/2x^2+7.
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
GRAPH FOR BRAINLIEST
Answers
Use the same steps as the first one to solve this one
Answer:y=(0,7) x=(2,5)
Step-by-step explanation:
smart
A spinner that has 4 equal parts that are the colors blue, green, red, and yellow. The spinner is spun 12 times. It lands on blue 1 time.
Part A) What is the experimental probability of the spinner landing on blue?
Part B) Compare the experimental and theoretical probabilities of the spinner landing on blue. If the probabilities are not close, explain a possible reason for the discrepancy.
Answers
Answer:
The experimental probability would be 1/12 and the theoretical probability would be 1/4. The probabilities were not close so a possible reason for the discrepancy would be the blue color on the spinner was slippery.
Step-by-step explanation:
So to start out you need to find out the experimental probability. If the spinner landed on blue 1 time out of 12 different times, you write that as a fraction of 1/12. So 1/12 is the experimental probability. It also asks for the theoretical probability. There are 4 parts of the spinner so 4 is the denominator, one of those possibilities is the one we want so 1 is the numerator, so the theoretical is 1/4. The probabilities were not close so a possible reason for the discrepancy would be the blue color on the spinner was slippery.
Just to tell you what theoretical and experimental probabilities mean is that the theoretical is the possible outcome before you do it. Experimental is where you judge your probability off of past events.
a square has the sides of 2 yards. plastic cues with sides of 8 inches are placed on the rug. if the cubes cost $2 each, how much money is needed to completely cover the rug with the cubes
Answers
The area of the square is 5184 inches squared.
Divide the area by 64 (area of cube) to equal 81 cubes.
Multiply 81 by 2 to find cost.
Cost = $162
Hope this helps!! :)
Hurry I'm TIMED!!!! The following graph shows the low temperatures for the past six nights. What was the range of temperatures for the six nights?
34°F
22°F
12°F
8°F
Answers
8, 12, 22, 34
Range is the difference between the highest number and lowest number in a set of data. To find the range for this data you take 34 and subtract 8 which gives you 28.
Answer:
the answer above is incorrect! So you take 22 which is the lowest on the graph and you take 34 which is the highest on the graph and 8 is not on the graph so 34-22=12
Step-by-step explanation:
SOYOUR ANSWER IS: 12YOU ARE WELCOME MY DEAREST FRIEND!there were 170 people at the concert. If 85% of the seats were filled how many seats are in the auditorium
Answers
In order to compute for the number of seats available in the auditorium, you just have to divide the number of people at the concert with the percentage of its utilized capacity.
Solution:
170 people / 85% = 200 seats available in the auditorium
To check the answer:
200 seats x 85% = 170 people are in the concert
what is the sum of 5/10 and 5/100
Answers
50/100 + 5/100
so the answer is 55/100
a simplified version is 11/20
hope this helped! :p
Round 2,406,251 to the nearest thousand.
A. 2,000,000
B. 2,406,000
C. 2,406,300
D. 2,407,000
Answers
Hope this helped☺☺
You have $85 in your bank account. Each week you plan to deposit $7 from your allowance and $25 from your paycheck. The equation bequals85plus(25plus7)w gives the amount b in your account after w weeks. How many weeks from now will you have $275 in your bank account?
Answers
number of weeks = 6 weeks
Explanation:
You initially have $85
Each week (w), you will deposit $7 in addition to $25
This means that the equation representing the amount (b) in the account will be:
b = 85 + (7+25) w
b = 85 + 32w
Now, we want to know in how many weeks will the amount saved be equal to $275.
To get the number of weeks, we will simply substitute with b = $275 in the above equation and solve for w as follows:
b = 85 + 32w
275 = 85 + 32w
275 - 85 = 32w
190 = 32w
w = 5.9 which is approximately 6 weeks.
Hope this helps :)
Use the formula A=bh , where A is the area, b is the base length, and h is the height of the parallelogram, to solve this problem.
Brittany is painting a mural on one of the walls in her room. The mural is in a parallelogram-shaped frame. The area of the mural is 1056 in² and the base is 32 inches.
What is the height of the mural?
Enter your answer in the box.
[___] in
Answers
1056/32
The answer is 33 in.
The area of the mural is 1056 in² and the base is 32 inches. We have to determine the height of the mural.
Area of parallelogram = [tex] b \times h [/tex]
where 'b' is the base and 'h' is the height.
1056 [tex] in^{2} [/tex] = 32 [tex] \times h [/tex]
[tex] h=\frac{1056}{32} [/tex] in
Therefore, the height of the mural is 33 inch.