Answers
Answer:
x = 13
Step-by-step explanation:
1. We can tell if the radical is in its simplest form if the square root term is a number that cannot be broken down to give a perfect square factor
what we are saying in this case is that if the number that is under the square root sign is one in which cannot be broken down to give a perfect square or that a perfect square is not its factor. Then it is in the simplest form
2. 512 = 2^(x-4)
512 = 2^9
2^9 = 2^(x-4)
since base is equal, we equate the powers
9 = x - 4
x = 9 + 4
x = 13
Related Questions
Beyonce is solving a system of equations: 2x – 3y = -2
4x + y = 24
She decides to use the elimination method to find the solution. She multiplies the second equation by 3 and adds it to the first equation to find 14x = 70, showing her that x = 5. Beyonce finds that y = 4.
Step 3: 4x + y = 24
4(5) + y = 24
20 + y = 24
-20 -20
y = 4
Step 1: 3(4x + y = 24) → 12x + 3y = 72
Step 2: 2x – 3y = -2
Solution: (5, 4)
+ 12x + 3y = 72
14x = 70
→ x = 5
Thinking about this process, Beyonce says out loud, “There are lots of ways I could go about solving this problem. I could do the method above or I could multiply the first equation by -2 and add the second.
Step 3: 4x + y = 24
4x + 4 = 24
-4 -4
4x = 20
x = 5
Step 1: -2(2x – 3y = -2) → -4x + 6y = 4
Solution: (5, 4)
Step 2: -4x + 6y = 4
+ 4x + y = 24
7y= 28
→ y = 4
“I seem to find that there is only one solution to the two equations, but I wonder if I will get the same solution if I use a different method?”
If Beyonce uses a different method, would she get the same solution? Be sure to show work or explain your reasoning.
Answers
Answer:
Step-by-step explanation:
HELP!!!!!! The right circular cylinder shown has a volume of 16 cubic meters. Find its height.
A. 3 m
B. 1 m
C. 4 m
D. 2 m
Answers
Answer:
A, 3m
Step-by-step explanation:
Two athletes practice for a marathon by running back and forth on a 11-mile course. They start running simultaneously, one at a speed 2 miles faster than the other. How fast does each run if they meet 1 hr 6 minutes after starting? (The faster one is already returning at this point.) How far from the starting point do the runners meet?
Answers
Answer:
Faster runner speed: 11 mph
Slower runner speed: 9 mph
Distance from starting point: 9.9 miles
Step-by-step explanation:
Let the slower runner speed be: x
Faster runner speed: x+2
1 hour 6 minutes = 1.1 hours
Slower: 1.1(x) = 1.1x miles
Faster: 1.1(x+2) = 1.1x+2.2 miles
This means that the faster runner had gone 2.2 miles more than the slower runner.
1.1x + 2.2 > 11 miles (This is true as we know the faster runner is coming back from the 11 mile run)
1.1x > 11 - 2.2 miles
1.1x > 8.8 miles
x > 8.8 / 2.2 miles
x > 8 mph
1.1x < 11 miles (we know this is true as the slower runner has to have gone less than 11 miles as the faster runner met him on his way back)
x < 11 / 1.1 miles
x < 10 miles
8 < x < 10
Although x could be any number including decimal between 8 and 10, the obvious first answer would be 9. However we need to check if this answer is correct.
Slower runner distance to the end:
1.1(9) = 9.9 miles
11 - 9.9 = 1.1 miles
Faster runners distance from the end (when coming back)
1.1(9+2) = 1.1(11) = 12.1 miles
12.1 - 11 = 1.1 miles
The speeds 9 mph and 11 mph are now proven to be the right speeds. Using our equation before, we can figure out the distance from the starting point that they meet at. This is just how far the slower runner has gotten. So, 1.1(9) = 9.9 miles from the starting point
The runners meet at a distance of 8.8 miles from the starting point.
How to determine the time required for two runners to meet each otherAccording to statement, each runner must run back and forth on a 11-mile course. After supposing that each runner moves at constant speed, expressions for each runner are presented below:
Fast runner reaches the end
[tex](v+2)\cdot 1.1 = 11[/tex] (1)
Fast runner comes back from the end
[tex]x = \left(v+2\right)\cdot (1.1-t)-(v+2)\cdot t[/tex] (2)
Slow runner meets fast runner
[tex]x = v\cdot 1.1[/tex] (3)
Where:
[tex]v[/tex] - Speed of the slow runner, in miles per hour.[tex]t[/tex] - Comeback time of fast runner, in hours.[tex]x[/tex] - Point of the track where runners meet each other, in miles.By (1), we obtain the speed of the slow runner:
[tex]v = \frac{11}{1.1}-2[/tex]
[tex]v = 8\,\frac{mi}{h}[/tex]
The position from the starting point is calculated by (3):
[tex]x = (8\,mi)\cdot \left(1.1\,h\right)[/tex]
[tex]x = 8.8\,mi[/tex]
The runners meet at a distance of 8.8 miles from the starting point. [tex]\blacksquare[/tex]
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Wednesday: Solve for x (can't use decimals), must use the rules.
Start by: What are the missing angles of this triangle?
What in the picture hints on the answer above?
X =
16
Answers
Answer:
missing angle isosceles angle and side (a)
Pythagoras theorem
a²+a²=16²
a²=256/2
a=√128=11.3=11
Write each polynomial in factored form.
h(x) = 3x^3 + 5x^2 +9x +15
Answers
Answer:
Step-by-step explanation:
[tex]3x^3+9x+5x^2+15\\ \\ 3x(x^2+3)+5(x^2+3)\\ \\ (3x+5)(x^2+3)[/tex]
In which quadrant does the terminal side of 225° angle in standard position lie
Answers
Answer:
4 th quadrant
Step-by-step explanation:
olz make me brainliest
Find the value of x:
Geometry 6th Grade
Answers
Answer:
120°
Step-by-step explanation:
construct a line parallel to the two parallel lines through x
x = 70 + 50 = 120
can someone please help me
The measure of the angle formed at the center of anoxygen atom in a water molecule is about 105. The angles formed at each hydrogen atom are congruent. What is the size of the angle at each hydrogen atom?
Answers
Answer:
The size is 37.5 degrees
Step-by-step explanation:
The total angle in the triangle is 180
Since the other two angles are congruent. it means that they are equal
Let us call each of the angles x
Mathematically,
x + x + 105 = 180
2x = 180-105
2x = 75
x = 75/2
x = 37.5
How far is the portion of her route from D to F? Round to the nearest whole number. Explain.
Answers
Answer:
DF = 1213ft
Step-by-step explanation:
HELLO help lolllllllll
Answers
Answer:
x = 7
y = 12
Step-by-step explanation:
ABCD is a parallelogram.
Measures of opposite sides of a parallelogram are equal.
Therefore,
2y - 18 = y - 6
2y - y = 18 - 6
y = 12
2x + 2 = y + 4
2x + 2 = 12 + 4
2x = 16 - 2
2x = 14
x = 14/2
x = 7
In equilateral triangles STU:
Answers
==========================================================
Explanation:
Equilateral triangles have three equal sides, ie the sides are all the same length.
Let's set sides ST and TU equal to each other and solve for x
7x-10 = 2x+25
7x-2x = 25+10
5x = 35
x = 35/5
x = 7
Then we use this to compute each side
ST = 7x-10 = 7*7-10 = 49-10 = 39TU = 2x+25 = 2*7+25 = 14+25 = 39US = x^2 - 10 = 7^2 - 10 = 49-10 = 39Each side is 39 units long, so this confirms we have the correct answer.
Lin's father is paying for a $20 meal. He has a 30%-off coupon for the meal. After the discount, a 8% sales tax is applied.
What does Lin's father pay for the meal? Just type the number answer (without the dollar sign), and be prepared to explain or
show your reasoning.
Answers
Answer:
15.12
Step-by-step explanation:
Cost of meal = $20
Discount (coupon) = 30%
Amount of discount = 30% of $20
= 30/100 * 20
= 0.3 * 20
= $6
Amount paid after discount= initial cost of meal - discount
= $20 -$6
= $14
Sales tax =8%
Amount of sales tax = 8% of $14
= 8/100 * 14
= 0.08 * 14
= $1.12
Total amount paid = Amount paid after discount + Amount of sales tax
= $14 + $1.12
= 15.12
PLEASE HELP I HAVT A 25 IN MATH
A college student shovels driveways to cover his weekly expenses. The student charges $7 for each hour he spend shoveling driveways
Which 2 unknown quantities in this situation are related?
A. The number of hours the student spends shoveling driveways
B. The number of driveways the student shovels
C. The amount of money the student earns
D. The number of college students shoveling driveways
Answers
Answer:
B and D.
Step-by-step explanation:
Hope this helps! :D
please help!! i’ll give you brainliest
Answers
Answer:
Step-by-step explanation:
The common ratio is 3, so multiply the numbers of the pattern by 3. So 1x3 is 3, 3x3 is 9, 9x3 is 27, 27x3 is 81, 81x3 is 243, and just continue until you're on the 7th number; 1 was the first, 3 was the second and 9 was the third.
What is an equation of the line that passes through the points (6,8) and (-3,2)?
Answers
Answer:
y=2/3x+4
Step-by-step explanation:
(6, 8) where x1 = 6 and y1 = 8
(-3, 2) where x2 = -3 and y2 = 2
Slope (m) = (y2-y1) / (x2-x1)
= (2-8) / (-3-6)
= -6 / -9
= 2/3
2. Use point-slope formula
y-y1=m(x-x1)
y-8=2/3(x-6)
y-8=2/3x -4
y = 2/3x + 4 :)
1 less than 1/4 Question: Peggy is pp years old. Maggie is 11 year less than \frac{1}{4} 4 1 of Peggy's age. What is Maggie's age in terms of p? ___ years
Answers
Answer:
[tex]M=\dfrac{(p-44)}{4}\ \text{years}[/tex]
Step-by-step explanation:
Given that,
Peggy is p years old.
Maggie is 11 year less than 1/4 of Peggy's age.
It means,
Maggie's age,
[tex]M=\dfrac{1}{4}\times p-11\\\\M=\dfrac{p}{4}-11\\\\M=\dfrac{(p-44)}{4}[/tex]
So, Maggie's age is [tex]\dfrac{(p-44)}{4}[/tex] years.
Which of the following describes the graph of y- V8x--64 - 5 compared to the parent cube root function?
O stretched by a factor of 2 and translated 64 units right and 5 units down
O stretched by a factor of 8 and translated 8 units right and 5 units down
O stretched by a factor of 2 and translated 8 units right and 5 units down
O stretched by a factor of 8 and translated 64 units right and 5 units down
Answers
Answer: option 4
Step-by-step explanation:
The transformation of the parent function is stretched by a factor of 2 and translated 8 units right and 5 units down
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the parent function be represented as f ( x )
Now , the value of f ( x ) = ∛x
And , the given function is y = ∛ ( 8x - 64 ) - 5
On simplifying , we get
Taking 8 as the common factor , we get
y = ∛ 8 ( x - 8 ) - 5
Now , the cube root of 8 is 2
So , y = 2∛(x - 8 ) - 5
The transformed function is y = 2∛(x - 8 ) - 5
And , the transformation is a vertical stretching by a factor of 2
And , a horizontal right shift by 8 and a vertical down shift by 5
Hence , the transformation of function is stretching by a factor of 2 and translated 8 units right and 5 units down
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Are the two triangles similar? If so, why
are
they similar?
Answers
Answer:
They aren't similar.
i need help with this equation ASAP pls: If you know that log5 x – logs 12 = 0, which of the following is false?
a. log5 (x – 12) = 0
b. logs (1)
= 0
c. log5 x = logs 12
d. x = 12
Answers
Answer:
the second is false
Step-by-step explanation:
because oe would match unlike 2
How to sketch an angle in standard position
Answers
Answer:
Drawing an angle in standard position always starts the same way, draw the initial side along the positive x-axis. To place the terminal side of the angle, you must calculate the fraction of a full rotation the angle represents.
Answer:
Get the number of rotations of the given angle by dividing 360 degrees with respect to positive x-axis.
Step-by-step explanation:
1. First draw a horizontal line (along x-axis).
2. Locate the terminal side of the angle by dividing 360 degrees. Recall that one full rotation is equal to 360 degrees. So, to sketch 360 degrees, we will divide it by 360 degrees resulting in 1.
3. Similarly to draw 180 degrees, divide 180 by 360. This will result in 1/2. Therefore, it is half the way from x-axis.
Helpp I’ll mark you brainlist
Answers
Answer: 1
hope it help
Alex dumped out his piggy bank and there were only
nickels, dimes, and quarters.
There were three times as many dimes as nickels, and 40
more quarters than nickels.
If the total amount of money was $17.20, how many of each
type of coin were there?
"There are
nickels,
dimes, and
quarters.
Answers
Answer:
12 nickels
36 dimes
52 quarters
Step-by-step explanation:
Let x = no. of nickels
3x = no. of dimes
x + 40 = no. of quarters
5x = value of the nickels since each nickel is 5 cents
10(3x) = 30x = value of the dimes since each dime is 10 cents
25(x + 40) = 25x + 1000 = value of the quarters since each quarter is 25 cents
Now, 5x + 30x + 25x + 1000 = 1720 ($17.20 = 1720 cents)
60x + 1000 = 1720
60x = 720
x = 12 nickels
3x = 36 dimes
x + 40 = 52 quarters
Check: 12 nickels are worth $.60
36 dimes are worth $3.60
52 quarters are worth $13
.60 + 3.60 + 13 = 17.20
Adam earn $25 per week for allowance plus an additional $10 per yard he mows around the neighborhood. Write an inequality to represent how many lawns Adam would have to mow in one week if he needs to earn more than $150 for a new bicycle. *Use y for the variable
Answers
10 is the variable in this case, he gets $10 per lawn.
25 is the constant because he gets a fixed value of $25 in a week.
Both of these values have to be greater than or equal to $150 if he wants enough for the new bike.
Can anyone tell me the area? I will give brainlist if I'm able to
Answers
Answer:
143 yds^2
Step-by-step explanation:
The image shows two angle measures. Which equation can be used to find the
value of x?
2x - 15 = 45
2x - 15 = 135
2x - 15 + 135 = 90
2x - 15 + 131 = 360
Answers
Answer:
(2x-15) = 45
Step-by-step explanation:
When two angles lie on a straight line, they are supplementary
what this mean is that the add up to equal 180 degrees
Mathematically, we have this as:
(2x-15) + 135 = 180
(2x-15) = 180-135
(2x-15) = 45
Answer:
Step-by-step explanation:
(2x-15) = 45
Step-by-step explanation:
When two angles lie on a straight line, they are supplementary
what this mean is that the add up to equal 180 degrees
Mathematically, we have this as:
(2x-15) + 135 = 180
(2x-15) = 180-135
(2x-15) = 45
8.12
Given the diagram below, what is cos(45") ?
450
Triangle not drawn to scale
A. 2-3
B. 4/2
C.
D. JE
Answers
The value of cos 45° in the given triangle is 1/√2, Option C is correct.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
In the given right triangle the hypotenuse is 8√2
In the given triangle the two legs are equal.
Let x be the length of the two legs
By Pythagoras theorem, let us find the length of a leg.
x²+x²=(8√2)²
2x²=64(2)
2x²=128
Divide both sides by 2
x²=64
Take square root on both sides
x=8
Now let us find the cosine function, the ratio of adjacent side and hypotenuse
cos45 = 8/8√2
=1/√2
Hence, the value of cos 45° in the given triangle is 1/√2, Option C is correct.
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Rita paid $82 for 5 trees and 1 shrub. Lilly bought 2 trees and 1 shrub for $37. Find the cost per tree and the cost per shrub.
Answers
Answer:
trees cost $15
Shrub cost $7
Step-by-step explanation:
Given data
Rita paid $82 for 5 trees and 1 shrub
5x+y= 82---------1
Lilly bought 2 trees and 1 shrub for $37
2x+y= 37----------2
from 1
y= 82-5x
put the value of y in 2
2x+82-5x= 37
2x-5x= 37-82
-3x=-45
x= 45/3
x=$15
put the value of x in 1
5(x)+y= 82
5*15+y=82
75+y=82
y=82-75
y=$7
Hence, trees cost $15
Shrub cost $7
Which point is located on the x-axis?
ТУ
D
A
B
3+
2
1
1
-4-3-2-1
-1
1
2
2
3
4 x
-2
-3+
-4
ОА
ОВ
Answers
Answer:
Point C
Step-by-step explanation:
Point C is located on the x-axis.
Help me work out the equation of the line on this graph. I'll give out the brainiest!
Answers
Answer:
y=-1/4x+2
Step-by-step explanation:
The equation would be y=-1/4x+2 because the rise is -1 and the run is 4 (you could also say the run is -4 and the rise is 1. It doesn't really matter). The line also crosses the y axis at 2, which means that 2 is the y-intercept. :)
Answer:
y = (-1/4)x +2
Step-by-step explanation:
Having the actual graph is an easy way to calculate the equation of the line. Since the format is y = mx +b we just need to plug in numbers.
b = y-intercept
m = slope
We can automatically see that the y-intercept is 2, so b = 2. To find the slope we just calculate rise over run. The line is decreasing 1 unit for every 4 units it is "running". Therefore, -1/4 is your slope.
b = 2
m = -1/4
Now, all we need to do is plug in numbers.
y = (-1/4)x +2
Can someone help me with 9,10, and 11 please you don’t have to do all of them just atleast one for me
Answers
Hi! So what you will need to know is pythagorean theorm.
What the theorm basically says is a^2 + b^2 = c^2.
-- The (a,b,c) are referring to the sides of the triangles (3 letters for 3 sides).
Take note that "c" is always the side opposite of the right angle.
The other known side could be "a" or "b"
Taking a look at problem 9, identify the "c" value. The "c" value would be 35.
Then indentify the value of "b" or "a". "a" would = 20.
Plug it into the equation:
20^2 + b^2 = 35^2
400 + b^2 = 1225
solve for b.
1. subtract 400 from both sides.
b^2 = 825
b = [tex]\sqrt{825}[/tex]
you could solve for the square root but it would give a decimal numbers but I'm not sure what the teacher is looking for.