what is the solution to x^2 = 121?
Answer: {11, -11}
Step-by-step-explanation: To solve for x in this equation, since x is squared, we simply take the square root of both sides of the equation to get x by itself.
It's important to remember however that when taking the square root of both sides of an equation, we always use plus or minus.
In other words in this problem, since x² = 121,
x = + or - 11.
A common mistake is to say that x is just equal to 11. But notice that if you plug a -11 back into the original equation, it also checks.
So our answer to this problem is {11, -11}.
Answer: either 11 or -11
Step-by-step explanation:
you have to square root both sides. Then, you are left with the equation [tex]\sqrt{x^{2} } = \sqrt{121}[/tex]. That means that x either equals to 11 or -11.
:)
2c = 112
A. c = 2
B. c = 42
C. c = 56
D. C = 224
Answer:
The answer is C. 56
Step-by-step explanation:
So if we replace C with 56, the equation would look like this, 2(56)=112.
determine the value of a so that when P(x)=a^2 x^3-3ax+1 is divided by x-2 there is no remainder
Turner mesuares 3/4 foot of a ribbon for a coustume. He needs 9 pieces of ribbon with the same length
Answer:
6¾
Step-by-step explanation:
¾ * 9/1 = 287/4
27/4=6 ¾
which equals 6.75
A combination lock uses 4 numbers, each of which can be 0 to 33. If there are no restrictions on the numbers, how many possible combinations are available?
Answer:
Solution for A combination lock uses 3 numbers, each of which can be 0 to 33. If there are no restrictions on the numbers, how many possible ...
Step-by-step explanation:
Find the domain of the rational function 9x/(x+5)(x+3)
Answer:
the domain is : D = ]-∞ , -5[ U ]-5 , -3[ U ]-3 , +∞[
Step-by-step explanation:
hello :
f(x) = 9x/(x+5)(x+3)
f exist for : (x+5)(x+3) ≠ 0
(x+5)(x+3)=0
x+5=0 or x+3=0 means : x= - 5 or x= -3
the domain is : D = ]-∞ , -5[ U ]-5 , -3[ U ]-3 , +∞[
what is the "X" in x2 − 70 = –69 plz need asap
Answer:
1,-1
Step-by-step explanation:
Answer:
X = 1/2
Step-by-step explanation:
x2 = -69 + 70
x2 = 1
x = 1/2
In the diagram below, what is the approximate length of the minor arc DE?
А. 6.3 cm
В. 3.1 cm
с. 5.2 cm
D. 7.9 cm
Answer:
6.3cm
Step-by-step explanation:
The approximate length of the minor arc DE will be 6.3 cm. Then the correct option is A.
What is a circle?It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
Then the angle is subtended by the arc is 36° and the radius of the circle is 10 cm.
Then the length of the arc DE will be
[tex]\rm ARC = \dfrac{\theta }{360} \times 2\pi r[/tex]
Then we have
[tex]\rm ARC = \dfrac{36}{360} \times 2\pi \times 10\\\\ARC = 6.283 \approx 6.3\ cm[/tex]
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Felix's parents opened a savings
account for him when he was born with
a $2,000 deposit. The account earns 6%
compound interest, compounded
annually. How much money will be in
Felix's account when he is 21?
The money in the Felix's account will be $6798 when he is 21.
Step-by-step explanation:
It is given that,
The amount deposited is $2000.The account earns 6% compound interest.It is compounded annually for 21 years.To find the money in Felix's account after 21 years :
The formula used here is,
⇒ [tex]A = P(1+r/n)^{nt}[/tex]
where A is the amount after 21 years.
P is the initial amount deposited ⇒ P = 2000r is the rate ⇒ r = 0.06n is the number of times interest is compounded per year⇒ n = 1 t is the time period ⇒ t = 21⇒ [tex]2000(1+0.06/1)^{21\times 1}[/tex]
⇒ [tex]2000(1.06)^{21}[/tex]
⇒ [tex]2000\times3.399[/tex]
⇒ [tex]6798[/tex]
Therefore, The money in the Felix's account will be $6798 when he is 21.
Which BEST describes the representation of the data on the given graph?
A) The graph represents the data appropriately.
B) The graph is misleading because the size of the sample is not shown.
C) The graph is misleading because the vertical scale does not begin at 0.
D) The graph is misleading because the scale is disproportional to the data.
Answer:
A) The graph represents the data appropriately.
Step-by-step explanation:
The graph above is a true representation of data showing the percent of political parties people who agreed with court.
From the graph above, three categories of political parties people are concerned; which are, the Democrats, the Republicans and the Independents.
It can therefore be deduced that 62% of the Democrats agreed with court. By implication, the percent of the Democrats who disagreed with court is 38%. Conversely, 54% of people agreed with court for both the Republicans and the Independents respectively. This implies that the percent of both the Republicans and the Independents who did not agree with court is 46% respectively.
However, the graph fails to provide us with information about what the people agree on; probably the outcome of an election or appointment of a minister.
The graph is not misleading in any way and it is not necessary that the vertical scale begin at zero. Therefore, the data represents the graph appropriately.
The supply and demand curves for a product line of bicycles are shown. Approximately where is the equilibrium point?
Answer:
The answer is B (132,220)
Step-by-step explanation:
I got it correct on the test
Plato tests
The required equilibrium point for the supply and demand curves for a product line of bicycles is (135, 225).
What is the graph?The graph is a demonstration of curves that gives the relationship between the x and y-axis.
here,
The graph shows the supply and demand curves for a product line of bicycles.
To determine the equilibrium point we to locate the intersection point of supply and demand.
From the graph, the intersection point is (135, 225), which is the approximate equilibrium point.
Thus, the required equilibrium point for the supply and demand curves for a product line of bicycles is (135, 225).
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What number must you add to complete the square?
x^2+12x=5
Answer:
36
Step-by-step explanation:
12/2 = 6
6^2 = 36
A pool is in the shape of a rectangular prism. On Monday, water was pumped out of the pool at a constant rate, starting at 12:00pm. At 12:15 pm, the water in the pool was 45 inches deep. At 12:35 pm, the water in the pool was 41 inches deep.
Part A
How many inches does the depth of the water decrease each minute?
Part B
Write an equation that represents y, the depth of the water (in inches) after x minutes.
Answer:
the equation is y = (-2/15 in/min)x + 43 in
Step-by-step explanation:
We'll represent elapsed time with the letter t. Then 12 p.m. corresponds to t = 0 sec. Between 12 p.m. and 12:15 p.m., the change in time was 15 min and the change in water depth was (45 - 41) in., or 4 in.
Thus, the water depth changes by 4 in (a decrease) over 30 min.
Part A: The water depth rate of change is -4 in/30 min, or -2 in/15 min, or
(-2/15 in)/min (the depth is decreasing).
Part B: We need to derive a linear function that describes the water depth at any given time x (or t). Two points on the graph of this line are
(15 min, 45 in) and (35 min, 41 in): the 'run' is 30 min and the 'rise' is -4 in.
As in Part A, the slope of this line is (-2/15 in)/min.
The desired equation is then y = mx + b, or 45 in = (-2 in/15 min)(15 min) + b, or 45 in = 2 in + b, or 43 in = b. Then, in its most general form,
the equation is y = (-2/15 in/min)x + 43 in
i really need help :( i dont get help from anyone :(
Answer:
D.) 12x -6x 90
Step-by-step explanation:
because it's right angle
A car traveling 9/10 of a mile per minute will travel _____ miles in 10 minutes
Answer:
It will travel 9 miles in 10 minutes
Step-by-step explanation:
A car travels 9/10 miles/minute
In 10 minutes, it will travel
10*9/10 = 9 miles
Final answer:
A car traveling at 9/10 of a mile per minute will travel 9 miles in 10 minutes by simply multiplying the car's speed by the time traveled.
Explanation:
To calculate how far a car traveling at a speed of 9/10 of a mile per minute will travel in 10 minutes, we simply multiply the speed of the car by the amount of time it travels.
Speed of car = 9/10 mile/minute
Time = 10 minutes
Distance traveled = Speed of car × Time
Distance traveled = (9/10) mile/minute × 10 minutes
Now we perform the multiplication:
Distance traveled = 9/10 × 10
Distance traveled = 9 miles
(giving 30 points/need answers STAT!!)
Four transformations of the function f(x) = 3x + 2 are given below.
For each transformation, drag the expression that shows the result of that transformation into the box under it.
Transformations can be applied to functions to change the appearance of
the (slope and intercept) of the function.
The result of the transformation are presented as follows;
[tex]\begin{tabular}{|c|c|c|c|}f(x-5)&f(x) - 5&-5 \cdot f(x) &f(-5\cdot x)\\3\cdot (x - 5) + 2&3 \cdot x - 5 + 2&-5\cdot (3 \cdot x + 2)&3 \cdot (-5\cdot x) + 2 \end{array}\right][/tex]Reasons:
The given function is; f(x) = 3·x + 2
The function -5·(3·x + 2) is the same as -5 × f(x) = -f(x)
Therefore;
-5·(3·x + 2) → -5·f(x)
The function 3·x - 5 + 2 = 3·x + 2 - 5 = f(x) - 5
Therefore;
3·x - 5 + 2 → f(x) - 5
The function 3·(x - 5) + 2 by comparison to 3·x + 2 is obtained when x is replaced by (x - 5), therefore;
f(x) = 3·x + 2
f(x - 5) = 3·(x - 5) + 2
3·(x - 5) + 2 → f(x - 5)
The function 3·(-5·x) + 2 is obtained when x in f(x) is replaced by (-5·x),
which gives;
f(x) = 3·x + 2
∴ f(-5·x) = 3·(-5·x) + 2
Which gives;
3·(-5·x) + 2 → f(-5·x)
The completed table is therefore;
[tex]\begin{tabular}{|c|c|c|c|}f(x-5)&f(x) - 5&-5 \cdot f(x) &f(-5\cdot x)\\3\cdot (x - 5) + 2&3 \cdot x - 5 + 2&-5\cdot (3 \cdot x + 2)&3 \cdot (-5\cdot x) + 2 \end{array}\right][/tex]
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The exponential function g(x) is shown on the graph. Suppose f(x) = x. Which statement is true when comparing the domain of f(x) to the domain of g(x)?
A) The domain for both functions is all positive numbers.
B) The domain for both functions is all integers.
C) The domain for both functions is all real numbers.
D) The domain for both functions is all real numbers greater than 0.
Answer: The domain for real numbers
Step-by-step explanation: taking it right now
The domain for both functions g(x) and f(x) is all real numbers. Then the correct option is C.
What is a domain?The domain means all the possible values of the x.
The exponential function g(x) is shown on the graph.
Suppose f(x) = x.
Then the domain of the function g(x) is a real number.
And the domain of the function f(x) is also a real number.
Then the domain for both functions is all real numbers.
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Which of the following formulas could be used to find the perimeter, P, of a regular hexagon? plz
Answer:
Just add up all the sides and you get the perimeter.
I need help:
The width of this rectangle is 1/3 of the length. Find the length and the width of the rectangle.
Answer:
3(y-4) =2y+6
3y - 12 = 2y +6
y = 18
so length is 42 in.
width is 14 in.
After solving the given equations, the length of the rectangle is 42 inches and the width of the rectangle is 14 inches.
What is an equation?Equations are mathematical expressions that have two algebra on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.
The given data in the question,
According to the given diagram,
Length of the rectangle, L = 2y + 6 inches (i)
Width of the rectangle, W = y - 4 inches (ii)
The width of the rectangle is 1/3 of the length,
1/3(2y + 6) = (y - 4)
2y + 6 = 3y - 12
y = 18.
Substitute y = 18 in equation (i)
L = 2(18) + 6
L = 42 inches
Substitute y = 18 in equation (ii)
W = (18 - 4)
W = 14 inches.
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Two of the world's longest rivers are the Nile, which is 4100 miles long, and the Rio
Grande, which is 1900 miles long. Find how much longer the Nile is than the Rio
Grande.
Answer:
The Nile River is 2,200 miles longer than the Rio Grande.
Step-by-step explanation:
4100-1900=2200
Answer:
Answer:
The Nile River is 2,200 miles longer than the Rio Grande.
Step-by-step explanation:
4100-1900=2200
Step-by-step explanation:
What is the positive negative square roots of 64?
The answer explains the positive and negative square roots of 64.
When dealing with the square roots of a number like 64, remember that the square root of 64 is 8, both positive and negative. This is because (-8) x (-8) equals 64 just like (8) x (8) equals 64, following the rule that multiplying two negative numbers results in a positive number.
Calculate the number in the middle of -4 and 5
Answer:
0.5 is in the middle plz give branliest
Step-by-step explanation:
The distance between the numbers is 9
so if you divide them in half, you get 4.5
add 4.5 to -4 or subtract it from 5 to get 0.5
Simplify 3 x y x 2 x y x 4 x y
Answer:
24y
Step-by-step explanation:
y*y*y = y^3 (y to the power of 3)
3*2*4 = 24
then your left with 24 times y^3 which is 24y^3
Hope this helps!
The expression 3 x y x 2 x y x 4 x y when simplified is 24y³
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
3 x y x 2 x y x 4 x y
Evaluate the product of similar variables
So, we have
3 x y x 2 x y x 4 x y = 24 x y x y x y
Evaluate the remaining product of similar variables
So, we have
3 x y x 2 x y x 4 x y = 24y³
Hence, the product is 24y³
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3x-4y=1 and x=2y+1 using substitution
Answer:
x =-1
y =-1
Step-by-step explanation:
to solve this system of equation, using substiution method
3x-4y=1 ........................ equation 1
x=2y+1 ............................ equation 2
subbstitute for x into equation 1
3x-4y=1 ........................ equation 1
3(2y + 1) - 4y = 1
6y + 3 -4y = 1
2y + 3 = 1
collect the like terms
2y = 1- 3
2y= -2
divide both sides by the coefficient of y which is y
2y/2 = -2/2
y = -1
put the value of y =-1 into equation 2
x=2y+1 ............................ equation 2
x = 2(-1) + 1
x = -2 + 1
x = -1
therefore x =-1 y = -1
Whitch fraction is equivalent to 5/20
Answer:
1/4
Step-by-step explanation:
5/20
Divide the top and bottom by5
1/4
If anyone answers ALL i will give all my points and will give Brainliest
Answer:
too compelx illegal
Step-by-step explanation:
I’m lost and unsure what is the first step to do find width of da roof
Answer:
You set up an equation, using the trig function "tan" to find half of the roof (the equation would be tan(24) = 3.5/x, where x = 1/2 roof width)
Step-by-step explanation:
That would be the first step.
You solve the equation for x, and then multiply x by 2 to get the width of the roof.
Which set of values makes the inequality n > -5 true?
{-5, -5.5, -6}
{-5, -4.5, -3)
{-6,0,5}
{-6, -7,-8}
Answer:
all false
Step-by-step explanation:
n > -5
{-5, -5.5, -6} False cannot = -5 ( all are greater than or equal to -5)
{-5, -4.5, -3) False cannot = -5
{-6,0,5} False cannot = -6
{-6, -7,-8}False these are less than -5
j/15=20 what does j equal?
Answer:
j=300
Step-by-step explanation:
You multiply each side by 15.
j=300
Answer:
j should equal 300.
Step-by-step explanation:
j/15=20
you have to get j by its self. what you do to one side you must do to the other.
j/15(15) = 20(15)
the fifteens cancel out
j=300
(9+q)(8-q)= polynomial in standard form
Answer:
- q² - q + 72
Step-by-step explanation:
To express the given expression as a polynomial in standard form, we would first multiply the individual elements in one parenthesis with the elements in the second.
We would then rearrange the outcome and simplify it algebraically.
The arrange it in the order of the unknown variable.
As such,
(9+q)(8-q) = 9(8-q) +q(8-q)
= 72 -9q + 8q - q²
= 72 - q - q²
= - q² - q + 72
To form the expression (9+q)(8-q) into a polynomial in standard form, we multiply the terms using the distributive property to get -q² - q + 72.
The student has asked for the expansion of a binomial expression into polynomial form, in this case, expanding (9+q)(8-q). The process involves using the distributive property, also known as the FOIL method (First, Outer, Inner, Last), to multiply each term in the first binomial by each term in the second.
Expanding the binomials, we have:
First: 9 × 8 = 72
Outer: 9 × (-q) = -9q
Inner: q × 8 = 8q
Last: q × (-q) = -q²
Combining like terms (-9q and 8q) gives -q and then adding to the remaining terms, we have:
72 - q - q²
Reordering to get the polynomial in standard form (highest degree first), the result is:
-q² - q + 72