Answer:
yes it is a solution
Step-by-step explanation:
o>-4
0<1
yes both work out to be equal
Answer:
It is a solution
Step-by-step explanation:
Check and see if (0,0) satisfies both inequalities.
The first inequality is:
[tex]y \geqslant {x}^{2} + x - 4 [/tex]
When we put x=0, and y=0, we get:
[tex]0\geqslant {0}^{2} + 0 - 4[/tex]
[tex] \implies0\geqslant- 4[/tex]
This part is true.
The second inequality is:
[tex]y \leqslant {x}^{2} + 2 x + 1[/tex]
We put x=0 and y=0 to get:
[tex]0 \leqslant {0}^{2} + 2 (0) + 1[/tex]
[tex]0 \leqslant 1[/tex]
This part is also true.
Since the (0,0) not satisfy both, inequalities, it is a solution.
if A= [-5,7] and B= [6,10], then find A u B
Answer:
[tex]\large\boxed{A\ \cup\ B=[-5,\ 10]}[/tex]
Step-by-step explanation:
Look at the picture.
The union of two sets A and B (A ∪ B) is the set of elements which are in A, in B, or in both A and B
What is the multiplicative inverse of −3/5?
Answer:
The multiplicative inverse is -5/3
Step-by-step explanation:
Multiplicative inverse means we want to end up with 1
-3/5 * what =1
Multiply by 5 to clear the fraction
-3/5 * what *5 = 1*5
-3 * what = 5
Divide by -3 to isolate what
-3*what /-3 = 5/-3
what = -5/3
The multiplicative inverse is -5/3
choose the equation that represents a line that passes through points -3,2 and 2,1
5x+y=-13
5x-y=17
x-5y=-13
x+5y=7
Answer:
D. X+5y=7
passes through both coordinates
Answer:
all work is shown and pictured
which of the following functions is graphed below
Answer:
B
Step-by-step explanation:
The vertex form of an absolute value function is f(x)=a|x-h|+k where (h,k) is the vertex.
a is positive means the absolute value function will face up.
a is negative means the absolute value function will face down.
So looking at the picture we see the vertex is (2,3) and all of the choices have a is 1.
So plugging in 2 for h and 3 for k and 1 for a into f(x)=a|x-h|+k
f(x)=|x-2|+3.
B.
The correct function represent in the graph are,
⇒ y = |x - 2| + 3
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The graph of the function shown in image.
Now, Let the parent function is,
⇒ y = |x|
Clearly, the function is move 2unit left and 3 unit up.
Hence, The correct function represent in the graph are,
⇒ y = |x - 2| + 3
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Rewrite each sum as a product of The GCF of the addends and another number 9 + 27
Answer:
9*4
Step-by-step explanation:
We can Factor out a 9 from each term
9 + 27
9 (1+3)
9 (4)
9*4
Which of the following describe an angle with a vertex at E?
Check all that apply.
O A. ZEFD
OB.HDEF
OC. ZFED
D. ZDFE
SUBMIT
Answer:
The answer would be option B and option C
∠DEF and ∠FED describe an angle with a vertex at E.
The correct answers are option (B) and option (C)
What is an angle?"It is the figure, in which two rays meet at a common point.""The common point is called the vertex.""It is denoted using the symbol ∠ "For given question,
We need to find the correct angle with a vertex at E.
We know that the vertex is the common point of the rays of an angle.
It is always written at the middle in an angle.
So, ∠DEF and ∠FED describe an angle with a vertex at E.
The correct answers are option (B) and option (C)
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Given: x + 5 > 10.
Choose the graph of the solution set.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{x + 5}\ >\huge\text{ 10}[/tex]
[tex]\huge\text{First you'll need to SUBTRACT by 5}[/tex][tex]\huge\text{on each of your sides!}[/tex]
[tex]\huge\text{x + 5 - 5}>\huge\text{ 10 - 5}[/tex]
[tex]\huge\text{Cancel out: 5 - 5 because it equals to 0}[/tex]
[tex]\huge\text{Keep: 10 - 5 because it gives us the result of 5}[/tex]
[tex]\huge\text{x}>\huge\text{5}[/tex]
[tex]\huge\text{It's an (o)(p)(e)(n)(e)(d) circle} \checkmark[/tex]
[tex]\huge\text{Starts off with \#5}\checkmark[/tex]
[tex]\boxed{\boxed{\huge\text{Answer: A.}}}[/tex] [tex]\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Answer:
[tex]\Large\textnormal{A. First graph}[/tex]
Step-by-step explanation:
[tex]\Large\textnormal{First, subtract by 5 from both sides of equation.}[/tex]
[tex]\displaystyle x+5-5>10-5[/tex]
[tex]\Large\textnormal{Then, simplify, to find the answer.}[/tex]
[tex]\displaystyle 10-5=5[/tex]
[tex]\Large \boxed{x>5}[/tex], which is our answer.
[tex]\Large\textnormal{The correct answer is A.}[/tex]
Find the diagonal of a square whose sides are of the given measure. Given = 3sqrt2
ANSWER
The diagonal of the square is 6 units.
EXPLANATION
A diagonal of a square divides the square into two congruent right isosceles triangles.
Let the sides of the square be 's' units. Then, the Pythagoras Theorem says that, the sum of the squares of the shorter legs will be equal to the square of the hypotenuse.
Let the diagonal which is the hypotenuse be 'd' units.
Then,
[tex] {d}^{2} = {s}^{2} + {s}^{2} [/tex]
[tex] \implies \: {d}^{2} = 2{s}^{2}[/tex]
From the question, the side length of the square is
[tex]s = 3 \sqrt{2} \: units[/tex]
We plug in this value to obtain:
[tex]\implies \: {d}^{2} = 2{(3 \sqrt{2} )}^{2}[/tex]
Or
[tex]\implies \: {d}^{2} = 2 \times { {3}^{2} (\sqrt{2} )}^{2}[/tex]
[tex]\implies \: {d}^{2} = 9 \times 2 \times 2 = 36[/tex]
We take the positive square root of both sides to get:
[tex]d = \sqrt{36} [/tex]
[tex]d = 6 \: units[/tex]
Find the coordinates of the midpoint of the segment whose endpoints are H(2,1) and K(10,7)
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ H(\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad K(\stackrel{x_2}{10}~,~\stackrel{y_2}{7}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{10+2}{2}~~,~~\cfrac{7+1}{2} \right)\implies \left( \cfrac{12}{2}~,~\cfrac{8}{2} \right)\implies (6,4)[/tex]
A country's population in 1990 was 46 million.
In 2002 it was 49 million. Estimate
the population in 2006 using the exponential
growth formula. Round your answer to the
nearest million.
P= Aekt
Answer:
50 million
Step-by-step explanation:
You don't need to go to the trouble to find the value of k in e^(kt). Rather, you can use the given ratio directly.
When t = years after 1990, the population of 49 million took 12 years to achieve. The estimate desired is for 16 years after the year 1990. The appropriate exponential formula for the population is ...
P = 46·(49/46)^(t/12)
Then for t=16, this is ...
P = 46·(49/46)^(16/12) ≈ 50.04 . . . . million
The population in 2006 is estimated at 50 million.
_____
The form of the exponential equation we used above is ...
f(x) = (baseline value)·(ratio to baseline)^(x/(interval corresponding to ratio))
evaluate 11 C4 and 1 P4
Answer:
Step-by-step explanation:
11C4 = 11! / (7!*4!) = 11 * 10 * 9 * 8 * 7!/ 7! * 4!
11C4 = 11*10 * 9 * 8 / 24
11C4 = 11*10 * 3
11C4 = 330
========
You can't do the second one. Permutations and Combinations always give an answer greater than 1 and integers.
If the price of 1 dozens of apples is Rs 84, find the price of 4 apples.
Answer:
The price of 4 apples is Rs 28
Step-by-step explanation:
The price of 1 dozen apple is Rs 84
12 apples =Rs 84
1 apple = Rs 84÷12
1apple =Rs 7
Again
Price of 4 apples = Rs 7 × 4
= Rs 28 Ans,,
if f(x)=4x^+1 and g(x)=x^-5, find (f-g)(x)
Answer:
(f-g)(x) = 4x - x^(-5)
Step-by-step explanation:
Please, enclose that negative exponent inside parentheses: g(x)=x^(-5). No need to type in the " + " in f(x)=4x^+1.
g(x) is to be subtracted from f(x). Write f(x):
f(x)=4x
followed by the negative of g(x): -g(x) = -x^(-5)
and now combine these two results:
f(x)=4x
-g(x)= -x^(-5)
---------------------
(f-g)(x) = 4x - x^(-5)
The expression for (f-g)(x) is (f-g)(x) = 4x² + 1 - 1/x⁵
What is a function?A function is a mathematical formula that describes how the dependent variable and independent variable are related. The dependent variable's value varies in the function together with the independent variable's value.
To find (f-g)(x), we need to subtract g(x) from f(x):
(f-g)(x) = f(x) - g(x)
We are given:
f(x) = 4x² + 1
g(x) = x⁻⁵ = 1/x⁵
Substituting these values into the expression for (f-g)(x), we get:
(f-g)(x) = f(x) - g(x) = (4x² + 1) - (1/x⁵)
Simplifying the expression, we can write:
(f-g)(x) = 4x^2 + 1 - 1/x⁵
Therefore, the expression for (f-g)(x) is:
(f-g)(x) = 4x² + 1 - 1/x⁵
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solve the equation
[tex]16 {}^{2x - 3} = 8 {}^{4x} [/tex]
Answer:
n = -3Step-by-step explanation:
[tex]16=2^4\\\\8=2^3\\\\16^{2n-3}=8^{4n}\\\\(2^4)^{2n-3}=(2^3)^{4n}\qquad\txt{use}\ (a^n)^m=a^{nm}\\\\2^{(4)(2n-3)}=2^{(3)(4n)}\iff4(2n-3)=12n\qquad\text{use the distributive property}\\\\(4)(2n)+(4)(-3)=12n\\\\8n-12=12n\qquad\text{subtract}\ 8n\ \text{from both sides}\\\\-12=4n\qquad\text{divide both sides by 4}\\\\\dfrac{-12}{4}=\dfrac{4n}{4}\\\\-3=n\to n=-3[/tex]
graph the linear equation -4y=-5x-18
Answer:
The graph intersect the y-axis at (0,4.5)
The graph intersect the x-axis at (-3.6,0)
Step-by-step explanation:
The equation is;
-4y=-5x-18
Dived every term by -4
[tex]\frac{-4y}{-4} =\frac{-5x}{-4} -\frac{18}{-4} \\\\\\y=\frac{5}{4}x+\frac{9}{2}[/tex]
plot using a graph tool to view the liner graph as below
What is the value of A?
Answer:
101
Step-by-step explanation:
The theorem to use this is the intercepted arc theorem, which tells us that if we take 2 points on the circumference of a circle and create an angle in the opposite side of the circumference, that angle is HALF that of the ARC intercepted.
If we look at 100 degree angle, we see the ARC intercepted is 99 degree and a degrees. According to theorem, we can say:
99 + a = 2(100)
99 + a = 200
a = 200 - 99
a = 101
Which of the following is not equal to the other values? cos31.7° cos211.7° cos328.3° cos(-391.7°)
Answer:
* cos 211.7 not equal the other values
Step-by-step explanation:
* Lets revise the angles in the four quadrant
- If the angle in the first quadrant is Ф, then the equivalent angles to
it in the other three quadrant are
# 180° - Ф ⇒ 2nd quadrant (sin only +ve)
# 180° + Ф ⇒ 3rd quadrant (tan only +ve)
# 360° - Ф ⇒ 4th quadrant (cos only +ve)
# -Ф ⇒ 4th quadrant (cos only +ve)
# -180 + Ф ⇒ 3rd quadrant (tan only +ve)
# -180 - Ф ⇒ 2nd quadrant (sin only +ve)
# -360 + Ф ⇒ 1st quadrant (all are +ve)
* Lets solve the problem
∵ Ф = 31.7°
∵ cos 31.7 = +ve value
∵ 180° + Ф° = 180° + 31.7° = 211.7°
∵ cos (180° + Ф°) = - cos Ф° ⇒ cos (180° + Ф°) in the 3rd quadrant is
same value as cos Ф but with -ve sign
∴ cos 211.7° = - cos 31.7°
∴ cos 31.7° ≠ cos 211.7°
∵ 360° - Ф° = 360° - 31.7° = 328.3°
∵ cos (360° - Ф°) = cos Ф° ⇒ cos (360° - Ф°) in the 4th quadrant has the
same value and sign with cos Ф°
∴ cos 328.3° = cos 31.7°
∴ cos 31.7° = cos 328.3°
∵ -391.7° + 360° = -31.7° ⇒ more then clockwise turn by 31.7°
∵ cos (-Ф°) = cos Ф° ⇒ cos (-Ф°) in the 4th quadrant has the same value
and sign with cos Ф°
∴ cos (-31.7°) = cos 31.7°
∴ cos 31.7° = cos (-390.7°)
* cos 211.7 not equal the other values
Use the drawing tool(s) to form the correct answer on the provided graph.
Plot a point at the y-intercept of the following function on the provided graph.
3y = -5^x + 7
Answer:
The y-intercept is the point (0,2)
see the attached figure
Step-by-step explanation:
we have
[tex]3y=-5^{x}+7[/tex]
we know that
The y-intercept is the value of y when the value of x is equal to zero
so
For x=0
substitute in the equation and solve for y
[tex]3y=-5^{0}+7[/tex]
[tex]3y=-(1)+7[/tex]
[tex]3y=6[/tex]
[tex]y=2[/tex]
therefore
The y-intercept is the point (0,2)
using a graphing tool
see the attached figure
Answer: For Plato users plot a point on 2 at the y intercept.
Step-by-step explanation:
A farmer is tracking the amount of corn his land is yielding each year. He finds that the function f(x) = −x2 + 20x + 50 models the crops in pounds per acre over x years. Find and interpret the average rate of change from year 1 to year 10. The crop yield increased by 9 pounds per acre from year 1 to year 10. The crop yield decreased by 0.09 pounds per acre from year 1 to year 10. The crop yield decreased by 11 pounds per acre from year 1 to year 10. The crop yield increased by 99 pounds per acre from year 1 to year 10.
Answer: The crop yield increased by 9 pounds per acre from year 1 to year 10.
Step-by-step explanation:
To solve this we are using the average rate of change formula: Av=\frac{f(x_2)-f(x_1)}{x_2-x_1}, where:
x_2 is the second point in the function
x_1 is the first point in the function
f(x_2) is the function evaluated at the second point
f(x_1) is the function evaluated at the first point
We know that the first point is 1 year and the second point is 10 years, so x_1=1 and x_2=10. Replacing values:
Av=\frac{-(10)^2+20(10)+50-[-(1)^2+20(1)+50]}{10-1}
Av=\frac{-100+200+50-[-1+20+50]}{9}
Av=\frac{150-[69]}{9}
Av=\frac{150-69}{9}
Av=\frac{81}{9}
Av=9
Since f(x) represents the number of pounds per acre and x the number of years, we can conclude that the crop yield increased by 9 pounds per acre from year 1 to year 10.
If the 7th of an AP is equal to 11 times the 11th term, find the 18th term
Answer:
-33 or 33
Step-by-step explanation:
The seventh term of an AP is written as:
[tex]a + 6d[/tex]
The eleventh term of an AP is written as:
[tex]a + 10d[/tex]
If the 7th term is 11 times the 11th term, then;
[tex]a + 6d = 11(a + 10d)[/tex]
Expand to get:
[tex]a + 6d = 11a + 110d[/tex]
[tex]11a - a = 6d - 110d[/tex]
[tex]10a = - 104d[/tex]
[tex] \frac{a}{d} = - \frac{104}{10} [/tex]
[tex] \frac{a}{d} = - \frac{52}{5} [/tex]
We must have a=-52 and d=5
Or
a=52 and d=-5
For the first case, the 18th term is :
[tex] - 52 + 5 \times 17 = 33[/tex]
For the second case,
[tex]52 - 5 \times17 = - 33[/tex]
Use the Pythagorean theorem to find x and round to the nearest tenth.
A. 3.61
B. 3.6
C. 9.22
D. 9.2
Final answer:
The Pythagorean theorem relates the lengths of the legs and hypotenuse of a right triangle. By substituting the given values into the equation, we can solve for x using the theorem. The rounded value of x is 3.6 (B).
Explanation:
The Pythagorean theorem relates the length of the legs of a right triangle, labeled a and b, with the hypotenuse, labeled c. The relationship is given by: a² + b² = c². This can be rewritten, solving for c: c = √(a² + b²).
In this case, we want to find the value of x using the Pythagorean theorem. Let's say that the lengths of the legs are 3 and x. Substituting these values into the theorem, we have:
3² + x² = c²
Now, we can solve for x by rearranging the equation:
x² = c² - 3²
x = √(c² - 3²)
Rounding to the nearest tenth, we can find the value of x to be approximately 3.6 (B).
Final answer:
The Pythagorean theorem allows us to calculate the length of the hypotenuse of a right triangle by squaring the lengths of the other two sides, adding them together, and then taking the square root. To round to the nearest tenth, we calculate and then round the final result accordingly.
Explanation:
To use the Pythagorean theorem to find x and round to the nearest tenth, we need to establish the components of the equation. The theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). The formula is written as a² + b² = c².
However, the problem provided does not include the initial lengths to insert into the equation; hence, we cannot compute the value directly. Nonetheless, I can illustrate with a hypothetical example:
If we have a right triangle with legs of lengths 9 (a) and 6 (b), then the hypotenuse (c) can be found as follows:
c = √(9² + 6²)
c = √(81 + 36)
c = √117
c = 10.82, round off to the nearest tenth would be c = 10.8
In this example, we squared the lengths of the legs, added them together, and took the square root of the result to find the hypotenuse to the nearest tenth. The same steps apply to any right-angled triangle where you are given the lengths of the legs and need to find the hypotenuse using the Pythagorean theorem.
3! + 0! / 2! * 1! =
a). 3/2
b). 3
c). 7/2
Answer:
6.5
Step-by-step explanation:
3! = 6
0! = 1
2! = 2
1! = 1
6 + 1/2*1 = 6.5
So all of the given answers are wrong.
What is the average rate of change for this quadratic function for the interval from x=-5 to x=-3?
Answer:
C 8
Step-by-step explanation:
The average rate of change is given by
f(x2) -f(x1)
---------------
x2-x1
x2 = -3 and x1 = -5
Looking at the graph
f(x2) = f(-3) = 1
f(x1)= f(-5) =-15
Substituting these values into the equation
1 - (-15)
---------------
-3 - (-5)
1+15
----------
-3 +5
16
----
2
8
Answer: OPTION C.
Step-by-step explanation:
You need to use this formula:
[tex]averate\ rate\ of\ change=\frac{f(b)-f(a)}{b-a}[/tex]
Knowing that we need to find the average rate of change for the given quadratic function, for the interval from [tex]x=-5[/tex] to [tex]x=-3[/tex], we need to find their corresponding y-coordinates.
We can observe in the graph that:
For [tex]x=b=-5[/tex] → [tex]y=f(b)=-15[/tex]
For [tex]x=a=-3[/tex] → [tex]y=f(a)=1[/tex]
Therefore, substitituting, we get:
[tex]averate\ rate\ of\ change=\frac{-15-1}{-5-(-3)}=8[/tex]
Choose the function that the graph represents.
Click on the correct answer.
y = f(x) = log1x
y = f(x) = x4
y = f(x) = log(1/4)*
Final answer:
To identify which function the graph represents, analyze the shape and pattern of the graph. The correct function could either be a polynomial such as y = x^4, which has a sharply rising curve, or a logarithmic function with a declining curve due to having a base between 0 and 1, like y = log(1/4)x, but not y = log1x as this is not mathematically valid.
Explanation:
The question requires the identification of a function based on its graph. Since the properties of functions are known, such as the logarithmic function increasing as x increases, and the behavior of exponential functions and their inverses, we can analyze the options given. The function y = log1x is not valid as the base of a logarithm cannot be 1. The function y = x4 is a polynomial function with a graph that rises sharply for positive and negative values of x. Lastly, y = log(1/4)x represents a logarithmic function with base 1/4, which is a declining curve because the base is between 0 and 1.
To choose the correct function that a graph represents, one should look for key characteristics such as the shape of the graph, increase or decrease pattern, as well as specific points like asymptotes or intercepts. If the graph is increasing as x increases and resembles a typical logarithmic curve, the correct choice is a logarithmic function. If the given graph is a sharp rising curve for all x-values and looks like a polynomial, then y = x4 would be correct. The given functions need to be analyzed based on their mathematical properties to select the one that best describes the graph in question.
Suppose you invest $300 at annual interest rate of 4.5% compounded continuously.
How much will you have in the account after 7.5 years?
Answer:
[tex]\$420.43[/tex]
Step-by-step explanation:
we know that
The formula to calculate continuously compounded interest is equal to
[tex]A=P(e)^{rt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
[tex]t=7.5\ years\\ P=\$300\\ r=0.045[/tex]
substitute in the formula above
[tex]A=300(e)^{0.045*7.5}[/tex]
[tex]A=\$420.43[/tex]
Match each of the following types of angles to the correct definition.
Answer: There Ya go
Explanation:
The difference of Mai's age and 12 is 60
so shes 72 i think
hope i'm right
Answer: 58 would be my guess, but need more info
HHHEEELLLPPP!!!! MY ENTIRE SUMMER DEPENDS ON THIS!!
IF YOU CAN’T LEGITIMATELY ANSWER, DON’T BOTHER EVEN TRYING.
Test to see how many boxes of Lucky Chocolate Oat Crunch need to be purchased to collect all eight dinosaurs. Use the spinner provided to simulate the purchase of the cereal boxes. Each time the spinner is spun, it represents the purchase of one cereal box. As you spin, you will need to keep track of your results. You will use the results to compute the experimental probability, which you will compare with the theoretical probability. Use the spinner below to determine how many boxes of cereal you might need to purchase to collect all eight dinosaurs. Continue until the spinner has landed on each dinosaur once. Be sure to stop spinning once the spinner has landed on each dinosaur one time. Each number on this spinner represents a different dinosaur. You need to complete the simulation three times. That is, after each dinosaur has been spun one time, record your results. Then, create a new chart for the next set of results. When you are finished, you will have three sets of data that will most likely not match.
(ALREADY COMPLETED THIS PART, THE CHARTS ARE BELOW)
Use all three sets of data to answer the following questions in complete sentences. For this exercise, the probabilities refer to the probability of getting any one dinosaur when making any one purchase. You do not need to determine the probability of the compound event of getting all eight of the dinosaurs. Make sure to have all three simulations done to help you answer these questions in the writer's box:
(NEED HELP WITH THIS. ANSWERED A FEW ALREADY, NEED HELP WITH THE ONES SHOWN)
1. How does the number of spins correlate to the number of boxes of cereal that you would need to purchase?
2. What was the experimental probability for EACH dinosaur from Trial 1? Trial 2? Trial 3?
3. How does the experimental probability of getting each dinosaur differ from the theoretical probability? Here, you are comparing the experimental vs. theoretical probability of getting each type of dinosaur in a single purchase. In other words, you are determining the probability for a single event, not a compound event.
4. If someone bought eight boxes of cereal and got all eight dinosaurs, would you be surprised? Why or why not?
5. How did the experimental probabilities change between the trials?
6. What are the advantages of using a simulation versus actually buying boxes of cereal?
have you finished this yet? im doing it rn and i need help on some of them. if you havent i can help you with a couple answers
¿Cuál de las siguientes funciones es una función constante? Seleccione una: a. Y=x+1 b. Y=x+2 c. X=y+3 d. Y=3
Answer:
Option D y=3
Step-by-step explanation:
The question in English is
Which of the following functions is a constant function?
we know that
A constant function is a function whose output value is the same for every input value
so
Verify each case
case A) y=x+1
This is not a constant function, this is a linear equation
Is a function whose output value is different for every input value
case B) y=x+2
This is not a constant function, this is a linear equation
Is a function whose output value is different for every input value
case C) x=y+3
This is not a constant function, this is a linear equation
Is a function whose output value is different for every input value
case D) y=3
This is a constant function
Is a function whose output value is the same for every input value
In a circle, a 90° sector has area 167 ft2. What is the radius of the circle?
Answer:
[tex] \sqrt{\frac{668}{\pi} } [/tex] feet given the area is 167 ft squared
Step-by-step explanation:
Since our sector as a central angle of 90 degree then it is only a 4th of the whole circle. The area of a circle is pi*r^2. We will only be using a 4th of that since are sector is only a 4th of the circle.
So the formula will be using for the area of our sector is A=1/4 *pi*r^2.
We are given the area is 167 so replace A with 167.
167=1/4 * pi *r^2
Multiply both sides by 4.
167*4 =pi * r^2
668=pi * r^2
Divide both sides by pi
668/pi =r^2
Square root both sides
[tex] \sqrt{\frac{668}{\pi} } =r [/tex]