Find the solution(s) to the system of equations represented in the graph. (5 points)
Answers
Answer:
(0, -2) and (2, 0)
Step-by-step explanation:
The solution to a systems of equations is when the x and y values are equal for two equations. This can also been seen as when the two equations intersect. So by looking at the graph you see the line and the circle intersect at the point (2, 0) and (0, -2) which are going to be the two solutions to the systems of equations.
Related Questions
the domain a function g(x) is x > 3, and the range is y> 1. What are the The domain of
domain and range of its
inverse function, g
(x)?
Answers
The domain of a function is the range of its inverse, and vice versa.
So, the domain is [tex]x > 1[/tex] and the range is [tex]y > 3[/tex].
1
10 ft
Cone 1
2.5 ft
8 ftl
2 ft
Cone 2
Answers
Rate can be found by dividing like measurements of the figure
8/10 and 2/2.5 both equal .8
So to check your work, if you apply the rate to cone 1 = 10 x .8 = 8, and 2.5 x .8 = 2
Problem solved
Suppose that the breaking strength of a rope (in pounds) is normally distributed, with a mean of 100 pounds and a standard deviation of 16. What is the probability that a certain rope will break before being subjected to 120 pounds? (You may need to use the standard normal distribution table. Round your answer to four decimal places.)
Answers
The probability that a certain rope will break before being subjected to 120 pounds is 89.4%.
What is the probability that a certain rope will break before being subjected to 120 pounds?The probability is calculated as follows:
Mean = 100
Standard deviation = 16
The probability is obtained from the z-score.
x = mean + z-score * standard deviation
120 = 100 + z-score * 16
z-score = 20/16
z-score = 1.25
From normal distribution table, the probability with a z-score of 1.25 is 89.4%
In conclusion, the probability is obtained from the z-score.
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Evaluate the sum (for math nerds)
[tex]i {}^{0!} + i {}^{1!} + i {}^{2!} + i {}^{3!} + ... + i {}^{100!} [/tex]
Note that :
[tex]i = \sqrt[]{ - 1} [/tex]
Answers
Answer: i+96
Step-by-step explanation:
Note that [tex]i^{4k}[/tex], where k is an integer, is equal to 1.
This means that [tex]i^{4!}=i^{5!}=i^{6}=\cdots=i^{99!}+i^{100!}=1[/tex]
So, we can rewrite the sum as [tex]i^{1}+i^{1}+i^{2}+i^3+97(1)=i+i-1-i+97=i+96[/tex]
[tex]n![/tex] is divisible by 4 for all [tex]n\ge4[/tex]. This means, for instance,
[tex]i^{4!} = \left(i^4\right)^{3!} = 1^{3!} = 1[/tex]
[tex]i^{5!} = \left(i^4\right)^{5\times3!} = 1^{5\times3!} = 1[/tex]
etc, so that [tex]i^{n!} = 1[/tex] for all [tex]n\ge4[/tex].
Meanwhile,
[tex]i^{0!} = i^1 = i[/tex]
[tex]i^{1!} = i^1 = i[/tex]
[tex]i^{2!} = i^2 = -1[/tex]
[tex]i^{3!} = i^6 = (-1)^3 = -1[/tex]
Then the sum we want is
[tex]i^{0!} + i^{1!} + i^{2!} + i^{3!} + 97\times1 = i + i - 1 - 1 + 97 = \boxed{95+2i}[/tex]
Find the constant of variation when t varies directly as the square of s, and t = 64 when S = 4.
Answers
Answer:
The constant of variation is 4
Step-by-step explanation:
We are looking for the constant of variation when t varies directly as the square of s
t = k s^2 where k is the constant of variation
t = 64 and s = 4
64 = k 4^2
64 = k * 16
Divide each side by 16
64/16 = k * 16/16
4 = k
The constant of variation is 4
Which of the following graphs includes the possible values for the number of people who still need to sign up for the team?
Number line with closed circle on 5 and shading to the left
Number line with closed circle on 5 and shading to the right.
Number line with open circle on 5 and shading to the left.
Number line with open circle on 5 and shading to the right.
Answers
The graph that includes the possible values for the number of people who still need to sign up for the team is:
Number line with closed circle on 5 and shading to the right.
What is the situation and which inequality models it?Researching this problem on the internet, a team currently has 4 players, and needs at least 9.
When x players are signed, the number of players will be of 4 + x. Since the team needs at least 9 players, the inequality is:
[tex]4 + x \geq 9[/tex]
The solution is:
[tex]x \geq 9 - 4[/tex]
[tex]x \geq 5[/tex]
Which is represented as follows:
Number line with closed circle on 5 and shading to the right.
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A party platter contains 38 cupcakes: 13 chocolate, 11 yellow, and 14 lemon. You randomly select one cupcake, eat it, then randomly select another cupcake. Find the probability of selecting from the platter a chocolate cupcake and then a yellow cupcake.
Answers
The probability of selecting from the platter a chocolate cupcake and then a yellow cupcake is 0.10.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability of selecting a chocolate cupcake and then a yellow cupcake = (number of chocolate cupcake / total number of cupcakes) x (number of yellow cupcakes / total number of cupcakes - 1)
(13 / 38) x (11 / 37) = 0.10
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f(x)=2^x. What is g(x)?
Answers
The function g(x) is g(x)= (3x)^2
How to solve for g(x)?The complete question is in the image
From the graph in the image, we have:
f(x) = x^2
The function f(x) is stretched by a factor of 3 to form g(x).
This means that:
g(x) = f(3x)
So, we have:
g(x)= (3x)^2
Hence, the function g(x) is g(x)= (3x)^2
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What can you say about the y-values of the two functions f(x) = 3x² -3 and
g(x) = 2* - 3?
A. g(x) has the smallest possible y-value.
B. The minimum y-value of g(x) approaches -3.
C. f(x) and g(x) have equivalent minimum y-values.
D. f(x) has the smallest possible y-value.
Answers
The y-values of the two functions f(x) = 3x² -3 and g(x) = 2* - 3 has the minimum y-value of g(x) approaches -3 and f(x) contains the smallest possible y-value.
What is a function?It exists described as a special kind of relationship and they contain a predefined domain and range according to the function every value in the domain exists connected to just one value in the range.
Given: f(x) = 3x² -3
As we can see in the graph the first term exists 3x² and exists still positive for all x.
The range for f(x) ∈ [-3, ∞)
When x = 0 then f(x) = -3
The above value exists as the smallest possible value on the y-axis.
Given: [tex]g(x) = 2^x - 3[/tex]
[tex]2^x[/tex] exists also a positive quantity and it exists as an exponential function.
The range for the g(x) ∈ (-3, ∞)
It signifies that g(x) never touches the y-axis at -3.
We can express the minimum value of g(x) approaches -3.
Therefore, the correct answer is option B. The minimum y-value of g(x) approaches -3 and option D. f(x) has the smallest possible y-value.
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On average, an American hummingbird flaps its wings about 3,180 times per minute.
About how many times per second does it flap its wings?
Enter your answer in the box.
times
Answers
Answer:
53 times per second
Step-by-step explanation:
There are 60 seconds in 1 minute, so divide the 3180 flaps per minute into 60 equal parts.
3180 / 60 = 53
x is directly proportional to y. When x = 4, y = 7. Work out the value
of y when x = 12
Answers
Answer:
y = 21
Step-by-step explanation:
When x is directly proportional to y:
When x increases, y also increases.
In this case, it is so you write,
1. Write down the formula: y=kx
k being the constant.
Let's use "When x = 4, y = 7" to work out the constant.
2. Substitute the 'when' values: 7=k×4
3. Rearrange to find the constant: 7÷4=k
4. Find k: k=1.75
Now let's see the new problem, 'what is y when x = 12'.
5. Substitute the values now but keep the constant: y = 1.75 × 12
6. Rearrange if needed.
7. Find the missing value: y = 21
Hope this helped and if you require further assistance from me please comment below! :)
Ps: If it was inversely proportional then the formula would be y = k / x
with k still being the constant.
5. a. The area of an isosceles triangle is 60cm² and its base is 10cm. Find the length of its equal side.
Answers
Answer:
H = 12cm
b
I hope I was able to help
What is the midpoint of the line segment graphed below?
Answers
Answer:
(4, 7/2)
Step-by-step explanation:
midpoint = x values/2, y values/2
0.1in has 4 threads how many threads are in 1 inch?
Answers
Answer:
40
Step-by-step explanation:
Set up a proportion
Inch/ threads = inch to threads
.1/4 = 1/x Cross multiple
.1x = 4 Divide both sides by .1
x = 40
What is the slope of the line containing (-2, 5) and (4,-4)?
A. 2
OB.
mle
O C. - /3/20
D. -2
Answers
Answer:
-1.5
Step-by-step explanation:
To work out the gradient of the line, we use this equation:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
Substituting in, we get:
[tex] \frac{5 - ( - 4)}{ - 2 - 4} [/tex]
Which simplifies to:
[tex] \frac{9}{ - 6} = \frac{3}{ - 2} = - \frac{3}{2} = - 1.5[/tex]
Simplify the following
Answer is 6
Answers
Firstly changing mixed fraction.
[tex] \frac{3}{2} - \frac{5}{4} + \frac{23}{4} [/tex]
By taking the LCM
[tex] \frac{6 - 5 + 23}{4} [/tex]
-5 + 23 (-) (+) = (-)
[tex] \frac{6 + 18}{4} [/tex]
[tex] \frac{24}{4} [/tex]
[tex]6[/tex]
Hope it helps you, any confusions you may ask!
Answer:
6 (work below)
Step-by-step explanation:
1 1/2 = 3/2
1 1/4 = 5/4
5 3/4 = 23/4
The least common multiple of the denominators is 4, so 3/2 will become 6/4.
6/4 - 5/4 = 1/4 + 23/4 = 24/4 = 6
Brainliest, please :)
Help me please!!!!!!!!
Answers
Answer:
The ratios are not equal, so this is not a dilation.
Step-by-step explanation:
4/3 is the first ratio
3/4 is the second ratio
Since these ratios are not equal there is not a dilation.
as part of a competition, diego must spin around in a circle 6 times and then run to a tree. the time he spends on each spin is represented by S AND THE TIME HE SPEND RUNNING is R. He gets to the tree 21 seconds after he starts spinning. If it takes diego 1.2 seconds to spin around each time, how many seconds did he spend running
Answers
The time he spent running is 13.80 seconds.
How much time did he spend running?
The equation that can be used to represent the time he gets to the tree is:
Time he gets to the tree = (time of each spin x total spins) + time he spent running
21 = (6 x 1.2) + r
21 = 7.20 + r
r = 21 - 7.20
r = 13.80 seconds
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Determine an approximate value for y if the coordinate (-0.5387 ,y) is on the unit circle
Answers
Answer:
y = 0.8425 or y = -0.8425
Step-by-step explanation:
All points in the Cartesian coordinate system have an x and y coordinate, defined by two perpendicular measurements.
If the point is on the unit circle, then the radius of the circle is defined to be 1 unit, and the corresponding right triangle follows the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
For a unit circle:
[tex]x^2+y^2=1^2[/tex]
Substituting the known value for x, and simplifying...
[tex](-0.5387)^2+y^2=(1)^2[/tex]
[tex]0.29019769+y^2=1[/tex]
Subtracting 0.29019769 from both sides to begin to isolate "y"...
[tex]y^2=1-0.29019769[/tex]
[tex]y^2=0.70980231[/tex]
Applying the square root property...
[tex]\sqrt{y^2}=\pm \sqrt{0.70980231}[/tex]
[tex]y=\pm 0.8424976171...[/tex]
So, (to 4 decimal places), the y coordinate could be either 0.8425 or -0.8425.
With only the given information, either result is a valid answer.
what is the sum of .74+.19+3.09+1.98=
Answers
Answer:
6
Step-by-step explanation:
no calculator at hand ?
really ? you are using us a simple calculator ?
Answer:
6
Step-by-step explanation:
what is the sum of .74+.19+3.09+1.98=
0.74+
0.19+
3.09+
1.98=
-----------------
6
3 5/6 + 2 4/9 in its simplest form
Answers
Answer:
>> [tex]6\frac{5}{18}[/tex]
Step-by-step explanation:
1) Add the whole numbers first.
[tex]5+\frac{5}{6} +\frac{4}{9}[/tex]
2) Find the Least Common Denominator (LCD) of [tex]\frac{5}{6} ,\frac{4}{9}[/tex] . In other words, find the Least Common Multiple (LCM) of [tex]6,9[/tex].
Method 1: By Listing Multiples
1. List the multiples of each number.
Multiples of 6 : 6, 12, 18, ...
Multiples of 9 : 9, 18, ...
2. Find the smallest number that is shared by all rows above. This is the LCM.
LCM = 18
3. Make the denominators the same as the LCD.
[tex]5+\frac{5\times 3}{6\times 3}+\frac{4\times 2}{9\times 2}[/tex]
4. Simplify. Denominators are now the same.
[tex]5+\frac{15}{18}+\frac{8}{18}[/tex]
5. Join the denominators.
[tex]5+\frac{15+8}{18}[/tex]
6. Simplify.
[tex]5+\frac{23}{18}[/tex]
7. Convert [tex]\frac{23}{18}[/tex] to mixed fraction.
[tex]5+1\frac{5}{18}[/tex]
8. Simplify.
[tex]6\frac{5}{18}[/tex]
Decimal Form: 6.277778
Cheers.
The addition of 3 5/6 + 2 4/9 is 113/18
What is fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
3 5/6 + 2 4/9
Now, writing it into normal fraction
3 5/6 + 2 4/9
= 23/ 6 + 22/9
= 23/6 x 3/3 + 22/9 x 2/2
= 69/ 18 + 44/18
= 113/18
Hence, the addition is 113/18
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(2x + 1) (x - 1) solve for X
Answers
Put brackets equal 0
(2x + 1) (x - 1) = 0
(2x + 1) = 0
-1, then ÷2
x = - 1/2 or - 0.5
(x - 1) = 0
+1
x = 1
So, x = - 0.5 & x = 1
Hope this helps!
Answer:
x = -0.5
x = 1
Step-by-step explanation:
Hello!
We can set each factor to 0 and solve for x in both.
(2x + 1) = 02x = -1
x = -0.5
(x - 1) = 0
x = 1
There are 2 solutions for x, -0.5 and 1.
Which function below has the following domain and range?
Domain: {-9, - 5, 2, 6, 10}
Range: { -2, 0, 8}
O {(-9, 10), (-2,8)}
O ((-9, -2), ( – 5, 0), (2, 8), (6, 5), (10, 9))}
O ((-2,-5), (8, 10), (0, 6), (-2, -9), (0, 2)}
O {(2,0), (-5, -2), (10, 8), (6, 0), (-9, -2)}
Answers
{(2,0),(-5,-2),(10,8),(6,0),(-9,-2)} is the correct answer (D)
Answer:
(d) {(2, 0), (-5, -2), (10, 8), (6, 0), (-9, -2)}
Step-by-step explanation:
The domain is the list of x-values. The range is the list of y-values. You are looking for the set that matches the given lists.
ChoicesA.The list of x-values is {-9, -2}. The list is too short.
B.The list of x-values is {-9, -5, 2, 6, 10}. This matches the required domain.
The list of y-values is {-2, 0, 8, 5, 9}. The list is too long.
C.The list of x-values is {-2, 8, 0, -2, 0}. The list does not match the given domain list.
D.The list of x-values is {2, -5, 10, 6, -9}. This matches the given domain.
The list of y-values is {0, -2, 8, 0, -2}. This matches the given range.
The function of interest is ...
{(2, 0), (-5, -2), (10, 8), (6, 0), (-9, -2)}
Suppose that the functions p and q are defined as follows. p(x)=x+1
q(x)=2x^2-2
Answers
The value of (p*q)(5) and (q*p)(5) is 288
How to determine the composite functions?The functions are given as:
p(x)=x+1
q(x)=2x^2-2
Calculate p(5) and q(5)
p(5)=5+1 = 6
q(5)=2(5)^2-2 = 48
The functions are then calculated as:
(p*q)(5) = p(5) * q(5)
(p*q)(5) = 6 * 48
(p*q)(5) = 288
Also, we have:
(q*p)(5) = (p*q)(5)
(q*p)(5) = 288
Hence, the value of (p*q)(5) and (q*p)(5) is 288
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Complete question
Suppose that the functions p and q are defined as follows. p(x)=-x-1 q(x)=-2x^2-2 Find the following. (p*q)(5) (q*p)(5)
please help!!!!!!nnnn
Answers
Similar: yes
Similarity statement: [tex]ADCB \sim SVUT[/tex]
Scale factor: 1/3
could anyone help me with this?
Answers
Answer:
Step-by-step explanation:
A=6x²
[tex]\frac{dA}{dt} =6\times 2x \times \frac{dx}{dt} \\\frac{dA}{dt}=12x \frac{dx}{dt}[/tex]
find the product xy if
2^(x)+3^(y)=5,
2^(x+2)+3^(y+1)=18
Answers
The solution to the system of equation is (0, 1)
System of equationsGiven the following system of equation as shown below
2^(x)+3^(y)=5,
2^(x+2)+3^(y+1)=18
Rewrite
2^(x)+3^(y)=5,
2^x*2^2 + 3^y*3^1 = 18
___________
2^(x)+3^(y)=5,
4(2^x) + + 3(3^y) = 18
Let a = 2^x and b = 3^y
Substitute
a + b = 5
4a + 3b = 18
a = 5 - b
Substitute
4(5-b) + 3b = 18
20 - 4b + 3b = 18
-b = -2
b = 2
since a = 5 - b
a = 5 - 2
a = 3
Recall that a = 2^x and b = 3^y
2^x = 2
x = 0
Similarly
3^y = 3
y =1
Hence the solution to the system of equation is (0, 1)
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Please tell me fast I am on a time crunch
Answers
Solve for the inequality x
A tower is composed of a prism with a square base and a pyramid. The base length is 20 meters, and the height of the prism is 40 meters, while the slant height of the pyramid is 10√2 meters. What is the total surface area, including the bottom base? 400√2 + 3,600 m2 200√2 + 3,600 m2 400√2 + 400 m2 4000√2 m2
Answers
The total surface area of the tower composed of a prism with a square base and a pyramid is 3600 + 400√2 m²
How to find the surface are of a composite figure?Total surface area of the tower = area of the base + 4(area of the rectangular surface) + 4(area of the triangular surface)
Therefore,
area of the base = 20² = 400 m²
4(area of the rectangular surface) = 4(40 × 20) = 3200 m²
4(area of the triangular surface) = 4(1 / 2 × 10√2 × 20) = 4(100√2) = 400√2 m²
Therefore,
total surface area = 400 + 3200 + 400√2
total surface area = 3600 + 400√2 m²
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Answer:
a)400V2 plus 3,600 m2
Step-by-step explanation:
A closed box has a square base with side length ll feet and height hh feet. Given that the volume of the box is 29 cubic feet, express the surface area of the box in terms of ll only.
Answers
The surface area of the closed box in terms of l only, which has the square base is,[tex]2l^2 + \frac{116}{l}[/tex]
How to determine the surface areaThe volume of cuboid or box can be given as,
Volume = l × b × h
Here, (l) is the length, (b) is the width of the box and (h) is the height of the box.
A closed box has a square base with side length l feet and height h feet. Therefore, the length and width will be the same.
Then the volume of the box is 29 cubic feet. Thus,
29 = l × l × h
29 = [tex]l^2 h[/tex]
[tex]h = \frac{l^2}{29}[/tex]
The surface area of the square base box is,
Area = [tex]2l^2 + 4lh[/tex]
Substitute the value of h
Area = [tex]2l^2 + 4l\frac{29}{l^2}[/tex]
Area = ,[tex]2l^2 + \frac{116}{l}[/tex]
Therefore, the surface area of the closed box in terms of l only, which has the square base is,[tex]2l^2 + \frac{116}{l}[/tex]
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