Answer:
Third option. I am sure it!
Step-by-step explanation:
Mark other guy brainliest. He's a great answer and he helped me before
Answer:
The third option choice
Step-by-step explanation:
Here you have the term (n^-6)(p^3)
(n^-6)(p^3) = (n^-6)(p^3)/1
[And whole number can be written over 1. For example, 4 = 4/1.]
You can see that n has a negative exponent, -6.
My teacher taught it to me like this:
If this is our expression;
(n^-6)(p^3)
--------------- <------ [and thats a fraction bar]
1
Think of the fraction bar as a bunk bed. Since the (n^-6) isn't happy being "on top of the bunk bed," [since its a negative exponent] move it to the bottom bunk.
So your new expression would be:
(p^3)
-------------- <-------- [fraction bar]
(n^6)
Moving n^6 to the bottom changes it into a positive exponent.
So, the third option choice would be correct.
That's the best way I can explain it! I hope this helps!!! :)
To solve the equation |x-6|= 0.5x, Kiana graphed the functions F(X) = |x-6|
and G(X) = 0.5x on the same set of coordinate axes. She then found that the
graphs intersected at the points (4, 2) and (12, 6). Finally, she concluded that
the solutions of the equation |X-6|= 0.5x are x = 4 and x = 12. Which of the
following reasons best justifies Kiana's conclusion?
Answer:
F(4) = G(4) and F(12) = G(12) ⇒ answer B
Step-by-step explanation:
* Lets explain the meaning of the common solutions of two equation
- If two equations intersect at one point, (x , y) where x and y have the
same values for both equations
- The point (x , y) belongs to the two graphs
- Ex: If (2 , 3) is a common solution of f(x) and g(x) , then the graphs of
f(x) and g(x) meet each other at the point (2 , 3) that means f(2) = 3
and g(2) = 3
- So f(2) = g(2)
* Lets solve the problem
∵ F(x) = Ix - 6I
∵ G(x) = 0.5 x
∵ The two graphs intersected at points (4 , 2) and (12 , 6)
- That means the two points (4 , 2) and (2 , 6) on the two graphs
∴ F(4) = 2 and G(4) = 2
∴ F(12) = 6 and G(12) = 6
- That means the two points are common solutions for both equations
∴ The solutions of the equation |x - 6|= 0.5 x are x = 4 and x = 12
∴ F(4) = G(4) and F(12) = G(12)
∴ The best reasons which justifies Kiana's conclusion is;
F(4) = G(4) and F(12) = G(12)
- Look to the attached graph to more understanding
- The red graph is F(x)
- The blue graph is G(x)
The best justification of Kiana's conclusion is ; F(4) = G(4) and F(12) = G(12) Option B
How to answer the problemThe justification for Kiana's conclusion is that the values of x and y at the points of intersection are the same for both equations.
This means that the point (x, y) belongs to both graphs.
For example, if (2, 3) is a common solution of f(x) and g(x), then the graphs of f(x) and g(x) intersect at the point (2, 3), which implies that f(2) = 3 and g(2) = 3. Therefore, f(2) = g(2).
To solve the problem at hand, we have
F(x) = |x - 6| and G(x)
= 0.5x.
Given that the two graphs intersect at the points (4, 2) and (12, 6),
Consequently, F(4) = 2 and G(4) = 2, as well as
F(12) = 6 and
G(12) = 6.
These common solutions indicate that the solutions of the equation
|x - 6| = 0.5x are
x = 4 and x = 12.
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what is the probability that a customer ordered a small given they ordered a hot
Answer:
.05
Step-by-step explanation:
See The attachment for explanation
Hope it helps you...☺
Follow the steps for division.
27/6
18. What is the y-intercept of the graph of the function y = 3x + 2x - 13?
[tex]y=3\cdot0 + 2\cdot0 - 13=-13[/tex]
The y-intercept is [tex](0,-13)[/tex]
Jillian is trying to save water, so she reduces the size of her square grass lawn by 8 feet on each side. The area of the smaller lawn is 144 square feet. In the equation
(x – 8)2 = 144, x represents the side measure of the original lawn.
What were the dimensions of the original lawn?
4 feet by 4 feet
8 + feet by 8 +
8 feet by 8 +
20 feet by 20 feet
Answer:
20 by 20
Step-by-step explanation:
the new dimensions have to be 12 because 12×12 =144 so you would add 8 to 12 and get 20 for each side
Answer:
D) 20 feet by 20 feet
Step-by-step explanation:
Given:
The area of the original grass lawn reduced by 8 feet on each side.
The smaller lawn's area = 144 square feet which is represented by the equation
[tex](x - 8)^2 = 144[/tex], where "x" is the side of the original lawn.
To find the original dimension of the lawn, we need to solve for x from the above equation.
To solve follow the steps.
Step 1:
To get rid of square on the right hand side, we need to take square root on both sides.
Taking the square root on both sides, we get
[tex]\sqrt{(x - 8)^2} = \sqrt{144}[/tex]
[tex](x - 8) = 12[/tex]
Step 2:
Now add 8 on both sides, we get
x - 8 + 8 = 12 + 8
x = 20
Therefore, the original dimensions of the lawn is 20 feet by 20 feet.
What is the distance from (−4, 0) to (2, 5)? Round your answer to the nearest hundredth. (4 points)
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[2-(-4)]^2+[5-0]^2}\implies d=\sqrt{(2+4)^2+(5-0)^2} \\\\\\ d=\sqrt{36+25}\implies d=\sqrt{61}\implies d\approx 7.81[/tex]
Which point on the x-axis lies on the line that passes through point C and is parallel to line AB?
a (1,0)
b (1,1)
c (0,2)
d (2.0)
Answer:
d. (2, 0)Step-by-step explanation:
Parallel lines have the same slope.
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points A(-4, 0) and B(2, -3). Substitute:
[tex]m=\dfrac{-3-0}{2-(-4)}=\dfrac{-3}{6}=-\dfrac{1}{2}[/tex]
C(-2, 2).
The point on the x-axis D(x , 0).
The slope:
[tex]m=\dfrac{0-2}{x-(-2)}=\dfrac{-2}{x+2}[/tex]
Put the value of the slope:
[tex]\dfrac{-2}{x+2}=\dfrac{-1}{2}[/tex] change the signs
[tex]\dfrac{2}{x+2}=\dfrac{1}{2}[/tex] cross multiply
[tex]x+2=(2)(2)[/tex]
[tex]x+2=4[/tex] subtract 2 from both sides
[tex]x=2[/tex]
Helpppppppppppppp meeee
Answer:
A
Step-by-step explanation:
To evaluate h(6) substitute x = 6 into h(x), that is
h(6) = (3 × 6) - 4 = 18 - 4 = 14 → A
The function f(x) is shown below.
00W
If g(x) is the inverse of f(x), what is the value of f(g(2)) ?
[tex]f(g(x))=x[/tex] when [tex]g(x)=f^{-1}(x)[/tex]
So [tex]f(g(2))=2[/tex]
The value of f(g(2)) is 2 since g(x) is the inverse of f(x).
What is an inverse function?An inverse function that does the opposite operation of the actual function. It is denoted by f⁻¹(x).
Calculation:The given function is f(x) and g(x) is the inverse of f(x) i..e, g(x) = f⁻¹(x).
Then,
f(g(x)) = f(f⁻¹(x))
= x
Thus,
f(g(2)) = 2 (since x=2)
Therefore, the value of f(g(2)) = 2.
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A right prism has a base in the shape of an octagon. The side length of the octagon is 4 inches. The length of the apothem is 4.83 inches. The height of the prism is 12 inches. What is the volume of the prism? Round your answer to the nearest whole number.
Answer:
927 Cubic Inches.
Answer:
Area of the prism = 927 in²
Step-by-step explanation:
Area of the prism is defined by A = Area of the base × height
Since base of the prism is an octagon with side length = 4 inches
and apothem = 4.83 inches
Now area of the octagonal base = [tex]\frac{1}{2}(\text{Perimeter})(\text{Apothem})[/tex]
= [tex]\frac{1}{2}(4)(8)(4.83)[/tex]
= 77.28 inch²
Now area of the prism = 12×77.28 = 927.36 inch²
Therefore, area of the prism having base in the shape of an octagon is 927 inch²
What is 720° converted to radians
Final answer:
To convert 720° to radians, multiply by π/180 to get 4π rad. This shows that 720° is equivalent to 4π radians.
Explanation:
To convert 720° to radians, we use the relationship that 1 revolution equals 360° or 2π radians. Therefore, to convert degrees to radians, you multiply the number of degrees by π/180. In this case:
720° × (π rad / 180°) = 4π rad
Thus, 720° is equal to 4π radians. The concept of angular velocity is related to radians as it is the rate of change of an angle with time, and using radians can be especially useful in calculations involving angular motion.
What is the true solution to the logarithmic equation below?
Answer:
x = 4/9
C
Step-by-step explanation:
log_2(6x/) - log_2(x^(1/2) = 2 Given
log_2(6x/x^1/2) = 2 Subtracting logs means division
log_2(6 x^(1 - 1/2)) = 2 Subtract powers on the x s
log_2(6 x^(1/2) ) = 2 Take the anti log of both sides
6 x^1/2 = 2^2 Combine the right
6 x^1/2 = 4 Divide by 6
x^1/2 = 4/6 = 2/3 which gives 2/3 now square both sides
x = (2/3)^2
x = 4/9
Answer:
Option c
Step-by-step explanation:
The given logarithmic equation is
[tex]log_{2} (6x)-log_{2}(\sqrt{x})=2[/tex]
[tex]log_{2}[\frac{(6x)}{\sqrt{x}}]=2[/tex] [since log[tex](\frac{a}{b})[/tex]= log a - log b]
[tex]log_{2}[\frac{(6\sqrt{x})\times\sqrt{x}}{\sqrt{x}}]=2[/tex] [since x = [tex](\sqrt{x})(\sqrt{x})[/tex]]
[tex]log_{2}(6\sqrt{x} )=2[/tex]
[tex]6\sqrt{x} =2^2[/tex] [logₐ b = c then [tex]a^{c}=b[/tex]
[tex]6\sqrt{x} =4[/tex]
[tex]\sqrt{x} =\frac{4}{6}[/tex]
[tex]\sqrt{x} =\frac{2}{3}[/tex]
[tex]x=(\frac{2}{3})^2[/tex]
= [tex]\frac{4}{9}[/tex]
Option c is the answer.
Order the relative frequencies from least to greatest
Final answer:
To order the relative frequencies from least to greatest, calculate the relative frequency for each data value by dividing the frequency by the total number of data values. Then, determine the cumulative relative frequency by adding all previous relative frequencies to the relative frequency for the current row. Finally, list the data values in increasing order of their relative frequencies.
Explanation:
The given data is:
114,950; 158,000; 230,500; 387,000; 389,950; 479,000; 488,800; 529,000; 575,000; 639,000; 659,000; 1,095,000; 5,500,000
To order the relative frequencies from least to greatest, we need to determine the relative frequency for each data value. The relative frequency is found by dividing the frequency by the total number of data values. The cumulative relative frequency is the sum of all previous relative frequencies. Here are the calculations:
Relative Frequency:
114,950 : 0.00002
158,000 : 0.00003
230,500 : 0.00005
387,000 : 0.00008
389,950 : 0.00008
479,000 : 0.00010
488,800 : 0.00010
529,000 : 0.00011
575,000 : 0.00012
639,000 : 0.00013
659,000 : 0.00013
1,095,000 : 0.00022
5,500,000 : 0.00100
Now we can order the relative frequencies from least to greatest:
114,950 : 0.00002
158,000 : 0.00003
230,500 : 0.00005
387,000 : 0.00008
389,950 : 0.00008
479,000 : 0.00010
488,800 : 0.00010
529,000 : 0.00011
575,000 : 0.00012
639,000 : 0.00013
659,000 : 0.00013
1,095,000 : 0.00022
5,500,000 : 0.00100
Which is a correct expansion of (3x + 2)(3x2 + 4)?
The correct expansion of (3x + 2)(3x² + 4) will be 9x³ + 12x + 6x² +8.
How to expand the factor?In order to expand any factor, we need to multiply the first term with all two-term with another bracket.
similarly, multiply the second term with all two-term with another bracket.
Since given that (3x + 2)(3x² + 4)
multiply 3x by (3x² + 4)
⇒ 9x³ + 12x
Now multiply 2 with (3x² + 4)
⇒ 6x² +8
By adding these two we get 9x³ + 12x + 6x² +8 which is the correct expansion of the (3x + 2)(3x² + 4).
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Final answer:
The correct expansion of the expression (3x + 2)(3x² + 4) is found by multiplying each term of the first binomial by each term of the second polynomial, resulting in the expanded form 9x³ + 12x + 6x² + 8.
Explanation:
The student's question refers to the process of expanding a binomial multiplied by a polynomial using the distributive property (also known as the FOIL method for binomials). To expand it, each term in the first binomial is multiplied by each term in the second polynomial and the results are then added together. Applying this method:
First, multiply 3x by 3x² to get 9x³.Next, multiply 3x by 4 to get 12x.Then, multiply 2 by 3x² to get 6x².Finally, multiply 2 by 4 to get 8.Adding all these products together gives the expanded form: 9x³ + 12x + 6x² + 8. It is important to also combine like terms if there are any; however, in this expansion, there are no like terms to combine.
PLEASE
I
NEED
HELP
−15x+4≤109 OR −6x+70>−2
Answer:
All values of x are solutions
Step-by-step explanation:
−15x+4 ≤ 109 OR −6x + 70 > −2
-15x ≤ 105 OR -6x > -72
-x ≤ 7 OR -x > - 12
x ≥ -7 OR x < 12
Answer
x ≥ -7 OR x < 12
All values of x are solutions
what is the range of f?
Answer:
[ -8 , 9 ]
Step-by-step explanation:
You are looking at where f(t), the function, is on its y values.
Please mark for Brainliest!! :D Thanks!!
For more questions or more information, please comment below!
According to the vent diagram below, what is P(AnBnC)? A.2/25 B.3/25 C.4/25 D.1/25
The correct option is B.
The probability [tex]\( P(A \cap B \cap C) \)[/tex] from the Venn diagram is [tex]\( \frac{2}{25} \)[/tex], as 4 out of 50 elements overlap.
To find [tex]\( P(A \cap B \cap C) \)[/tex] from the given Venn diagram, we need to identify the part of the diagram where all three sets A, B, and C overlap, and then calculate the probability of landing in that part of the diagram.
The numbers within each section of the Venn diagram represent the number of elements in that section. The overlapping section of A, B, and C is the center where all three circles intersect, which has the number 4 in it. This means there are 4 elements that are in all three sets A, B, and C.
To calculate the probability [tex]\( P(A \cap B \cap C) \)[/tex], we need to divide the number of elements in [tex]\( A \cap B \cap C \)[/tex] by the total number of elements in the sample space. The sample space in this case is all the numbers within the Venn diagram.
The total number of elements in the Venn diagram is the sum of all the numbers inside the circles.
Let's calculate it step by step.
The probability [tex]\( P(A \cap B \cap C) \)[/tex] is [tex]\( \frac{4}{50} \)[/tex], which simplifies to [tex]\( \frac{2}{25} \)[/tex]. Therefore, the answer is 2/25. Here is the step-by-step calculation:
1. Count the number of elements in the intersection of A, B, and C, which is 4.
2. Count the total number of elements in the sample space, which is 50.
3. Divide the number of elements in [tex]\( A \cap B \cap C \)[/tex] by the total number of elements in the sample space to find the probability:
[tex]\[ P(A \cap B \cap C) = \frac{4}{50} = \frac{2}{25} \][/tex]
This is the required probability.
The complete question is here:
Options
A.2/25
B.3/25
C.4/25
D.1/25
Answer: On APEX it’s 2/25
Step-by-step explanation:
A boy purchased (bought) a party-length sandwich 54 in. long. He wants to cut it into three pieces so that the middle piece is 6 in. longer than the shortest piece and the shortest piece is 9 in. shorter than the longest piece. How long should the three pieces be?
Answer:
length of shortest piece = 13 in
length of middle piece = 19 in
length of longest piece = 22 in
Step-by-step explanation:
Total length of sandwich = 54 inch
Let shortest piece = x
Middle piece = x+6
Longest piece = x+9
Add this pieces will make complete sandwich
x+(x+6)+(x+9) = 54
Solving
x+x+6+x+9 = 54
Combining like terms
x+x+x+6+9 = 54
3x + 15 = 54
3x = 54 -15
3x = 39
x = 13
So, length of shortest piece = x = 13 in
length of middle piece = x+6 = 13+6 = 19 in
length of longest piece = x+9 = 13+9 = 22 in
Answer:
The three pieces should be 13 , 19 , 22 inches
Step-by-step explanation:
* Lets study the information to solve the problem
- The length of the sandwich is 54 in
- The sandwich will cut into three pieces
- The middle piece is 6 inches longer than the shortest piece
- The shortest piece is 9 inches shorter than the longest piece
* Lets change the above statements to equations
∵ The shortest piece is common in the two statements
∴ Let the length of the shortest piece is x ⇒ (1)
∵ The middle piece is 6 inches longer than the shortest piece
∴ The length of the middle piece = x + 6 ⇒ (2)
∵ The shortest piece is 9 inches shorter than the longest piece
∴ The longest piece is 9 inches longer than the shortest piece
∴ The longest piece = x + 9 ⇒ (3)
∵ the length of the three pieces = 54 inches
- Add the length of the three pieces and equate them by 54
∴ Add (1) , (2) , (3)
∴ x + (x + 6) + (x + 9) = 54 ⇒ add the like terms
∴ 3x + 15 = 54 ⇒ subtract 15 from both sides
∴ 3x = 39 ⇒ divide both sides by 3
∴ x = 13
* The length of the shortest piece is 13 inches
∵ The length of the middle piece = x + 6
∴ The length of the middle piece = 13 + 6 = 19 inches
* The length of the middle piece is 19 inches
∵ The length of the longest piece = x + 9
∴ The length of the longest piece = 13 + 9 = 22 inches
* The length of the longest piece is 22 inches
* The lengths of the three pieces are 13 , 19 , 22 inches
The slope-intercept form of the equation of a line that passes through point (–2, –13) is y = 5x – 3. What is the point-slope form of the equation for this line?
Answer:
y+13 = 5(x+2)
Step-by-step explanation:
y = 5x-3
The slope is 5 since it is in the form y= mx +b where m is the slope
The point slope form of the equation of a line is
y-y1 = m(x-x1) where (x1,y1) is the point
y--13 = 5(x--2)
y+13 = 5(x+2)
Answer:
B or y + 13 = 5(x + 2)
Step-by-step explanation:
Find the slope-intercept form of an equation for the line that passes through (–1, 2) and is parallel to y = 2x – 3.
Question 8 options:
a)
y = –0.5x – 4
b)
y = 0.5x + 4
c)
y = 2x + 4
d)
y = 2x + 3
Answer:
c
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( where m is the slope and c the y- intercept )
Given y = 2x - 3 ← in slope- intercept form
with m = 2
• Parallel lines have equal slopes, hence
y = 2x + c ← is the partial equation of the parallel line
To find c substitute (- 1, 2) into the partial equation
2 = - 2 + c ⇒ c = 2 + 2 = 4
y = 2x + 4 → c
Suppose you are determining the growth rate of two species of plants. Species A ls 25 cm tall and grows 3 cm per month. Species
B is 10 cm tall and grows 8 cm per month. Which system of equations models the height of each species H(m) as a function of m
months
Answer: Last Option
[tex]H (m) = 25 + 3m\\H (m) = 10 + 8m[/tex]
Step-by-step explanation:
The initial height of the plant of species A is 25 cm and grows 3 centimeters per month.
If m represents the number of months elapsed then the equation for the height of the plant of species A is:
[tex]H (m) = 25 + 3m[/tex]
For species B the initial height is 10 cm and it grows 8 cm each month
If m represents the number of months elapsed then the equation for the height of the plant of species B is:
[tex]H (m) = 10 + 8m[/tex]
Finally, the system of equations is:
[tex]H (m) = 25 + 3m\\H (m) = 10 + 8m[/tex]
The answer is the last option
Asphere has a diameter of 14 units. What is the volume of the sphere in cubic units? If a cylinder has the same radius as the sphere and a height of
14 units, what is the volume of the cylinder? Use 3.14 for
A.
The volume of the sphere is about 1,077.02 cubic units, and the
volume of the cylinder is about 718.01 cubic units
The volume of the sphere is about 1,436 03 cubic units, and the
volume of the cylinder is about 2.154 04 cubic units
C.
The volume of the sphere is about 1,436.03 cubic units, and the
volume of the cylinder is about 957 35 cubic units
D
The volume of the sphere is about 1,077 02 cubic units, and the
volume of the cylinder is about 1,615 53 cubic units
if the diameter is 14, then its radius must be half that, or 7.
[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} r=7 \end{cases}\implies V=\cfrac{4\pi (7)^3}{3}\implies \stackrel{\pi =3.14}{V=1436.03} \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=7\\ h=14 \end{cases}\implies V=\pi (7)^2(14)\implies \stackrel{\pi =3.14}{V=2154.04}[/tex]
What is the factored form of the polynomial?
x2 + 9x +20
i
(x - 4)(x - 5)
(x - 2)(x - 10)
(x + 4)(x + 5)
(x + 2)(x + 10)
Mark this and return
Save and Exit
Answer:
(x + 4)(x + 5)
Step-by-step explanation:
Given
x² + 9x + 20
Consider the factors of the constant term (+ 20) which sum to give the coefficient of the x- term (+ 9)
The factors are + 4 and + 5, since
4 × 5 = 20 and 5 + 4 = 9, hence
x² + 9x + 20 = (x + 4)(x + 5)
Solve each proportion 2/8=x/24
Answer:
x = 6
Step-by-step explanation:
First, write the proportion, using a letter to stand for the missing term. We find the cross products by multiplying 8 times x, and 2 times 24. Then divide to find x. Study this step closely, because this is a technique we will use often in algebra. We are trying to get our unknown number, x, on the left side of the equation, all by itself. Since x is multiplied by 8, we can use the "inverse" of multiplying, which is dividing, to get rid of the 8. We can divide both sides of the equation by the same number, without changing the meaning of the equation. When we divide both sides by 8, we find that the x would equal 6.
Hope this helped!
The answer is B) x = 12.
Here are the steps I did. 1. Simplify 2/8 to 1/4 ( 1/4 = x/48)2. Multiply both sides by 48 ( 1/4 x 48 = x)3. Simplify 1/4 x 48 to 48/4 ( 48/4 = x)4. Simplify 48/4 to 12 ( 12 = x)5. Now reverse it ( x = 12)
need help asap!!!! thanks
Answer:
g(- 8) = - 62
Step-by-step explanation:
Equate 8x + 2 to - 62
8x + 2 = - 62 ( subtract 2 from both sides )
8x = - 64 ( divide both sides by 8 )
x = - 8
Hence g(- 8) = - 62
Expressions, Equations & inequalities Question 1
Solve the inequality
12x + 151 - 19
Answer:
I believe the answer is 12 • (x + 11) .
A class of 40 students has 11 honor students and 10 athletes. Three of the honor students are also athletes. One student is chosen at random. Find the probability that this student is an athlete if it is known that the student is not an honor student. Round to the nearest thousandth.
Final answer:
To find the probability of choosing a random non-honor student who is an athlete, subtract the number of non-honor students who are athletes but not in the 3 honor athletes group from the total non-honor students.
Explanation:
The question: A class of 40 students has 11 honor students and 10 athletes. Three of the honor students are also athletes. One student is chosen at random. Find the probability that this student is an athlete if it is known that the student is not an honor student.
Step-by-step explanation:
Calculate the total number of students who are not honor students: 40 - 11 = 29.Calculate the number of non-honor students who are athletes but not part of the 3 honor athletes: 10 - 3 = 7.Find the probability that a randomly chosen student who is not an honor student is an athlete: 7 (non-honor athletes) / 29 (total non-honor students) ≈ 0.241.Classify the triangle.
obtuse
equiangular
right
acute
Answer:
right
Step-by-step explanation:
there is a right angle in the triangle
Answer:
Right
Step-by-step explanation:
Right... the giveaway was the right angle in the pic
15p!!what is the percent of change from 86 to 77? round to the nearest percent!
Answer:
10%
Step-by-step explanation:
The difference between 86 and 77 is 9.
Divide 9 by 86
[tex]\frac{9}{86} = .1046511[/tex]
Multiply by 100
[tex].1046511 * 100 = 10.46511[/tex]
Round to the nearest percent
[tex]10.46511 \rightarrow 10 \textrm{ percent}[/tex]
Does the ordered pair (-11/3,2/3) satisfy the following system of equations -x+5y=7 and -x-7y=-1
The answer is:
The ordered pair satisfies the following system of equations since it satisfies both equations.
Why?If we need to know if the ordered pair (-11/3,2/3) satisfies the system of equations we need to evaluate it and check if it satisfies both equations, we must remember that the condition that determines if the system of equations is satisfied is that both equations must be satisfied.
So, evaluating the ordered pair, we have:
First equation:
[tex]-x+5y=7\\\\-(\frac{-11}{3})+5*\frac{2}{3}=7\\\\\frac{11}{3}+\frac{10}{3}=7\\\\\frac{11+10}{3}=7\\\\\frac{21}{3}=7\\\\7=7[/tex]
We have that the equation is satisfied.
Second equation:
[tex]-x-7y=-1\\\\-(\frac{-11}{3})-7*\frac{2}{3}=-1\\\\\frac{11}{3}-\frac{14}{3}=-1\\\\\frac{11-14}{3}=7\\\\\frac{-3}{3}=-1\\\\-1=-1[/tex]
We have that the equation is satisfied.
Hence, we have that the ordered pair satisfies the system of equations since it satisfies both equations
Have a nice day!
Final answer:
The ordered pair (-11/3, 2/3) satisfies both equations in the given system, making it a solution to the system of equations.
Explanation:
To determine if the ordered pair (-11/3, 2/3) satisfies the given system of equations, we substitute x with -11/3 and y with 2/3 into both equations.
For the first equation -x + 5y = 7, we get:
-(-11/3) + 5(2/3) = 7
11/3 + 10/3 = 7
21/3 = 7
7 = 7
This confirms that the ordered pair satisfies the first equation.
For the second equation -x - 7y = -1, we calculate:
-(-11/3) - 7(2/3) = -1
11/3 - 14/3 = -1
-3/3 = -1
-1 = -1
The ordered pair also satisfies the second equation.
Since the ordered pair satisfies both equations, it is a solution to the system.