Part (a)
We'll use the distance formula.
[tex](x_1,y_1) = (-4,-7) \text{ and } (x_2, y_2) = (5,-2)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-4-5)^2 + (-7-(-2))^2}\\\\d = \sqrt{(-4-5)^2 + (-7+2)^2}\\\\d = \sqrt{(-9)^2 + (-5)^2}\\\\d = \sqrt{81 + 25}\\\\d = \sqrt{106}\\\\d \approx 10.2956\\\\[/tex]
The diameter is exactly [tex]\sqrt{106}[/tex] units long which approximates to roughly 10.2956 units. Round that decimal value however your teacher instructs.
========================================================
Part (b)
We divide the diameter in half to get the radius.
Therefore, the radius is exactly [tex]\frac{\sqrt{106}}{2}[/tex] units long which is approximately 5.1478 units.
In the power function f(x) = -2x, what is the end behavior of f(x) =3^-x 2 as x goes to [infinity]?
The end behavior of the power function is as x tends to infinity, f(x) tends to zero.
In this question,
The power function is [tex]f(x)=3^{-x}2[/tex]
The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.
The graph below shows the behavior of the function f(x).
The above equation has the degree of 1, which is odd and the leading coefficient has the positive coefficient.
Then the end behavior is
As x -> ∞,
⇒ [tex]\lim_{x \to \infty} f(x)[/tex]
⇒ [tex]\lim_{x \to \infty} 3^{-x}2[/tex]
⇒ [tex]2\lim_{x \to \infty} 3^{-x}[/tex]
⇒ [tex]2\lim_{x \to \infty} 3^{-\infty}[/tex]
⇒ 2(0)
⇒ 0
Thus as x → ∞, f(x) → 0.
Hence we can conclude that the end behavior of the power function is as x tends to infinity, f(x) tends to zero.
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Which expression is equivalent to StartRoot StartFraction 128 x Superscript 5 Baseline y Superscript 6 Baseline Over 2 x Superscript 7 Baseline y Superscript 5 Baseline EndFraction EndRoot? Assume x Greater-than 0 and y > 0.
The equivalent expression of the expression is 128x^5y^6/2x^7y^5
How to determine the equivalent expression?The expression is given as:
128x^5y^6/2x^7y^5
Divide 128 by 2
64x^5y^6/x^7y^5
Apply the law of indices
64y^(6-5)/x^(7-5)
Evaluate the differences
64y/x^2
Hence, the equivalent expression of the expression is 128x^5y^6/2x^7y^5
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There are an average of 45 buffalos for every 125 acres in the Canadian wilderness. How many buffalos are there in 150 acres?
Answer:
there are 54 buffalos in 150 acres
Step-by-step explanation:
1. determine the rate of buffalos per acres
45 buffalos per 125 acres =
45 / 125 =
0.36 buffalos per 1 acre
now we know the rate of buffalos per 1 acre, we can multiply it by the required amount of acres (in this case 150)
buffalos per 1 acre x total acres = total buffalos per total acres
0.36 x 150 = 54 buffalos
therefore, there are 54 buffalos per 150 acres.
hope this helps :)
Which is the inequality in factored form that represents the region greater than or equal to the quadratic function with zeros –3.5 and 11.5 and includes the point (8.5, –54) on the boundary?
The inequality is represented by the polynomial y ≥ 3.6 · (x - 11.5) · (x + 3.5).
What is the expression of the quadratic inequality?
Herein we must derive the quadratic expression within an inequality of the y ≥ f(x) based on its two roots and a known point on the curve. We can find the coefficients of the quadratic equation by solving this system of linear equations:
(x₁, y₁) = (- 3.5, 0)
12.25 · a - 3.5 · b + c = 0 (1)
(x₂, y₂) = (11.5, 0)
132.25 · a + 11.5 · b + c = 0 (2)
(x₃, y₃) = (8.5, - 54)
72.25 · a + 8.5 · b + c = - 54 (3)
The solution of the system is a = 3.6, b = - 54, c = 144.9. Thus, the inequality is represented by the polynomial y ≥ 3.6 · x² - 54 · x + 144.9, whose factored form is determined by the quadratic formula:
y ≥ 3.6 · (x² - 15 · x + 40.25)
y ≥ 3.6 · (x - 11.5) · (x + 3.5)
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PLSSS
C= [tex]\frac{12^{3} . 6^{5} }{9^{4} . 2^{10}}[/tex]
Answer:
2
Step-by-step explanation:
The trick here is to reduce each of the bases to lowest form first
[tex]12 = 3.4 = 3 .2.2 = 3.2^{2}\\12^{3} = (3.2^{2} )^{3} = 3^{3}2^{6} \\6 = 3.2\\6^{5} = (3.2)^{5} = 3^{5} .2^{5} \\\\Numerator = 3^32^63^52^5 = 3^82^{11}\\Denominator computation\\9 = 3^2\\9^{4} = (3^{2} )^4 = 3^{8} \\Denominator = 3^82^{10} \\\\\frac{Numerator}{Denominator } =\frac{{3^8}{2^{11} }}{3^82^{10}} = \frac{2^{11}} {2^{10}} = 2^1 = 2[/tex]
Pls answer I’ll mark brainliest if first person is correct
Based on these data, it is better to describe the centers of distribution in terms of: B. median for both coffee shops because the data distribution is not symmetric.
What is a median?A median can be defined as the middle number (center) of a sorted data set, which is typically when the data set is arranged in from the least to greatest or the greatest to least.
In Mathematics, the median of a data set is generally considered to be a better measure of center than the mean when there's an outlier in the data set.
Next, we would calculate the mean and median for the two coffee shops as follows.
For coffee shop A, we have:
Mean = [F(x)]/n
Mean = [12+15+33+45+46+51+52+57]/8
Mean = [311]/8
Mean = 38.875.
Median = (45+46)/2
Median = 91/2
Median = 45.5.
For coffee shop B, we have:
Mean = [F(x)]/n
Mean = [17+16+36+35+12+9+34+15]/8
Mean = [174]/8
Mean = 21.75.
Median = (16+17)/2
Median = 33/2
Median = 16.5.
Since both the mean and median are not close, we can infer and logically deduce that the data distribution isn't symmetric for both coffee shops A and B.
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Charlie throws a ball up into the air. while the ball is airborne, which is the greatest force acting on the ball to slow it down?
The greatest force acting on the ball to slow it down is Gravitational force.
Which forces will act on the ball?When ball is thrown upwards then there will be two forces on the ball opposite to the motion of ball
1. Gravitational force (mg)
2. Air friction or air drag
Both forces are opposite to the motion of the ball and it will cause the decrease in the speed of the ball.
Now here due to less value of drag coefficient on the ball we will say that ball will decrease its speed more due to gravitational force compare to friction force of air.
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The diameter of the wheel in wades el camino is 15 inches. If the wheel made 5 complete revaluations how far would the wheel have rolled? Round your answer to the nearest hundredth of an inch
Step-by-step explanation:
solution
here
15×5
=75inches
Identify a possible explicit rule for the nth term of the sequence 2, 8, 26, 80, 242.
The explicit rule for the nth term of the sequence is an = (an-1)*3 +2.
According to the given statement
we have to find the explicit rule for the nth term of the given sequence,.
So, For this purpose
The given sequence is :
2, 8, 26, 80, 242.
And according to the ap series formula
[tex]a_{n} = (a_{n-1} -1)*3 +2[/tex]
If we put the terms in it then we get the exact value as the value in the sequence.
So,
[tex]a_{n} = (a_{n-1} -1)*3 +2[/tex]
For [tex]a_{2}[/tex]
[tex]a_{2}[/tex] [tex]= a_{1} *3 +2[/tex]
[tex]a_{2}[/tex] [tex]= 2*3 + 2[/tex]
[tex]a_{2}[/tex] [tex]= 8[/tex]
and by this way we get all the values as same as the sequence.
So, The explicit rule for the nth term of the sequence is an = (an-1)*3 +2.
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PLEASE HELP ME!! I'M TIMED
All the digits of a number A are different. A number can be formed using digits that are each larger than the digits of A by one. What is the largest such number of A?
Answer: 87,654,321
Step-by-step explanation: All the digits of the number A are different so the max length of the number A is 10 digits. But, then you realise that 9 can't be used because 9+1 = 10. So, A is only 9 digits long. If we arrange them from largest to least it would be 87,654,321.
2. Solve for x.
9
6
8
X
Answer:
I think the answer is 12 because 8/6 is 1.3333.... Continously so the smaller traingel is 1.33333 times smaller then the bigger one. So you jus do 9 x 1.3333... To get the bigger angels side
Can anyone tell me how you could describe this answer to the equation?
[tex]f(x)=\frac{5x}{x-25}[/tex]
The end behavior of the given polynomial is that as x → -∞ or x → ∞, then, f(x) → 5
What is the end behavior of the Polynomial?
We are given the polynomial;
f(x) = 5x/(x - 25)
Now, we want to find the limits as x → ±∞. Let us rearrange the given polynomial to get;
f(x) = 5/(1 - (25/x))
Thus, applying limits we have;'
lim x → ±∞ [5/(1 - (25/x))]
From algebraic limit laws we know that;
If f(x) = k, then;
lim x → +∞ [f(x)] = k
Also, lim x → -∞ [f(x)] = k
Thus, applying limits at infinity to our polynomial gives;
lim x → ±∞ [5/(1 - (25/x))] = 5/(1 - 0) = 5
This is because lim x → ∞ for 1/x is 0.
Thus, f(x) has horizontal asymptotes at y = 5
Thus, we conclude that the end behavior is that as x → -∞ or x → ∞, then, f(x) → 5
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PLEASE HELP!!
Part C
What is the difference of the x-coordinate of point A and the x-coordinate of point B?
The difference of the x-coordinate of point A and the x-coordinate of point B is 0
Coordinates of a pointThe coordinate of a point on an xy-plane is written in the form (x, y). The given figures are circles A and B where the circle A is greater than circle B.
The position of the dots in both sides are positioned at the centre and as such the coordinate point at the centre of both circle will be the origin (0, 0)
According to the question, we are to find the difference of the x-coordinate of point A and the x-coordinate of point B
x-coordinate of pint A = 0
x-coordinate of point B = 0
Take the difference
Difference = 0 - 0
Difference = 0
Hence the difference of the x-coordinate of point A and the x-coordinate of point B is 0
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A(n) _____is a type of group design in which the species of animals within the study constitutes one of the independent variables.
A comparative design is a type of group design in which the species of animals within the study constitutes one of the independent variables.
A group of animals, plants, or other living things that all have similar traits and are categorized as one species are considered to be living organisms. All humans are one species, for instance.
It is essential for both biologists and the general public to comprehend what species are and how to recognize them. As species disappear, biological variety is lost, and the only way to influence the social, political, and economic factors that influence conservation efforts is to understand the nature of species.
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Evaluate the logarithm.
Answer:
-7.1931540532314155
Step-by-step explanation:
-7.1931540532314155
in a given figure if o is the centre of circle and oabc is a parallelogram find the value of abc
From the given information, we get the value of ABC = 120°.
How to estimate the value of ABC?
Given: In the figure, O exists the center of the circle and OABC exists as a parallelogram.
Now, the radius of the circle exists
OA = OB = OC
Opposite sides of a parallelogram are equal
AB = OC and OA = BC
In ∆OAB,
OA = OB = AB and,
In ∆OCB,
OC = OB = BC
Therefore, ∆OAB and ∆OCB exist in equilateral triangles.
All angles of an equilateral triangle are equivalent to 60°.
Hence, ∠ABC = ∠OBA + ∠OBC
∠ABC = 60° + 60°
∠ABC = 120°
Therefore, the value of ∠ABC = 120°.
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Need help with this questionnn!!!
The coordinates of F is (8.5, 7)
How to determine the coordinates of F?The coordinates of the points are given as:
D = (-2, -5)
F = (5, 3)
DF : FE = 4 : 2
Rewrite the ratio as
m = 4 : 2
The coordinate of the partition is calculated as:
F = 1/(m + n) * (mx2 + nx1, my2 + ny1)
This gives
(5, 3) = 1/(4 + 2) * (4 * x + 2 * -2, 4 * y + 2 * -5)
Evaluate the sum and the product
(5, 3) = 1/6 * (4x - 4, 4y - 10)
Multiply both sides by 6
(30, 18) = (4x - 4, 4y - 10)
By comparison, we have:
4x - 4 = 30
4y - 10 = 18
Solve the equations
x = 8.5
y = 7
So, we have:
F = (8.5, 7)
Hence, the coordinates of F is (8.5, 7)
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one end of a tent is a triangle. the height of the triangle is 1.5 m and the base is 2.5 m. what is the area of the triangle?
Answer:
1.5×2.5/2=1.875.
Step-by-step explanation:
We all know that area of triangle is base into hight upon 2.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct representation of the inequality is -6x + 15 < 10 - 5x and an open circle is at 5 and a bold line starts at 5 and is pointing to the right.
What is inequality?In mathematical concept, an inequality is a representation of an order linking two numbers or algebraic expressions together. These orders are called inequality signs such as greater than (>), less than (<), greater than or equal to(≥), or less than or equal to(≤). Either questions or theorems can be used to express inequality problems, and both can be solved using methods similar to those used to solve equations.
From the given information, we are given the inequality:
= -3(2x - 5) < 5(2 -x)
Open brackets, we get:
= -6x + 15 < 10 - 5x
Subtract 15 from both sides, we have:
= -6x + 15 - 15 < 10 - 5x - 15
= -6x < -5x - 5
Add 5 to both sides
= -6x + 5 < -5x - 5 + 5
= -6x + 5 < -5x
= -x < - 5
= x < 5
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Stephen and alice are reading the same book stephen reads 278 pages in 7 weeks alice reads 31 pages in a week about how many more page does stephen reads then alice
Stephen read about 9 pages more each week.
What is a linear equation in math?
A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.If stephen reeds 278 pages in 7 week ,
To find number of pages read in 1 week, divide 278 by 7
= [tex]\frac{278}{7}[/tex] ⇒ 39.71
Another person reads 31 pages each week.
So stephen reads allmost 40 per week and alice 31.
Then, we need to find the difference between them
Difference = 40 - 31 = 9
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Which algebraic expression represents the following: the sum of four times a number and six? (1 point) 4x + 6
Answer:
4x +6
Step-by-step explanation:
No explanation
Straight answer
Identify the factors of x2 − 4x − 21. (x − 7)(x 3) (x 7)(x − 3) (x 21)(x − 1) (x − 21)(x 1)
The factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.
A quadratic expression is of the form ax² + bx + c, which can be factorized using the mid-term factorization method, where b is shown as the sum or difference of two such numbers, whose product is equal to the product of a and c.
In the question, we are asked to factorize the quadratic expression, x² - 4x - 21.
In the given expression, a = 1, b = -4, and c = -21.
Thus, ac = -21.
The numbers having a product 21 are:
1*21 = 21,
3*7 = 21.
Since, 3 - 7 = -4 (That is b), we break b into 3 and -7.
Thus, the expression can now be shown as:
x² - 4x - 21
= x² + (3 - 7)x - 21
= x² + 3x - 7x - 21
= x(x + 3) - 7(x + 3) {By taking common}
= (x - 7)(x + 3) {By taking common}.
Thus, the factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.
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1. What is the length of RT?
Q
T
S
60°
60°
32
Answer:
RT = 16[tex]\sqrt{3}[/tex]
Step-by-step explanation:
using the sine ratio in right triangle QRT and the exact value
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{RT}{QR}[/tex] = [tex]\frac{RT}{32}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2 RT = 32[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
RT = 16[tex]\sqrt{3}[/tex]
Please help me（ '人' ）
Answer:
S(1,2)
Step-by-step explanation:
The value that is being altered is the y value if you go from Q to T and then T to S. The x value = 1 and remains the same for point S.
To go from Q to T, you go from 8 to 5 on the y value. Remember x remains the same. That's three units (8 - 5 = 3)
To go from T to S must be 3 units as well, since the small diagonal is bisected. 5 - 3 = 2 is the answer.
So point S is noted as S(1,2)
A graph titled Speed as a Function of Time with horizontal axis time (seconds) and vertical axis speed (meters per second). A straight orange line labeled A starts at 0 seconds 4 meters per second and runs to 6 seconds 7 meters. A straight blue line labeled B starts at 0 seconds 4 meters and upward to 6 seconds 4 meters. A straight green line starts at 0 seconds 4 meters and runs to 4 seconds 0 meters.
Use the graph of speed versus time to answer the questions about acceleration.
Which of the cars is speeding up?
Which of the cars is slowing down?
Which of the cars is maintaining a constant speed?
From the attached speed versus time graph, it can be seen that the orange or first or car is speeding up. The third or green car is slowing down, and the blue or second car is maintaining a constant speed.
Speed Analysis from the Graph
The graph in the attachment shows the linear increase in speed of the first car over time. Therefore, we can say that it is accelerating at a certain rate.
The graph shows how the speed of the third car is decreasing with time. This demonstrates that the green vehicle is de-accelerating.
The graph shows a straight line for the second car. It displays that the speed does not alter as seconds or minutes pass. We might infer that the blue car is continuing to travel at its current pace as a result.
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Answer:
A C B
Step-by-step explanation:
Which of the cars is speeding up?
A
Which of the cars is slowing down?
C
Which of the cars is maintaining a constant speed?
B
The sector area of a region of a circle is 23 mi². The central angle, 0 (theta), is 25°. What is the radius?
The radius of the sector is 10.27 miles
How to find the radius of a sector?The area of a sector can be represented as follows;
area of a sector = ∅ / 360 × πr²
where
r = radius∅ = central angleTherefore,
∅= 25 degrees
area of the sector = 23 miles²
area of a sector = ∅ / 360 × πr²
23 = 25 / 360 × πr²
cross multiply
23 × 360 = 25πr²
8280 = 25πr²
divide both sides by 25
πr² = 8280 / 25
πr² = 331.2
r² = 331.2 / 3.14
r² = 105.477707006
r = √105.477707006
r = 10.2702336877 miles
Therefore, the radius of the sector is 10.27 miles
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Trevor’s total employment compensation is $33,500. If Trevor has no job expenses and his gross pay is $28,600, then his total employee benefits are _____% of his gross pay.
a.
4.9
b.
8.5
c.
14.6
d.
17.1
The equation be x/100 [tex]*[/tex] 28,600 = 33,500, then we get 17%.
Trevor's total employee benefits exists 17.1% of his gross pay.
Therefore, the correct answer is option d. 17.1.
How to find Trevor's total employee benefits?If you would like to know Trevor's total employee advantages, you can estimate this utilizing the subsequent steps:
To find the percentage of the total employee benefits x% of $28,600 exists $33,500.
To estimate the value of x, bring the variable to the left side and bring all the remaining variables to the right side. Simplify the values to estimate the result.
x/100 [tex]*[/tex] 28,600 = 33,500
x = 33,500 [tex]*[/tex] 100 / 28,600
x = 117.13% = 117%
117% - 100% = 17%
x = 17%
The correct result would be 17%.
Trevor's total employee benefits exists 17.1% of his gross pay.
Therefore, the correct answer is option d. 17.1.
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Answer:
It is D
Step-by-step explanation:
Which linear inequality is represented by the graph?
y > 2x + 2
y ≥ One-halfx + 1
y > 2x + 1
y ≥ One-halfx + 2
Tthe inequality that describes this graph is y ≤ 1/3x - 4/3
How to determine the linear inequality represented by the graph?The graph that completes the question is added as an attachment
From the attached graph, we have the following points
(0, -1.3) and (3, -0.3)
The slope is calculated as:
m = (y2 - y1)/(x2 - x1)
Substitute the known values in the above equation
m = (-0.3 + 1.3)/(3 - 0)
Evaluate
m = 1/3
The equation is then calculated as:
y = m(x - x1) + y1
This gives
y = 1/3(x - 0) - 1.3
Evaluate
y = 1/3x - 4/3
From the graph, we have the following highlights:
The line of the graph is a closed lineThe upper part is shadedThe first highlight above implies, the inequality can be any of ≥ and ≤
While the second highlight above implies, the inequality is ≤
Hence, the inequality that describes this graph is y ≤ 1/3x - 4/3
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What are the lengths of A D ¯ , D B ¯ , A E ¯ , and E C ¯ ? Measure and record them.
For this exercise, you could get the following lengths by using a scale (ruler):
AD = 7.5 units. DB = 18.5 units. AE = 7.01 units. EC = 17.28 units.What is a line segment?A line segment can be defined as the part of a line in a geometric figure such as a triangle, that is bounded by two (2) distinct points and it typically has a fixed length.
In Geometry, a line segment can be measured by using the following measuring instruments:
A scale (ruler)A dividerIn this scenario, you're required to determine the lengths of the given line segments. However, the geometric figure wasn't included and as such an accurate answer can't provided.
For instance, you could get the following lengths by using a scale (ruler):
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Classify the expression: 5x 2. linear expression quadratic expression cubic expression quartic expression
The given expression is a (A) linear expression.
What are linear expressions?A linear expression is an algebraic expression in which each term is a constant or a variable raised to the first power. To put it another way, none of the exponents may be greater than 1. x2 is a variable raised to the second power, whereas x is a variable raised to the first power. A constant is represented by the number 5.Reduce the equation as much as feasible to the form y = mx + b. Examine your equation for exponents. It is nonlinear if it has exponents. Your equation is linear if it contains no exponents.2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x - y + z = 3 are some instances of linear equations.Therefore, the given expression is a (A) linear expression.
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The correct question is given below:
Classify the expression: 5x 2.
(A) linear expression
(B) quadratic expression
(C) cubic expression
(D0 quartic expression