Let's apply the distance formula:⇒d=√(x2−x1)²+(y2−y1)²⇒d=√(5−2+(−4−(−3))² ⇒d=√3²+(−7)²⇒d=√9+49 ⇒d=√58 Therefore, the distance between the two points (2,−3) and (5,−4) is √58 units.
Which of the following statements are true of the hypotenuse of a right triangle?
Its length is the sum of the lengths of the other two sides.
It is one of the legs.
It is the longest side of a right triangle.
It is opposite the right angle.
It forms a right angle with an adjacent side.
Answer:
It is the longest side of a right triangle.
Step-by-step explanation:
Hope this helps!
If not, I am sorry.
Which polynomial function has a leading coefficient of 1 and roots (7 i) and (5 – i) with multiplicity 1? f(x) = (x 7)(x – i)(x 5)(x i) f(x) = (x – 7)(x – i)(x – 5)(x i) f(x) = (x – (7 – i))(x – (5 i))(x – (7 i))(x – (5 – i)) f(x) = (x (7 – i))(x (5 i))(x (7 i))(x (5 – i))
It looks like you might have intended to say the roots are 7 + i and 5 - i, judging by the extra space between 7 and i.
The simplest polynomial with these characteristics would be
[tex]f(x) = (x - (7 + i)) (x - (5 - i))[/tex]
but seeing as each of the options appears to be a quartic polynomial, I suspect f(x) is also supposed to have only real coefficients. In that case, we need to pair up any complex root with its conjugate to "complete" f(x). We end up with
[tex]f(x) = (x - (7 + i)) (x - (7 - i)) (x - (5 - i)) (x - (5 + i))[/tex]
which appears to most closely resemble the third option. Upon expanding, we see f(x) does indeed have real coefficients:
[tex]f(x) = (x^2 - (7^2 - i^2)) (x^2 - (5^2 - i^2)) = (x^2 - 8) (x^2 - 6) = x^4 - 14x^2 + 48[/tex]
Answer:
C on edge 23
Step-by-step explanation:
because i said so
Find the measure of angle x. Round your answer to the nearest hundredth
Grayson measured a line to be 10.9 inches long. If the actual length of the line is 13.4 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
The percent error of the measurement, to the nearest tenth of a percent is 18.6%
Calculating percent errorThe formula for calculating the percent error is expressed as:
%error = actual - measure/actual * 100
Given the following
actual length = 13.4 in
Measured =10.9in
Substitute
%error = 13.4-10.9/13.4 * 100
%error = 2.5/13.4 * 100
%error = 18.65%
Hence the percent error of the measurement, to the nearest tenth of a percent is 18.6%
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Alice weighs 20 dogs and 20 cats. The mean weight for the dogs is 32kg and the mean weight for cats is 4kg. The range in weight for dogs is 45kg and the range in weight for cats is 0.5kg. State two conclusions you can draw from this information.
PLEASE HELP
Answer:
1. Dogs are generally heavier than the cats.
2. The dogs have a much larger variety in their weights and size than cats.
Step-by-step explanation:
find the value of x to the tenths place
Answer:
x = 15
[x = 15.0]
Step-by-step explanation:
we can find the length of the hypotenuse of a right triangle using the Pythagorean theorem
[note: "c" is what they are referring to as "x" here]
a² + b² = c²
a : 12
b : 9
[c = hypotenuse/x/unknown side]
12² + 9² = c²
144 + 81 = c²
225 = c²
√225 = √c²
15 = c
{x = 15.0}
Find the diameter of a sphere with a surface area of 196π square centimeters
[tex]\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ SA=196\pi \end{cases}\implies \begin{array}{llll} 196\pi =4\pi r^2\implies \cfrac{196\pi }{4\pi }=r^2 \implies 49=r^2 \\\\\\ \sqrt{49}=r\implies 7=r~\hfill \underset{diameter}{\stackrel{2(7)}{14}} \end{array}[/tex]
2. Which statement is false about the relationship of the sides in the triangle shown in the picture below?
x=3
none of these are false.
x=1
x=7
Based on the triangle inequality theorem, the that is false about the relationship of the side of the triangle given is: D. x = 7.
What is the Triangle Inequality Theorem?The triangle inequality theorem holds that the length of any side of a triangle is less than the sum of the length of the sides of the other two sides.
Applying the triangle inequality theorem, it means the following should be true for any value of x given:
x + 2 + x + 3 > 3x - 2
2x + 5 > 3x - 2
Plug in x = 3 to find out:
2(3) + 5 > 3(3) - 2
11 > 4 (True)
Plug in x = 1 to find out:
2(1) + 5 > 3(1) - 2
8 > 2 (True)
Plug in x = 7 to find out:
2(7) + 5 > 3(7) - 2
19 > 19 (FALSE)
Therefore, the false statement is: D. x = 7.
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Find A and B if Cos(A - B) = (sqrt(3))/2 ; Sin(A + B) = 1
Which statements are true about the graph of function f? f(x)=logx
The true statement about is the graph has a range of {y|-∞ < y < ∞} and decreases as x approaches 0.
What is a logarithm function?A logarithm function is a type of function that represents the inverse of an exponential function. Mathematically, a logarithmic function is written as [tex]y =log_ax[/tex].
The domain of the given logarithm function f(x) = logx is (x > 0) and its graph wouldn't touch the vertical axis but moves to the right.
Also, the logarithmic function increases as the value of x increases. Thus, this function would decrease when x approaches zero (0).
In conclusion, we can deduce that the range of this function is -∞ < y < ∞.
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Answer:
domain:
c. The graph has a domain of {x|0<x<∞} and approaches 0 as x decreases.
and pretty sure the range is:
b. The graph has a range of {y|-∞<y<∞}and decreases as x approaches 0.
because all real numbers
Step-by-step explanation:
hope this helped
frank says that he typically makes about $27 per day because the mode is 27. is frank's conclusion appropriate? explain.
If Frank says that he typically makes about $27 per day because the mode is 27. Yes, Frank's conclusion is appropriate. And mean is 28.
The complete question is given below.
Frank kept track of the amount of money he earned each day for 2 weeks. The amounts, in dollars, are listed below. 25, 30, 24, 20, 20, 22.5, 75, 27, 27, 22, 22, 27, 22.5, 28 Part A Find and calculate the measures of center and variability that best summarize Frank's data. Explain. Part B Frank says that he typically makes about $27 per day because the mode is 27. Is Frank's conclusion appropriate? Explain.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.
The data is given below.
25, 30, 24, 20, 20, 22.5, 75, 27, 27, 22, 22, 27, 22.5, 28.
The measures of center and variability that best summarize Frank's data will be
Mean = (25+30+24+20+20+22.5+75+27+27+22+22+27+22.5+28) / 14
Mean = 392 / 14
Mean = 28
If Frank says that he typically makes about $27 per day because the mode is 27.
Yes, Frank's conclusion is appropriate.
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GUYSS PLSS I NEED HELP ON ALL OF THEMM PLSSS
Answer:
acute triangle
Step-by-step explanation:
4 6 7 - Acute scalene triangle, area = 11.98
Esperanza buys a new toy for $10.50 plus 4% tax. Then she buys new shoes for $28 plus 6% tax. Enter the sum that Esperanza paid, including tax.'
Answer:
$40.60
Step-by-step explanation:
10.50+4%=10.92
28+6%=29.68
10.92+29.68=40.60
Question content area top
Part 1
Darcy gave her nail technician a $5.10 tip. The tip was 15% of the cost of the manicure. Write an equation to find b, the cost of the manicure
Answer:
Let b the cost of the manicure
15% of b= 5.10$
15% × b= 5.10$
b= 5.10×100/15
b= 34$
Twice a number x increased by 32 is translated to 2x+32
Answer:
If you are asking if that's correct then yes it is
Step-by-step explanation:
6. In both Mr. Jacquez's Math 2 classes, Period 2 and Period 3 were given the same test. The table below shows the results from the two classes.
a. Find the probability that a randomly selected student from Period 2's class failed the test.
b. Find the probability that a randomly selected student who failed the test is from Period 3's class.
*would help out big time if someone could help me out, thankyou*
Answer: pass 12 fail 12 passes 15 fail1 3
Step-by-step explanation:
pass 12 fail 12
pass 15 fail 13
Points X and Y lie on (circle)P so that PX = 5 meters and mXPY = 90. Find the length of XY to the nearest hundredth.
(there is no picture)
answer choices: 15.71 m, 3.93 m, 7.85 m, 19.63 m
Step-by-step explanation:
all that means is that the radius is 5 meters, and that we are looking for the length of the circle arc that represents 90° of the whole circle (360°).
90/360 = 1/4
so, we need 1/4 of the circle circumference :
2×pi×r × 1/4 = 2×pi×5 × 1/4 = pi×10/4 = pi × 5/2 =
= 7.853981634... m
therefore, the third answer is correct.
HELP!!! 100 PNTS+BRANLIEST TO QUICK AND CORRECT ANSWER!!!!!!!!
In the small town of Middleton, there are only two restaurants that serve pizza- a small family owned Italian restaurant and a new franchise pizza restaurant. In a recent review of the franchise, a food critic reported that the pizza was delicious as promised. The only negative review that the franchise received from the critic was in reference to the inaccurate delivery time quoted during the online order process. In response to the article, the franchise owner used a program to analyze the online pizza orders that took place during the week before the review. He chose to track the orders at 6pm each day. He recorded his results in the frequency table below. Use the frequency table to create a box and whisker plot of the On Time data values. In your final answer, include all calculations necessary to create the box and whisker plot. Use the frequency table to create a box and whisker plot of the Late data values. In your final answer, include all calculations necessary to create the box and whisker plot.
The attached figure represents the box and whisker plots
How to create a box and whisker plot?To do this, we start by converting the tallies in the frequency table to numerical values.
So, we have:
Monday Tuesday Wednesday Thursday Friday
On Time 6 3 2 10 10
Late 1 0 3 4 10
Next, we enter these data on a graphing/statistical calculator to create the box and whisker plots
See attachment
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In 2005, there were 12,000 students at Beachon High. In 2010, there were 12,250. What is the rate of change un the number of students
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
so in this case we have the provided ones (2005 , 12000) and (2010 , 12250)
[tex](\stackrel{x_1}{2005}~,~\stackrel{y_1}{12000})\qquad (\stackrel{x_2}{2010}~,~\stackrel{y_2}{12250}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{12250}-\stackrel{y1}{12000}}}{\underset{run} {\underset{x_2}{2010}-\underset{x_1}{2005}}} \implies \cfrac{12250 -12000}{2010 -2005}\implies \cfrac{250}{5}\implies \underset{\textit{rate of change}}{50}[/tex]
Solve the equation
5x+6=2(2x - 3)
X=
Answer:
[tex] x = - 12[/tex]
Step-by-step explanation:
[tex]5x + 6 = 2(2x - 3) \\ 5x + 6 = 4x - 6 \\ 5x - 4x = - 6 - 6 \\ x = - 12[/tex]
the equation y=6.75x models the cost in dollars to purchase x pounds of steak at grocery store 1.
The true statement is the cost of steak at grocery store 1 is $0.75 less per pound than at grocery store 2.
What is the true statement?In store 1, the cost of 1 pound of steak is $6.75.
Cost of 1 pound of steak in store 2 is 15 /2 = $7.50
Difference in the cost : $7.50 - $6.75 = $0.75
Here is the complete question:
The equation y = 6.75x models the cost, in dollars, to purchase x pounds of steak at grocery store 1. This table shows the cost to buy different weights of steak at grocery store 2.
Cost of Steak at Grocery Store 2
Weight (pounds) Cost
2..........................$15.00
3..........................$22.50
5......................... $37.50
9......................... $67.50
Which statement is true?
answer choices
The cost of steak at grocery store 1 is $0.75 less per pound than at grocery store 2.
The cost of steak at grocery store 1 is $0.75 more per pound than at grocery store 2.
The cost of steak at grocery store 1 is $0.50 less per pound than at grocery store 2.
The cost of steak at grocery store 1 is $0.50 more per pound than at grocery store 2. R
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Find the value of each variable.
Step-by-step explanation:
b is per the identity of angles on parallel lines when intersected by one inclined line the same as the 40° angle.
so,
b = 40°
due to the parallel nature of the 2 lines there is a symmetry effect for such shapes inscribed a circle. the upper and the lower triangle must be similar. and when applying a vertical line through the central crossing point, everything to the left is mirrored by everything on the right.
so, angle c must be equal to angle b.
c = 40°
and as the sum of all angles in a triangle is always 180°, d is then
d = 180 - 40 - 40 = 100°
the interior angle of the arc angle a is the supplementary angle of d (together they are 180°), because together with d they cover the full down side of the top-left to bottom-right line.
interior angle to a = 180 - 100 = 80°
due to the symmetry again, the arc angle opposite to a is the same as a.
as we know, the interior angle to a pair of opposing arc angles is the mean value of the 2 angles.
so, we have
(a + a)/2 = 80
2a/2 = 80
a = 80°
there might (and actually should) be some more direct approaches for "a" out of the other pieces of information, but that was the most straight one right out of my mind, and I don't spend time on finding additional shortcuts, when I have already a working approach.
A debate team consists of five freshmen and four sophomores. (Everyone is distinguishable.) How many ways can they stand in line, so that at least two of the freshmen are standing next to each other
Using the arrangements formula, it is found that they can stand in the line in 80,640 ways.
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem, we have that:
The 2 freshmen are in 2! positions, in any of the 8 positions from 1 to 8.The other 7 students are arranged in 7! positions.Hence the number of ways in which they can be lined up is given by:
N = 2! x 8 x 7! = 80,640.
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What is the solution to x² - 11x + 24 = 0
Answer:
(x - 8)(x - 3)=0
x - 8=0 or x - 3=0
x =8 x =3
What is the midpoint of the segment shown below?
Answer:
answer is c (0,2)
hope it helps
Simplify the expression 3x(x – 12x) + 3x2 – 2(x – 2)2. Which statements are true about the process and simplified product? Select three options
To solve the problem we must know about the Like terms and expressions.
What is an Expression?In mathematics, an expression is a set of numbers, variables, and mathematical operations formed according to rules.
Given ;
[tex]3x(x - 12x) + 3x^2 - 2(x - 2)^2[/tex]
To solve the algebraic expression,
[tex]3x(x - 12x) + 3x^2 - 2(x - 2)^2\\\\3x(x - 12x) + 3x^2 - 2(x^2 - 4x + 4)\\\\3x(x - 12x) + 3x^2 - 2x^2 + 8x - 8\\\\3x^2 - 36x^2 + 3x^2 - 2x^2 + 8x - 8\\\\-33x^2 + x^2 + 8x - 8\\\\\\-32x^2 + 8x - 8\\[/tex]
To solve the problem we must know about the Like terms and expressions.
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Can you solve this??
[tex]9-\underline{9\div 9} + 9 - \underline{9 \div 9}\implies 9-\underline{1}+9-\underline{1}\implies 8+9-1\implies 17-1\implies 16\\[/tex]
recall PEMDAS, MD are before AS, and both are performed from left to right.
Answer:
20
Step-by-step explanation:
first lets apply PEMDAS
[tex]9 - (9 \div 9) + 9 - (9 \div 9) [/tex]
9 ÷ 9 = 1
1 × (-) = -1
9-(-1)= 10
( than do the same for other side )
and than you get
[tex]10 + 10[/tex]
the answer is 20
Solve the system of equations using substitution.
y=x+2,5x-4y=-3
Answer:
x=5 and y=7
Step-by-step explanation:
Just substitute in y=x+2 into the equation 5x-4y=-3 to get 5x-4(x+2)=-3 which simplifies to x=5. Substitute x into y=x+2 to find y=7
To counteract race-related violence, the fourteenth amendment was ratified to give african american men the right to vote. grant citizenship to african americans. establish military control of the south. make white supremacy groups illegal.
To counteract race-related violence, the 14 th amendment was ratified to grant citizenship to African Americans. Thus, option B is correct.
What is the fourteenth amendment?The main purpose of the 14th Amendment is to guarantee and protect the citizenship and rights of African Americans.
The 14th Amendment was ratified in 1868, and it granted citizenship to all the people that born or naturalized in the United States.
This was a particularly significant development for former slaves.
This is to give them equal protection from the laws.
To counteract race-related violence, the 14 th amendment was ratified to grant citizenship to African Americans. Thus, option B is correct.
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Can i have some help Please! (Brainliest As Well if it lets me) Pick question 16 or 17 to answer i only have to do one Be specific in your comparisons - think about K (dilation scale factor) and how K changed for circumference versus area. You will need to look up the formula for surface area of a sphere.
For problem 17, if you double the diameter of the moon, then the surface increases by a factor of 4 and the volume by a factor of 8.
How to compare the change in surface and volume?
Let's answer question 17.
Remember that for a sphere of radius R, the volume is:
[tex]V = (4/3)*pi*R^3[/tex]
And the surface area is:
[tex]S = 4*pi*R^2[/tex]
So the volume depends on the cube of the radius and the surface on the square of the radius.
Now, if we double the diameter of the moon, then we also double the radius.
So the new volume will be:
[tex]V' = (4/3)*pi*(2*R)^3 = 8*[(4/3)*pi*R^3] = 8*V[/tex]
The new volume is 8 times the original volume.
And for the surface:
[tex]S' = 4*pi*(2*R)^2 = 4*[4*pi*R^2] = 4*S[/tex]
So the new surface is 4 times the original surface.
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