In a right triangle, the hypotenuse has endpoints XY, shown on the graph.
below...
If Z represents the third vertex in the triangle and is located in the second quadrant with integer coordinates, what is the length of YZ?
A)3
B)4
C)5
D)6
Answers
Answer:
The correct option is C.
Step-by-step explanation:
In a right triangle, the hypotenuse has endpoints XY as shown in the given graph.
Since XY is hypotenuse and Z is third vertex in the triangle, therefore XZ and YZ must be perpendicular at point Z.
The coordinates of X are (-4,2), so draw a vertical line x=-4 and a horizontal line y=2.
The coordinates of Y are (-1,-3), so draw a vertical line x=-1 and a horizontal line y=-3.
From the below figure it is clear that the vertcal and horizontal lines intersect each other at [tex]Z_1[/tex] and [tex]Z_2[/tex].
It is given that Z is located in the second quadrant with integer coordinates, therefore the only possible location of Z is
[tex]Z=Z_2(-1,2)[/tex]
Since the length of YZ₂ is 5 units and Z=Z₂, therefore the length of YZ is 5 units.
Hence the correct option is C.
Related Questions
find the difference
15 - (-15)
Answers
Answer:
30
Step-by-step explanation:
Note that, when two negative signs are directly next to each other, they mean addition. Note the rule:
A positive sign & A positive sign = Positive number.
A positive sign & A negative sign = Negative number.
A negative sign & A negative sign = Positive number.
In this case:
- (-15) = + 15
Simplify. Combine like terms:
15 + 15 = 30
30 is your answer.
~
a students skipped a step when he tried to convert 720 seconds into hours and he got the following incorrect result : 720 seconds (1hour/60 minutes)=12 hours. What conversion ratio did he skip in this multiple step conversion?
Answers
The student skipped the step of converting seconds to minutes in the process of converting seconds to hours. He directly converted seconds to hours, which led to the erroneous result. This emphasizes the importance of correctly applying conversion ratios in mathematical calculations.
Explanation:The student missed the step of converting minutes into seconds. When attempting to convert seconds to hours, a two-step conversion is required: first, convert seconds into minutes, then, convert the minutes into hours. The correct conversion would therefore be: 720 seconds * (1 minute/60 seconds) * (1 hour/60 minutes) = 0.2 hours.
In the step the student skipped, he directly went from seconds to hours without taking into account that there are 60 seconds in a minute. Therefore, the conversion ratio that the student skipped is '1 minute equals 60 seconds'.
This process of using conversion ratios to convert between units of measure is an important mathematical skill that is often seen in science calculations, such as in physics and chemistry.
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The student erred by skipping the conversion ratio 1 hour/60 minutes. After converting 720 seconds into 12 minutes, they didn't convert these minutes into hours, which would give the correct result, 0.2 hours.
Explanation:The student trying to convert 720 seconds into hours made an error by skipping a crucial conversion ratio. The correct process of converting seconds to hours involves two steps. Firstly, we know that there are 60 seconds in a minute. So, 720 seconds = 720/60 = 12 minutes. However, the student stopped here, forgetting that there are also 60 minutes in an hour. So the skipped conversion ratio is 1 hour/60 minutes. Therefore, to convert the 12 minutes into hours we use this ratio and get 12 minutes * (1 hour/60 minutes) = 0.2 hours.
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What makes a trapezoid an isosceles trapezoid?
Answers
Answer:
A trapezoid is a quadrilateral with exactly one pair of parallel sides. In a trapezoid the parallel sides are called bases. ... A trapezoid with the two non-parallel sides the same length is called an isosceles trapezoid. This conjecture tells us that the base angles of an isosceles trapezoid are equal in measure
Step-by-step explanation:
Answer:
A trapezoid with the two non-parallel sides the same length is called an isosceles trapezoid.
Solve the following quadratic equation using the quadratic formula.
5x^2 − 8x + 5 = 0
Write the solutions in the following form, where r, s, and t are integers, and the fractions are in simplest form.
x = r − si/t,x = r + si/t
Answers
Answer:
Step-by-step explanation:
5x² − 8x + 5 = 0
delta = b²- 4ac a =5 and b = - 8 and c=5
delta = (-8)²- 4(5)(5) = 64 - 100 = -36 = (6i)² . i² = -1
x1 = (8-6i)/10 =(4-3i)/5
x2 = (8+6i)/10 =(4+3i)/5
so r=4 and s=3 and t= 5
Answer:
Step-by-step explanation:
a = 5; b = -8; c = 5
b² -4ac = (-8)² - 4 * 5 * 5 = 64 - 100 = (-36) < 0
x = -b ± √(4ac - b²) i / 2a
= - (-8) ±√ 4 * 5 * 5 - (-8)² i / 2 *5
= 8 ± √36 i
10
= 8 ± 6 i
10
= 2 (4 ± 3i) = 4 ± 3i
10 5
= 4 ± 3i
5 5
x = 4/5 + 3i/5 ; x = 4/5 - 3i/5
-3 is which type of number? Select all that apply.
natural number
rational number
whole number
integer
Answers
-3 is classified as the following:
Rational number
Whole number
Integer
Ifn || m, find the value of x and the value of y.
A. y = 3.75 x = 11.25
B. y=4,x = 11
c. y = 5, x = 10
D. not enough information to determine
at the boot anewer from the choices provided
Answers
Answer: Option C
[tex]y=5[/tex], [tex]x=10[/tex]
Step-by-step explanation:
If the lines m and n are parallel then the large triangle and the small triangle are similar triangles, because they have equal angles.
By definition for similar triangles it is satisfied that if they have sides of length a, b, c and a', b', c' then:
[tex]\frac{a}{a'}=\frac{b}{b'} =\frac{c}{c'}[/tex]
In this case
[tex]a = 12\\a' = 4\\c = 15\\c' = y[/tex]
So:
[tex]\frac{12}{4}=\frac{15}{y}[/tex]
Now solve the equation for the variable y
[tex]3=\frac{15}{y}[/tex]
[tex]y=\frac{15}{3}[/tex]
[tex]y=5[/tex]
We know that
[tex]x+y=15[/tex] and [tex]y=5[/tex]
Then
[tex]x+5=15[/tex]
[tex]x=10[/tex]
Finally the answer is:
[tex]y=5[/tex], [tex]x=10[/tex]
What is the area of a triangle with a base of 5 units and a height of 15 units?
A. 75 sq. units
B. 37.5 sq. units
C. 18.75 sq. units
D. 150 sq. units
Answers
Answer:
B. 37.5 sq. units
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the length of the base and h is the height
A = 1/2 (5 * 15)
A =37.5 units^2
Answer:375 units
Hope this helps
Which shows the graph of x – 4y = 4? Image for option 1 Image for option 2 Image for option 3 Image for option 4
Answers
Answer:
Look at the picture
Step-by-step explanation:
I don't know what the option choices were, but I graphed the equation on a website called desmos.com so the answer is the one that looks like this graph:
In the equation 5 - 10m = 3m 2, the value of b is:
Answers
I think you mean the value of 'm' not 'b' as there is no 'b' variable given in the equation.
Assuming you meant 'm' then,
5 - 10m = 3m
+ 10m + 10m
5 = 13m
/13 /13
0.384615385 = m
Answer:
It is 10. I know you are trying to apply it with the quadratic formula.
Step-by-step explanation:
Is -22.96 an integer
Answers
Answer:
no it is not an integer
Step-by-step explanation:
nope.
Integers are whole numbers that are not fractions.
this is not the case in -22.96 as the decimal 0.96 constitutes the faction component of the number
Hello There!
-22.96 is not an integer.
An integer is any whole number that is positive or negative. A whole number includes 0 and counting numbers so -22.96 would not be considered an integer.
The mean of 10 values is 19. If further 5 values are
included the mean becomes 20. What is the mean
these five additional values?
a) 10
b) 15
c) 11
d) 22
Answers
Answer:
22
Step-by-step explanation:
Pretend the 10 values in the first sentence are a,b,c,d,e,f,g,h,i,j
Pretend the addition 5 values is k,l,m,n,o
So the mean of all the 15 data is (a+b+c+d+e+f+g+h+i+j+k+l+m+n+o)/15=20
So the sum of all 15 data is a+b+c+d+e+f+g+h+i+j+k+l+m+n+o=300 since 15(20)=300
Now let's look at the first 10: We have their mean so we can write:
(a+b+c+d+e+f+g+h+i+j)/10=19
so a+b+c+d+e+f+g+h+i+j=190 since 10(19)=190
So that means using our first sum equation and our equation sum equation we have
190+k+l+m+n+o=300
k+l+m+n+o=300-190
k+l+m+n+o= 110
So the average of those 5 numbers mentioned in your problem is 110/5=22
The area of a rectangle is 15+5y square feet. Which of the following expressions could be the length of the sides of the rectangle, in feet
a. 5 and 3y
b. 5 and 3+y
c. 5 and 5+y
d. 3 and 5+3y
Answers
Answer:
B. 5ft and (3 + y)ft
Step-by-step explanation:
Area of a rectangle = 15 + 5y
Possible sides of the rectangle would measure 5ft and (3 + y)ft
Because: 5ft × (3 + y)ft = 15 + 5y ft
A line has a slope of -1 over two and a Y intercept of -2 what is the X intercept of the line
Answers
Answer: [tex]x=-4[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
We know that the slope of this line is:
[tex]m=-\frac{1}{2}[/tex]
And the y-intercept is:
[tex]b=-2[/tex]
Since the line intersects the x-axis when [tex]y=0[/tex], we can substitute values into [tex]y=mx+b[/tex]:
[tex]0=-\frac{1}{2}x-2[/tex]
The final step is to solve for "x", then:
[tex]2=-\frac{1}{2}x\\\\(2)(-2)=x\\\\x=-4[/tex]
Shontel has a job as a barista at a local coffee shop that pays $12 per hour. She works between 15 and 25
hours every week. Her salary can be modeled by the equation s = 12.5h, where s is her weekly salary and h
is the number of hours she worked in a week
A. Describe the independent variable for this problem.
B. Describe the domain and range for this problem using appropriate notation.
C. What does each value in the ordered pair (11, 137.5) represent in the context of this problem.
Answers
B. Domain
Minimum is 15 maximum is 25
C. When she works for 11 hours she will earn $137.5
Hope this helps!
Which of the following statements are true of 13 and -13? Select all that apply.
They are opposites.
Their sum is 0.
They are the same distance from zero on the number line.
They are equivalent.
Answers
A positive number and a negative number with the same digits are opposite.
13 + -13 = 13 -13 = 0
13 to 0 is 13 units, -13 to 0 is also 13 units.
The answers are:
They are opposites.
Their sum is 0.
They are the same distance from zero on the number line.
Answer:
They are opposites.
Their sum is 0.
They are the same distance from zero on the number line.
Step-by-step explanation:
They are opposites. True
- -13 = 13
Their sum is 0. True
-13+13=0
They are the same distance from zero on the number line. True
|-13| = |13|
They are equivalent. False
-13 does not = 13
A snail moves 18 millimeters every 24 seconds. What is the snail's rate of speed ?
Answers
Answer:
0.75m/s
Step-by-step explanation:
Speed formula: ⇒ [tex]S=\frac{V}{T}[/tex]
Divide by the numbers from left to right.
S=18
T=24
18/24=0.75
0.75m/s is the correct answer.
I hope this helps you, and have a wonderful day!
[tex]\frac{3}{4}[/tex] millimeter per second
Explanation:You simply need to divide [tex]\frac{18}{24}[/tex]. This is a fraction, so you can just simplify it.
Divide the numerator and the denominator each by 6, which is the greatest common factor. [tex]\frac{\frac{18}{6}}{\frac{24}{6}} = \frac{3}{4}[/tex]
This is as simple as the result can get, so [tex]\frac{3}{4}[/tex] millimeter per second is the final answer.
Use properties of equality to solve these equations. Identify the properties used and describe how you used them. 65 • 92 • 17 = 92 • 17 • x
Answers
Answer:
65
Step-by-step explanation:
To solve this equation, we should simplify it as much as possible, which means multiply everything together.
[tex]65*92*17=101660[/tex]
[tex]92*17*x=1564x[/tex]
Now we can solve for [tex]x[/tex] by dividing each side by the coefficient.
[tex]101660=1564x[/tex]
[tex]x=65[/tex]
Write the simplified form of -64^1/3
Answers
Answer:
-4
Step-by-step explanation:
Factor by the numbers from left to right.
[tex]64^\frac{1}{3}[/tex]
[tex]64=4^3[/tex]
[tex](\frac{4}{3})^\frac{1}{3}=4^3^*^\frac{1}{3}=4[/tex]
It changes to positive to negative.
-4
-4 is the correct answer.
PLEASE HELP 12 POINTS
Answers
Answer:
taxes is 22%
utilities is 4%
transportation is 11%
Step-by-step explanation:
basically divide 95000 by 100 to get the size of 1% which is 950 then take each number for ex: 20900 divide it by 950 and that's how much percentage is being used to pay for that
Can you please answer without guessing fast and explain thank you so much
Answers
Answer:
2nd and 3rd options are correct
Step-by-step explanation:
Option 1 is wrong because there are obviously 13 scores
Option 2 is correct (quite obvious, just count the number of scores larger than 75)
Option 3 is correct. The method to find the median is to arrange all the numbers in ascending value (this is already done for you), and then locating the middle number. This happens to be 82.
Option 4 is wrong because the only 2 scores between 90 and 100 are 93 and 99
Option 5 is not necessarily true. The max score could be 99? or 102?, or 150? we just don't know. Hence this does not apply.
A family recycled 66 cans in February, 94 cans in March, 122 cans in April, and 150 cans in May. If this pattern went from January through May, how many cans did the family recycle in January?
Answers
Step-by-step explanation:
Difference per month = 28
=> January = February - 28 = 66-28 = 38
Final answer:
The number of cans recycled by the family increased by 28 cans each month. By using the established pattern of accumulation, we calculated that the family recycled 38 cans in January.
Explanation:
To determine how many cans the family recycled in January, we need to identify the pattern in the increase of the number of cans recycled from February to May. We see that from February to March, it increased by 94 - 66 = 28 cans, from March to April by 122 - 94 = 28 cans again, and from April to May by 150 - 122 = 28 cans once more.
Therefore, the pattern is that the number of recycled cans increases by 28 each month. Using this accumulation of change in discrete steps, we can work backwards to find out how many cans were recycled in January.
If 66 cans were recycled in February, and each month they recycle 28 less than the previous month, then in January the family recycled 66 - 28 = 38 cans.
Jim had 15 minutes to do 5 laps around his school what would his time be
Answers
Answer:
Step-by-step explanation:
per lap? If it is not per lap, you are going to have to edit the question.
5 laps = 15 minutes
1 lat = x Cross multiply this is a proportion
5x = 15 minutes Divide by 5
5x/5 = 15/5
x = 3 minutes.
It takes him 3 minutes to do one lap.
What is the solution to the equation 3(2x+5) = 3х+4x?
Answers
[tex]3(2x+5) = 3x+4x\\6x+15=7x\\x=15[/tex]
Answer:
x = 15
Step-by-step explanation:
Given
3(2x + 5) = 3x + 4x ← collect like terms
3(2x + 5) = 7x ← distribute parenthesis on left side by 3
6x + 15 = 7x ( subtract 6x from both sides )
15 = x ⇒ x = 15
what is the additive inverse of the expression below, where a and b are real numbers ?
2a+b
Answers
Answer:
The additive inverse is equal to [tex]-2a-b[/tex]
Step-by-step explanation:
we know that
The additive inverse of a number is equal to its opposite ( the sum of a number and its additive inverse is equal to zero)
so
we have
[tex]2a+b[/tex]
Multiply by -1
[tex]-1(2a+b)=-2a-b[/tex]
therefore
The additive inverse is equal to [tex]-2a-b[/tex]
Ida is walking dogs to help pay for sports equipment. She gets paid $10 for every dog walked and made a total of $70 on Saturday. Write an equation to show how many dogs Ida walked Saturday.
A.10x = 70
B.10 − x = 70
C.70x = 10
D.70 − x = 10
Answers
Hope this helps!
The equation to show how many dogs Ida walked Saturday is A.10x = 70
System of linear equationsA system of linear equations exists usually a set of two linear equations with two variables.
A linear equation only includes one or two variables. No variable in a linear equation exists raised to a power greater than 1 or utilized as the denominator of a fraction. When you discover pairs of values that create a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.
Given,
Ida gets paid $10 for every dog walked and made a total of $70 on Saturday.
It will be A. She earned 10 dollars per hour 10x= 70.
Hence, the correct answer is option A. 10x = 70
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What is the value of (-7 +31) - (2-61)?
Answers
Answer: 83
Step-by-step explanation:
(-7+31) - (2-61)
(24) - 2+61
22+61
83
The following shape is made by cutting an equilateral triangle from a rectangle. Find its perimeter.
Answers
Answer:
47.6 cm
Step-by-step explanation:
Since the triangle is equilateral then the 2 inclined sides = 7.2 cm
Perimeter is then the sum of the 5 sides
P = 13 + 7.2 + 13 + 7.2 + 7.2 = 47.6 cm
Answer:
47.6 cm
Step-by-step explanation:
you just bought a fish tank that is 30 in long 18 in wide and 13 in tall. how many square inches of glass are used if the sides and the bottom are made of glass?
Answers
Length x width x height = volume
Answer:
Number of square inches glasses = 1788
Step-by-step explanation:
Formula
Surface area of cuboid = 2(lb + lh + bh)
l - Length of cuboid
b - Breadth of cuboid
h - Height of cuboid
To find the number of glasses needed
Here fish tank is like a open cuboid, we have to find the surface area of top open cuboid.
Here l = 30 in , b = 18 in and h = 13 in
Surface area = 2(lb + lh + bh) - lb
= 2[(30 * 18) + ( 30 * 13) + (18 * 13)] - (30 * 18)
= 2[540 + 390 + 234] - 540
= 2[1164] - 540
= 1788 square inches
Number of square inches glasses = 1788
What is 110% of 80
(With work please)
Answers
if we take 80 as the 100%, what is 110% of that?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 80&100\\ x&110 \end{array}\implies \cfrac{80}{x}=\cfrac{100}{110}\implies \cfrac{80}{x}=\cfrac{10}{11}\implies 880=10x \\\\\\ \cfrac{880}{10}=x\implies 88=x[/tex]
All we need to do to answer this question is find 10% of 80, and add that to 80 to find 110%.
To find 10% of 80, multiply it by the decimal of 10%, or .1.
80*.1=8.
Now, add 8 to 80 to get 110% of 80.
80+8=88
110% of 80 is 88.
Hope this helps!
Seven more than the product of a number and 8 equals 2
Use the variable w for the unknown number
Answers
Answer: w • 8 + 7 = 2
Step-by-step explanation:
Just translate the words into numbers. Product is multiplication and seven more means add.
Answer:
Equation:
(W * 8) + 7 = 2
W = - 0.625
Step-by-step explanation:
8W = - 5
W = - 0.625