Answer:
A. Line k bisects PQ
B. PR is congruent to QR
C. Line k intersects PQ at a 90 angle
Step-by-step explanation:
A perpendicular bisector of a line is a segment that cuts right in the middle a line, and that segment forms a 90º degree angle with the line. This means that the point where the segment cuts the line would be exactly the half, making both resultant segments on the line congruent. So the options that are correct are ABC.
Answer:
In the diagram below, is the perpendicular bisector of PQ. Which of the following statements must be true?
Check all that apply.
A. PQ is the perpendicular bisector of
√B. mPTR = 90
√C. PT = QT
D. RT = ST
√E.↔rs⊥pq↔
√F. T is the midpoint of PQ
Step-by-step explanation:
Two parallel lines are intersected by a transversal. Prove: Angle bisectors of the same side interior angles are perpendicular.
Answer:
The answer is given below
Step-by-step explanation:
From the diagram below,Let the line AB and CD be parallel line. Let transversal line EF cut AB at Y and transversal line EF cut CD at Z.
The bisector of ∠BYZ and ∠DZY meet at O. Therefore ∠YZO = ∠DZY/2 and ∠ZYO = ∠BYZ/2
∠BYZ and ∠DZY are interior angles.
∠BYZ + ∠DZY = 180 (sum of consecutive interior angles)
∠BYZ/2 + ∠DZY/2 = 180/2
∠BYZ/2 + ∠DZY/2 = 90°
In ΔOYZ:
∠YZO + ∠ZYO + ∠YOZ = 180 (sum of angles on a straight line).
But ∠YZO = ∠DZY/2 and ∠ZYO = ∠BYZ/2
∠DZY/2 + ∠BYZ/2 + ∠YOZ = 180
90 + ∠YOZ = 180
∠YOZ = 180 - 90
∠YOZ = 90°
Therefore Angle bisectors of the same side interior angles are perpendicular.
23 more than the product of 7 and a number
Answer:
7x + 23
Step-by-step explanation:
Remember BPEMDAS.
Product of 7 and a number means 7 times a variable: 7x
23 more than part means 23 + whatever we just did, so:
7x + 23
Answer:
23+7x
Step-by-step explanation:
23 + (7 * x)
23+7x
Last year, a local amusement park recieved 286, 758 visitors. It was open everyday of the year except 7 holidays. What was the average number of visitors to the park per day? a. 786 visitors b. 801 visitors c. 957 visitors d. 1,204 visitors Please include the work!
Answer:
c
Step-by-step explanation:
i took this test yesterday
i promise its right
Answer:
B
Step-by-step explanation:
Last year local amusement park received 286758 visitors.
Park was open for every day except 7 holidays means park was open for (365 - 7) = 358 days
Now average numbers of visitors per day =
=
= 801
Jonathan has 2/3 of a pound of bird seed left to share equally among 6 bird cages in his pet shop. How many pounds can he put in each bird cage.
Answer: 4 scoops
Step-by-step explanation:
2/3 % 1/6 = 4 scoops
Answer:
1/9 pounds
Step-by-step explanation:
2/3 divide by 6
flip the 6 when dividing and then change division sign to multiplication
2/3 (1/6)
[tex] \frac{2}{3} \times \frac{1}{6} [/tex]
then multiply and simplify 2/18
Construction crews A,B,C and D build a 1200 meter long road. Team A builds 1/2 of the total length built by the other 3 teams. Team B builds 1/3 of the total length built by the other 3 teams. C builds a section that is 1/4 of the length built by the other teams. How many meters did Team D build
Answer:
260 meters.
Step-by-step explanation:
It is given that construction crews A,B,C and D build a 1200 meter long road.
[tex]A+B+C+D=1200[/tex] ...(1)
Team A builds 1/2 of the total length built by the other 3 teams. So,
[tex]A:(B+C+D)=1:2[/tex]
It means total distance divided in 1:2.
[tex]A=1200\times \dfrac{1}{1+2}=1200\times \dfrac{1}{3}=400[/tex]
Similarly,
Team B builds 1/3 of the total length built by the other 3 teams.
[tex]B:(A+C+D)=1:3[/tex]
It means total distance divided in 1:3.
[tex]B=1200\times \dfrac{1}{4}=300[/tex]
C builds a section that is 1/4 of the length built by the other teams.
[tex]C:(A+B+D)=1:4[/tex]
It means total distance divided in 1:4.
[tex]C=1200\times \dfrac{1}{5}=240[/tex]
Now, put A=400, B=300 and C=240 in (1).
[tex]400+300+240+D=1200[/tex]
[tex]D=1200-940[/tex]
[tex]D=260[/tex]
Therefore, 260 meters build by D.
Need help ASAP the numbers are correct I just need to know the other missing numbers
Step-by-step explanation:
1.32:24
32/8:24/8
4:3
2.20:32
20/4:32/4
5:8
3.24:76
24/4:76/4
6:19
4.24:32:20
24/4:32/4:20/4
6:8:5
Simplify (*x* +2x? - 5x)+(-3x + x +1)+(3+* + 2x).
A. 3x + 2x* - 3x2 – 3x² +1
B 4x*- 3x + x2 + 4x +2
C. 4x4 - 3x + 3x² + 4x +2
D. 4x*- 3x + 3x? - 3x + 1
Answer:
D
Step-by-step explanation:
4x^4+3x^2-3x^3-3x+1
Using the graphing function on your calculator, find the solution to the system
of equations shown below.
y-2x = -2
y- x = 1
A. More than 1 solution
B. x = 4, y = 3
C. No solution
O D. x = 3, y = 4
Answer:a x=3 y=-4
Step-by-step explanation:
You can buy shampoo in a 6 oz bottle for 2.79 or in a 14 oz bottle for 10.89
Answer:
Step-by-step explanation:
Find and compare the unit costs of the two different bottle sizes.
First:
$2.79/(6 oz) = $0.465/oz
Second:
$10.89/(14 oz) = $0.778/oz
Clearly, the larger (14 oz) bottle is a much better buy
Answer: 14oz bottle for 10.89
Step-by-step explanation:
Did it before
PLSSSS HELPPP>> Show work solve the sysytem- y=1/2x^2+4x+4 y=-4x+12 1/2
Answer:
The solution is (-17,80.5) and (1,8.5)
Step-by-step explanation:
Equation 1 : [tex]y=\frac{1}{2}x^2+4x+4[/tex]
Equation 2: [tex]y = -4x+12.5[/tex]
Substitute the value of y from equation 2 in equation 1
Equation 1 : [tex]y=\frac{1}{2}x^2+4x+4[/tex]
After substitution :
[tex]-4x+12.5=\frac{1}{2}x^2+4x+4\\\frac{1}{2}x^2+8x+4-12.5=0\\\frac{1}{2}x^2+8x-8.5=0\\x^2+16x+17=0\\x=-17,2[/tex]
Substitute the value of x = -17
y = -4x+12.5
y = -4(-17)+12.5
y=80.5
Substitute the value of x = 1
y = -4(1)+12.5
y=8.5
Hence the solution is (-17,80.5) and (1,8.5)
PLLLEASEEEEE!!!!!
Find the value of v and w.
Answer:
v=20, w=80
Step-by-step explanation:
First, we can find v by determining that angle 5v and angle 4v and supplementary to each other. This means that their sum adds up to 180 degrees.
5v + 4v=180
9v=180
v=20
We also know 4v is equivalent to w.
4(20)=w
w=80
Answer:
Step-by-step explanation:
5v + 4v = 180 {co-interior angles}
9v = 180
v = 180/9
v = 20
Angles opposite to equal sides are equal.
So, w = 4v
w = 4*20
w = 80
Which of the following systems of equations is an example of one where substitution is the best method?
Answer:
The answer is option D.
I hope this helps.
Answer:
y = 2/7x +11
3x-4y = -24
Step-by-step explanation:
We would want to use substitute on the last set of equations since the first equation is already solved for y. It is easy to substitute for y in the second equation
The tabletop below is made from right triangles, each the same size. Your company charges $0.20 per square inch for sanding the tabletop. Which of the following is closest to the tabletop’s area, in square inches? 550 950 2,800 3,950 5,600
Answer:
correct answer is 2800.
Step-by-step explanation:
You take the area of the square which is 20x20 = 400.
There is 5 squares 400x5 = 2000
There is 4 triangles--which is 1/2 the area of 1 square (In this case).
One triangle = 200
200x4 = 800
2000 + 800 = 2800
Answer:
Step-by-step explanation:
550
h(t)=-16t^{2}+100t+10 find the domain and range. please
Answer:
Step-by-step explanation:
The graph of this function is that of a parabola that opens down (due to the negative coefficient of t^2). The axis of symmetry is
-b -100
x = --------- = ----------- = 50/16 = 25/8.
2a 2(-16)
The y value of the vertex is h(25/8) = -16(25/8)^2 + 100(25/8) + 10, or 166/25.
The largest value this function can take on is 166/25. Thus, the range is
(-infinity, 166/25).
Since the given function is a polynomial, the domain consists of all real numbers.
When solving the following system of equations, which variable would be the easiest to solve for?
Answer:
the y is the second equation.Answer:
The y in the second equation
Step-by-step explanation:
hope this helps
What are the units for the variable in the following scenario?
Sherry bought 6 apples at 43° per apple. She then bought 4 oranges at 51c
per orange. How much was her grocery bill?
Answer:
Her grocery bill is $4.62
Step-by-step explanation:
The first step is to multiply 6 and .43 to get how much it was for all of the apples.
Then the next step is to do the same thing with the oranges.
Then the last step is to add the two together.
Answer:
$4.62
Step-by-step explanation:
Which of the following is the correct scientific notation for 0.00566 meters?
A. 566 x 10-5 m
B. .566 x 10-3 m
C. 5.66 x 10-3 m
D. 5.66 x 103 m
5 mL =____gtt
A. 75
B. 100
C. 50
D. 25
Answer:
Answer:
b. 100
Step-by-step explanation:
Christina's family is building a house. On the blueprint, Christina's rectangular room measures 10cm by 12cm. The map has a scale of 1 cm=1.5 ft. What is the actual area of Christina's room?
Answer:
270 ft square
Step-by-step explanation:
10cm * 1.5ft = 15 ft
12cm * 1.5ft = 18ft
18ft * 15ft = 270ft square
Answer:
270 sq ft
Step-by-step explanation:
Find the distance d(A,B) between points A and B
A(2.-6), B(2.1)
d(A,B) =
Answer:
d = 7
Step-by-step explanation:
Distance Formula: [tex]d = \sqrt{(x2 - x1)^2+(y2-y1)^2}[/tex]
Plug in our 2 coordinates:
[tex]d = \sqrt{(2-2)^2+(1+6)^2}[/tex]
And you should get 7 as your final answer.
Answer:
7 units
Step-by-step explanation:
Since the x coordinates are the same, we only have to look at the difference between the y coordinates to determine the distance
1 - -6 = distance
1+6 = 7
The distance is 7 units
Find the perimeter of the right triangle. If necessary, round to the nearest tenth.
A right triangle with side 13 inches, side 14 inches, and blank hypotenuse.
a.
91 in.
b.
46.1 in.
c.
19.1 in.
d.
182 in
Answer:19.1
Step-by-step explanation:
Answer:
B. 46.1 in
Step-by-step explanation:
First, we must find the hypotenuse of the triangle.
Since this is a right triangle, we can use Pythagorean Theorem.
a^2+b^2=c^2
where a and b are the legs and c is the hypotenuse.
13 and 14 are the legs, because they form the right angle. x is the hypotenuse because it is opposite the right angle.
13^2+14^2=x^2
Evaluate each exponent.
13^2=13*13=169
14^2=14*14=196
169+196=x^2
Add 169 and 96
365=x^2
Take the square root of both sides.
√365=√x^2
√365=x
19.1049732=x
Round to the nearest tenth.
19.1=x
The hypotenuse is 19.1 inches
Now, find the perimeter. Add up all the sides of the triangle: the legs (13 in and 14 in) and the hypotenuse (19.1 in)
13 in +14 in +19.1 in
46.1 in
The perimeter is 46.1 inches and B is correct.
20 points + brainliest, give explanation
Answer:
The answer is 72 degrees Z is also 180 by the way
Step-by-step explanation:
A straight line is 180 so subtract 108 and you will get the angle 72 degrees
Answer:
Step-by-step explanation:
Since Angle BCD is parallel to EDC, it means they both equal 108 degree. So x = 108
the supplementary angle for 108 is 72 degree, which means Angle c = Angle y, so angle y = 72 degrees.
all angles in a triangle = 360, so use the formula to find out what angle z is
360 = 72 + 72 + z
360 = 144 + z
360 - 144 = z
216 = z
if the first and third of three consecutive odd integers are added, the result is 75 less than five times the second integers. find the third integer. please show work
Answer:
The third integer is 27
Step-by-step explanation:
Given
Represent the consecutive odd numbers with [tex]T_1, T_2; and\ T_3[/tex]
Since they are consecutive odds, then
[tex]T_2 = 2 + T_1[/tex]
[tex]T_3 = 2 + T_2[/tex]
From the first statement in the question, we have that
[tex]T_1 + T_3 = 5 T_2 - 75[/tex]
Required
Find the third integer
Recall that
Substitute [tex]T_2 = 2 + T_1[/tex] in [tex]T_3 = 2 + T_2[/tex]
[tex]T_3 = 2 + 2 + T_1[/tex]
[tex]T_3 = 4 + T_1[/tex]
Substitute [tex]T_3 = 4 + T_1[/tex] and [tex]T_2 = 2 + T_1[/tex] in [tex]T_1 + T_3 = 5 T_2 - 75[/tex]
[tex]T_1 + 4 + T_1 = 5(2 + T_1) - 75[/tex]
Open Brackets
[tex]T_1 + 4 + T_1 = 10 + 5T_1 - 75[/tex]
Collect like terms
[tex]T_1 + T_1 + 4 = 5T_1 - 75 + 10[/tex]
[tex]2T_1 + 4 = 5T_1 - 65[/tex]
Collect like terms
[tex]2T_1 - 5T_1 = - 65 - 4[/tex]
[tex]-3T_1 = - 69[/tex]
Divide both sides by -3
[tex]\frac{-3T_1}{-3} = \frac{- 69}{-3}[/tex]
[tex]T_1 = 23[/tex]
Recall that [tex]T_3 = 4 + T_1[/tex]
[tex]T_3 = 4 + 23[/tex]
[tex]T_3 = 27[/tex]
The third integer is 27
25. Simplify the following expression.
Question 25 please
I hope this helps you
Answer:
3 -√5
Step-by-step explanation:
(√5 + 1) / (2 + √5)
Multiply top and bottom of the fraction by the conjugate of 2 + √5 which is 2 - √5.
By doing this we rationalise the denominator:
= (√5 + 1 ) * ( 2 - √5) / (2 + √5)(2 - √5)
= (√5 + 1 ) * ( 2 - √5)/ (4 - 2√5 + 2√5 - 5)
= (2√5 - 5 + 2 - √5) / (4 - 5)
= (√5 - 3) / -1
= 3 -√5
Use the diagram at the right to answer questions 22–27.
Find the measure of each angle.
22. DBC
23. ADC
24. BCD
25. DCE
26. BCF
27. ECF
22. 30 degrees because line DB bisects(meaning cuts in half) angle ABC so DBC should be 30 degrees because 30+30 is 60 which is what angle ABC is.
23. 60 degrees because if we assume that it is a parallelogramand that the opposite angle are congruent.
24. 120 degrees because a quadrilatteral has sides that will equal to 360 degrees, and I said that a parallelogram will have its opposite angles congruent we take away 120 from 360 (from the previous angles ABC and BCD) we end up with 240, we divide 240 by 2 and end up with 120 degrees
25. 60 degrees. I found that angle DCB is 120 degrees so angles DCB and DCE are supplementary(add up to 180 degrees) and we subtract 120 from 180 which is 60 degrees.
26. 60 degrees vertical to angle DCE.
27. 120 degrees supplementary to DCE
What's the answerrrrr?
Answer:
A. Positive
Step-by-step explanation:
Since 48 is way larger than 39, we know that if we subtract 39 from 48, we will still get a positive number.
Answer:
A. Positive
Step-by-step explanation:
Im not very good at explaining. I hope I helped :)
Determine the total number of roots for each polynomial function.
g(x) = 5x - 12/2 + 3
g(x) = (x - 5)^2 + 2x^3
At the root this function is equal to 0
(x - 5)^2 + 2x^3= 0
Rearrange:
(x - 5)^2 = -2x^3
Now if you plot these two functions you need to check how many times they intersect. For this you do not need to be precise just scetch approximately.
If you do that, you will see that they meet once. I cannot really use this site to plot, but you can use other tools for that if you do not know how to do it.
Alexis wants to make a paperweight at pottery class. He designs a pyramid-like model with a base area of 100 square centimeters and a height of 6 centimeters. He wants the paperweight to weigh at least 300 grams.
Answer:
The density of the material must be at least 1.5 g/cm³.
Step-by-step explanation:
Hey guys please help find the area
Answer:
70.15 ft²
Step-by-step explanation:
The figure consists of two adjacent equilateral triangles (all angles are 60 degrees and all outer edges are 9 ft).
If we focus on one of these equilateral triangles, we can get the final area by multiplying the area of that one triangle by 2.
The formula for the area of a triangle is (1/2)(base)(height). Remembering to multiply this by 2, we get
area of figure = (base)(height)
√3
= (9 ft)(9 ft)(--------) = (81 ft²)(1.732) = 70.15 ft²
2
The question, “How many ways can 4 different students be selected in order from a class of 30 students?”, is a(n) _____. permutation mutually exclusive event combination independent event
Answer:
permutation
Step-by-step explanation:
The permutation refers to the arrangement of a people, person, number, colors, alphabets or any other thing
While on the other hand the combination refers to the selection or choosing a particular thing like - clothing, menu, subjects, etc
But in the given question it asks for the number of ways can different students be selected so its a case of permutation and the same is to be considered