Answers
Answer:
GH = 16; CH = 12
Step-by-step explanation:
First of all, you need to understand the meaning of "perpendicular bisector." It means that GH is divided into two equal parts by line AC, and that AC makes a right angle to GH.
The right angle is marked.
(a) The length of one of the halves of GH is marked as being 8 units long, so the other half will also be 8 units long. Of course, the length of GH is the sum of its two halves:
GH = GB +BH = 8 + 8
GH = 16
__
(b) Triangles CBG and CBH share side CB, so have that length in common. They have equal lengths BG and BH because BC bisects GH. They have a right-angle at B in common, so can be considered congruent by SAS, the fact that two congruent sides have a congruent angle between them.
Since triangles CBG and CBH are congruent, their corresponding sides CG and CH are also congruent. Side CG is marked 12 units long, so CH will be 12 units long, also.
CH = 12
You could shortcut all of the congruent triangle logic by recognizing that an altitude (CB) is a perpendicular bisector of the base (GH) if and only if the triangle is isosceles. The sides of an isosceles triangle are always congruent, so CG = CH = 12.
__
In part (c), you're supposed to choose possible theorems for demonstrating the congruence of the triangles we described above.
Related Questions
Ramona works in a clothing store where she earns a base salary of $140 per day plus 14% of her daily sales. She sold $600 in clothing on Saturday and $1200 in clothing on Sunday. How much did she earn over the two days? A. $252 B. $291 C. $392 D. $532
Answers
Answer:
I hope this helps!
Answer D
Step-by-step explanation:
Step-by-step explanation:
salary per day =$140
bonus on sales =14%
sales on Saturday =$600
bonus on Saturday sales=14/100*$600
=$84
sales on Sunday =$1200
bonus on Sunday sales=14/100*$1200
=$168
total amount she earned over the two days=$140+$84+$168
=$532
What are the solutions of |3x + 2| > 9?
Answers
Answer:
see below (I hope this helps!)
Step-by-step explanation:
We can split this into 2 cases:
3x + 2 > 9 or -(3x + 2) > 9
3x > 7 or 3x + 2 < -9
x > 7/3 or x < -11/3
All of the following are true about the standard error of the mean except a. it is larger than the standard deviation of the population. b. its value is influenced by the standard deviation of the population. c. it decreases as the sample size increases. d. it measures the variability in sample means.
Answers
Answer:
The correct option is a.
Step-by-step explanation:
The standard deviation of the sampling distribution of sample mean ([tex]\bar x[/tex]) is known as the standard error. It is denoted by [tex]\sigma_{m}[/tex].
The formula to compute the standard error is:
[tex]\sigma_{m}=\frac{\sigma}{\sqrt{n}}[/tex]
As the population standard deviation is divided by the square root of the sample size, the standard error can never be more than the population standard deviation, σ.
Also, since the population standard deviation is directly proportional to the standard error, the value of [tex]\sigma_{m}[/tex] is affected by the value of σ.
And since the sample size is inversely proportional to the standard error, the value of [tex]\sigma_{m}[/tex] decreases as the value of n increases.
The sample mean is a statistic, i.e. it represents a specific characteristic (here, the average) of the sample.
The standard deviation of any statistic measures the variability of the statistic.
So, the standard error measures the variability in sample means.
Thus, the correct option is a.
What is the smallest number than can be subtracted from 438 to make it
exactly divisible by 5? Give a reason for your answer.
Answers
Answer:
3
Step-by-step explanation:
basically the largest number decided by 5 smaller than 438 is 435. so the answer is 3
Answer:
Any number divisible by 9 must have the sum of its digits divisible by 9. The sum of the digits of 456 is 15, so you need to subtract 6.
-5x-10=10 solve for x
Answers
Answer:
x = -4
Step-by-step explanation:
-5x-10=10
Add 10 to each side
-5x-10+10=10+10
-5x = 20
Divide each side by -5
-5x/-5 = 20/-5
x = -4
Answer: x= -4
Step-by-step explanation:
[tex]-5x-10=10[/tex]
add 10 on both sides
[tex]-5x=20[/tex]
divide -5 on both sides
[tex]20/-5=-4[/tex]
[tex]x=-4[/tex]
Determine the intercepts of the line.
y= 10x - 32
y-intercept:
x-intercept:
Answers
Answer:
see below
Step-by-step explanation:
To find the x intercept set y =0 and solve for x
0= 10x - 32
32 = 10x
Divide by 10
3.2 = x
The x intercept
( 3.2,0)
To find the y intercept set x =0 and solve for y
y= 0 - 32
y = -32
( 0, -32)
Answer:
(0, -32)
(3.2, 0)
Step-by-step explanation:
The line is in slope intercept form. It is easy to identify the y-intercept.
[tex]y=mx+b[/tex]
The y-intercept is (0,-32). '-32' replaces the 'b' in the equation.
To find the x-intercept, set the value of 'y' to zero and solve for 'x'.
[tex]0=10x-32\\\\0 + 32 = 10x-32+32\\\\32=10x\\\\\frac{32}{10}=\frac{10x}{10}\\\\\frac{32}{10}=x\\\\\rightarrow \frac{32/2}{10/2}=\frac{16}{5}\\\\ \boxed{x=\frac{16}{5}}[/tex]
The x intercept is (16/5, 0).
This can also be expressed as (3.2, 0).
Hope this helps.
3(x-4)=-5 solve for x
Answers
Answer:
x = 7/3
Step-by-step explanation:
3(x-4)=-5
Distribute
3x - 12 = -5
Add 12 to each side
3x -12+12 = -5+12
3x = 7
Divide by 3
3x/3 = 7/3
x = 7/3
Answer:
x = 7/3
Step-by-step explanation:
3(x-4)=-5
3x -12= -5
3x = 7
x =7/3
Keisha, Felipe, and Manuel sent a total of 100 text messages during the weekend. Keisha sent 8 more messages than Felipe. Manuel sent 2 times as many
messages as Felipe. How many messages did they each send?
Answers
Answer:
Felipe = 23 messages
Keisha = 31 messages
Manuel = 46 messages
Step-by-step explanation:
Keisha = K
Felipe = F
Manuel = M
=> There are a total of 100 messages.
=> K sent 8 +F => K = 8 + F
=> M sent 2 * F => M = 2F
=> F = F
=> 8 + F + 2F + F = 100
=> 8 + 4F = 100
=> 8 - 8 +4F = 100 -8
=> 4F = 92
=> 4F/4 = 92/4
=> F = 23
So, Felipe = 23 messages.
Keisha = 8 + F = 8 + 23 = 31 messages.
Manuel = 2F = 2* 23 = 46 messages.
46 + 31 + 23 = 77 + 23 = 100 messages.
So, the answer is correct.
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Stacy goes to the county fair with her friends. The total cost of ride tickets is given by the equation c = 3.5t, where c is the total cost of tickets and t is the number of tickets. If Stacy bought 15 tickets, she would spend $
Answers
Answer:
$52.2Step-by-step explanation:
Given her total cost of ride tickets modeled by the equation c = 3.5t where c is the total cost of tickets and t is the number of tickets, If Stacy bought 15 tickets, to know the amount she would spend on 15 tickets, we will substitute t = 15 into the modeled equation as shown;
[tex]c = 3.5t\\when t = 15\\\\c = 3.5(15)\\\\c = \frac{35}{10} * 15\\ \\c = \frac{5*7}{5*2} * 15\\\\[/tex]
[tex]c = \frac{7}{2} * 15\\ \\c = \frac{105}{2}\\ \\c = \ 52.2[/tex]
Hence Stacy would spend $52.2 on 15 tickets
Answer:
I hope this helps!
Step-by-step explanation:
Dtermine the answer to (−5) + 4 and explain the steps using a number line
Answers
Answer:
Step-by-step explanation:
=-5 +4
= -1
put a dot on -1 and go from -5 to -1 and then from -1 to -5
Art walked 4.1 km in preparation for the Community Walk–a–thon. Bill walked 3600 m. How many more metres did Art walk than Bill?
Answers
Answer:
.5 more kilometres.
Step-by-step explanation:
3600 m = 3.6 km. 4.1 is .5 greater than 3.6
First you need to convert 4.1 km into meters.
1 kilometer (kilo=1000) equals 1000 meters, so to convert 4.1 kilometers into meters you need to multiply 4.1 x 1000
4.1 x 1000 = 4,100
4.1 km = 4,100 m
To find out how many more meters art walked than Bill, you need to subtract the amount of meters Bill walked (3600 m) from the amount of meters Art walked (4100 m).
4,100 - 3,600 = 500
Art walked 500 more meters than Bill
Please help me understand this number sequence
Answers
Answer:
Step-by-step explanation:
A=a(r)^t
a=1
time=2.5 hours=25/10 ×60=150 minutes
10t=150
t=150/10=15
[tex]A=1(2)^{15}=32,768[/tex]
The circumference of a circle is 6 inches. What is the area of the circle?
A. 3π in. squared
B.9π in squared
C.12π in. squared
D.36π in squared
Answers
Answer:
(B) 9π in²
Step-by-step explanation:
I’m going to assume that by 6 inches you meant 6π inches.
If the circumference of a circle is 6π inches, then it’s radius will be half of 6 (because the circumference of a circle is [tex]2\pi r[/tex]).
[tex]6\div2=3[/tex]
So the radius is 3.
Now that we know the radius, we can find the area by using the equation [tex]\pi r^2[/tex].
[tex]\pi 3^2\\\pi9\\9\pi[/tex]
Hope this helped!
Answer:
Step-by-step explanation:
2πr = 6, r = 3/π
πr² = π(3/π)² = 9/π in.²
What is the value of the expression below when y = 4?
3y2 + y + 8
Answers
Answer:
3y²+y+8
=3(4)²+4+8
=3(16)+4+8
=48+4+8
=60
find y.
picture attached
Answers
y = 2.97167
A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle? Round to the nearest tenth. Area of a triangle = One-halfbh 68.7 cm2 161.8 cm2 381.3 cm2 450.0 cm2
Answers
Answer:
161.8 cm²
Step-by-step explanation:
The given formula works if you have both legs of the triangle. Using the given information, a better formula is ...
A = (1/2)ab·sin(C) . . . . C is the angle between sides 'a' and 'b'
A = (1/2)(27.6 cm)(30 cm)sin(23°) ≈ 161.8 cm²
Answer:
B on edg 2020
Step-by-step explanation:
Just took test
Find the number of four-digit numbers which are not divisible by 4?
Answers
Answer:
6750
Step-by-step explanation:
4 digit numbers are 1000,1001,1002,...,9999
let numbers=n
d=1001-1000=1
9999=1000+(n-1)1
9999-1000=n-1
8999+1=n
n=9000
now let us find the 4 digit numbers divisible by 4
4| 1000
______
| 250
4 |9999
_____
| 2499-3
9999-3=9996
so numbers are 1000,1004,1008,...,9996
a=1000
d=1004-1000=4
let N be number of terms
9996=1000+(N-1)4
9996-1000=(N-1)4
8996=(N-1)4
N-1=8996/4=2249
N=2249+1=2250
so number of 4 digit numbers not divisible by 4=9000-2250=6750
Right or wrong ????
Octagon ABCDEFGH and its dilation, octagon A'B'C'D'E'F'G'H', are shown on the coordinate plane below:
G
H
5
G
Н"
F
2
A
חד
A
2
7
B
B
-7-6-5-4-2-2=1
E
-2
E
D.
-5
D
C
С
If the center of dilation is at the origin, by what scale factor was octagon ABCDEFGH dilated? (4 points)
Answers
Answer:
c 1/2
Step-by-step explanation:
You are incorrect.
We are going from ABCDEFGH to A'B'C'D'E'F'G'H'. We are going from the large octagon to the small octagon. The scale factor of a dilation is the number you multiply the original lengths to get the lengths of the dilation.
[tex]scale~factor = \dfrac{length~of~dimension~in~dilated~image}{length~of~corresponding~dimension~in~original~figure}[/tex]
Look at point (6, 0) which becomes (3, 0) in the dilation.
The distance from the origin to (6, 0) is 6 units.
The distance from the origin to (3, 0) is 3 units.
scale factor = dilated/original = 3/6 = 1/2
The scale factor of the dilation is 1/2.
Also look at segment AB whose length is 4. The length of segment A'B' is 2.
scale factor = dilated/original = 2/4 = 1/2
Answer: 1/2
Draw graph x + y = 7 and x - y = 2 on the same graph
Answers
Graphed in attached file and drawn!
Answer:
see attachment
Step-by-step explanation:
Cam’s tent (shown below) is a triangular prism.
Find the surface are, including the floor of his tent
PLEASE HELP
Answers
Answer:
21.4 m²
Step-by-step explanation:
To find the surface area of this whole triangular prism, we have to look at the bases (the triangles), find their surface area, then look at the sides (the rectangles) and find theirs.
Let's start with the triangles. The area of any triangle is [tex]\frac{bh}{2}[/tex]. The base of this triangle is 2m (because there are 2 one meters) and the height is 1.7m.
[tex]\frac{2\cdot1.7}{2} = \frac{3.4}{2} = 1.7[/tex]
So the area of one of these triangles is 1.7m. Multiplying this by two, because there are two triangles in this prism:
[tex]1.7\cdot2=3.4[/tex]
Now let's find the area of the sides.
The side lengths are 2 and 3, so
[tex]2\cdot3=6[/tex], and there are 3 sides (including the bottom/floor) so [tex]6\cdot3=18[/tex].
Now we add.
[tex]18+3.4=21.4[/tex] m².
Hope this helped!
Answer: 21.4 square meters^2
Step-by-step explanation:
LAST QUESTION TO MY SUMMER HOMEWORK PLEASE HELP 'BRAINLIEST i will give 25 POINTS at ONCE also its a simple question please answer it quickly I thank you very much and will answer a non math question if you would like.
Answers
Answer:
Step-by-step explanation:
here,
132 degree + 54 degree + x + 90 degree = 360 degree ( angles around a point)
therefore ,
x+ 276 degree =360 degree
x = 360-276
x= 84 degree
hope it helps and pls do mark my answer as the brainliest.............
help me plzzzzz and ASAP. on a coordinate grid point P is at (4, 3) and point R is at (-2, -5) points Q and S are reflection of both points across the x-axis what are the coordinates of Q and S please answer correctly
Answers
Answer:
B
Step-by-step explanation:
The rules for reflecting across the x axis are just multiply the y value by -1
your answer is the second answer choice
For y axis refection, it is the same but for the x value, not the y .
Question
De acuerdo con la experiencia de una empresa dedicada al desarrollo de software, para realizar un proyecto mediano se requieren seis programadores para finalizarlo en 21 días. Teniendo en cuenta que la relación entre el número de programadores y el número de días necesarios para el desarrollo es inversa, la cantidad de programadores que se deben contratar para finalizar el proyecto en 14 días es nueve.
Answers
Answer:
u should put his is English and then translate it to read it
If m is 21 inches, k is 34 inches, and ∠J measures 60°, then find j using the Law of Cosines. Round your answer to the nearest tenth.
Answers
Answer:
j = 29.7 inches
Step-by-step explanation:
The following data were obtained from the question:
m = 21 inches
k = 34 inches
Angle L = 60°
j =?
Using Cosine rule, the value of j can be obtained as follow:
j² = m² + k² – 2mk Cos J
j² = 21² + 34² – 2 × 21 × 34 × Cos 60°
j² = 441 + 1156 – 1428 × 0.5
j² = 1597 – 714
j² = 883
Take the square root of both side
j = √883
j = 29.7 inches
Therefore, the value of j is 29.7 inches.
Find the slope of the line that passes through the points (-8,-3) and (2, 3)
0
1
3/5
5/3
Answers
Answer:
The answer is
[tex] \frac{3}{5} [/tex]Step-by-step explanation:
To find the slope passing through two points we use the formula
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]Where
m is the slope
( x1 , y1) and ( x2 , y2) are the points
From the question the points are
(-8,-3) and (2, 3)
So the slope is
[tex]m = \frac{3 + 3}{2 + 8} = \frac{6}{10} = \frac{3}{5} [/tex]Hope this helps you
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
the third option
Step-by-step explanation:
as any number is greater than -2
La presa de Hidroituango tiene una altura de 225 m., alberga 20 millones de m^3 de volumen y una cresta de 550 metros de longitud, suponiendo que es un cuadrilátero con la base inferior de 200 m de longitud, determine las dimensiones y área superficial de la presa
Answers
Answer:
El ancho de la superficie = 444,44 my el largo = 200 m
La superficie de la superficie de la presa = 88888,89 m²
Step-by-step explanation:
Los parámetros dados son;
La altura del agua en la presa = 225 m
El volumen de agua en la presa, d = 20 millones de m³
La longitud de la base = 200 m
Sea el ancho de la presa = x
El volumen viene dado por la relación;
200 × 225 × x = 20 millones de m³
x = 20.000.000 / (200 × 225) = 444,44 m
Por tanto, las dimensiones de la superficie son ancho = 444,44 my largo = 200 m
El área de superficie de la superficie de la presa = 444.44 × 200 = 88888.89 m².
Lennox owns a big apple orchard. She ships her apples to various markets using a fleet of trucks. Every week, each truck goes on 333 trips, and for each trip Lennox gets 300300300 dollars. On a single trip, a truck delivers 505050 packs, and each pack contains 121212 kilograms of apples. Overall, Lennox sells 450045004500 dollars worth of apples in a week. How much does Lennox get for a single kilogram of apples? Dollars per kilogram
Answers
Using proportions, it is found that Lennox gets 2.5 dollars per kilogram.
During each week:
The truck goes on 3 trips.In each trip, 50 packs are delivered.Each pack contains 12 kilograms of apples.Hence, the amount of kilograms delivered each week are:
[tex]A = 3(50)(12) = 1800[/tex]
He sells 4500 dollars each week(1800 kilograms), hence, the amount of dollars per kg is:
[tex]D = \frac{4500}{1800} = 2.5[/tex]
Lennox gets 2.5 dollars per kilogram.
To learn more about proportions, you can take a look at https://brainly.com/question/24372153
Answer:0.50
Step-by-step explanation:
A statistical survey shows that 28% of all men take size 9 shoes. What is the probability that your friend's father takes size 9 shoes
Answers
Answer:
7/25 of a chance or a 28% chance as said in the questiom
Step-by-step explanation:
So, the question says it's a 28% chance or a 28/100 chance.
All you have to do is simplify the fraction or just still right 28% chance. But for the fraction:
Divide the numerator and denominator by 2 to get 14/50.
Divide both by two again to simplify fully to 7/25
mr.wright judges the annual jelly bean challenge at the summer fair.every year he encourages the citizens in his town to guess the number of jelly beans in the jar.he keeps in record of everyones guesses and the number of the jelly beans each person was off by. what is the independent and dependent quantity?
Answers
Answer: Independent quantity : number of jelly beans in the jar guessed.
Dependent quantity : number of the jelly beans each person was off by.
Step-by-step explanation:
Independent quantity : A quantity that the experimenter can change or control.Dependent quantity : A quantity that depends on each independent quantity.In the given scenario, there are two quantities introduced:
number of jelly beans in the jar guessed. number of the jelly beans each person was off by.Since, "number of the jelly beans each person was off by." depends on "number of jelly beans in the jar guessed.".
So,
Independent quantity : number of jelly beans in the jar guessed.
Dependent quantity : number of the jelly beans each person was off by.
