BCD is a straight line.
ABC is a triangle.
Show that triangle ABC is an isosceles triangle.
Give a reason for each stage of your working.
Answers
Using the exterior angle is equal to the interior angles property, angle A is equal to 117 - 54 (which is 63).
Because these two angles are equal to eachother, the triangle is isosceles.
Hope this helps and please mark me brainliest
Yes, Triangle ΔABC is an isosceles triangle.
What are the properties of Triangle?The properties of the triangle are:
The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.We can prove that triangle ABC is an isosceles triangle using the fact that BCD is a straight line, and the angles of a triangle add up to 180 degrees.
First, we note that the angles of triangle ABC add up to 180 degrees:
∠ABC + ∠ACB + ∠BAC = 180 degrees
Since ∠ACD and ∠ACB are adjacent angles, we know that:
∠ACD + ∠ACB = 180 degrees
Substituting the value of ∠ACD (117 degrees) into this equation gives:
117 degrees + ∠ACB = 180 degrees
Simplifying, we get:
∠ACB = 63 degrees
Now we can rewrite the equation for the sum of the angles of triangle ABC as:
∠ABC + 63 degrees + ∠BAC = 180 degrees
Substituting the value of ∠ABC (54 degrees) and simplifying, we get:
∠BAC = 63 degrees
Since ∠ABC = ∠BAC, we have shown that triangle ABC is an isosceles triangle.
Reasoning:
The angles of a triangle add up to 180 degrees.Adjacent angles on a straight line add up to 180 degrees.Substituting the value of ∠ACD into the equation for adjacent angles on a straight line gives ∠ACB = 63 degrees.Substituting the value of ∠ABC and simplifying the equation for the sum of the angles of triangle ABC gives ∠BAC = 63 degrees.Since ∠ABC = ∠BAC, triangle ABC is an isosceles triangle.Learn more about triangles here:
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Related Questions
Simplify the expression by combining like terms
16h + 10 + 4h
Answers
Answer:
20h + 10
Step-by-step explanation:
16h + 10 + 4h
The like terms in this expression are 16h and 4h
20h + 10
Hope this helps! May I please have brainliest? :)
What is the distance in between coordinate points -10 and 15 and 15 and 15
Answers
Answer:
25x
Step-by-step explanation:
Answer:
use pythagoras
Step-by-step explanation:
Find the least common denominator of the rational expressions below:
15/2x + 10 and -13/7x + 35
Answers
9514 1404 393
Answer:
14(x +5)
Step-by-step explanation:
The denominator of the first expression is ...
2x+10 = 2(x +5)
The denominator of the second expression is ...
7x +35 = 7(x +5)
The least common denominator (LCD) is the product of the unique factors in these denominators:
2×7×(x +5)
= 14(x +5) . . . . least common denominator
= 14x +70
how do i find the angles of a parallelogram
Answers
Answer:
opposite angle are equal and sum of adjecent angle = 180
WILL GIVE BRAINLIEST GIVE CORRECT ANSWER
Answers
Answer:
everything u chose is right
Step-by-step explanation:
50 = 20 + 4h
-20. -20
30/4= 4h/4
7.5 = h
So 50 = 20 + 4(7.5)
50 = 30 + 20
50 = 50
What is the VALUE of the underlined digit? 4,289,302 7,390,276
Answers
Answer:
8 is 10trillion and 7 is 1 million hope this helps!
Step-by-step explanation:
Whoever answers this for me gets brainliest
Answers
60 i have nothing more to add
uh how do i make histogram??
Answers
Answer:
Step-by-step explanation:
To make a histogram, follow these steps:
On the vertical axis, place frequencies. Label this axis "Frequency".On the horizontal axis, place the lower value of each interval. Draw a bar extending from the lower value of each interval to the lower value of the next interval.What does a histogram mean?
Histograms are equivalent to bar charts; they are a means for data counts to be displayed. Real counts against categories are seen in a bar graph; the bar height represents the number of objects in that category. In "bins", a histogram reveals the same categorical variables.
Create a Histogram: Stages for Steps
Sample question: With the following test scores, construct a histogram: 99, 97, 94, 88, 84, 81, 80, 77, 71, 25.
Phase 1: Diagram the x and y axes and label them. The x-axis would be labelled "score" for this case, and the y-axis would be labelled "relative percentage of frequency ."
Phase 2: Pick the number of bins (in statistics, how to choose bin sizes) and mark your graph. Query, Grou, Grou, for this sample,It's a smart option for groups of 10 (the x-axis values are the bins) (it looks like you'll have 5 bars of one or two objects in the group).
Step 3: To get an indication of where to put the frequency "ticks," divide 100 by the number of data points. In our data collection, we have 10 objects, so it makes sense to count 100/10 = 10 percent (one item would equal 10 percent of the total).
Build a histogram
Step 4: Count how many objects are in each bin and then outline a rectangle corresponding to the percentage of the total filled by the bin on the graph. The first bin (20-30) has 1 object in this sample data package, with 70-80 getting two items. When an object lands on a bin boundary (i.e. 80), bring it up in the next bin (80 will go to 80-90)
(hope this helps can i plz have brainlist :D hehe)
I need help please it’s worth13 points with explanation please
Answers
Answer:
1/7
Step-by-step explanation:
-(x + 3) = 8x - 4 - 2x
-x - 3 = 8x - 4 - 2x
combine like terms
-x - 3 = 6x - 4
add
-x = 6x -1
subtract
-7x = -1
divide
x = 1/7
Answer:
x = 1/7
Step-by-step explanation:
-(x + 3) = 8x - 4 - 2x
-x - 3 = 8x - 4 - 2x
-x - 3 = 6x - 4
-x = 6x -1
-7x = -1
x = 1/7
What is the product?
Answers
Answer:
-3
4
Step-by-step explanation:
You need to take something called the dot product
12 for the bottom one
What is the answer for 4(r-2+y) ?
Answers
Answer: 4R+4y-8
Step-by-step explanation:
Answer:
i hope my answer help u:))
Step-by-step explanation:
4r-8+4y it is easy :))
In the diagram, ABCD is a parallelogram. The diagonals of the parallelogram intersect at point T. D 16 If m<ABC =3y+5 and m<ADC =5y-45, what is m<BCD
Answers
Step-by-step explanation:
m<ABC =3y+5
m<ADC =5y-45
3y+5 = 5y-45
2y = 50
y = 25
.............
m<BCD = 180 - 80 = 100°
What is the area of the triangle given below?
O A. 6 sq. units
B. 12 sq. units
o C. 16 sq. units
O D. 8 sq. units
Answers
Answer:
I think its b sorry if it's wrong tho
The area of the triangle given in the figure is 6 square units.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
We need to find the area of triangle.
Area of triangle is 1/2 × Base × Height
The length of base is 6 units.
The length of height is 2 units.
Now let us plug in the value of base and height into the given formula of triangle.
Area of triangle =1/2×2×6
=6 square units
Hence, the area of the triangle given in the figure is 6 square units.
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Point M is the midpoint of AB. Find AM.
2x + 34
6x + 26
+
A
M M
B
Answers
Answer: AM = 76 and AB = 152
Step-by-step explanation:A little annoying but basically AM times 2 shoud equal AB or (2x+34)*2 = 6x+26 solve to get x equals 21 plug back in to get 76 for AM and 152 for AB
A department store buys 300 shirts at a cost of $3,600 and sells them at a selling price of $20 each. Find the percent markup. The percent markup is 1%. (Round to the nearest whole number as needed)
Answers
Answer:
40%
Step-by-step explanation:
A department store buys 300 shirts at a cost of $3,600 and sells them at a selling price of $20 each. Find the percent markup.
The formula for Percent Markup is given as:
Selling price - Cost price/Cost price × 100
Cost price = $3,600
Selling price = $20 × 300 shirts
= $6000
Percent Markup = $6000 - $3600/6000 × 100
= 2400/6000 × 100
= 40%
The percent Markup is 40%
Under his cell phone plan, Bentley pays a flat cost of $64.50 per month and $4 per gigabyte. He wants to keep his bill at $78.90 per month. How many gigabytes of data can he use while staying within his budget?
Answers
Answer:
3.6 gB
Step-by-step explanation:
You can think of this question in terms of the y = mx+b equation.
$78.90 is y because it is the total amount per month, $4 is m because it is the cost per gB, and $64.50 is b because it is the flat rate.
78.9 = 4x + 64.5
4x = 14.4
x = 3.6 gB of data (or 3 if it wants a whole number)
ANSWER QUICKLY PLEASE
Given the triangles are similar, find BD.
Answers
Answer:
The answer is 10
Step-by-step explanation:
Trust me
2). Stuart took his wife out to dinner. The bill came to $72.00 and he
wants to leave a 15% tip. How much should Stuart leave the server for the
tip? *
Hellllpppppop!?!?!!?????
Answers
Answer:
10.8
Step-by-step explanation:
Answer:
$10.8
Step-by-step explanation:
First, you would multiply 72 x 15 to get 1,080. Then, you would divide 1,080 by 100 to get 10.8. I hope this helps :)
5 (a) Write the ratio 15:35 in its simplest form.
Answers
Answer:
Step-by-step explanation:
5 is a factor of 15 and 35
15:35 = 3:7
Plz tell me if I’m wrong
Please help!!!!me!!!!!!
Answers
Answer:
y= 163 because of vertical angle
Answer:
y° = 163°
Step-by-step explanation:
In this question we have to find the value of y.
We can solve this using the property of vertically opposite angles, I.e, vertically opposite angles are equal to each other. In this case the vertically opp. angle of y is 163°. So that makes y° = 163°
3 Write the statement "10 is 7 less than the product of 5 and a" as a
mathematical equation.
Answers
How do I start a concat function and use the Index function with the first arguments list as the text1 argument?
Answers
Answer:
ask
Step-by-step explanation:
Hello, I really struggle with math and I was wondering if you could help me with the following problem please? It will be much appreciated and I will give brainliest to the answer that explains it to make it the easiest. Thanks
Answers
Answer:
x=7
Step-by-step explanation:
Simplifying
3x + 2(4 + 6x) = 113
3x + (4 * 2 + 6x * 2) = 113
3x + (8 + 12x) = 113
Reorder the terms:
8 + 3x + 12x = 113
Combine like terms: 3x + 12x = 15x
8 + 15x = 113
Solving
8 + 15x = 113
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-8' to each side of the equation.
8 + -8 + 15x = 113 + -8
Combine like terms: 8 + -8 = 0
0 + 15x = 113 + -8
15x = 113 + -8
Combine like terms: 113 + -8 = 105
15x = 105
Divide each side by '15'.
x = 7
Simplifying
x = 7
Answer:
x=7
Step-by-step explanation:
3X+2(4+6X)=113
=> 3X +2x4+2x6X=113
=> 3X+8+12X=113
=> 3X+12X=113-8
=>15X=105
=>X=7
5. A store sells milk in three different sizes. The 128 fl oz size costs $4.59. The 64 fl. oz container
costs $329. And, the 32 oz container cost $1.99. Which size has the lowest price per fluid
ounce?
Answers
128 divided by $4.59 = 27.88671023965142
64 divided by $329 = 0.19452887537994
32 divided by $1.99 = 16.08040201005025
Therefore, the size which has lowest price per fluid ounce is 32 fl. oz container .
You're just suppose to divide the fluid oz and the cost for all the sizes,which ever has the lowest price is the answer.
ratio in its simplest form 114 : 95
Answers
Answer:
Step-by-step explanation:
114:95 = 6:5
6:5
Step-by-step explanation:
What is the probability of rolling a standard six sided number cube to a number with 3 letters in the spelling of that number?
A) 1/6
B) 2/6
C) 3/6
D) 4/6
Answers
Answer:
C because six, one and two all have 3 letters in the spelling
Suppose management could improve the process by reducing the mean time required for an oil change (but keeping the standard deviation the same). How much change in the mean service time would be required to allow for a 10-minute guarantee that gives a coupon to no more than 1 out of every 25 customers on average
Answers
This question is incomplete, the complete question is;
The owners of Spiffy Lube want to offer their customers a 10-minute guarantee on their standard oil change service. If the oil change takes longer than 10 minutes to complete, the customers is given a coupon for a free oil change at the next visit. Based on past history, the owners believe that the timer required to complete an oil change has a normal distribution with a mean of 8.6 minutes and a standard deviation of 1.2 minutes.
Suppose management could improve the process by reducing the mean time required for an oil change (but keeping the standard deviation the same). How much change in the mean service time would be required to allow for a 10-minute guarantee that gives a coupon to no more than 1 out of every 25 customers on average
Answer:
Required change in the mean service time is 7.8988
Step-by-step explanation:
Given the data in the question;
How much change in the mean service time would be required to allow for a 10-minute guarantee that gives a coupon to no more than 1 out of every 25 customers on average
let mean = μ
p( x > 10 ) ≤ (1/25)
p( x > 10 ) ≤ 0.4
p( x-μ / 1.2 > 10-μ / 1.2 ) ≤ 0.4
(10-μ / 1.2 ) ≤ 0.4
(10-μ / 1.2 ) ≥ [tex]q_{norm}[/tex] ( 0.96 )
(10-μ / 1.2 ≥ 1.751
10-μ = ≥ 1.751 × 1.2
10-μ ≤ 2.1012
μ ≤ 10 - 2.1012
μ ≤ 7.8988
Therefore, required change in the mean service time is 7.8988
Find the equation of the line that passes through points A and B.
y.
AA (1,7)
-X
B (-3,-1)
Answers
Answer:
y=2x+5
Step-by-step explanation:
start with by stating your formula: y=MX +C
m= Y2-Y1÷X2-X1
m=-1-7÷-3-1
m=-8÷-4
m=2
substitutionUsing A's coordinates
7=2(1)+c
7=2+c
7-2=c
5=c
therefore y=2x+5
find the value of each variable using sine and cosine round your answers to the nearest tenth
Answers
9514 1404 393
Answer:
r ≈ 19.0
s ≈ 17.7
Step-by-step explanation:
The relevant trig relations are ...
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
So, you have ...
cos(43°) = r/26
r = 26·cos(43°) ≈ 19.0
__
sin(43°) = s/26
s = 26·sin(43°) ≈ 17.7
Can somebody help will give brainliest thank you
Answers
Step-by-step explanation:
1. the equation of a line is y = mx + c
m is the gradient and you can work this out by the change in y ÷ by the change in x
c is the y-intercept, which is where the line intercepts the y line.
2i.
(4 - 1) ÷ (2 - 1) = 3