In Triangle BCD, BC=BD, and angle B =13x-35, angle C = 5x-19, angle D=2x+14. Find the measure of each angle
Answer:
[tex]B = 108[/tex]
[tex]C = 36[/tex]
[tex]D = 36[/tex]
Step-by-step explanation:
Given
[tex]B =13x - 35[/tex]
[tex]C = 5x - 19[/tex]
[tex]D=2x+14[/tex]
[tex]BC = BD[/tex]
Required
Determine the measure of each angle
The angles in a triangle sum up t 180. i.e.
[tex]B + C + D = 180[/tex]
Since [tex]BC = BD[/tex], then [tex]C = D[/tex]
[tex]B + C + D = 180[/tex] can then be rewritten as:
[tex]B + C + C = 180[/tex]
[tex]B + 2C = 180[/tex]
Substitute values for B and C
[tex]13x - 35 + 2(5x - 19) = 180[/tex]
Open Bracket
[tex]13x - 35 + 10x - 38 = 180[/tex]
Collect Like Terms
[tex]13x + 10x = 180 + 38 + 35[/tex]
[tex]23x= 253[/tex]
Divide both sides by 23
[tex]x = 11[/tex]
To get the measure of each angle, substitute 11 for x in the expressions of B, C and D
[tex]B =13x - 35[/tex]
[tex]B = 13 * 11 - 35[/tex]
[tex]B = 108[/tex]
[tex]C = 5x - 19[/tex]
[tex]C = 5 * 11 - 19[/tex]
[tex]C = 36[/tex]
[tex]D=2x+14[/tex]
[tex]D = 2 * 11 + 14[/tex]
[tex]D = 36[/tex]
The measure of m<B, m<C and m<D are 108, 36 and 46 respectively
What are triangles?From the triangle BCD, if BC=BD, then
m<C = m<D (Base angles are equal)
Given the following paramters:
m<C = 5x-19m<D = 2x + 14Hence;
5x - 19 =2x + 14
5x- 2x = 14 + 19
3x = 33
x = 11
m<B = 13x - 35
m<B = 13(11) - 35
m<B = 108 degres
m<C = 5x - 19
m<C = 55- 19
m<C = 36
m<D = 180 - 144
m<D = 36 degreees
Hence the measure of m<B, m<C and m<D are 108, 36 and 46 respectively
learn more on angles here: https://brainly.com/question/16281260
let a(-a -b) b(-a -b) distance between two points
fast
Answer:
A(-a,-b)and B(-a,-b) be
distance between AB= square root(x2-x1)^2+(y2-y1)2
AB= square root (-a)-(-a)^2+(-b)-(-b)^2
AB= squareroot (-a+a)^2+(-b+b)^2
AB= square root (0)^2+(0)^2
AB=square root 0+0
AB= square root 0
AB=0 answer
this may help you !!!!!
At the beginning of a baking session, there were 2.26 kilograms of flour in a bag. By the end of the baking session, there were 0.98 kilograms of flour in the bag. What is the percent decrease in the amount of flou
Answer: 56.64%
Step-by-step explanation:
Given: Previous amount of flour = 2.26 kilograms
By the end of the baking session, amount of flour = 0.98 kilograms
Decrease in amount = 2.26-0.98 = 1.28 kilograms
Percent decrese = [tex]\dfrac{\text{decrease in amount }}{\text{previous amount}}\times100[/tex]
[tex]=\dfrac{1.28}{2.26}\times100\approx56.64\%[/tex]
Hence, the percent decrease in the amount of flour = 56.64%
plz help me its do today
What's the recursive rule for this sequence? 75, 100, 125, 156,
Answer:
The recursive rule for the sequence is a[tex]_{1}[/tex] = 75; a[tex]_{n}[/tex] = a[tex]_{n-1}[/tex] + 25
Step-by-step explanation:
the recursive rule of an arithmetic function is a[tex]_{1}[/tex] = first term; a[tex]_{n}[/tex]= a[tex]_{n-1}[/tex] + d, where
a[tex]_{1}[/tex] is the first terma[tex]_{n-1}[/tex] is the nth termd is the common difference between each 2 consecutive terms∵ The given is 75, 100, 125, 150, .......
∵ 100 - 75 = 25
∵ 125 - 100 = 25
∵ 150 - 125 = 25
∴ The common difference is 25
∴ d = 25
∵ The first term is 75
∴ a[tex]_{1}[/tex] = 75
→ Substutute the values of a1 and d in the formula above
∴ The recursive rule for the sequence is a[tex]_{1}[/tex] = 75; a[tex]_{n}[/tex] = a[tex]_{n-1}[/tex] + 25
Add 3 level scoops of mini chocolate chips and 1 level scoop of raisins to Container 1. If each scoop has the same number of items, what percent of the items in Container 1 are mini chocolate chips? (This value is known as the percent concentration of chips.) Explain how you decided. Label the container appropriately Answer: 50% because when there is only 2 variables and they are each 1 cup there is an even amount of stuff and when you ask for only one percentage that would be 50% because everything is even. Even if you asked for the percentage for the cup of raisins it would also be 50% Add 2 scoops of mini chocolate chips and 3 scoops of raisins to Container 2. What is the percent concentration of mini chocolate chips? Explain how you decided. Label the container appropriately. Stir the chips and raisins in each container to ensure that the chips and raisins are evenly mixed.
Answer:
Container 1
The percentage of mini chocolate chip is 3/4 * 100= 75 % to raisins.
Container 2
The percentage of mini chocolate chip is 2/5 * 100= 40 % to raisins.
Step-by-step explanation:
Container 1
Mini Chocolate Chips: Raisins
3 scoops: 1 scoop
The percentage of mini chocolate chip is 3/4 * 100= 75 % to raisins.
Container 2
Mini Chocolate Chips: Raisins
2 scoops: 3 scoop
The percentage of mini chocolate chip is 2/5 * 100= 40 % to raisins.
This is simplified with the help of the ratios . We find out the ratio of the mini chocolate to the total of both the ratios and mulitply it with 100 to get the percentage concentration.
estimate 1scoop chips and 2scoops rice percentage
Molly is making bags of trail mix for the hiking club. She will use 20 ounces of walnuts. 11.1 ounces of almonds, and 24.8 ounces of cashews. This amount makes 26 bags of trail mix. How many ounces are in each bag?
Answer:
2.15 ounces
Step-by-step explanation:
The total ounces of nuts in the bag is calculated as:
20 ounces of walnuts + 11.1 ounces of almonds + 24.8 ounces of cashews = 55.9 ounces.
From the question we are told that these amounts make 26 bags.
The number of ounces that are in each bag is calculated as:
26 bags = 55.9 ounces
1 bag = x ounces
Cross Multiply
26 bags × x ounces = 1 bag × 55.9 ounces
x ounces = 1 bag × 55.9 ounces/26 bags
x ounces = 2.15 ounces
Therefore, there are 1.94 ounces in each bag
What is an equation of the line that passes through the points (-3, 8) and (4, 1)?
Answer:
The equation of the line is:
[tex]y=-x+5[/tex]
Step-by-step explanation:
Given the points
(-3, 8)(4, 1)Finding the slope between the points
[tex]\left(x_1,\:y_1\right)=\left(-3,\:8\right),\:\left(x_2,\:y_2\right)=\left(4,\:1\right)[/tex]
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{1-8}{4-\left(-3\right)}[/tex]
[tex]m=-1[/tex]
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope
substituting the values m = -1 and the point (-3, 8)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-8=-1\cdot \left(x-\left(-3\right)\right)[/tex]
[tex]y-8=-\left(x+3\right)[/tex]
Add 8 to both sides
[tex]y-8+8=-\left(x+3\right)+8[/tex]
[tex]y=-x+5[/tex]
Therefore, the equation of the line is:
[tex]y=-x+5[/tex]
x-6y + 4-12
x+y- 43 12
2+2y +5-13
Solve using substitution
Answer:
x-6y-8
x+y-4312
2y-6
Answer:
x-6y-8
X+y-4312
2y-6
Step-by-step explanation:
given
X-6y + 4-12
x+y- 43 12
2+2y +5-13
Solution
x-6y-8
X+y-4312
2y-6
PLEASE HELP ME
An alloy is a mixture of metals.Suppose that a certain alloy is made by mixing 70 grams of an alloy that contains 12% copper with 90 grams of pure copper.
Answer the questions below. Do not do any rounding.
(a) How many grams of copper are in the resulting mixture?
Il grams
(b) What percentage of the resulting mixture is copper?
Answer:
(a) How many grams of copper are in the resulting mixture?
= 160 grams
(b) What percentage of the resulting mixture is copper?
= 61.5%
Step-by-step explanation:
(a) How many grams of copper are in the resulting mixture?
From the question: Suppose that a certain alloy is made by mixing 70 grams of an alloy that contains 12% copper with 90 grams of pure copper.
The number of grams of copper in the resulting mixture = 70 grams + 90 grams = 160 grams
(b) What percentage of the resulting mixture is copper?
70 grams of an alloy that contains 12% copper = 70 × 12%
= 70 grams × 0.12
= 8.4 grams
The number of grams of copper in the resulting mixture = 160 grams
The percentage of the resulting mixture that is copper is
=( 8.4 grams + 90 grams of pure copper/160) × 100
= 98.4/160 × 100
= 61.5%
$25 with a 300% increase
Answer:
100 dollars
Step-by-step explanation:
So amount of increase = (300/100) * 25
= 3 * 25
= 75 dollars
Then the final amount = (25 + 75) dollars
= 100 dollars
A gas station sells unleaded regular and unleaded premium gasoline. The price per gallon charged by the station is$1.299 for unleaded regular and $1.379 for unleaded premium. The cost per gallon from supplier is$1.219 for unleaded regular and $1.289 for unleaded premium. If equals the number of gallons sold of regular and equals the number of gallons sold of premium:(a) Formulate the revenue function from selling and gallons of the two grades of gasoline respectively?(b) Formulate total cost for purchasing and gallons?(c) Formulate the total profit? d) what is the total profit expected to equal if the station sells 100,000 gallons of unleaded and regular and 40000 of unleaded premuim?
Answer:
a) Revenue function = 1.299r + 1.379p
where: r = gallon of unleaded regular gasoline and p = gallon of regular unleaded premium gasoline
b) cost function = 1.219f + 1.289p
c) profit function = (1.299r + 1.379p) - (1.219f + 1.289p) = 1.299r - 1.219r + 1.379p - 1.289p = 0.08p + 0.09p
d) total profit = (0.08 x 100,000) + (0.09 x 40,000) = $8,000 + $3,600 = $11,600
Completing Proofs Involving Linear Pairs
Given: m ZELG = 124°
Prove: x = 28
Statements
Reasons
1. m ZELG = 124
1. given
2. m ZELD = 2x
2. given
H
L
3. ZELG and ZELD are
a linear pair
3. definition of a linear pair
(2x)
G
4. m ZELD + m ZELG = 180
4.
Ε
• F.
5. 2x + 124 = 180
5. substitution
Complete the steps in the two-column proof.
6.
6. subtraction property
7. x = 28
7. division property
Intro
Done
vity
Answer:
1. angle addition post
2. 2x=56
The corresponding angles of the lines solved and the value of x = 28°
What are angles in parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.
We can conclude three factors determining parallel lines ,
Alternate angles are equal
Corresponding angles are equal
Co-interior angles add up to 180°
Given data ,
Let the measure of ∠ELG = 124°
The measure of ∠ELD = 2x
∠ELG and ∠ELD are a linear pairs of angles
So , the measure of ∠ELG + ∠ELD = 180°
On simplifying , we get
2x + 124° = 180°
Subtracting 124° on both sides , we get
2x = 56°
Divide by 2 on both sides , we get
x = 28°
Therefore , the value of x is 28°
Hence , the angle is x = 28°
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Question: If an electric train is moving north at 100mph and a wind is blowing to the west at 10mph, which way does the smoke blow?
Answer:
There is no smoke due to it being an electric train.
Step-by-step explanation:
Didn't fool me. ;)
what is 1/2 of 6/7
Answer:
3/7
Step-by-step explanation:
6/14 which equals 3/7
In row 2, write the equation of a quadratic function that satisfies f(0) = 2.
Find the center and radius of the equation of the circle
a). x2 + y2 – 8x +6y + 9 = 0
Compare the given equation with the general equation of a circle
Given equation: x² + y² - 8x +6y +9 = 0
Equation of a circle: x² + y² + 2gx + 2fy + c = 0
2g= -8; g = -8÷2= -4
2f = 6; f = 6÷2 = 3
c= 9
Solving for radius of the circle...
r =√g² + f² - c
g= -4, g² = ±16
f = 3, f² = 9
Substituting, we have
r = √16 + 9 - 9
r = √25-9
r=√16
r = 4
Therefore, the centre and radius of the circle is 9 and 4 respectively.
Hope this helped!
Please mark brainliest;-)
When Makayla moved into a new house, she planted two trees in her backyard. At the
time of planting, Tree A was 19 inches tall and Tree B was 35 inches tall. Each year
thereafter, Tree A grew by 6 inches per year and Tree B grew by 2 inches per year. Let
A represent the height of Tree At years after being planted and let B represent the
height of Tree B t years after being planted. Write an equation for each situation, in
terms of t, and determine the number of years after the trees were planted when both
trees have an equal height.
Answer:A=6t+29
B=3t+35
Same height in 4 years
Step-by-step explanation:
Answer:
A=6t+19
B=2t+35
4 years
Step-by-step explanation:
A-
The tree Orginal Length- 19 inches
Rate the tree grew every year- 6 inches per year
Equation- 6t+19
B-
The tree Orginal Length- 35 inches
Rate the tree grew every year- 2 inches per year
Equation- 2t+35
6(4)+19
24+19
43
2(4)+35
8+35
43
y=3/8x−4 write in standard form
Answer:
3x-8y=32
Step-by-step explanation:
What is the volume of a container that is 5cm tall by 10cm long and 4cm deep
Answer:
200cm³
Step-by-step explanation:
lenght×width×height=Volume
10cm×4cm×5cm=200cm³
Hey can someone pls help me will give brainliest I will be very grateful thx!!!!
Answer:
17) 4 inches
18) 14 inches
19) 162 inches
20) 30 inches
Step-by-step explanation:
For the first two, you use the formula π× (radius)². Since you have the area, divide it by two then find the square root. For the second two, you just divide the by pi.
Answer:
17) D=4in
18)D=14yd
19)D=162yd
20)D=30yd
Step-by-step explanation:
17)
[tex]d = 2 \times \sqrt{4} = 4[/tex]
m/9 - 9 = -8. please help
What is the slope of the line?
1.What is the slope of the line?
(simplify your answer)
2. What is the value of a?
3. What is the value of b?
4. What is the y-coordinate when x = 0?
Answer:
1. slope is 2
2. a is 5
3. b is 6
4. 0
Step-by-step explanation:
A circle is divided into 3 equal parts. What is the total angle measure of 1 part?
Answer:
120 degrees each
Step-by-step explanation:
360 degress divided by 3 = 120
80 students were at the volleyball game.
Some went home and now there are only 52. What is the percent of change?
what is -40+7r=-5(8+5r)
Answer:
r= -40/9 or r=-4 4/9
Step-by-step explanation:
You're welcome :)
A recipe calls for 3 cups of flour to 4 cups of sugar. Find the unit rate of flour to cups of sugar.
Answer: 0.75 cups of flour to 1 cup of sugar.
Step-by-step explanation:
From the question, we are informed that a recipe calls for 3 cups of flour to 4 cups of sugar and told to calculate the unit rate.
It simply means what we need to calculate much of flour to one cup of sugar. This will be:
= 3/4 = 0.75
Therefore, the unit rate will be:
0.75 cups of flour to 1 cup of sugar.
can someone please help and explain
Answer:
Im not sure how you are supposed to answer this but they are similar by side angle side
Step-by-step explanation:
We are given that NO/OQ=PO/OM
This tells us that the sides are in a ratio.
We also know that angle NOM is equal to angle POQ
Now we have 2 sides and 1 angle thus they are similar by side angle side
I hope this helps you come up with your statements and reasons
Answer:
I think the answer is scalpel porators
Step-by-step explanation:
(50 points) Use the spinner below. Show your work, making sure to simplify your answers. (Note: The smallest section of the circle is 1/16 of the circle.) 16. What is P(red, yellow, blue)? 17. What is P(orange, yellow)? 18. P(green, blue, purple)? 19. P(pink)? 20. P(red, orange, yellow, green, blue, purple)? Thank you!!
Answer:
I have the same questions and I got them right
Step-by-step explanation:
16. What is P(red, yellow, blue)?
P(red, yellow, blue)= 6/16= 3/8.
4/16+ 1/16+ 1/16= 6/16= 3/8
17. What is P(orange, yellow)?
P(orange, yellow)= 1/8
1/16+1/16= 2/16= 1/8
18. P(green, blue, purple)?
P(green, blue, purple)= 5/8
7/16+1/16+2/16= 10/16= 5/8.
19. P(pink)?
P(pink)=0
There is no pink color.
20. P(red, orange, yellow, green, blue, purple)?
P(red, orange, yellow, green, blue, purple)= 16/16= 1.
4/16+ 1/16+ 1/16+ 7/16+1/16+2/16 =16/16= 1.