Answers
Answer:
C. 90°Step-by-step explanation:
Angle ABC is the sum of angles ABD and DBC as per angle addition postulate
As per given we have isosceles triangles ABD and BCD
ADC is straight angle, therefore:
2x + x = 180°3x = 180°x = 60°Triangle ABD∠BAD = ∠ABD = 1/2(180° - 2x) = 1/2(180° - 120°) = 1/2(60°) = 30°Triangle BCD∠BDC =∠ BCD = x = 60°∠DBC = 180° - 2*60° = 180° - 120° = 60°So the angle ABC∠ABC = ∠ABD + ∠DBC∠ABC = 30° + 60° = 90°Related Questions
A store is having a sale on almonds and jelly beans. For 2 kilograms of almonds and 3 kilograms of jelly beans, the total cost is $11. For 6 kllograms of almonds and 5 kilograms of jelly beans, the total cost is $23. Find the cost for each kilogram of almonds and each kilogram of jelly beans.
Find cost for each kilogram of almonds :?
Ans find the cost for each kilogram of jelly beans :?
Answers
Answer:
The cost of each kg of almonds is $1.75
The cost of each kg of jelly beans is $2.5
Step-by-step explanation:
We will use the system of linear equations to solve the question
Assume that the cost of 1 kg of almonds is $x, and the cost of 1 kg of jelly beans is $y
∵ For 2 kilograms of almonds and 3 kilograms of jelly beans,
the total cost is $11
→ Multiply 2 by x and 3 by y, then equate their sum by 11
∴ 2x + 3y = 11 ⇒ (1)
∵ For 6 kilograms of almonds and 5 kilograms of jelly beans, the
total cost is $23
→ Multiply 6 by x and 5 by y, then equate their sum by 23
∴ 6x + 5y = 23 ⇒ (2)
Now we need to solve this system of equations to find the values of x and y
→ Multiply equation (1) by -3 to make the coefficient of x in it equals
the coefficient of x in equation (2) in values and differences in signs
∵ -3(2x) + -3(3y) = -3(11)
∴ -6x + -9y = -33 ⇒ (3)
→ Add equations (2) and (3) to eliminate x
∵ (6x + - 6x) + (5y - 9y) = (23 + -33)
∴ -4y = -10
→ Divide both side by -4 to find the value of y
∵ [tex]\frac{-4y}{-4}=\frac{-10}{-4}[/tex]
∴ y = 2.5
→ Substitute the value of y in equation (1) to find x
∵ 2x + 3(2.5) = 11
∴ 2x + 7.5 = 11
→ Subtract 7.5 from both sides
∵ 2x + 7.5 - 7.5 = 11 - 7.5
∴ 2x = 3.5
→ Divide both sides by 2 to find the value of x
∵ [tex]\frac{2x}{2}=\frac{3.5}{2}[/tex]
∴ x = 1.75
∵ x represents the cost of 1 kg of almonds
∴ The cost of each kg of almonds is $1.75
∵ y represents the cost of 1 kg of jelly beans
∴ The cost of each kg of jelly beans is $2.5
Find m\angle Am∠Am, angle, A. Note that m\angle Am∠Am, angle, A is acute. Round to the nearest degree. \Large{^\circ} ∘ degrees
Answers
Answer:
The answer is that the measure of ∠α is ≈ 20° when rounded to the nearest °
Step-by-step explanation:
To find the measure of ∠α you need to use the reciprocal of the formula for the law of sine which says that a/Sinα = b/Sinβ = c/Sin C. The reciprocal of this gives the new equation that states Sinα/a = Sinβ/b = Sin C/c, and this will help you to find the measure of the missing angle in °'s.
In the triangle line segment BC = 5units is opposite to point A & ∠α. Line segment AC = 7units is opposite of point and ∠β which is = 28°. And finally, the hypotenuse length and the values of point C & ∠C are unknown, so they aren't important to solving the problem. Knowing all this you can plug in all the known values into the new formula, and start working on figuring things out.
To find the measure ∠α, you first write down everything, putting things into their proper places, so since you're solving for sinα you want the equation to look like this:
sinα/5 = sin28°/7
Then for the second step, you want to isolate the sinα. (To get it by itself × both left and righthand sides by 5 to begin simplifying).
This leaves you with :
sinα = sin28°÷7 · (5) [And allows you to now solve for the right side of the equation, bringing us to our third step which is to once again simplify. So what you want to do is whip out your calculator and set it to degree mode, so you can find the of sin28° which is = 0.46947156278. Then ÷ that by 7, which will get you a number = 0.06706736611. Finally, take 0.06706736611 × 5, and you will get the value = 0.33533683056, as your final answer in the third step]
Your equation should now look something like this :
sinα = 0.06706736611 × 5 or 0.33533683056
Moving onto the fourth step, you need to use the inverse of the trig function of sin to get your absolute value. (remember the inverse of sine or acrsin = sin^-1) Here you will need to multiply sin^-1 by 0.33533683056.
And also by now, you'll want to stop writing the equation as sinα = sin^-1 ×
0.33533683056, otherwise you won't get an answer, instead, you'll need to write:
α = sin^-1 × 0.33533683056
So once you do that for the fifth and final step, you'll need to simplify the equation on the righthand side one last time, and you should get the answer of α = 19.5930217327°. Which when rounded to the nearest ° is ≈ 20°.
Tickets to a basketball game can be ordered online for a set price per ticket plus a $5 service fee. The total cost in dollars for ordering 5 tickets is $110.00. Which linear function represents c, the total cost, when x tickets are ordered?
c(x) = 5 + 21x
c(x) = 5x + 21
c(x) = 5 + 25x
c(x) = 5x + 21x
Answers
Answer:
A, c(x)=5+21x
Step-by-step explanation:
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The cost of a lamp was reduced from $40 to $22.
By what percent did the cost of the lamp decrease?
A 4.5%
B 25%
C 35%
D 45%
Answers
Answer:
45 %
Step-by-step explanation:
decreasing by half would be 50 percent making it only 20 dollars. In this situation it is 2 dollars more. 45 percent of 40 is 18. subtract: 40-18=22
The decreased percent of the cost of the lamp is 45%.
What is a percentage?A percentage is expressed as a number or ratio that can be expressed as fraction of 100. It is denoted by % symbol.
The cost of a lamp was reduced from $40 to $22.
Initial price = $40
Final price= $22
Decreased percentage =[tex]\frac{initial price-final price}{initial price} *100[/tex]
=[tex]\frac{40-22}{40} *100[/tex]
= 45%
Hence, the decreased percent of the cost of the lamp is 45%.
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Help plz and thank you I would appreciate it
Answers
Answer:
Positive Slope
Step-by-step explanation:
The slope is going up Right
B=10, 20 30, 40, 50, , in set builder notation
Answers
Answer:
40
Step-by-step explanation:
bexause u are a kid so dont ask this question again
20 POINTS!! what is the slope of this line
Answers
Answer: I really don't know?????
Step-by-step explanation:
Simplify 3x*3y^2/9xy^5 and explain please
Answers
A department store will place a sale item in a special display for a one-day sale. Previous experience suggests that 43 percent of all customers who pass such a special display will purchase the item. If 1,462 customers will pass the display on the day of the sale, and if a one-item-per-customer limit is placed on the sale item, how many units of the sale item should the store stock in order to have at most a 1 percent chance of running short of the item on the day of the sale? Assume here that customers make independent purchase decisions. (Round your answer to nearest whole number.)
Number of units?
Answers
Answer:
672.7436 units of the sale item should the store stock in order to have at most a 1 percent chance of running short of the item on the day of the sale
Step-by-step explanation:
No. of customers pass the display on the day of sale = 1462
Proportion of people will purchase if pass such a special display = 0.43
Mean = E(X)=np
E(X)=[tex]1462 \times 0.43[/tex]
E(X)=628.66
Standard deviation = [tex]\sqrt{npq}[/tex]
Standard deviation =[tex]\sqrt{1462 \times 0.43 \times (1-0.43)}=18.92[/tex]
Now we are supposed to find how many units of the sale item should the store stock in order to have at most a 1 percent chance of running short of the item on the day of the sale
P(X<x)=0.01
Using z table
[tex]P(\frac{x-\mu}{\sigma})= 2.33 \\\frac{x-628.66}{18.92}=2.33\\x=(2.33 \times 18.92)+628.66\\x=672.7436[/tex]
Hence 672.7436 units of the sale item should the store stock in order to have at most a 1 percent chance of running short of the item on the day of the sale
The number of units should be 672.7436 units.
Calculation of number of units:Since No. of customers pass the display on the day of sale is 1462 and the proportion of people who will purchase if pass such a special display is 0.43
So,
Mean should be = 43% of 1,462
= 628.66
Now the standard deviation should be
[tex]= \sqrt{1462 \times 0.43 \times (1-0.43)}[/tex]
= 18.92
Now the number of units should be
[tex]x - 628.66 \div 18.92 = 2.33[/tex]
x = 672.7436
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The triangles shown below must be congruent.
60°
60"
12
12
101
619
O A. True
O B. False
Answers
Answer:
true
Step-by-step explanation:
T(X,Y)_____
Name a line segment parallel to RS
Answers
Answer:
PQ
Step-by-step explanation:
Parallel lines are a pair of lines in a plane that do not meet/intersect
The jewelry store had a watch sale for Father’s Day. The watch I want is priced $75 but is on sale for 40% off what, is the sale price of the watch?
Answers
Answer:
$45
Step-by-step explanation:
The watch was sold on sale of 40%. This means that the price of the watch on sale is 60% of the original price. (100%-40%=60%)
So, you find the 60% of the original price, $75.
75*0.6=45
Hope that helps!!!
What is the image point of (1,0)(1,0) after a translation right 1 unit and up 4 units?
Answers
Answer:
0,4
Step-by-step explanation:
Kelsey wants to buy a new video game.
he has a $50 gift card and wants to spend less than $20 on his own money.
which of the following amounts would kelsey be willing to spend on the video game?
a. $75
b. $70
c. $65
Answers
Answer: c: $65
Step-by-step explanation:
1/ (12b + 5) for b = 5/6
Answers
Answer:
1/15
Step-by-step explanation: Just equate the values like my last ans
Answer:
Step-by-step explanation:
Step 1:
Put value of b = 5/6
1/(12(5/6)+5
1/60/6 +5
1/10+5
Answer:
1/15 or 0.06666
A researcher wants to test to see if husbands are significantly older than their wives. To do this, he collects the ages of husbands and pairs them with the ages of their respective wives for a random set of married couples. Suppose that data were collected for a random sample of 12 couples, where each difference is calculated by subtracting the age of the wife from the age of the husband. Assume that the ages are normally distributed. The test statistic is t≈1.434, α=0.05, the corresponding rejection region is t>1.796, the null hypothesis is H0:μd=0, and the alternative hypothesis is Ha:μd>0. Which of the following statements are accurate for this hypothesis test in order to evaluate the claim that the true mean difference between the age of the husband and the age of the wife is greater than zero?
Answers
Complete Question
The complete is shown on the first uploaded image
Answer:
The correct option are option 2 and option 4
Step-by-step explanation:
From the question we are told that
The sample size is n = 12
The test statistics is [tex]t \approx 1.434[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The rejection region is t>1.796
The null hypothesis [tex]H_o: \mu_d=0[/tex]
The alternative hypothesis is [tex]H_a : \mu_d >0[/tex]
From the given values we see that t < 1.796(i.e 1.434 < 1.796 ) which implies that t is not within the rejection region
Hence we fail to reject the null hypothesis
The conclusion is that there is insufficient evidence to suggest that that the husbands are significantly older than the wife.
Four times the sum of a number and 20 is at most -17
Answers
Answer:
4(20+b)≤-17
Step-by-step explanation:
I hope this helps!
Solve for b.
2(b + 7) = 20
b = ??
Answers
Answer:
6.5
Step-by-step explanation:
Answer:
7/9.
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
Step 2: Subtract 20b from both sides.
Step 3: Subtract 14 from both sides.
Step 4: Divide both sides by -18.
A rectangular table top has an area of 8ft and a perimeter of 12ft.What are the dimensions of the table?
Answers
Answer:
Dimensions are 2 and 4
Step-by-step explanation:
Area= a*b=8
Perimeter=2(a+b)=12 => a+b = 12/2. a+b = 6
a+b=6 =>a=6-b
If a=2=>b=4 so 4+2=6 , 4*2=8 and 4*2+2*2=12
If a=4=>b=2 so 4+2=6 , 4*2=8 and 4*2+2*2=12
Dimensions are 2 and 4
The possible dimensions of the table are -
L = 2, B = 4.
or
L = 4, B = 2.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a rectangular table top has an area of 8 ft and a perimeter of 12 ft.
Let the dimensions of the rectangular table be {x} ft and {y} ft respectively.
We can write -
xy = 8 ....... Eq(1)
2(x + y) = 12
x + y = 6 ....... Eq(2)
y = (6 - x)
Then, we can write -
x(6 - x) = 8
- x² + 6x = 8
x² - 6x + 8 = 0
(x - 2)(x - 4) = 0
We get -
x = 2 and x = 4
Now,
For x = 2, y = 4.
For x = 4, y = 2.
Therefore, the possible dimensions of the table are -
L = 2, B = 4.
or
L = 4, B = 2.
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`jae is costructing an open box froma piece of cardboard that is 9in. wide and 12in. long.
Answers
Answer:4
Step-by-step explanation:
m
m
m
What is the measure of Z CZD?
PLEASE HELP!
Answers
9514 1404 393
Answer:
34°
Step-by-step explanation:
∠FZE and ∠BZC are vertical angles, so are congruent. The angle sum theorem tells us ...
∠BZC +∠CZD = ∠BZD
(2x+5) +x = 107
3x = 102
x = 34
The measure of ∠CZD is 34°.
A company rents paddleboards by charging a rental fee of $15 plus an hourly rate of $12. Write an expression that represents the cost in dollars of renting a paddleboard for ,h, hours.
Answers
I need 20 characters
Answer:
x= 12h +15
Step-by-step explanation:
2/7(x+4)=−6 solve for x
Answers
Answer:
x = -25
Step-by-step explanation:
solve for x by simplifying both sides of the equation, then isolating the variable.
Do someone know how much is 3/4 of 12?
Answers
3/4 of 12 is 9
I hope it helps!
Answer:
9 is 3/4 0f 12
Step-by-step explanation:
Multiply by the numerator of the fraction and divide by the denominator.
You can do this in either order.
12 × 3 = 36 then 36 ÷ 4 = 9 OR
12 ÷ 4 = 3 then 3 × 4 = 9
I need help please I’m struggling in this Question can you please help me .
Answers
Answer:
i forget how to get it :)
Step-by-step explanation:
Answer: B
Step-by-step explanation: logical answer but if its nit right my bad
I really need help. So one please help me it will be greatly appreciated.
Answers
Answer:
C
Step-by-step explanation:
Write each equation in slope-intercept form.
19. y - 4 = 3(x - 2)
20. y + 2 = -(x + 4)
21. y - 6 = -2(x + 2)
22. y + 1 = -5(x - 3)
23. y - 3 = 6(x - 1)
24. y - 8 = 3(x + 5)
Answers
Answer:
Lol, here is the answer again. Good luck
5 x 9 = 45 times as many is
Answers
NEED HELP ASAP!!!!!!!!!!!!!!!
Answers
Answer: c is the answer
Tyler's mom purchased a savings bond for Tyler. The value of the savings bond increases by 4% each year. One year after it was purchased, the value of the savings bond was $156. Find the value of the bond when Tyler's mom purchased it. Explain your reasoning
Answers
Answer:
I think it is 6.24
Step-by-step explanation:
not really sure
Answer:
150
Step-by-step explanation: