Answers
Answer:
a) 10.7 cm
b) 11.6 cm
c) 29.9 cm²
Step-by-step explanation:
a) sin(α)/a = sin(β)/b
sin(∠BCD)/BD = sin(DBC)/DC
sin(41°)/BD = sin(55°)/13.4
BD = 13.4*sin(41°)/sin(55°) = 10.73 cm ≈ 10.7 cm
b) From ΔBCD , ∠BDC = 180-(41+55) = 84°
∠ABD and ∠BDC are alternate interior angles, so they are congruent, and
∠ABD = ∠BDC = 84°
AD²= AB² + BD² - 2*AB*BD*cos (∠ABD) =
= 5.6² + 10.73² - 2*5.6*10.73*cos(84°) = 133.93 cm²
AD =√(133.93) ≈11.6 cm
c) Area(ADB) = (1/2)*AB*BD*sin(∠ABD)=(1/2)*5.6*10.73*sin(84°) ≈ 29.9 cm²
Related Questions
Kyra was building a bed for her dollhouse. She used her bed, which is 4 feet × 5 feet, as a guide. She scaled down the dimensions of her bed by a factor 1/5. What are the dimensions of the model bed she built?
A,) 0.8 ft × 0.1 ft
B.) 0.4 ft × 0.5 ft
C.) 0.8 ft × 1 ft
D.) 0.04 ft × 0.05 ft
Answers
Answer: C. 0.8 ft x 1 ft
Step-by-step explanation:
The scale factor of 1/5 means you multiply
the dimensions by 1/5
4 * 1/5 = 0.8
5 * 1/5 = 1
Answer:
C. 0.8 ft x 1 ft
Step-by-step explanation:
If HK is an altitude of triangle HIJ, IKH = (4x + 50)º, HIK = 43, and KI = x - 7, find Kl.
Plz help now plz
Answers
[tex]answer \\ option \: a \\ 3 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]
Convert 2 3/4 to a decimal number.
Answers
Answer:
2.75
Step-by-step explanation:
3/4 is .75 in decimal
The two triangles in the diagram are similar. There are two possible values of x. Work out each of these values. State ALL of your workings out.
Answers
Answer:
X = 2
Step-by-step explanation:
Since two triangles ΔACD and ΔABE are similar triangles, their corresponding sides will be proportional.
Therefore, [tex]\frac{\text{AC}}{\text{AB}}=\frac{\text{AD}}{\text{AE}}[/tex]
By substituting the measures of the sides in the expression,
[tex]\frac{(x+10)}{10}=\frac{(15+3)}{15}[/tex]
15(x + 10) = 180
x + 10 = 12
x = 12 - 10
x = 2
Therefore, for the given similar triangles value of x = 2
I really need help!! I don't get this could someone help me?
Answers
Answer:
Side a is 35/5=7 inches long
Side b is 30/5=6 inches long
Side c is 15/5=3 inches long
help me for brainliest answer
Answers
Answer:
Step-by-step explanation:
Pattern 6 will have 35
The formula would be 2+5n
the area of polygon MNOPQR = area of a rectangle that is 15 square units + area of a rectangle that is ___ square units. (input whole numbers only, such as 8)
im not understanding too well so...please help :/
Answers
Answer:
The answer is 2.
Step-by-step explanation:
3 - 2 = 1
7 - 5 = 2
2 x 1 = 2
If the graphs of the linear equations in a system are parallel, what does that mean about the possible solution(s) of the system
ОА.
There is no solution.
OB.
The lines in a system cannot be parallel.
Ос.
There are infinitely many solutions.
OD.
There is exactly one solution.
Answers
Answer:
A
Step-by-step explanation:
The solution to a system of equations given graphically is at the point of intersection of the 2 lines.
If the lines are parallel then they never intersect, thus there can be no solution.
Answer:
ОА.
There is no solution
Step-by-step explanation:
If lines are parallel, they will have no common points, so no solution
uses
Katherine has 27 cups of yogurt to make smoothies. Each smoothie
1 cup of yogurt. What is the maximum number of smoothies that
Katherine can make with the yogurt?
Answers
Answer:
27 smoothies
Step-by-step explanation:
if you have 27 cups and one requires one cup, it would be 27 smoothies Katherine can make :)
A person places $728 in an investment account earning an annual rate of 4.4%, compounded continuously. Using the formula V = Pe^rt where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 16 years.
Answers
Answer:
Step-by-step explanation:
For us,
P = 728,
r = .044,
e is Euler's number (a constant), and
t is 16. Filling in:
[tex]V=728e^{(.044)(16)}[/tex] and
[tex]V=728e^{(.704)}[/tex] and
V = 728(2.02182385) so
V = $1471.89
A person places $728 in an investment account earning an annual rate of 4.4%, compounded continuously. The value of the account in t years is $1471.89.
We have given that,
P = 728,
r = 0.044,
e is Euler's number (a constant), and
t = 16.
What is the formula of the account in t years?The formula of the account in t years is,
[tex]V = Pe^{rt}[/tex]
Use the given value in the above formula,
V = 728(2.02182385)
Therefore we get,
V = $1471.89
Therefore, the value of the account in t years is $1471.89.
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Find EF, Im having trouble with this
Answers
Answer:
EF = 6
Step-by-step explanation:
(whole secant) x (external part) = (whole secant) x (external part)
(4+2x) * 4 = (5+x) * 5
Distribute
16+8x = 25+5x
Subtract 5x
16+3x = 25
Subtract 16
3x = 25-16
3x = 9
Divide by 3
x = 9/3
x=3
We want EF
EF = 2x = 2*3 = 6
Patel squeezed oranges so that his family could have fresh-squeezed juice for breakfast. He squeezed 4/17 cups from the first orange, 3/10 cups from the second orange, 9/20cups from the third orange, 3/11 cups from the fourth orange, and 7/15 cups from the fifth orange. Patel estimates that he needs 2 cups of orange juice for his family. About how much more orange juice does he need to reach his estimate
Answers
Answer:
He needs 0.275 cups of orange juice to reach his estimates
Step-by-step explanation:
Patel estimates he needs 2 cups of orange juice for his family . He squeezed fresh juice from 5 different oranges and got the following quantities measured in cups.
4/17 cups, 3/10 cups , 9/20 cups, 3/11 cups and 7/15 cups.
Adding them together we will know the amount he got. Therefore,
4/17 + 3/10 + 9/20 + 3/11 + 7/15
(40 + 51)/170 + 9/20 + 3/11 + 7/15
91/170 + 9/20 + (45 + 77)/165
(1820 + 1530)/3400 + 122/165
3350/3400 + 122/165
0.98529411764 + 0.73939393939
1.72468805703
Patel got approximately 1.725 cups of orange juice . He will require 2 - 1.725 = 0.275 cups of orange juice to reach his estimates.
1/2 cup of orange juice
What is the value of the expression when n = 3?
GO
- 2 n(5 + n-8-3n)
Answers
Answer:
54
Step-by-step explanation:
since n = 3
= -2n ( 5n+n-8-3n)
= -2 (3) ( 5+(3)-8-3(3) )
= -6 (5+3-8-9)
= -6 (5-5-9)
= -6 (-9)
= 54.
Can I get the answer to this?
Answers
m<JKL=45°
Please see the attached picture for full solution
hope it helps..
Good luck on your assignment...
Answer:45°
Step-by-step explanation:
An increase in walking has been shown to contribute to a healthier life-style. A sedentary American takes an average of 5000 steps per day (and 65% of Americans are overweight). A group of health-conscious employees of a large health care system volunteered to wear pedometers for a month to record their steps. It was found that a random sample of 40 walkers took an average of 5430 steps per day, and the population standard deviation is 600 steps. At = 0.05 can it be concluded that they walked more than the mean number of 5000 steps per day?
Answers
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ = 5000
For the alternative hypothesis,
H1: µ > 5000
Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = population standard deviation
n = number of samples
From the information given,
µ = 5000
x = 5430
σ = 600
n = 40
z = (5430 - 5000)/(600/√40) = 4.53
Looking at the normal distribution table, the probability corresponding to the z score is < 0.0001
Since alpha, 0.05 > than the p value, then we would reject the null hypothesis. Therefore, at a 5% level of significance, it can be concluded that they walked more than the mean number of 5000 steps per day.
Since the margin of error is 0.11, it can't be concluded that they walked more than the mean number of 5000 steps per day.
Standard deviationGiven that it was found that a random sample of 40 walkers took an average of 5430 steps per day, and the population standard deviation is 600 steps, to determine if at = 0.05 can it be concluded that they walked more than the mean number of 5000 steps per day the following calculation must be made:
5430 = 100600 = X600 x 100 / 5430 = X60000 / 5430 = X11.04 = XTherefore, since the margin of error is 0.11, it can't be concluded that they walked more than the mean number of 5000 steps per day.
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Marcus spent 10 hours doing his homework last week. This week he spent 11 hours doing homework. He says that he spent 110% more time doing homework this week. Is he correct?
Answers
Answer:
[ 11 - 10 ] / 10 x 100%
= 1 /10 x 100%
= 10%
Only 10% longer
Gabriella drives her car 300 miles and averages a certain speed. If the average speed had been 9mph less, she could have traveled only 240 miles in the same length of time. What is her average speed?
Answers
Answer:
Her average speed is 45 mph
Step-by-step explanation:
Let the average speed be x mph
Time taken complete the journey = distance/ average speed
Time = 300/x
Now , at 9 mph less, she could have only traveled 240 miles in same time
At 9 mph less, the average speed is x-9
so the time would be 240/x-9
since the time is same as before;
300/x = 240/x-9
Divide both sides by 60
5/x = 4/x-9
Cross multiply
5(x-9) = 4(x)
5x - 45 = 4x
5x -4x = 45
x = 45 mph
Find the solutions to x^2=27 A x= +/- 9 √3 B x= +/- 3 √9 C x= +/- 3 √3 D x= +/- 9 √2 FIRST TO ANSWER CORRECTLY GETS BRAINLIEST :-)
Answers
Answer:
The answer is C.
Step-by-step explanation:
You have to square both sides :
[tex] {x}^{2} = 27[/tex]
[tex]x = ± \sqrt{27} [/tex]
Then, you have to simplify it :
[tex]x = ± \sqrt{9 \times 3} [/tex]
[tex]x = ±( \sqrt{9} \times \sqrt{3} )[/tex]
[tex]x = ±( 3 \times \sqrt{3} )[/tex]
[tex]x = ±3 \sqrt{3} [/tex]
Answer:
Option C) x = ±[tex]3\sqrt{3}[/tex]
Step-by-step explanation:
=> [tex]x^2 = 27[/tex]
Taking sqrt on both sides
=> x = ±[tex]\sqrt{27}[/tex]
=> x = ±[tex]\sqrt{3 * 3*3}[/tex]
=> x = ±[tex]3\sqrt{3}[/tex]
Please help me………………………
Answers
The square root of 81/625 = 0.36
The square root of x^2 = x
The square root of y^2 = y
25 x 0.36 = 9
X *x = x^2
Y*y = y^2
Final answer = 9x^2y^2
Answer:
The answer is option d. 9x²y²
Step-by-step explanation:
25xy√81/625x²y²
= 25xy × 9/25xy
= 9x²y²
Hope this helps.
The end behaviour for the polynomial function h(x)=−x3+x4−2x+1 h ( x ) = - x 3 + x 4 - 2 x + 1 is: x→−[infinity], y→−[infinity] x → - [infinity] , y → - [infinity] and x→[infinity], y→[infinity] x → [infinity] , y → [infinity] x→−[infinity], y→[infinity] x → - [infinity] , y → [infinity] and x→[infinity], y→[infinity] x → [infinity] , y → [infinity] x→−[infinity], y→−[infinity] x → - [infinity] , y → - [infinity] and x→[infinity], y→−[infinity] x → [infinity] , y → - [infinity] Unable to tell.
Answers
Answer:
[tex]\text{As } x \to \infty, y \to \infty,$and as x \to -\infty, y \to \infty[/tex]
Step-by-step explanation:
Given the polynomial function: [tex]h(x)=-x^3+x^4-2x+1[/tex]
To examine its end behavior, we create a table of values that we can then examine.
[tex]\left|\begin{array}{c|c}x&h(x)\\--&--\\-4&329\\-3&115\\-2&29\\-1&5\\0&1\\1&-1\\2&5\\3&49\\4&185\end{array}\right|[/tex]
From the table, we see a repeating pattern of positive values of h(x) with h(1)=-1 being an axis of symmetry.
Therefore, as:
[tex]x \to \infty, h(x) \to \infty\\x \to -\infty, h(x) \to \infty[/tex]
Angela bought 10 stamps that cost $1 or $1.20.
Altogether, her total was $11. How many of each $1 stamps and how many of
each $1.20 stamps did she buy?
Answers
Answer:
Let the first equation be x + y = 10
x = 10 -y
2nd equation will be 1x + 1.2y = 11
Substituting in 2nd equation
(10 - y) + 1.2y = 11
10 - y + 1.2y = 11
.2y = 1
y = 5
If y = 5, x = 5: coz x + y = 10
She have buy 5 stamps of each $1 stamps and 5 stamps of each $1.20 stamps.
What is a linear equation?
A linear equation is an equation that has the variable of the highest power of 1.
The standard form of a linear equation is of the form Ax + B = 0.
Let the first equation be;
x + y = 10
x = 10 -y
2nd equation will be,
1x + 1.2y = 11
Substituting in 2nd equation;
(10 - y) + 1.2y = 11
10 - y + 1.2y = 11
0.2y = 1
y = 5
If y = 5, x = 5:
x + y = 10
Hence, She have buy 5 stamps of each $1 stamps and 5 stamps of
each $1.20 stamps.
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A firefighter sees a woman trapped in a building 15 feet up from the bottom floor. The firetruck is parked 35 feet away from the bottom of the building. At what angle of elevation, to the nearest degree, should the firefighter extend the ladder to reach the woman?
Answers
Answer:
70 degrees
Step-by-step explanation:
Answer:
70 that my answer and so they can reach
Please I need help, DONT SKIPP
Answers
Answer:
P(Take the bus | Sophomore) = 0.83
Step-by-step explanation:
For a conditional probability (As given in the example),
P(A|B) is read as,
"The probability of event A occurring given that event B has occurred"
Here event A = Sophomore take a bus
Event B (occurred) = (Drive to school + Take the bus + Walk)
Therefore, P(Take a bus | Sophomore) = [tex]\frac{25}{(2+25+3)}[/tex]
= [tex]\frac{25}{30}[/tex]
= 0.833
≈ 0.83
P(Take the bus | Sophomore) = 0.83 will be the answer.
Describe the transformations from the parent function, and define the function of the following graph.
Answers
Answer:
From the parent graph f(x) = x², the graph moved horizontally left by 3 units and vertically down by 5 units.
The equation of the new graph is f(x) = (x + 3)² - 5
Step-by-step explanation:
Can somebody help me with this ?? :)
Answers
Answer:
Step-by-step explanation:
You need the value of one of angles. If height angle is 90°, then you have 2 90° angles. So you have 2 triangles SAS.
I hope I've helped you.
A thirty-five ounce bottle of Pedialyte contains 2,500 mg of dextrose. If a child drinks 7 ounces straight from the bottle, how many mg of dextrose will he consume?
Answers
Answer:
500 mg
Step-by-step explanation:
amount of dextrose in 35 ounce Pedialyte = 2500 mg
dividing LHS and RHS by 35
amount of dextrose in 35/35 ounce Pedialyte = 2500 /35 mg = 500/7 mg
Thus,
amount of dextrose in 1 ounce Pedialyte = 500 /7 mg
since we have to find amount of dextrose in 7 ounce Pedialyte
we multiply LHS and RHS by 7
Thus,
amount of dextrose in 1 *7 ounce Pedialyte = 500 /7 * 7 mg = 500 mg
amount of dextrose in 7 ounce Pedialyte = 500 mg
Thus, As child consumed 7 ounces of Pedialyte, He consumed 500 mg of dextrose.
how many 3/8’s are in 3
Answers
Answer: 8 times
Step-by-step explanation:
Youre essentially doing 3 divided by 3/8.
3 is equivalent to 3/1. And when you divide fractions, you have to multiply by the reciprocal. the reciprocal of 3/8 is 8/3.
[tex]\frac{3}{1} *\frac{8}{3} = \frac{24}{3} = 8[/tex]
There are eight (8) 3/8’s are in 3
The number of 3/8’s in 3 can be obtained by dividing 3 by 3/8. That is;3 ÷ 3/8N.B: Due to the division sign, the 3/8 is arranged inversely while the sign changes to multiplication (×) as follows:= 3 × 8/3= 24/3= 8This means that there are eight (8) 3/8’s are in 3.Learn more at: https://brainly.com/question/25353016?referrer=searchResults
Find the values of a and b such that
x^2 + 3x + 4 = (x + a)^2 + b
URGENT!
*silly answers will be reported
Answers
Answer:
a = 1.5
b = 1.75
Step-by-step explanation:
First, we need to solve [tex](x+a)^2[/tex] and replace the result in the initial equation as:
[tex]x^2+3x+4=(x+a)^2+b\\x^2+3x+4=x^2+2ax+a^2+b[/tex]
Then, this equality apply only if the coefficient of [tex]x[/tex] is equal in both sides and the constant is equal in both sides.
It means that we have two equations:
[tex]3x=2ax\\4=a^2+b[/tex]
So, using the first equation and solving for a, we get:
[tex]3x=2ax\\3=2a\\a=\frac{3}{2}=1.5[/tex]
Finally, replacing the value of a in the second equation and solving for b, we get:
[tex]4=a^2+b\\4=1.5^2+b\\b=4-1.5^2\\b=4-2.25\\b=1.75[/tex]
Which expression gives the distance between the points (2,3) and (4,-3)?
Answers
Answer:
D
Step-by-step explanation:
D is the only answer with the correct distance formula format and the correct numbers inside the parentheses
Jenny wants to buy a new dress for her first school dance. She borrows $25.63 from her sister to help pay for the dress. Then Jenny earns $16.33 helping her dad organize his home office. If she gives all the earnings to her sister, Jenny will still owe her sister $__ .
Answers
Answer:
$9.30
Step-by-step explanation:
If you subtract 16.33 from the total of 25.63 you will have 9.3 or 9.30. (They're the same number.)