Answers
As one side of the rectangle is given length of 4cm, the parallel other must also be equal to 4cm. Hence, Length of A to E is equal to 11cm-4cm=7cm.
Now, we use this length of 7 cm as this is opposite to our desired angle(a colored green) and by making 16cm our hypotenuse we find angle a to be 25.9°. [tex]sin x^{-1}(7/16)=25.9^{o} [/tex]
Next we find angle b by adding angle a with 90. hence getting 115.9°.
Finally we consider our triangle ABC to find the length of AC. We know one angle and length of two sides and can easily use cosine rule to find the remaining length AC. The equation and working is shown in diagram.
Answer= 18.1
Related Questions
Use the table to determine the following probabilities. The probability that a randomly chosen person from this group has type B is . The probability that a randomly chosen person from this group has type AB is . The probability that a randomly chosen person from this group has type B or type AB blood is .
Answers
Use the table to determine the following probabilities.
The probability that a randomly chosen person from this group has type B is 3/25
The probability that a randomly chosen person from this group has type AB is 1/25
The probability that a randomly chosen person from this group has type B or type AB blood is 4/25
The probability that a randomly chosen person is:
first person: 3/25
second person: 1/25
third person: 4/25
ProbabilityUse the table to determine the following probabilities.
The probability that a randomly chosen person from this group has type B is 3/25.
The probability that a randomly chosen person from this group has type AB is 1/25.
The probability that a randomly chosen person from this group has type B or type AB blood is 4/25.
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On average, Scott drinks ½ of a 6-ounce glass of water in ⅔ hour. How much water does he drink in an hour?
a) 0.75 ounces b) 2 ounces c) 4.5 ounces d) 9 ounces
Answers
3/2 = 1.5. He drinks 1.5 ounces in one third of an hour. 1.5 * 3 = 4.5
C. 4.5 ounces in one hour
How many solutions are there for the system of equations shown on the graph?
No solution
One solution
Two solutions
Infinitely many solutions
Answers
If the lines are parallel then No solution.
Answer:
D. Infinitely many solutions
Step-by-step explanation:
We have been given an image of two lines on coordinate plane. We are asked to find the number of solutions for our given lines.
Upon looking at our given graph, we can see that both lines are same. Since both lines coincide, therefore, each point on the line will be solution of our given lines.
Therefore, our given lines will have infinitely many solutions and option D is the correct choice.
Find the value of x.
The polygons are similar, but not necessarily drawn to scale.
Answers
Cross multiply:
[tex]12x = 3 \times 40[/tex]
Evaluate RHS:
[tex]12x = 120[/tex]
Divide both sides by 12:
[tex]x = 10[/tex]
Answer:
[tex]x=10 units[/tex]
Step-by-step explanation:
Given: The polygons ABCD and JKLM are similar.
To find: The value of x.
Solution: Since, the given polygons are similar, therefore using the similarity condition, we have
[tex]\frac{AD}{JM}=\frac{CD}{LM}[/tex]
Substituting the given values, we get
[tex]\frac{12}{40}=\frac{3}{x}[/tex]
On cross multiplying, we get
[tex]\frac{3\times40}{12}=x[/tex]
[tex]x=10 units[/tex]
Therefore, the value of x is 10 units.
What is the surface area of the prism? Include steps.
Answers
Area of a rectangle: Area = Length x Height
- Rectangular Prism Dimensions:
Length: 3m
Width: 4m
Height: 2m
To calculate the surface area of a rectangular prism we first need to realize that he has 3 pairs of equal rectangles.
- The first pair (Photo 1):
Two rectangles with the same measure, so we can say that the area of this pair is: (L x H) x (L x H) or 2 x (L x H).
-> Area (Pair 1) = 2 x (3 x 2) = 2 x 6 = 12m^2
But if we will do the same thing to 3 different pairs, we can describe that:
- Total Surface Area (At):
At = 2 x (L x H) + 2 x (L x H) + 2 x (L x H)
-> At = 2 x ((L x H) + (L x H) + (L x H))
So now, just put the values inside de formula,
- Pair 1: Length = 3m ; Height = 2m
- Pair 2: Length = 4m ; Height = 2m
- Pair 3: Length = 4m ; Height = 3m
*I know that this pair doesn't have a "real Height" but this doesn't change anything when solving, you can consider the 4m as height and the 3m as length or vice versa, the order of the factors doesn't change the product.
-> At = 2 x ((3 x 2) + (4 x 2) + (4 x 3))
-> At = 2 x (6 + 8 + 12)
-> At = 2 x (26)
-> At = 52 m^2
For what value of a does (1/9)^a+1 = 81^a+1 x 27^2-a?
Answers
Solution:
(1/9)^(a+1)=81^(a+1) x 27^(2-a), then the answer would be a=-3.
Answer:
-4
Step-by-step explanation:
Next time use the internet :)
Calculate cos theta where theta is the angle between u and v
Answers
However, I can explain how to solve the problem so that you can determine the angle.
cos theta = side opposite of theta divided by the hypotenuse.
Reminder that the hypotenuse is the side NOT touching the 90° angle.
Hope this helps! If not, upload an image of the drawing.
Sara loves to go hiking this weekend she hiked 3 miles on Monday 4 miles on Tuesdays and 3 miles on Thursday .last week Sara hiked 8 miles. How many more miles did Sara hike this week than last week
Answers
Last week: 8
Difference: 10 - 8 = 2
Sarah walked two more miles this week than last week.
Answer:
2 miles
Step-by-step explanation:
Sara loves to go hiking.
She hiked 3 miles on Monday 4 miles on Tuesdays and 3 miles on Thursday.
Last week Sara hiked 8 miles
This week sara hiked = Monday + Tuesday + Thursday
= 3 + 4 + 3
= 10 miles
Last week hiked = 8 miles
Difference in two week hiked by Sarah = 10 - 8
= 2 miles
So, Sarah hike 2 miles more than last week.
Stephanie rdes her bike 2 miles to the post office, and then another 50 yards to the train station. How many yards long was her trip?
Answers
Multiply 1,760 by 2 = 3,520
Add 50 to 3,520 = 3,570
Stephanie's trip was 3,570 yards long.
24 inches is 250% of what length
Answers
________________________________________________________
Explanation:
________________________________________________________
24 = 250/100 * x ;
24 = 2.5 x ;
↔ 2.5 x = 24 ;
2.5 x / 2.5 = 24/ 2.5 ;
x = 9.6 ;
The answer is: " 9.6 inches " .
_________________________________________________________
Find the first six terms of the sequence. a1 = -3, an = 2 ● an-1
Answers
According to the formula each next term will be obtained by multiplying the previous term by 2.
So, next terms will be:
Second term = 2 x First Term = 2 x (-3) = - 6
Third term = 2 x (-6) = -12
Fourth term = -24
Fifth term = -48
Sixth term = -96
So, the sequence will be:
-3, -6, -12, -24, -48, -96 ...
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Ratios
Ms. Grande brought 24 apples and 18 oranges for a party after a class play. Find the ratio of the number of apples to the total number of fruits Ms. Grande bought.
There are 44 chicken and fish filets altogether in a freezer. There are 12 chicken filets. Which is the ratio of the number of chicken filets to the number of fish filets in the freezer?
There were 12 boys and 18 girls in a class. Then, 3 more boys joined the class and 2 girls left. What is the ratio of the number of boys to the number of girls in the class now?
Monica had $42 and Naomi had $18 at first. Monica then gave $6 to Naomi. What is the ratio of the amount of money Monica has to the amount of money Naomi has in the end?
Answers
2) 11:3
3) 15:16
4) 3:2
To find the ratio of the number of apples to the total number of fruits, divide the number of apples by the total number of fruits. Simplify the ratio by dividing both numbers by their greatest common factor. For the ratio of chicken filets to fish filets, divide the number of chicken filets by the total number of filets. Simplify the ratio if possible. To find the ratio of boys to girls, determine the new number of boys and girls after some changes. For the ratio of money, calculate the amounts each person has and simplify the ratio.
Explanation:To find the ratio of the number of apples to the total number of fruits, we divide the number of apples (24) by the total number of fruits (24 apples + 18 oranges = 42). This gives us a ratio of 24:42. We can simplify this ratio by dividing both numbers by their greatest common factor, which is 6. So the simplified ratio is 4:7.
For the second question, we need to find the ratio of the number of chicken filets to the number of fish filets. There are 12 chicken filets and a total of 44 filets in the freezer. So the ratio is 12:44. This can also be simplified by dividing both numbers by 4, giving us a simplified ratio of 3:11.
In the third question, we start with 12 boys and 18 girls. Then, 3 more boys join and 2 girls leave. So the new number of boys is 12 + 3 = 15, and the new number of girls is 18 - 2 = 16. The ratio of boys to girls is therefore 15:16.
In the fourth question, Monica has $42 and Naomi has $18. When Monica gives $6 to Naomi, Monica will have $42 - $6 = $36 left, and Naomi will have $18 + $6 = $24. The ratio of the amount of money Monica has to the amount of money Naomi has is 36:24, which can be simplified to 3:2.
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A bus covered the 400-km distance between points a and b at a certain speed. on the way back the bus traveled at the same speed for 2 hours and then increased the speed by 10 km/hour until it reached a, thus spending 20 fewer minutes on the return trip. how long did the return trip take?
Answers
xt=400,
On the way back, the 2x+(x+10)(t-7/3), where it was total time minus 2 hours already driven minus 1/3 of hour, the 20 minutes.
2x+xt-(7/3)x+10t-70/3=400
2x+400-(7/3)x+10t-70/3=400
thus
-(1/3)x+4000/x=70/3
multiplying through by x we get:
-(1/3)x^2-(70/3)x+4000=0
x^2+70x-12000=0
x=(1/2)(-70+/-sqrt52900)
x=80 kmp
thus:
it took 5 hours to make the first trip
on way back 2 hours at 80 kph which means he traveled for 160 km at this speed
2 h 40 min at 90 k/h=90*8/3=240 km
The speed going to B is x, the time t and the distance, 400 km.
xt=400, x kph and t in hours
on the way back, the 2x+(x+10)(t-7/3), where it was total time minus 2 hours already driven minus 1/3 of an hour, the 20 minutes.
2x+xt-(7/3)x+10t-70/3=400
2x+400-(7/3)x+10t-70/3=400, 400 cancels, t=400/x
-(1/3)x+4000/x=70/3
multiply by x
-(1/3)x^2-(70/3)x+4000=0
x^2+70x-12000=0
x=(1/2)(-70+/- sqrt 52900); sqrt term=230
x=80 kph
took 5 hours to go there
on way back 2 hours at 80 kph=160 km
2h40m at 90kph=90*8/3=240 km
They add to 400 km.
The return trip took 4h40m
Use double angle to rewrite 12sinxcosx
Answers
To rewrite 12sinxcosx using the double angle formula, multiply by (1/2) and use the formula for sin(2x) to obtain the answer of 12sin(2x).
Explanation:To rewrite 12sin(x)cos(x) using the double angle formula, we need to know the formula for sin(2x) and cos(2x). The double angle formula for sine is sin(2x) = 2sin(x)cos(x), and for cosine it is cos(2x) = cos^2(x) - sin^2(x). Let's use these formulas to rewrite the expression:
12sin(x)cos(x) = 12 * (1/2) * 2sin(x)cos(x), since 1/2 is the value of cos^2(x) - sin^2(x).12 * (1/2) * 2sin(x)cos(x) = 6 * 2sin(x)cos(x).6 * 2sin(x)cos(x) = 12sin(2x). This is our final answer, using the double angle formula to rewrite the original expression.Learn more about double angle formula here:https://brainly.com/question/34830073
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Final answer:
The expression 12sinxcosx can be rewritten as 6sin(2x) by using the double angle formula for sine.
Explanation:
The expression 12sinxcosx can be rewritten using the double angle formula for sine, which is sin(2a) = 2sina ⋅ cosa. By comparing this to the given expression, we can see that it is in the form of the right-hand side of the double angle formula, where a is equivalent to x. Therefore, the expression can be rewritten as 6sin(2x). Such double angle formulae are available for other trigonometric ratios as well.
geometry question!! 50 POINTS
Answers
Area ratio is
250 yd^3
radii? First solid has vol 250 yd^3 = (4/3)*pi*r^3; find r^3 = --------------
(4/3)*pi
Then r^3 = 187.5 yd^3, and r = 5.724 yd
Second solid has vol 686 yd^3 .... Please find the radius R using precisely the same method.
Then calculate the ratio of the surface areas of the 2 solids:
Solid 1 surface area 4*pi* R^2
----------------------------- = --------------- where R is the radius of the larger
Solid 2 surface area 4*pi*r^2 solid and r is the radius of the smaller
R^2
This ratio comes out to ----------
r^2
Scale factor? Obviously one solid is larger than the other. We have to figure out by how much, by comparing volumes. Actually, we've already done that (see above). We could also determine how much larger R is than r. That, too, would give us the scale factor.
Answer:
2.74
Step-by-step explanation:
If you shift the linear parent function, f(x)=x, down 7 units what is the equation of the new function
Answers
1- You have that following parent function (the most basic function of the linear functions) given in the problem above:
f(x)=x
2- When you graph this parent function, you obtain the graph shown in the figure attached.
3- If you shift the linear parent function 7 units down, you have the following new function:
f(x)=x-7
4- The graph of the new function is shown in the second figure attached.
The answer is: f(x)=x-7
f(x)=x-7 is indeed the correct answer.just got it right
In the circle below, radius mn = 1.4 m and mlmn = 52°. determine the length of arc ln. round your answer to the nearest tenth and use π = 3.14.
Answers
Arc length=θ/360×π×d
θ=52
d=2×1.4=2.8 m
thus
Arc length will be:
52/360×3.14×2.8
=1.27 m
Answer:
1.27 is the answer
Step-by-step explanation:
Write an equation and solve: Twice a number, increased by 3 is 7.
Answers
2x +3=7
-3 -3
2x=4
divide both sides by 2
x=2
the answer is 2
students have 40 minuets to complete 50 questions on the aspire ___ test
A) math
B) reading
C) english
D) writing
Answers
Answer:
english C)
Step-by-step explanation:
The diameter of Jupiter is 88,000 miles This is about 11.1 times the diameter of Earth What is the diameter of the earth
Answers
linear sale factor=(diameter of Jupiter) /(diameter of earth)=11
thus:
diameter of earth=(diameter of Jupiter)/(linear scale factor)
=88000/11
=8000 miles
The diameter of earth is 8000 miles
Simplify i to the power 41
Answers
Answer:
It should be just "i"
help please, i don't understand it!!!!
Answers
Substitute to S.A.
[tex]S.A.=4\pi r^2=4\pi\cdot\dfrac{3V}{4\pi r^2}=\dfrac{3V}{r}[/tex]
[tex]\dfrac{S.A.}{V}=\dfrac{4\pi r^2}{\frac{4}{3}\pi r^3}=\dfrac{3}{r}[/tex]
[tex]\dfrac{S.A.}{V}=1\to\dfrac{3}{r}=1\to r=3[/tex]
Answer: B
What is 6.8 rounded to the nearest ones place?
Answers
6.8 is nearer to 7 than to 6. so, 6.8 ≈ 7
↓
|------|------|------|------|------|------|-----|------|------|------|
6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7
Answer: 7
A piggy bank contains the same number of quarters, nickels, and dimes. the coins total $4.40. how many of each type of coin does the piggy bank contain?
Answers
The total sum of these coins is $4.40. So we can write:
n Nickles + n Dimes + n Quarters = 4.40
0.05n + 0.10n + 0.25n = 4.40
0.40n = 4.40
n = 11
So this means, there are 11 coins of each type.
Answer: 11 of each type
Step-by-step explanation:
A fair coin is tossed three time sin succession. the set of equally likely outcomes is {hhh,hht,hth,thh,htt,tht,tth,ttt}. find the probabilty of getting exactly zero tails
Answers
Now, there is only one of the eight outcomes that has zero tails.
Therefore the probability of getting zero tails after tossing a fair coin three times in succession is
[tex] \frac{1}{8} [/tex]
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What is the average rate of change of the function over the interval x = 0 to x = 6? f(x)=2x−1
____
3x+5
Answers
[tex]\bf \cfrac{\left[ \frac{2(6)-1}{3(6)+5} \right]~~-~~\left[ \frac{2(0)-1}{3(0)+5} \right]}{6}\implies \cfrac{\left[ \frac{11}{23}\right]~~-~~\left[-\frac{1}{5} \right]}{6} \\\\\\ \cfrac{\frac{11}{23}+\frac{1}{5}}{6}\implies \cfrac{\quad \frac{78}{115}\quad }{\frac{6}{1}}\implies \cfrac{78}{115}\cdot \cfrac{1}{6}\implies \cfrac{13}{115}[/tex]
On a map, the distance between two cities is 2.4 inches. the two cities are actually 768 miles apart. on this same map, what would be the distance between two cities in miles that are 4.8 inches apart on the map?
Answers
Is the mean value theorem for integrals the same as the mean value thoerem for derivatives?
Answers
Answer:
a^2 + b^2 =C^2
Step-by-step explanation:
triston is baking specity bread for the school bake sale. she has 10 1/2 cups of flour. the recipe for 1 loaf of bread calls for 2 1/3 cups of flour. How many whole loaves of bread can she make.
Answers
Triston can make 4 whole loaves of bread using her 10 1/2 cups of flour. This was determined by dividing the total flour available by the flour required per loaf. Fractional or partial loaves are not counted.
To determine how many whole loaves of bread Triston can make, we need to perform a simple division of the total amount of flour by the amount required for one loaf.
First, let's convert the mixed numbers to improper fractions:
10 1/2 cups of flour = 21/2 cups of flour2 1/3 cups of flour = 7/3 cups of flourNext, we will divide the total flour by the flour needed per loaf:
(21/2) ÷ (7/3) = (21/2) × (3/7) = (21 × 3) / (2 × 7) = 63/14 = 4.5 loaves
Since we can only make whole loaves, Triston can make 4 whole loaves of bread.
Rewrite 0.85 as a fraction in lowest terms.
Answers
well, 0.85 has two decimals, so we use two zeros,00, at the bottom of the fraction and lose the dot, let's do so,
[tex]\bf 0.\underline{85}\implies \cfrac{085}{1\underline{00}}\implies \cfrac{85}{100}\implies \stackrel{simplified}{\cfrac{17}{20}}[/tex]