In the diagram at right, DE is a midsegment of triangle ABC. If the area of triangle ABC is 96 square units, what is the area of triangle ADE? Explain how you know.
Answers
The area of triangle ADE is,
⇒ A = 48 square units
We have to given that,
In the diagram , DE is a midsegment of triangle ABC.
And, The area of triangle ABC is 96 square units
Now, We know that,
Since DE is a midsegment of triangle ABC, it is parallel to AB and half the length of AB. Therefore, DE is half the length of AB.
Hence, the area of triangle ADE is half the area of triangle ABC,
That is,
A = 96 / 2
A = 48 square units
Thus, The area of triangle ADE is,
⇒ A = 48 square units
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Related Questions
The line passes through the points (3, 7) and (4, 9)
Answers
Answer:
I'm confused as to what your asking?
Answer:
y= 2x +1
Step-by-step explanation:
slope 9-7/4-3 = 2/1= 2
y-7 = 2(x -3)
y-7 = 2x -6
y = 2x +1
Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as divergent.
Answers
The integral\int(1/x^4 + 9x^2) dx converges by comparison to a convergent integral, and its value is 1/3
To determine whether the integral converges or diverges, we can use the limit comparison test with the integral:
Since for all x > 0, we have:
Thus, by the limit comparison test:
converges if and only if converges.
We can evaluate using the power rule of integration:
where C is the constant of integration. Evaluating this integral from 1 to infinity, we get:
∫(1/x^4) dx from 1 to infinity = lim as b → infinity
=>
=> 0 - (-1/3)
=> 1/3
Since the integral dx converges by comparison to a convergent integral, and its value is 1/3.
To learn more about Convergent integral :
Note: The full question is
Determine whether the integral converges or diverges; if it converges, evaluate. (If the quantity diverges, enter DIVERGES. Do not use the [infinity] symbol in your answer.) [infinity] dx x4 + 9x2 1
Please help me
Adjust to compatible numbers that count by 50s, and then subtract to
estimate the difference.
301 - 52 =
Answers
Answer:
249
Step-by-step explanation:
301 - 52 = 249
6 times 10 to the power of -10 Normal numbers
Answers
Answer:
0.0000000006
Step-by-step explanation:
6* 10^-10= 0.0000000006
basically think of it as moving the decimal back 10 times.
Sinx-sin3x /sin^2x -cos^2x
Answers
The answer is (sin x - 2 sin 3x cos x) / (1 - 2 cos² x). To simplify the given expression, we can use the identity sin 2x = 2sin x cos x.
Substitute the numerator with sin x - sin 3x. Substitute the denominator with sin² x - cos² x to get a common factor.
Substitute sin² x with (1 - cos² x) to get sin x - sin 3x / (1 - cos² x - cos² x).Then substitute sin² x with (1 - cos² x) to get sin x - sin 3x / (1 - 2 cos² x).
Now, use the identity sin 2x = 2sin x cos x to simplify the numerator. sin x - sin 3x can be written as sin x - sin (x + 2x) which equals sin x - [sin x cos 2x + cos x sin 2x].
Now, simplify the expression: sin x (1 - cos² x - cos² x) - sin x cos 2x - cos x sin 2x. We will simplify this expression further, leading us to get sin x (1 - 2 cos² x) - sin 2x cos x.
Finally, the expression becomes sin x (1 - 2 cos² x) - sin 2x cos x / (1 - 2 cos² x). Therefore, the answer is (sin x - 2 sin 3x cos x) / (1 - 2 cos² x).
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10 decreased by the sum of 3 + 5
Answers
Answer:
-2
Step-by-step explanation:
Answer:
answer is -2
Step-by-step explanation:
5+3=8
8-10= -2
4.
A restaurant offers seven kinds of main
courses, nine types of drinks, and four types of
desserts. How many different meals
consisting of a main course, a drink, and a
dessert does the restaurant offer? |
Answers
Answer:
252
Step-by-step explanation:
Types of main courses available = 9
Types of drinks offered = 7
Types of deserts = 4
Number of different meals consisting of a main course, a drink and a desert offered
Using the combination rule :
9C1 * 7C1 * 4C1
nCr = n! ÷ (n-r)!r!
So using calculator we obtain :
9 * 7 * 4 = 252
Select all numbers that have and absolute value of 0.6
Answers
l-0.6l and 0.6 and l 0.6 l
Step-by-step explanation:
a number in l x l for is to be changed to positive if not already!
21 students are going on a field trip and 3 students are staying at school what is the ratio of the numbers of students who are going on a field trip to the number of students who are staying at school?
Answers
Answer:
21/3 or 7/1
Step-by-step explanation:
Answer:
21/3
Step-by-step explanation:
hope this helps you
wines at $ 4.50 and
$5 per litres are mixed
with a third wine in
the ration 2:3:4.If the mixture Cost $5.20 a litre, what is
the Cost of the third wine?
Answers
Answer:
The third wine costs $5.70 per litre
Step-by-step explanation:
so we've got 2 parts $4.50 wine, 3 parts $5 wine and 4 parts x wine. The result is $5.20 per part.
2l*$4.50/l + 3l*$5/l + 4l*x = (2l+3l+4l)*$5.20/l
$9 + $15 + 4l*x = $46.80
4l*x = $22.80
x = $5.70/l
Exit
Use the table to answer the question.
Frank mows 1 lawn for $30. He made a table of values to show his earnings.
What error did Frank make in completing the table?
A. Frank multiplied 2 by 2 to get 4 and $60 by 2 to get $120.
B. Frank added $15 to $60 to get $75 instead of adding $30 to $60 to get $90.
C. Frank multiplied $15 by 5 to get $75 instead of multiplying $15 by 3 to get $45.
D. Frank incorrectly added to get the amount of money earned for mowing 4 lawns.
Answers
Answer:
B
Step-by-step explanation:
a study of the effects of exercis used rats bred to have high or low capacity for exercise. The 8 high capacity rats had mean blood pressure 89 mm Hg and variance 81; the 8 low-capacity rats had mean blood pressure 105 mm Hg with variance 169. What is the value of the two-sample t statistic for comapring the two population means
Answers
Answer:
[tex]t=-2.86[/tex]
Step-by-step explanation:
From the question we are told that:
Sample 1 [tex]n_1=8[/tex]
Sample 1 mean blood pressure [tex]\=x_1=89mmHg[/tex]
Sample 1 variance [tex]\sigma_1=81[/tex]
Sample 2 [tex]n_2=8[/tex]
Sample 2 mean blood pressure [tex]\=x_2=105mmHg[/tex]
Sample 2 variance [tex]\sigma_2=169[/tex]
Generally the equation for the test of statistic is mathematically given by
[tex]t=\frac{\=x_1-\=x_2}{\sqrt{\frac{\sigma_2}{n_1}+\frac{\sigma_2}{n_2} } }[/tex]
[tex]t=\frac{89-105}{\sqrt{\frac{81}{8}+\frac{169}{8} } }[/tex]
[tex]t=-2.86[/tex]
therefore the samples test for comparing the two population means
[tex]t=-2.86[/tex]
A recipe calls for ¾ cups of molasses. If you triple the recipe, how much molasses is needed?
Answers
A recipe calls for ¾ cups of molasses. If you triple the recipe, 9/4 cups of molasses would be needed
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A recipe calls for ¾ cups of molasses. If you triple the recipe, the molasses is:
Amount of molasses needed = 3 * (3/4) cup = 9/4 cups
A recipe calls for ¾ cups of molasses. If you triple the recipe, 9/4 cups of molasses would be needed
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What equals 18 to the third power
Answers
Answer:
5832
Step-by-step explanation:
18 × 18 = 324
324 × 18 = 5832
Factor the expression
10x + 25
A. 2(5x + 10)
B. 5(2x + 5)
C. 10(x + 5)
D. 5(2x + 25)
Answers
Answer:
B. 5(2x+5)
Step-by-step explanation:
Factor 5 out of 10x+25. and you get 5(2x+5)
Answer:
B. 5(2x + 5
Step-by-step explanation:
If you have any questions feel free to ask in the comments
May I have some help with this please?
Answers
f(x) = |7m + 4| = 1
First equation by taking positive modules
7m + 4 = 1
7m = -3
m = -3/7 . Ans.
Second equation by taking negative modules
-7m - 4 = 1
-7m = 5
m = -5/7 . Ans.
∴ m = [ -5/7 U -3/7 ] Ans .
Please please help please
Answers
Answer:
5/4
Step-by-step explanation:
6 1/4 is equal to 25/4 and if you do 5 times 5/4 you get 25/4 which is 6 1/4
Answer:
5/4
Step-by-step explanation:
pleasee help me i’ll give you brainliest
Answers
Answer:
X and y are supplementary.
Step-by-step explanation:
Choose the first option:
x + y = 180 degrees is the relationship that is always true.
Select the correct comparison
Answers
Answer:
b
Step-by-step explanation:
Add 1
1/2 and 3/4 and then subtract 1/3
Answers
Answer:
1/2 + 1/4 _ 1/3 = 0.91667
Step-by-step explanation:
the arithmetic sequence ai is defined by the formula: a1 = -53 ai = ai-1 + 6 find the sum of the first 880 terms in the sequence
Answers
Answer:
The sum of the first 880 terms in the sequence is 2,273,920.
Step-by-step explanation:
Arithmetic sequence:
The difference between consecutive terms is always the same, called common difference, and the nth term is given by:
[tex]a_{n} = a_0 + (n-1)d[/tex]
In which d is the common difference.
Sum of the first n terms:
The sum of the first n terms of an arithmetic sequence is given by:
[tex]S_{n} = \frac{n(a_1+a_n)}{2}[/tex]
ai = ai-1 + 6
This means that [tex]d = 6[/tex]
In this question:
Sum of the first 800 terms, so [tex]n = 800[/tex]
First term is -53, so [tex]a_1 = -53[/tex]
The 880th term is:
[tex]a_{880} = -53 + (880-1)*6 = 5221[/tex]
Sum
[tex]S_{n} = \frac{880(-53+5221)}{2} = 440(-53+5221) = 2273920[/tex]
The sum of the first 880 terms in the sequence is 2,273,920.
Tammy will run more than 28 miles this week. So far, she has run 18 miles. What are the possible numbers of additional miles she will run?
Answers
Answer:
Any number that is greater than 10
Step-by-step explanation:
Tammy is wanting to run more than 28 miles. Having already ran 18, she has to run 10 more to even reach 28 miles in total. She wants to run MORE than 28 so the number of miles she has yet to run in possibility is any number that is GREATER than 10.
ex: 11, 12,13, 14.....
Which statement is true about angle DCB and angle ACF
Answers
Answer: they are complementary but not necessarily congruent
Step-by-step explanation:
-9b+2n-4+2b
Solve please
Answers
Answer:
-9b+2n-4+2b
-7b+2n-4 is your answer
When a real zero x = a of a polynomial function fis of even multiplicity, the graph of f ---Select-- the x-axis at x = a, and when it is of odd multiplicity, the
graph of f ---Select-- the x-axis at x = a.
Answers
Answer:
touches
crosses
Step-by-step explanation:
[tex]x=a[/tex] is said to be a zero of a function [tex]f(x)[/tex] if [tex]f(a)=0[/tex]
A zero say [tex]x=a[/tex] has a "multiplicity" equal to [tex]n[/tex], if the factor [tex](x-a)^n[/tex] appears in the polynomial.
When a real zero [tex]x=a[/tex] of a polynomial function [tex]f[/tex] is of even multiplicity, the graph of [tex]f[/tex] touches the x-axis at [tex]x=a[/tex], and when it is of odd multiplicity, the
graph of [tex]f[/tex] crosses the x-axis at [tex]x=a[/tex].
Kei buys a table and 12 chairs. Each chair cost the same price. The table cost $165. The total cost for the table and 12 chairs is $ 465. What is the cost of one chair?
Answers
Answer:
$38.75
Step-by-step explanation:
$465/12=$38.75
please help me with this
Answers
Answer:
8 nights
Step-by-step explanation:
MATH
Which expression is equivalent to -8?
O-2-3
-3
9
2-3
Answers
Answer:
the answer would be c
Step-by-step explanation:
the answer would be c because its a fraction
in the month of July 3/8 of the shoes that were sold at the Houston of style footwear were sandals and 1/16 were clogs. what fraction of the shoes where either sandals or clogs?
Answers
Answer:
7/16 of the shoes were either sandals or clogs.
Step-by-step explanation:
Find a CD, which is 16.
Because we multiplied the denominator, we multiply the numerator as well.
3/8 becomes 6/16.
Now, because both of the denominators are the same, we are free to add both of the fractions together.
6/16 + 1/16 = 7/16.
Because this fraction isn't reducible, the answer will be 7/16.
20141
ID
NJ008306927
10
Name
Manuel Negron
Tune Remaining
00:24:41
A toy manufacturer is using
this design to package its
latest toy, What is the volume
of the box?
4.5 in.
6.5 in.
-6.5 in.
DinO-BO
315.5 cubic in
389 cubic in
4.5
435.8 cubic in
650.5 cubic in
-10.4 in.
with y width x height)
Answers
Answer:
315.5cubic in
10.4 x 4.5 x 6.5=
Step-by-step explanation: