Answers
Answer:
5.4 & 5.4
Step-by-step explanation:
CD²=5²+2²=29
CD=AB=5.4
Answer:
C) 5.4 and 5.4
Step-by-step explanation:
CD: 5²+2²=c² = 25+4=c² = 29=c² = c=√29 = 5.4
AB: 5²+2²=c² = 25+4=c² = 29=c² = c=√29 = 5.4
Related Questions
integral of x+2/
[tex] \sqrt{x { + 2x + 3}^{2} } [/tex]
Answers
Looks like the integral should be
[tex]\displaystyle\int\frac{x+2}{\sqrt{x+(2x+3)^2}}\,\mathrm dx[/tex]
Expand the denominator:
[tex]\displaystyle\int\frac{x+2}{\sqrt{4x^2+13x+9}}\,\mathrm dx[/tex]
Notice that
[tex]u=4x^2+13x+9\implies \mathrm du=(8x+13)\,\mathrm dx[/tex]
In order to use this substitution, expand the integral as
[tex]\displaystyle\frac18\int\frac{8x+13}{\sqrt{4x^2+13x+9}}\,\mathrm dx+\frac38\int\frac{\mathrm dx}{\sqrt{4x^2+13x+9}}[/tex]
In the first integral, use the previously mentioned substitution:
[tex]\displaystyle\frac18\int\frac{8x+13}{\sqrt{4x^2+13x+9}}\,\mathrm dx=\frac18\int\frac{\mathrm du}{\sqrt u}=\frac14\sqrt u[/tex]
[tex]=\dfrac14\sqrt{4x^2+13x+9}[/tex]
In the second integral, complete the square in the denominator:
[tex]4x^2+13x+9=4\left(x+\dfrac{13}8\right)^2-\dfrac{25}{16}[/tex]
Now substitute
[tex]x=\dfrac58\sec t-\dfrac{13}8\implies\mathrm dx=\dfrac58\sec t\tan t\,\mathrm dt[/tex]
so that
[tex]\sec t=\dfrac{8x+13}5[/tex]
Then
[tex]4x^2+13x+9=\dfrac{25}{16}(\sec^2t-1)=\dfrac{25}{16}\tan^2t[/tex]
and the integral becomes
[tex]\displaystyle\frac{\frac{15}{64}}{\frac54}\int\frac{\sec t\tan t}{\sqrt{\tan^2t}}\,\mathrm dt=\frac3{16}\int\sec t\,\mathrm dt[/tex]
[tex]=\dfrac3{16}\ln|\sec t+\tan t|[/tex]
[tex]=\dfrac3{16}\ln\left|\dfrac{8x+13}5+\dfrac{\sqrt{(8x+13)^2-25}}5\right|[/tex]
So, the integral is
[tex]\dfrac14\sqrt{4x^2+13x+9}+\dfrac3{16}\ln\left|\dfrac{8x+13}5+\dfrac{\sqrt{(8x+13)^2-25}}5\right|+C[/tex]
Evaluate –32 + (2 – 6)(10)
Answers
Answer:
-72
Step-by-step explanation:
-32 + (2-6)(10)
-32 + (-4)(10)
-32 + -40
-72
Answer:
-72
Step-by-step explanation:
Use PEMDAS and solve from left to right.
2 - 6 = -4
Parenthesis means multiplication.
-4 x 10 = -40
Then you add the negatives.
-32 + -40 or
-32 - 40 = -72
HHEELLPP ME PLEASE
1/2x + 1/3y = 3
Which of the following equations is equivalent to the given equation?
A. 3x + 2y = 3
B. 2x + 3y = 18
C. 3x + 2y = 18
Answers
1/2x•6= 3x
1/3y•6= 2y
A footballer scores in one out of five matches. What percentage of the matches does the footballer score in?
Answers
Answer:
20%
Step-by-step explanation:
100 divided by 5 =20 20x1=20
Evaluate 4-0.25g+0.5h when g=10 and h=5
Answers
Add -0.25 and 0.25
4-0=4
Rewrite the following linear equaton in slope intercept form Y-5=3(x+1)
Answers
An arhitect wants to draw a rectangle with a diagonal of 20 inches. The length of the rectangle is to be 8 inches more than twice the width.what dimensions should she make the rectangle
Answers
The diagonal of a rectangle = sqrt(w^2 + l^2)
w = width
l = length
In this problem,
The diagonal = 20 in
w = x
l = 2x + 8
Let's plug our numbers into the formula above.
20in = sqrt((x)^2 + (2x + 8)^2)
Let's simplify the inside of the sqrt
20 in = sqrt(5x^2 + 32x + 64)
Now, let's square both sides.
400 = 5x^2 + 32x + 64
Subtract 400 from both sides.
0 = 5x^2 + 32x - 336
Factor
0 = (5x - 28)(x + 12)
Set both terms equal to zero and solve.
x + 12 = 0
Subtract 12 from both sides.
x = -12
5x - 28 = 0
Add 28 to both sides.
5x = 28
Divide both sides by 5
x = 28/5
The width cant be a negative number so now we know that the only real solution is 28/5
Let's plug 28/5 into our length equation.
Length = 2(28/5) + 8 = 56/5 + 8 = 96/5
In conclusion,
Length = 96/5 inches
Width = 28/5
Aaron is a high school graduate working as a retail clerk. He earns a median salary for a high school graduate. Aaron is thinking about going to college to get an associate's degree. If he completes his degree in 2 years and college costs total $30,000, how long will it take Aaron to recover his investment, assuming that he earns the median salary and continues to work full time while he is attending school? A graph titled Median Annual Household Income by Educational Attainment of Householder, 1997. Professional degree, 92,228 dollars; doctorate degree, 87,232 dollars; master's degree, 68,115 dollars; Bachelor's degree or more, 63,292 dollars; Bachelor's degree, 59,048 dollars; associate degree, 45,258 dollars; some college, no degree, 40,015 dollars; high school graduate, 33,779 dollars; ninth to twelfth grade, 19,851 dollars; than twelfth grade, 15,541 dollars. a. about 2.5 years b. about 5.5 years c. about 8.5 years d. about 11.5 years
Answers
Answer:
i would say c
Step-by-step explanation:
The baker fits 26 rolls onto a pan that measures 1 5/ 8 ft.² how many square feet does the Baker use for each roll? Show your work.
Answers
Answer:
1/16ft²
Step-by-step explanation:
If 26 rolls fits into 1 5/8 ft² pan, then for us to get the number of square feet for each roll, we will fillw the steps;
26rolls = 1 5/8ft²
1 roll = xft²
26 rolls = 13/8 ft²
1roll = xft²
Cross multiply
26×x = 1×13/8
26x = 13/8
Ceoaa multiply
26x×8 = 13
208x = 13
x =13/208
x = 1/16 ft²
Hence the baker uses 1/16ft² for each roll
Find an equation of a line with slope m=−2/5 that contains the point (10,−5). Type your answer is slope-intercept form.
Answers
The equation of a line in slope intercept form with slope (-2/3) and point (10,-5) is y = (-2/3) - 1.
What is the slope?The slope is the rate of change of y-axis with respect to x-axis.
We know that equation of a line in slope intercept form is y = mx + b.
To find the y-intercept b we will substitute the value of m and point (x,y).
∴ The equation of the line in slope intercept form with slope -2/5 and points (10,-5) is,
-5 = -(2/5)×10 + b.
-5 = -4 + b.
b = -1.
So the given equation of the line is y = (-2/3)x - 1.
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Graph the solution of 5 ≤ 9 - 4a
A) A
B) B
C) C
D) D
Answers
Answer:
D
Step-by-step explanation:
♡ The Question ♡
Graph the solution of 5 ≤ 9 - 4a
A) A
B) B
C) C
D) D
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ The Answer ♡
-I believe the answer should be the first choice, A!
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ The Explanation/Step-By-Step ♡
-No Explanation/Step-By-Step provided!
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ Tips ♡
-No Tips provided!
A grid that represents 1 whole , what would you shade for 0.4 and 0.04? 100 squares in rows of 10.
Answers
Answer:
40/4 shaded in squares
Step-by-step explanation:
for 0.4, since 100 is a whole, multiply by 100.
0.4*100=40
shade in 40 squares
for 0.04, multiply by 100
0.04*100=4
shade in 4 squares
Suppose 7 quarters, 4 dimes, 4 nickels, and 3 pennies are in a box. One coin is selected at random. What is the expected value of the money drawn from the box?
Answers
First, let's get the total amount of coins inside the box.
7 quarters + 4 dimes + 4 nickels + 3 pennies = 18 total coins.
(7 quarters / 18 coins) * 100 = 38.89% chance of picking a quarter
(4 dimes / 18 coins) * 100 = 22.22% chance of picking a dime
(4 nickels / 18 coins) * 100 = 22.22% chance of picking a nickel
(3 pennies / 18 coins) * 100 = 16.67% chance of picking a dime
Since the quarters have a higher percentage of being picked, we can expect to draw $0.25 from the box
john is going to invest $1234 at 9% simple interest. how long will it take for it to be worth $2308? use I=Prt and solve
Answers
Answer:
approximately 21 years
Step-by-step explanation:
-From the problem, we are given the equation I = Prt
-We're also given three numbers
-From that, we can determine which number should be plugged into the equation:
P = $1234 (this is the principle amount/original amount)r = 0.09 (this is the rate of simple interest)I = $2308 (this is the ending amount)-The only value we are not given is t as we need to solve for this value
-Now plug all these values into the equation:
I=Prt$2308 = ($1234)(0.09)t$2308 = 111.06tDivide both sides by 111.06t = 20.7816It takes approximately 21 years for the investment amount to be worth $2308.
A gallon of gas cost $2.16. Rob buys 13.5 gallons of gas. How much did he pay?
Answers
Answer:
$29.16
Step-by-step explanation:
Each gallon of gas is $2.16.
13.5 gallons of gas is 2.16 (13.5) = $29.16.
Why did I get this question wrong?
Answers
Step-by-step explanation:
∫ 9 arctan(1/x) dx
If u = 9 arctan(1/x), then:
du = 9 / (1 + (1/x)²) (-1/x²) dx
du = -9 dx (1/x²) / (1 + (1/x²))
du = -9 dx / (x² + 1)
If dv = dx, then v = x.
∫ u dv = uv − ∫ v du
= 9x arctan(1/x) − ∫ -9x dx / (x² + 1)
= 9x arctan(1/x) + 9/2 ∫ 2x dx / (x² + 1)
= 9x arctan(1/x) + 9/2 ln(x² + 1)
Evaluate from x=1 to x=√3.
[9√3 arctan(1/√3) + 9/2 ln(3 + 1)] − [9 arctan(1) + 9/2 ln(1 + 1)]
[9√3 (π/6) + 9/2 ln(4)] − [9 (π/4) + 9/2 ln(2)]
(3π√3)/2 + 9/2 ln(4) − (9π/4) − 9/2 ln(2)
(6π√3)/4 + 9 ln(2) − (9π/4) − 9/2 ln(2)
(6π√3 − 9π)/4 + 9/2 ln(2)
Answer:
[tex]9\left(\frac{1}{2}\ln \left(2\right)-\frac{\pi }{4}+\frac{\pi }{2\sqrt{3}}\right)[/tex]
Step-by-step explanation:
We are given the integral 9 arctan(1/x)dx on the interval x[ from 1 to √3 ].
Now let's say that u = arctan(1/x). The value of 'du' would be as follows:
du = - x / (1 + x²) * dx
If we apply integration by parts, v = 1, and of course u = arctan(1/x):
=> 9x arctan(1/x) − ∫ -9x dx / (x² + 1)
=> 9[x arctan(1/x) - ∫ - x / (1 + x²) * dx] on the interval x[ from 1 to √3 ]
Let's now simplify the expression ' ∫ - x / (1 + x²) * dx':
=> (Take the constant out, in this case constant = - 1), - ∫ x / (1 + x²) * dx
=> (Apply u-substitution, where u = 1 + x²), - ∫ 1/2u * du
=> (Take constant out again, in this case 1/2), - 1/2 ∫ 1/u * du
=> (Remember that 1/u * du = In( |u| )), - 1/2In( |u| )
=> (Substitute back 'u = 1 + x²), - 1/2In| 1 + x² |
So now we have the expression '9[x arctan(1/x) + 1/2In| 1 + x² |]' on the interval x[ from 1 to √3 ]. Let's further simplify this expression;
[tex]9\left[x\arctan \left(\frac{1}{x}\right)+\frac{1}{2}\ln \left|1+x^2\right|\right]^{\sqrt{3}}_1\\\\=> 9\left[\frac{1}{2}\left(2x\arctan \left(\frac{1}{x}\right)+\ln \left|1+x^2\right|\right)\right]^{\sqrt{3}}_1[/tex]
Now computing the boundaries we have the following answer:
[tex]9\left(\frac{1}{2}\ln \left(2\right)-\frac{\pi }{4}+\frac{\pi }{2\sqrt{3}}\right)[/tex]
Which unit should be used to measure mass of pencil?
Answers
Answer:
Grams
Step-by-step explanation:
Pencils are pretty light, so they should be measured in grams.
Answer:
grams :)
Step-by-step explanation:
I looked it up
simplify. can you please help? I don’t know how to do negative exponents. And I forgot how to do exponents.
Answers
1/5832
Decimal Form:
0.00017146
3
Simplify the following expression.
99 + 5 [15 – (17 - 6)]
O A.
229
ОВ.
119
OC.
163
Reset
Submit
2 of 10 Answere
Answers
Answer:
416 is your answer
hope this helped you
please mark as the brainliest (ㆁωㆁ)
Answer:
119
Step-by-step explanation:
Following the order of operations as stated in PEMDAS
Given
99 + 5 [ 15 - (17 - 6) ] ← evaluate parenthesis
= 99 + 5 (15 - 11)
= 99 + 5( 4) ← evaluate multiplication
= 99 + 20 ← evaluate addition
= 119
True or false 16.-84.-184-284 is an arithmetic sequence?
O True
O False
Answers
Answer:
false
plz tell me if im wrong i hope i helped
Tim biked 40 miles in 2 hours. His Rate is
every hour.
This means Tim biked
miles for every hour ?
Answers
Answer:
20 miles/hour
Step-by-step explanation:
40 miles in 2 hours,
thus,
40/2 miles in 2/2 hours = 20 miles in 1 hour.
Therefore, Tim bikes 20 miles per hour.
Factor by grouping.
8y2 + y + 40y + 5
Answers
Step by step:
8y2 + y +40y + 5
y(8y+1) + 5(8y+1)
(8y+1)(y+5)
Write the point-slope form of the line's equation satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation.
Slope,=4 passing through (7,5)
What is the point-slope form of the equation of the line?
?
Answers
Answer:
Step-by-step explanation:
y - 5 = 4(x - 7)
y - 5 = 4x - 28
y = 4x - 23
A carton has a length of fraction 2 and 1 over 6 feet, width of fraction 1 and 1 over 5 feet, and height of fraction 2 and 1 over 2 feet. What is the volume of the carton?
Answers
Answer:
6 1/2 cubic feet
Step-by-step explanation:
A carton has a length of 2 1/6 feet
The width is 1 1/5 feet
The height is 2 1/2 feet
Therefore the volume of the carton can be calculated as follows
= length × width × height
= 2 1/6 × 1 1/5 × 2 1/2
= 13/6 × 6/5 × 5/2
= 390/60
= 13/2
= 6 1/2 cubic feet
Hence the volume of the carton is 6 1/2 cubic feet
what is the least common multiple of 6, 12 , and 15
Answers
Answer:
It's 3.
Step-by-step explanation:
3x2=6
3x4=12
3x5=15
solve each inequality -3x<12
Answers
Answer:
-3x<12
/-3 /-3
x<-4
Step-by-step explanation:
Value of the expression when n=3
-2n(5+n-8-3n)
Answers
Answer:
54
Step-by-step explanation:
Substitute n into the equation:
-2(3)[5+3-8-3(3)]
-6[-9]
+54
A store offers customers a 40% discount on the price of x of selected items. Then, the store takes off an additional 16% at the cash register. Write a price function P(x) that computes the final price of the item in terms of the original price x.
P(x) = ?
Answers
Answer:
x-40%-16%
Step-by-step explanation:
Suppose two trains leave a station at the same time, traveling in opposite directions. Train B travels 10 mph faster than Train A. In 4.5 hours, the trains are 432 miles
apart. Find the speed of each train.
Answers
Train A's speed = x
Train B's speed = x + 10
4.5(x + x + 10) = 432
Distribute both sides by 4.5
x + x + 10 = 96
Combine like terms.
2x + 10 = 96
Subtract 10 from both sides.
2x = 86
Divide both sides by 2
x = 43
Train A = x = 43 mph
Train B = x + 10 = 43 + 10 = 53 mph
Speed is the ratio of distance and time.
Speed = Distance /Time
Distance = Speed x Time
If Train B travels 10 mph faster than Train A.
The speed of train A is 48 mph.
The speed of train B is 58 mph.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
Example:
The speed of a car moving 4km in 2 hours is 2km per hour.
We have,
Train A:
Speed = x
Train B:
Speed = x + 10
Speed = Distance / Time
Distance = Speed x Time
At time = 4.5 hours, the train is 432 miles apart.
This can be written as,
Distance = (Speed of train A + Speed of train B) x Time
432 = (x + x + 10) x 4.5
Divide both sides by 4.5.
432 / 4.5 = 2x + 10
96 = 2x + 10
Subtract 10 on both sides.
96 - 10 = 2x
86 = 2x
Divide both sides by 2.
2x = 96
x = 96/2
x = 48
Now,
x + 10 = 48 + 10 = 58
Thus,
If Train B travels 10 mph faster than Train A.
The speed of train A is 48 mph.
The speed of train B is 58 mph.
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Tom has cases of soda. If there are 12 cans in a case, how many cans does tom have?
Answers
Answer:54
4 1/2times 12
Convert 4 1/2 to an improper fraction.
9/2 times 12
Cancel the common factor of 2
9 times 6
Multiply
9 by 6 the you'll get 54