The area of the rectangle is 3[tex]\sqrt{56}[/tex]
Given,
A rectangle has a length of √7 and a width of 3√8.
We need to find the area of the rectangle.
What is the area of a rectangle?The area is given by:
Area = Length x width
Find the length and width of a rectangle.
Length = [tex]\sqrt{7}[/tex]
Width = 3[tex]\sqrt{8}[/tex]
Find the area of the rectangle.
Area = Length x width
= [tex]\sqrt{7}[/tex] x 3[tex]\sqrt{8}[/tex]
When there are two different square roots we multiply them together under one root.
[tex]\sqrt{a\times b} ~~=~~\sqrt{a}\times\sqrt{b}[/tex]
Now,
= 3[tex]\sqrt{7\times8}[/tex]
= 3[tex]\sqrt{56}[/tex]
Thus the area of the rectangle is 3[tex]\sqrt{56}[/tex]
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Answer:
∠ R = 120°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 angles from 180 , that is
subtract 60 from 180
∠ R = 180° - 60° = 120°
find the average rate of change, in simplest form, of the function over the interval 4\le x \le 74≤x≤7.
Answer:
[tex]Average\ Rate = \frac{104}{3}[/tex]
Step-by-step explanation:
Given
See attachment for table
Required
Determine the average rate of change over: 4≤x≤7.
Average rate of change is calculated as:
[tex]Average\ Rate = \frac{f(b) - f(a)}{b - a}[/tex]
Where:
[tex]a=4[/tex]
[tex]b = 7[/tex]
So:
[tex]Average\ Rate = \frac{f(b) - f(a)}{b - a}[/tex]
[tex]Average\ Rate = \frac{f(7) - f(4)}{7 - 4}[/tex]
[tex]Average\ Rate = \frac{f(7) - f(4)}{3}[/tex]
From that table:
f(4) =
f(7) =
So:
[tex]Average\ Rate = \frac{f(7) - f(4)}{3}[/tex]
[tex]Average\ Rate = \frac{108-4}{3}[/tex]
[tex]Average\ Rate = \frac{104}{3}[/tex]
The points (-1,r) and (11, -1) lie on a line with slope 3/4
Find the missing coordinate r.
Answer:
The value of the missing coordinate 'r' is -10
Step-by-step explanation:
The two points have the following given parameters;
The point coordinates = (4, -17) and (8, r)
The line on which the two points rests has a slope of, m = 3/4
To find the value of 'r', we use the slope formula as follows;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Plugging in the values gives;
[tex]m = \dfrac{3}{4} = \dfrac{-1-r}{11-(-1)} =\dfrac{-1-r}{11 + 1} = \dfrac{-1 - r}{12}[/tex]
[tex]\dfrac{3}{4} =\dfrac{-1 - r}{12}[/tex]
∴ 3 × 12 = 4 × (-1 - r)
36 = -4 - 4·r
36 + 4 = -4·r
r = 40/(-4) = -10
r = -10
Write a system of linear equations for the problem below(you do not have to solve it) Twenty-six students attended the community service event. The number of girls was 4 fewer than twice the number of boys. How many boys attended the community service event?
Answer:
Number of boys who attended the community service event = 10
Step-by-step explanation:
Let [tex]x[/tex] denotes number of girls and [tex]y[/tex] denotes number of boys.
Twenty-six students attended the community service event.
So,
[tex]x+y=26[/tex]
The number of girls was 4 fewer than twice the number of boys.
[tex]x=2y-4[/tex]
Put [tex]x=2y-4[/tex] in [tex]x+y=26[/tex]
[tex]2y-4+y=26\\3y=26+4\\3y=30\\y=10[/tex]
So,
Number of boys who attended the community service event = 10
Elia rode her bicycle from her house to the beach at a constant speed of 18 1818 kilometers per hour, and then rode from the beach to the park at a constant speed of 15 1515 kilometers per hour. The total duration of the rides was 1 11 hour and the distances she rode in each direction are equal. Let b bb be the number of hours it took Elia to ride from her house to the beach, and p pp the number of hours it took her to ride from the beach to the park.
Answer: hello your question is not well written but it seems you are asking for the Total distance covered during the rides hence i will give you a general solution
Total distance travelled during rides = 16.36 km
Total duration of rides = 1 hour
Step-by-step explanation:
Given that :
b = number of hours from house to beach
p = number of hours from beach to park
since the total duration of the rides = 1 hour
hence: b + p = 1 ------ ( 1 )
Also ; speed from house to beach = 18 km/hr
speed from beach to park = 15 km/hr
Given that distance covered in both directions are equal and distance = s * t
Hence distance covered : 18b = 15p ------ ( 2 )
determine the total distance travelled
b + p = 1 ------ ( 1 )
18b = 15 p ----- ( 2 )
from equation 1 : b = 1 - p
18 ( 1 - p ) = 15p
18 = 15p + 18p
p = 18 / 33 = 6/11
back to equation 1
b + 6/11 = 1
hence b = 1 - 6/11 = 5/11
Distance covered in one direction
18 ( 5/11 ) = 15 ( 6/11 )
90 / 11 = 90 /11
hence Total distance covered = ( 90 / 11 ) * 2 = 16.36 km
x^2-4x+3=0 write it in standard form.
solve by completing the square.
solve by quadratic formula
Answer:
x
=
2
±
√
7
Explanation:
there are no whole numbers which multiply to - 3
and sum to - 4
we can solve using the method of
completing the square
the coefficient of the
x
2
term is 1
∙
add subtract
(
1
2
coefficient of the x-term
) 2 to x2 − 4 x ⇒ x 2 +2(− 2 ) x + 4 − 4 − 3 = 0 ⇒ ( x − 2 )2 − 7 =0 ⇒ ( x − 2 ) 2 = 7
take the square root of both sides
⇒ x − 2 = ± √ 7 ←
note plus or minus
⇒ x = 2 ± √ 7←
exact solutions
Step-by-step explanation:
x²-4x+3=0
x²-4x=-3
take half of -4 square it and add it to both side
x²-4x+(-2)²=4-3
(x-2)²=1
x-2=±1
x=2±1
x=1,3
Gas from a local station costs $2.85 per gallon (in US dollars). Tara's car gets 13.4 kilometers to the liter.
About how much will it cost Tara to drive 640 kilometers if she buys the gas from that local gas station?
Answer:
$250.8
Step-by-step explanation:
13.4 = $2.85
13.4 x 15 = 111.0
111.0 = $42.75
111.0 x 6 = 666.0
666.0 - 26.0 = 640.0
$42.75 x 6 = $256.5
$2.85 x 2 = $5.07
$256.5 - $5.07 = $250.8
not gona lie this took forever lol
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The total cost of 640 liters of gas is $35.91.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, Gas from a local station costs $2.85 per gallon (in US dollars).
We know that, 1 gallon = 3.785 liters
Tara's car gets 13.4 kilometers to the liter.
Number of liters of gas = 640/13.4
= 47.76 liters
Number of gallons = 47.76/3.785
= 12.6 gallons
Total cost = 12.6×2.85
= $35.91
Therefore, the total cost of 640 liters of gas is $35.91.
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(2x-5y)^2
Find the square using identity
Class 8
Answer:
=4x^2−20xy+25y^2
Step-by-step explanation:
(2x−5y)^2
=(2x+−5y)(2x+−5y)
=(2x)(2x)+(2x)(−5y)+(−5y)(2x)+(−5y)(−5y)
=4x^2−10xy−10xy+25y^2
=4x^2−20xy+25y^2
Hope it helped!
Answer:
(2x)^2- 2*(2x)*(5y)+(5y)^2= 4x^2-20xy+25y^2
Step-by-step explanation:
Identity- (a-b)^2= a^2-2ab+b^2
A scientist has a sample of bacteria that initially contains 10 million microbes. They observe the sample and finds that the number of bacterial microbes doubles every 20 minutes. Which exponential function represents M, the total number of bacterial microbes in millions, as a function of t, the number of minutes the sample has been observed?
Answer:
M(t) = 6.7 * 10⁷ (67 million)
Minutes (t) =55
Step-by-step explanation:
1. Write an exponential equation that represents M, the total number of bacterial microbes in millions, as a function of t, the number of minutes the sample has been observed.
For answering this question, we will use the following formula:
M(t) = B₀ * g ^(t/m), where:
•M(t) represents the total number of bacterial microbes in millions.
• B₀ represents the initial population of bacteria in millions.
• g represents the growth factor.
• t represents the total number of minutes we will observe the bacteria growing.
• m represents the time in minutes it takes to the growth factor g to occur.
2. Then, determine how much time, to the nearest minute, will pass until there are 67 million bacterial microbes.
M(t) = B₀ * g ^(t/m)
Replacing with the values we know:
6.7 * 10⁷ = 10⁷ * 2 ^(t/20)
6.7 = 2 ^(t/20) (Dividing by 10⁷ at both sides)
ln 6.7 = ln 2 ^(t/20)
ln 6.7 = t/20 ln 2
ln 6.7/ ln 2 = t/20
t = ln 6.7/ln 2 * 20
t = 2.74 * 20
t = 54.88
t ≅ 55 (rounding to the nearest minute)
someone please help me
Answer:
can't see the question ⁉️
The base of a triangular pyramid is 21 inches squared. The volume is 63 inches cubed. What is the height of the pyramid?
Answer:
9
Step-by-step explanation:
So the formula for a triangular pyramid is v=1/3bh
you plug in the values and you get 63=1/3(21)(h) and since you are finding the height, you get h=63*3/21
and then you check answers with
63=1/3(21)(9) which is true so the height is 9
) The diagram shows a quadrant of a circle . If the curved edge is 15 cm long, what is the length of a straight edge?
Answer:
9.55 cm
Step-by-step explanation:
A quadrant of a circle is 1/4 of a circle.
Since the curved edge is 15 cm, a full circle would be 60 inches.
60/Pi = diameter
diameter = 60/3.14 = 19.11 cm
diameter/2 = radius
radius = 19.22/2 = 9.55 cm which is the length of a straight edge.
someone please help and explain. i need this rnnn.
Answer:
x=8
Step-by-step explanation:
63+90+2x+11=180
Answer:
B
Step-by-step explanation:
Add 63 and 90 to find the left angle. Then subtract by 180.
Since that answer is 27, add it to 90 and subtract by 180 to find the last angle in the middle. then finally the angle in the corner should equal 27 since the triangles are congruent.
Need help!!!! PLZ I don't know
Answer:
Step-by-step explanation:
First factor the polynomials and reduce the fractions.
Help!!
Find the volume. Around to the nearest Hundredth.
1326cm
1026.04mi
1526.82mi
6104.16mi
Answer:
V=1526.82 mi³
Step-by-step explanation:
The formula for the volume of a right circular cone is V=πr²(h/3).
The radius is half of the diameter of 18, so it is 9 mi.
The height is 18 mi.
Plug in your numbers into the formula.
V=π9²(18/3)
V=π81(6)
V=π486
V=1526.82 mi³
Val is going to plant b vegetable seeds in one garden and 5b + 2 vegetable seeds in another. How
many seeds is Val going to plant?
Val is going to plant seeds.
(Simplify your answer.)
Answer:
6b + 2
Step-by-step explanation:
If Val is planting b seeds in one and 5b + 2 in the other, the expression showing the total is: b + (5b + 2) or 6b + 2 seeds.
question in photo—————————-
Answer:
there is two solutions to that problem. you can find x is equal to two numbers.
how 2 do?
(n)(n+7)(n+8)
Answer:
[tex]n^{3} + 15n^{2} + 56n[/tex]
Step-by-step explanation:
First FOIL (n + 7)(n + 8) and then distribute n
(n + 7)(n + 8) = [tex]n^{2} +15n + 56[/tex]
n ([tex]n^{2} +15n + 56[/tex])
= [tex]n^{3} + 15n^{2} + 56n[/tex]
The nth term of a sequence is n + 5
Work out the 5th term of the sequence.
5th term =
Answer:
10
Step-by-step explanation:
Tₙ=n+5
T₅=5+5=10
What is the value of the expression 20 ÷ 4 + (6 x 2) − 2?
15
17
22
28
Find the value of x and y.
Answer:
x= 73
y= 13
Step-by-step explanation:
The sum of the angles opposite the exterior angle = the exterior angle so
x= 141-68
x= 73
The angle sum of a triangle= 180.
180-68-73= 39
since there are 3 "y"s we need to divide 39 by 3
39/3= 13
Wich graph matches the equition x=5
Answer:
option 1
Step-by-step explanation:
do i need to?
The area of a rectangle is 48x®y7
square yards. If the length of the
rectangle is 6x2y4 yards, which
expression represents the width of the
rectangle in yards?
A. 42x4y3
B. 42x6y3
C. 8x4y3
D. 8x6y3
Answer:
D
Step-by-step explanation:
Remember, area equals width x height so you can set up this equation.
[tex]48x^8y^7=6x^2y^4 * w[/tex]
Solving for w,
[tex]\frac{48x^8y^7}{6x^2y^4} =w[/tex]
Simplifying,
[tex]8x^6y^3[/tex]
Thus, D is the answer
Sorry for asking again.
The options are cut out so it says
2
3
4
5
Answer:
2
Step-by-step explanation:
For A and B, count to the y axis (vertical line)
Marty has a driveway that is 200 feet long. The tires on her car have a diameter of 18 inches. What is the fewest number of tire rotations a tire will make tot travel the entire distance of the driveway?
The the fewest number of tire rotations is 42 to travel the entire distance of the driveway.
It is given that the driveway that is 200 feet long and the tire diameter is 18 inches.
It is required to find the fewest number of tire rotations a tire will make to travel the entire distance of the driveway.
What is a circle?It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).
Driveway length = 200 feet
Diameter of the tire = 10 inches
For converting it to feet divide by 12.
Now the diameter of tire = 18/12 = 1.5 feet
Radius of the tire = 0.75 feet
We know the perimeter of the circle:
[tex]\rm P = 2\pi r[/tex]
P = 2(π)(0.75)
P = 4.71 feet ( π =3.14 and P = 0.75)
[tex]\rm number \ of \ tire \ rotations = \frac{Driveway \ length}{Perimeter \ of tire}[/tex]
[tex]= \frac{200}{4.71}[/tex]
Number of tire rotation = 42.462 ≈ 42
Thus, the the fewest number of tire rotations is 42 to travel the entire distance of the driveway.
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60
13cm
x cm
Find the value of x to the nearest tenth:
Answer:
4.6cm
Step-by-step explanation:
There are 15 counters. One-third of the counters are yellow. How many
counters are yellow? *
Answer:
3
Step-by-step explanation:
15*1/5= 3
A Y U D E N P O R F A :(
Answer:
x=2
Step-by-step explanation:
Primero, necesitamos calcular <<a>>
Sabemos que AD=BC y AB=CD porque lados opuestos congruentes
Entonces, vamos a calcular <<a>>.
Usamos AD y BC
2a-1=4a-15
suma 15 a ambos lados
2a+14=4
añada 2 en ambos lados
14=2a
divida
7=a
Ahora, usamos esta información para calcular <<x>>
Usamos CD=AB
2a-8=4x-2
pero sabemos que <<a>> es 7
entonces:
14-8=4x-2
6=4x-2
8=4x
2=x
<<x>> es 2
(¡lo siento mi español no es perfecto!
The scores on a mathematics exam have a mean of 70 and a stadard deviation of 7. Find the x-value that corresponds to the z-score -1.45.
Answer:
59.85
Step-by-step explanation:
The scores on a mathematics exam have a mean of 70 and a stadard deviation of 7. Find the x-value that corresponds to the z-score -1.45.
We solve the above question using z score formula
z = (x-μ)/σ, where
x is the raw score
μ is the population mean = 70
σ is the population standard deviation = 7
z = -1.45
Hence:
-1.45 = x - 70/7
Cross Multiply
-1.45 × 7 = x - 70
-10.15 = x - 70
x = -10.15 + 70
x = 59.85
Is y proportional to x and y? Why or why not
Answer:
X is directly proportional to y means the value of x is dependent on the value of y. y may not be dependent on x in this case.
Y is directly proportional to x means the value of y is dependent on the value of x. Same as above, in this case, the value of x may not depend on y.