Surface Area
For the two figures below, the base area and the heights have been provided.
Figure A
Figure B
4 cm
5 cm
25 cm?
20 cm
what the volume for both figures?
Answer:
V of both A and B is 100 cm³
Step-by-step explanation:
the volume (V) of a prism is calculated as
V = Ah ( A is the area of the base and h the height )
A
A = 20 and h = 5 , then
V = 20 × 5 = 100 cm³
B
A = 25 and h = 4 , then
V = 25 × 4 = 100 cm³
Given: f(x) = -2x² +x+6
5.1 Calculate the coordinates of the turning point of f.
Answer:
[tex]\left(\dfrac{1}{4},\dfrac{49}{8}\right)[/tex]
Step-by-step explanation:
Turning points (stationary points) occur when the gradient of a graph is zero.
To find when the gradient of the graph is zero, differentiate the function, set it zero, then solve for x.
Given function:
[tex]f(x)=-2x^2+x+6[/tex]
Differentiate:
[tex]\implies f'(x)=(2)(-2)x^{2-1}+(1)x^{1-1}+6(0)[/tex]
[tex]\implies f'(x)=-4x+1[/tex]
Set the differentiated function to zero and solve for x:
[tex]\implies f'(x)=0[/tex]
[tex]\implies -4x+1=0[/tex]
[tex]\implies 4x=1[/tex]
[tex]\implies x=\dfrac{1}{4}[/tex]
To find the y-coordinate, input the found value of y into the given function:
[tex]\implies f\left(\dfrac{1}{4}\right)=-2\left(\dfrac{1}{4}\right)^2+\left(\dfrac{1}{4}\right)+6[/tex]
[tex]\implies f\left(\dfrac{1}{4}\right)=\dfrac{49}{8}[/tex]
Therefore, the turning point of the function is:
[tex]\left(\dfrac{1}{4},\dfrac{49}{8}\right)[/tex]
answers
f=1/4=49/8
Step-by-step explanation:
identify the coefficients
a=-2, b=1
substitute the coefficient into the expression
x= -1/((2x(-2))
then solve it out the equation
x=1/4
evaluate the function x =1/4
f(x) =-2x²+x+6(1/4)
f=1/4=49/8
Valentina has a tray where she keeps all of her important papers. the tray is in the shape of a rectangular prism with no top. a rectangular prism with a length of 12 inches, width of 10 inches, and height of 2.5 inches. what is the volume of papers that the tray can hold? 160 inches cubed 180 inches cubed 280 inches cubed 300 inches cubed
The volume of a rectangular prism with a length of 12 inches, width of 10 inches, and height of 2.5 inches is 300 cubic inches
Volume of a rectangular prismLength= 12 inchesWidth = 10 inchesHeight = 2.5 inchesVolume of a rectangular prism = length × width × height
= (12 × 10 × 2.5) inches
= 300 inches
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What is the answer please?
Answer: D (bottom option)
Not Congruent
Step-by-step explanation:
Assuming the trapezoids are to scale, they are not the same shape. This means that they could not be congruent even if they were centered on top of each other.
I need help with this equation. Please solve for k
Hey there!
18 = -k + 3
-k + 3 = 18
-1k + 3 = 18
SUBTRACT 3 to BOTH SIDES
-1k + 3 - 3 = 18 - 3
SIMPLIFY IT!
-1k = 18 - 3
-1k = 15
DIVIDE -1 to BOTH SIDES
-1k/-1 = 15/-1
SIMPLIFY IT!
k = 15/-1
k = -15
Therefore, the answer is: k = -15
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Rewrite 4-3.4-18 using positive exponents.
Answer:
Step-by-step explanation:
4^-3
= 1/4^3
4^-18
= 1/4^18.
a A boat is heading towards a lighthouse, where Lillian is watching from a vertical distance of 145 feet above the water. Lillian measures an angle of depression to the boat at point A to be 10°. At some later time, Lillian takes another measurement and finds the angle of depression to the boat (now at point B) to be 68°. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The distance from point A to point B is 763.752ft.
What is Tangent (Tanθ)?The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
A.) The distance between the boat and the lighthouse when the angle of depression is 10°.
Tan(10°) = Height of lighthouse/ distance between the boat and the lighthouse
Distance between the boat and the lighthouse
= 145/Tan(10°) = 822.336ft
B.) The distance between the boat and the lighthouse when the angle of depression is 68°.
Tan(68°) = Height of lighthouse/ distance between the boat and the lighthouse
Distance between the boat and the lighthouse
= 145/Tan(68°) = 58.584ft
The distance between point A and B = 822.336ft - 58.584ft = 763.752 ft
Hence, the distance from point A to point B is 763.752ft.
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Answer:
764
Step-by-step explanation:
Rounded. Just did the question
what are the solutions to 0=x^2-x+1?
Answer: No solutions
Step-by-step explanation:
There are no solutions to 0 = x² - x + 1.
[Method One]
We can solve this by rewriting the equation, but it is quicker to graph it when there are no solutions. See attached.
[Method Two]
I said we can solve this by solving an equation, here it is. We will use the quadratic formula since the equation given is already in the proper form.
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\displaystyle x=\frac{1\pm\sqrt{(-1)^2-4(1)(1)} }{2(1)}[/tex]
[tex]\displaystyle x=\frac{1\pm\sqrt{-3} }{2}[/tex]
-> Negative numbers don't have real square roots, so there is no solution
3
x + 2
3
3
12
32
12
Solve for x.
Answer:
6
explanation
[tex]since \: they \: are \: similar \\ \frac{x + 2}{32} = \frac{3}{12} \\ crossmultiplying \\ 32 \times 3 = 12(x + 2) \\ 96= 12x + 24 \\ 12x = 96 - 24 \\ 12x = 72 \\ dividing \: bothsides \: y \: 12 \\ x = \frac{72}{12} \\ x = 6[/tex]
What additional information do you need to prove the triangles are congruent by SAS
Answer:
Step-by-step explanation:
Need help with this problem
answer with procedure
Answer:
2
Step-by-step explanation:
there needs to be qtr with 88 by 779900
3) If 5 pencils costs $0.75, 7 pencils will cost
Your answer
dollars. *
Answer:
$1.05
Step-by-step explanation:
Find the unit price by dividing $0.75 by 5.
$0.75/5 = $0.15
Now find the price of 7 pencils by multiplying 7 and the unit price of $0.15.
$0.15 x 7 = $1.05
buffy's beverages has increasing profits each week during the hot summer months. Buffy finds that each week his profits increase by 20% over what they were the previous week. In his first week of business his profits were $200
The exponential function that gives the profit after x weeks is given by:
[tex]P(x) = 200(1.2)^x[/tex].
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem:
Buffy finds that each week his profits increase by 20% over what they were the previous week, hence r = 0.2.In his first week of business his profits were $200, hence A(0) = 200.Thus, the equation is given by:
[tex]A(x) = 200(1 + 0.2)^x[/tex]
[tex]A(x) = 200(1.2)^x[/tex]
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please answer asap!!!!!
Answer:
It is B kid you need to study this is basic shhhhhiz
Step-by-step explanation:
Answer:
it is B kid you need to study
Point B is between A and C. If AB = 3x, BC = 4x-2, and AC = 12, find the length of BC
Answer:
BC = 6 units
Step-by-step explanation:
given that B is between A and C , then
AB + BC = AC ( substitute values )
3x + 4x - 2 = 12
7x - 2 = 12 ( add 2 to both sides )
7x = 14 ( divide both sides by 7 )
x = 2
Then
BC = 4x - 2 = 4(2) - 2 = 8 - 2 = 6
Answer:
6
Step-by-step explanation:
from the question, since point B is between Ac
AC = AB + BC
12 = 3X+4X -2
3X+4X-2 = 12
7X = 12+2
7X = 14
dividing bothsides by 7
7X/7 = 14/7
X = 2
the length BC = 4X-2 = 4(2)-2 = 8-2= 6
length of BC = 6
PLEASE HELP THIS IS DUE AFTER 20 MINS!! I’LL GIVE BRAINLIEST!
Answer:
lol
Step-by-step explanation:
lol
There are 48 cards in a pack and each card is either red or black.
The ratio of the number of red cards to the number of black cards is 1 : 1
8 red cards are removed from the pack.
Find the ratio of the number of red cards now in the pack to the number
of black cards now in the pack.
Give your answer in its simplest form.
Answer:
2 : 3
Step-by-step explanation:
Given :
Ratio of black cards and red cards = 1 : 1Total cards = 48Solving :
Let the cards be denoted by xx + x = 48x = 24 of each (red and black)8 red cards have been removed from the pack.
So, now the ratio is :
Red : Black = 24 - 8 : 24Red : Black = 16 : 24Red : Black = 2 : 3Write the repeating decimal as a fraction.
1.4979
Answer:
1 4979/9999
Step-by-step explanation:
1.497949794979....
= 1 4979/9999
HI IM GIVING BRAINLIESST CAN SOMEONE PLEASE EXPLAIN AND HELP
Answer:
∠FDE or ∠GDA
Step-by-step explanation:
The adjacent angle refers to the angle which lies right next to an angle, and the sum of the angles is 180, meaning they are supplementary.
Here, in this diagram, there are 2 adjacent angles for ∠FDG :
∠FDE∠GDAPlease awnser the question does anyone want to help me with my math assignments
The two angles are supplementary angles and form a straight line which equals 180 degrees
x = 180 - 125
X = 55 degrees
Answer:
hope this will help you
Step-by-step explanation:
x+125=180
x=180-125
x=55°
diring the repair the mechanics will need to connect a cable between chairs b and j, and then continue that cable to chair g. what is the anhle formed by the cable
The angle that will be formed by the cable based on the information given will be 15°.
How to calculate the angle?From the complete information, it's important to divide the total angle by 12. This will be:
= 360°/12 = 30°
Then, the relations that will be used will be:
= 1/2(60° - 30°)
= 1/2 × 30°
= 15°
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#11 can someone help with this and also explain how they found the answer so ik how to do it
Answer:
24 units
Step-by-step explanation:
I really don't understand this, except for the fact that i found a workbook that has an answer with no work
hope this helps?:)
Find the center and radius of the circle represented by the equation below.
Answer:
Centre (5,-9) and radius is 14
Step-by-step explanation:
The circle equation is of form,
[tex] = > {(x - a)}^{2} + {(y - b)}^{2} = {r}^{2} [/tex]
where centre is (a,b) and radius is 'r'.
What is the probability of pulling a card from a deck of 52 cards and getting a king and a queen?
Answer:
4/52 or 1/13
Step-by-step explanation:
In a standard deck of 52 cards, there are 4 suits and each suit has 13 cards.
There are 4 kings, 4 queens, 4 aces, and 4 jacks.
So the probability of drawing a king would be:
4/52 = 1/13
Answer:
The probability of drawing a King is 4/52 or about . 0769, which is also the probability of drawing a Queen. The probability that a card drawn from the deck will be both a King and a Queen is zero. The probability that a card will be either a King or a Queen is 8/52.
Step-by-step explanation:
52 cards in a deck 4 queens and 4 kings
PLEASE ANSWER ASAP!!!!!!!!!!
Step-by-step explanation:
sqrt(5x - 2) <= 3
5x - 2 <= 9
5x <= 11
x <= 11/5
but also : 5x -2 >= 0
otherwise the square root is not valid for real numbers.
5x >= 2
x >= 2/5
so the solution is for all x out of R (real numbers), where
2/5 <= x <= 11/5
PLEASE HELP, I NEED THE ANSWER BEFORE 3 HOURS 1. In the fraction the 11 represents the? a. Dividend b. Divisor c. Denominator 2. In the decimal number 125.795 the 9 represents the d. Quotient e. Both B & C place.
Answer:
e. Both B & ChundredthsStep-by-step explanation:
Q1
In the fraction 5/11, 11 represents the divisor and the denominator.The correct option is eQ2
In the number 125.795, the 9 represents the hundredths placeAnswer:mbvcdhfguh
Step-by-step explanation:kvghjve5yr
How many times can you subtract the number five from 25.
Answer:
one time
Step-by-step explanation:
because after that you would subtract by 20
What's the mean, median, mode, and range of 8, 10, 8, 14, 8 and 15
Answer: Mean: 10.5, Median: 9 Mode: 8 Range: 7
Step-by-step explanation
mean put the numbers in order, so 8,8,8,10,14,15 the mean is adding all numbers together and dividing by the number so 8 + 8 + 8 + 10 + 14 + 15 divided by 6 is 10.5,
median is middle so 9 since theres two middle numbers u add them both and then divide by 2
mode is the most so its 8 since 8 is there 3 times
range is the highest number and lowest number and u subtract them so 15 - 8 = 7
sorry if this is long but the answers are at the top
Answer:
Below in bold.
Step-by-step explanation:
Mean = ( 8 + 10 + 8 + 14 + 8 + 15) / 6
= 10.5.
Arrange in ascending order to find the median:
8 8 8 10 14 15
Median = mean of the middle 2 numbers
= (8 + 10)/2
= 9.
Mode = most occurring number = 8.
Range = greatest - least = 15 - 8 = 7.
Mary bought an aquarium that is cuboid in shape. The bottom is a rectangle with sides of 50 cm and 70 cm. The height of the aquarium is 4 dm. Find how many gallons of water this aquarium can hold. How much a square decimeter of glass was used to make the aquarium when it was open at the top and the bottom was plastic?
Answer:
Area of the paper required =7000 cm²
Step-by-step explanation:
Dimensions of an Aquarium:
Length (l) = 80 cm,
Breadth (b) = 30 cm,
Height (h) = 40 cm
/* According to the problem given,
Area of the paper required =
Area of the base + 2×Area of two side faces + Area of the back side
(Front side should be visible,So, it is not covered )
= lb+2×bh+lh
= 80×30+2×(30×40)+80×40
= 2400+2×1200+3200
= 2400+2400+3200
= 7000 cm²
Therefore,
Area of the paper required =7000 cm²
Step-by-step explanation: