Area of triangle = 1/2 bh
60 = 1/2 (15) h
8 = h
Quadrilateral area = h x (b1 + b2)/2 = 8 x (15+9)/2 = 96 sq units
96 -60 = triangle BAD area = 36 sq units
The length of side BC in the triangle BCD is 8.
What is an area?An area is the amount of space occupied by a two dimensional shape or figure.
From the diagram:
Area of triangle BCD = (1/2) * base * height = (1/2) * CD * BC
60 = (1/2) * 15 * BC
BC = 8
The length of side BC in the triangle BCD is 8.
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A motorist drives at an average speed of 80 km/hr. How far does she travel in 3(1/2)
hours?
Answer: 280 km
Step-by-step explanation:
[tex]3\dfrac{1}{2} \: hours = 3.5 \: hours[/tex]
S = V × t
V = 80 km/h
t = 3.5 h
S = 80 × 3.5 = 280 km
Evaluate 2(x + 1) - 3 when x= 6.
A. 8
B. 5
c. 11
D. 10
Answer:
11
Step-by-step explanation:
2(x + 1) - 3
Let x= 6
2(6+1) -3
Parentheses first
2(7) -3
Then multiply
14-3
Then subtract
11
x² + 8x + 16 =
I need the steps and the answer
and the box
Answer:
The answer is (x+4)
Step-by-step explanation:
Just write the expression as a product with the factor x and 4
x²+2×x×4+4+16
then write the number in the exponential form with an exponent of 2
x²+2×x×4+4²
then use a² +2ab +b² = (a+b)² yo factor the expression which you get (x+4)
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
Answer:
3 < x
Step-by-step explanation:
3(8 – 4x) < 6(x – 5)
Divide each side by 3
3/3(8 – 4x) < 6/3(x – 5)
(8 – 4x) < 2(x – 5)
Distribute
8-4x < 2x-10
Add 4x to each side
8-4x+4x < 2x-10+4x
8 < 6x-10
Add 10 to each side
8+10 < 6x-10+10
18 < 6x
Divide by 6
18/6 < 6x/6
3 < x
which one of the following is product of(-3n)and(4mn-5n)
What is the probability of landing on a number on the spinner that is less than 3?
1/4
3/8
5/8
1/2
Answer: 1/4
Step-by-step explanation:
Reword the problem. It says what is the probability of landing on 2 or 1. That is 2 possibilities out of 8 so 2/8 = 1/4
If sally completed 6 laps around a circular track with the dimensions shown below, how many meters will she have run? Use 3.14 for up and round your answer to the nearest tenth
Answer/Step-by-step explanation:
The diagram of the circular track is missing, and so also its dimensions.
However, let's assume the dimensions of the circular track given is diameter (d) = 20 meters or radius (r) = 10 meters.
Since it's a circular track, the circumference of the track would give us the number of meters she runs in 1 lap.
Circumference = πd
d = 20 m (we are assuming the diameter is 20 meters)
π = 3.14
Circumference of circular track = 3.14 × 20 = 62.8 m.
This means that 1 lap = 62.8 m that she would have to run.
Therefore,
6 laps would be = 6 × 62.8 = 376.8 m
Therefore, if she completes 6 laps around the circular track that has a diameter of 20 m, she will have to run about 376.8 m.
(1.8 + 1.3) + 0.7 = 1.8 + (1.3 + 0.7) is an example of which property?
Answer:
Associative property
Step-by-step explanation:
The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.
Hope this helps
please find the result !
Answer:
[tex] \displaystyle - \frac{1}{2} [/tex]
Step-by-step explanation:
we would like to compute the following limit:
[tex] \displaystyle \lim _{x \to 0} \left( \frac{1}{ \ln(x + \sqrt{ {x}^{2} + 1} ) } - \frac{1}{ \ln(x + 1) } \right) [/tex]
if we substitute 0 directly we would end up with:
[tex] \displaystyle\frac{1}{0} - \frac{1}{0} [/tex]
which is an indeterminate form! therefore we need an alternate way to compute the limit to do so simplify the expression and that yields:
[tex] \displaystyle \lim _{x \to 0} \left( \frac{ \ln(x + 1) - \ln(x + \sqrt{ {x}^{2} + 1 } }{ \ln(x + \sqrt{ {x}^{2} + 1} ) \ln(x + 1) } \right) [/tex]
now notice that after simplifying we ended up with a rational expression in that case to compute the limit we can consider using L'hopital rule which states that
[tex] \rm \displaystyle \lim _{x \to c} \left( \frac{f(x)}{g(x)} \right) = \lim _{x \to c} \left( \frac{f'(x)}{g'(x)} \right) [/tex]
thus apply L'hopital rule which yields:
[tex] \displaystyle \lim _{x \to 0} \left( \frac{ \dfrac{d}{dx} \ln(x + 1) - \ln(x + \sqrt{ {x}^{2} + 1 } }{ \dfrac{d}{dx} \ln(x + \sqrt{ {x}^{2} + 1} ) \ln(x + 1) } \right) [/tex]
use difference and Product derivation rule to differentiate the numerator and the denominator respectively which yields:
[tex] \displaystyle \lim _{x \to 0} \left( \frac{ \frac{1}{x + 1} - \frac{1}{ \sqrt{x + 1} } }{ \frac{ \ln(x + 1)}{ \sqrt{ {x}^{2} + 1 } } + \frac{ \ln(x + \sqrt{x ^{2} + 1 } }{x + 1} } \right) [/tex]
simplify which yields:
[tex] \displaystyle \lim _{x \to 0} \left( \frac{ \sqrt{ {x}^{2} + 1 } - x - 1 }{ (x + 1)\ln(x + 1 ) + \sqrt{ {x}^{2} + 1} \ln( x + \sqrt{ {x }^{2} + 1} ) } \right) [/tex]
unfortunately! it's still an indeterminate form if we substitute 0 for x therefore apply L'hopital rule once again which yields:
[tex] \displaystyle \lim _{x \to 0} \left( \frac{ \dfrac{d}{dx} \sqrt{ {x}^{2} + 1 } - x - 1 }{ \dfrac{d}{dx} (x + 1)\ln(x + 1 ) + \sqrt{ {x}^{2} + 1} \ln( x + \sqrt{ {x }^{2} + 1} ) } \right) [/tex]
use difference and sum derivation rule to differentiate the numerator and the denominator respectively and that is yields:
[tex] \displaystyle \lim _{x \to 0} \left( \frac{ \frac{x}{ \sqrt{ {x}^{2} + 1 } } - 1}{ \ln(x + 1) + 2 + \frac{x \ln(x + \sqrt{ {x}^{2} + 1 } ) }{ \sqrt{ {x}^{2} + 1 } } } \right) [/tex]
thank god! now it's not an indeterminate form if we substitute 0 for x thus do so which yields:
[tex] \displaystyle \frac{ \frac{0}{ \sqrt{ {0}^{2} + 1 } } - 1}{ \ln(0 + 1) + 2 + \frac{0 \ln(0 + \sqrt{ {0}^{2} + 1 } ) }{ \sqrt{ {0}^{2} + 1 } } } [/tex]
simplify which yields:
[tex] \displaystyle - \frac{1}{2} [/tex]
finally, we are done!
9514 1404 393
Answer:
-1/2
Step-by-step explanation:
Evaluating the expression directly at x=0 gives ...
[tex]\dfrac{1}{\ln(\sqrt{1})}-\dfrac{1}{\ln(1)}=\dfrac{1}{0}-\dfrac{1}{0}\qquad\text{an indeterminate form}[/tex]
Using the linear approximations of the log and root functions, we can put this in a form that can be evaluated at x=0.
The approximations of interest are ...
[tex]\ln(x+1)\approx x\quad\text{for x near 0}\\\\\sqrt{x+1}\approx \dfrac{x}{2}+1\quad\text{for x near 0}[/tex]
__
Then as x nears zero, the limit we seek is reasonably approximated by the limit ...
[tex]\displaystyle\lim_{x\to0}\left(\dfrac{1}{x+\dfrac{x^2}{2}}-\dfrac{1}{x}\right)=\lim_{x\to0}\left(\dfrac{x-(x+\dfrac{x^2}{2})}{x(x+\dfrac{x^2}{2})}\right)\\\\=\lim_{x\to0}\dfrac{-\dfrac{x^2}{2}}{x^2(1+\dfrac{x}{2})}=\lim_{x\to0}\dfrac{-1}{2+x}=\boxed{-\dfrac{1}{2}}[/tex]
_____
I find a graphing calculator can often give a good clue as to the limit of a function.
Can someone help me? Which of the following verifies that triangle YXZ is similar to triangle QPR?
Answer:
a
Step-by-step explanation:
Profit is the difference between revenue and cost. The revenue, in dollars, of a company that manufactures cell phones can be modeled by the polynomial 2x2 + 55x + 10. The cost, in dollars, of producing the cell phones can be modeled by 2x2 – 15x – 40. The variable x represents the number of cell phones sold.
What expression represents the profit, and what is the profit if 240 cell phones are sold?
40x – 30; $2,400
40x – 30; $9,570
70x + 50; $16, 850
70x + 50; $28,800
Answer:
C
Step-by-step explanation:
Given that the equation of the revenue is R=2x2+55x+10 and the equation of the cost is C=2x2 – 15x – 40, you will get the profit by subtracting the revenue from the cost: R-C=P. Therefore, P=(2x2+55x+10)-(2x2 – 15x – 40). You will get P=70x+50 where x is is the number of cellphones sold. If 240 cellphones are sold, then the profit is 16850 dollars.
The profit, if 240 cell phones are sold, is $16,850.
Profit = 70x + 50
Option C is the correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example: so
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The profit, in dollars, can be found by subtracting the cost from the revenue:
Profit = Revenue - Cost
= (2x² + 55x + 10) - (2x² - 15x - 40)
= 70x + 50
The expression for profit is 70x + 50.
To find the profit if 240 cell phones are sold, we substitute x = 240 into the expression for profit:
Profit = 70x + 50
= 70(240) + 50
= 16,850
Therefore,
The profit, if 240 cell phones are sold, is $16,850.
Learn more about expressions here:
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a. x ll y
b. y ll z
c. a ll b
d. x perpendicular to b
Answer:
Option B
Step-by-step explanation:
By applying the converse theorem of corresponding angles,
"If corresponding angles formed between two parallel lines and the transversal line are equal then both the lines will be parallel"
Angle between line B and Y = 90°
Angle between line B and Z = 90°
Therefore, corresponding angles are equal.
By applying converse theorem, line Y and line Z will be parallel.
Option B will be the answer.
Which is the graph of f(x) = (x + 3)(x - 2
Answer:
Step-by-step explanation:
f(x) = (x + 3)(x - 2) has two zeros: One stems from (x + 3) = 0 and is (-3, 0); the other stems from (x - 2) = 0 and is (2, 0).
The axis of symmetry is a vertical line located halfway between -3 and 2:
x = -1/2.
The graph opens up because the given (x + 3)(x - 2) has a positive leading coefficient (+1).
With this information we can eliminate the last two possible answers. Note that the x-intercepts of the first graph are -3 and 2, Thus, the first graph is the correct one.
the length of a pond is 1700 CM breadth is 14m and height is 1000 CM if a point is half filled calculate the volume of a water in the pond
Answer:
1190 m^3
Step-by-step explanation:
l = 1700 cm = 17 m
b = 14 m
h = 1000 cm = 10 m
Total volume = l × b × h
= 17 × 14× 10
= 2380 m^3
since it is half filled ,
Volume is half , so,
volume of water in pond = 2380 ÷ 2
= 1190 m^3
Kharter goes to a gas station near his house where it costs $2.95 per gallon. Kharter’s car hold’s 13.2 gallons. The gas station near Devin’s house sells gas for $3.03 per gallon and his car holds 11.8 gallons
Devons current financial goals are to reduce his credit card debt start a retirement plan and save for a down payment on a house which smart goal attribute in the table applies to each of devons financial goals
Answer:
timely, timely,measurable
Step-by-step explanation:
Answer:
specific, timely, measurable
Step-by-step explanation:
i took the test on plato
WILL GET BRAINLIEST
Which does NOT represent the interior angle measures of a triangle? A.5°, 75°, 100°B.10°, 80°, 90°C.20°, 60°, 100°D.45°, 45°, 45°E.50°, 50°, 80°
Answer:
3 * 45 = 135 which is NOT 180
45, 45, 90 would work
Step-by-step explanation:
hope it helps!
What type of transformation does shape A undergo to form shape B?
Answer:
Rotated 90° counterclockwise, then reflected across the y-axis
Step-by-step explanation:
John owns shares in a mutual fund and shares of individual stocks in his brokerage account. The Form 1099-DIV from the mutual fund indicates $2,000 of capital gains distributions and the form from the brokerage firm indicates $6,000 of capital gains distributions. The brokerage statement also indicated a long term capital loss of $1,850 on a stock sale. How should John report the capital gains distributions?
Question options:
A. He should report them directly on form 1040
B. He should report them on form 8949 and then on schedule D
C. He should report them on schedule D
D. He is not required to report them until he sells the underlying securities
Answer:
B. He should report them on form 8949 and then on schedule D
Explanation:
John has shares which have capital gains from a mutual fund and a brokerage account. In order to report his taxes, he would need to use the Schedule D(form 1040) for his mutual fund capital gains and the form 8949 for his brokerage capital gains. The brokerage capital gains is then transferred to schedule D.
please help asap!!
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Two large parallel metal plates carry opposite charges. They are separated by 85mm. The work done by the field is 6x10-3J and its field exerts on a particle with charge +8µC. Calculate the surface charge density on each plate.
Answer:
The surface charge density is [tex]7.8\times10^{-8} C/m^2[/tex].
Step-by-step explanation:
separation, d = 85 mm
Work, W = 6 x 10^-3 J
charge , Q = 8µC
The potential difference is given by
W = q V
[tex]V=\frac{6\times 10^{-3}}{8\times 10^{-6}}=750 V[/tex]
Let the charge on he capacitor is q.
[tex]q = CV\\\\q = \frac{\varepsilon oA}{d}\times V\\\\\frac{q}{A} = \frac{8.85\times 10^{-12}\times750}{0.085} =7.8\times10^{-8} C/m^2[/tex]
Please help! Pleaseeeeeee
Answer:
The answer is D
Step-by-step explanation:
-x is n
Y=0
Answer:
D
Step-by-step explanation:
Basically....... graph shown in picture
The school bought 957 science books, 1054 mathematics books, and 458 reading books. Put the books in order from least to greatest.
Answer:
reading books (458), science books (957), mathematics books (1054)
Step-by-step explanation:
458 is less than 957 and 1054, while 957 is less than 1054 but more than 458, and 1054 is more than 957 and 458.
458<957<1054
What is an equation of the line that passes through the points (-5, -1) and (5, 3)?
Solve for x when y = 4
2x + 2y = 20
Answer:
x=6
Step-by-step explanation:
2x + 2y = 20
Let y=4
2x +2(4) = 20
Multiply
2x+8 = 20
Subtract 8 from each side
2x+8-8= 20-8
2x = 12
Divide by 2
2x/2 = 12/2
x = 6
Answer:
[tex]x=6\\[/tex]
Step-by-step explanation:
[tex]2x+2(4)=20[/tex]
[tex]2x+8=20[/tex]
Subtract both sides by 8
[tex]2x=12[/tex]
Divide both sides by 2 to get x alone
[tex]x=6[/tex]
Hope this is helpful
Find the length of the hypotenuse to the nearest tenth. (example 4.5)
7
2

Answer:
hypotenuse = 7.3
Step-by-step explanation:
the length two legs of the given triangle are 7 and 2 respectively.
using pythagoras theorem
a^2 + b^2 = c^2
7^2 + 2^2 = c^2
49 + 4 = c^2
53 = c^2
[tex]\sqrt{53}[/tex] = c
7.3 = c
what is f(0) for the function f(x) =2x+3
Answer:
3
Step-by-step explanation:
f(x) =2x+3
Let x=0
f(0) =2*0+3
Multiply
f(0) =0+3
Add
f(0) =3
Answer:
3
step-by-step explanation
f ( x ) = 2 x + 3
f ( 0 ) = 2 × 0 + 3 .. ( f ( x = 0 ) - given )
multiply
f ( 0 ) = 0 + 3
Add the numbers
f ( 0 ) = 3
Help please thanks! :)
Answer:
Option A = 1/15 cubic meters
Step-by-step explanation:
Formule to find volume of rectangular prism:
Volume = width × height × length
V = w×h×l
V = 1/3 × 1/4 × 4/5
V = 1/15 cubic meters
Mr yates owns a smoothie shop. To mix a batch of his famous orange punch smoothies, he uses 18 ounces of freshly squeezed orange juice. Each day he squeezes 560 ounces of fresh orange juice. How many batches of orange punch smoothies can he make in a day?
Answer:
31 batches
Step-by-step explanation:
Find how many batches of orange punch smoothies he can make by dividing 560 by 18:
560/18
= 31.11
Since we can only have a whole number answer, round down.
So, he can make 31 batches of orange punch smoothies.
Express 5m2 in cm2 please answer fast!
Answer:
500000 cm2
Step-by-step explanation:
