Answer:
4.5 sq. units.
Step-by-step explanation:
The given curve is [tex]y = (3x)^{\frac{1}{2} }[/tex]
⇒ [tex]y^{2} = 3x[/tex] ...... (1)
This curve passes through (0,0) point.
Now, the straight line is y = 3x - 6 ....... (2)
Now, solving (1) and (2) we get,
[tex]y^{2} - y - 6 = 0[/tex]
⇒ (y - 3)(y + 2) = 0
⇒ y = 3 or y = -2
We will consider y = 3.
Now, y = 3x - 6 has zero at x = 2.
Therefor, the required are = [tex]\int\limits^3_0 {(3x)^{\frac{1}{2} } } \, dx - \int\limits^3_2 {(3x - 6)} \, dx[/tex]
= [tex]\sqrt{3} [{\frac{x^{\frac{3}{2} } }{\frac{3}{2} } }]^{3} _{0} - [\frac{3x^{2} }{2} - 6x ]^{3} _{2}[/tex]
= [tex][\frac{\sqrt{3}\times 2 \times 3^{\frac{3}{2} } }{3}] - [13.5 - 18 - 6 + 12][/tex]
= 6 - 1.5
= 4.5 sq. units. (Answer)
I need help ASAP i will mark you are whatever and give thanks but pls help me
i cant see the whole problem
Answer:
64.28 m
Step-by-step explanation:
In the attached file
what are the solutions of x²-4x+5=0?
Answer:
x=2+i, x=2-i
Step-by-step explanation:
x^2-4x+5=0
Apply the quadratic formula.
There are are no real solutions for this equation.
What is a quadratic equation?An equation whose highest degree is 2, is called a quadratic equation.
How to solve a quadratic equation?We can solve a quadratic equation by two ways:
Factorization- If the quadratic expression is factorizable then we can factorize it and equate it to 0. Then we can apply the concept that when product of two or more expressions is 0 then at least one of the expression or both must be 0By Shreedhar Acharya formula- A quadratic equation of the [tex]ax^{2} +bx+c=0[/tex] form can be solved by the formula given below:[tex]x=\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]
or
[tex]x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]
This [tex]\sqrt{b^{2}-4ac }[/tex] is called discriminant.If the discriminant is negative, then the equation have no real solution.How to find the solutions of x²-4x+5=0?Comparing with the standard equation [tex]ax^{2} +bx+c=0[/tex],
a = 1b = -4c = 5How to check the discriminant?∴ Discriminant = [tex]\sqrt{b^{2}-4ac }[/tex] = [tex]\sqrt{-4}[/tex]
Here, the discriminant is negative, so there are no real solutions.There are imaginary solutions.Find out more about 'Quadratic Equation' here: brainly.com/question/1214333
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I will give 100 points to whoever has the best answer
1. Seiji and Gavin both worked hard over the summer. Together they earned a total of $525. Gavin earned $25 more than Seiji.
(a) Write a system of equations for the situation. Use s for the amount Seiji earned and g for the amount Gavin earned.
(b) Graph the equations of the system on the graph
(c) Use your graph to estimate how much each person earned, and explain your results.
Answer:
a)
[tex]\left\{\begin{matrix}g=525-s\\ g=s+25\end{matrix}\right.[/tex]
c)
Gavin earned $275
Seiji earned $250
Step-by-step explanation:
a) Denoting s as the earning of Seiji and g the earnings of Gavin, we know they together earned $525. This forms the equation
s+g=525, or equivalently
[tex]g=525-s[/tex]
We also know that Gavin earned $25 more than Seiji. It can be written as
[tex]g=s+25[/tex]
Combining both equations we get the system
[tex]\left\{\begin{matrix}g=525-s\\ g=s+25\end{matrix}\right.[/tex]
b) The graph is shown below
c) Both functions have one point in common. It's the solution of the system. We can conclude that
Gavin earned $275
Seiji earned $250
A parallelogram has an interior angle measuring 81º. Which MUST also be the measure of an interior angle of the
parallelogram?
A)9°. C)49°
B)19° D)99°
Answer:
D)99 degrees
Step-by-step explanation:
The answer is D. All the angles in any quadrilateral add up to 360 degrees. And since the figure is a paralledlogram, for each angle there is another angle with the same measurement. So 81 + 81 + x + x = 360 which gives us 162 + 2x = 360. If you solve for x you get 99 degrees.
What is 3-2x>-5 in an inequality form
Answer:
[tex]\displaystyle 4 > x[/tex]
Step-by-step explanation:
3 - 2x > −5
- 3 - 3
_________
[tex]\displaystyle \frac{-2x}{-2} > \frac{-8}{-2} \\ \\ x < 4[/tex]
Whenever you divide\multiply by a negative, you reverse the inequality symbol.
** The above answer is written in reverse, which is the exact same result.
I am joyous to assist you anytime.
An investor invested a total of $2,800 in two mutual funds. One fund earned 5% profit while the other earned 3% profit. If the investor's total profit was $104, how much was invested in each mutual fund? The amount invested in the mutual fund that earned 5% was $(blank). The amount invested in the mutual fund that earned 3% was $(blank). (show your work)
Answer:
The amount invested in the mutual fund that earned 5% was $1,000
The amount invested in the mutual fund that earned 3% was $1,800
Step-by-step explanation:
Let
x ----> the amount invested in the mutual fund that earned 5%
y ----> the amount invested in the mutual fund that earned 3%
we know that
[tex]x+y=2,800[/tex] ----> [tex]y=2,800-x[/tex] ----> equation A
[tex]5\%=5/100=0.05[/tex]
[tex]3\%=3/100=0.03[/tex]
[tex]0.05x+0.03y=104[/tex] ----> equation B
Solve the system by substitution
substitute equation A in equation B
[tex]0.05x+0.03(2,800-x)=104[/tex]
Solve for x
[tex]0.05x+84-0.03x=104[/tex]
[tex]0.05x-0.03x=104-84[/tex]
[tex]0.02x=20[/tex]
[tex]x=\$1,000[/tex]
Find the value of y
[tex]y=2,800-x[/tex]
[tex]y=2,800-1,000=\$1,800[/tex]
therefore
The amount invested in the mutual fund that earned 5% was $1,000 and the amount invested in the mutual fund that earned 3% was $1,800
Which segment is a median of triangle GFH
Answer:
The segment GT is a median of triangle GFH
Step-by-step explanation:
we know that
A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.
The angle bisector of a triangle is a line segment that bisects one of the vertex angles of a triangle.
In this problem
SH represent a line segment that bisects the vertex angle H of triangle GFH, so represent an angle bisector.
GT represent a median of triangle GFH, because the point T is the midpoint of segment FH (FT=TH)
therefore
The segment GT is a median of triangle GFH
Which theorem or postulate proves the two triangles are similar?
Answer:
The corresponding pair of sides are in the same ratio.
Step-by-step explanation:
For two triangles to be similar, the theorem that is required is the corresponding sides of the two triangles are in the same ratio.
Now, see the diagram of two triangles given with the question.
The ratios of the corresponding sides are [tex]\frac{20}{16} = \frac{19}{\frac{76}{5} } = \frac{5}{4}[/tex]
If two pairs corresponding sides are in 5 : 4 ratio, then the third pair of corresponding sides will also be in 5 : 4 ratio.
Therefore, the two triangles are similar. (Answer)
To prove that two triangles are similar, you can use the AA (Angle-Angle) Postulate, SSS (Side-Side-Side) Similarity Theorem, or SAS (Side-Angle-Side) Similarity Theorem. These methods involve comparing the angles and sides of the triangles to see if they meet the similarity conditions.
Triangle Similarity Theorem
To determine whether two triangles are similar, you can use several different theorems or postulates. These include the AA (Angle-Angle) Postulate, the SSS (Side-Side-Side) Similarity Theorem, and the SAS (Side-Angle-Side) Similarity Theorem.
AA (Angle-Angle) Postulate: If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
SSS (Side-Side-Side) Similarity Theorem: If the three sides of one triangle are proportional to the three corresponding sides of another triangle, then the triangles are similar. For example, if triangle ABC and triangle DEF have corresponding sides such that AB/DE = BC/EF = AC/DF, then the triangles are similar.
SAS (Side-Angle-Side) Similarity Theorem: If an angle of one triangle is congruent to an angle of another triangle and the sides containing these angles are proportional, then the triangles are similar. For example, if ∠A = ∠D and AB/DE = AC/DF, then triangles ABC and DEF are similar.
By using these theorems, you can determine if two triangles are similar by comparing their angles and sides as per the given conditions.
What does it mean to say that the amount
Of money from the previous month but is quadrupled
Answer: The amount of money from the previous month times 4.
Step-by-step explanation:
PLEASE HELP ME ASAP PLEASE!!!
If c is the hypotenuse of a right triangle, find the missing side. If necessary, round to the nearest hundredth.
c= 155, b = 31, a =[ ]
Answer:
a= 151.87 units
Step-by-step explanation:
Given:
Consider,a right triangle Δ ACB with Angle C as 90°,
and side a, b, and c be the sides opposites to the respective angles. Such that
c = Hypotenuse = 155
b = Shorter leg = 31
a = Longer leg = ?
To Find:
a = Longer leg = ?
Solution:
In Right angle Δ ACB
If we apply Pythagoras Theorem we get
[tex](\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}[/tex]
Now substituting the given above values we get,
[tex]c^{2}= b^{2} + a^{2}\\x^{2} 155^{2}= 31^{2}+ a^{2}\\ 24025=961+a^{2}\\\therefore a^{2}=24025-961\\a^{2} = 23064\\ a=\pm 151.8683\\\therefore a = 151.87 .......\textrm{Distance cannot be in negative}[/tex]
∴ a= 151.87 units......(rounded to nearest hundredth)
If one pencil weighs 9g.What does a box of 8 pencils weight?
Answer:
82g
Step-by-step explanation:
You multiply 9×8 to find the answer as each pencil is 9g and there is 8 pencils in a box.
72g because 8*9g is 72
Bodens account has a principal of $500 and a simple interest rate of 3.3% . complete the double number line. HOW MUCH money will be in the account after 4 years, assuming Boden does not add or take out any money.
Answer:
$66.00
Step-by-step explanation:
first we need multiply :D I will use the formula I =prt
principal= $500
rate=3.3%
time= 4 years
but we need to convert the percent, 3.3%, to a decimal
3.3%=0.033 or .033
now we multiply !
500 × 0.033 × 4 = 66 = $66.00
:D
Answer:$66.00
Step-by-step explanation:
first we need multiply :D I will use the formula I =prt
principal= $500
rate=3.3%
time= 4 years
but we need to convert the percent, 3.3%, to a decimal
3.3%=0.033 or .033
now we multiply !
500 × 0.033 × 4 = 66 = $66.00
Match the real-world problem to its constant of proportionality.
$18.36 for 3 pizzas [box]
$4.17 for 3 pounds of bananas [box]
$16.48 for 4 pounds of potatoes [box]
2 cups of flour to make 24 cookies [box]
Place in the box 12 4.12 6.12 1.39
Answer:
6.12
1.39
4.12
12
Step-by-step explanation:
If y ∝ x, then y = kx.
So, the constant of proportionality is given by [tex]k = \frac{y}{x}[/tex]
Case 1:
$18.36 for 3 pizzas
Therefore, the constant of proportionality is [tex]\frac{18.36}{3} = 6.12[/tex]
Case 2:
$4.17 for 3 pounds of bananas.
Hence, the constant of proportionality is [tex]\frac{4.17}{3} = 1.39[/tex]
Case 3:
$16.48 for 4 pounds of potatoes.
Hence, the constant of proportionality is [tex]\frac{16.48}{4} = 4.12[/tex]
Case 4:
2 cups of flour to make 24 cookies.
Hence, the constant of proportionality is [tex]\frac{24}{2} = 12[/tex] (Answer)
Solve the system using elimination.
7x - 5y = 26
2x+4y= 2
Answer:
x=3, y=-1. (3, -1).
Step-by-step explanation:
7x-5y=26
2x+4y=2
--------------
simplify 2x+4y=2 into x+2y=1
-------------
7x-5y=26
x+2y=1
-----------------
x=1-2y
7(1-2y)-5y=26
7-14y-5y=26
7-19y=26
19y=7-26
19y=-19
y=-19/19
y=-1
x+2(-1)=1
x-2=1
x=1+2
x=3
Answer: x=-1,y=0
Step-by-step explanation:
7x - 5y = 26 multiplied by factor of 2 becoming 14x-10y=52
2x+4y= 2 multiplied by factor of 7 becoming 14x+28y=14
now solve by elimination
14x+28y=14
-(14x-10y=52)
--------------------
38x=-38
x=-1
to find y plug in x to an equation
2(1)+4y= 2
y=0
The measure of ZABC is 130º. Find
the value of x.
(6x+40)°
Answer:
x = 15
Step-by-step explanation:
If ZABC = 130º
ZABC = (6x+40)° = 130º
This equation can be rearranged to solve for x by isolating it (moving everything over to the other side).
(6x+40)° = 130º
Solve it without the degrees sign because it looks confusing.
6x+40 = 130
6x+40 - 40 = 130 - 40 (subtract 40 from both sides)
6x = 90
6x/6 = 90/6 (divide both sides by 6)
x = 15
Therefore x is 15. The degrees symbol is already included outside the bracket.
39 times 49 times 81
Answer:
154,791
Step-by-step explanation:
Answer:
39 times 49 times 81 = 154791
Solve for z
-153=-19z
36, 17, 22, 43, 11, 56, 17,71
Range:
Answer:
Range = highest value - lowest value
= 71-11
= 60
Hope this helps!
78 was divided by some number then added to 10. next this was multiplied by 8 which gave a product of 184 .find the number
Answer:
The number is 6.
Step-by-step explanation:
(78/x+10)*8=184
8(78/x+10)=184
78/x+10=184/8
78/x+10=23
78/x=23-10
78/x=13
x=78/13
x=6
Answer:The unknown number can be calculated by the following formula;
Step-by-step explanation:
2/67 = 18/x
..............................................................................................................................................................
Answer:
{ } should be the answer glad i could help
Step-by-step explanation: could i get marked as brainliest on this it took up alot of my time
The solution of the given proportionality is x = 603
The given proportionality is,
2/67 = 18/x
Since we know that,
Proportion is mostly discussed using ratios and fractions. A fraction is written as a/b, whereas a ratio is expressed as a:b, and a percentage says that two ratios are equal.
In this case, a and b can be any two numbers. The ratio and proportion are important foundations for understanding numerous ideas in mathematics and science.
Now proceeding the expression,
⇒ 18/x = 2/67
Taking reciprocal both sides we get,
⇒ x/18 = 67/2
Multiply 18 both sides we get,
⇒ x = (67x18)/2
= 67x9
= 603
Hence,
x = 603
To learn more about proportionality visit:
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Simplify . 16x3y2/36xy2z3
[tex] \frac{16 {x}^{3} {y}^{2} }{36x {y}^{2} {z}^{3} } = \frac{4 {x}^{2} }{9 {z}^{3} } \\ \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{ - a} = \frac{1}{ {x}^{a} } [/tex]
61.05 as a fraction?
Answer:
61 ¹/₂₀
Step-by-step explanation:
You cannot get a proper fraction while converting 61.05 into a fraction. You will only end up with improper fractions. This is your answer as a simplified improper fraction. If you also want a mixed number answer, that is down below.
61 1/20
I hope this helps you! :)
I need help on it, I don’t know what I’m supposed to do
Answer:
The length of river frontage for each lot are 96.55 ft. 98.85 ft, 101.15 ft and 103.45 ft.
Step-by-step explanation:
See the attached diagram.
The river frontage of 400 ft will be divided into 84 : 86 : 88 : 90 for each lot as AP, BQ, CR, DS and ET all are parallel.
Therefore, PQ : QR : RS : ST = 84 : 86 : 88 : 90 = 42 : 43 : 44 : 45
Let, PQ = 42x, QR = 43x, RS = 44x and ST = 45x
So, (42x + 43x + 44x + 45x) = 400
⇒ 175x = 400
⇒ x = 2.2988.
So, PQ = 42x = 96.55 ft.
QR = 43x = 98.85 ft.
RS = 44x = 101.15 ft and
ST = 45x = 103.45 ft
(Answer)
A car travels 300 miles on level terrain in the same amount of time it travels 175 miles on mountainous terrain. If the rate of the car is 25 miles per hour less in the mountains than on level ground, find its rate in the mountains.
Answer
x = 50 mph (level rate)
x-30 = 20 mph (mountain rate)
Explain:
time = time
160/(x-30) = 400/x
160x = 400(x-30)
160x = 400x - 12000
-240x = -12000
PLEASE..EXPERT IN MATH
Answer:
x=3
Step-by-step explanation:
one property of a trapezoid and medians is the middle line is half of the bottom and top combined. so the equation would look like this
3x+2+4x+3/2=13.
7x+5/2=13
7x+5=26
x=3
hope this helps,
the first 3 terms of a geometric sequence are as follows. -2, 10, -50. find the next 2 terms
Answer:
The next two terms for the geometric sequence are 250 and - 1,250
Step-by-step explanation:
1. Let's find the next two terms for the geometric sequence which first three terms are as follows:
- 2, 10, - 50.....
Aₓ = Aₓ₋₁ * - 5 ; A₁ = - 2
A₁ = - 2
A₂ = A₁ * - 5 = -2 * - 5 = 10
A₃ = A₂ * - 5 = 10 * - 5 = - 50
A₄ = A₃ * - 5 = - 50 * - 5 = 250
A₅ = A₄ * - 5 = 250 * - 5 = - 1,250
The next two terms for the geometric sequence are 250 and - 1,250
A city map has the scale 1inch - 1.000 feet. If a map of the city limits is 36 inches (East to West) by 24 inches (North to
South), how many miles long (5.280 feet = 1 mile) is a straight north-South road in this scale?
Answer:
4.5 miles.
Explanation:
24 x 1,000 = 24,000
24,000 ÷ 5380 = 4.5
1/2 - [-1/4+2/3] how do you solve this value of the expression
Answer:
1/12
Step-by-step explanation:
1/2-[-1/4+2/3]
1/2-[-3/12+8/12]
1/2-[5/12]
1/2-5/12
6/12-5/12
1/12
Please help
-2/3 (x-3) - x = 8
Answer:
-18/5 or - 3 3/5.
Step-by-step explanation:
-2/3 (x-3) - x = 8
-2/3x + 2 - x = 8
-2/3x - 3/3x = 8 - 2
-5/3 x = 6
x = 6 * -3/5
x = -18/5
Help with this (surds)
Raise 2 to the 4th power:
√(16*9)
Multiply:
√144
Find square root:
Answer = 12