Your answer is correct. The two "bases" of the trapezoid are the line segments (0, 0)-to-(y, 0) and (0, x)-to(z, x), with lengths y and z, respectively. Then the average of the bases is [tex]\frac{y+z}2[/tex]. (We know they're the bases because the line segments are parallel.)
We multiply this by the height, which is given by the length of the line segment (0, 0)-to-(0,x), or x.
Hence the area is
[tex]\dfrac{x(y+z)}2[/tex]
(which is identical to what you have).
This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!
Step-by-step explanation:
[tex] \frac{5 {}^{ - 4x + 7} }{125 {}^{x} } [/tex]
[tex] \frac{5 {}^{ - 4x + 7} }{5 {}^{3x} } [/tex]
[tex]5 {}^{ - 4x + 7 - 3x} [/tex]
[tex]5 {}^{ - 7x + 7} [/tex]
Determine the equation of the tangent line in both cases
1. x^2/x+2 at (2,1)
2. x^3+2y^2=10y at (2,1)
Differentiate the function/equation with respect to x and solve for the derivative, dy/dx. The value of dy/dx at the given point is the slope of the tangent line to the curve at that point. Then use the point-slope formula to get the equation of the tangent.
1.
[tex]y = \dfrac{x^2}{x+2} \implies \dfrac{dy}{dx} = \dfrac{2x\times(x+2) - x\times1}{(x+2)^2} = \dfrac{x(x+4)}{(x+2)^2}[/tex]
When x = 2, the derivative is
[tex]\dfrac{dy}{dx}\bigg|_{x=2} = \dfrac{2(2+4)}{(2+2)^2} = \dfrac34[/tex]
Then the equation of the tangent line at (2, 1) is
[tex]y - 1 = \dfrac34 (x - 2) \implies \boxed{y = \dfrac{3x}4 - \dfrac12}[/tex]
2.
[tex]x^3 + 2y^2 = 10y \implies 3x^2 + 4y \dfrac{dy}{dx} = 10 \dfrac{dy}{dx} \implies \dfrac{dy}{dx} = \dfrac{3x^2}{10-4y}[/tex]
When x = 2 and y = 1, the derivative is
[tex]\dfrac{dy}{dx}\bigg|_{(x,y)=(2,1)} = \dfrac{3\times2^2}{10-4\times1} = 2[/tex]
Then the tangent at (2, 1) has equation
[tex]y - 1 = 2 (x - 2) \implies \boxed{y = 2x - 3}[/tex]
Hamish and Harry work as plumbers. harry earns a dollar more than 5/4 the amount Hamish earns per hour. the amount Harry earns per hour is 2$ less than 7/5 the amount Hamish earns per hour. how much to both of them earn per hour?
Answer:
Hamish earns $20 per hour, and Harry earns $26 per hour.
Step-by-step explanation:
Harry earns
$1+(5/4)•x and also (7/5)•x-$2
$1+(5/4)•x = (7/5)•x-$2
$1+$2= (7/5)•x-(5/4)•x
3=(7•4•x-5•5•x)/20
3=3x/20
3•20=3x
X=20, Hamish earns $20
Substitute x in one of the expressions
1+(5/4)•20=1+25=26, Harry earns $26
How many yards are in 1 mile 60 feet?
Answer:
1780
Step-by-step explanation:
multiply the length value by 1760
and then divide the length value by 3
The number of cars at a car dealership is reduced by 10% in the first sales quarter of the year. If the number of cars decreased an additional 20% over the second sales quarter of the year, then by what percent did the number of cars decrease over the two sales quarters? A) 25% B) 28% C) 30% D) 45%
Answer:
B) 28%=================
Let the initial price be x.
After the first sales quarter the price is reduced by 10% and became:
x - 10% = x - 0.1x = 0.9xAfter the second sales quarter the price is reduced by 20% and became:
0.9x - 20% = 0.9x - 0.2*0.9x = 0.9x - 0.18x = 0.72xThe decrease over the two quarters is:
x - 0.72x = 0.28xThis is equivalent of 28%, hence the correct answer choice is B.
If y = 2x-3, then which of the following ordered pairs lies on the graph?
O (-3,0)
O (1,-1)
O (5,4)
Plug in the points and see if they satisfy the equation.
y = 2x - 3
(1, -1)
-1 = 2(1) - 3
-1 = 2 - 3
-1 = -1
So (1, -1) satisfies the equation.
(-3, 0)
0 = 2(-3) - 3
0 = -6 - 3
0 = -9
So (-3, 0) does not satisfy the equation.
(5, 4)
4 = 2(5) - 3
4 = 10 - 3
4 = 7
So (5, 4) does not satisfy the equation.
Therefore your answer is (1, -1).
Answer:
the answer is 5,4
what is −4/5+40/75+100%=
-0.8+1.875+100%
1.05+100%
0.1
Superman needs to save lois from the clutches of lex luthor. It take superman 5 seconds to get to Lois who is 210 feet away. What is supermans rate?
Answer:
42 ft/s
Step-by-step explanation:
if superman travels 210 feet in 5 seconds, he will travel a fifth of 210 ft in 1 second
a fifth of 210ft is 210/5=42
hence 42ft/s is his rate.
A rake is priced at $28.49. Tax is $1.85. What is
the total cost of the rake?
find the indicated side of the right triangle
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = 3\sqrt3 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: \tan(60) = \cfrac{x}{3} [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{3} = \dfrac{x}{3} [/tex]
[tex]\qquad \tt \rightarrow \: x = 3 \sqrt{3} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Use a calculator to graph the functions y=-3x-21 and y=x³-3x-3. How many points of intersection do the
functions share?
0
1
2
3
Answer:
1
Step-by-step explanation:
When you graph the functions they intersect at one point
(-3.368119, -31.10436)
The difference between two numbers is -1 and their sum is 1. Find the two numbers.
Answer:
Let the no. be X and Y
X - Y = (-1)
X + Y = 1
X = (-1)+ Y
X = 1 - y
- 1.+ y = 1 - y
Y + Y = 1 + 1
2y = 2
Y = 1
X = 0
Answer:
x = 0 (first number), y = 1 (second number)
Step-by-step explanation:
x will represent the first number, and y will represent the second.
x - y = -1
x + y = 1
Now, it's time to get y by itself in one equation so that we can substitute.
x - y = -1 (subtract x from both sides)
-y = -1 - x (multiply both sides by -1)
y = x + 1
Plug in x + 1 for y in the second equation.
x + x + 1 = 1 (combine the x with the x)
2x + 1 = 1 (subtract 1 from both sides)
2x = 0 (divide both sides by 2)
x = 0
Since x = 0, we can plug 0 in for x into any equation to solve for y.
0 + y = 1
y = 1
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Which is true of dependent events?
ANSWER CHOICES:
The probability of all dependent events can be calculated using the OR formula P(A+B) =P(A) +P(B)-P(A and B) .
You can use a two-way frequency table to calculate the conditional probability of events that are dependent.
You can find the AND probability of dependent events using the formula P(A or B)= P(A) times P(B) .
The outcome of one event has no effect on the outcome of a second event.
Probability helps us to know the chances of an event occurring. The correct option is A.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Dependent events are those events in which the outcome of the first event affects the outcome of the second event. The statement that is correct about the dependent event is that the probability of all dependent events can be calculated using the "OR" formula P(A+B) =P(A) +P(B)-P(A and B).
Hence, the correct option is A.
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What is the perimeter in units ?
Answer:
12 + [tex]4\sqrt{5}[/tex] approximates to 20.944
Step-by-step explanation:
VU - 8 units
UW - 4 units
VW - [tex]\sqrt{64+16} = \sqrt{80} =4\sqrt{5}[/tex]
12 + 4sqrt(5)
Answer:
6 (2 + √5) units
Step-by-step explanation:
Finding the length of the 3rd side :
*Applying Pythagorean Theorem*
VW² = 4² + 8²VW² = 16 + 64VW = √80VW = 6√5The perimeter :
4 + 8 + 6√512 + 6√56 (2 + √5) unitsWhich of the following statements is true?
Answer:
B
Step-by-step explanation:
1/9 can be simplified to 1/3 as 1/3 x 1/3 = 1/9 and 49/25 can be simplified to 7/5 as 7/5 x 7/5 = 49/25.
Now looking at both the fraction 1/3 and 7/5
1/3 simplifies to 0.34
It is an irrational value as the 3 keeps repeating.
7/5 simplifies to 1.4
It is a rational value as the decimal value is not repeating.
Thus making the second option the answer.
the data below shows the number of workers employed in the various section s of each a construction company in the Lagos
Carpenter 24
plumber 12
labourers 27
plasterers 15
painters 9
Messengers 3
bricklayers 18
if the Worker is retrenched, what is the probability that he is a plumber or a plasterer?
If the Worker is retrenched, the probability that he is a plumber or a plasterer will be 0.0152.
What is probability?The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,
The probability that the employee is a plumber;
[tex]\rm P(plumber)= \frac{No \ of \ plumber}{Total \ number \ of \ employ} \\\\ P(plumber)=\frac{12}{108} \\\\\ P(plumber)= 0.11[/tex]
The probability that the employee is a plasterer;
[tex]\rm P(plasterers )= \frac{No \ of \ plasterers }{Total \ number \ of \ employ} \\\\ P(plasterers )=\frac{15}{108} \\\\\ P(plasterers )= 0.13[/tex]
The probability that he is a plumber or a plasterer:
P = 0.13 × 0.11
P= 0.0152
Hence, if the worker is retrenched, the probability that he is a plumber or a plasterer will be 0.0152.
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Find the value of c that makes the expression a perfect square trinomial. x2 + 9 4 x + c
A) 9/16
B) 9/64
C) 81/16
D) 81/64
The value of c is 81/64 for the expression a perfect square trinomial.
What is an Expression?An expression can be defined as a mathematical statement that consists of variables, constants and mathematical operators simultaneously.
It is given that an expression
x² +9/4x +c is a perfect square polynomial
c =?
(a+b)² = a² +2ab+b²
2ab = 9/4
b = 9/8
c = b² = 81/64
Therefore the value of c is 81/64 for the expression a perfect square trinomial.
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Which of the following is a requirement for multiple regression?
3.
Categorical variables only
O b. A small sample size
O c. Obiective measures only
O d. Absence of multicollineerity between variables
0 e.
Subjective measures onlv
Answer:
insectistics a category variable also called various validity variable is a variable that can take on a limited as usually fixed number two possible values assigning each into visual or other unit of the vision 2 a particular group aur nominacle category of the basis some qualitative
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What are the foci of this ellipse?
ANSWER CHOICES: are in picture
Use the sequence 1, 5, 9, 11, 13, ...
Find the 150th term of the sequence.
Answer: 597
Step-by-step explanation:
The common difference is 5-1=4, so the explicit formula is [tex]a_{n}=1+(n-1)(4)[/tex]
Substituting in n=150,
[tex]a_{150}=1+(150-1)(4)=\boxed{597}[/tex]
how much would $500 invested at 3% interest compounded continuously be worth after 6 years? Round your answer to the nearest cent. Use 2.718 for e. A(t)=Pe^(rt)
You are given the equation
A(t) = P*e^(rt)
Where P = Principal
r = interest rate
t = time
e is a mathematical constant equivalent to approx 2.71828
You're told the initial Principal is $500, the interest rate is 3%, over 6 years. So you have everything that you need to solve the problem, just plug in the values and solve for A(6)
A(t) = P*e^(rt)
A(6) = 500 * e^(0.03 * 6)
A(6) = 500 * e^(0.18)
A(6) = 500 * 2.71828^(0.18)
A(6) = 500 * 1.19721
A(6) = 598.60861
So $500 invested 6 years ago at 3% would be worth $598.61 today.
528 a weekend.
10% of 480 is 48
480 + 48 = 528
Answer:
ffhjjrhjzxuzdjzdjzsjezjdifi
Integration by Parts Evaluate e-2x cos(2x) dx.
Let
[tex]I = \displaystyle \int e^{-2x} \cos(2x) \, dx[/]tex
Integrate by parts:
[tex]\displaystyle \int u \, dv = uv - \int v \, du[/tex]
with
[tex]u = e^{-2x} \implies du = -2 e^{-2x} \, dx \\\\ dv = \cos(2x) \, dx \implies v = \dfrac12 \sin(2x)[/tex]
Then
[tex]\displaystyle I = \frac12 e^{-2x} \sin(2x) + \int e^{-2x} \sin(2x) \, dx + C[/tex]
Integrate by parts again, this time with
[tex]u = e^{-2x} \implies du = -2 e^{-2x} \, dx \\\\ dv = \sin(2x) \, dx \implies v = -\dfrac12 \cos(2x)[/tex]
so that
[tex]\displaystyle I = \frac12 e^{-2x} \sin(2x) - \frac12 e^{-2x} \cos(2x) - \int e^{-2x} \cos(2x) \, dx + C\\\\ \implies I = \frac{\sin(2x)-\cos(2x)}{2e^{2x}} - I + C \\\\ \implies 2I = \frac{\sin(2x) - \cos(2x)}{2e^{2x}} + C \\\\ \implies I = \boxed{\frac{\sin(2x) - \cos(2x)}{4e^{2x}} + C}[/tex]
Dr. Hick writes an order for Amoxicillian 300 mg by mouth daily. Pharmacy dispenses 200 mg/2 mL. How many mL per dose?
a. 4
b. 3
c. 2
d. 1
Answer:
b
Step-by-step explanation:
2 ml/200 mg so divide and you get 1 ml per 100 mg then multiply that my 3 to get 3ml/300 mg therefore the answer is b
Answer:
b. 3 ml
Step-by-step explanation:
300 mg / 200 mg/ 2 ml = 300 * 2 / 200 ml = 3 ml
Three fourths of X added to twice of X is more than eleven
On Sunday, a local hamburger shop sold a combined total of 512 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Sunday?
Answer:
512? xd
Step-by-step explanation:
Answer:
128
Step-1by-step explanation:
An easy way of solving these sort of problems is to set up an equation
Since we have a total, that being 512 burgers, we can set an equation equal to that number.
We can say that hamburgers is represented by x. Since we sold 3 times more cheeseburgers than the amount of hamburgers, we can represent this as 3x.
Since these totals are combined, we can represent this via an equation:
512 = x + 3x
Solve for x accordingly, and we are given 128, which is equal to the amount of hamburgers.
How to 24-[5408÷48{×41+701]-240}-240÷16
do in oder of pemdas....
work hours
frequency
0 - <10
45
10 - <20
33
20 - <30
20
30 - <40
7
40 - <50
8
Use your calculator to find the mean and standard deviation
The mean and the standard deviation are 16.15 and 12.03, respectively
How to determine the mean and the standard deviation?The table of values is given as:
Work hours Frequency
0 - <10 45
10 - <20 33
20 - <30 20
30 - <40 7
40 - <50 8
Start by rewriting the table using the midpoint of each class
x f
5 45
15 33
25 20
35 7
45 8
The mean is then calculated as:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
This gives
[tex]\bar x = \frac{5 * 45 + 15 * 33 + 25 * 20 35 * 7 + 45 * 8}{45 + 33 + 20 + 7 + 8}[/tex]
Evaluate the sum and the products
[tex]\bar x = \frac{1825}{113}[/tex]
Divide
[tex]\bar x = 16.15[/tex]
The standard deviation is:
[tex]\sigma =\sqrt{\frac{\sum f(x - \bar x)^2}{\sum f}}[/tex]
This gives
[tex]\sigma= \sqrt{\frac{45 * (5 - 16.15)^2 + 33 * (15 - 16.15)^2 + 20 * (25 - 16.15)^2 + 7 * (35 - 16.15)^2 + 8 * (45 - 16.15)^2 }{45 + 33 + 20 + 7 + 8}}[/tex]
Evaluate the sum and the products
[tex]\sigma= \sqrt{\frac{16350.4425}{113}}[/tex]
Divide
[tex]\sigma= \sqrt{144.694181416}[/tex]
Take the square root
[tex]\sigma= 12.03[/tex]
Hence, the mean and the standard deviation are 16.15 and 12.03, respectively
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what is the first shape
Answer:
The first type of solid shapes to be discovered are known as Platonic solids, which include the cube, the tetrahedron, the octahedron, the dodecahedron, and the icosahedron
Which expression is equivalent to (r^-7)^6?
Answer:
Step-by-step explanation:
Answer:
[tex]\frac{1}{r^4^2}[/tex] (option B)
Step-by-step explanation:
[tex]\left(a^b\right)^c=a^{bc},[/tex]
So, we need to first multiple -7 × 6 (= -42)
our new value is [tex]r^{-42\\}[/tex]
[tex]\:a^{-b}=\frac{1}{a^b}[/tex]
So, we simplify [tex]r^{-42\\}[/tex] to [tex]\frac{1}{r^4^2}[/tex]
