The slope of the straight line is 3.
What is slope of a line?
Slope is the measure of steepness. Slope is determined by the tangent of angle a line makes with the x-axis. It is calculated as rise over run. Mathematically for the coordinates (a, b) (c, d) it can be given as [tex]\frac{d-b}{c-a}[/tex].
We are given a table which contains some coordinates of a straight line
We have to find the slope of the line
This can be done as
Slope[tex]=\frac{8-5}{2-1}[/tex]
Slope[tex]=3[/tex]
Hence the slope of the line is 3.
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A rocket is launched straight up with a velocity of 6.11 m/s. How high does the rocket go?
The rocket reaches a maximum height of 1.903 meters.
What is the maximum height reached by a rocket?
Herein we find the case of a rocket being launched at an initial speed and is later decelerated uniformly by gravity. Then, the maximum height reached by the rocket is found by the following formula:
v'² = v² + 2 · a · h
Where:
v - Initial speed, in meters per second.v' - Final speed, in meters per second.a - Acceleration, in meters per square second.h - Maximum height, in meters.If we know that v = 6.11 m / s, v' = 0 m / s and a = - 9.807 m / s², the maximum height of the rocket is:
h = (v'² - v²) / (2 · a)
h = (0² - 6.11²) / [2 · (- 9.807)]
h = 1.903 m
The maximum height reached by the rocket is 1.903 meters.
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help me please
thank you
Answer:
Domain: [-6, 2]
Range: [-4, 0]
Function: Yes
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
A relation is a function if each x value corresponds to only one y-value.
37. A scrapbook is 3 in. longer than it is wide. Find the length and the width if the area is 108in?
Length = 12 in
Width = 9 in
Explanations:Let the length of the scrapbook be represented as L
Let the width of the scrapbook be represented as W
The scrapbook is 3 in longer than its width.
This can be represented mathematically as:
L = W + 3........................(1)
Since the length of the scrapbook is longer than the width, the scrapbook has a rectangular shape.
Area of a Rectangle = Length x Width
Let the area be represented as A
A = L X W........................(2)
The Area is 108 in²
A = 108 in²
Put the value of A into equation (2). The equation becomes:
108 = L X W...................(3)
Substitute equation (1) into equation (3):
108 = (W + 3) x W
108 = W² + 3W
W² + 3W - 108 = 0
W² -9W + 12W - 108 = 0
W(W - 9) + 12(W - 9) = 0
(W + 12)(W - 9) = 0
W + 12 = 0
W = -12
W - 9 = 0
W = 9
Since the width of a scrapbook cannot be negative, we will choose W = 9 in
Substitute the value of W (i.e. W = 9) into equation (1)
L = W + 3
L = 9 + 3
L = 12
Therefore, the length of the scrapbook is 12 in and the width is 9 in
What is the slope of the line passing through the points (-1, 7) and (4, - 1)?
Answer:
− 8/5
Step-by-step explanation:
How to get 16 using numbers 6, 9, 2, 2
(can be -16 or 16)
The expression that gives a solution of 16 using the numbers is 6 + 9 + 2/2
How to get a solution of 16?From the question, we have the following parameters that can be used in our computation:
Solution = 16
Numbers to use = 6, 9, 2, 2
There are no straight ways to solve this question
So, we make use of the trial-by-error
This trial-by-error method would be done mostly off this worksheet
After several trials, we have the following expression
6 + 9 + 2/2
When the above equation is solved, we have
6 + 9 + 2/2 = 16
Hence, to get a solution of 16 we can use the equation 6 + 9 + 2/2
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The histogram below shows the number of children per student in one section of MAT110 during the spring semester of 2015. (*If you can't see the histogram below, click on the attached pdf to view.) MAT 110-002 students, Spring 2015 12. 10 Frequency 2 O 2 3 Number of children
mean = (12 + 4 + 3 + 2 + 0 + 1)/6 = 3.6666
Please help urgent 30 points
Answer:
1. How do we transform System A into System B
Answer is First choice with -3 filled in box
-3 x Equation [A1] ⇒ Equation [B1] (first choice; fill in -3)
2. How do we transform System B into System A
answer is the Last choice with 5 filled in the box
5 x Equation [B2] + Equation [B1] => Equation [C1]
In the last choice fill in 5 in the box
Step-by-step explanation:
-3 x [A1] => -3 (-9x - 5y = -2)
=> - 3(-9x) -3(-5y) = 3(-2)
=> 27x + 15y = 6 which is B1
5 x [B2]
=> 5(-4x - 3y) = 5(3)
=> -20x -15y = 15
5 x [B2] + B1
=>
-20x -15y = 15
+
27x + 15y = 6
----------------------
7x + 0 = 21
or 7x = 21 which is C1
Step-by-step explanation:
system A to system B :
-3 × equation A1 -> equation B1
5 × equation B2 + equation B1 = equation C1
What is the area of this regular octagon that has been divided into eight congruent triangles?A)90 cm2B)360 cm2C)45 cm2D)180 cm2
Given:
One octagon is given
Required:
To calculate the area of regular octagon
Explanation:
Since we have been divided regular octagon into eight congruent triangles
so firstly we calculate area of triangle with base 5 cm and height 9 cm and then gonna multiply this 8 times to calculate the total area
In the first step we are calculating the area of triangle
there are 14 boy and 16 girls in Mr. Allen's class. What is the ratio of girls to the total numbers of students in the class? Write the ratio in 3 ways
Answer:
16/30, 8/15, 24/45
Answer:
8:15
8/15
8 to 15
Step-by-step explanation:
Express with radical signs instead of fractional exponents. Rationalize the dominator.
Given:
[tex]3^{-\frac{1}{2}}.x^{\frac{1}{2}}[/tex]To find:
Express with radical signs instead of fractional exponents. also, rationalize the denominator.
Explanation:
The radical sign is a symbol used to indicate a root, i.e.,
[tex]\sqrt[n]{x}[/tex]For our given expression, we can write it using the radical sign as given below:
[tex]\begin{gathered} \frac{x^{\frac{1}{2}}}{3^{\frac{1}{2}}} \\ \Rightarrow\frac{\sqrt{x}}{\sqrt{3}} \end{gathered}[/tex]Now, to rationalize, the following form can be used,
[tex]\frac{\sqrt{a}}{\sqrt{b}}=\frac{\sqrt{a}}{\sqrt{b}}(\frac{\sqrt{b}}{\sqrt{b}})=\frac{\sqrt{ab}}{b}[/tex]So, we can also rewrite our expression to rationalize the denominator,
[tex]\frac{\sqrt{x}}{\sqrt{3}}=\frac{\sqrt{x}}{\sqrt{3}}\times(\frac{\sqrt{3}}{\sqrt{3}})=\frac{\sqrt{3x}}{3}[/tex]Final answer:
The required expression with radical signs and simplified form is as given below:
[tex]\frac{\sqrt{3x}}{3}[/tex]Large drinks cost $2.75 each and medium drinks cost $2.15 each. A restaurant sold 52 drinks yesterday and took in a total of $131.60. How many medium drinks did they sell? Show work
Given:
Large drink cost $ 2.75.
Let x be the number of large drinks.
Let y be the number of medium drinks and it cost $2.15 each.
A restaurant sold 52 drinks yesterday and took in a total of $131.60.
The equations are,
[tex]\begin{gathered} x+y=52\ldots\ldots\ldots.....\ldots\ldots\ldots.....(1) \\ 2.75x+2.15y=131.60\ldots.\ldots..\ldots\ldots\ldots\text{.}(2) \end{gathered}[/tex]Solve the equations,
From equation 1)
[tex]\begin{gathered} x+y=52 \\ x=52-y \\ \text{Put it in equation 2)} \\ 2.75(52-y)+2.15y=131.60 \\ 143-2.75y+2.15y=131.60 \\ 143-131.60=0.6y \\ 11.4=0.6y \\ y=\frac{11.4}{0.6} \\ y=19 \end{gathered}[/tex]Put the value of y in equation 1)
[tex]\begin{gathered} x+y=52 \\ x+19=52 \\ x=52-19 \\ x=33 \end{gathered}[/tex]Answer: The number of medium drink sells are y = 19.
grade 12 calculus please help with question 3. i) ?image attached much appreciated
We have a height function
[tex]h(t)=-16t²+96t+112[/tex]Now, to find the average rate of change the height function on [1,3] seconds we have the following
[tex]A_{\lbrack1,3\rbrack}=\frac{h(3)-h(1)}{3-1}=\frac{-16(3)^2+96(3)+112-(-16(1)^2+96(1)+112)}{3-1}=\frac{-16(-8)+96(2)}{2}[/tex]Then the average rate on [1,3] is given by
[tex]A_{\lbrack1,3\rbrack}=\frac{320}{2}=160[/tex]Then the average rate of change of the height function on the interval from 1 to 3 seconds is 160 meters
Factor the following expression completely:
y² + 6y − 40 =
Answer:
(y+10)(y-4)
Step-by-step explanation:
-40y^2
/ \
10y -4y
I need help with number 17 pls I need the equation plssimplify
-2
Explanation:[tex]17)\text{ }\frac{-4\text{ + 2i}}{2\text{ - i}}[/tex]To simplify, we will use the conjugate of the denominator
conjugae of 2 - 1 = 2 + i
Multiply the conjugate of the denominator to the numerator and denominator:
[tex]\begin{gathered} \frac{-4\text{ + 2i}}{2\text{ - i}}\text{ }\times\frac{2+i}{2\text{ + i}} \\ =\text{ }\frac{(-4+2i)(2+i)}{(2-i)(2+i)} \\ \text{Expand:} \\ =\text{ }\frac{-4(2+i)+2i(2+i)}{(2-i)(2+i)} \end{gathered}[/tex][tex]\begin{gathered} =\text{ }\frac{-8-4i+4i+2i^2}{(2-i)(2+i)} \\ \\ \text{expand the denominator:} \\ =\text{ }\frac{-8-4i+4i+2i^2}{2(2+i)-i(2+i)} \\ =\text{ }\frac{-8-4i+4i+2i^2}{4+2i-2i-i^2} \end{gathered}[/tex][tex]\begin{gathered} In\text{ complex number, } \\ i^2\text{ = -1} \\ \text{substitute for i}^2 \\ =\text{ }\frac{-8-4i+4i+2i^2}{4+2i-2i-i^2}\text{ = }=\text{ }\frac{-8-4i+4i+2(-1)}{4+2i-2i-(-1)} \\ =\text{ }\frac{-8+0+2(-1)}{4+0-(-1)}\text{ = }\frac{-8-2}{4+1}\text{ } \\ =\text{ }\frac{-10}{5} \\ =\text{ -2} \end{gathered}[/tex]The simplified answer is -2
Find the value of x which optimises the total surface area of the box, and showthat it minimises the total surface area.
Solution:
Given data:
Let the width of the box be
[tex]=x[/tex]The volume of the box is
[tex]V_{\text{box}}=400\operatorname{cm}[/tex]The height of the box is
[tex]=h[/tex]Let the length of the box be
[tex]=l[/tex]The length is four times the width of the base, this can be represented below as
[tex]\begin{gathered} l=4\times x \\ l=4x\ldots\ldots\ldots\text{.}(1) \end{gathered}[/tex]Part A:
Show that the height h of the box is given by
[tex]\frac{400}{x^2}[/tex]Concept:
To show that the height is given as above, we will use the volume of the box which is given below as
[tex]\begin{gathered} V_{\text{box}}=\text{length}\times width\times height \\ V_{\text{box}}=l\times x\times h \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} V_{\text{box}}=l\times x\times h \\ \text{Substituite equation (1) in the formuka above,} \\ 400=4x\times x\times h \\ 400=4x^2h \\ \text{divide both sides by 4x}^2 \\ \frac{4x^2h}{4x^2}=\frac{400}{4x^2} \\ h=\frac{100}{x^2}(\text{PROVED)} \end{gathered}[/tex]Part B:
Show that the total surface area A of the box is given by
[tex]A=4x^2+\frac{1000}{x}[/tex]Concept:
To prove the above relation, we will use the formula of the area of the box below
[tex]\begin{gathered} A_{\text{box}}=2(lw+lh+wh) \\ \text{where,} \\ l=\text{length}=4x \\ w=\text{width}=x \\ h=\text{height}=\frac{100}{x^2} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} A_{\text{box}}=2(lw+lh+wh) \\ A_{\text{box}}=2(4x\times x+4x\times\frac{100}{x^2}+x\times\frac{100}{x^2}) \end{gathered}[/tex]By simplifying the relation above, we will have
[tex]\begin{gathered} A_{\text{box}}=2(4x\times x+4x\times\frac{100}{x^2}+x\times\frac{100}{x^2}) \\ A_{\text{box}}=2(4x^2+\frac{400}{x}+\frac{100}{x}) \\ A_{\text{box}}=2(4x^2+\frac{500}{x}) \\ A_{\text{box}}=8x^2+\frac{1000}{x} \end{gathered}[/tex]Hence,
The Total surface area of the box will be given below as
[tex]A_{\text{box}}=8x^2+\frac{1000}{x}[/tex]To determine the value of x which optimizes the total surface area of the box, and show
that it minimizes the total surface area, we will have to look for the first derivative of the function above
[tex]\begin{gathered} A_{\text{box}}=8x^2+\frac{1000}{x} \\ \frac{dA}{dx}=\frac{d}{dx}(8x^2+\frac{1000}{x}) \\ \frac{dA}{dx}=16x-\frac{1000}{x^2} \end{gathered}[/tex]To find the value of x, we will substitute the value of dA/dx to be = 0
[tex]\begin{gathered} \frac{dA}{dx}=0 \\ 16x-\frac{1000}{x^2}=0 \\ 16x=\frac{1000}{x^2} \\ \frac{16x^3}{16}=\frac{1000}{16} \\ x^3=62.5 \\ x=\sqrt[3]{62.5} \end{gathered}[/tex]To show the minimum value of x, we will have to look for the second derivative
[tex]\frac{d^2A^{}}{dx^2}[/tex][tex]undefined[/tex]f(x)= 3× g(x)= 3×+2 -4
We can observe that f(x) is a parent function and g(x) is transformation of f(x).
Specifically, the applied transformations are:
• A vertical shift 4 units downside.
,• A horizontal shift of 2 units left side.
The image below shows the functions
As you can observe, the blue function g(x) was shifted two units left and 4 units down.
Additionally, the functions intercept at (-0.631, 0.5).
Every week you buy a lottery ticket in 50 lotteries, in each
of which your chance of winning a prize is 0.01.
(a) Use the Poisson approximation to calculate the probability that you will winat least one prize in a randomly chosen week.
(b) Find the probability that you win at least once in a 4-week period.
(c) Find the probability that it takes exactly 5 weeks to win for the first time.
(a) The probability of winning at least one prize in a randomly chosen week is 0.3935.
(c) The probability that it takes exactly 5 weeks to win for the first time is 0.041.
A lottery ticket is bought every week in 50 lotteries. The chance of winning a prize in each of the lotteries is 0.01.
The Poisson's distribution is given below :
P(X=x) = (e^-λ)(λ^x)/x!
λ = np
λ = 50*0.01 = 0.5
The probability of getting at least one prize is :
P(x≥1) = 1 - P(x<1)
P(x≥1) = 1 - P(x=0)
P(x≥1) = 1 - [(e^-0.5)(0.5^0)/0!]
P(x≥1) = 1 - 0.6065
P(x≥1) = 0.3935
The probability of winning exactly in the fifth week is :
The probability of losing in the first four weeks and winning in the fifth week is :
P = [(e^-0.5)^4]*P(x=1)
P = [(e^-0.5)^4]*(e^-0.5)(0.5)
P = [(e^-0.5)^5]*(0.5)
P = (e^-2.5)*(0.5)
P = 0.041
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A student ran a distance of 3 1/2 miles each day for 5 days. Then the student ran a distance of 4 1/4 miles eah day for the next 5 days. What
was the total distance in miles the student ran during these 10 days?
Answer:
3 1/2 x 5 = 17.5
4 1/2 x 5 = 22.5
17.5 + 22.5 = 40
The student ran 40 miles in those 10 days.
Answer:
38.75 or 38 3/4
Step-by-step explanation:
3 1/2 * 5 = 17.5
4 1/4 * 5 = 21.25
17.5 + 21.25 = 38.75
Find the weighted mean. Round your answer to the nearest tenth. Deliveries Each Week 2 4 6 8 Frequency 3 7 5 2 Weighted mean =
Given:
Deliveries each week: 2 4 6 8
Frequency: 3 7 5 2
Let's use the deliveries each week as the weighting.
We have:
Deliveries x Frequency:
[tex]\begin{gathered} 2\ast3\text{ + 4}\ast7\text{ + 6}\ast5\text{ + 8}\ast2\text{ } \\ =\text{ 6 + 28 + 30 + 16 = 80} \end{gathered}[/tex]Now, add up the number of deliveries each week:
2 + 4 + 6 + 8 = 20
To find the weighted mean, we have:
[tex]\text{Weighted mean = }\frac{80}{20}=\text{ 4}[/tex]Therefore, the weighted mean is 4
ANSWER:
Weighted mean = 4
Which inequality's solution is represented by the graph?A)-2x + 6 5 52B)-2x + 6 2 522x + 6 5 -52D)2x - 6 2 -52
From the graph, the inequality is
x ≤ -23
Multiplying by -2 at both sides we get:
-2x ≥ (-23)*(-2)
-2x ≥ 46
Adding 6 at both sides:
-2x + 6 ≥ 46 + 6
-2x + 6 ≥ 52
My teacher wrote the answer on the side but can you please tell me how he got it
now solve further.
[tex]7.77\text{ \%}[/tex]thus, the answer is 7.77% of 90 is 7.
[tex]\frac{7}{90}\times100=\frac{70}{9}=7.77^{}[/tex]thus, the answer is 7.77% of 90 is 7.
Periodic deposit $8000 at the end of the year Rate 4.5% time 20 years
Using the future value formula, it is found that:
After 20 years you will have approximately $250,971.
What is the future value formula?The future value formula is given by the following equation:
[tex]V(n) = P\left[\frac{(1 + r)^n - 1}{r}\right][/tex]
In which the parameters are given as follows:
P is the payment.n is the number of payments.r is the interest rate.From the information given, the values of the parameters are given by:
P = 8000, r = 0.045, n = 20.
Hence the balance of the account in 20 years is given by:
[tex]V(n) = P\left[\frac{(1 + r)^n - 1}{r}\right][/tex]
[tex]V(20) = 8000\left[\frac{(1 + 0.045)^{20} - 1}{0.045}\right][/tex]
V(20) = $250,971.
Which is the amount you will have.
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How far does jaylen go if he drive 2 hours at 60 mph
Info given
For this problem we know that Jaylen drive for 2 hours at 60 mph
The velocity is v= 60 mi/hr and the time t= 2 hr
Solution
We can use the definition of distance given by:
[tex]d=vt[/tex]And replacing we got:
[tex]d=60\frac{mi}{hr}\cdot2hr=120mi[/tex]And then the answer would be 120 mi
During one day of trading in the stock market,
an investor lost $2500 on one stock, but gained
$1700 on another stock. At the end of trading
that day, the two stocks were worth $52,400.
What were they worth when the market opened
that day?
Using mathematical operations, we know that the cost of the 2 stocks when the market opened was $51,600.
What exactly are mathematical operations?Any mathematical function that transforms zero or more discrete input values into discrete output values is referred to as an operation.The complexity of the operation varies with the number of operands.In the four mathematical operations, numerical inputs are transformed into numerical outputs (i.e., another number).Addition, subtraction, division, and multiplication are these.So, the cost of 2 stocks when the market opened:
The investor lost (-) $2500.Investor gained (+) $1700.At the end of the day, the cost of those 2 stocks was $52,400.
Now, calculate the cost when the market was opened as follows:
52400 - 2500 + 170049,900 + 1700$51,600Therefore, using mathematical operations, we know that the cost of the 2 stocks when the market opened was $51,600.
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Why is 1-1/4 equal to 3/4 And 1-1/3 equal 2/3
SOLUTION
TO SHOW THAT;
[tex]1-\frac{1}{4}=\frac{3}{4}[/tex]Step 1:
[tex]\begin{gathered} \frac{1}{1}-\frac{1}{4} \\ \frac{4-1}{4}=\frac{3}{4} \end{gathered}[/tex]TO SHOW THAT;
[tex]1-\frac{1}{3}=\frac{2}{3}[/tex]Step 2:
[tex]\frac{1}{1}-\frac{1}{3}=\frac{3-1}{3}=\frac{2}{3}[/tex]1. Use the word back to complete the following flow chart proof to show that is ABCD is a parallelogram and ZABEZBAE, then ABCD is a rectangle. Glyen: ABCD is a parallelogram and ZABEZBAE Prove: ABCD is a rectangle Word Bank SE AE Definition of a diagonalsofa ZABEZBAE rectangle parallelogram bisecleach ather Segment Addition ABCD is a ABCD B a rectangle BEE DE 2 CE E AE Postulate paralelogram Note: You can use the answers in the word bank mone than once fif needed) DEBE Transitive Property of Conguence CEAE Given BD EAC Converse Oilsosceles Trange Theorem Given NATION odbor
see the attached image
Please, Do you understand all the steps so far?
The base of a triangle exceeds the height by 3 yards. If the area is 65 square yards, find the length of the base and the height of the triangle.
The length of the base is 13 yards and the height of the triangle is 10 yards.
Let h = ht of the triangle
let (h + 3) = base of triangle
A = (1/2)bh is the formula for the area of a triangle
65 = (1/2) (h + 3)h
130 = [tex]h^2[/tex] + 3h
[tex]h^2[/tex] + 3h - 130 = 0
(h + 13)(h - 10) = 0
h = -13, h = 10
Height = 10 yards, base = 13 yards
What is geometry ?
Geometry is one of the oldest branches of mathematics, along with arithmetic. It concerns the properties of space, like the distance, shape, size and relative position of figures. A mathematician who works in geometry is called a geometer.
Three geometries
History of Euclidean geometry and non-Euclidean geometry. Spherical geometry. Hyperbolic geometry.To learn more geometry, visit;
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A pet store has 6 cats. Here are their weights (in pounds).
12, 9, 9, 12, 16, 6
Find the mean weight of these cats.
If necessary, round your answer to the nearest tenth.
pounds
Answer:
mean ≈ 10.7 pounds
Step-by-step explanation:
mean is calculated as
mean = [tex]\frac{sum}{count}[/tex] = [tex]\frac{12+9+9+12+16+6}{6}[/tex] = [tex]\frac{64}{6}[/tex] ≈ 10.7 pounds ( to the nearest tenth )
Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms
From the given picture, the hypotenuse is 100, then, we get
[tex]\begin{gathered} \sin B=\frac{28}{100} \\ \text{tanB}=\frac{28}{96} \end{gathered}[/tex]Which in simplest form is given by
[tex]\begin{gathered} \sin B=\frac{7}{25} \\ \tan B=\frac{7}{24} \end{gathered}[/tex]The probability of an adult owning a landline telephone is 0.41 and the probability of an adult owning a cell phone
is 0.79. The probability that an adult owns both a landline and a cell phone is 0.27. What is the probability that a person
owns a landline or a cell phone
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.
The probability that a person owns a landline or a cell phone = 0.80
What is probability ?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.The likelihood of an event can also be expressed as a percentage and can only range from 0 to 1. It is common to write P (A) P(A) P(A)P, left parenthesis, and A, right parenthesis, to represent the probability of event A.P( tele phone) = 0.41
P(cell) = 0.79
P(tel phone and cell) = 1-0.41-0.79 = 0.20
P (tele phone only) = 0.41 -0.20 =0.21
P( cell only) = 0.79 - 0.20 = 0.59
P( telephone or cell ) = 0.21+ 0.59 = 0.80
The probability that a person owns a landline or a cell phone = 0.80
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