5. A rock is thrown directly upward with an initial velocity of 79 feet per second from a cliff 50 feet above a beach. The height of the rock above the beach (h) after t seconds is given by the equation h = -16t² + 79t + 50. The graph below shows the rock's height as a function of time.
Answers
5. The quadratic function for the height of the rock, h = -16·t² + 79·t + 50, indicates;
a. The height of the rock will be 125 feet above the beach at 1.28 seconds and 3.66 seconds after it is thrown
b. The maximum height reached is about 147.5 feet
The time it takes the rock to reach the maximum height is about 2.47 seconds
What is a quadratic function?
A quadratic function is a function of the form; f(x) = a·x² + b·x + c, where, a, b, and c are numbers, and a ≠ 0.
The initial velocity of the rock = 79 ft/s
Height of the cliff above the beach from which the rock is thrown = 50 feet
The function for the height of the rock above the beach is; h = -16·t² + 79·t + 50
Please find attached the graph of the height of the rock as a function of time, created with MS Excel.
Required; When the height of the rock will be 125 feet above the beach
When the height of the rock is 125 feet, we get;
h = 125 = -16·t² + 79·t + 50
-16·t² + 79·t + 50 - 125 = 0
-16·t² + 79·t - 75 = 0
The value of t obtained using an online tool are;
t = (79 + √(1441))/32 ≈ 3.66 and t = (79 - √(1441))/32 ≈ 1.28
The times at which the height of the rock will be 125 feet above the beach are; 1.28 seconds and 3.66 seconds after the rock is thrown
b. The maximum height of the rock can be obtained from the formula for finding the maximum height of a quadratic equation of the form; f(x) = a·x² + b·x + c, which is;
At the maximum point, x = -b/(2·a)
The function for the height; h = -16·t² + 79·t + 50, indicates that we get;
a = -16, b = 79, and c = 50
Therefore;
The time it takes the rock to reach the maximum height, t(max), is therefore;
t(max) = -79/(2 × (-16)) ≈ 2.47
It takes about 2.47 seconds for the rock to reach the maximum height
The maximum height, h(max) = -16 × 2.46875² + 79×2.46875 + 50 ≈ 147.5
The maximum height reached by the rock is about 147.5 feet
Possible part of the question, obtained from a similar online question, includes;
a. The time it takes the rock to reach a height of 125 feet above the beach
b. The maximum height reached by the rock and the duration it takes the rock to reach the maximum height.
Please find attached the possible graph in the question, created with MS Excel, using the function for the height of the rock.
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Related Questions
Rafael wants to find the slope of the line
Answers
The correct formula for the slope will be:
m = (100 - 50)/(4 - 2) = 50/2 = 25 . Rafael took the reciprocal of the values.
Explain about the slope of the line?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. Δy and Δx are the net changes in the y and x coordinates, respectively.
So,
m = Δy / Δx
Using the slope-intercept form, as illustrated below, we can quickly get the slope for just a given line:
Y = mx + c can be used to represent a line.
where the slope's numerical value is m, the x-coefficient.A line's slope and steepness are both referred to as its slope.For the stated question:
The slope calculated by Rachel is:
m = (4 - 2) / (100 - 50) = 2/50 = 1/25
Which is incorrect .
Thus, the correct formula for the slope will be:
m = (100 - 50)/(4 - 2) = 50/2 = 25
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Suppose you roll two number cubes and find the probability distribution for the sum of the numbers. Which two sums have the same probability distribution and would be represented with equal bars on a bar graph? 4 and 11 2 and 12 5 and 10 6 and 9
Answers
The sum of two dice has a total of 36 possible outcomes. The sum can range from 2 (rolling a 1 on each die) to 12 (rolling a 6 on each die).
To find the probability distribution, we can make a table that lists all the possible sums, the number of ways to obtain each sum, and the corresponding probability.
Sum Ways to obtain Probability
2 1 1/36
3 2 2/36 = 1/18
4 3 3/36 = 1/12
5 4 4/36 = 1/9
6 5 5/36
7 6 6/36 = 1/6
8 5 5/36
9 4 4/36 = 1/9
10 3 3/36 = 1/12
11 2 2/36 = 1/18
12 1 1/36
From the table, we can see that the sums 6 and 9 have the same probability distribution, and would be represented with equal bars on a bar graph
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6 In the diagram below, BPCR is a rhombus. P is (0, 6), C is (6, t) and B is (2, 0). The lines PR. and BC bisect at Q, PR = 2BC and PR = 8√2. Find: (a) the value of t and the coordinates of R, (b) the equation of PR, (c) the area of the rhombus.
Answers
The value of t is equal to 4.
The equation of PR is y = -x + 6.
The area of the rhombus is equal to 32 square units.
How to determine the value of t and the coordinates of R?Since BPCR is a rhombus and all the side lengths of a rhombus are always equal in length, we would use the distance formula to determine the length of BP as follows:
Distance BP = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance BP = √[(0 - 2)² + (6 - 0)²]
Distance BP = √[4 + 36]
Distance BP = √40 units.
Also, side length BP is equal to side length PC:
√40 = √[(t - 6)² + (6 - 0)²]
√40 = √[(t - 6)² + 36]
40 = (t - 6)² + 36
(t - 6)² = 4
t - 6 = ±2
t = 6 ± 2
t = 8 or t = 4.
Therefore, C should be located at (6, 4).
Since Q is the midpoint PR and BC, we know that B is shifted 2 units right and 6 units down from P. Therefore, point R is represented by R(8, -2).
In order to determine the equation of PR, we would use the point-slope form:
[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y - 6 = \frac{(-2-6)}{(8 - 0)}(x - 0)[/tex]
y - 6 = -1(x)
y = -x + 6
In Mathematics, the area of a rhombus is calculated by using this formula:
Area = 1/2(d₁ × d₂)
Where:
d₁ and d₂ represent the diagonals of a rhombus.
PR = 2BC
8√2 = 2BC
BC = (8√2)/2
BC = 4√2
Area of rhombus = 1/2(PR × BC)
Area of rhombus = 1/2(8√2 × 4√2)
Area of rhombus = 1/2(64)
Area of rhombus = 32 square units.
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(CLASSKICK) HELP ASAP!!!
Answers
Answer:
94.3
Step-by-step explanation:
You want to know how to fill in the proportion associated with the question, "What is 115% of 82?"
ProportionThe diagram is intended to help you match parts of the question to parts of the proportion. The attachment shows the intended relation.
The solution is found by multiplying both sides by 82:
(x/82)·82 = (115/100)·82
x = 94.3
EquationThe question can also be written as a statement:
"what" is 115% of 82
When written as an equation, "is" means "equals", and "of" means "times":
what = 115% × 82
Of course, you can use any variable name of your choosing in place of "what". In your diagram, that is "x". And, you know how to write a percentage as a fraction or decimal, so this becomes ...
x = 115/100 × 82 = 1.15 × 82
All that remains is to evaluate this expression.
x = 1.15 × 82 = 94.3
So, the answer to the question is ...
94.3 is 115% of 82.
PLEASE HELP ASAP THANK YOU
On Tuesday, a local hamburger shop sold a combined total of 408
hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Tuesday?
Answers
The number of hamburger sold on Tuesday is 136.
How to find the number of hamburgers sold on Tuesday?On Tuesday, a local hamburger shop sold a combined total of 408
hamburgers and cheeseburgers. The number of cheeseburgers sold was
two times the number of hamburgers sold.
Therefore, the number of hamburger sold on Tuesday can be calculated as follows:
Let
x = number of hamburger
y =number of cheeseburger
Therefore,
x + y = 408
2x = y
x + 2x = 408
3x = 408
divide both sides by 3
x = 408 / 3
x = 136
Therefore,
number of hamburger = 136
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Jake is traveling 12 mph in his boat. After 3 hours, how far will he have traveled?
Answers
Answer:
36 miles
Step-by-step explanation:
speed = distance/time
distance = speed × time
distance = 12 miles/hour × 3 hours
distance = 36 miles
you draw two marbles without replacement from a bag containing 3 green marbles and 4 black marbles the number of possible outcomes in the sample spaces
Answers
The sοlutiοn οf the given prοblem οf unitary methοd cοmes οut tο be there are 21 pοtential οutcοmes in the sample space.
What is an unitary methοd?One may use this cοmmοn cοnvenience, already-existing variables, οr all impοrtant elements frοm the οriginal Bishοp custοmizable questiοn that adhered tο a particular methοd tο achieve the gοal. If sο, there will be anοther chance tο get in tοuch with the οbject. If it dοesn't, all οf the crucial elements that make up an expressiοn prοοf οutcοme will be lοst.
Here,
Using the fοrmula fοr the number οf cοmbinatiοns, we can determine hοw many pοssibilities are pοssible in the sample space:
=> nCk = n!/(k!*(n-k))!
where k is the number οf οbjects being selected, and n denοtes the οverall number οf οbjects in the set.
As there are 7 marbles in the cοntainer, we want tο select 2 οf them, sο n = 7 and k = 2.
the sample space has the fοllοwing amοunt οf οutcοmes that cοuld οccur:
=> 7C2 = 7! / (2! * (7-2)!)
=> 21
Therefοre, when twο marbles are drawn frοm the given bag withοut a replacement, there are 21 pοtential οutcοmes in the sample space.
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Complete Question:
'You draw two marbles without replacement from bag containing three green marbles and four black marbles_ The number of possible outcomes in the sample space is'
A golf course rents golf clubs for $10 plus $4 for each hour the golf clubs are rented. An expression for the total cost of renting the golf clubs for h hours is 10 + 4h.
Complete the table by finding the total cost of renting the golf clubs for h hours.
Answers
To complete the table, we can use the expression 10 + 4h to calculate the total cost of renting the golf clubs for different values of h.
Table below:h Total cost
1 14
2 18
3 22
4 26
5 30
For example, if the golf clubs are rented for 1 hour, the total cost is $14 (10 + 4(1) = 14). If they are rented for 2 hours, the total cost is $18 (10 + 4(2) = 18), and so on.
What is the expression for the total cost of renting golf clubs for h hours at a golf course that charges $10 plus $4 for each hour rented?The expression for the total cost of renting golf clubs for h hours at a golf course that charges $10 plus $4 for each hour rented is 10 + 4h.
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please helpp!!! A sum of money was shared among three children John, Bob and Henry in the ratio 3:2:1 respectively. If Bob's share was $1 000, how much was John's share?
Answers
$1500
Step-by-step explanation:
if $1000 is equal to 2 parts then .....1 part is given by 1000÷2 =500
so John's share is given by 3x500
1500
The width of a rectangle is 2 units less than the length. The area of the rectangle is 24 square units. What is the length, in units, of the rectangle?
Answers
The width of a rectangle is 2 units less than the length. The area of the rectangle is 24 square units. The length of the rectangle is 6 units.
Let's denote the length of the rectangle as L and the width as W. According to the given information, the width is 2 units less than the length, so we can express this relationship as:
W = L - 2
The formula for the area of a rectangle is A = L * W, and in this case, the area is given as 24 square units. Substituting the values, we have:
24 = L * (L - 2)
Expanding the equation, we get:
24 = L^2 - 2L
Rearranging the equation and setting it equal to zero, we have:
L^2 - 2L - 24 = 0
We can now factor the quadratic equation:
(L - 6)(L + 4) = 0
Setting each factor equal to zero, we have two possible solutions:
L - 6 = 0 or L + 4 = 0
Solving each equation, we find:
L = 6 or L = -4
Since the length cannot be negative, the length of the rectangle is 6 units.
The length of the rectangle is 6 units.
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Calculate the area of the trapezoid, which is not drawn to scale.
Answers
Answer:
38 in²
Step-by-step explanation:
We can solve for the area of this trapezoid by using the area formula:
[tex]A = \dfrac{b_1 + b_2}{2} \cdot h[/tex]
First, we need to identify the trapezoid's bases ([tex]b_1[/tex] and [tex]b_2[/tex]). We know that the bases of a trapezoid are parallel. Using this information, we can identify 8 in and 11 in as the bases.
Next, we need to identify the height ([tex]h[/tex]). We know that the height of a trapezoid is the length from [tex]b_1[/tex] and [tex]b_2[/tex] that is perpendicular (at a right angle) to both of the bases. We can identify this as 4 in because we can see that it adjoins at a right angle to both of them.
Finally, we can plug these values into the area formula and solve for A.
[tex]A = \dfrac{8 + 11}{2} \cdot 4[/tex]
[tex]A = \dfrac{19}{2} \cdot 4[/tex]
[tex]A = \dfrac{76}{2}[/tex]
[tex]\boxed{A = 38 \text{ in}^2}[/tex]
please help im begging you!
Part C
Now you will attempt to copy your original triangle using only two of its sides and the included angle:
Using point E as the center, draw a circle with a radius equal to the length of
, which you calculated in part B.
Using point E as the vertex and
as one side of the angle, create an angle that is equal to the measure of
. Draw ray
.
Locate the intersection of the ray and the circle, and label the point F.
Complete
by drawing a polygon through points D, E, and F.
Take a screenshot of your results, save it, and insert the image below.
Answers
Below given are the steps to copy the original triangle using only two of its sides and the included angle.
What is triangle?It is a fundamental geometric shape in mathematics and has many applications in science, engineering, and everyday life. They can be classified based on the lengths of their sides and the measures of their angles.
Using point E as the center, draw a circle with a radius equal to the length of n×CA that was calculated in part B.
Using point E as the vertex, draw a ray DE in the direction of one of the sides of the angle to be copied (in this case, ∠BCA).
Create an angle at point E that is equal to the measure of ∠BCA. To do this, place the point of a compass at point E and adjust the compass to the length of segment CA. Then, draw an arc that intersects both sides of the ray DE. Without changing the width of the compass, place the compass at point C and draw an arc that intersects the previous arc. Draw a line connecting point E to the intersection of the two arcs to create an angle that is equal to ∠BCA.
Draw ray ED' from point E through the intersection of the two arcs.
Locate the intersection of ray ED' and the circle drawn in step 1. Label this point F.
Draw a polygon through points D, E, and F to complete the copied triangle, which is ΔDEF.
The resulting triangle ΔDEF will be a copy of the original triangle, with side EF corresponding to the included angle and sides DE and DF corresponding to the sides used to construct the copy.
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3x=42 round to the nearest hundredth
Answers
Answer:
42 /3 = x
Step-by-step explanation:
it is 14 for sure.....
Simplify each expression to a single term: 5.5.1 cos² 19⁰-sin² 19° = 5.5.2 cos² 19° + sin² 19⁰ = 5.5.3 2 cos² 50° -1 =.... 5.5.4 1-2 sin² 50° = ........ 5.5.5 6cos² 2 -3= orpress cos169
Answers
Answer:
Step-by-step explanation:
5.5.1 cos² 19⁰ - sin² 19° = cos² 19° - (1 - cos² 19°) = 2cos² 19° - 1
5.5.2 cos² 19° + sin² 19⁰ = 1
5.5.3 2 cos² 50° -1 = cos 100° - 1
5.5.4 1-2 sin² 50° = cos² 50°
5.5.5 6cos² 2 -3 = 6cos²(180°-11°) -3 = 6cos²11° -3 = 6cos²(360°-349°) -3 = 6cos²349° - 3
Note: cos(360°-x) = cos x and cos(180°-x) = -cos x, so we can write cos169° = cos(180°-11°) = -cos11°.
Based on her past experiences, a homeowner estimates that appliances lose 27% of their
resale value each year. If her estimate is accurate, how much will an appliance currently
valued at $1,128 be worth in 10 years?
Answers
Step-by-step explanation:
If the LOSE 27% per year, they RETAIN 100- 27 = 73% (.73 in decimal) per year
after ten years :
$ 1128 ( .73)^10 = $48.48
Answer:
$48.48
Step-by-step explanation:
Using compound depreciation
time
amount × percentage^
10
1128 × 0.73^ =48.477
Find the value of an in the parallelogram shown to the right. Note that the figure is not drawn to scale.
59°
(2a+27)°
Answers
The value of a in the given parallelogram such that 2a + 27 and 59 are opposite angles is 16
Finding the value of a in the parallelogramGiven the attached parallelogram
Opposite angles in a parallelogram are equal in measure.
This property is known as the "Opposite Angles Property" or "Alternate Angles Property" of a parallelogram.
So, we have
2a + 27 = 59
Evaluating the like terms, we have
2a = 32
Divide both sides by 2
a = 16
Hence, the value of a is 16
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(Q: 8) find the value of p in this proportion show where below answer here P=
Answers
Answer:16
Step-by-step explanation:
10/p=5/8
can be shown as
1/p=5/80
p=80/5=18
Answer:
[tex]P=16[/tex]
Step-by-step explanation:
Given
[tex]\frac{10}{P} =\frac{5}{8}[/tex]
We can use cross multiplication to find the value of [tex]P[/tex].
Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.
Following these steps we can evaluate [tex]P[/tex].
[tex]10*8=5P[/tex]
Multiply [tex]10[/tex] by [tex]8[/tex].
[tex]80=5P[/tex]
Divide both sides of the equation by [tex]5[/tex]. [tex]P[/tex] cancels out on the right side.
[tex]\frac{80}{5} =\frac{5P}{5}[/tex]
[tex]\frac{80}{5} =P[/tex]
Divide [tex]80[/tex] by [tex]5[/tex].
[tex]16=P[/tex]
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solve for x.
find m∠HJB
you'll get 50 points!!!
Answers
Also, x = -1.5 because you do 22x+88+52-2x=180 and solve the equation
please show your work as well
Answers
By trigonometric functions, the missing sides of the right triangles are:
Case 7: AC = 9.725, BC = 10.071
Case 8: AB = 21.301, BC = 18.807
Case 9: BC = 4.585, AC = 8.999
Case 10: AB = 10.461, BC = 7.774
How to determine the missing sides in right triangles
In this problem we have four cases of right triangles, each of which has a known side and a known angle and we must determine all the missing lengths by trigonometric functions:
sin θ = y / r
cos θ = x / r
tan θ = y / x
Where:
x - Leg adjacent to an angle.y - Leg opposite to an angle.r - Hypotenuse.θ - Angle, in degrees.Now we proceed to determine the values of the missing lengths:
Case 7
AC = 14 · sin 44°
AC = 9.725
BC = 14 · cos 44°
BC = 10.071
Case 8
AB = 10 / cos 62°
AB = 21.301
BC = 10 · tan 62°
BC = 18.807
Case 9
BC = 10.1 · sin 27°
BC = 4.585
AC = 10.1 · cos 27°
AC = 8.999
Case 10
AB = 7 / cos 48°
AB = 10.461
BC = 7 · tan 48°
BC = 7.774
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Using the substitution method to solve the following system .if the equations of the systems are dependent ,or if the system is inconsistent,so indicate.
y = 3x
x + y = 8
Answers
Answer:
[tex]x = 2 , y = 6[/tex]
Step-by-step explanation:
The substitution method suggests that you will "substitute" a portion of one given equation to another in the system of equation:
In this case, substitute 3x for y in the 2nd equation:
[tex]y = 3x\\x + y = 8\\\\x + (3x) = 8[/tex]
Simplify. Combine like terms. Like terms are terms with the same amount of the same variable.
[tex]x + 3x = 8\\4x = 8[/tex]
Next, isolate the variable, x. Divide 4 from both sides of the equation:
[tex]4x = 8\\\frac{4x}{4} = \frac{8}{4} \\x = \frac{8}{4}\\ x = 2[/tex]
Next, plug in 2 for x in one of the equations, and simplify to solve for y:
[tex]y = 3x\\y = 3(2)\\y = 6[/tex]
Check: Plug in 2 for x and 6 for y in the second equation:
[tex]x + y = 8\\(2) + (6) = 8\\8 = 8[/tex](True)
~
[tex]x = 2 , y = 6[/tex] is your answer.
~
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Multiply the complex’s numbers
(7-2i)(1+3i)
Answers
The multiplicatiοn οf the cοmplex number is 13+19i.
What is cοmplex number?Cοmplex numbers are the numbers that are stated in the fοrm οf a+ib where, a,b are real numbers and I is an imaginary number termed "iοta".
Cοmplex numbers allοw sοlutiοns tο all pοlynοmial equatiοns, even thοse that have nο sοlutiοns in real numbers. Mοre precisely, the fundamental theοrem οf algebra asserts that every nοn-cοnstant pοlynοmial equatiοn with real οr cοmplex cοefficients has a sοlutiοn which is a cοmplex number.
Here the given cοmplex number is ,
=> (7-2i)(1+3i)
Nοw simplifying the expression then,
=> [tex]7\times1+7\times3i-2i \times1 -2i \times3i[/tex]
=> 7+21i-2i-[tex]6i^2[/tex]
=> 7+19i -6(-1) [[tex]i^2=1[/tex]]
=> 7+19i+6
=> 13+19i
Hence the multiplication of cοmplex number is 13+19i.
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b. Find the quadratic equation whose roots are aß² and a²ß. If a and b
are the roots
of the quadratic equation x^2- 3x + 2 = 0
Answers
The quadratic equation is; x^2 -6x + 8 = 0
What is a quadratic equation?A quadratic equation is a mathematical equation of the form ax^2 + bx + c = 0, where x is the unknown variable, and a, b, and c are constants (numbers). The exponent of x in the equation is 2, which means it is a second-degree polynomial equation.
We know that the solution of x^2- 3x + 2 = 0 is x = 2 and x = 1 hence;
α = 2, β = 1
We have that;
αβ^2 = 2
α^2β = (2)^2(1) = 4
The equation would now be;
x^2 - (2 + 4)x - (2 * 4) = 0
x^2 -6x + 8 = 0
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I need help please!!!
Answers
The amount that would be in the account after 20 years would be $33,277.48.
The doubling time of the emissions would be 23.45 years
The total emissions will be higher in 2030 than 2010 by 100.96%
How to find the amount after years of investment ?To find the amount in the account after 20 years, we can use the formula:
A(t) = P(1 + r)^t
Take the 12th root of both sides:
(1 + r) = 2^(1/12)
Now find r:
r = 2^(1/12) - 1 ≈ 0.05946
Now we can find the amount in the account after 20 years with the investment of $10,000:
A(20) = 10000(1 + 0.05946)^20
A(20) = $33,277.48
How to find the doubling time ?To find the doubling time for emissions, we can use the formula:
Doubling time = ln(2) / ln(1 + r)
Doubling time = ln(2) / ln(1 + 0.03)
Doubling time = 23.45 years
To find how much higher total emissions will be in 2030 than in 2010, we can use the exponential growth formula:
E(t) = E₀(1 + r)^t
We want to find the ratio of emissions in 2030 to emissions in 2010:
E(20) / E(0) = (1 + 0.03)^20
E(20) / E(0) ≈ 2.0096
Higher emissions = E(20) / E(0) - 1
Higher emissions ≈ 1.0096
So, total emissions will be approximately 100.96% higher in 2030 than in 2010.
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Find the average rate of change of the function on the interval, specified for real number b ???
Answers
[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x)= 6x^2-7 \qquad \begin{cases} x_1=1\\ x_2=b \end{cases}\implies \cfrac{f(b)-f(1)}{b - 1}[/tex]
[tex]\cfrac{[6(b)^2-7]~~ - ~~[6(1)^2-7]}{b-1}\implies \cfrac{6b^2-6}{b-1}\implies \cfrac{6(b^2-1)}{b-1}\implies \cfrac{6(b^2-1^2)}{b-1} \\\\\\ \cfrac{6(b-1)(b+1)}{b-1}\implies 6(b+1)[/tex]
Workout AG in the cuboid below. (3d trig)
Answers
The length of the diagonal AG = 7.56 cm.
Finding diagonal of cuboid:A cuboid is a three-dimensional shape that is bounded by six rectangular faces. It is also known as a rectangular prism. A cuboid has six faces, twelve edges, and eight vertices.
To find the Length of the side AG, find the length of AC by using the Pythagorean formula. Now using the trigonometric ratios formulas find the length of AG.
Here we have a cuboid
Where
AD = 23 cm
DC = 18 cm
∠GAC = 75°
From the right angle triangle, ADC
=> AC² = AD² + DC² [ Using the Pythagorean formula ]
=> AC² = (23)² + (18)²
=> AC² = 529 + 324
=> AC = √853 = 29.20
From the right angle triangle, AGC
=> Cos B = AC/AG
=> Cos 75° = 29.20/AG
=> AG = Cos 75° (29.20)
=> AG = (0.26)(29.20)
=> AG = 7.56
Therefore
The length of the diagonal AG = 7.56 cm.
Learn more about Cuboid at
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A serving of Cereal A contains 4 more grams of carbohydrates than a serving of Cereal B. If you eat a serving of each cereal, you will consume 66 g of carbohydrates. Find the amount of carbohydrates in each cereal.
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Answer:
Let's assume that a serving of Cereal B contains x grams of carbohydrates.
According to the problem, a serving of Cereal A contains 4 more grams of carbohydrates than Cereal B. So, the amount of carbohydrates in Cereal A is (x + 4) grams.
The total amount of carbohydrates consumed from both cereals is 66 grams:
x + (x + 4) = 66
Simplifying the equation:
2x + 4 = 66
Subtracting 4 from both sides:
2x = 62
Dividing by 2:
x = 31
So a serving of Cereal B contains 31 grams of carbohydrates.
And a serving of Cereal A contains 4 more grams:
31 + 4 = 35
Therefore, a serving of Cereal A contains 35 grams of carbohydrates.
Pack of card has 52 cards, how many cards in 36 packs?
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Answer:
1872 cards
Step-by-step explanation:
1 cards=52
36×52
=1872 cards
1. In the Khan academy video, the ratio of boys to girls is 2 : 3. What is the ratio of boys to girls if there are 40 students in the classroom?
Answer: ____
a) 8 : 12 b) 10 : 5 c) 20 : 40 d) 16 : 24
Answers
Answer:
16:24
Step-by-step explanation:
The ratio of boys to girls is 2 : 3
total of the ratio is 5
∴ fraction of the class are boys = 2/5
and the girls= 3/5
Ratio of boys =( 2/5)×40=16
Ratio of girls=3/5 ×40 =24
Which expression is equivalent to 9(2x+5y)
Answers
Answer: 18x + 45y.
Step-by-step explanation:
Expanding the brackets, we get:
9(2x+5y) = 92x + 95y
Simplifying the products, we get:
9(2x+5y) = 18x + 45y
Therefore, the expression equivalent to 9(2x+5y) is 18x + 45y.
Answer:
18x+45y
Step-by-step explanation:
9(2x+5y) = 18x + 45y
Therefore, the expression equivalent to 9(2x+5y) is 18x + 45y.
A bag of 100 marbles contains an equal amount of marbles that are blue, green, red, yellow, and orange. If one marble is pulled at random from the bag, the probability that it is a green marble is
Answers
The probability of pulling a green marble is the number of green marbles (20) divided by the total number of marbles (100):
P(green marble) = 20/100 = 0.2 = 20%
Therefore, the probability of pulling a green marble from the bag is 20%.