Answer:
(A)
[tex] - 4.9 {t}^{2} + 43t + 339 = 0[/tex]
[tex]49 {t}^{2} - 430t - 3390 = 0[/tex]
[tex]t = \frac{ - ( - 430) + \sqrt{ {( - 430)}^{2} - 4(49)( - 3390)} }{2(49)} = \frac{430 + \sqrt{849340} }{98} = 13.79[/tex]
The rocket splashes down after 13.79 seconds.
(B) h'(t) = -9.8t + 43 = 0
t = 43/9.8 = 215/49 = 4.39 seconds
h(4.39) = 433.34 meters
At t = 4.39 seconds, the rocket peaks at
433.34 meters above sea level.
Solve for x. Round to the nearest tenth, if necessary.
Answer:
x=38.6
Step-by-step explanation:
x=b/cos(alpha)
x=30/cos(39⁰)
x=38.602
Find the surface area of each composite figure. Use 3.14 for π. Round to the nearest tenth. 12m. 6cm. 6cm. 4cm.
The Surface area of the composite figure is calculated as approximately: 234 sq. cm
How to Find the Surface Area of a Composite Figure?The surface area of the composite figure is the area surrounding the faces of the solid as a whole. Therefore, we have:
Surface area (SA) = Surface area of the square prism + surface area of the square pyramid - 2(area of base)
Area of base = area of square = 6 * 6 = 36 sq. cm.
Surface area of the square prism = 2a² + 4ah
a = 6 cm
h = 4 cm
Plug in the values:
Surface area of the square prism = 2(6²) + 4*6*4
= 72 + 96
= 168 sq. cm.
Surface area of the square pyramid = 2bs + b²
b = side length = 6 cm
s = slant height = √(8² + 3²) = 8.5 cm
Plug in the values:
Surface area of the square pyramid = 2 * 6 * 8.5 + 6² = 138 sq. cm.
Surface area of the composite figure = 168 + 138 - 2(36) = 234 sq. cm
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Can someone help me with this? I can't figure it out
In linear equation, 9 is the constant of variation k.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to be linear equations. axe+b = 0 is a one-variable example in which a and b are real numbers and x is the variable.
given x varies inversely with y then
xy = k ← k is the constant of variation
to find k use the condition x = - 4 when y = - 9, hence
k = -4 × -9 = 36
x = 36/y
when x = 4 , then y = 36/4
x = 9
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Suppose that $2000 is invested at a rate of 4.6%, compounded quarterly. Assuming that no withdrawals are made, find the total amount after 6 years
Do not round any intermediate computations, and round your answer to the nearest cent.
Answer:
$2,631.55
Step-by-step explanation:
To find the total amount in the account after 6 years, we can use the compound interest formula.
Compound Interest Formula[tex]\boxed{\sf A=P\left(1+\dfrac{r}{n}\right)^{nt}}[/tex]
where:
A = Final amount.P = Principal amount.r = Interest rate (in decimal form).n = Number of times interest is applied per year.t = Time (in years).Given values:
P = $2,000r = 4.6% = 0.046n = 4 (quarterly)t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=2000\left(1+\dfrac{0.046}{4}\right)^{4 \cdot 6}[/tex]
[tex]\implies \sf A=2000\left(1+0.0115\right)^{24}[/tex]
[tex]\implies \sf A=2000\left(1.0115\right)^{24}[/tex]
[tex]\implies \sf A=2000\left(1.3157739...\right)[/tex]
[tex]\implies \sf A=2631.54794...[/tex]
Therefore, the total amount after 6 years is $2,631.55 rounded to the nearest cent.
A catering service offers 5 appetizers, 11 main courses, and 4 desserts. A customer is to select 4 appetizers, 9 main courses, and 3 desserts for a banquet. In how many ways can this be done?
There are 1100 many ways can be done that is when catering service offers 5 appetizers, 11 main courses, and 4 desserts.
Given that,
A catering service offers 5 appetizers, 11 main courses, and 4 desserts. A customer is to select 4 appetizers, 9 main courses, and 3 desserts for a banquet.
We have to find how many ways can this be done.
We know that,
Number of appetizers offered = 5
Number of appetizers customer is to select = 4
Number of main courses offered = 11
Number of main courses customer is to select = 9
Number of desserts offered = 4
Number of desserts the customer is to select = 3
So,
To determine the number of ways this can be selected,
By using the combination formula that is
[tex]^nC_r = \frac{n!}{r!(n-r)!}[/tex]
[tex]^nC_r = ^5C_4\times ^{11}C_9\times^4C_3[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!(5-4)!} \times \frac{11!}{9!(11-9)!}\times \frac{4!}{3!(4-3)!}[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!1!} \times \frac{11!}{9!2!}\times \frac{4!}{3!1!}[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!} \times \frac{11!}{9!(2)}\times \frac{4!}{3!}[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 =[/tex] 5 × 11 × 5 × 4
[tex]^5C_4\times ^{11}C_9\times^4C_3 =[/tex] 1100
Therefore, There are 1100 many ways this can be done.
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Find mJKM
J= 3x
L=64
JKM=(5x+4)
The measure of angle JKM is 26°
What is exterior angle theorem?The exterior angle theorem states that the exterior angle of a triangle is equal to the sum of the opposite angles in the triangle.
Also the sum of angle in a triangle is 180°
Therefore ;
3x+64 = 5x+4
collecting like terms
5x -3x = 64-4
2x = 60
x = 60/2
x = 30
since x = 30
value of the exterior angle = 5x+4
= 5×30+4
= 150+4 = 154
therefore angle JKM = 180-( 154)
= 26°
Therefore the measure of angle JKM is 26°
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A glass jug can hold (p+6) quarts less water than a plastic container. 2 glass jugs and 2 plastic containers contain 6p quarts of water in all.
How much water can the plastic container hold? Give your answer im terms of p.
The amount of water that the plastic container can hold is -p + 3.
How to determine the amount of water that can be heldTo determine the amount of water that can be held, we will first assume that the container can hold x quantity of water.
So, the glass jug can hold:
p + 6 - x
2 glass jugs and 2 plastic containers can hold 6p quarts of water.
= 2(p + 6 - x) - 2x = 6p
2p + 12 - 2x -2x = 6p
2p + 12 -4x = 6p
12 - 4x = 6p - 2p
-4x = 6p -2p - 12
-4x = 4p -12
x = 4p - 12/-4
x = -p - 3
or -p + 3
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McKenzie painted a yellow rectangle that measured 8 1/2 in. wide and 11 in. long for part of a mural she was working on. She also painted a
purple rectangle that was 1/4 the size of the yellow rectangle. What is the area of the purple rectangle that McKenzie painted?
Answer:
23.375 in^2
Step-by-step explanation:
To find the area of a rectangle or square, you need to multiple the length by the width.
The length: 8.5
Width: 11
8.5*11 = 93.5
Now we divide by 4
93.5/4
23.375
A sample of a radioactive substance has an initial mass of 45.1 mg. This substance follows a continuous exponential decay model and has a half-life of 19
minutes.
(a)let t be the time (in minutes) since the start of the experiment, and
let y be the amount of the substance at time t.
Write a formula relating y to t.
Use exact expressions to fill in the missing parts of the formula.
Do not use approximations.
y = ()e^()t
(b) How much will be present in 9 minutes?
Do not round any intermediate computations, and round your
answer to the nearest tenth.
a) The formula relating y to t is: y = 45.1 * e^(-0.693/19 * t) b) there will be approximately 30.1 mg of the substance present after 9 minutes.
How to Write a formula relating y to t.(a) The general formula for exponential decay is y = y0 * e^(-kt), where y is the amount at time t, y0 is the initial amount, k is the decay constant, and e is Euler's number.
To find the decay constant, we can use the fact that the half-life is 19 minutes. The formula for half-life is t1/2 = ln(2) / k, where ln(2) is the natural logarithm of 2.
Substituting t1/2 = 19 and ln(2) = 0.693 into the formula gives:
19 = 0.693 / k
k = 0.693 / 19
So the formula relating y to t is:
y = 45.1 * e^(-0.693/19 * t)
(b) To find how much will be present in 9 minutes, we can plug t = 9 into the formula we found in part (a):
y = 45.1 * e^(-0.693/19 * 9) ≈ 30.1 mg
So, there will be approximately 30.1 mg of the substance present after 9 minutes.
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a2=25 i cant find the ancer to thiss
The value of the variable a in the equation is 5 from the calculation here.
How to determine the value?We need to square of a number is described as a number that when multiplied by itself give the original number.
Also, index forms are described as those mathematical forms that are used to represent numbers that are too large or small.
From the information given, we have the equation;[tex]a^2[/tex]=25
find the square root of value of 25,
We have;25 = [tex]5^2[/tex]
Substitute the value, we get;[tex]a^2[/tex] = [tex]5^2[/tex]
Take out the similar factor, this is their exponents.
We then have;
a = 5
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Complete question;
Find the value of a in the equation;a² = 25
Explain how you know what a fraction was multiplied by when the product is greater than a factor.
When the product of a fraction and a factor is greater than the factor, it means that the fraction is greater than 1.
Why is this true of fractions ?Due to the principles of multiplication, when multiplying a value greater than 1 with a given amount, the product will be larger than the original number. To provide an example, if we multiply 5 by 2, the result will be 10, which is greater than 5.
By extension, if we multiply a fraction with a factor that's greater than 1, the resulting product will be greater in size as compared to the initial quantity. For instance, when we calculate 1/2 multiplied by 3, the outcome is 3/2, which surpasses the worth of 1/2. Hence, it can be deduced that any result which exceeds its own source was obtained through multiplication by value greater than 1.
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solve the rational equation 2/x-2+3/x-4=1/x^2=6x+8
the solution to the original rational equation is: [tex]x = 4.678[/tex] (rounded to three decimal places)
What is the rational equation?A rational number is a number that can be expressed as a ratio of two integers, where the denominator is not zero. In other words, it is a number that can be written in the form of a/b, where a and b are integers and b is not equal to zero
According to InformationThere are two equal signs in the equation, which is incorrect. Assuming you meant to write:
[tex]2/(x-2) + 3/(x-4) = 1/(x^2 + 6x + 8)[/tex]
We can start by finding a common denominator for the left-hand side of the equation:
[tex]2/(x-2) + 3/(x-4) = 1/[(x+2)(x+4)][/tex]
Multiplying both sides of the equation by (x-2)(x-4)(x+2)(x+4), we get:
[tex]2(x-4)(x+2)(x+4) + 3(x-2)(x+2)(x+4) = (x-2)(x-4)[/tex]
Expanding and simplifying, we get:
[tex]5x^3 - 19x^2 - 39x + 56 = 0[/tex]
This polynomial equation does not factor nicely, so we can use the rational root theorem or numerical methods to find approximate solutions. Using a calculator or computer, we find that there is one real solution to the equation:
[tex]x \approx 4.678[/tex]
Therefore, the solution to the original rational equation is:
[tex]x = 4.678[/tex] (rounded to three decimal places)
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prove that:
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1)
The given identity (P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1) is proven below
How to prove the given identityGiven the following equation
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1)
We start by simplifying the left-hand side of the equation:
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)= [(P²+1)/(P(P-1))] + [(P²+1)/(P(P+1))] - [(P²-1)/((P+2)P)] - [(P²+1)/((P-2)P)]
Next, we have the following steps to simplify the expression
= [(P³ + P² + P + 1)/(P(P²-1))] - [(P³ - 3P)/(P(P²-4))]
= [(P³ + P² + P + 1)(P²-4) - (P³ - 3P)(P²-1)]/[(P(P²-1))(P(P²-4))]
= [(P⁵ - 3P³ + P³ - 3P² + P² - 4P + P² - 4P - 4 + P³ - 3P)/(P⁴ - 5P² + 4)]
= [P⁵ - 2P³ - 6P² - 8P - 4]/[(P²-4)(P²-1)]
= -4(2p² + 1)/(p²-4) (p² - 1)
Hence, the given identity is proven.
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How many different ways are there to arrange the letters in the word MISSISSIPPI?
Answer: 34,650 permutations
Which of the following is the graph of the quadratic function y = x² - 4x+4?
A. Graph C
B. Graph B
C. Graph D
D. Graph A
Answer:
The correct answer is C, Graph D.
x^2 - 4x + 4 = (x - 2)^2.
help!!!
in the fridge below, m WXZ =72, abs m 1 is 6 degrees more than m 2. find m2
Step-by-step explanation:
m ∠WXY = 72°
m ∠ 1 = m ∠ 2 + 6°
m ∠WXY = m ∠ 1 + m ∠ 2
72° = (m ∠ 2 + 6°) + m ∠ 2
72° = 2 × (m ∠ 2) + 6°
2 (m ∠ 2) = 72° - 6°
2 (m ∠ 2) = 66°
(m ∠ 2) = 33°
#CMIIWOn a scale drawing of a soccer field, 0.5 cm equals 8 m.
If the drawing has dimensions 6.5 cm X 3.25 cm, what is the actual length of the soccer field, in meters?
[tex]\sf Length\, of\,the\,field=\boxed{\sf 104(m)}}.[/tex]
Step-by-step explanation:1. Create a conversion factor.A conversion factor is just a fraction that contains an equivalence. We make the numerator be the unit we want to have as a result and the denominator is the current unit that we have.
The problem states that 0.5 cm equals 8 m, and we want to convert from cm to m, therefore, a conversion factor for this problem is:
[tex]\sf \dfrac{8(m)}{0.5(cm)}[/tex]
2. Use the conversion factor to convert each unit,To use the conversion factor, just multiply each measure by the fraction:
[tex]\sf 6.5(cm) \dfrac{8(m)}{0.5(cm)}[/tex]
Here the centimeters (cm) cancel out each other and the ending answer is expressed in meters:
[tex]\sf 6.5(cm) \dfrac{8(m)}{0.5(cm)}=\boxed{\sf 104(m)}.[/tex]
For the other measure:
[tex]\sf 3.25(cm) \dfrac{8(m)}{0.5(cm)}=\boxed{\sf 52(m)}.[/tex]
So a soccer field, as you may already know, is always longer than it is wide, therefore, the greatest measure (104m) should be the length of the field.
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I deposited #300.00 in a bank for
four years. If it earned simple
interest at the rate of 6% per annum,
how much interest did I get for the
four years?
Answer:
Simple interest= PRT/100
parameters
price =300
Rate=6%
Time=4years
300*6*4/100
7200/100
=72
what's equivalent to x^2-4x-l2
Answer:
Assuming you meant to write "x^2 - 4x - 12", there are a few equivalent forms that you could use to represent this expression. One common form is:
(x - 6)(x + 2)
Step-by-step explanation:
This is the factored form of the expression, which shows that it can be written as a product of two linear factors. To see why this is true, you can use the distributive property to expand the product:
(x - 6)(x + 2) = x(x + 2) - 6(x + 2) = x^2 + 2x - 6x - 12 = x^2 - 4x - 12
How many quarters do you need to add to 31/4 to get 41/2
Answer:
51/4 quarters
Step-by-step explanation:
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator for 4 and 2 is 4x2=8.
So we need to convert both fractions to have a denominator of 8:
31/4 = (31/4) x (2/2) = 62/8
41/2 = (41/2) x (4/4) = 164/8
Now we can add the fractions:
62/8 + x/4 = 164/8
Subtracting 62/8 from both sides:
x/4 = 102/8
Simplifying:
x = 51/4
Therefore, we need to add 51/4 quarters to 31/4 to get 41/2
A bag contains 19 blue, 28 purple, 21
red, and 29 orange balls. You pick
one ball at random. Find the
probability that it is purple or orange.
P(purple or orange) =
Simplify your answer completely.
Thus, the probability for the outcome of either purple or orange: P(purple or orange) = 57/97.
Explain about the term random selection:a choice that is made at random (entirely by chance, with no predictability). Every person in the population under study need to have an equal probability of getting chosen. Every person who is under investigation has an equal probability of being chosen at random for the sample.
Given bag with balls:
19 blue, 28 purple, 21 red, and 29 orange ballsTotal = 97 ballsprobability = favourable outcome / total outcome
P(purple) = 28/97
P(orange) = 29/97
Thus,
P(purple or orange) = 28/97 + 29/97
P(purple or orange) = 57/97
Thus, the probability for the outcome of either purple or orange ball : P(purple or orange) = 57/97.
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(x+3) (x-2) =2x
find the valűe of x
Step-by-step explanation:
[tex](x + 3)(x - 2) = 2x\\ {x}^{2} + x - 6= 2x \\ {x}^{2} - x - 6 = 0 \\ (x - 3)(x + 2) = 0 \\ x = 3 \: or \: x = - 2[/tex]
i need answer please
The surface area of the rectangular prism is 210 in²
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators.
The surface area of a rectangular prism is the sum of each area for the surface.
Hence:
Surface area = 2(8 in * 5 in) + 2(5 in * 5 in) + 2(8 in * 5 in) = 210 in²
The surface area of the prism is 210 in²
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Which linear equation is represented in the graph?
A. y = x – 1
B.y = 2x – 1
C. y = x + 1
D. y = 3x – 1
Please Factorise 8x - 6
Answer:
2(4x-3)
Step-by-step explanation:
Find common numbers between 8 and 6, which is 2. 2x4= 8 2x3=6
x is only on 8 so you can't put x on the outside of the bracket. so you put it with the 4 so it comes out correct
for each pair of lines determine whether they are parallel, perpendicular, or neither
Answer:
All lines are parallel.
Step-by-step explanation:
Get each equation in Slope-Intercept form:
1. Divide both sides by 3: [tex]y=-\frac{4}{3}x+\frac{7}{3}[/tex]
2. No change
3. Subtract 8x and divide by 6 on both sides: [tex]y=-\frac{4}{3}x-\frac{2}{3}[/tex]
Notice:
a. All slopes are -4/3
b. All y-intercepts are different
I would love some help please 18-20
18. C
(m / 2) - 6 = (m / 4) + 2
---Multiply everything by the LCM of the denominators
---LCM = 4
2m - 24 = m + 8
m - 24 = 8
m = 32
19. A
k / 12 = 25 / 100
---We can simplify 25/100
---We want to simplify enough to where the denominator of 25/100 is a multiple or factor of 12
k / 12 = 1 / 4
---4 x 3 = 12, 1 x 3 = 3
k = 3
20. A
9 / 5 = 3x / 100
---Cross multiply and solve algebraically
(5 * 3x) = (9 * 100)
15x = 900
x = 60
Hope this helps!
3⋅f(−4)−3⋅g(−2) = ?
Ayuda por favor
The value of the 3 × f( - 4 ) - 3 × g( - 2 ) is 40
Given the following expression 3 × f( - 4 ) - 3 × g( - 2 ), to find the required values, we can assume that;
f( - 4 ) = 15
g( - 2 ) = 5
Substitute the given parameters into the expression to have:
3 × f(- 4 ) - 3 × g(- 2) = 3 × 15 - 3 × 5
= 45 - 5
= 40
Hence the value of the 3 × f( - 4) - 3 × g( - 2) is 40
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The figure on the right is a scaled copy of the figure on the left
Which side in the figure on the right corresponds to segment UV?
What is the scale factor
The side that corresponds to uv is LK
The scale factor is 3 : 1
How to solve for the scale factorTo solve for the scale factor between two geometric figures, follow these steps:
Identify corresponding sides or corresponding lengths between the two figures.
Choose one pair of corresponding sides and write a proportion using the lengths of those sides.
Solve for the scale factor by simplifying the proportion.
The shape in UV occupies the space of 6 boxes
The space in LK is made of 2 boxes
Hence we have 6 : 2
= 3 : 1
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Find the distance from G to S.
Answer:
i think its b sorry if it's wrong
Step-by-step explanation: