Answer:
14.2 feet
Step-by-step explanation:
Use the Pythagorean Theorem to solve both parts.
Part 1.
35 is the hypotenuse and 21 is a leg.
[tex]a^{2} +b^{2} =c^{2} \\a^{2} +21^{2} =35^2\\a^2 + 441 = 1225\\a^2 +441-441=1225-441\\a^2 =784\\\sqrt{a^2} =\sqrt{784} \\a = 28 feet[/tex]
28 feet represents how far the base of the ladder is from the house.
Part 2.
Now move the ladder 4 feet farther from the house. 28 + 4 = 32 ft.
Now you have a leg that is 32 feet and the hypotenuse is still 35 feet. Solve for the other leg.
[tex]a^{2} +b^{2} =c^{2} \\a^{2} +32^{2} =35^2\\a^2 + 1024 = 1225\\a^2 +1024-1024=1225-1024\\a^2 =201\\\sqrt{a^2} =\sqrt{201} \\a = 14.177 feet[/tex]
Round to the nearest tenth and you have 14.2 feet
Given the example below, the zero product rule is exhibited correctly
because it take the factored form of the quadratic and sets equal to zeros
and solves.
x²+4x-21-
(x+7)(x-3)=0
x+7=0 or x-3=0
x=-7
x=3
True or false
The statement is true. This is an example of Factorization being correct as it takes the factors of the quadratic equation set them equal to 0 and then calculates the value of x.
In the given question, an example of factorization is taken for the equation x²+4x-21 which is factorized using the Middle-Term split rule. We have to find out if the example is conducted correctly.
Factorization is the rule to factorize an equation such that its factors if multiplied together form the equation itself.
We will verify the factorization, for equation x²+4x-21
=> x² + 4x - 21
=> x² + 7x -3x -21
=> x(x + 7) -3(x + 7)
=> (x + 7)(x - 3) = 0
=> x = -7, x = 3
Hence, the statement is True.
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Lesson 18: Use Systems of Equations to Solve Protstems A bag of popcorn and a juice box contains 518 calories. Two bags of popcorn and 6 juice boxes have a total of 1,456 calories. How many calories are in each Bag of popcorn and juice box? A. 182 calories in each bag of popcorn and each juice box B. 259 calories in each bag of popcorn and each juice box C. 364 calories in each bag of popcorn and 121 calories in each juice box D. 413 calories in each bag of popcorn and 105 calories in each juice box
According to the given information, the sum of the calories of a bag of popcorn and a juice box is 518. Taking x as the number of calories of a bag of popcorn and y as the number of calories of a juice box, we have that:
[tex]x+y=518[/tex]Then, 2 bags of popcorn (it means 2x) and 6 juice boxes (it means 6y) have a total of 1456 calories, this is:
[tex]2x+6y=1456[/tex]Use this system of equations and solve the problem, this way:
Solve the first equation for x:
[tex]x=518-y[/tex]Use this expression and replace for x in the second equation:
[tex]\begin{gathered} 2(518-y)+6y=1456 \\ 1036-2y+6y=1456 \\ 4y=1456-1036 \\ y=\frac{420}{4} \\ y=105 \end{gathered}[/tex]Use this value to find the value of x:
[tex]x=518-105=413[/tex]It means that there are 413 calories in each bag of popcorn and 105 calories in each juice box.
According to one mathematical model, the average life expenctancy for American men born in 1900 was 55 years. Life expectancy has increased by about 0.2 year for each birth year after 1900. If this trend continues, for which birth year will the average life expentancy be 71 years?
a) Write an equation to model the problem. Let t represent the number of years after 1900 and let n represent men's life expectancy at that time. For example t=12 and n=57.4 in the year 1912.
Answer: ?
b) Solve the equation, then answer the question given above. (Note: You are asked for a year, not a value for t.
Answer: ?
a) An equation to model the problem of determining the birth year when the average life expectancy will be 71 years is y = 55 + 0.2x.
b) From the equation above, from 1980 or in the 80th birth, the average life expectancy will be 71 years.
What is the average life expectancy?The average life expectancy refers to the average time in years that a person is expected to live after birth.
The average life expectancy has been a statistical tool for understanding a person's lifespan on earth based on some demographics.
What is an equation?An equation is a mathematical statement that equates two or more variables, numbers, or values or regards them as equivalent or equal.
For this situation, we can use the formed equation to predict a person's life expectancy average in the future, given the current years and increasing rate of life expectancy.
Life expectancy in 1900 = 55 years
Life expectancy increase for each birth year after 1900 = 0.2
Life expectancy = y
Year = x
y = 55 + 0.2x ... Equation
71 = 55 + 0.2x
0.2x = 16
x = 16/0.2
= 80 birth year
1980 = (1900 + 80)
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what is the answer?
If y = -3 cos (2x), then derivative d²y / dx² is 12 cos (2x)
Given,
y = -3 cos (2x)
We have to find derivative d²y / dx²
d²y / dx² = -3 (d² cos x / dx²) = -3 d/dx (d cos 2x / dx)
According to the concept:
d cos x / dx = - sin x
Here,
d cox 2x / dx = - sin 2x
So,
d²y / dx² = (- 3 × 2) d/dx (- sin 2x)
d²y / dx² = -6 (d sin 2x / dx)
d²y / dx² = 2 × 6 cos 2x
d²y / dx² = 12 cos (2x)
That is, if y = -3 cos (2x), then derivative d²y / dx² is 12 cos (2x)
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what is x3+y3+z3=k explain what the answer is.
Answer:
x=1/3k-y-z
Step-by-step explanation:
3x+3y+3z=k
Move the variables to the right
3x= -3y-3z+k
Divide both sides of the equation by 3
x=1/3k-y+z
how would you do this?
P( A and B) is [tex]\frac{1}{15}[/tex].
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is accurate. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given Data
P(A) = [tex]\frac{1}{3}[/tex]
P(B) = [tex]\frac{1}{5}[/tex]
P (A or B) = [tex]\frac{1}{2}[/tex]
1) No, events are not mutually exclusive. as P(A) + p(B) is not equal to P(A or B)
2) P( A and B) = P(A) × P (B)
P( A and B) = [tex]\frac{1}{3}[/tex] ×[tex]\frac{1}{5}[/tex]
P( A and B) = [tex]\frac{1}{15}[/tex]
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A math test has 12 multiplication problems and 24 division problmes what is the ratio value
The ratio value of multiplication problems to division problems is 1:2.
What is the ratio value?The ratio value compares two quantities or values.
The ratio value shows the quantity of one variable contained in another.
Ratios are depicted by the ratio sign (:) or in fractions, decimals, or percentages.
The number of multiplications problems in the math test = 12
The number of division problems in the math test = 24
The ratio value of their relationship = 12:24 or 1:2
Thus, the math test shows that there are twice as many division problems as multiplication problems.
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An object oscillates as it moves along the
x-axis. Its displacement varies with time
according to the equation
x = 4 sin(pi(t)+ pi/2)
where t = time in seconds and
x = displacement in meters
What is the displacement between t = 0
and t = 1 second?
[?] meters
It is found that the displacement between t= 0 and t = 1 second is of 0.536 m.
The equation of motion is given by:
x(t) = 4 sin(πt + π/2)
The displacement between t= 0 and t = 1 second is given by:
d = x(1) - x(0)
Hence,
position of the object when t = 1
x(1) = 4sin(π(1) + 1 (π/2))
= 4 sin (π + π/2)
= 4 sin (3π/2)
= 4 x √3/2
= 2√3
= 3.464
position of the object when t = 0
x(0) = 4sin(π(0) + (π/2))
= 4 sin (0 + π/2)
= 4 x 1
= 4
Then,
d = x(1) - x(0)
= 4 - 3.464
= 0.536(approx)
Therefore, the displacement of the object between t = 0 and t = 1 is 0.536.
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What is the y-intercept of the given graph?
A) -4
B) 3
C) 4
D) None of these choices are correct.
Answer: The Y intercept is B) 3.
Step-by-step explanation:
you just have to see where the line crosses the y axis which in this case is it crosses the y axis on 3
provide the correct reason for the statement in line 6. (please help)
Answer:
Step 6: Subtraction Property of =
Step-by-step explanation:
You have $100 in a savings accoun and save an additional $40 each week. Your friend has $80 in a savings account and saves and addtional $10 each week. Find and intepret the sum and difference of the amounts of money in each of your savings accounts?
The sum and the difference in the amount saved in the accounts will be 180 + 50w and 20 + 30w respectively.
How to calculate the value?From the information, I have have $100 in a savings accoun and save an additional $40 each week.
Let the number of weeks be represented by w. The expression to represent this will be:
= 100 + 40w
My friend has $80 in a savings account and saves and addtional $10 each week. This will be:
= 80 + 10w
The sum will be:
= 100 + 40w + 80 + 10w
= 180 + 50w
The difference in the amount will be:
= 100 + 40w - (80 + 10w)
= 20 + 30w
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1. How much does it cost to use a yard of ribbon?
#9 satin ribbon
Cost $4.99 per roll
100 yards per roll
Step-by-step explanation:
You will want to divide the cost of $4.99 by 100, this will give you the cost per yard.
Answer:
$4.99 / 100 = $0.0499
About 5 cents per yard.
Please give thanks, 5 stars, and brainliest answer :)
What is the length of segment KL? Round the answer to
the nearest tenth of a units.
K=(-4,-6) L =(5,1)
Answer:
d ≈ 11.40
Step-by-step explanation:
K: (-4, -6); L: (5, 1)
(x₁, y₁) (x₂, y₂)
d = √(x₂ - x₁)² + (y₂ - y₁)²
d = √(5 - (-4))² + (1 - (-6))²
d = √(5 + 4)² + (1 + 6)²
d = √(9)² + (7)²
d = √81 + 49
d = √130 ≈ 11.40
I hope this helps!
Which property is illustrated by the statement? K(mp) = (km)p
Solution:
[tex]\begin{gathered} An\text{ associative property of addition;} \\ a+(b+c)=(a+b)+c \\ An\text{ associative property of multiplication;} \\ a\times(b\times c)=(a\times b)\times c \end{gathered}[/tex]Thus;
Given;
[tex]k(mp)=(km)p[/tex]FINAL ANSWER: Associative Property.
12. (01.02)
Which function below is the inverse of f(x) = x² - 9?
FOR EQUATION INVERSES IT MEANS ... x and y swap positions.
[tex]x = (f(x))^{2} - 9 \\ (f(x))^{2} = x + 9 \\ \sqrt{(f(x))^{2} } = \sqrt{x + 9} \\ f(x) = \sqrt{x + 9} [/tex]
ATTACHED IS THE SOLUTION.
will give you brainliest
Answer:
[tex]\sqrt{8}[/tex]
We use the process of elimination to solve:
When we solve [tex](\sqrt{10})^{2}[/tex] we get 10 and we know that 10 is a integer and we know all integers are rational numbers, therefore, this is rational.
When we solve [tex]\sqrt{196}[/tex] we get 14 and we know its a rational number because it can be expressed as the quotient of two integers: 14 ÷ 1. Therefore this one is, rational.
0.63, The decimal 0.6 is a rational number. It is the decimal form of the fraction 6/10. A rational number is, by definition, any number that results when one integer is divided by another. Since both 6 and 10 are integers, or whole numbers, 0.6 is a rational number.
And lastly this leaves is with [tex]\sqrt{8}[/tex] and It is a non-terminating decimal with non-repeating digits. The number 2.828427125... can't be written in p/q form. Hence, the square root of 8 is a irrational number.
A lawnmower with a 3-gallon gas tank uses an average of 0.6 gallons per hour. A function modeling this situation, where x represents the amount of gas in the tank, has a domain described by which inequality?
A. 0 ≤ x ≤ 5
B. 0 < x < 5
C. 0 < x < 3
D. 0 ≤ x ≤ 3
x represents the amount of gas in the tank, has a domain described by which inequality
[tex]0 \leq x \leq 3[/tex]
This is further explained below.
What is inequality?Generally, A typical 3-gallon lawnmower requires 0.6 gallons of petrol per hour.
This circumstance is modeled by a function, where x is the volume of gas in the tank.
The lawnmower's gas tank has a maximum capacity of gallons and may be completely empty (having 0 gallons of gas).
In conclusion, a function's domain is
[tex]0 \leq x \leq 3[/tex]
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A street that is 270 ft long is covered in snow. City workers are using a snowplow to clear the street. A tire on the snowplow has to turn 27 times in traveling the length of the street. What is the diameter of the tire?
Use the value 3.14 for π. Round your answer to the nearest tenth. Do not round any intermediate steps.
If a street that is 270 ft long is covered in snow. City workers are using a snowplow to clear the street. The diameter of the tire is: 3.2 meters.
Diameter of the tireFirst step is to determine the circumference of the tire
Circumference of the tire = (270 m / 27)
Circumference of the tire = 10 meters
Second step is to make use of 3.14 for π to determine the diameter of the tire using this formula
Diameter of the tire = Circumference of the tire / π
Let plug in the formula
Diameter of the tire = 10 / 3.14
Diameter of the tire = 3.18 meters
Diameter of the tire = 3.2 meters (Approximately)
Therefore 3.2 meters is the diameter.
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Evaluate.(-2).(-2)·2=060-6O 80 -8
Evaluate (-2) (-2) . 2
[tex]\begin{gathered} -2\text{ }\times\text{ -2 = 4} \\ 4\text{ }\times\text{ 2 = }\text{\textcolor{#FF7968}{8}} \end{gathered}[/tex]
Suppose the top of the minute hand of a clock is 2 in. From the center of the clock. For the duration, determine the distance traveled by the tip of the minute hand (30 minutes)
yes
yes
yes
yes
yes
yes
no
1: Find the equation of a polynomial with given zeros
For this problem, we are given the zeros of a polynomial, we need to determine its expression.
The zeros are:
[tex]1,1,2+\sqrt{2},2-\sqrt{2}[/tex]Therefore we can write:
[tex]\begin{gathered} f(x)=(x-1)^2(x-2+\sqrt{2})(x-2-\sqrt{2})\\ \\ f(x)=(x^2-2x+1)(x^2-4x+2)\\ \\ f(x)=x^4-4x^3+2x^2-2x^3+8x^2-4x+x^2-4x+2\\ \\ f(x)=x^4-6x^3+11x^2-8x+2 \end{gathered}[/tex]The correct answer is option A.
A toy manufacturer is going to produce a new toy car. each one costs $3 dollars to make and the company will also have spent 200$ to set up the machinery to make them. what will it cost to produce the first hundred cars?ar. each one costs $3 dollars to make and the company will also have spent 200$ to set up the machinery to make them. what will it cost to produce the first hundred cars?
Answer:
$500
Step-by-step explanation:
Startup cost: $200
Cost of 1 car: $3
Cost of 100 cars: $3 × 100 = $300
$200 + $300 = $500
20. The mean IQ score for 1500 students is 100, with a standard deviation of 15. Assuming the scores have a normal distribution, answer the following b. How many have an IQ between 70 and 130? 2. How many have an IQ between 85 and 115? e. How many have an IQ over 145?
Given the normal distribution, the following can be illustrated:
1. The number of people who have an IQ between 70 and 130 is 1024.
2. The number of people who have an IQ between 85 and 115 is 1024.
The number of people who have an IQ over 145 is 3.
How to compute the value?1. The The number of people who have an IQ between 70 and 130 will be:
z(115) = (130-100)/15 = 2
z(85) = (70-100)/15 = -2
P(-2< z < 2) = 0.6827
The number of 1500 that have IQ between 70 and 130 will be:
= 0.6827 × 1500
= 1024
2. The number of people who have an IQ between 85 and 115 will be:
z(115) = (115-100)/15 = 1
z(85) = (85-100)/15 = -1
We need to consult Z-table to find P value with this Z value
P(85< x < 115) = P(-1< z < 1) = 0.6827
Number of people of 1500 that have IQ between 85 and 115:
= 0.6827 × 1500
= 1024
3. The number of people who have IQ over 145?
Z(>145)
=( 145-100)/15
=3
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If the account is overdue, what is the probability that it is new?
Answer:
we need more info than this
Step-by-step explanation:
The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3. If an elephant weighs 2400 pounds on Planet A, find the elephant's weight on Planet B.
The weight of the elephant on planet B given the ratio of the weights on planet A an B is 72 pounds.
What is the weight of the elephant on Planet B?Ratio is used to compare two or more quantities together. It shows the number of times that one quantity is contained in another quantity. In this question, the weight of the elephant on Planet B is 100/3 times that of Planet A.
In order to determine the weight of the elephant on Planet B, multiply the ratio of the weight in planet B by the weight in Planet A and divide by the ratio of weight in planet A.
Weight in Planet B = (3 x 2400) / 100 = 72 pounds
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i need help with the question please
The number of customers surveyed is 499.
UESTION A
ehe age ranges that fall within the required one for this question are 20-29, 30-39, and 40-49.
The number of people in these groups in total will be:
[tex]\Rightarrow65+87+70=222[/tex]Therefore, the probability of this occurring is calculated to be:
[tex]\Rightarrow\frac{222}{499}=0.4449[/tex]he probability is 0.4449.
QUESTION B
he age ranges for this question are >≥60, <20, and 20-29.
The number of people in these groups in total will be:
[tex]\Rightarrow84+93+65=242[/tex][tex]\Rightarrow\frac{242}{499}=0.4850[/tex]he probability is 0.4850.
QUESTION C
is ≥60.
The number of people in this group is 84.
[tex]\Rightarrow\frac{84}{499}=0.1683[/tex]Write the equation of a Circle with the given information.Center: (-14,9) Point on the Circle: (-11, 12)
The equation of a circle with center (a, b) and radius r is
[tex](x-a)^2+(y-b)^2=r^2[/tex]We are given the center as
[tex](a,b)\Rightarrow(-14,9)[/tex]To find the radius, we can use the formula to find the distance between two points, that is, the point on the circle and the center.
[tex]r=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2_{}_{}}[/tex]where (x₁, y₁) = (-14, 9)
(x₂, y₂) = (-11, 12)
Thus, we have
[tex]\begin{gathered} r=\sqrt[]{(12-9)^2+(-11-\lbrack-14\rbrack)^2} \\ r=\sqrt[]{3^2+3^2} \\ r=\sqrt[]{9+9} \\ r=\sqrt[]{18} \\ r=3\sqrt[]{2} \end{gathered}[/tex]Therefore, inputting all the values into the equation for a circle, we have
[tex]\begin{gathered} (x-\lbrack-14\rbrack)^2+(y-9)^2=3\sqrt[]{2} \\ \therefore \\ (x+14)^2+(y-9)^2_{^{}}=3\sqrt[]{2} \end{gathered}[/tex]need help with these due tomorrow morning do 1-6
Answer:
Step-by-step explanation:
5 over 12 is 5/17
how much interest would $1,000 earn in 1 year at an annual rate of 2% compounded annually
The Compound Interest would be $1104.895
What is Compound Interest ?
The interest charged on a loan or deposit is known as compound interest. It is the idea that we use the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The main distinction between compound and simple interest is this. If we examine our bank statements, we will typically see that our account is credited with interest on a yearly basis. Even though the principal remains the same, the interest changes annually. We can observe that interest rises over time. As a result, we can infer that the interest the bank charges is compound interest, or CI, rather than simple interest.
Number of quarters in 5years =5×4=20
Quarterly rate of compound interest
r=24=0.5%
Initial amount
P=$1000
hence the total amount after 5years
= P(1+r/100)n
=1000(1+0.5/100)^20
=1000(1.005)^20
=$1104.895
Hence, The Interest will be $1104.895
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HURRY On a coordinate plane, a curve goes through (negative 6, 0), has a maximum at (negative 5, 500), decreases to (negative 2.5, negative 450), increases through (0, negative 50), increases again through (1, 0), and then goes through (2, 400).
The real solutions to the equation 3x5 + 25x4 + 26x3 – 82x2 + 76x = 48 are shown on the graph. What are the nonreal solutions?
StartFraction 1 + i StartRoot 5 EndRoot Over 3 EndFraction, StartFraction 1 minus i StartRoot 5 EndRoot Over 3 EndFraction.
StartFraction negative 1 + i StartRoot 5 EndRoot Over 3 EndFraction, StartFraction negative 1 minus i StartRoot 5 EndRoot Over 3 EndFraction.
StartFraction negative 1 + StartRoot 5 EndRoot Over 3 EndFraction, StartFraction negative 1 minus StartRoot 5 EndRoot Over 3 EndFraction.
StartFraction 1 + StartRoot 5 EndRoot Over 3 EndFraction, StartFraction 1 minus StartRoot 5 EndRoot Over 3 EndFraction.
The non-real solutions of the polynomial expression are x = (1 + 2√-5)/3 and x = (1 - 2√-5)/3
How to determine the non-real solutions?The equation of the polynomial expression is given as:
3x5 + 25x4 + 26x3 – 82x2 + 76x = 48
Rewrite the equation as
3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48 = 0
The points on the graph are given as
(-6, 0), (-5, 500), (-2.5, -450), (0, - 50), (1, 0), (2, 400).
Write out the x-intercepts
(-6, 0) and (1, 0)
This means that
Real solution = -6
Real solution = 1
Rewrite the above as
x = -6 and x = 1
So, we have
x + 6 = 0 and x - 1 = 0
Multiply
(x + 6)(x - 1) = 0
The next step is to divide the polynomial equation 3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48 = 0 by (x + 6)(x - 1) = 0
This is represented as
3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48/(x + 6)(x - 1)
Using a graphing calculator, we have
3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48/(x + 6)(x - 1) = 3x^3 + 10x^2 - 6x + 8
So, we have
3x^3 + 10x^2 - 6x + 8
Factorize
(x + 4)(3x^2 - 2x + 2)
Next, we determine the solution of the quadratic expression 3x^2 - 2x + 2 using a quadratic formula
So, we have
x = (-b ± √(b² - 4ac))/2a
This gives
x = (2 ± √((-2)² - 4 * 3 * 2))/2 * 3
So, we have
x = (2 ± √-20)/6
This gives
x = (2 ± 4√-5)/6
Divide
x = (1 ± 2√-5)/3
Split
x = (1 + 2√-5)/3 and x = (1 - 2√-5)/3
So, the conclusion is that
Using the polynomial expression, the non-real solutions are x = (1 + 2√-5)/3 and x = (1 - 2√-5)/3
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