The requried it takes 8.37 seconds for the object to hit the ground.
The polynomial 16T² - 1120 gives the height of the object in feet as a function of time T in seconds after it is dropped from a height of 1120 feet. When the object hits the ground, its height is zero. So we can set the polynomial equal to zero and solve for T:
16T² - 1120 = 0
T² - 70 = 0
T² = 70
T = ±√70
Since time cannot be negative, we can disregard the negative solution. Therefore, the object hits the ground after:
T = √70 ≈ 8.37 seconds
So it takes 8.37 seconds for the object to hit the ground.
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Round to the nearest 10th
Answer: What are we finding?
Step-by-step explanation:
?
The width of a rectangle is 1 units less than the length. The area of the rectangle is 56
square units. What is the length, in units, of the rectangle?
Quadratic Word Problems
Apr 30, 11:47:01 PM
Answer:
Submit Answer
DELL
www.
attempt 1 out of 2
Answer:
Let's assume that the length of the rectangle is "x" units.
According to the problem, the width of the rectangle is 1 unit less than the length. Therefore, the width can be represented as (x-1) units.
We know that the area of a rectangle is equal to its length multiplied by its width. So, the area of this rectangle is given as 56 square units.
Using the formula for the area of a rectangle, we can write:
Length x Width = Area
x(x-1) = 56
Expanding the left side of the equation, we get:
x^2 - x = 56
Rearranging the terms, we get a quadratic equation:
x^2 - x - 56 = 0
Now we can solve for x by factoring the quadratic equation:
(x-8)(x+7) = 0
This gives us two possible values for x: x=8 and x=-7.
Since length cannot be negative, we reject x=-7 and conclude that the length of the rectangle is 8 units.
Therefore, the length of the rectangle is 8 units and the width is (8-1) = 7 units.
Step-by-step explanation:
3y-1/3=5
*we have to figure out the value of y*
Answer:
To solve for y in the equation:
3y - 1/3 = 5
First, we need to isolate the term containing y by adding 1/3 to both sides of the equation:
3y - 1/3 + 1/3 = 5 + 1/3
Simplifying the left-hand side:
3y = 5 + 1/3
Next, we need to isolate y by dividing both sides of the equation by 3:
3y/3 = (5 + 1/3)/3
Simplifying the right-hand side by finding a common denominator:
3y/3 = (15/3 + 1/3)/3
3y/3 = 16/3
Simplifying the left-hand side:
y = 16/9
Therefore, the solution to the equation 3y - 1/3 = 5 is y = 16/9.
Step-by-step explanation:
Find the sine of ∠Y. Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
Angle Y from the given triangle XYZ is 62° and sine of ∠Y is 60/68.
From the given triangle XYZ, XY=32 and YZ=68.
By using Pythagoras theorem, we get
YZ²=XY²+XZ²
68²=32²+XZ²
XZ²=68²-32²
XZ²=3600
XZ=√3600
XZ=60
We know that, sinθ= Opposite/Hypotenuse
sinY=XZ/YZ
sinY=60/68
sinY=0.8823
Y=61.92
Y≈62°
Therefore, angle Y from the given triangle XYZ is 62° and sine of ∠Y is 60/68.
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Help me
Five times the difference of a number and two is seven more than that number
Twice a number decreased by four is greater than ten, what numbers satisfy this condition?
Twice a number decreased by two is equivalent to than number increased by five.
The equation in each case will be 5(x - 2) = x + 7, 2x - 4 > 10, and 2x - 2 = x + 5 and their solution will be 4.25, more than 7, and 7, respectively.
1. Let the number be x. Then the equation can be written as,
5(x - 2) = x + 7
5x - 10 = x + 7
4x = 17
x = 4.25
2. Let the number be x. Then the equation can be written as,
2x - 4 > 10
2x > 14
x > 7
3. Let the number be x. Then the equation can be written as,
2x - 2 = x + 5
x = 7
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Solve the equation lx + 5= -6.
The possible values lx + 5| = 6 of x in the equation are x = -11 or x = 1
Solving the equation for xFrom the question, we have the following parameters that can be used in our computation:
lx + 5= 6
Express properly
So, we have
lx + 5| = 6
The above equation is an absolute value equation
When the above equation is expanded, we abe
x + 5 = -6 or x + 5 = 6
Solving for x in the equations. we have
x = -11 or x = 1
This means that the values of x in the equation are x = -11 or x = 1
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find the probability that a randomly selected point within the circle falls in the red shaded circle.
Answer:
[tex] \frac{\pi( {4}^{2}) }{\pi( {8}^{2}) } = \frac{16}{64} = \frac{1}{4} = .25[/tex]
The regular ticketed prices of four items at Grumbell's Clothier are as follows: coat, $139.99;
blouse, $43.99; shoes, $89.99; jeans, $32.99.These four items were placed on sale at 20% off the regular price.
a. Find, correct to the nearest cent, the sale prices of these four items.
b. Describe two different ways to find the sale prices.
The sale prices of the four items are Coat: $111.99, Blouse: $35.19, Shoes: $71.99, Jeans: $26.39 , Using the discount percentage and Using the discount amount are two different ways to find the sale prices.
To find the sale price of each item, we need to multiply the regular price by the discount percentage, which is 20% or 0.2.
Then we subtract this discount amount from the regular price to get the sale price. We can use the following formula:
Sale price = Regular price - Discount amount
Using this formula, we can calculate the sale prices of the four items:
Coat: Sale price = $139.99 - ($139.99 x 0.2) = $111.99
Blouse: Sale price = $43.99 - ($43.99 x 0.2) = $35.19
Shoes: Sale price = $89.99 - ($89.99 x 0.2) = $71.99
Jeans: Sale price = $32.99 - ($32.99 x 0.2) = $26.39
Therefore, the sale prices of the four items are:
Coat: $111.99, Blouse: $35.19, Shoes: $71.99, Jeans: $26.39.
b. There are different ways to find the sale prices. Here are two methods:
Method 1: Using the discount percentage
Multiply the regular price of each item by the discount percentage (20% or 0.2).
Subtract the result from step 1 from the regular price to find the sale price.
Method 2: Using the discount amount
Multiply the regular price of each item by the discount percentage (20% or 0.2) to find the discount amount.
Subtract the discount amount from the regular price to find the sale price.
Both methods will give you the same sale prices, but some people may find one method easier or more intuitive than the other.
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To give animals essential minerals and nutrients, farmers and ranchers often have a block of salt (called a "salt-lick") available for their animals to lick.
A rancher is ordering a box of cube-shaped salt licks. The edge lengths of each salt lick are 5/12 -foot. Is the volume of one salt lick greater or less than 1 cubic foot? Explain why or why not.
The volume of one salt lick is 125/1728 feet which is less than one cubic foot.
All the edges of the cube are congruent with each other. Suppose that: The side length of the considered cube is L units. Then, we get:
V = L³ cubic units.
The edge length of the cube is 5/12 feet. Then the volume of the cube will be given as,
V = (5/12)²
V = 125 / 1728 feet
The volume is less than one cubic foot.
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The average individual in a country earns an annual salary of $82,000, of which $32,800 is spent on housing, $14,760 on food, $14,760 on transportation, and $19,680 on other goods and services. Suppose the government in this country mandates that all salaries and the prices of all goods and services be reduced by 40 percent. Instructions : Enter your answers as a whole number .
The new budget for each category would be:
Housing: $19,680
Food: $8,856
Transportation: $8,856
Other goods and services: $11,808
After the government mandate, the average individual's salary would be reduced by 40%:
New annual salary = $82,000 - (40% x $82,000) = $49,200
Similarly, the prices of all goods and services would be reduced by 40%. Therefore, the new amounts spent on each category would be:
Housing: $32,800 - (40% x $32,800) = $19,680
Food: $14,760 - (40% x $14,760) = $8,856
Transportation: $14,760 - (40% x $14,760) = $8,856
Other goods and services: $19,680 - (40% x $19,680) = $11,808
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Find the indicated measure.
Length of JK
7 in.
J
L75°
K
The calculated value of the length of the arc JK is 35π/12
Finding the length of the arc JKFrom the question, we have the following parameters that can be used in our computation:
central angle = 75 degrees
Radius = 7
Using the above as a guide, we have the following:
Arc JK = central angle/360 * 2 * π * Radius
Substitute the known values in the above equation, so, we have the following representation
JK = 75/360 * 2 * π * 7
Evaluate
JK = 35π/12
Hence, the length of the arc JK is 35π/12
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Complete question
Find the indicated measure. Length of JK
See attachment
Select the correct answer.
If no denominator equals zero, which expression is equivalent to 15/x-6 + 7/x+6?
A.
OB.
OC.
OD.
22 +132
²36
22-48
236
22
C.36
22 +48
²36
The expression in the options which is equivalent to the given expression is D. (22x + 48) / (x² - 36).
Given expression is,
[15 / (x - 6)] + [7 / (x + 6)]
Cross multiplying the two fractional expressions,
= [15 (x + 6) + 7 (x - 6)] / [(x - 6) (x + 6)]
= [15x + 90 + 7x - 42] / [x² - 6²]
= (22x + 48) / (x² - 36)
Hence the equivalent expression is D.
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The diagram shows the amount of fabric that Christine
needs to make 1 tablecloth, including the fabric that will
hang over the sides. The fabric costs $1.50 per square
foot. Christine plans to make 1 tablecloth for each of the
4 seasons of the year. What is the total cost of the fabric
that Christine needs for the tablecloths?
The total cost of the fabric that Christine needs for the tablecloths is $90.0.
What is the area of a rectangle?A rectangle is a figure which has four sides of which opposite sides have equal length.
The area of a rectangle is the amount of space to be covered by the figure in a 2 dimensional plane.
Area of a rectangle = length x width
In the information given, we have;
area of the tablecloth = length x width
= 6 x 5/2
= 3 x 5
= 15
The area of the tablecloth is 15 sq. ft.
But Christine plans to make 1 tablecloth for each 4 seasons of the year.
So that;
total area of tablecloth needed for the year = 15 x 4
= 60 sq. ft
Then the fabric costs $1.50 per square foot,
total cost of fabric needed = 60 x $1.5
= $90.0
The total cost of the fabric that Christine needed for the tablecloth is $90.0
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What is the position of B on the number line below?
Write your answer as a fraction or mixed number
The requried position of point B on the number line is 1/4 or 0.25.
Since point B represents the number 0.25 on the number line, its position can be described as 0.25 units to the right of 0 or as 0.25 units to the left of 0.5.
Alternatively, we can describe its position as a fraction or mixed number using the length of the number line as the denominator. If the number line extends from 0 to 1, then the position of point B can be expressed as:
B = 0 + 0.25 = 1/4
Therefore, the position of point B on the number line is 1/4 or 0.25.
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The total cost of a meal, including a 20% tip, can be calculated by the formulaT = C + 0.20C. where T is the total cost and O'is the price of the meal including the appropriate tax.
Complete the following statements.
To solve the equation for C, first factor out the common monomial C to rewrite the equation as [Drop Down 1]. Then, divide both sides by the factor [Drop Down 2] to isolate the variable.
To solve the equation for C, first factor out the common monomial C, then rewrite the equation as C(1 + 0.20) = T.
Then, to isolate the variable, divide both sides by the factor (1 + 0.20) or 1.20: C = T/1.20.
How to explain the equationAn equation is essentially a statement that illustrates the variables presented. In this circumstance, it is critical to notice that two or more components are taken into account in order to represent the scenario.
Based on the information, to solve the equation for C, first factor out the common monomial C to rewrite the equation as C(1 + 0.20) = T.
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In ΔRST, m < R = 98°, r = 24, and t = 14. Find the m < S, to nearest degree..com
The measure of the angle S is 54 degrees
How to determine the valueUsing the Pythagorean theorem, we have that;
r² = t² + s²
Subsitute the values
s² = 24² - 14²
Find the square values
s² = 576 - 196
s² = 380
find the square root value
s = 19. 5
Then, using the law of sines, we have that;
sin R/r = sin S/s
Substitute the values, we get;
sin 98/24 = sin S/19.5
cross multiply the values
sin S = 19.3/24
Divide the values
sin S = 0. 8045
S = 54 degrees
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5. El bloque de la figura se encuentra en reposo en el momento en que empiezan a actuar las fuerzas.
F₁ = 25 N
F, = 22.6 N
m = 2 kg
a. Encontrar el valor de la fuerza resultante.
b. Determina su aceleración.
C. Calcula la velocidad del bloque a los 5 segundos de movimiento.
The resultant force acting on the block is 47.6N.
The acceleration of the block will be 23.8 m/s².
The speed of the block after 5 seconds of movement is 119 m/s.
What is the resultant force?In this question, we need to make use of Newton's second law, hence:
resultant force = mass × acceleration
So, for question a. The value of the resultant force will be obtained by adding the two forces together:
resultant force = F₁ + F₂
= 25N + 22.6N
= 47.6N
b. Its acceleration will be:
acceleration = resultant force / mass
= 47.6N / 2kg
= 23.8 m/s²
c. The speed of the block after 5 seconds of movement will be:
Velocity (v) = u + at
velocity = initial velocity + acceleration x time
Based on the block was initially at rest, the initial velocity is 0.
Hence:
V = acceleration x time
= 23.8 m/s² x 5s
= 119 m/s
Hence the speed of the block after 5 seconds of movement will be: 119 m/s.
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See full text below
The block in the figure is at rest when the forces begin to act.
F₁ = 25N
F, = 22.6 N
m = 2kg
to. Find the value of the resultant force.
b. Determine its acceleration.
C. Calculate the speed of the block after 5 seconds of movement.
If the linear equation 2x+3y=14 is rewritten in function notation as
f(y)=−32y+7,
what is the dependent variable?
If the linear equation 2x+3y=14 is rewritten in function notation as f(y)=−32y+7, the dependent variable is x
In the linear equation 2x+3y=14, we can solve for y by isolating it on one side of the equation:
2x + 3y = 14
3y = -2x + 14
y = (-2/3)x + 14/3
Now, we can write this equation in function notation by replacing y with f(y) and x with the independent variable, usually denoted by 'x'. Therefore, we have:
f(y) = (-2/3)x + 14/3
The function f(y) tells us the value of x for any given value of y. In other words, y is the independent variable, and x is the dependent variable.
Therefore, the dependent variable in the function f(y) = (-2/3)x + 14/3 is x. The value of x is determined by the value of y, which is the input to the function. This means that for any value of y, we can determine the corresponding value of x by plugging in y into the equation and solving for x.
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A goat is tied to the corner of a rectangular shed in a large field full of grass. The rope is 3 yards long. The shed is a 4 yard by 6 yard shed. Calculate the area of grass that the goat can eat
Mrs. Chauvet has an unfair number cube that lands with 6 facing up 40% of the time
Let X= the number of times that she rolls a 6 among 3 trials.
What is PEX s 2)? Enter your answer to 3 decimal places
By 11
X
P(X)
10
0216
1
0.432
2
0288
3
0.064
The probability of getting a 6 on a biased dice is 0.4. The P(X ≤ 2) is 0.936.
The probability of rolling a 6 is 0.4 and the probability of not rolling a 6 is 0.6. The probability mass function for X is given in the table. To find P(X ≤ 2), we need to sum the probabilities for X = 0, 1, and 2.
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
= 0.216 + 0.432 + 0.288
= 0.936
Therefore, the probability of rolling a 6 two or fewer times in three trials is 0.936 (rounded to 3 decimal places).
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Answer:0.432
Step-by-step explanation:
edge
The net of a rectangular prism and its dimensions are shown in the diagram. What is the total surface area of the rectangular prism in square inches?
The surface area of the rectangular prism is 216 square inches
What is the surface area of the rectangular prism?From the question, we have the following parameters that can be used in our computation:
10 in by 3 in by 6 in
The surface area of the rectangular prism is calculated as
Surface area = 2 * (Length * Width + Length * Height + Width * Height)
Substitute the known values in the above equation, so, we have the following representation
Area = 2 * (3 * 10 + 3 * 6 + 10 * 6)
Evaluate
Area = 216
Hence, the area is 216 square inches
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Simplify the expression:
5(-6 + 2n) =
Answer:
5(-6 + 2n) can be simplified using the distributive property of multiplication as follows:
5(-6 + 2n) = 5*(-6) + 5*(2n)
= -30 + 10n
Therefore, the simplified expression is -30 + 10n.
Let u = - 3i + 2i v = 2i - 2j and w = - 4j Find the specified scalar or vector. 5u(3v - 4w)
If u = - 3i + 2i, v = 2i - 2j and w = - 4j, 5u(3v - 4w) is a scalar quantity with a value of 440.
To evaluate the expression 5u(3v - 4w), we need to first perform the scalar multiplication and then the vector subtraction. We can start by computing the scalar multiplication of 3v - 4w:
3v - 4w = 3(2i - 2j) - 4(-4j) = 6i + 14j
Next, we can perform the scalar multiplication of u and the vector 6i + 14j:
5u(3v - 4w) = 5(-3i + 2j)(6i + 14j)
Expanding the product, we get:
5(-18i² + 36ij + 42ij - 28j²)
Since i² = j² = -1, we can simplify this expression as:
5(18 + 70) = 440
Therefore, 5u(3v - 4w) is a scalar quantity with a value of 440.
The key concept used in this problem is the distributive property of scalar multiplication over vector addition and subtraction. This property allows us to simplify expressions that involve scalar multiplication and vector operations by distributing the scalar to each component of the vector.
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I'm a little stuck on some of these math problems I don't understand what they're asking please help! Whoever get's it right receives a brainly!
Answer:
4 months
Step-by-step explanation:
This question is just asking you to construct a system of equations!
The amount that they will start with will be the y-intercept, because that's the amount in the bank account when no time has passed (aka since no additional deposits were made).
Chrisitiana: 10x + 50 = y
Marlena: 15x + 30 = y
Y in this case is going to be the amount of money in the bank account when x amount of months have passed. We want both y values to be the same.
10x + 50 = y = 15x + 30
Cut out the y as a middleman and we have
10x + 50 = 15x + 30
-10x
50 = 5x + 30
-30
20 = 5x
/5
4 = x
They will have the same amount of money in their accounts after 4 months.
In miss Franco‘s class for every six boys there are a girls write the ratio of boys to girls in simplest form
The ratio of boys to girls in Mrs. Franco's class is 3:2 .
Here, we have,
The Ratio is defined as the comparison of two quantities that have the same units .
In the question ,
it is given that
In Mrs. Franco's class
For every 6 boys there are 4 girls in the class
we have to find the ratio of , boys to girls
the number of boys = 6
the number of girls = 4
So , the ratio can be written as
boys / girls = 6/4
writing the ratio in the simplest form , we get
boys/girls = 3/2
the ratio is 3:2 .
Therefore , The ratio of boys to girls in Mrs. Franco's class is 3:2 .
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complete question:
In Mrs. Franco‘s class for every 64 is there a April right the ratio of boys to girls in simplest form
(1) If DoS and D=140 where S-35 find (a) the relationship between DoS (
b) the value of S when D is 176.
(2) Alfa and Aisha share 210 Naira so that Aisha get twice as much as Alfa. How much does each get?
Alfa receives 70 Naira, and since Aisha gets twice as much, she receives 2 * 70 = 140 Naira.
(1)
(a) The relationship between D, o, and S can be expressed as follows:
DoS (D divided by o multiplied by S) = D / (35 * S)
(b) To find the value of S when D is 176, we can substitute D = 176 into the equation from part (a):
DoS = 176 / (35 * S)
Since the relationship between DoS is not specified further, we cannot determine a specific value of S without additional information. We need more context or a specific equation to solve for the value of S.
Let's denote the amount Alfa gets as x Naira. According to the given information, Aisha gets twice as much as Alfa, so Aisha receives 2x Naira.
The sum of the amounts they receive is 210 Naira, so we can set up the equation:
x + 2x = 210
Combining like terms:
3x = 210
Dividing both sides by 3:
x = 70
Therefore, Alfa receives 70 Naira, and since Aisha gets twice as much, she receives 2 * 70 = 140 Naira.
In summary, Alfa receives 70 Naira, while Aisha receives 140 Naira.
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Robert is preparing to run a marathon. He runs 7 1/5 miles on Saturday and two times that amount on Monday and Wednesday. Robert wants to run a total of 60 miles this week. How many more miles does he need to run?
Answer:
25 miles
Step-by-step explanation:
Robert runs 7 1/5 miles on Saturday. To find out how much he runs on Monday and Wednesday, we can multiply 7 1/5 by 2:
7 1/5 x 2 = 14 2/5
Robert runs 14 2/5 miles on both Monday and Wednesday, so his total distance for the week is:
7 1/5 + 14 2/5 + 14 2/5 = 35 miles
Robert wants to run a total of 60 miles this week, so he needs to run:
60 - 35 = 25 miles
Therefore, Robert needs to run 25 more miles to reach his goal of running 60 miles this week.
You are planning a deck along two sides of a pool. The deck is to have a total perimeter of 124 feet. The diagram, which is not drawn to scale, shows the division of the deck into 3 sections. What are the dimensions of each section?
The dimension of section 1 is
15 ft by 3 ft
The dimension of section 2 is
3 ft by 3 ft
The dimension of section 3 is
10 ft by 3 ft
Option A is the correct answer.
How to solveFrom the figure given below,
We have,
Section 1: 15 ft by 3 ft
Section 2: 3 ft by 3 ft
Section 3: 10 ft by 3 ft
The perimeter of all these sections.
= 15 + 3 + 15 + 3 + 3 + 10 + 3 + 10
= 62 feet
Thus,
The dimensions of each section are:
Section 1: 15 ft by 3 ft
Section 2: 3 ft by 3 ft
Section 3: 10 ft by 3 ft
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Which of the following is a statistical question that can result in numerical data?
What is the name of your favorite pizza store?
How many hours this week did you spend on homework?
How many times did you go swimming this year?
How many pink erasers do the students in your class have?
A statistical question that can result in numerical data is How many times did you go swimming this year? So, the correct option is A).
The statistical question that can result in numerical data is "How many hours this week did you spend on homework?" and "How many times did you go swimming this year?".
These questions involve counting or measuring quantities, which can be represented using numerical data. The other two questions do not involve numerical data and therefore cannot be considered statistical questions that result in numerical data. So, the correct answer is B).
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Answer:
How many pink erasers do the students in your class have?
Find the center and radius of the circle with equation
x? +14x + y - 8y = - 16.
Rewrite the equation in the form (x - h) + (y - K) =72 by completing the square twice.
The equation of the circle in the form (x - h)² + (y - k)² = r² is (x + 7)² + 7(y - 33/7)² = 49.
Solving Equation of CircleThe equation of a circle is given by the standard form:
(x - h)² + (y - k)² = r²
where
h = center of the circle
r = radius of the circle.
To find the center and radius of the circle in the given equation:
x² + 14x + y - 8y = -16
we need to rewrite the equation in standard form
(x - h)² + (y - k)² = r²
First, let's group the x-terms and y-terms separately:
x² + 14x + y - 8y = -16
Decompose the equation on the left
x² + 14x = (x + 7)² - 49
y - 8y = -7y
Substituting the above expressions back into the original equation, we get:
(x + 7) - 49 - 7y = -16
Simplifying the equation:
(x + 7)^2 + 7y = 33
Now, we can rewrite the equation in standard form by completing the square again, this time for y:
(x + 7)² + 7(y - 33/7)² = 49
Comparing this with the standard form (x - h)² + (y - k)² = r², we have:
centre of the circle = (-7, 33/7)
radius = 7.
Learn more about equation of circle here:
https://brainly.com/question/1506955
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