The time taken by the ball to hit the ground is 2.88 sec.
What is termed as the distance?Distance is defined as an object's total movement without regard for direction. Distance can be defined as how much surface an object has covered regardless of its starting or closing point.For the given question,
The total height from which the ball is thrown is 156 feet.
Let 'h' be the height after the time 't' sec.
The equation for the relation of the height and the times is;
h = 156 - 8t - 16t²
The initial velocity of the ball is 8 ft/s. .
When the ball hit the ground the height will become zero.
156 - 8t - 16t² = 0.
Divide the equation by -4.
4t² + 2t - 34 = 0
Solve the quadratic equation using the quadratic formula to find the time.
t = 2.88 sec.
Thus, the time taken by the ball to hit the ground is 2.88 sec.
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The correct question is-
A ball is thrown from a height of 156 feet with an initial downward velocity of 8 ft/s . The ball's height h (in feet) after t seconds is given by the following. h=156-8t-16t²
How long after the ball is thrown does it hit the ground?
Round your answer(s) to the nearest hundredth.
The given pair of triangles are similar. Find X and Y.
Given that the pair of triangles are similar, then their corresponding sides are in proportion, this means that:
[tex]\frac{\text{longer leg of the triangle on the left}}{\text{shorter leg of the triangle on the left}}=\frac{\text{longer leg of the triangle on the right}}{\text{shorter leg of the triangle on the right}}[/tex]Substituting with the information of the diagram:
[tex]\frac{27}{x}=\frac{x}{9}[/tex]Cross multiplying:
[tex]\begin{gathered} 27\cdot9=x\cdot x \\ 243=x^2 \\ \sqrt[]{243}=x \\ 15.58\approx x \end{gathered}[/tex]Considering the triangle on the left, and applying the Pythagorean theorem with c = y (the hypotenuse), a = 27, and b = x (the legs), we get:
[tex]\begin{gathered} c^2=a^2+b^2 \\ y^2=27^2+x^2 \\ y^2=729+243 \\ y^2=972 \\ y=\sqrt[]{972} \\ y\approx31.18 \end{gathered}[/tex]
Based on the diagram below, which statement is true? b a C 110° 115° d 60° e 120° Oь || с Oa || ь alle Odlle
we have that
Verify each statement
1) b parallel to c
If b is parallel to c then
115+60=180
175=180 ----> is not true
2) a parallel to b
If a is parallel to b
then
110+60=180
170=180 -----> is not true
3) a parallel to c
If a is parallel to c
then
110=115 -----> is not true
4) d parallel to e
If d is parallel to e
then
60+120=180
180=180 -----> is true
therefore
the answer is
d parallel to ePart 2
In this problem
If n and m are parallel
then
the interior angles of the triangle are
30, 80 and x degrees
so
30+80+x=180
110+x=180
x=180-110
x=70 degreesidentify whether each phrase is an expression equation or quantity
the last one of the right column is a inequality, because it has the sign "<"
the second one of the right column in an expression because it doen't have the sign "="
the first one of the right column is a equation because it has the sign "=".
Consider the following inequality:x < -2Step 2 of 2: What type of interval does the following inequality represent?
You have the following inequality:
x≤2
the prevous inequality can be written in interval notation as follow:
(-oo, 2]
then, you can conclude that the inequality is represented by a half-open interval (this happens when you have an open parentheses and a close parentheses)
Oaks Hardware purchases an extension ladder list priced at $120. It is available at a 15% discount. What is the available price?
A 15% discount means that the retail price is 85% of the original price.
To calculate said retail price, we'll use a rule of three:
Thereby,
[tex]x=\frac{120\cdot85}{100}\rightarrow x=102[/tex]Therefore, we can conclude that the available price is $102
1. Are these ratios equivalent? 8:7 and 4:2
EXPLANATION
The answer is no, because 8:7 and 4:2 are different relationships.
Solve 39 - 5 = 13 for q.q=
We are given the following equation:
[tex]3q-5=13[/tex]We are asked to solve for "q". To do that, we will first add "5" on both sides, like this:
[tex]\begin{gathered} 3q-5+5=13+5 \\ 3q=18 \end{gathered}[/tex]Now we will divide by 3 on both sides, like this:
[tex]\begin{gathered} \frac{3q}{3}=\frac{18}{3} \\ q=6 \end{gathered}[/tex]Therefore, the value of q is 6.
ok, remember that the answer will be available in your profile.
four tenths squared minus 19 plus the quantity negative 5 divided by the absolute value of 6.7 minus 9.2 end quantity times 3.81
The expression has a value of -26.46 when evaluated
How to evaluate the expression?From the question, the expression is given as
four tenths squared minus 19 plus the quantity negative 5.......
Rewrite the expression properly as
0.4² - 19 + (-5)/|6.7 - 9.2| * 3.81
Start by evaluating the exponent
So, we have
0.16 - 19 + (-5)/|6.7 - 9.2| * 3.81
Remove the expression in the bracket
0.16 - 19 - 5/|6.7 - 9.2| * 3.81
So, we have
0.16 - 19 - 5/|-2.5| * 3.81
Remove the absolute bracket
0.16 - 19 - 5/2.5 * 3.81
Divide
0.16 - 19 - 2 * 3.81
Evaluate the products
0.16 - 19 - 7.62
So, we have
-26.46
Hence, the value of the expressions is -26.46
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The function, f. is drawn on the accompanying set of axes. On the same set of axes, sketch the graph of f-?, the inverse of f
We are given the following graph:
The inverse of the graph is shown below:
24. How many gallons of ethanol are in a 100 gal mixture that is 10%
ethanol?
By working with percentages, we will see that there are 10 gallons of ethanol in the mixture.
How many gallons of ethanol are in the mixture?We know that we have a mixture with a volume of 100 gallons, and 10% of that mixture is ethanol, so we just need to find the 10% of 100 gallons.
To work with percentages, we will use the equation:
Volume of ethanol = total volume*ratio of ethanol.
V = 100gal*(10%/100%)
V = 100gal*0.10 = 10 gal
There are 10 gallons in the mixture.
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alex was late on his property tax payment to the county. he owed $6,915 and paid the tax 9 months late. the county charges a penalty of 5% simple interest. find the amount of the penalty. (round to the nearest cent as needed)
We have to use the simple interest formula.
[tex]A=P(1+rt)[/tex]Replacing the given information, we have.
[tex]\begin{gathered} A=6,915(1+0.05\cdot\frac{9}{12}) \\ A=6,915(1.0375) \\ A=7,174.31 \end{gathered}[/tex]The final amount is $7,174.31, where the penalty is $259.31.second number when the list is sorted from greatest to least
5.2% = 0.052
1/7 = 0.14
-11/5 = -2.2
From the greatest to least:
[tex]0.14>0.052>-0.8>-2.2[/tex]The second number is: 5.2%
Answer:
5.2%
15. I need help on this question. How do you do it?
Solution:
Given the expression:
[tex]-5^2[/tex]This expression is evaluated as
[tex]\begin{gathered} -5\text{ multiplied in 2 places} \\ \Rightarrow-5\times-5 \\ =25 \end{gathered}[/tex]Hence,
[tex]-5^2[/tex]is evaluated to be 25
33Select the correct answer from each drop-down menu.A75°B40°AoIn the figure, line segment AB is parallel to line segment CD.СDdegreesThe measure of angle Cisdegrees, and the measure of angles Dis>254075ResetNext
Answer:
Angle C = 40 degrees
angle D = 75 degrees
Explanation:
From the information given,
Angle A = 75 degrees
Angle B = 40 degrees
AB is parallel to CD. This means that AD and BC are transversals.
Angles A and D have similar positions but they are opposite sides of the transversal. This means that they are alternate angles. Alternate angles are congruent. Thus,
angle D = 75 degrees
Angles B and C have similar positions but they are opposite sides of the transversal. This means that they are alternate angles. Alternate angles are congruent. Thus,
Angle C = 40 degrees
If a line passes thru the points (5,5) and (9,3) the slope of this line is
The initial point is (5,5)
the final point is (9, 3)
The formula for determining slope is expressed as
slope = (y2 - y1)/(x2 - x1)
y2 and y1 are the final and initial y values
x2 and x1 are the final and initial x values
From the information given,
x1 = 5, y1 = 5
x2 = 9, y2 = 3
Slope = (3 - 5)/(9 - 5) = - 2/4
Slope = - 1/2
the price of a gallon of unleaded gas has risen to $2.92 today. yesterday's price was $2.85. find the percentage increase. round to the nearest 10th of a percent
Given:
[tex]\begin{gathered} P_{\text{today}}=2.92,P_{today}=Price\text{ of a gallon of unleaded gas today} \\ P_{\text{yesterday}}=2.85, \\ P_{yesterday}=Price\text{ of a gallon of unleaded gas today} \end{gathered}[/tex]To Determine: The percentage increase round to the nearest 1oth of a percent
The formula for percentage increase is given below:
[tex]\begin{gathered} P_{in\text{crease}}=\frac{increase}{P_{\text{initial}}}\times100\% \\ In\text{crease}=P_{final}-P_{in\text{itial}} \end{gathered}[/tex]Substitute the given into the formula
[tex]\begin{gathered} P_{\text{yesterday}}=P_{i\text{nitial}}=2.85 \\ P_{\text{today}}=P_{\text{final}}=2.92 \\ \text{Increase}=2.92-2.85=0.07 \end{gathered}[/tex][tex]\begin{gathered} P_{in\text{crease}}=\frac{increase}{P_{\text{initial}}}\times100\% \\ P_{in\text{crease}}=\frac{0.07}{2.85}\times100\% \\ P_{in\text{crease}}=0.02456\times100\% \\ P_{in\text{crease}}=2.456\% \\ P_{in\text{crease}}\approx2.5\%(nearest\text{ 10th)} \end{gathered}[/tex]Hence, the percentage increase to the nearest 10th of a percent is 2.5%
When an integer is subtracted from 4 times the next consecutive odd integer, the difference is 23. Find the value of the lesser integer.
The value of the lesser integer is 5.
According to the question,
We have the following information:
When an integer is subtracted from 4 times the next consecutive odd integer, the difference is 23.
Let's take the lesser integer to be x.
So, the next consecutive odd integer is (x+2).
Now, we have:
4(x+2)-x = 23
4x+8-x = 23
3x+8 =23
3x = 23-8
3x = 15
x = 15/3
(3 was in multiplication on the left hand side. So, it is in the division on the right hand side.)
x = 5
Hence, the lesser integer in the given situation is 5.
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Please help asap will give Brainly!!!
The following completes the proof: D. The Alternate Interior Angles Theorem shows that the angles BAC and DCA are congruent.
The Alternate Interior Angles Theorem: What is it?
According to the alternate interior angles theorem, when a transversal cuts over two (2) parallel lines, the alternate interior angles that are created are congruent.
We can infer and logically derive from the Alternate Interior Angles Theorem that the sentence that correctly concludes the proof is that angle BAC and angle DCA are congruent.
Segment AB is parallel to segment DC, while segment BC is parallel to segment AD, according to the information provided. Create the diagonals A and C using a straight edge. By virtue of the Reflexive Property of Equality, it is congruent to itself.
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Identify the function rule from the values in the table.
we are given a table of inputs and ouputs of a function. We notice that each output is obtained by multiplying the input by -4:
[tex]\begin{gathered} (-2)(-4)=8 \\ (0)(-4)=0 \\ (1)(-4)=-4 \\ (3)(-4)=-12 \end{gathered}[/tex]Therefore, the right answer is A.
What is the answer to 6x + =5
Answer:
x = 5/6 or x = 0.83
Step-by-step explanation:
6x + =5
6x + 0 = 5
6x = 5
6x/6 = 5/6
x = 5/6 or x = 0.83
? QuestionWhat is the equation of the quadratic function represented by this table?х5678910f(x)-4585-4-19HolaType the correct answer in each box. Use numerals instead of words.f(x) =(x -12 +
To determine the equation of the quadratic equation, which is a parabola, we substitute the coordinates of the vertex of the parabola (h,k) into the general equation.
[tex]y=a(x-h)^2+k[/tex]From the given, notice that the only value of f(x) that does not repeat is 8. This means that the vertex is at (7,8).
[tex](h,k)=(7,8)[/tex]Thus, we only need to obtain the value of a.
Substitute the coordinate of a point (x,y) into the equation and the vertex as well. In this case, let us use the first given point, (5,-4).
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ (5,-4)\rightarrow-4=a(5-7)^2+8 \end{gathered}[/tex]Simplify the obtained equation.
[tex]\begin{gathered} (5,-4) \\ -4=a\mleft(5-7\mright)^2+8 \\ -4=a\mleft(-2\mright)^2+8 \\ -4=a(4)+8 \\ -4-8=4a \\ -12=4a \\ a=\frac{-12}{4} \\ a=-3 \end{gathered}[/tex]Now that we have the value of a, substitute the coordinates of the obtained vertex and the value of a into the equation of the quadratic equation.
[tex]\begin{gathered} y=a(x-h)^2+k \\ y=-3(x-7)^2+8 \end{gathered}[/tex]To check, the graph of the given function is as follows:
Therefore, the equation of the quadratic equation is y=-3(x-7)²+8.
A saw blade is rotating at 2700 revolutions per minute. Find theangular speed in radians per second.
The rule of the angular speed is
[tex]\omega=No\text{ of revolution per min }\times\frac{2\pi}{60}[/tex]Since the number of revolutions is 2700 per min, then
[tex]\begin{gathered} \omega=2700\times\frac{2\pi}{60} \\ \\ \omega=90\pi\text{ rad per sec} \end{gathered}[/tex]The answer is 90pi rad per second
The answer is the 3rd answer
A 90% confidence interval for a proportion is found to be (0.52, 0.58). What isthe sample proportion?
A 90% confidence interval for a proportion is given as (0.52,0.58).
It is required to find the sample proportion.
Recall that for confidence interval (x,y), the sample proportion is the midpoint:
[tex]c=\frac{x+y}{2}[/tex]Substitute x=0.52 and y=0.58 into the equation:
[tex]c=\frac{0.52+0.58}{2}=\frac{1.1}{2}=0.55[/tex]The answer is C.
I have the answers for 1 and 2 3. Use your answers from # 1 and # 2 to find the length of each arc between gondola cars . Use 3.14 for and round to the nearest hundredth . You must write out all the numbers you are multiplying together meaning show your work for full credit . ( 5 points ) Central angle = 8°Radius = 95 ft
The length of an arc = 13.26 ft
Explanation:The length of an arc is given by the formula:
[tex]\begin{gathered} l=\frac{\theta}{360}\times2\pi r \\ \end{gathered}[/tex]Substitute θ = 8°, r = 95 ft, and π = 3.14 into the formula
[tex]\begin{gathered} l=\frac{8}{360}\times2\times3.14\times95 \\ \\ l=13.26\text{ ft} \end{gathered}[/tex]The length of an arc = 13.26 ft
I need help with this practice problem The subject is trigonometry
SOLUTION
The range of the function is given as:
[tex](-\infty,-9\rbrack\cup\lbrack5,\infty[/tex]The asymptote of the function is at points
[tex]x=0,x=2\pi[/tex]The function is shown in the graph below
Therefore, the equation of the session is
[tex]f(x)=7\csc (\frac{x}{2})-2[/tex]the product of (2-x)and (1-x)is equal to x^2-3x+2
So the product of (2-x) and (1-x) is equal to x^2 - 3x + 2
a carpentar has 16 1/2m of wood he cuts the wood into peices that are each 2 3/4m long PLSSSSS HURRY!!!!!!!!
The most appropriate choice for fraction will be given by
6 pieces of wood are cut by the carpenter
What is a fraction?
Suppose there is a collection of objects and some part of the objects are taken from the collection. The part which has been taken is called fraction. In other words, part of a whole is called fraction.
The upper part of the fraction is called numerator and the lower part of the fraction is called denominator.
Total length of wood = [tex]16\frac{1}{2}[/tex] m
= [tex]\frac{33}{2}[/tex] m
Length of one piece of a wood = [tex]2\frac{3}{4}[/tex] m = [tex]\frac{11}{4}[/tex]
Number of pieces of wood cut by carpenter = [tex]\frac{33}{2}[/tex] ÷ [tex]\frac{11}{4}[/tex]
= [tex]\frac{33}{2}[/tex] [tex]\times \frac{4}{11}[/tex]
= 6
6 pieces of wood are cut by the carpenter
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The table below shows the average price of a Miami Marlins baseball ticket between 2006 and 2021.
Ticket price as a function of time. If you write the number [tex]2040[/tex] where you see [tex]x[/tex] in this function and take the value where you see [tex]y[/tex], you will reach the correct answer.
[tex]y=1.83(2040)-2225.5[/tex][tex]y=1507.7[/tex]given the function r(t)=t^2, solve for r(t)=4
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
r(t)=t^2
r(t)=4
t = ?
Step 02:
r(t)=4
t ² = 4
t = √4
t = 2
The answer is:
t = 2
Answer: t=2
Step-by-step explanation:
Because we know that for some value of t, r(t)= 4, and for ALL values of t, r(t)= t^2, then we know for some value of t, that t^2 = 4.
Based off of this information, we can take the square root of both sides, resulting in this equation.
t = [tex]\sqrt{4}[/tex]
This can be simplified.
t=2
The graph above shows the graph of the cost in blue and revenue in red function for a company that manufactures and sells small radios.ABCD
a) 500 radios
b) Going out = $5000
Coming in = $5000
c) P(x) = 6x - 3000
d) Profit of $900
Explanation:a) To get the number of radios that must be produced to break even, we will equate the cost function and the revenue function:
[tex]\begin{gathered} \cos t\text{ function:} \\ C(x)\text{ = 3000 + 4x} \\ \text{revenue function:} \\ R(x)\text{ = 10x} \\ \\ \text{Break even:} \\ C(x)\text{ = R(x) } \\ \text{3000 + 4x = 10x} \end{gathered}[/tex]collect like terms:
[tex]\begin{gathered} 3000\text{ = 10x - 4x} \\ 3000\text{ = 6x} \\ \text{divide both sides by 6:} \\ x\text{ = 3000/6} \\ x\text{ = 500} \\ \text{If x represents number of radios produced,} \\ \text{Then to break even, 500 radios will have to be produced } \end{gathered}[/tex]b) The dollar amount going in and coming out is gotten by replacing the value of x in both function with 500:
[tex]\begin{gathered} \text{when x = }500 \\ C(x)\text{ = 3000 + 4x = 3000 + 4}(500) \\ C(x)\text{ = }5000 \\ \text{Amount going out = \$5000} \\ \text{when x = 500} \\ R(x)\text{ = 10x = 10(500)} \\ R(x)\text{ = 5000} \\ \text{Amount coming in = \$5000} \end{gathered}[/tex]c) Profit = Revenue - Cost
[tex]\begin{gathered} \text{Profit function, }P(x)\text{= R(x) - C(x)} \\ P(x)\text{ = 10x - (3000 + 4x)} \\ P(x)\text{ = 10x - 3000 - 4x} \\ P(x)\text{ = 6x - 3000} \end{gathered}[/tex]d) To find the profit when the number of radios is 650
[tex]\begin{gathered} \text{Profit function: P(x) = 6x - 3000} \\ \text{for 650 radios, x = 650} \\ P(650)\text{ = 6(650) - 3000} \\ P(650)\text{ = 900} \\ \text{The company will make a profit of \$900} \end{gathered}[/tex]