The answer is:
The correct option is the option D
[tex]g=1.63\frac{m}{s^{2}}[/tex]
Why?To calculate the acceleration, we need to use the following formula that involves the given information (initial speed, final speed, and time).
We need to use the following free fall equation:
[tex]V_{f}=V_{o}-g*t[/tex]
Where:
[tex]V_{f}[/tex] is the final speed.
[tex]V_{o}[/tex] is the initial speed.
g is the acceleration due to gravity.
t is the time.
We are given the following information:
[tex]V_{f}=8.15\frac{m}{s}[/tex]
[tex]V_{o}=0\frac{m}{s}[/tex]
[tex]t=5seconds[/tex]
Then, using the formula to isolate the acceleration, we have:
[tex]V_{f}=V_{o}-g*t[/tex]
[tex]V_{f}=V_{o}-g*t\\\\g*t=V_{o}-V_{f}\\\\g=\frac{V_{o}-V_{f}}{t}[/tex]
Now, substituting we have:
[tex]g=\frac{V_{o}-V_{f}}{t}[/tex]
[tex]g=\frac{0-8.15\frac{m}{s}}{5seconds}=-1.63\frac{m}{s^{2}}[/tex]
Therefore, since we are looking for a magnitude, we have that the obtained value will be positive, so:
[tex]g=1.63\frac{m}{s^{2}}[/tex]
Hence, the correct option is the option D
[tex]g=1.63\frac{m}{s^{2}}[/tex]
Have a nice day!
Given the equation 10x + 20y + 40 = 0, Find it’s gradient and intercept
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange the given equation into this form
10x + 20y + 40 = 0 ( divide all terms by 10 to simplify )
x + 2y + 4 = 0 ( subtract x + 4 from both sides )
2y = - x - 4 ( divide all terms by 2 )
y = - [tex]\frac{1}{2}[/tex] x - 2 ← in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex] and y- intercept c = - 2
The histogram shows the number of gallons of gasoline purchased weekly by some drivers. According to the histogram, what is the greatest number of gallons the drivers purchase during the week?
A) 25 gallons
B) 29 gallons
C) 30 gallons
D) 31 gallons
Answer:
31
Step-by-step explanation:
I beleve
Answer:
It is actually C) 30 gallons
a cone has a diameter of 12 and a height of 7 what is the area
[tex]\bf \textit{surface area of a cone}\\\\ SA=\pi r\sqrt{r^2+h^2}+\pi r^2~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} \stackrel{\textit{half of diameter}}{r=6~\hfill }\\ h=7 \end{cases}\implies SA=\pi (6)\sqrt{6^2+7^2}+\pi 6^2 \\\\\\ SA=6\pi \sqrt{85}+36\pi \implies SA=6\pi (\sqrt{85}+6)\implies SA\approx 286.88[/tex]
21. How many times larger is the volume of a cone if the height is multiplied by 3?
The volume of a cone increases by a factor of 27 when its height is multiplied by 3, as the volume of a cone scales with the cube of its linear dimensions.
The question asks how many times larger the volume of a cone becomes if its height is multiplied by 3. The volume of a cone is given by the formula V = ([tex]\frac{1}{3}[/tex]1/3)πr²h, where r is the radius and h is the height. If you multiply the height by 3, the volume will increase by a factor of 3 since volume scales with the third power of the linear dimensions. Therefore, the new volume would be 3³, or 27 times the original volume. This result can also be demonstrated by the mathematical expression Vnew = ([tex]\frac{1}{3}[/tex])πr²(3h) = 27Voriginal.
Which expression is equivalent to sec2x − 1?
Answer:
tan²x
Step-by-step explanation:
Using the Pythagorean identity
sin²x + cos²x = 1
Divide all terms by cos²x
[tex]\frac{sin^2x}{cos^2x}[/tex] + [tex]\frac{cos^2x}{cos^2x}[/tex] = [tex]\frac{1}{cos^2x}[/tex], that is
tan²x + 1 = sec²x ( subtract 1 from both sides )
tan²x = sec²x - 1
Marking Brainliest!
Look at polygon ABCD and its translation
If B is 120°, what is the measure of B?
The graph of y = ax 2 + bx + c is a parabola that opens up and has a vertex at (-2, 5). What is the solution set of the related equation 0 = ax 2 + bx + c?
Answer:
The solution set is ∅
Step-by-step explanation:
The expression
y = ax^2 + bx + c
is a quadratic equation.
The vertex is located at (-2, 5) and the graph opens up, this means that it never intercepts the x-axis.
The solution set is ∅
Please see attached image
Answer:
[tex]y=\frac{-5}{4}x^{2} -5b[/tex]
Step-by-step explanation:
Assume c = 0
Using the formula for the x-coordinate of the vertex, b can be calculated in terms of a:
[tex]x=\frac{-b}{2a} \\-2=\frac{-b}{2a} \\b=4a[/tex]
B can then be substituted into the quadratic equation, along with the coordinates of the vertex, to solve a:
[tex]y=ax^{2}+bx\\y=ax^{2}+4ax\\5=a(-2)^{2}+4(-2)a\\5=4a-8a\\5=-4a\\a=\frac{5}{-4}[/tex]
AND
[tex]b=4a\\b=\frac{-5}{4} *4\\b=-5[/tex]
Substituting into the quadratic equation:
[tex]y=\frac{-5}{4}x^{2} -5b[/tex]
Because a is negative, the parabola opens up.
What is the range of the following data set?
7.7, 8.4, 9, 8, 6.9
0.8
2.1
0.4
1.4
I am pretty sure its 2.1
The range is given by: largest number in the data set - smallest number in the data set.
In our case, the largest value is 9 and the smallest value is 6.9. Therefor:
Range = 9 - 6.9 = 2.1
Thus, you have correctly identified the answer as the second choice (2.1). It is easy to get confused with much larger data sets but always keep in mind that the range is simply the largest value minus the smallest value. This makes sense since 'range' refers to the spread in something, for example if you were testing your vocal range you would find the highest note you could sing and the lowest note - this is the same here, we are just finding the range of a data set instead.
Answer:
The correct answer is second option
2.1
Step-by-step explanation:
Points to remember
Range of a data set
The range of a data set means that, the difference between the highest and lowest value of the data set.
To find the range of data set
It is given that, a data set
7.7, 8.4, 9, 8, 6.9
Highest value = 9 and lowest value = 6.9
Range = Highest value - lowest value
= 9 - 6.9 = 2.1
Therefore the correct answer is second option
What is the slope-intercept equation of the line going through (-2,5) and (1,-1)?
Answer:
y = -2x+1
Step-by-step explanation:
The slope is found by
m = (y2-y1)/(x2-x1)
= (-1-5)/(1--2)
= -6/(1+2)
= -6/3
= -2
Then we can use point slope form to make an equation
y-y1 = m(x-x1)
y-5 = -2(x--2)
y-5 = -2(x+2)
Distribute
y-5 = -2x -4
Add 5 to each side
y-5+5 = -2x-4+5
y = -2x+1
This is in point slope form
Evaluate this equation: -4(9+5)
Answer:
-56
Step-by-step explanation:
Simplify the following:
-4 (9 + 5)
9 + 5 = 14:
-414
-4×14 = -56:
Answer: -56
Given the function f(x) = x + 3 and g(x) = a + bx2. If gf(x) = 6x2 + 36x + 56,
find the value of a and of b.
Answer:
a = 2, b = 6
Step-by-step explanation:
To obtain g(f(x)) substitute x = f(x) into g(x), that is
g(x + 3) = a + b(x + 3)²
= a + b(x² + 6x + 9) = a + bx² + 6bx + 9b
For a + bx² + 6bx + 9b = 6x² + 36x + 56
Then coefficients of like terms must be equal
Comparing like terms
x² term ⇒ b = 6
constant term ⇒ a + 9b = 56 ⇒ a + 54 = 56 ⇒ a = 56 - 54 = 2
[tex]g(f(x))=a+b\cdot(x+3)^2=a+b(x^2+6x+9)=a+bx^2+6bx+9b=\\=bx^2+6bx+9b+a\\\\6x^2+36x+56=bx^2+6bx+9b+a\\b=6\\9b+a=56\\9\cdot6+a=56\\a=2\\\\\\\boxed{a=2,b=6}[/tex]
What is the solution to this system of equations?
4x + 5y = 7
3x – 2y = –12
Answer:
x = -2 and y = 3
Step-by-step explanation:
It is given that,
4x + 5y = 7 ----(1)
3x – 2y = –12 ---(2)
To find the solution of given equations
eq(1) * 3 ⇒
12x + 15y = 21 ----(3)
eq(2) * 4 ⇒
12x - 8y = -48 ---(4)
eq(3) - eq(4) ⇒
12x + 15y = 21 ----(3)
12x - 8y = -48 ---(4)
0 + 23y = 69
y = 69/23 = 3
Substitute the value of y in eq(1)
4x + 5y = 7 ----(1)
4x + 5*3 = 7
4x = 7 - 15 = -8
x = -8/4 = -2
Therefore x = -2 and y = 3
which choices are equivalent to the exponential expression below? check all that apply. (2/3)^3
A. 6/9
B. (2/3) x (2/3) x (2/3)
C. 8/27
D. 2^3 /3^3
E.16/81
F. 3 x (2/3)
Answer:
B. (2/3) x (2/3) x (2/3)
C. 8/27
D. 2^3 /3^3
Step-by-step explanation:
You need to know the following property
[tex]\LARGE \left(\frac{a}{b} \right)^c = \frac{a^c}{b^c}[/tex]
Exponent also means you're multiplying the same number for an 'n' number of times.
For example, 2^3 = 2 * 2 * 2
we multiply it by itself 3 times since 3 is the exponent.
x^y
x is the base, y is the exponent
we read it as x to the power of y
If the exponent is 2, we say it as x squared
If the exponent is 3, we say it as x cubed
The exponential expression (2/3)^3 is equivalent to options B: (2/3) x (2/3) x (2/3), C: 8/27, and D: 2^3 /3^3, because they all result in the same value.
Explanation:The exponential expression (2/3)^3 can be interpreted as multiplying 2/3 by itself three times. Here's how it works:
(2/3) x (2/3) x (2/3) = 8/27. In other words, 2 cubed (2^3 = 8) divided by 3 cubed (3^3 = 27), which equals 8/27.
So, the equivalent expressions among the given options are:
B. (2/3) x (2/3) x (2/3) C. 8/27 D. 2^3 /3^3 Learn more about Exponential Expressions here:
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if x does not equal 0, then u/x+5u/x-u/5x=
Answer:
[tex]\frac{29u}{5x}[/tex]
Step-by-step explanation:
If 'x' does not equal 0 then:
[tex]\frac{u}{x}+\frac{5u}{x}-\frac{u}{5x}[/tex] ⇒ [tex]\frac{6u}{x}-\frac{u}{5x}[/tex]
⇒ [tex]\frac{29u}{5x}[/tex]
Then, the solution is: [tex]\frac{29u}{5x}[/tex]
Find the equation of the line that passes through the pair of points. (-4,3), (-4,-2)
Answer:
x = -4
Step-by-step explanation:
Using the slope formula,
we would get (3+2)/(0),
which isn't possible. Then, we realize why. A line will not have an equation when going straight up and down. And that's what this line is doing. Both of the x values are the same, so it's only going up. So therefore, the equation is x = a constant.
This constant is -4
Hope this helps!
If 8 tablespoons of extract are mixed with distilled water to total 300 mL, what is the final concentration?
Answer:
28.2 US tablespoons
Step-by-step explanation:
If 8 tablespoons of extract are mixed with distilled water to total 300 mL, the final concentration is 28.2 US tablespoons.
8 tablespoons + 300 mL = 28.2 US tablespoons
Answer:
418.294 milliliters or 28.28 tablespoons.
Step-by-step explanation:
As we know 1 tablespoon = 14.7868 ml.
8 tablespoons = 14.7868 × 8
= 118.294 ml.
Final concentration = 300 ml + 118.294 ml
= 418.294 ml.
If you want to convert the final concentration to tablespoon
418.294 ÷ 14.7868 = 28.28 tablespoons.
The final concentration would be 418.294 milliliters or 28.28 tablespoons.
A barrel in Jim's yard contains 60 gallons of water. Water leaks out of the barrel at a rate of 1 gallon every 10 minutes. Create and graph the solution set of the equation for the gallons of water, y, remaining in the barrel in terms of the number of minutes elapsed, x.
The equation that shows the water remaining in the barrel is given by y = -(1/10)x + 60
What is a linear equation?A linear equation is in the form:
y = mx + b
Where y,x are variables, m is the rate of change and b is the initial value of y.
Let y represent the amount of water remaining after x minutes.
Jim's yard contains 60 gallons of water. Hence b = 60.
The water leaks out of the barrel at a rate of 1 gallon every 10 minutes. Hence m = -1/10. The equation is:
y = -(1/10)x + 60
The equation that shows the water remaining in the barrel is given by y = -(1/10)x + 60
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What is the factored form of 8x^2+12x
Answer:
4x(2x+3)
Step-by-step explanation:
Since the common factor of 8x^2 and 12x is 4x, put that out and separate the distributed remaining factors.
What of the following best describe XW
XW represents the altitude.
The correct answer is an option (C)
What is median?"It is a line segment that joins a vertex of triangle to the mid-point of the side that is opposite to that vertex."
What is altitude of triangle?"It is the perpendicular drawn from the vertex of the triangle to the opposite side."
What is perpendicular bisector?"A line that intersects another line segment perpendicularly and divides it into two parts of equal measurement. "
What is angle bisector?"A line drawn from the vertex of a triangle to its opposite side such that it divides the angle into two equal or congruent angles."
for given question,
XW is altitude of triangle XYZ.
Therefore the correct answer is an option (C)
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1/2x=1/4 what does x =???
Answer:
x=2
Step-by-step explanation:
First of all cross-multiply.
1/2x=1/4
(1) x (4) =1 x 2x
4=2x
After flip the equation.
2x=4
Then divide both sides by 2.
2x/2=4/2
x=2
X+y-3z=8
Slove for x
[tex]x+y-3z=8\\x=-y+3z+8[/tex]
( NEED ANSWER NOW ) How many possible outcomes exist when Louisa spins the spinner below twice?
A. 8
B. 10
C. 16
D. 64
Answer:
Step-by-step explanation:
64
There are 8 numbers on the spinner.
The first spinner could be 1 of 8 and the second spin could also be 1 of 8.
To find the total outcomes, multiply the number of outcomes of each spin by each other.
Spin 1 : 8 out comes
Spin 2: 8 outcomes
Total outcomes = 8 x 8 = 64
The answer is D. 64
Solve 2x - 1 < 7 and 5x + 3 < 3.
Step-by-step explanation:
2x-1 <7
2x <7+1
2x/2 <8/2
x <4
5x+3 <3
5x <3-3
5x <0
x <0
The solution of the given inequalities is x < 0.
What is inequality ?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
We have,
2x - 1 < 7
And
5x + 3 < 3.
Now,
Take 2x - 1 < 7 ,
Now,
Rearrange variable terms to the left side of the equation,
i.e.
2x < 7 + 1
2x < 8
We get,
x < 4
Now,
Take 5x + 3 < 3,
Now,
Rearrange variable terms to the left side of the equation,
i.e.
5x < 3 - 3
5x < 0
We get,
x < 0
So,
The intersection of the two solution will give us the solution to the system of inequalities, i.e.
x < 0 is the solution to the inequalities.
Hence, we can say that the solution of the given inequalities is x < 0.
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2/1 = 8x - 2/ 9 ! help
Answer: 5/2
Step-by-step explanation:
Cross multiply
18 = 8x - 2
20 = 8x
20/8 reduces to 5/2
Answer:
x = 5/2
Step-by-step explanation:
Step 1: Cross multiply
18 = 8x - 2
Step 2: Use the Addition Property of Equality
20 = 8x
Step 3: Use the Division Division Property of Equality
20/8 = x
Step 4: Simplify
5/2 = x
what is 16% of 90 helpppp plssss
Answer:
first off, welcome to brainly, second, your answer is 14.4
Step-by-step explanation:
What is the total surface area of the square pyramid
Answer:
The formula is a^2+2a+ sqrt a^2+h^2
Step-by-step explanation:
a=base edge
h=height
Answer:
The formula is A=a²+2a(√a^2 )/4+h²
Step-by-step explanation:
Jonathan's piggy bank contains 20 nickels, 30 quarters, and 50 one-dollar coins. He picks 20 coins from the bank at random; 12 of these coins are one-dollar coins. The theoretical probability of picking a one-dollar coin from the piggy bank before the draw is %, but the experimental probability, based on the draw, is %.
Answer:
Theoretical probability: 50/100 or 50%
Experimental probability: 12/20 or 60%
Step-by-step explanation:
Let's find out both probabilities asked.
Theoretical probability:
In the whole bank, here are 100 coins (20 nickels + 30 quarters + 50 one-dollars), among which there are 50 one-dollar coins. So the probability to pick up a one-dollar coin is 50 out 100, so...
TP = 50/100 or 50%
Experimental probability:
For the experimental probability, we know Jonathan picked out 20 coins, out of which 12 were one-dollar coins, so the probability is 12 out of 20...
EP = 12 / 20 = 60%
What number must you add to complete the square?
x2 - 18x= 29
Answer:
81
Step-by-step explanation:
Given
x² - 18x = 29
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 9)x + (- 9)² = 29 + (- 9)²
x² + 2(- 9)x + 81 = 29 + 81
(x - 9)² = 110
Answer:
81
Step-by-step explanation:
An electrical tower casts a 120-foot shadow. At the same time, a 10-foot
street sign casts a shadow of 8 feet. What is the height of the tower?
Answer:
The height of the tower is 150 ft
Step-by-step explanation:
Let the height of the tower be H feet.
The corresponding sides will then be in the same proportion.
The ratio of the shadows will be in the same proportion as the ratio of the heights.
[tex]\frac{H}{10}=\frac{120}{8}[/tex]
We multiply both sides by 10 to get:
[tex]\frac{H}{10}\times 10=\frac{120}{8}\times 10[/tex]
[tex]H=150[/tex]
Therefore, the height of the tower is 150 ft
Answer:
Height of the tower = 150 foot
Step-by-step explanation:
We need to find height of the tower with 120-foot shadow.
We have a 10-foot street sign casts a shadow of 8 feet.
[tex]\texttt{Ratio of height to shadow height =}\frac{10}{8}=\frac{5}{4}[/tex]
We have
[tex]\frac{\texttt{Height of tower}}{\texttt{Shadow height of tower}}=\frac{5}{4}\\\\\frac{\texttt{Height of tower}}{120}=\frac{5}{4}\\\\\texttt{Height of tower}=\frac{5}{4}\times 120=150feet[/tex]
Height of the tower = 150 foot
Please someone help me
Answer: Third option.
Step-by-step explanation:
When you divide fractions you can multiply the first fraction by the reciprocal of the second fraction.
To find the reciprocal of the fraction, you need to flip it. Then the original denominator will be the new numerator and the original numerator will be the new denominator.
Then, the reciprocal of the fraction [tex]\frac{1}{3}[/tex] is:
[tex]\frac{3}{1}=3[/tex]
Therefore, you can find the quotient of [tex]8[/tex]÷[tex]\frac{1}{3}[/tex] by multiplying [tex]8[/tex] by [tex]3[/tex]:
[tex]8[/tex]÷[tex]\frac{1}{3}=8*3=24[/tex]
When dividing fractions these are the steps you will take:
1. The first number in the expression stays the same (if it is a whole number then you may just place a one in the denominator and keep the numerator as the whole number like so)
[tex]\frac{8}{1}[/tex] ÷ [tex]\frac{1}{3}[/tex]
2. Change the division sign into a multiplication sign
[tex]\frac{8}{1}[/tex] × [tex]\frac{1}{3}[/tex]
3. Take the reciprocal (switch the places of numerator and denominator) of the second number in the expression
[tex]\frac{8}{1}[/tex] × [tex]\frac{3}{1}[/tex]
4. Multiply across
[tex]\frac{8*3}{1*1}[/tex]
As you can see to find the quotient of [tex]\frac{8}{1}[/tex] ÷ [tex]\frac{1}{3}[/tex] you must multiply 8 by 3 (C)
Hope this helped!
~Just a girl in love with Shawn Mendes