Answer:
A. They are the same.
Step-by-step explanation:
The sine of any acute angle is equal to its cosine.
What constant acceleration is required to increase the speed of a car from 26 mi/h to 51 mi/h in 3 seconds? (Round your answer to two decimal places.) ft/s2
Answer: 12.22 ft/sec²
Step-by-step explanation:
An increase from 26 to 51 is an increase of 51 - 26 = 25 mi/hr
We need to do this in 3 seconds --> 25 mi/hr ÷ 3 sec
Note the following conversion: 1 mile = 5280 ft
[tex]\dfrac{25\ miles}{hr}\times \dfrac{1}{3\ sec}\times \dfrac{5280\ ft}{1\ mile}\times \dfrac{1\ hr}{60\ min}\times \dfrac{1\ min}{60\ sec} \\\\\\=\dfrac{5280(25)\ ft}{3(60)(60)\ sec^2}\\\\\\=\large\boxed{12.22\ ft\slash sec^2}[/tex]
The constant acceleration that is required to increase the speed of a car from 26 mi/h to 51 mi/h in 3 seconds is 12.22 ft/s².
What is acceleration?Acceleration can be defined as the rate of change of the velocity of an object with respect to time.
[tex]\rm Acceleration=\dfrac{Final\ velocity- Initial\ Velocity}{Time}[/tex]
As the velocity that is given to us is 51 miles/hour and 26 miles/hour, therefore, we first need to convert the units of the velocity in order to get the acceleration in ft/s².
[tex]\rm Final\ velocity= 51\ mi/hr = \dfrac{51\times 5280}{3600} = 74.8\ m\s^2[/tex]
[tex]\rm Initial\ velocity= 26\ mi/hr = \dfrac{26\times 5280}{3600} = 38.134\ m\s^2[/tex]
Now, acceleration is written as the ratio of the difference between the velocity and the time needed to increase or decrease the velocity of the object.
[tex]\rm Acceleration=\dfrac{Final\ velocity- Initial\ Velocity}{Time}[/tex]
Substituting the values we will get,
[tex]\rm Acceleration = \dfrac{74.8-38.134}{3} = 12.22\ \ ft/s^2[/tex]
Hence, the constant acceleration that is required to increase the speed of a car from 26 mi/h to 51 mi/h in 3 seconds is 12.22 ft/s².
Learn more about Acceleration:
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This is a ratio question, is this correct?
Answer:
C
Step-by-step explanation:
Before expressing as a ratio the quantities must have the same denomination
$2 = 200 cents, thus
40 cents : $2
= 40 cents : 200 cents ( divide both parts by 40 )
= 1 : 5 → C
does not
Ether.
1-36. If y varies directly with x and y is 12 when x is 4, then
what is y when x is 8?
what is when x is 3?
what is x when y is 6?
a.
b.
n.
C.
Answer:
Step-by-step explanation:
Hello!
Y varies directly with X, meaning that every time X increases/ decreases, the value of Y is modified.
If Y=12 when X=4 then you can say that Y varies 3 times every time X varies 1 unit
12= 4*z
z=12/4= 3
So Y= 3x
With this in mind:
1) x= 8
Y= 3*8= 24
2) x= 3
Y= 3*3= 9
3) Y= 6
Y= 3x
x=Y/3= 6/3= 1
I hope this helps!
Here is the histogram of a data distribution. All class widths are 1.
Which of the following numbers is closest to the mean of this distribution?
A.6
B.7
C.3
D.4
E.5
=======================================================
Explanation:
The distribution is perfectly symmetrical about the center 6. Notice how the left side is a mirror copy of the right side, due to the heights being the same. Because of this, the mean, median and mode are all the same value and that is 6. The mode is equal to 6 as this is the most frequent value.
The longer way to do this problem is to add up each value shown. We have four copies of '2', six copies of '3', and so on. The total sum you would get is 372. Divide this over 62 because there are 62 smaller green squares. The final result is the mean of 6.
The number closest to the mean of the given distribution is 6. Therefore, option A is the correct answer.
What is mean?In statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations).
From the given histogram,
Number Frequency
2 4
3 6
4 7
5 9
6 10
7 9
8 7
9 6
10 4
Here, the mean = [2(4)+3(6)+4(7)+5(9)+6(10)+7(9)+8(7)+9(6)+10(4)]/[4+6+7+9+10+9+7+6+4]
= [8+18+28+45+60+63+56+54+40]/62
= 372/62
= 6
Therefore, option A is the correct answer.
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Find the area in square centimeters of the composite shape shown
below. Enter only a number as your answer.
A
E
13 cm
D
11 cm
7 cm
B
18 cm
C
Answer:
73cm²
Step-by-step explanation:
Area of rectangle=½ length×width
=½×18×7
=63cm²
Area of triangle=½b×h
base=18-13= 5cm
height=11-7 =4cm
½×b×h
½×5×4
=10cm²
Area of total=63+10
73cm²
Answer: 73c2
Step-by-step explanation:
I'll mark you brainlyist, if I know how to do it, if you help me out real quick thx
Answer:
4 in
Step-by-step explanation:
as you see from the first rectangle it has been reduced 3 times of length
so the breadth also should be reduced 3 times
Answer:
x = 4
Step-by-step explanation:
the simplest way to do that is to divide
12 / 18 = 2 / 3
then we move to the another square:
x / 6 = 2 / 3
x = 6 x 2 / 3
x = 4
.. ..
A chemist is mixing two solutions, solution A and solution B Solution A is 15% water and solution Bis 20% water. She already has a
beaker with 10mL of solution A in it. How many mL of solution B must be added to the beaker in order to create a mixture that is 18%
water?
Answer:
15 mL of the solution with 20% water will be needed.
Step-by-step explanation:
Use the inverse relationship
10 mL * (18-15)% = x mL * (20-18)%
x = 10 mL * (3/2) = 15 mL
Answer: 15mL
Step-by-step explanation:
Create a table. Multiply across and add down. The bottom row (Mixture) creates the equation.
Qty × % = Total
Solution A 10 15% → 0.15 10(0.15) = 1.5
Solution B x 20% → 0.20 x(0.20) = 0.20x
Mixture 10 + x × 18% → 0.18 = 1.5 + 0.20x
(10 + x)(0.18) = 1.5 + 0.20x
1.8 + 0.18x = 1.5 + 0.20x
1.8 = 1.5 + 0.02x
0.3 = 0.02x
15 = x
A triangle has side lengths of 13, 9, and 5. Is the triangle a right triangle? Explain.
2Points
Use complete sentences in your explanation.
Hint: Pythagorean Theorem: a^2+ b^2 = c^2
Answer: This triangle is not a right triangle
Step-by-step explanation:
In a right triangle, the hypotenuse(c) is always the longest side and a and b are the shorter sides. Thus, 5^2+9^2=13^2. Simplify this to get 25+81=169, then 106=169. Because 106 does not equal 169, it is not a right triangle.
Hope it helps <3
Which choice is equivalent to the expression below?
V-64
Explanation:
By definition, i = sqrt(-1)
Which means,
sqrt(-64) = sqrt(-1*64)
sqrt(-64) = sqrt(-1)*sqrt(64)
sqrt(-64) = i*sqrt(8^2)
sqrt(-64) = i*8
sqrt(-64) = 8i
On the second line, I used the rule sqrt(x*y) = sqrt(x)*sqrt(y). The fourth line used the rule sqrt(x^2) = x when x is nonnegative.
Answer:
Click 8i for Correct Answer
Step-by-step explanation:
For each of the following system of linear equations, state the number of solutions without solving the system. a) -x+3y=9, -4x+12y=12 b) 2x-y-4=0,6x=3y+12
Answer:
a) ONE SOLUTIONb) INFINITE SYSTEM OF SOLUTIONSStep-by-step explanation:
Given the system of equations;
a) x+3y=9
-4x+12y=12
This equation is a linear simultaneous equation with 2 equations and two unknown values. When the number of equations given is equal to the number of unknown variables, this means that the solution sets of the equations are unique and real and will provide us with just one solution.
b) For the system of linear equation
2x-y-4=0 .... *3
6x=3y+12 ... *1
First lets multiply equation 1 by 3, om multiplying by 3 we will have;
6x-3y-12 = 0
6x-3y = 0+12
6x-3y = 12
Rearranging equation 2 will give;
6x - 3y = 12
It is seen that both equation ate the same. This means that what we have is one equation with two unknowns. For a system of equation with one equation and two unknowns, there will be infinite number of solutions after solving the equation. Hence, the number of solutions for this system of equation is INFINITE
i attached the question in the image below
Answer:
45°
Step-by-step explanation:
[tex]tan^{-1}(1)[/tex] = 45°
Answer:
[tex]\huge\boxed{\theta=45^o\ \vee\ \theta=225^o}[/tex]
Step-by-step explanation:
[tex]\tan\theta=1[/tex]
[tex]\bold{METHOD\ 1}\\\\\text{Use the table in the attachment}\\\\\tan45^o=1\to\theta=45^o\ \vee\ \theta=45^o+180^o=225^o\\\\\bold{METHOD\ 2}\\\\\tan\theta=1\to\tan^{-1}1=\theta\to\theta=45^o\ \vee\ \theta=225^o[/tex]
PLSSSS HELPPP. The price of a tennis racquet is inversely proportional to its weight. If a 20 oz. racquet cost $30.00, what would a 25 oz. racquet cost?
Answer:
$24 will be the cost of tennis racquet with weight 25 oz.
Step-by-step explanation:
Given that Price of racquet is inversely proportional to its weight.
i.e.
[tex]Price \propto \dfrac{1}{Weight}[/tex]
We can replace the proportional sign with a constant of proportionality.
[tex]Price = \dfrac{C}{Weight}[/tex]
Where C is a constant named as constant of proportionality.
Given that cost of 20 oz. racquet is $30.00
Putting both the values :
[tex]30 = \dfrac{C}{20}\\\Rightarrow C = 600[/tex]
So, the equation becomes:
[tex]Price = \dfrac{600}{Weight}[/tex]
Now, we have to find the price of 25 oz. racquet.
Putting Weight = 25 oz and finding Price:
[tex]Price = \dfrac{600}{25}\\\Rightarrow Price = \$24[/tex]
So, $24 will be the cost of tennis racquet with weight 25 oz.
How many more unit tiles must be added to the function
f(x)=x2-6x+1 in order to complete the square?
-X
--X
0 0
Answer:
8 more unit of tiles
Step-by-step explanation:
The function is given as;
f(x) = x² - 6x + 1
Now, we want to add more unit tiles to complete the square.
The given function(f(x)) is of the order 2 due to the highest power of 2 attached to x, but the side of the square will be of the order 1.
Now, Let's make a general order 1 expression ax + b to be the side of the square.
From the function forming the square after adding some p unit tiles, we have;
f(x) + p = (side of square)²
Thus;
x² - 6x + 1 + p = (ax + b)²
x² - 6x + 1 + p = a²x² + 2abx + b²
Comparing both sides of the equation, we have;
a² = 1
2ab = 6
b² = 1 + p
From a² = 1, a = 1
From 2ab = 6,putting 1 for a, we have;
2(1)b = 6
b = 6/2
b = 3
From b² = 1 + p
Putting 3 for b, we have;
3² = 1 + p
9 = 1 + p
9 - 1 = p
p = 8
Thus, 8 more unit of tiles are required to complete the square.
Select the correct answer. Compare the two functions.
-
Which statement is true?
A. As x increases, the rate of change of f(x) exceeds the rate of change of g(x).
B. As x increases, the rate of change of g(x) exceeds the rate of change of f(x).
C. At x = 2, the rate of change of g(x) is equal to the rate of change of f(x).
D. On every interval of x, the rate of change of f(x) exceeds the rate of change of g(x).
In other words, f(x) grows faster after a certain point. This is true when comparing any exponential curve to a linear one.
Choice B is false as it contradicts choice A.
Choice C is false as the tables show the function outputs are equal at x = 2, not the rates of change
Choice D is false because there are infinitely many intervals where f(x) grows slower compared to g(x). That's why I mentioned the "after a certain point" portion.
Answer:
A
Step-by-step explanation:
The sum of two even consecutive integers is −46. If the smaller integer is divided by 4 and the larger integer is increased by 11, what is the product of the two resulting integers? PLEASE HELP!!!
Answer is 66.
I hope it will help you:)
Answer:
= 66
Step-by-step explanation:
The two integers are -22 and -24, because they are both even and consecutive, and adding them equals -46.
-24 divided by 4 is -6, and -22 plus 11 is -11
Now all we have to do is find the product (multiply -11 and -6)
And this gives us the answer: 66
Marta Fuentes had a balance of $1,200.50 in her checking account. The bank issued her a credit of
$505 and charged her $12 for new checks. Thee will be no outstanding checks or deposits. What
should her checkbook balance be?
Answer:
$683.50Step-by-step explanation:
Initial balance of Marta Fuentes = $1200.50
Charge made by her bank;
Credit of $505 and Charge on new checks is $12.
Total charge incurred = $505+$12
Total charge incurred = $517
Since there will be no outstanding checks or deposit, her checkbook balance will be the difference between the initial balance and amount charged by the bank.
Checkbook balance = $1200.50 - $517
Checkbook balance = $683.50
Hence her checkbook balance should be $683.50
True or False? All equiangular triangles are similar.
Answer:
True
Step-by-step explanation:
All equiangular triangles are similar.
The formula for working out the cost of hiring a canoe is : cost=£15+6* number of hours. Megan paid £27 to hire a canoe. How long did she hire the canoe for
Answer:
Megan hired the canoe for 2 hours
Step-by-step explanation:
Given:
Cost(h) = 6h+15 = 27
Solution
6h+15 = 27
6h = 27-15 = 12
h = 2
HELP ME ASAP! BRAINLIEST UP FOR GRABS
Answer:
-5 ≤ x≤ 3
Step-by-step explanation:
The domain is the values for x
x starts and -5 and includes -5 since the circle is closed
and goes to 3 and includes 3 since the circle is closed
-5 ≤ x≤ 3
Answer:
first option
Step-by-step explanation:
The domain are the values from the x- axis that can be input into the function.
The closed circles at the ends of the graph indicate that x can equal these values.
left side value of x = - 5 and right hand value of x = 3, thus
domain is - 5 ≤ x ≤ 3
I been stuck on this question for the longest please help
Answer: C. [tex]\sqrt{9} * \sqrt{4}[/tex]
Step-by-step explanation:
There is a square root rule that states [tex]\sqrt{x*y} = \sqrt{x} * \sqrt{y} \\[/tex]
We can apply this rule to this problem.
Given [tex]\sqrt{9*4}[/tex]
We can use the rule to make it equal to [tex]\sqrt{9} * \sqrt{4}[/tex]
This is answer choice C.
Answer: c
Step-by-step explanation: 9*4=36 36* 36 = 1296
9 * 9 = 81 4 * 4 = 16 81 * 16 = 1296 hope this helps
: Resolver el sistema de ecuaciones por el método de reducción. -x + 3y = 6 x + y = 2
Answer:
[tex]x=0\\y=2[/tex]
Step-by-step explanation:
El método de reducción también llamado Suma y Resta, consiste en multiplicar una o ambas ecuaciones de tal manera que los coeficientes de una de las incógnitas sean iguales y de signo contrario, de tal forma que se eliminen al sumar las ecuaciones.
Nuestras ecuaciones son:
[tex]-x+3y=6\\x+y=2[/tex]
En este caso podemos observar que x y -x son iguales y de signo contrario así que no tendremos que multiplicar y podemos sumar ambas ecuaciones.
Al sumarlas tenemos que:
[tex]4y=8\\y=2[/tex]
Ahora sustituímos el valor que encontramos de y en la segunda ecuación para poder obtener el valor de x.
[tex]x+y=2\\x+2=2\\x=2-2\\x=0[/tex]
Por lo tanto, x = 0 y y = 2
the product of two rational number is -10/9. If one of the number is -5/27 ,find the other.
Answer:
Step-by-step explanation:
Let the unknown number = x
[tex]x *\frac{-5}{27}=\frac{-10}{9}[/tex]
x = [tex]\frac{-10}{9}[/tex] ÷ [tex]\frac{-5}{27}[/tex]
[tex]x=\frac{-10}{9}*\frac{-27}{5}\\\\\\x=-2* - 3\\x = 6[/tex]
Please answer it now in two minutes
Answer:
[tex]2\sqrt{33}[/tex].
Step-by-step explanation:
This triangle is a 30-60-90 triangle. That means that the hypotenuse is double the length of the smaller side.
Since the smaller side measures [tex]\sqrt{33}[/tex], the hypotenuse is [tex]2\sqrt{33}[/tex].
Hope this helps!
Which set of ordered pairs represents a function?
{(-3,4), (-7,2), (-7,-4),(-9, -5)}
{(-2,4), (0,5),(-9,9),(-9,7)}
{(-4,-6), (-7, -5),(-4,-7), (1,1)}
{(5,-2), (-8,-6),(4, -2), (-6,3)}
Answer:
The correct answer is D.
Step-by-step explanation:
A function is when an input value has only one output value.
It cannot be A, because -7 produces both 2 and -4.
It cannot be B, because -9 produces both 9 and 7.
It cannot be C, because -4 produces both -6 and -7.
Therefore, it has to be D.
Find the equation of the line.
Answer:
y = [tex]-\frac{1}{3}x+5[/tex]
Step-by-step explanation:
Let the equation of the given line is,
y = mx + b
where 'm' = slope of the line
b = y-intercept of the line
Since slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is represented by,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
If the points are (0, 5) and (-3, 6),
Slope of the line 'm' = [tex]\frac{6-5}{-3-0}[/tex]
= [tex]-\frac{1}{3}[/tex]
y-intercept of the line 'b' = 5
Therefore, equation of the given line will be,
y = [tex]-\frac{1}{3}x+5[/tex]
PLEASE HELP! Manufacturers often alter different packages to save money and to grab customers attention. Explain using an example, how changes in the dimensions of common geometric shapes will affect the volume of the following shapes: prisms, cylinders, cones and spheres.
Answer:
An example of a prism could be a an amazon box to represent a rectangular prism. As the height, length, or width of the box increases, the volume increases allowing more items to fit within the box.
An example of a cone would be an ice cream cone. As the height or the radius of the cone increases, the more volume the cone can hold, meaning more ice cream for you.
An example of a cylinder could be a cup. As the height or the radius of the cup increases, the larger the volume. More drink for you.
An example of a sphere would be a soccer ball. As the radius increases, the volume of the ball increases. Hence, larger soccer balls have a bigger radius than smaller soccer balls. This allows for different varients of the ball to be created (i.e., youth, highschool, college, pro).
Note, the volume can also be decreased by simply shrinking the measurements instead of increasing them.
Step-by-step explanation:
Let's simply look at the equations of each shape.
Volume of a prism = base * height
Volume of a cone = Pi * r^2 * (height/3)
Volume of a cylinder = Pi * r^2 * height
Volume of a sphere = (4/3) Pi r^3
Notice that the volumes of prisms, cones, and cylinders directly correlate to height. As height increases, the volume increases. The sphere is unique in that the height is 2 * radius; however, the volume is related to the cube of the radius. Consider if you expanded the radius of the sphere, the volume will increase.
Answer:
Increase or decrease the dimensions of objects. See below for an explanation!
Step-by-step explanation:
An amazon box, which is a rectangular prism, is an example of a prism. If you increase the height, length, or width of the box, you can fit more stuff inside.
A cup is an example of a cylinder; by increasing the height or radius of the cup, you can fit more of a drink inside.
An icecream cone is an example of a cone; if the height or radius were increased, you might fit more ice cream inside.
A soccer ball is an example of a sphere; increasing the radius makes it larger, and various sizes are available for different levels.
You may also shrink the dimensions for each of these objects to make them smaller.
Hope this helps!
pleaz!!! some body help with number #4 at the bottom
Answer:
See my explanation
Step-by-step explanation:
-2x + (x - 4) = 18
-x - 4 = 18
-x = 22 <- this is wrong in question writing as x = 22
so, x = -22
I need help answer quickly please this is timed! What is the product? Assume x greater-than-or-equal-to 0 (StartRoot 3 x EndRoot + StartRoot 5 EndRoot) (StartRoot 15 x EndRoot + 2 StartRoot 30 EndRoot)
Answer:
3x√5 + 6√10x + 5√3x + 10√6
Step-by-step explanation:
(√3x + √5)(√15x + 2√30)
The above expression can be evaluated as follow:
(√3x + √5)(√15x + 2√30)
Expand
√3x (√15x + 2√30) + √5(√15x + 2√30)
x√45 + 2√90x + √75x + 2√150
Express in the best possible surd form.
x•3√5 + 2•3√10x + 5√3x + 2•5√6
3x√5 + 6√10x + 5√3x + 10√6
We can not simplify further.
Therefore,
(√3x + √5)(√15x + 2√30) =
3x√5 + 6√10x + 5√3x + 10√6
Let f(x) = 1/x . Find the number b such that the average rate of change of f on the interval [2, b] is − 1/8
Answer:
b=4
Step-by-step explanation:
So, we have the function [tex]f(x)=1/x[/tex]. We need to find b such that the average rate of change or the slope is -1/8 between the intervel [2, b]. First, let's find f(2).
f(2) = 1/(2) = 1/2
So, we have the point (2, 1/2)
At point b, f(b) = 1/b.
Let's plug this into the slope formula:
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{.5-\frac{1}{b} }{2-b} =-1/8[/tex]
Now, we just need to solve for b. First, let's multiply both the numerator and denominator by b (to get rid of the annoying fraction in the numerator).
[tex]\frac{.5b-1}{2b-b^2} =\frac{-1}{8}[/tex]
Now, cross multiply.
[tex]4b-8=b^2-2b[/tex]
[tex]b^2-6b+8=0[/tex]
Solve for b. Factor using the numbers -4 and -2.
[tex]=(b-4)(b-2)=0[/tex]
Thus, b=4 or b=2.
However, b=2 is not a possible solution since the interval [2,2] means nothing. Thus, b=4.
We want to find an interval such that the given equation, f(x) = 1/x, has an average rate of change of -1/8 in that interval.
We will see that the interval is [2, 4]
-------------------------------
For a function f(x), the average rate of change in the interval [a, b] is given by:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
Here we have:
[tex]f(x) = 1/x[/tex]
And the interval is [2, b] such that r in that interval is -1/8, so we need to solve:
[tex]r = -1/8 = \frac{f(b) - f(2)}{b - 2} = \frac{1/b - 1/2}{b - 2}[/tex]
We can rewrite it to:
[tex]-1/8 *(b - 2)= 1/b - 1/2\\\\-1/8 *(b - 2)= 2/2b - b/2b = (2 - b)/2b = -(b - 2)/2b[/tex]
Now we can remove the term (b - 2) because it appears on both sides, so we get:
[tex]-1/8 = -1/2b\\1/8 = 1/2b\\2/8 = 1/b\\1/4 = 1/b\\b = 4[/tex]
Then we found that b must be equal to 4, so the interval is [2, 4]
If you want to learn more, you can read:
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HELP PLS WITH BRAINLIEST
Answer:
cos C
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos C = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{12}{13}[/tex]