Distribution of
a(b + c) = ab + ac
Then
36 + 12 is equivalent to
Find composed numbers
36= 3•12
12 = 3•4
THEN ANSWER IS
3• (12 + 4)
let k(x)=3h(x)+4x^4/g(x). given the following table of values, find k'(-1)
Given the following table of values, k'(-1) is 3.
What is differentiation?The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative. finding a function's derivative, or rate of change, in mathematics. Differentiation is the process of determining a function's derivative. The derivative is the rate at which x changes in relation to y when x and y are two variables.
Given Data
k(x) = -3h(x) + [tex]\frac{4x^{4} }{g(x)}[/tex]
k(x) = -3h'(x) + 4 [tex]\frac{4x^{3}g(x)-x^{4}g'(x) }{gx^{2} }[/tex]
k'(-1) = -3h'(-1) + 4 [tex]\frac{4g(-1)-g'(-1)}{g(-1^{2}) }[/tex]
k'(-1) = -3(-1) + 4(0)
k(-1) = 3 + 0
k'(-1) = 3
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nitrogen has half-life of 15 hours. how much nitrogen will remain in an 18.0 g sample after 60 hours?
If the half-life is 15 hours and there are 18 g, it means that after 15 hours,
18/2 grams would decay, leaving behind 18/2 grams
This means that 9 grams would be left.
After another 15 hours (making a total of 30 hours), 9/2 grams would decay leaving behind 9/2 grams (i.e 4.5 grams.
After another 15 hours (making a total of 45 hours), 4.5/2 grams would decay leaving behind 4.5/2 grams. Hence 2.25 grams are left
After another 15 hours (making a total of 60 hours), 2.25/2 grams would decay leaving behind 2.25/2 grams.
Hence after 60 hours, only 1.125 grams would be left
A fan in a baseball stadium is sitting in a seat withtheir eye level is a vertical distance of 350 ftabove level.A) When the fan is looking at home plate, theangle of depression is 30°. What is the horizontaldistance from the fan to home plate? Round to thenearest 10th. Explain two different ways todetermine this distanceB) The same fan makes eye contact with a secondfan in the stands that is seated at a lower row inthe stadium. The straight-line distance betweenthe eyes of the two fans is 300 ft and the angle ofdepression is 48°. What is the vertical distancebetween field level and the eyes of the secondfan? Round to the nearest tenth.
GIVEN:
We are told that a baseball fan is sitting at a point where his eyes are 350 feet vertical distance from the ground. When the fan is looking at the home plate the angle of depression is 30 degrees.
Required;
Find the horizontal distance from the fan to the home plate.
Step-by-step solution;
We begin by making a sketch of the scene to determine the shape and angles formed. This is shown below;
From the sketch above we can see the that the baseball fan has effectively formed a right triangle with the home plate from his position and the dimensions, that is, angles and sides, have been labeled.
We have the reference angle given as 60 degrees and the opposite is x (horizontal distance from the fan to home plate). That means the adjacent side is 350.
We can now use the following trig ratio;
[tex]tan\theta=\frac{opposite}{adjacent}[/tex][tex]tan60\degree=\frac{x}{350}[/tex]We now cross multiply;
[tex]\begin{gathered} tan60\degree\times350=x \\ \\ 1.73205080757\times350=x \\ \\ 606.217782649=x \\ \\ x=606.2ft\text{ }(rounded\text{ }to\text{ }the\text{ }nearest\text{ }tenth) \end{gathered}[/tex]A second way to determine this distance is by using the triangle formed by the angle 30 degrees, in which case the horizontal distance will be the green line as shown in the sketch above. In that case, the vertical distance of 350 feet will be the opposite while the horizontal distance will be the adjacent while the reference angle will be 30 degrees.
For the second scenario, the straight line distance between both sets of eyes is 300 feet, and the angle of depression is 48 degrees. Note that the second fan is being watched at an angle of depression of 48 degrees which means he is at a lower level.
Now we are required to determine the vertical distance between the field level and the eyes of the second fan.
Let us begin by calculating the value of x as indicated in the triangle.
We shall use the trig ratio of;
[tex]cos\theta=\frac{adjacent}{hypotenuse}[/tex][tex]cos42\degree=\frac{x}{300}[/tex]Now we cross multiply;
[tex]\begin{gathered} cos42\degree\times300=x \\ \\ 0.743144825477\times300=x \\ \\ 222.943447643=x \\ \\ x=222.9ft\text{ }(rounded\text{ }to\text{ }the\text{ }nearest\text{ }tenth) \end{gathered}[/tex]Observe carefully that the distance calculated as x (222.9 ft) is the vertical distance between both fans. If we subtract this value from 350 feet we will now derive the vertical distance from the second fan to the field level.
[tex]\begin{gathered} Vertical\text{ }distance=350-222.9 \\ Vertical\text{ }distance=127.1ft \end{gathered}[/tex]Therefore,
ANSWER:
[tex]\begin{gathered} (A)\text{ }606.2ft \\ \\ (B)\text{ }127.1ft \end{gathered}[/tex].As the operations manager of the post-sales department, you need to estimate the average duration of an on-site visit by your technical staff. Based on the information in the service call log shown, what is the average time needed for an on-site visit? Service Call Duration 45 min 55 min 1 hr 35 min 1 hr 15 min 50 min O A 40 minutes O В. 1 hour 4 minutes O С. 1 hour 20 minutes D 4 hours O E 5 hours 20 minutes
The mean (or average) is given as:
[tex]\frac{\sum ^{}_{}x_i}{n}[/tex]where xi is the value of each data and n is the total number of data. In this case we have:
[tex]\frac{45+55+95+75+50}{5}=64[/tex]Therefore the average is 1 hour 4 minutes and the answer is B.
For the following exercises, consider this scenario: There is a mound of g pounds of gravel in a quarry. Throughout the
day, 400 pounds of gravel is added to the mound. Two orders of 600 pounds are sold and the gravel is removed from
the mound. At the end of the day, the mound has 1,200 pounds of gravel.
The value of g for the given conditions is obtained from linear equations as 2000.
What is a linear equation?A linear equation in one variable has only one variable of order 1. It has the formula ax + b = 0, where x is a variable. There is only one solution to this equation.
The initial amount is given as g.
400 pounds is added.
2 times 600 pounds is taken out.
The remaining amount is 1200 pounds.
Form a linear equation from the given constraints.
g+400-2(600)=1200
Solve the linear equation using basic mathematical functions.
g+400-1200=1200
g=2400-400
g=2000
So, the value of g is obtained using the linear equation as 2000.
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Gina's books has 349 fewer pages than terri's. if Gina's books has 597 pages, how many pages does Terri's books have?
Gina's books has 349 fewer pages than Terri's, if Gina's books has 597 pages, Terri's books have 946 pages. In mathematics, an operation is function which takes zero or more input values (also called the "operands" or "arguments") to a well-defined output value. The number of the operands is the arity of the operation.
What is mathematical operations?In mathematics, an operation is function which takes zero or more input values (also called the "operands" or "arguments") to a well-defined output value. The number of the operands is the arity of the operation.
The most commonly studied operations are the binary operations (i.e., the operations of arity 2), such as addition and multiplication, and the unary operations (i.e., the operations of arity 1), such as additive inverse and the multiplicative inverse. An operation of arity zero, or nullary operation, is constant. The mixed product is example of operation of arity 3, also called ternary operation.
Generally, arity is taken to be finite. However, the infinitary operations are sometimes considered, in which case "usual" operations of finite arity are called finitary operations.
A partial operation is defined similarly to operation, but with partial function in place of a function.
Gina's book = 597 pages
Terri's book= (597+349) pages
= 946 pages
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3. The number of zeroes in the end of perfect square is never_______
(vi) The cube of a two digit number may have seven or more digits. (vii) The cube of a single digit number may be a single digit number. Q. The number of zeroes at the end of a perfect square is always odd.
I hope it will be helpful for you.
Graph the solution set of the following linear equation
2x+2y<-6
Graph the inequality by finding the boundary line, then shading the appropriate area.
y < −x −3
What is the x-intercept of the following equation?15x + 5y =30
the Given
[tex]15x+5y=30[/tex]We are asked to find the x-intercept of the linear equation. This can be seen below.
Explanation
To find the x-intercept, we must recall that x-intercept is the point at which the graph of the equation crosses the x-axis. We can find this point by plotting the given equation.
From the graph, we can determine the x-intercept as
Answer: (2,0)
A spinner has 3 equal sections that are white, yellow, and green. Another spinner has 3 equal sections that are blue, purple, and red. How many different combinations of colors are possible if you spin each spinner once?A. 6B. 9C. 12D. 16
ANSWER
[tex]B)9[/tex]EXPLANATION
We want to find the number of different combinations of colors possible if both spinners are spun at once.
To do this, we have to find the product of the number of colors on each spinner.
That is:
[tex]\begin{gathered} 3\cdot3 \\ \Rightarrow9 \end{gathered}[/tex]The answer is option B.
PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!ON NUMBER 4!!!!!
The absolute value function y = 3|x + 1| + 9 is y ≥ (x + 4)/3 when x ≥ 0 and
y > - (x - 2)/3 when x < 0.
What is the absolute value function?The absolute value function always outputs a positive value irrespective of the input.
Given we have to write the absolute value function as a piecewise function.
We know | x | = a implies x ≥ a and - x < a.
y = 3| x + 1 | + 9.
y - 9 = 3| x + 1|.
(y - 9)/3 = | x+ 1 |.
∴ (y - 9)/3 ≥ x + 1.
y/3 - 3 ≥ x + 1.
y/3 ≥ x + 4.
y ≥ (x + 4)/3.
OR
(y - 9)/3 = | x+ 1 |.
- (y - 9)/3 < x + 1.
-y/3 + 3 < x + 1.
-y/3 < x - 2.
-y < (x - 2)/3.
y > - (x - 2)/3.
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PLEASE HELP!! I DON'T KNOW THE ANSWER BUT OF I CLOSE IT I CAN'T GET BACK IN I CAN ONLY ACCESS THIS ONE PLEASE HELP!!!!! ⚠⚠⚠⚠⚠⚠
Answer:
The answer is the third one.
Step-by-step explanation:
They show the points plotted correctly.
Find the solution of each equation if the replacement set is 10 11 12 13
If we replace with 10:
[tex]\frac{10}{5}=2[/tex][tex]2=2[/tex]10 is a solution.
Let's try with 11:
[tex]\frac{11}{5}=2[/tex][tex]2.2\ne2[/tex]11 is not a solution.
WIth 12:
[tex]\frac{12}{5}=2[/tex][tex]2.4\ne2[/tex]12 is not a solution
WIth 13
[tex]\frac{13}{5}=2[/tex][tex]2.6\ne2[/tex]13 is not a solution.
Therefore, the solution to this equation is 10
Your lunch in the hospital cadet cost $6.50. Based on working 50weeks per year , how much will you spend on your lunch per year?
Answer:
Step-by-step explanation:
if they are working 7 days a week, lunch will cost $2,275
hope this helped :)
The grounds crew at a college is installing a path around a pond on campus as shown.9x + 10x2 - x4x2 - 7x + 8- x?+ 9x + 12What is the perimeter of the path?A. – 3 + 15x2 + 25% + 20B. 12x2 + 2x + 20C. -13 + 13x2 + 11x + 20D. 1232 + 25x + 20
The perimeter of a figure or shape is the distance around it.
The perimeter of the given path would be
9x + 10x^2 - x^3 + 4x^2 - 7x + 8 - x^2 + 9x + 12
We would collect like terms. It becomes
- x^3 + 10x^2 + 4x^2 - x^2 + 9x + 9x - 7x + 8 + 12
= - x^3 + 13x^2 + 11x + 20
The correct option is C
16. In Barry's state, the weekly unemployment compensation is 58% of the 26-week average forthe two highest-salaried quarters. A quarter is three consecutive months. For July, August, andSeptember, Ben earned a total of $17,500. In October, November, and December, he earned atotal of $18,300. Determine Barry's weekly unemployment compensation.
~ 399.3 $ / w
. The average for the 2 highest-salaried quarters:
(17 500 $ + 18 300 $ ) / 2 = 35 800 $ / 2 = 17 900$
. The 58% compensation representing the total amount Barry will be compensated:
17 900 * 58 / 100 = 10 382 $
. The weekly compensation:
10 382 $ / 26 week ~= 399.307692 $ / w
what's the perimeter of 3x2-1x2-4x+3 for parallelogram?
Answer:
The perimeter of the parallelogram is;
[tex]8x^2-8x+4[/tex]Explanation:
Given the figure of a parallelogram in the attached image.
With sides;
[tex]\begin{gathered} a=x^2-4x+3 \\ b=3x^2-1 \end{gathered}[/tex]The perimeter of a parallelogram can be calculated using the formula;
[tex]P=2(a+b)[/tex]substituting the given sides;
[tex]\begin{gathered} P=2(a+b) \\ P=2(x^2-4x+3+3x^2-1) \\ P=2(x^2+3x^2-4x+3-1) \\ P=2(4x^2-4x+2) \\ P=8x^2-8x+4 \end{gathered}[/tex]Therefore, the perimeter of the parallelogram is;
[tex]8x^2-8x+4[/tex]
Bobby read a total of 20 books over 2 months. If Bobby has read 90 books so far, how many months has he been with his book club? Solve using unit rates
Step 1
From the question;
[tex]\begin{gathered} Bobby\text{ reads 20 books in 2 months} \\ \end{gathered}[/tex]We are required to find how many months it will take him to read 90 books
Step 2
We will use the ratio below to solve the problem.
[tex]\begin{gathered} \frac{20\text{ books}}{90\text{ books}}=\frac{2months}{x} \\ x=months\text{ to read 90books} \\ x=\frac{90\times2}{20} \\ x=9\text{ months} \end{gathered}[/tex]Answer; It will take Bobby 9months to read 90 booj
[tex]9\text{ months}[/tex]Select all of the answer choices that are solutions to the equation2x+2y=0.Ox=0y = -1O x = 1, y = -1Ox= -2O x = -2, y = -2O x = 0, y = 0
If the sum of two terms = 0, then the 2 terms must have the same value but different signs
That means x and y must have the same value but different signs
Look at the given answers
The 1st, 2nd, and 4th answers are wrong because the solution of this equation must have a value of x and a value of y together
In the 3rd answer
x = 1 and y = -1
Both have the same value and different signs
Then 3rd answer is a solution
In the 5th answer
x = -2 and y = -2
They have the same value with the same signs
The 5th answer is not a solution
In the last answer
x = 0 and y = 0
They have the same value but the zero has no sign
Then substitute them in the equation to check if it is solution or not
2(0)+2(0) = 0
0 + 0 = 0
The 2 sides of the equation are equal, then
The last answer is a solution
The answer is the 3rd and last answers
The question is below:
If function f(x) = √(x + 1) - 5 is translated three (3) units to the right and two (2) units up, the equation which represents g(x) is: D. f(x) = √(x - 2) - 3
What is a translation?In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image while translating a geometric figure down simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
Translating f(x) = √(x + 1) - 5 three (3) units to the right and two (2) units up, we have:
f(x) = √(x + 1) - 5
f(x) = √(x + 1 - 3) - 5 + 2
f(x) = √(x - 2) - 3
In Geometry, g(x - 3) simply means shifting a graph three (3) units to the right while adding two (2) to the function simply means moving the graph up.
In this context, we can reasonably infer and logically deduce that the parent function f(x) was shifted 3 units to the right and 2 units up.
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can you please help me with this algebra 2 question please
If we consider a, b and c all positive constants and b > 1, a exponential growth in general is represented by a function like:
[tex]f(t)=a\cdot b^{ct}[/tex]In otherwise, a exponential decay can be represent by:
[tex]g(t)=a\cdot b^{-ct}=a\cdot(\frac{1}{b})^{ct}[/tex]Now we can check whose functions are similar to one of these:
h(x) = 3x + 1.3 is a linear function, therefore, this is neither exponential growth or decay;
f = 3*(4.2^x) is an exponential growth;
y = (5/6)*(7^x) is an exponential growth;
T = 0.6*(1.3^x) is an exponential growth;
W(x) = (1/8)*[(3/5)^x] is an exponential decay, since in this case we have 3/5 < 1.
K = 4.2*(0.28^x) is an exponential deacay by the same argument.
Which expression uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3x(2x8) + 7 ?
7 + 3 × (2 × 8) is the expression that uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3 × (2 × 8) + 7.
Given, 3 × (2 × 8) + 7
Following the application of the Commutative property of addition, which stipulates that altering the order of addends does not affect the result.
The expression will be,
7 + (2 × 8) × 3
Then, using the associative principle of multiplication, which states that how elements are arranged in a multiplication issue does not affect the product.
The expression will be,
7 + 3 × (2 × 8)
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Describe the slope of the line.AY|(-3, 1)2|-22X-25(2,-2)
A = (-3, 1)
B = (2, -2)
First we will calculate the slope of the line
[tex]m=\frac{y2-y1}{x2-x1}[/tex][tex]m=\frac{-2-1}{2-(-3)}=\frac{-3}{5}_{}[/tex]The slope is negative
Now, we are gonna calculate the equation, with (2, -2)
[tex]b=y-mx[/tex][tex]b=-2-(-\frac{3}{5})\cdot2[/tex][tex]b=-\frac{4}{5}[/tex]An initial population of 350 flying squirrels triples every year. Write an exponential equation to represent the population growth of the flying squirrels after any given number of years, x.
The exponential equation that represents the growth of the flying squirrels is F = 350 X 3^t.
What is the exponential function?An exponential equation can be described as an equation with exponents. The exponent is usually a variable. An exponential equation exhibits a compound growth rate.
The general form of exponential function is f(x) = [tex]e^{x}[/tex]
Where:
x = the variable e = constantThe population of the bird = present population x (1 + growth rate)^number of years
350 x (1 + 2)^t
F = 350 X 3^t
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Given g(-2) = -4 and g'(-2) = 5, find the value of h'(-2) based on the function below.
h(x) = (-2x + 6) • g(x)
Step-by-step explanation:
so,
h(x) = f(x) × g(x)
h'(x) = f'(x) × g(x) + f(x)×g'(x)
with f(x) = -2x + 6
f'(x) = -2
so,
h'(-2) = -2 × g(-2) + (-2×-2 + 6) × g'(x) =
= -2 × -4 + 2 × 5 = 8 + 10 = 18
Q:Find the distance from the red point to the origin. Sketch on the graph to convince us.
Distance Between Two Points
We are given two points on the graph attached to the question.
The red point has coordinates (7,3) and the origin is at (0,0)
I'll work out the graph to show the required distance.
The required distance (in the red drawing) is the hypotenuse of a right triangle of lengths 7 and 3, thus the distance is calculated as:
[tex]d=\sqrt[]{7^2+3^2}=\sqrt[]{49+9}=\sqrt[]{58}[/tex]Calculating, we get d is approximately 7.62
You're flying from Joint Base Lewis-McChord (JBLM) to an undisclosed location 165 km south and 152 km east. Mt. Rainier is located approximately 56 km east and 40 km south of JBLM. If you are flying at a constant speed of 800 km/hr, how long after you depart JBLM will you be the closest to Mt. Rainier?
For the constant speed, it take 5 minutes 3 seconds after you depart JBLM will you be the closest to Mt. Rainier.
Speed:
Speed means a rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered.
Given,
You're flying from Joint Base Lewis-McChord (JBLM) to an undisclosed location 165 km south and 152 km east. Mt. Rainier is located approximately 56 km east and 40 km south of JBLM.
Here we need to find the time taken after you depart JBLM will you be the closest to Mt. Rainier for the constant speed of 800 km/hr.
Let us consider +x direction is east, and the -y direction is south.
We know that, JBLM is at the origin (0, 0). All distance units are presented in kilometers.
While we consider that, you are flying on line
165x + 152y = 0
We know that the slope of the line
ax + by = c
is given by -a/b, which suggests we can form the equation of a perpendicular line by swapping x and y coefficients and negating one of them.
Then, we get the equation as,
152x - 165y = c
That is perpendicular to the flight path.
Now we need to find c so that this is true at the coordinates of Mt. Rainier.
The perpendicular line through (56, -40) is
152x - 165y - (152(56) - 165(-40)) = 0
When we expand it then we get,
152x - 165y - (8512 + 6600 ) = 0
152x - 165y - 15112 = 0
We know that the distance in km from JBLM (0, 0) to this line is given by
So, when we apply the value of (x,y) as (0,0) then we get,
=> | 152(0) - 165(0) - 15112 |/√(152²+165²)
=> 15112/√50329
=> 15112/224.34
≈ 67.362
Therefore at the constant speed of 800 km/hr, you will have flown that 67. 362 km.
Then for one km you would take,
=> 62.076/800 hr ≈ 0.0842 hr
When we convert this then we get,
=> 0.0842 = 5 minutes 3 seconds.
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the graph of a quadratic function is given. determine the function's equation.
Here, we are given a quadratic equation graph and we are tasked with getting the equation of the quadratic equation from the graph
The first thing we need to note here is the shape of the parabola.
This in the sense that if the parabola opens up or faces down
On the graph we can see that the parabola faces the positive x-direction
Generally, the equation of a quadratic graph is usually in the form below;
[tex]y=ax^2\text{ + bx + c}[/tex]So by identifying the values of a,b and c, we can get the complete equation of the graph
The above form is called the standard form while the form we have in the options is referred to as the vertex form
The vertex form can be written as;
[tex]y=a(x-h)^2\text{ + k}[/tex]Now, looking at the graph, we can see that the graph crosses the y-axis at the point y = 6
At this point, the value of x is 0
The vertex (h,k) represents the center point of the parabola
In the case of this question, the point is (-2,2)
so h =-2 and k is 2
What is left is to get a
we can obtain this from the value of y = 6 and x = 0
Thus;
6 = a(0-(-2))^2 + 2
6 = a(2)^2 + 2
6 = 4a + 2
4a = 6-2
4a = 4
a = 4/4 =1
So the equation in the vertex form is f(x) = (x + 2)^2 + 2
Write the coordinates of the vertices after a reflection over the x-axis.-10-8-6-4-2246810-10-8-6-4-2246810xyDEFG
Solution:
Given the graphed polygon below:
To determine the coordinates of the vertices after reflection over the x-axis,
step 1: Give the coordinates of DEFG.
Thus, we have
[tex]\begin{gathered} D(0,\text{ -10\rparen} \\ E(0,\text{ 0\rparen} \\ F(10,\text{ 0\rparen} \\ G(10,\text{ -10\rparen} \end{gathered}[/tex]step 2: Give the reflection formula, over the x-axis.
For reflection over the x-axis, we have
[tex]D(x,\text{ y\rparen}\rightarrow D^{\prime}(x,\text{ -y\rparen}[/tex]step 3: Give the coordinates after reflection over the x-axis.
From the formula in step 2,
we thus have
[tex]\begin{gathered} D^{\prime}(0,\text{ 10\rparen} \\ E^{\prime}(0,0) \\ F^{\prime}(10,\text{ 0\rparen} \\ G^{\prime}(10,\text{ 10\rparen} \end{gathered}[/tex]Determine the probability of occurence of the following single eventsA "4" appears in a single toss of a die
SOLUTION
The probability of an event occuring is found using the formula
[tex]\frac{possible\text{ outcome}}{\text{total possible outcome }}[/tex]There is only "one" 4, in a die, out of a total of "six" numbers labelled 1 to 6.
So, possible outcome = 1
Total possible outcome = 6, since the die was tossed once.
Probability becomes
[tex]\frac{1}{6}[/tex]Hence the answer is
[tex]\frac{1}{6}[/tex]