Answer: Option C
Step-by-step explanation:
Given the quadratic equation [tex]y = x^2 - 13x[/tex], substitute [tex]y=0[/tex]:
[tex]0 = x^2 - 13x[/tex]
In this case, to find the solutions of the given quadratic equation, you must factor out the variable "x". Then:
[tex]0=x(x-13)[/tex]
Therefore, you get that the solutions of this equation are the following:
[tex]x=0\\\\\\x-13=0\\x=13[/tex]
Then, the answer is:
[tex]x = 0\ or\ x = 13[/tex]
This matches with the option C.
What is the degree of x4 – 3x + 2?
Answer: 4
Step-by-step explanation:
The degree is the highest exponent , in which in this problem it is 4. The 3x counts as an exponent of 1 because the variable x is 1, and the 2 counts as an exponent of zero. Which means the degree is 4.
this year,15 of the 40 computers in the math lab are not new. which representation is equivalent to the fraction of computers that are new.
Answer:
5/8
Step-by-step explanation:
Subtract the total computers from the old computers.
40-15=25
Then put the number of new computers over the total computers
25/40
Then, simplify
5/8
Solve for a!
264=π×a×(20-a)
Thank you!
Answer:
a ≈ 14 or 6
Step-by-step explanation:
264 = π × a × (20 - a)
a(20 - a) = [tex]\frac{264}{Pi}[/tex] ≈ 84 (rounded off to nearest whole number)
Opening the brackets we get;
a² - 20a + 84 = 0
Applying the quadratic formula we get:
a ≈ 14 or 6
what is 48 35 26 31 27 52 55 63 18 74 35 61 28 42 76 35 38 64 71 26 53 65 47 41 102 38 35 84 41 26 73 62 35 39 62 49 104 62 54 19 28 64 36 39 53 89 26 53 43 75 35 39 29 26 45 39 31 30 70 42 37 54 85 42 36 91 25 28 53 65 78 42 68 44 41 50 46 48 75 29 53 72 17 28 38 30 48 43 27 46 36 48 62 31 42 48 61 22 124 27 53 86 60 47 41 37 27 36 45 80 45 70 53 25 29 16 30 36 38 42 48 51 38 39 43 61 75 38 42 55 72 39 28 51 43 49 67 25 37 39 46 41 50 93 53 82 47 36 38 51 42 40 24 68 38 36 34 49 65 68 62 53 67 23 51 40 43 49 57 61 26 54 35 32 38 39 24 added all together
The numbers added together resulted in 8419.
What is addition?In addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as an addition in mathematics. The terms "addends" and "sum" refer to the numbers that are added and the result of the operation, respectively.
To find the addition of all 177 numbers.
First, we arrange in ascending terms, we get,
16, 17, 18, 19, 22, 23, 24, 24, 25, 25, 25, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 28, 28, 28, 28, 28, 29, 29, 29, 30, 30, 30, 31, 31, 31, 32, 34, 35, 35, 35, 35, 35, 35, 35, 36, 36, 36, 36, 36, 36, 36, 37, 37, 37, 38, 38, 38, 38, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, 39, 39, 39, 40, 40, 41, 41, 41, 41, 41, 42, 42, 42, 42, 42, 42, 42, 42, 43, 43, 43, 43, 43, 44, 45, 45, 45, 46, 46, 46, 47, 47, 47, 48, 48, 48, 48, 48, 48, 49, 49, 49, 49, 50, 50, 51, 51, 51, 51, 52, 53, 53, 53, 53, 53, 53, 53, 53, 53, 54, 54, 54, 55, 55, 57, 60, 61, 61, 61, 61, 62, 62, 62, 62, 62, 63, 64, 64, 65, 65, 65, 67, 67, 68, 68, 68, 70, 70, 71, 72, 72, 73, 74, 75, 75, 75, 76, 78, 80, 82, 84, 85, 86, 89, 91, 93, 102, 104, 124.
Therefore, the sum is 8419.
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The question 'what is 48 35 26 31 27 52 55 63... added all together?' is asking for the sum of all the provided numbers. This can be calculated with a calculator or by manual addition. Be aware it may take time due to the large number of values.
Explanation:To answer the question, 'what is 48 35 26 31 27 52 55 63 18 74 35 61 28 42 76 35 38 64 71 26 53 65 47 41 102 38 35 84 41 26 73 62 35 39 62 49 104 62 54 19 28 64 36 39 53 89 26 53 43 75 35 39 29 26 45 39 31 30 70 42 37 54 85 42 36 91 25 28 53 65 78 42 68 44 41 50 46 48 75 29 53 72 17 28 38 30 48 43 27 46 36 48 62 31 42 48 61 22 124 27 53 86 60 47 41 37 27 36 45 80 45 70 53 25 29 16 30 36 38 42 48 51 38 39 43 61 75 38 42 55 72 39 28 51 43 49 67 25 37 39 46 41 50 93 53 82 47 36 38 51 42 40 24 68 38 36 34 49 65 68 62 53 67 23 51 40 43 49 57 61 26 54 35 32 38 39 24 added all together?', you would have to add up all the numbers provided. Calculating this would involve simply adding the given values together. To get the answer, you can use a calculator or manually add each number, but it may take a bit of time due to the large number of values given.
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A sales representative from a local radio station is trying to convince the owner of a small fitness club to advertise on her station. The representative says that if the owner begins advertising on the station today, the club's total number of members will grow exponentially each month. She uses the given expression to model the number of club members, in hundreds, after advertising for t months. 1.8(1.02)^12t What does the value 1.8 represent?
Answer:
The value 1.8 represent the club's total number of members today or the present number of members
Step-by-step explanation:
Given an exponential function;
[tex]y=ab^{x}[/tex]
b is the base or the growth factor
a is the initial value, that is the value of y when x = 0
We have been given the exponential function;
[tex]y=1.8(1.02)^{12t}[/tex]
The value 1.8 simply represents the initial value of y. Plug in t = 0 in the equation;
[tex]y=1.8(1.02)^{12(0)}=1.8[/tex]
Therefore, the value 1.8 represent the club's total number of members today or the present number of members.
Which line is the best model for the data in the scatter plot? I need this question answer really fast and who ever gets it gets a brain list plz I need it ASAP
I think it is bottom right because it goes through the most points.
PLEASE HELP RIGHT AWAY
Answer:
203 minutes
Step-by-step explanation:
This can be expressed as an arithmetic sequence, that is
20, 23, 26, 29,...
With first term a = 20 and common difference d = 3
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a + (n - 1)d ], hence
[tex]S_{7}[/tex] = [tex]\frac{7}{2}[/tex] [ (2 × 20) + (6 × 3) ]
= 3.5 ( 40 + 18) = 3.5 × 58 = 203
What proportion results in the equation 9m=10n
It might have come from
9/n = 10/m
Answer: Hi, in the equation 9*m = 10*n the proportion is 9 to 10, which means that 9 times the number m is equal to 10 times the number n.
So n is proportional to m in the way that n= (9/10)*m
and m is proportional to n in the way that m= (10/9)*n
This means that the proportion can be written as 9 to 10, or 9:10.
[need this done] (5/3) (2/3) (21)
A. 1/20
B. 20/3
C. 3/70
D. 70/3
The answer is D.
If you multiply them all together the answer (without simplifying), it should equal 210/9, you then simplify the numerator and denominator by 3 and you get 70/3.
Answer:
D
Step-by-step explanation:
Given
[tex]\frac{5}{3}[/tex] × [tex]\frac{2}{3}[/tex] × [tex]\frac{21}{1}[/tex]
Multiply numerators/ denominators
= [tex]\frac{5(2)(21)}{3(3)(1)}[/tex]
= [tex]\frac{210}{9}[/tex]
Cancel the numerator/denominator by dividing both by 3
= [tex]\frac{70}{3}[/tex] → D
What is the midpoint of the segment shown below
Answer:
D
Step-by-step explanation:
Using the midpoint formula
midpoint of 2 points (x₁, y₁ ) and (x₂, y₂ ) is
[ [tex]\frac{1}{2}[/tex](x₁ + x₂), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]
let (x₁, y₁ ) = (- 1, 5) and (x₂, y₂ ) = (5, 5), then midpoint is
[ [tex]\frac{1}{2}[/tex](- 1 + 5), [tex]\frac{1}{2}[/tex](5 + 5) ]
= (2, 5) → D
The midpoint of the segment is (2,5).
To find the midpoint of a line segment with endpoints [tex]\((-1, 5)\) and \((5, 5)\)[/tex], we can use the midpoint formula:
[tex]\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Given the endpoints:
[tex]\( x_1 = -1 \), \( y_1 = 5 \)[/tex] (coordinates of the first point)
[tex]\( x_2 = 5 \), \( y_2 = 5 \)[/tex] (coordinates of the second point)
Now, let's plug these values into the midpoint formula:
[tex]\[ \text{Midpoint} = \left( \frac{-1 + 5}{2}, \frac{5 + 5}{2} \right) \][/tex]
[tex]\[ = \left( \frac{4}{2}, \frac{10}{2} \right) \][/tex]
[tex]\[ = \left( 2, 5 \right) \][/tex]
Therefore, the midpoint of the segment is (2, 5)
Among the given options, the correct one is option D: (2, 5).
Find the value of 21 + 4(3^2 - 5). 25 37 100
Answer:
21 + 4(3^2 - 5 = 37
Step-by-step explanation:
Examine the following table of points, which are all on a certain line.
x y
−2 4
0 2
1 1
3 −1
What is the slope of this line? Enter your answer as a number, like this: 42, or, if the slope is undefined, enter the lowercase letter "u".
[tex]\bf \begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} {-2}~~\ast&{4}~~\ast\\ 0&2\\ 1&1\\ {3}~~\ast&{-1}~~\ast\\ \cline{1-2} \end{array}~\hspace{10em} (\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-4}{3-(-2)}\implies \cfrac{-5}{3+2}\implies \cfrac{-5}{5}\implies -1[/tex]
The slope of this line is -1.
The slope formula is useful:
m = (y2 -y1)/(x2 -x1)
where:
m is the slope of the line
y1 and y2 are the y-coordinates of two points on the line
x1 and x2 are the x-coordinates of the two points on the line
m = (2 -4)/(0 -(-2)) = -2/2 = -1
The slope of this line is -1.
The points on the line drop 1 unit for each 1 unit to the right.
m = rise/run = -1/1 = -1
A ladder rests against the top of a wall. The head of a person 6 feet tall
just touches the ladder. The person is 9 feet from the wall and 6 feet
from the foot of the ladder. Find the height of the wall
The height of the wall is calculated to be approximately 12 feet using the Pythagorean theorem with the given measurements.
Explanation:This problem can be solved using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Here, we have a triangle formed by the wall, the ground and the ladder. Let's say the ladder's length is 'c', the wall's height is 'a' and the base from the person to the wall is 'b'. According to the problem:
The person is 6 feet from the bottom of the ladder, hence one side of the triangle (b) is 9 feet.Since the person's height just touch the ladder, so the ladder's length (c) is the height of the person plus the distance from the person to the wall, hence c = 6 feet + 9 feet = 15 feet.Using the Pythagorean theorem, we get:
a^2 + b^2 = c^2
Where a is the height of the wall. Substituting in the values we get:
a^2 + 9^2 = 15^2
Solving for 'a', we find that the height of the wall is approximately 12 feet.
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Using the Pythagorean theorem, the length of the ladder and subtract the person's height to find the wall's height is 4.82 feet.
Explanation:To find the height of the wall, we can use similar triangles. The person's height and distance from the wall create a right triangle with the ladder. The ladder acts as the hypotenuse of this right triangle. Using the Pythagorean theorem, we can find the length of the ladder. Then, we subtract the person's height from this length to find the height of the wall.
Let's denote the height of the wall as h. The person's height is 6 feet and they are 9 feet from the wall. The foot of the ladder is 6 feet from the person, so it forms a right triangle with legs measuring 6 feet and 9 feet.
Using the Pythagorean theorem: a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse, we have:
6^2 + 9^2 = c^2
36 + 81 = c^2
117 = c^2
c = sqrt(117) = 10.82 feet (rounded to two decimal places)
Therefore, the height of the wall is 10.82 feet - 6 feet (person's height) = 4.82 feet.
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Please help me with this circle area problem for geometry
Answer:
circle area = PI * radius^2
circle area = 11^2 * PI
circle area = 121 * PI
That would be the area for the ENTIRE area but the circle but we are only dealing with 135 degrees of a circle so the area equals
121 * (135 / 360) * PI
= 45.375 PI
Answer is C
Step-by-step explanation:
Please someone answer this
Answer:
CD = 9
Step-by-step explanation:
DB is a perpendicular bisector, thus ΔADC is isosceles with
CD = AD = 9
Roger needs to buy supplies for his model airplane. He needs glue and paint, but he
wants to spend less than $3. Glue costs $0.75 a tube, and paint costs $0.95 a bottle. If x
is the cost of the glue and y is the cost of the paint, which inequality should Roger solve?
Answer:
TELL HIM TO STOP BEING SO CHEAP!!!!!!!!! <3
and i oop-
Step-by-step explanation:
what are two division expressions that have the same value as 61.12 divided by 3.2
Answer:
Other division expression that have the same value as 61.12 divided by 3.2 are
122.24 divided by 6.4 AND
183.36 divided by 9.6
Step-by-step explanation:
61.12/3.2 = 19.1
Other division expression that have the same value as this:
122.24/6.4 = 19.1
183.36/9.6 = 19.1
Given the polynomial function below, find F(-1). F(x) = -x ^3 - x ^2 + 1
Answer:
[tex]f(-1) = 1[/tex]
Step-by-step explanation:
Given
f(x) = [tex]-x^{3}-x^{2} +1[/tex]
Finding f(-1) means, we have to put -1 in the places of x in the function,
So, putting x=-1 in the function
[tex]f(-1) = (-1)^{3} - (1)^{2} +1[/tex]
As the power 3 is odd, the minus will remain the same, while in the 2nd term minus will be eliminated due to even power. So,
=> [tex]-1-1+1[/tex]
=> 1
Hence,
[tex]f(-1) = 1[/tex]
The zero of F -1(x) in F(x) = x + 3 is
Answer:
-3
Step-by-step explanation:
We have
y = F(x) = x + 3
so
x = y - 3
so
F⁻¹(y) = y - 3
which we can write
F⁻¹(x) = x - 3
We solve
0 = F⁻¹(x) = x - 3
x = 3
Answer: 3
Given: - 1/2x > 6.
Choose the solution set.
{x | x R, x > -12}
{x | x R, x < -12}
{x | x R, x > -3}
{x | x R, x < -3}
Answer:
It's option 2.
Step-by-step explanation:
- 1/2x > 6
Divide both sides by -1/2:
x < -12 (Note the inequality sign flips when we divide by a negative value).
Answer: {x |x ∈ R, x < -12}
Step-by-step explanation:
Given the following inequality:
[tex]-\frac{1}{2}x>6[/tex]
You can find the solution set by solving for the variable "x".
Then, to solve for the variable "x" you need to multiply both sides of the inequality:
[tex](-\frac{1}{2}x)(2)>(6)(2)[/tex]
[tex]-x>12[/tex]
And finally, you must multiply both sides of the inequality by (-1). Notice that the direction of the symbol of the inequality will change:
[tex](-x)(-1)>(12)(-1)[/tex]
[tex]x<-12[/tex]
Therefore, the solution set is: {x |x ∈ R, x < -12}
Identify the domain and range of the relation. Use a
mapping diagram to determine whether the relation is
a function
((9,6), (3,8),(4,9.5), (9,2)}
Answer:
Domain = {3,4,9}
Range = {2, 6, 8, 9.5}
Given relation is NOT a function.
Step-by-step explanation:
Given relation is relation is ((9,6), (3,8),(4,9.5), (9,2)}.
Now we need to determine if given relation is a function or not.
We also need to find the domain and range.
((9,6), (3,8),(4,9.5), (9,2)}
Domain is basically the collection of x-values
So Domain = {3,4,9}
Range is basically the collection of y-values
So Range = {2, 6, 8, 9.5}
Since given relation contains repeated x-value "9".
So the given relation is NOT a function.
What is the area of the regular hexagon? This is due tomorrow please help! :)
Check the picture below.
so then, the perimeter of that hexagon will just be the sum of all its 6 sides, or namely 3⅖ + 3⅖ + 3⅖ + 3⅖ + 3⅖ + 3⅖, or just 6( 3⅖ ).
[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ a=3\\ p=6\left(3\frac{2}{5} \right) \end{cases}\implies A=\cfrac{1}{2}(3)\left[ 6\left(3\frac{2}{5} \right) \right]\implies A=\cfrac{1}{2}(3)\left[ 6\left(\cfrac{17}{5} \right) \right] \\\\\\ A=\cfrac{1}{2}(3)\left(\cfrac{102}{5} \right)\implies A=\cfrac{1}{2}\left( \cfrac{306}{5} \right)\implies A=\cfrac{153}{5}\implies A=30\frac{3}{5}[/tex]
NEED HELP FAST!!!!!!!!!!
Answer:
A. [tex]h=\dfrac{2A}{b}[/tex]
Step-by-step explanation:
You are given formula
[tex]A=\dfrac{1}{2}bh[/tex]
Multiply this equation by 2 to get rid of fraction:
[tex]2A=bh[/tex]
Divide this equation by b to find h in terms of A and b:
[tex]h=\dfrac{2A}{b}[/tex]
how many solutions do these equations have
Answer:
[tex]\large\boxed{\bold{one\ solution}\ (1,\ -4)\to x=1,\ y=-4}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=2x-6\\y=-x-3\end{array}\right\\\\\text{These are linear functions. We only need two points to draw a graph.}\\\\\text{Choice two values of x, substitute to the equation,}\\\text{and calculate the values of y.}\\\\y=2x-6\\for\ x=0\to y=2(0)-6=0-6=-6\to(0,\ -6)\\for\ x=3\to y=2(3)-6=6-6=0\to(3,\ 0)\\\\y=-x-3\\for\ x=0\to y=-0-3=0-3=-3\to(0,\ -3)\\for\ x=-3\to y=-(-3)-3=3-3=0\to(-3,\ 0)\\\\\text{Look at the picture}[/tex]
[tex]\text{The intersection of the line is the solution of the system of equations:}\\\\(1,\ -4)\to x=1,\ y=-4[/tex]
what is the range of sequence for 2,10,50,250,1250?
q=5 the first one is 2 so T1=2
and for the end we use the formula:
[tex]an = 2 \times {5}^{(n - 1)} [/tex]
Question: A manufacturer keeps track of his monthly costs by using a “cost function” that assigns a total cost for a given number of manufactured items, x. The function is C(x) = 7,500 + 2.4x a) What is the reasonable domain of the function? b) What is the cost of 3,500 items? c) If costs must be kept below $20,000 this month, what is the greatest number of items she can manufacture? You must show your work
Answer:
a) Domain: -∞ < x < ∞
b) Cost required to manufacture 3500 items is $15,900.
c) Number of items she can manufacture is 5208 if cost is kept at $20,000
Step-by-step explanation:
a) What is the reasonable domain of the function?
The function is C(x) = 7,500 + 2.4x
The domain of the function is the set of values for which the function is defined and valid.
In the given function there is no constraint or undefined points so domain is:
-∞ < x < ∞
b) What is the cost of 3,500 items?
We are given x = 3500 and we need to find the cost.
Putting values in the function given:
C(x) = 7,500 + 2.4x
C(x) = 7,500 + 2.4 (3500)
C(x) = 7500 + 8400
C(x) = 15,900
Cost required to manufacture 3500 items is $15,900.
c) If costs must be kept below $20,000 this month, what is the greatest number of items she can manufacture?
We are given cost, and we need to find x
C(x) = 7,500 + 2.4x
20,000 = 7500 +2.4x
20,000 - 7500 = 2.4x
12500 = 2.4 x
=> x = 12500/2.4
x= 5208.3 ≅ 5208
So, Number of items she can manufacture is 5208 if cost is kept at $20,000
John wants to measure the height of a tree. He walks exactly 100 feet from the base of the tree and looks up. The angle from the ground to the top of the tree is 33o . How tall is the tree?
Answer:
The height of the tree is [tex]64.94\ ft[/tex]
Step-by-step explanation:
Let
y ----> the height of the tree
we know that
[tex]tan(33\°)=y/100[/tex] ----> the function tangent is equal to divide the opposite side angle of 33 degrees by the adjacent side angle of 33 degrees
Solve for y
[tex]y=(100)tan(33\°)=64.94\ ft[/tex]
The height of the tree can be calculated using the formula 'Height of tree = tan(33 degrees) * distance from the tree'. Substituting the given values, the tree should be approximately 65.45 feet tall.
Explanation:John can measure the height of the tree using trigonometric principles. In this case, the problem involves a right triangle, where the height of the tree forms one side (opposite to the angle of elevation), the distance John is from the tree forms the base (adjacent to the angle of elevation), and the line of sight to the top of the tree forms the hypotenuse. The tangent of the angle of elevation (33 degrees in this case) is equal to the height of the tree divided by the distance from the tree.
Therefore, to calculate the height of the tree, we need to find the tangent of the given angle and multiply it by the distance from the tree:
Height of tree = tan(33 degrees) * distance from tree
= tan(33) * 100 feet
Approximately, the tree should be around 65.45 feet tall.
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3 1/3 divided by 2/3
Answer:
5
Step-by-step explanation:
(3 1/3)/(2/3) = (10/3)/(2/3) = 10/2 = 5
In the above, both the numerator fraction and the denominator fraction have the same denominator (3), so the result is the ratio of their numerators.
____
The other way to divide fractions is to "invert and multiply". For this, the denominator gets inverted (from 2/3 to 3/2) and that is then used to multiply the numerator.
(3 1/3)/(2/3) = (10/3) · (3/2) = (10·3)/(2·3) = 10/2 = 5
You will note that the denominators of 3 cancel, resulting in 10/2 as above.
Answer:
5
Step-by-step explanation:
Expression: 3 ¹/₃ ÷ ²/₃
Mixed to improper: ¹⁰/₃ ÷ ²/₃
Divide by fraction = multiply by its reciprocal:
Change: ¹⁰/₃ × ³/₂
Simplify: ¹⁰/₁ × ¹/₂
Simplify: ⁵/₁ × ¹/₁
Multiply: 5
Part A
a national achievement test is administered annelida to third graders. The test has a mean score of 100 and a standard deviation of 15. if Jane z-score is 120, what was her score on the test?
Part B
the grades on a history midterm at Gardiner high School are normally distributed with a mean of 73 and standard deviation of 4.0. The z score for Ben is 0.50. find the Ben's score
Answer:
Step-by-step explanation:
z score= x - mean/standard deviation
1.20= x -100/15
18= x -100
118=x
z score= x - mean/standard deviation
0.5=x-73/4
2=x-73
75= x
Which of the following would best be solved using factoring by grouping?
1) x^2+3x- 10=0
2)3x^2+12x=8
3)x^2=25
4)x^3+ 5x^2- 9x- 45=0
Answer:
The fourth
Step-by-step explanation:
It has 4 terms
ANSWER
4)x^3+ 5x^2- 9x- 45=0
EXPLANATION
Factoring by grouping is used to factor expressions that have four terms.
Among the given options, the fourth option is
[tex]x^3+ 5x^2- 9x- 45=0[/tex]
There are already four terms in this expression.
So we group the first two and the last two and factor.
We can see that x² is common to the first two terms and -5 is common to the last 2 terms.
The fourth choice is correct.