The vertex (3, -16) is the maximum point on our quadratic equation.
Maximum and minimum values of the function:When we compare the given Quadratic function with the general form
ax² +bx +c,
If the value of a is positive then the Quadratic function will have a minimum value, and the graph of the function opens up.
If the value of a is negative then the Quadratic function will have a maximum value, and the graph of the function opens downwards.
Here we have
f(x) = -2(x - 5)(x-7)
f(x) = -2 [x²-7x - 5x + 35 ]
f(x) = -2 [x²-12x + 35 ]
f(x) = -2x² + 12x - 35
Compare f(x) with ax²+ bx + c
=> a = -2, b = 12, and c = - 35
Here,
a = -2 is a negative value then the function f(x) will have maximum value
And the graph of the function opens down.
The formula for the x coordinate of the vertex = -b/2a
The coordinate of x = -(12)/2(-2) = 3
Now substitute x = 3 in f(x) to find y-coordinate
=> f(3) = - 2(3)² +12(3) - 35
=> f(3) = -2(9) + 36 - 35
=> f(3) = - 16
Therefore, y-coordinate = -16
Therefore,
The vertex (3, -16) is the maximum point of the quadratic equation.
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Probability and Statistics Question
we want to find the number of hours (or rather days) until only 4.25% of the drives fail.
that means for an exponential distribution we have
P(X < x) = 1 - e^(-Lx)
L = 1/mean = 1/12500
and we need to find x, so that P(X <x) = 0.0425 (that is 4.25% converted into a probability).
so, we get
0.0425 = 1 - e^(-x/12500)
0.0425 - 1 = -e^(-x/12500)
-0.9575 = -e^(-x/12500)
0.9575 = e^(‐x/12500)
ln(0.9575) = -x/12500
-x = ln(0.9575)×12500
x = -ln(0.9575)×12500 = - -0.043429558...×12500 =
= 0.043429558...×12500 = 542.8694741... hours
after 542.8694741... hours = 22.61956142... days
it is expected that 4.25% of the hard drives fail.
you left out to what decimal this should be rounded. and if you need hours or days. in case of doubt use hours (as the only other time information is given in hours).
please round yourself as you need.
Help me thank y so much
The relation is:
(1, 2), (-3, 5), (6, 6), (-2, 0), (1, 2)
Is a function, because each element in the domain is mapped to a single element in the range.
Do the ordered pairs represent a function?A relation maps elements from one set, called the domain, into another set, called the range.
For example, the element x mapped into element y is written as (x, y).
Particularly, a relation is a function if each element from the domain is mapped into only one element of the range.
So, if we had two points like (2, 4) and (2, 5), then the relation is not a function (because the element 2 is mapped into two different elements of the range).
Here the relation is:
(1, 2), (-3, 5), (6, 6), (-2, 0), (1, 2)
So the input x = 1 appears twice, but both times is mapped to the same element, so this relation is a function.
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If f(x) = 4x - 5 and g(x) = 6 - 3x, what is f (x) + g(x)?
If f(x) = 4x - 5 and g(x) = 6 - 3x then f(x) + g(x) = x + 1.
What is a composite function?When the output of one function is given to the input of another function they are called composite functions. In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).
We know f(x) + g(x) = (f + g)(x).
Given, f(x) = 4x - 5 and g(x) = 6 - 3x.
∴ f(x) + g(x) = (4x - 5) + (6 - 3x).
f(x) + g(x) = 4x - 3x - 5 + 6.
f(x) + g(x) = x + 1.
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Use the formula A=(1+r/n)^nt to solve the compound interest problem.
Find how long it takes for 900$ to double if it is invested at 6% interest compounded monthly.
The money will double in value in approximately ? years.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
In 11.56 years the given amount of $ 900 will be double.
What is Compound interest:The interest charged on a loan or deposit is known as compound interest which depends on both the principal amount and rate of interest.
The formula used for
Amount, A = P(1+r/n)^ntwhere P = Principal amount
r = Rate of interest in decimal
n = Number of compounds per year
t = Time period
Here from the given data,
Principal amount, p = $ 900
Rate of interest, r = 6% = 6/100 = 0.06
Number of compounds, n = 12 [ ∵ compounded mothly ]
Here we need to find the time period
Assume that after 'n' years the amount will be doubled i.e $ 1800
From the given problem,
Amount, A = 900(1+0.06/12)¹²ⁿ
= 900(1+0.06/12)¹²ⁿ
= 900(1 + 0.005)¹²ⁿ
= 900 (1.005)¹²ⁿ
As we assumed after 'n' years the amount is $ 1800
=> 900 (1.005)¹²ⁿ = 1800
=> (1.005)¹²ⁿ = 2
Apply to log on both sides
=> log (1.005)¹²ⁿ = log 2
=> 12n log(1.005) = log 2
=> 12n = log 2/log(1.005)
[ use calculator for log (1.005) and log 2]
=> 12n = 0.301029996/ 0.00216606176
=> 12n = 138.975722
=> n = 11.5813102
=> n = 11.56
Therefore,
In 11.56 years the given amount of $ 900 will be double.
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Tim's mathematics teacher asked him to explain the expression -8. 7. Which answer should Tim give?
A The expression represents 7 groups of 8 positives.
B The expression represents 8 groups of 7 positives.
(C) The expression represents 7 groups of 8 negatives.
(D) The expression represents 8 groups of 7 negatives.
Answer:
C
Step-by-step explanation:
Because it says -8 x 7, the * is negative and the 7 is positive.
Find an angle θ with 0∘ < θ < 360∘ that has the same:
sine as 30°:∅= degrees
cosine as 30°:∅= degrees
Angle θ with 0∘ < θ < 360∘ that has the same: sine as 30°:∅= degrees
cosine as 30°:∅= degrees are 150 and 330 degrees.
What is trigonometric function?
Trigonometric functions are referred to as Circular Functions may be merely outlined because the functions of an angle of a triangle
Main Body:
We have to find an angle θ with 0° < θ < 360° that has the same:
(a) sin(30∘)
We know that sin(θ) is positive in 2nd quadrant and in the 2nd quadrant θ lies between 90∘ and 180∘.
sin(30∘)=sin(180∘−30∘)
[∵sin(180∘−θ)=sin(θ)]=sin(150∘)
Thus:
sin as 30∘:θ=150 degrees
(b) cos(30∘)
We know that cos(θ) is positive in the 4th quadrant and in the 4th quadrant θ lies between 270∘ and 360∘.
cos(30∘)=cos(360∘−30∘)
[∵cos(360∘−θ)=cos(θ)]=cos(330∘)
Thus:cos as 30∘
:θ=330 degrees
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3/5x = 12 x 5
_x = _
Answer:
X=100
Step-by-step explanation:
I assume you want to find the value of x.
3/5x=60
5/3*60=x
x=20*5=100
If η. is an even positive integer, the double factorial notation represents the product of all the even integers from to η. For example 8! = 2 . 4. 6. 8 . What is the units digit of the following sum?
a. 0
b. 2
c. 4
d. 6
e. 8
The units digit of the double factorial notation is the units digit of the product of all the even integers from 2 to 8, which is 8! The units digit of 8! is 8, so the answer is 8.
What is meant by the term factorials?Factorials are mathematical operations symbolized by an exclamation point following a number. To find the factorial of a number, such as 5, write it down as 5! then multiply it by all the positive integers less than 5, including 1. Therefore, 5! is equivalent to 5 x 4 x 3 x 2 x 1, or 120. Factorials are frequently employed in mathematical equations and computations, especially in probability and statistics, where they are used to calculate the number of combinations or permutations that may be made from a given collection of numbers or variables. For example, if you had 5 distinct objects and want to determine how many various combinations , you used the factorial of 5.
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Write y-2=-1(x+7) in standard form
Y=mx+b is standard form.
y-2= -x-7
+2 +2
y= -x-5
WORD PROBLEM:
You have 200 meters of fencing to enclose two adjacent rectangular pens for livestock. The total area of the enclosed region is 1400 square meters. What are the dimensions of each pen?
The dimensions of each of the rectangular pens are given as follows:
8.41m and 41.58 m.
How to obtain the dimensions of the pen?The pen have rectangular format, as shown by the image given at the end of the answer, hence the dimensions are obtained from the area and the perimeter of the pen.
For each pen, the dimensions are given as follows:
Length: x.Width: y.For the entire pen, the dimensions are given as follows:
Length: 2x.Width: y.You have 200 meters of fencing to enclose two adjacent rectangular pens for livestock, hence the perimeter is given as follows:
2(2x + y) = 200
2x + y = 100.
The total area of the enclosed region is 1400 square meters, hence:
2xy = 1400.
From the first equation, we have that:
y = 100 - 2x.
Replacing in the second, the length x is obtained as follows:
2x(100 - 2x) = 1400
-4x² + 200x - 1400 = 0
4x² - 200x + 1400 = 0.
The solutions are of:
8.41m and 41.58 m.
Which gives the dimensions of the pen.
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What is the correct to this answer ???????( answers only)
Answer:
x > 24 goes to the bottom
x < 24 goes to the 3rd slot
x ≤ 24 goes to the 1st slot
x ≥ 24 goes to the 2nd slot
Step-by-step explanation:
Hope this helps.
Regroup to express the number in a different way.
71{,}83071,83071, comma, 830 ==equals 7\text{ ten thousands}7 ten thousands7, start text, space, t, e, n, space, t, h, o, u, s, a, n, d, s, end text ++plus 1\text{ thousand}1 thousand1, start text, space, t, h, o, u, s, a, n, d, end text ++plus 8\text{ hundreds}8 hundreds8, start text, space, h, u, n, d, r, e, d, s, end text ++plus 3\text{ tens}3 tens3, start text, space, t, e, n, s, end text
71{,}83071,83071, comma, 830 ==equals 6\text{ ten thousands}6 ten thousands6, start text, space, t, e, n, space, t, h, o, u, s, a, n, d, s, end text ++plus
++plus 8\text{ hundreds}8 hundreds8, start text, space, h, u, n, d, r, e, d, s, end text ++plus 3\text{ tens}3 tens
Answer:
11 thousands---------------------------------
Given number is 71830.
The last part: 830 is same on both lines.
We need to represent 71000 in different way, instead of 7 ten thousands and 1 thousands we have 6 ten thousands then we need:
71000 - 60000 = 11000It is 11 thousands.
Answer:
11,000 (or) 11 thousands
Step-by-step explanation:
Now we have to,
→ find the missing number.
→ Let the number be x.
Forming the equation,
→ 60,000 + x + 800 + 30 = 71,830
Then the value of x will be,
→ 60,000 + x + 800 + 30 = 71,830
→ x + 60,830 = 71,830
→ x = 71,830 - 60,830
→ [ x = 11,000 ]
Hence, the value of x is 11,000.
Ling must spend no more than $40.00 on decorations for a party. She has spent $10.00 on streamers and wants to buy bags of balloons as well. Each bag of balloons costs $2.50. The inequality below represents x, the number of bags she can buy given the spending limit and how much she has already spent on streamers.
Ling can therefore purchase 0 to 12 bags, but no more is the right decision.
How to calculated the inequality?Ling has been instructed to spend no more than $40.00 on party décor. She has already spent $10.00 on streamers but also plans to purchase bags of balloons. The price of a bag of balloons is $2.50.
Given her spending cap and how much she has already spent on streamers, the inequality 10 + 2.5x ≤ 40 indicates x, the number of bags she can purchase.
Subtracting 10 from both sides of our inequality, let's find x by reversing the inequality.
10 - 10 + 2.5 x ≤ 40 - 10
2.5 x ≤ 30.
We will now divide our inequality by 2.5 on both sides.
2.5 x / 2.5 ≤ 30 / 2.5
x ≤ 12.
Ling can therefore purchase 0 to 12 bags, but no more is the right decision.
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Answer:
Step-by-step explanation:
Ling can therefore purchase 0 to 12 bags, but no more is the right decision.
. When the length of a side of a square is increased by 5, the perimeter of the new
square is 60.
Which equation can be used to find the length of the side of the original square?
A. 4(x + 5) = 60
B.
4(x-5) = 60
C.
4x + 5 = 60
D.
4x5 = 60
The equation that can be used to find the length of the side of the original square is 4(x+5) = 60. Option A. is the answer
How to determine which equation can be used to find the length of the side of the original square?Given that:
When the length of a side of a square is increased by 5, the perimeter of the new square is 60.
Let x represent the length of the side of the original square
when x is increased by 5, you have (x+5)
Perimeter (P) = 4 × length of the side
Thus, 4(x+5) = 60
Therefore, the equation to find the length of the side is 4(x+5) = 60
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Answer to these required:
Window Rock Recruitment Agency just placed Alejandro Rivera in a job as an assistant
pharmacist. The job pays $71,500 annually. The agency fee is equal to 40% of the first
5 weeks' pay. Demonstrate and explain how you would be able to determine what he will
earn during the first 4 weeks if he pays the agency fee weekly?
Answer: To determine Alejandro's earnings for the first 4 weeks, we first need to calculate his weekly pay. To do this, we divide his annual salary by the number of weeks in a year:
Annual salary / 52 weeks/year = weekly pay
$71,500 / 52 weeks/year = $1,375/week
Next, we need to determine the agency fee that Alejandro will pay each week. The agency fee is equal to 40% of the first 5 weeks' pay, so we multiply Alejandro's weekly pay by 40% to get the agency fee:
Weekly pay * 40% = agency fee
$1,375/week * 40% = $550/week
Finally, to determine Alejandro's earnings for the first 4 weeks, we multiply his weekly earnings by the number of weeks:
Weekly pay * number of weeks = earnings
$1,375/week * 4 weeks = $5,500
So, Alejandro will earn $5,500 during the first 4 weeks of his new job, after paying the agency fee each week.
Choose the slope-intercept form of 3x + 2y = 5. y =
Answer: [tex]y = \frac{-3}{2} x + \frac{5}{2}[/tex]
Given: [tex]3x + 2y = 5[/tex]
We are needed to find the slope-intercept form.
We know that the slope-intercept form of an equation is given by
[tex]y = mc + c[/tex]
[tex]3x + 2y = 5[/tex]
[tex]2y = 5 -3x[/tex]
[tex]2y = -3x + 5[/tex]
[tex]y = \frac{-3}{2} x + \frac{5}{2}[/tex]
Thus, the answer is [tex]y = \frac{-3} {2} x + \frac{5}{2}[/tex]
Three less than the product of 7and a number is 4 .
Answer:
Step-by-step explanation:
Let
n--------> the number
we know that
1) the sentence" Three less than the product of seven and a number" represent the expression------>
2) the sentence" is four more than the number"
represent the expression ------->
3) the complete sentence" Three less than the product of seven and a number is four more than the number" represent the expression
represent the expression ------->
therefore
the answer is
(7n-3) =(n+4)
Which point shows the approximate location of [tex]\sqrt{7}[/tex] plotted on the number line
The position of the √7 on the number line is slightly right of the 2.6.
What is a number line?
A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.
Here,
In general conclusion,
√4< √7 < √9
2 < √7 < 3
So, the value of the √6 lies between 2 and 3.
√6 = 2.6457
Hence, the position of the √7 on the number line is slightly right of the 2.6.
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A line has a slope of 14/19 and passes through the point 0,15 what is its equation in slope intercept form
Answer: y = 14/19x+15
Step-by-step explanation: using the equation y = mx+b, m is your slope and b is the y-intercept. plug your slope (14/19) and y-intercept (15) into the equation and you’ve got your answer in slope-intercept form
Determine the slope of the line that passes through the following points. m=5/7, or m=7/5, or m=1/3, or m=3
Between (5,10) and (15,70), a line runs. As a result, the slope of the line through the supplied locations is 3.
What is slope?A line's steepness and direction are measured by the line's slope.
Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line.
A line's slope is determine by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.
Two locations located on a straight line can be used to determine a line's slope. We can use the slope of line formula if we know the two spots' coordinates. These two points' coordinates should be-
P1 = (x1, y1) and P2 = (x2, y2)
Hence, Between (5,10) and (15,70), a line runs. As a result, the slope of the line through the supplied locations is 3.
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Nina deposited $6,000 in a savings account with simple interest. Six months later, the
account held $6,270. What was the interest rate?
Answer:
Step-by-step explanation: 270
Help me thank u very much
Answer:
y = 3x + 2
y = 1/2 x -1
Step-by-step explanation:
The slope intercept form of a line is
y = mx + b You substitute in the slope for m and the y intercept for b
leght multipy by breath
Answer:
equal to area of rectangle
Step-by-step explanation:
Please mark me brainlest
A transversal runs across two parallel lines, forming two angles. One measures 80 degrees. How large is the other angle
Answer:
100°
Step-by-step explanation:
180°- 80°= 100°
The angles are supplementary, meaning that they have to add up to 180.
Hope this helps!!! :)
The snack bar sold 75% of its inventory of bags of chips. If the snack bar still has 37 bags of chips, how many
bags did they sell?
The bags of chips sold are 111.
What is percentage?The percentage is the term use to tell the hundredth part of something.
Given that, The snack bar sold 75% of its inventory of bags of chips, and the snack bar still has 37 bags of chips,
Let the original number of bags of the chips be x,
Since, 75% is already sold, so left number of bags are = 100%-75% = 25%
Therefore,
25% of x = 37
x = 37x4
x = 148
The number of bags sold = 75% of 148
= 75x148/100
= 111
Hence, they sold 111 bags of chips.
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What is the distance between the points (-2,3) and (5, -1)?
Answer:
√65
Step-by-step explanation:
Compute the Euclidean distance between the following points:
p_1 = (-2, 3) and p_2 = (5, -1)
The Euclidean distance between points (x_1, y_1) and (x_2, y_2) is:
sqrt((x_1 - x_2)^2 + (y_1 - y_2)^2)
Substitute (x_1, y_1) = (-2, 3) and (x_2, y_2) = (5, -1):
= sqrt((-2 - 5)^2 + (--1 + 3)^2)
(-1)^2 = 1:
= sqrt((-2 - 5)^2 + (1 + 3)^2)
-2 - 5 = -(2 + 5):
= sqrt((-(2 + 5))^2 + (3 + 1)^2)
2 + 5 = 7:
= sqrt((-7)^2 + (3 + 1)^2)
Multiply each exponent in -7 by 2:
= sqrt((-1)^2×7^2 + (3 + 1)^2)
7^2 = 49:
= sqrt((-1)^2×49 + (3 + 1)^2)
(-1)^2 = 1:
= sqrt(49 + (3 + 1)^2)
3 + 1 = 4:
= sqrt(49 + 4^2)
4^2 = 16:
= sqrt(49 + 16)
| 1 |
| 4 | 9
+ | 1 | 6
| 6 | 5:
Answer: √65
Select all that apply.
Which of the following are proportions?
2/8=3/12
3/4=8/10
25/10=5/2
3/4=15/20
In the following proportions:-
A. [tex]\frac{2}{8} =\frac{3}{12}[/tex]
C. [tex]\\\\\ \frac{25}{10} =\frac{5}{2}[/tex]
D. [tex]\\\\ \frac{3}{4} =\frac{15}{20}[/tex] Are Equal
What are proportion?
A part, share, or quantity that is compared to a total is referred to as a proportion. According to the concept of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
When two ratios are equal, they are said to be in proportion.For instance, the time it takes a train to go 50 kilometers per hour is equal to the time it needs to travel 250 kilometres in 5 hours. e.g., 250km/5 hours at 50 km/h.
[tex]A) \\\\\frac{2}{8} =\frac{3}{12} =\frac{1}{4}\\\\(B) \\\\\frac{3}{4} \ !=\frac{8}{10}= \frac{4}{5}\\\\\ (C)\\\\\frac{25}{10} =\frac{5}{2}\\\\(D)\\\\ \frac{3}{4} =\frac{15}{20}[/tex]
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g(x)=x^4-3x^3-8x^2-6x-20, find zeros
Answer:x=-2,5, -[tex]i\sqrt{2}[/tex], +[tex]i\sqrt{2}[/tex]
Step-by-step explanation:
y + 3 = (x - 6)
“Identify the slope and a point on a line, then graph the line”
How would I graph it with no slope and only one point?
Answer:
see attached
Step-by-step explanation:
Given the equation for a line, y +3 = (x -6), you want to identify the slope and a point on the line, then graph it.
Point-slope formThe point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . . . . line with slope m through point (h, k)
Comparing this to the given equation, you can see ...
k = -3m = 1 . . . . . . . . . . a coefficient of 1 is often "missing" or "implied"h = 6This tells you the slope is 1 and a point on the line is (6, -3).
GraphYou graph this equation by plotting point (6, -3) and drawing a line through it that goes up 1 unit for each 1 unit to the right. A graph is attached.
__
Additional comment
If you like, you can rearrange the equation to slope-intercept form by subtracting 3:
y +3 -3 = (x -6) -3
y = x -9
This tells you another point is -9 on the y-axis.