Statement 1 is correct and Statement 2 is not correct.
As A, B and C represent distinct non-zero digits
For least value of x
Let A=1, B=2, C=3
The possible numbers that can be formed using 1,2,3 are 6 {using permutations}
123, 132, 213, 312, 231, 321
x is the sum of all possible 3-digit numbers formed by A, B and C without repetition so
x= 123+ 132+ 213+ 312+ 231+ 321
x=1332
So statement 1 is correct
statement 2 cannot be correct as least value of x is 4-digit so greatest value of x cannot be a three digit number.
The 4-digit least value of x is 1332 so Statement 1 is correct and Statement cannot be correct.
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2x³ +x² -25x +12 factorised
The correct solutions for "x" after factorizing the cubic equation are:
x1 = -4
x2 = 0.5
x3 = 3
Cubic Equation:
A cubic polynomial in mathematics is a polynomial whose highest degree is three. A cubic equation is one that contains a cubic polynomial.
Either one real root or three real roots are present in every cubic equation. The cubic equation is written as ax^3+bx^2+cx+d=0.
Therefore, standard form of the cubic equation is: ax^3 + bx^2 + cx + d = 0
Given: 2x³ +x² -25x +12
On comparing with the standard form of the cubic equation, we get;
a=2
b=1
c=-25
d=12
After factorizing the cubic equation, we have three roots.
x1 = -4
x2 = 0.5
x3 = 3
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Solve the inequality. Graph the solution. -3y<-14
Answer:
y > 14/3
Step-by-step explanation:
-3y<-14
Divided both sides by -3. Because divided by a negative number, the < will switch to the >
y > 14/3
Find the VOLUME of the figure below
Answer: 12 yd^3
Step-by-step explanation:
(base area x height)/3
1/2 x base x height = base
1/2 x 4 x 3 = 6
36/3 = 12yd^3
A designer is planning a trail mix box that is shaped like a rectangular prism. The front of the box must have the width and height shown. Volume of the box must be 162 cubic inches. What must be the depth, d, of the box?
Answer:
The box must be 2.4 in deep.
Step-by-step explanation:
Front dimensions are 9 in by 7.5 in. Find the area of the front: it is
A = (9 in)(7.5 in) = 67.5 in^2. One way to complete this work would be to divide the given volume by this area, 67.5 in^2.
A slightly different approach follows:
The volume must be 162 in^2. Given V = (width)(height)(depth),
V
(depth) must be -----------------------
(width)(height)
In this particular case,
162 in^3
(depth) must be ----------------------- = 2.4 in
(7.5 in)(9 in)
The box must be 2.4 in deep.
Line 1 has slope 2 and goes through (1,3). Which is one form of the equation for line ??
Step-by-step explanation:
y = 2x + b ---> 3 = 2(1) + b ---> b = 1
Therefore, y = 2x + 1
Does (9, 0) make the equation y = 8x + 9 true?
nope. bc...
0 ≠ 72 + 9.
yw!
Answer:
no.
Step-by-step explanation:
y (0) = 8(9) + 9
0 = 72 + 9
0 = 81
0 does not equal 81
Which graph represents the function?
f(x)=3√x + 2
What is 26633646376+63761876784
Answer:63,761,876,784
Step-by-step explanation:
Is (3,6) a solution to this system of equations?
y=2x+1
y=4x+6
Step-by-step explanation:
y = 2x + 1 -------- (I)
y = 4x + 6 --------(ii)
from eqn (I)
y = 2x + 1
sub y = 2x + 1 in eqn (ii)
2x + 1 = 4x + 6
2x - 4x = 6 - 1
-2x = 5
x = -5/2
sub x = -5/2 in eqn (I)
y = 2(-5/2) + 1
y = -5 + 1
y = -4
Therefore, (x, y) = (-5/2, -4)
There are 5,280 feet in a mile. Round answers
nany miles does a car traveling at 65 mi/h.
b. How many feet does a car traveling at 65 mil
c How many feet does a car traveling at 65 mi/h
d. How many feet does a car traveling at 65 mi/h o
3. There are 5,280 feet in a mile. Round answers t o
nswers to the nearestur
5 mi/h go in one hour
+ 65 mi/h go in one hour]
65 mi/h go in one minute
+ 65 mi/h go in one second?
343200 fts distance travelled in an hour
5720 ft was travelled in 1 minute and,
95.33 ft distance was travelled in 1 second.
What is miles and foot ?The mile is a customary unit of measurement in the United States and the United Kingdom that is based on the older English unit of length equal to 5,280 English feet, or 1,760 yards. It is often referred to as the international mile or statute mile to distinguish it from other miles.
The British imperial and American customary systems of measurement both use the foot as a unit of length, denoted by the standard symbol: ft. An other sign that is frequently used is the prime symbol, ′. One foot is precisely equal to 0.3048 meters as of the International Yard and Pound Agreement of 1959.
5,280 feet per mile, sometimes known as a statute mile, is a unit of measurement (1.609 km). It derives from the mille passus, or "thousand paces," of the Romans, which was equivalent to 5,000 Roman feet.
65 miles per hour
so 65 * 5280 = 343200 ft travelled in 1 hr
in one minute distance travelled = 343200/60 = 5720 fts
and in one second distance travelled = 5720/60 = 95.33 fts.
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What is the inverse of 9 by 7?
-9/7 is the inverse of 9/7.
-9/-7 = 9/7
9/7 + (-9/7) = 0
-9/7 is consequently the additive opposite of -9/-7.
By merely switching the integer's sign, you can add the original number and the additive inverse to produce a result equal to 0. The value that, when added to the original number, results in zero is known as a number's additive inverse. It is what we add to a number to make it equal to zero. Considering that an is the starting number, its additive inverse will be a minus one, or -a, such that;
a+(-a) = a – a = 0
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What is the rule for quadrant 4?
All points in Quadrant IV have a positive x-coordinate and a negative y-coordinate.
The fourth quadrant, indicated as Quadrant IV, is in the bottom right quadrant. The x-axis in this quadrant has positive values, whereas the y-axis has negative numbers.
A two-dimensional Cartesian system's axes split the plane into four infinite areas called quadrants, each of which is limited by two half-axes. These are frequently numbered from first to fourth.
A quarter of a circle; a 90° arc. the region enclosed by an arc and two radii are drawn one to each extreme. As a mechanical component, anything is shaped like a quarter of a circle.
All Quadrant I points have two positive coordinates.
Quadrant II points all have a negative x-coordinate and a positive y-coordinate.
All Quadrant III locations have two negative coordinates.
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How do you write an expression in vertex form?
Therefore a quadratic function can be written in vertex form as
y = a(x - h)^2 + k.
Define quadratic function.In mathematics, a polynomial of degree two in one or more variables is referred to as a quadratic polynomial. The polynomial function that a quadratic polynomial defines is known as a quadratic function.
What is a polynomial function?In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
A quadratic function can be written in vertex form as y = a(x - h)^2 + k
Where (h, k) is the vertex, and a is the leading coefficient.
y = ax^2 + bx + c (standard form)
y = a(x + b/2a)^2 + c - b^2/4a
y = a(x - h)^2 + k where h = -b/2a and k = c - b^2/4a
For example,when y = 3x^2 - 6x - 5
y = 3x^2 - 6x - 5
y = 3(x^2 - 2x) - 5
y = 3(x^2 - 2x + 1 - 1) - 5 = 3(x - 1)^2 - 8
So, the equation is in vertex form y = 3(x - 1)^2 - 8
Note that this only works for parabolas that opens upwards or downwards, if the parabola opens to the sides, the vertex form is y = a(x-h)^2 +k
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Write an explicit formula for the sequence 1,4,7,10... Then find a14.
Answer:
The formula is [tex]a_n = 3n-2[/tex]
The 14th term is 40, in other words, [tex]a_{14} = 40[/tex]
========================================================
Explanation:
The given sequence is 1, 4, 7, 10, ...
Subtract each adjacent term:
4-1 = 37-4 = 310-7 = 3This shows that each term is increasing by 3. This is the common difference, so d = 3.
The first term is [tex]a_1 = 1[/tex]
The nth term of the arithmetic sequence is...
[tex]a_n = a_1 + d(n-1)\\\\a_n = 1 + 3(n-1)\\\\a_n = 1 + 3n-3\\\\a_n = 3n-2\\\\[/tex]
As a check, let's plug in say n = 3 to find that:
[tex]a_n = 3n-2\\\\a_3 = 3(3)-2\\\\a_3 = 9-2\\\\a_3 = 7\\\\[/tex]
The third term is 7, which matches with the sequence given to us. I'll let you confirm the other values.
-----------
We'll repeat this idea but now for n = 14 to find the 14th term of the sequence.
[tex]a_n = 3n-2\\\\a_{14} = 3(14)-2\\\\a_{14} = 42-2\\\\a_{14} = 40\\\\[/tex]
The 14th term is 40.
You can make a table of values to help confirm the answer. In the first column you'll have the values of n (1,2,3,...) all the way up to 14. The second column will consist of the sequence 1, 4, 7, 10, ... each time going up by 3 until you reach the 14th term of 40.
In its prime, Mr. Ford's 2002 Focus would get 36 miles/gallon. Mr. Ford starts a road trip to San Bernardino, Barstow, Kingman, Winona, and Flagstaff, AZ. He starts with 13.2 gallons of gas in his gas tank. a) Write a slope-intercept equation that models how much gas remains in his tank after each mile of of travel(hint: g/mi)
Given :
Mr. Ford's 2002 Focus would get 36 miles/gallon.
He starts with 13.2 gallons of gas in his gas tank.
To Find :
Write a slope-intercept equation that models how much gas remains in his tank after each mile of of travel(hint: g/mi).
Solution :
Let, required equation is :
y = mx + c
Here, y is gas remains in gallons.
Here, m is slope i.e. miles travelled per gallon.
So, m = -36 ( since gas is decreasing )
Initially distance travelled is 0 i.e. putting x = 0
y = c = 13.2
Therefore, y = -36x + 13.2 this is the required equation.
A fifth grader takes a standardized achievement test (mean = 125, standard deviation = 15) and
scores a 148. What percent of children made higher than a 148?
the child's percentile rank is 93 th percentile. It means he performed better than [tex]$93 \%$[/tex]of the total number of students.
What is Percentile rank?When compared to other students in the same grade and topic, for instance, a student's percentile rank shows how well they performed. The percentile rank of a student indicates whether their score was on par with or higher than that of the norm group's percentage of pupils. In statistics, the percent of scores in a frequency distribution that are lower than a specific score is known as the percentile rank of that score. A percentile rank returns a numerical value, which really indicates the proportion of people who fall inside that range. Since it is a percentile, its range is always between 1 and 99, with 50 serving as its mean or average rank. Only normalized values or data are ever usable in this fashion.- Mean, $\boldsymbol{\mu}=125$.- Population standard deviation, $\sigma=15$.- Marks obtained by child $(X)=148$Need to find the percentile rank for child's score.
Let[tex]$\mathrm{X}$[/tex]denote marks obtained by the child in the achievement test.
The [tex]$\mathrm{Z}$[/tex]value is given as,
[tex]$$Z=\frac{X-\mu}{\sigma}$$[/tex]
Using equation (1), the required percentile rank for child's score is expressed as,
[tex]& Z=\frac{148-125}{15} \\[/tex]
[tex]& Z=1.533[/tex]
The probability value corresponding to the Z=1.533, obtained from the Z table is 0.93736.
Thus, the percentile is 0.93736.
Therefore, the child's percentile rank is 93 th percentile. It means he performed better than [tex]$93 \%$[/tex]of the total number of students.
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Solve for q.
q + 7 = 61
q = ____
Answer:
q+7=61
soln
Step-by-step explanation:
q=61-7=54answer
How do you add a function in FG?
To add a function in FG, open the functions. php file in your theme folder, add the code for the function at the bottom of the file, save the file, and add the code for the function in the template files where you want it to appear.
To add a function in FG, you first need to open the functions. php file in your theme folder. This is where all the functions for your theme will be stored. Once you have the file open, you can add the code for the function that you want to create. This code should go at the bottom of the file. After you have added the code, save the file. Now, you need to add the code for the function in the template files where you want it to appear. To do this, add the following code: <?php your_function_name(); ?>. This code will call the function that you created in the functions.php file. Once you have added this code, save the file and the function should now appear in your theme.
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How do you find the area of a isosceles triangle without the height?
Since an isosceles triangle has two equal sides, it has two equal angles and two equal heights. Therefore, if you know the length of two sides, you can use the formula A = (1/2)bh to calculate the area, where b is the length of the base and h is the length of the two equal heights.
An isosceles triangle is a triangle with two equal sides and two equal angles. Since the two equal sides also have two equal heights, we can use the formula A = (1/2)bh to calculate the area of the triangle without the height. The formula A = (1/2)bh requires the length of the base (b) and the length of the equal heights (h). Therefore, if you know the length of two sides, you can use the formula to calculate the area of the isosceles triangle without the height.
1. Determine the length of two sides of the triangle.
2. Calculate the area of the triangle using the formula A = (1/2)bh, where b is the length of the base and h is the length of the two equal heights.
3. Plug the known values into the formula and solve for the area.
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Which form of payment can Courtney lose and not get back?
Can u please help.............
Answer:
152°
Step-by-step explanation:
2x + 48 = 3x - 4 (the measure of an exterior angle of a triangle = the sum of the measures of the two non-adjacent interior angles of the triangle)
=> 4 + 48 = 3x - 2x (on transposing)
=> 52 = x
Substituting the vale of x in the m∠JKM,
m∠JKM = 3x - 4 = 3(52) - 4 = 152°
Hope you understood!!
What must be added to x³ 3x² 12x 19?
The expression x3 3x2 12x 19 is a polynomial expression in standard form.
To add 24 to this expression, we need to add 24 to each of the terms. This means that the answer is x3 + 3x2 + 12x + 43. To check our work, we can use theFOIL method to expand the expression and make sure that the coefficients of each of the terms are correct. The FOIL method stands for First, Outer, Inner, Last. The first and last terms are the x3 and 43, the outer terms are 3x2 and 12x, and the inner terms are 3x2 and 12x. When we multiply these terms, we get x3 + 3x2 + 12x + 43, which is our final answer.
Calculation
x3 + 3x2 + 12x + (19 + 24)
= x3 + 3x2 + 12x + 43
The expression x3 3x2 12x 19 is a polynomial expression in standard form.
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expressions equivalent to -2(x-5)
Answer:
-2x + 10
Step-by-step explanation:
Apply the distributive law: a(b - c) = ab - ac
-2(x - 5 ) = -2x - ( -2) x 5
= - 2x - ( - 2 ) x 5
- ( -2 ) x 5 = 10
= -2x + 10
3 2. A square pyramid has volume 147cm . The height of the pyramid is 9 cm. a.) What is the length of each side of the square base? b.) What is the slant height? c.) What is the surface area? PLEASE REAL ANSWERES I HAVE POSTED 5 TIMES AND NOONE WILL ANSWERE!!!
A blood bank needs 13 people to help with a blood drive. 20 people have volunteered. Find how many different groups of 13 can be formed from the 20 volunteers.plsss help I'm stuck
Answer:
20 C 13 = 77520
Step-by-step explanation:
That's the answer that it told me on delta math.
An ambulance travels 120 miles in 1 1/2 hours. plz answer this!!!!
Answer:
80 mph
Step-by-step explanation:
help please give me the answer and no links please
Answer:
x= 69°
Step-by-step explanation:
First find the inner angle of the 159°
so you would do 180-159=21
next you add 21 ° to the 90° from the right angle
that gives you 111°
last you do 180-111 and you get 69
Answer:
x = 69
Step-by-step explanation:
180 - 159 = 21
The sum of the three angles of any triangle is equal to 180 degrees, so:
21 + 90 + x = 180
111 + x = 180
180 - 111 = x
x = 69
Have a nice day!
A pair of fair dice will be rolled. Let the random variable X = the sum of the numbers shown on their faces. The probability distribution of X is given in the table.
A 2-column table with 11 rows. Column 1 is labeled sum with entries 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. Column 2 is labeled probability with entries 0.028, 0.056, 0.083, 0.111, 0.139, 0.167, 0.139, 0.111, 0.083, 0.056, 0.028.
What is the probability that the dice show a sum of at least 6?
P(X ≥
) =
Answer: 12 and 0.972
Step-by-step explanation: am doing it
Plz help this is due today!!!
Answer: 636.28
Step-by-step explanation:
first calculate the area of the square and the semicircle after u find the area of semicircle, multiply by four and add it to the area of the square. formula for area of semicircle = [tex]\frac{\pi r^2 }2\\[/tex]
formula of area of square [tex]side^2[/tex]
The function f is given by f(x)= (x-2) (x+4) . Without using graphing technology, answer the following questions.
1. What are the x-intercepts of the graph representing f?
2. What are the x- and y-coordinates of the vertex of the graph?
3. What is the y-intercept?
Answer:
Step-by-step explanation:
1. What are the x-intercepts of the graph representing f? They are the points on the horizontal axis where the graph touches or crosses the axis. Note that on this axis, y = 0.
2. What are the x- and y-coordinates of the vertex of the graph? Since the function is written as the product of two binomials, we can take these coordinates directly from the binomials: (x - 2) yields x = 2 and (x + 4) yields x = -4.
3. What is the y-intercept? Multiply out these binomials. We get:
f(x) = x^2 + 2 - 8. When x = 0, y = -8. The y-intercept is (0, -8).
1) The x-intercepts of the graph representing f are; 2 and 4
2) The x- and y-coordinates of the vertex of the graph are; (1, -5)
3) The y-intercept is at; (0, -8)
We are given the function; f(x) = (x - 2)(x + 4)
1) The x-intercepts of a graph are the points where the graph crosses the x-axis. The x-intercepts are the value of x when f(x) = 0. Thus, the x-intercepts here are 2 and 4.
2) The vertex is the lowest point of the graph in this case as the parabola opens upwards.
Let us expand the function to get;
f(x) = x² - 2x + 4x - 8
f(x) = x² + 2x - 8
where; a = 1, b = 2, c = -8
Formula for the x-coordinate of the vertex is;
x = -b/2a
x = -2/2(1)
x = 1
Thus;
y = (1 - 2)(1 + 4)
y = -5
x- and y-coordinates of the vertex of the graph are; (1, -5)
3) The y-intercept is the point at which x = 0. Thus;
y = 0² + 2(0) - 8
y = -8
The y-intercept is (0, -8).
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