Performing LCM, the least number of pencils and pens that she needs to buy are 60 pencils and 60 pens.
LCM refers to the least common multiple. The LCM of two or more numbers is the one that can divide all the numbers by the single number itself.
Pencils come in packages of 20 and pens come in packages of 12.
So, the possible lowest common multiplier is LCM of 20 and 12, and it is 60.
So she has to buy 3 packages of pencils (60/20 = 3 ) as well 5 packages of pens ( 60/12 = 5 ).
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Write the equation of the line that passes through the points (0,8) and (6,-2). Put
your answer in fully simplified point-slope form, unless it is a vertical or horizontal
line.
Answer:
[tex]y - (-2) = (-5/3)\, (x - 6)[/tex].
.Step-by-step explanation:
The [tex]x[/tex]-coordinates of the two given points are different. Therefore, the line that goes through these points would not be vertical. Likewise, this line would not be horizontal since the [tex]y[/tex]-coordinates of the given points are different.
If a line in a plane is of slope [tex]m[/tex] and goes through point [tex](x_{0},\, y_{0})[/tex], the point-slope equation of this line would be [tex]y - y_{0} = m\, (x - x_{0})[/tex].
If a line in a plane goes through the points [tex](x_{0},\, y_{0})[/tex] and [tex](x_{1},\, y_{1})[/tex] (where [tex]x_{0} \ne x_{1}[/tex],) the slope of this line would be [tex]m = (y_{1} - y_{0}) / (x_{1} - x_{0})[/tex].
Since the line in this question goes through points [tex](6,\, -2)[/tex] and [tex](0,\, 8)[/tex], the slope of this line would be:
[tex]\begin{aligned} m &= \frac{8 - (-2)}{0 - 6} \\ &= \frac{10}{(-6)} \\ &= -\frac{5}{3}\end{aligned}[/tex].
Let [tex](6,\, -2)[/tex] be the point [tex](x_{0},\, y_{0})[/tex]. The point-slope equation of this line would be:
[tex]y - (-2) = (-5 / 3)\, (x - 6)[/tex].
Help brainliest for correct answer
Answer:
14 degrees.
Step-by-step explanation:
I am assuming that the 56 degree angle is at the centre of the circle.
The angle at the top in the circle = 1/2 * 56 = 28 degrees.
The reflex angle = 360 - 56 = 304 degrees.
If we draw a line from the vertex of the 56 degrees angle to the vertex of 28 degree angle we bisect the reflex angle and the 28 degree angle. Also the 2 triangles formed are congruent ( by SSS).
So x = 180 - 1/2 * 28 - 1/2 * 304
= 180 - 14 - 152
= 180 - 166
= 14 degrees.
Susan and Kelvin each receive $100
$
100
as a gift.
Part A
Susan buys a movie ticket for $12.50
$
12.50
and 3
3
buckets of popcorn that cost $14.20
$
14.20
each with her $100
$
100
. Which statement is true?
Answer:
c
Step-by-step explanation:
2. If f(x) = 2(x - 3)2 find f(-8).
Answer:
-44
Step-by-step explanation:
The smallest composite number that can be written as a product of 4 different prime number are
Answer:
6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
the smallest composite number that can be written as a product of four different prime numbers is 6
What equation makes the line go through the following points.
(11, -3) and (7, 9)
Answer:
y = -3x + 30
Step-by-step explanation:
First, find the slope using the slope formula:
m = (y2 - y1) / (x2 - x1)
m = (9 - (-3)) / (7 - 11)
m = -12/4
m = -3
Next, find the y-intercept by substituding one of the two points into what the equation is so far:
y = -3x + b
(7, 9)
9 = -3(7) + b
9 = -21 + b
30 = b
Now you have the full equation:
y = -3x + 30
brian buys 1 pack of baseball cards to add to the 2 cards his friend gave him. then his mother gives him 2 more packs as a special treat. now he has as many cards as marcus who owns 1 pack plus 12 loose cards. how many cards are in each pack? SHOW WORK
Can give brainliest
Which of the following shows the length of the third side, in inches, of the triangle below? (1 point)
A right triangle is shown. One side of the triangle is labeled as 25 inches. The height of the triangle is labeled as 15 inches.
20 inches
Square root of 850 inches
Square root of 10 inches
40 inches
Answer:
20
Step-by-step explanation:
what values of b will cause 4x^2+bx+25=0 to have one real solution?
Answer:
b=20 or b=-20
Step-by-step explanation:
Keep in mind the meanings of the values of the discriminant:
If b^2-4ac=0, then the quadratic will have only 1 solution (double root)
If b^2-4ac<0, then the quadratic will have no real solutions
If b^2-4ac>0, then the quadratic will have 2 unique solutions
In this case, to get one real solution, the discriminant must be set up as b^2-4ac=0. Setting up the equation we get:
b^2-4(4)(25)=0
b^2-400=0
b^2=400
b=20 or b=-20
So the values of b would have to be either 20 or -20
The values of b will cause 4x^2+bx+25=0 to have one real solution is -20 and 20
Given the quadratic equation [tex]4x^2+bx+25= 0[/tex], for this expression to have a real solution, the discriminant must be greater than zero
D > 0
b^2 - 4ac > 0
Given that a = 4, b = b, c = 25
b^2 - 4(4)(25) > 0
b^2 - 400 > 0
b^2 > 400
b > ±20
Hence the values of b will cause 4x^2+bx+25=0 to have one real solution is -20 and 20
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please help I'm almost out of time
Answer:
3/2
Step-by-step explanation:
move the 3x to the other side and divide it by 2
Point G lies between points F and H on Line segment F H.
A line contains points F, G, H. The space between F and G is 4 x. The space between G and H is 2 x.
If the length of FH is 18 units, what is the value of x?
Answer:
We get the value of x: x = 3
Step-by-step explanation:
Point G lies between points F and H on Line segment F H.
Space between F and G = 4x
Space between G and H = 2x
Length of FH = 18
We need to find value of x.
As point G lies between point F and H, sum of FG and GH will give FH, we can write
[tex]FG + GH = FH[/tex]
Putting values to make equation
[tex]4x + 2x = 18[/tex]
Now, solving the equation we can find value of x
[tex]4x + 2x = 18 \\6x=18\\x=\frac{18}{6}\\x=3[/tex]
So, we get the value of x: x = 3
Answer:
dlfkv
Step-by-step explanation:
Rotation 90 degrees counterclockwise around the origin of the point (6,5)
The rotation of the point is (-5, 6)
How to determine the rotation of the point?The point is given as:
Point = (6,5)
The rule of 90 degrees counterclockwise rotation around the origin is
(x, y) = (-y, x)
So, we have
Image = (-5, 6)
Hence, the rotation of the point is (-5, 6)
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Which inequality is shown in the graph?
Consider the system y=ax+b and y=cx+d. State the conditions on the constants a, b, c, and d for which the system below has...
A. Exactly 1 solution.
B. No solutions
C. Infinitely
The following cases for the solutions of a system of linear equations are listed below:
The system has infinite solutions when a = k · c and b = k · d. The system of linear equations has no solutions for a = c. The system has only one solution if and only if a ≠ k · c and b ≠ k · d.How to infer the nature of the dependent constants in a system of linear equations
In this problem we find the case of a system of linear equations with two variables, of which we must determine the nature of its dependent constants for the following three cases:
The system has one solution.The system has no solutions.The system has infinite solutions.The implicit form of this system is shown below:
a · x - y = - b (1)
c · x - y = - d (2)
According to the linear algebra, a system of linear equations has no solutions if the determinant of the matrix of dependent coefficients is equal to zero. Then, by Cramer's law we find that:
a - c = 0
a = c
Therefore, the system of linear equations has no solutions for a = c.
Also by linear algebra, we know that the two linear equations have infinite solutions if and only if both equations are multiples of each other, then:
a · x - y + b = k · (c · x - y + d)
a · x - y + b = (k · c) · x - k · y + (k · d)
The system has infinite solutions when a = k · c and b = k · d.
Then, the system has only one solution if and only if a ≠ k · c and b ≠ k · d.
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How would you discover a mathematical relationship between corresponding terms that occur in two separate number sequences, and what can you say about those terms?
Explain answer for brainiest, 5 stars, plus a thanks!!!
Every 3rd term that occurs after the first term in the second pattern (that is, the 4th term, 7th term, 10th term, 13th term, 16th term, etc.), all represent the terms of the first pattern.
Both Patterns start at 0
Pattern 1 follows the rule, add 9.
Pattern 1 has terms, 0, 9, 18, 27, 36, 45, 54, 63, 72, 81....
Pattern 2 follows the rule, add 3.
Pattern 2 has terms, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54...
It is evident that all of the terms of the first pattern will eventually occur in the second pattern at some regular points.
They both have the same first terms.
Both Patterns have terms that are all multiples of 3.
Every 3rd term that occurs after the first term in the second pattern (that is, the 4th term, 7th term, 10th term, 13th term, 16th term, etc.), all represent the terms of the first pattern.
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2y + 7x = -5
5y - 7x = 12
x =
y =
Answer:
x = - 1, y = 1
Step-by-step explanation:
Given the 2 equations
2y + 7x = - 5 → (1)
5y - 7x = 12 → (2)
Adding the2 equations term by term will eliminate the term in x, that is
7y = 7 ( divide both sides by 7 )
y = 1
Substitute y = 1 into either of the 2 equationsand solve for x
Substituting into (1)
2(1) + 7x = - 5
2 + 7x = - 5 ( subtract 2 from both sides )
7x = - 7 ( divide both sides by 7 )
x = - 1
solution is x = - 1, y = 1
What is the range of fx) = 3^x
A. All positive real numbers
B. All real numbers greater than 3
C. All real numbers
D. All real numbers greater than or equal to 3
Answer:
d brainest plz
Step-by-step explanation:
What is
32747 written 4
significant figure?
Answer:
words are big and if words are big am I small
Holly begins with 1 penny in her piggy bank. She adds 2 pennies on day 1, 4 pennies on day 2, and 8 pennies on day 3. She continues this pattern for 30 days.
Which statement describes why this sequence is a function?
Select each correct answer.
Each amount of pennies corresponds to a unique day in this sequence.
The graph of this sequence would pass the horizontal line test.
The graph of this sequence would pass the vertical line test.
Each day corresponds to a unique amount of pennies in this sequence.
Answer:
-The graph of this sequence would pass the horizontal line test.
-Each day corresponds to a unique amount of pennies in this sequence.
Step-by-step explanation:
Answer:
B)The graph of this sequence would pass the horizontal line test.
D)Each day corresponds to a unique amount of pennies in this sequence.
Step-by-step explanation:
I took the test
A line that includes the point (4, 2)has a slope of
1
2
. What
is it equations
slope -intercept
form?
Answer: y = 1/2x + 1
(4,2)
4=x1
2=y1
y = mx + b
2 = 1/2(4) + b
2 = 2 + b
b = 1
y = 1/2x + 1
Why is the first step when solving
2x – 15 - 4x = 3 to combine like terms?
Answer:
-9 is the final answer
Step-by-step explanation:
2x-4x=-2x
so the equation would be -2x-15=3
add 15 to both sides -2x=18
divide both sides by -2
(b) Factorise fully 2 a²b + 6ab2
Answer:
2ab(a+3b)Step-by-step explanation:
[tex]2 {a}^{2} b + 6a {b}^{2} [/tex]
Factor out common term : 2ab
[tex] 2 {a}^{2}b \div 2a = a \\ 6a {b}^{2} \div 2ab = 3b \\ 2ab(a + 3b)[/tex]
[tex]2a^2b+6ab^2[/tex]
Perhaps, you mean 6ab² (If not please remind me.)
Factoring the polynomials can be done by pulling out the terms that can be divided by that terms.
For example, [tex]2x^2+4[/tex] We can divide the whole polynomial by 2. Thus, we factor 2 out of the polynomial as we get [tex]2(x^2+2)[/tex] -- Factoring is like dividing, but instead - we pull them out.
Now let's get back to the question.
Notice that the polynomial can be divided by 2, a and b.
So we pull 2, a and b out of the polynomial and divide them.
[tex]\frac{2a^2b+6ab^2}{2ab}\\a+3b[/tex]
When dividing, we should get a + 3b.
Then we pull out 2ab outside the bracket.
[tex]2ab(a+3b)[/tex]
Thus, the answer is 2ab(a+3b)
Which of the following inequalities matches the graph?
graph of an inequality with a solid vertical line through the point (negative 7, 0) and shading to the left of the line
Answer:
d
Step-by-step explanation:
5 =5v^+^
a cube of 3cm lengths is put in a cube of 5cm lengths. How much volume is left?
Answer:
2cm
Step-by-step explanation:
because?
1.1.3 what is a function? Question 5 out of 10 Mark all the statements that are true
A. The domain for this function is the set {-5}
B. The range for this function is the set {-5}
C. All real numbers are in the range of this function
D. The domain for this function is all real numbers
C. This graph is not a function because the value of Y is the same for every value of X
Jin has pounds of birdseed. If he uses 1/8 pound a
day, for how many days will Jin be able to fill the bird
feeder?
A) 6days
B)1 3/32 days
C)7/8 days
D)1 day
Answer:
C. 7/8 days
Step-by-step explanation:
The ratio of boys to girls in Coach Sheppard's class is 3 to 5. There are 20 girls
in the class.
What is the total number of students in Coach Sheppard's class?
Answer:
umm i am pretty sure it is 20 to 22
Step-by-step explanation:
What is the slope of the line graph shown below?
Answer:
5/3
Step-by-step explanation:
Between the two points, the line goes up 5 points and to the right 3 points. The slope is rise over run, so in this case the rise is 5 and the run is 3.
This makes our slope:
5/3
how many lines of symmetry does this have? 5?
Answer:
3
Step-by-step explanation:
I think ttttttttttttttttttttt