The equation, that Sebastian can use to find p, the number of pencils each friend will receive is given by: Option C: 6p = 30
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
For this case, we're given that:
Sebastian has 30 pencilsSebastian will distribute p pencils to each of his 6 friends.Now, that means, if we collect all those p pencils, then they should be 30 in count.
Sum of pencils from 6 friends = p + p + p + p + p + p = 30
or
[tex]6 \times p = 30[/tex] (since p was added 6 times itself, so we write it as 6 times p)
we don't write the "×" sign, (Using sign of multiplication is often hidden if there are non numeric symbols and numbers being multiplied are written together) Thus, the equation is 6p = 30 (well both equations are same).
Thus, the equation, that Sebastian can use to find p, the number of pencils each friend will receive is given by: Option C: 6p = 30
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Answer:C
Step-by-step explanation:
Write the vertex form of y = -x^2 + 6x + 6.
Answer:
y = - (x - 3)² + 15
Step-by-step explanation:
using the method of completing the square
y = x² + 6x + 6 ← factor out - 1 from the first 2 terms
y = - (x² - 6x) + 6
to complete the square
add/subtract ( half the coefficient of the x- term )² to x² - 6x
y = - (x² + 2(- 3)x + 9 - 9) + 6
= - (x - 3)² + 9 + 6
= - (x - 3)² + 15
expression that is equivalent to 27e+24
Answer:
3(9e + 8)
Step-by-step explanation:
the highest common factor is 3 so factor it out.
Answer:
[tex]\displaystyle 3[9e + 8][/tex]
Explanation:
Sinse you were not specific in your approach, it is safe to assume that you were probably looking for how to factour this expression, and the way to do to this is to factour a 3 out the expression sinse both quantities have a common divisour of 3:
24: 1, 2, 3, 4, 6, 8, 12, 24
27: 1, 3, 9, 27
I am joyous to assist you at any time.
Suppose that $x,y,z$ are positive integers satisfying $x \le y \le z$, and such that the product of all three numbers is twice their sum. What is the sum of all possible values of $z$
The possible values of z is an illustration of the sum operator
The sum of all possible values of z is 17
How to determine the possible sum of z?The conditions in the question are:
x <= y <= z
xyz = 2(x + y + z)
Using the trial by error method, the possible values of x, y and z are:
x = 1 , y = 3 , z = 8x = 1 , y = 4 , z = 5x = 2 , y = 2 , z = 4The sum of the z values are:
z = 8 + 5 + 4
Evaluate the sum
z = 17
Hence, the sum of all possible values of z is 17
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Help..............lllllllllllllllllll
Answer:
4 pepperoni pizzas
Step-by-step explanation:
3 cheese => 1 pepperoni
12cheese (3x4) => 4 (1x4) pepperoni
Find the length of the altitude.
[tex]135 = \frac{22 + 8}{2} \times h \\ 135 = \frac{30}{2} \times h \\ 135 = 15 \times h \\ h = \frac{135}{15} \\ h = \frac{27}{3} = 9cm[/tex]
Answer:
Area of a trapezoid :
[tex]area = \frac{a + b}{2} h[/tex]
The measures given are trapezoid
Area = 135
base 1 = 22
base 2 = 8
[tex]135 = \frac{22 + 8}{2} h \\ \\135 = \frac{30}{2} h \\ 2(135) = ( 2)\frac{30}{2} h \\ 270 = 30h \\ \frac{270}{30 } = \frac{30h}{30} \\ 9 = h[/tex]
Step-by-step explanation:
We can check if the answer is right
[tex] \frac{22 + 8}{2} \times 9 \\ \frac{30}{2} \times 9 \\ 15 \times 9 = 135[/tex]
sin 60 =11/x
x=11/sin (60)
Answer:
sixt
Step-by-step explanation:
thats easy the sin should be six
Use the equation, (1/27)^x=3^(-4x+6), to complete the following problems.
Rewrite the equation using the same base.
Solve for x. Write your answer as a fraction in simplest form.
Please show all work, and refrain from posting links, thank you!
Answer:
Given equation:
[tex]\left(\dfrac{1}{27}\right)^x=3^{(-4x+6)}[/tex]
27 can be written as [tex]3^3[/tex]
Also [tex]\dfrac{1}{a^b}[/tex] can be written as [tex]a^{-b}[/tex]
[tex]\implies \dfrac{1}{27}=\dfrac{1}{3^3}=3^{-3}[/tex]
Therefore, we can rewrite the given equation with base 3:
[tex]\implies (3^{-3})^x=3^{(-4x+6)}[/tex]
To solve, apply the exponent rule [tex](a^b)^c=a^{bc}[/tex]
[tex]\implies 3^{-3 \cdot x}=3^{(-4x+6)}[/tex]
[tex]\implies 3^{(-3x)}=3^{(-4x+6)}[/tex]
[tex]\textsf{If }a^{f(x)}=a^{g(x)}, \textsf{ then } f(x)=g(x)[/tex]
[tex]\implies -3x=-4x+6[/tex]
Add [tex]4x[/tex] to both sides:
[tex]\implies x=6[/tex]
in which quadrant is point (-4,5) located?
Find 3 ratios that are equivalent to the given ratio.
2:9
Answer:
4:18
6:27
8:36
Hope this helps! :)
I need help! Giving brainiest. Please answer as many questions as you can!!!!
Answer:
2. 12
3. 1 6/8
4. 8 5/8
5. 4 4/8
6. Eli is incorrect 1 3/8 x 3 is 4 1/8 which is greater than 3 1/8
on a blueprint, the area of a tennis court is 16.25cm². a) if the scale on the blueprint is 1cm: 4m, what is the actual area of the tennis court? b) if the length of the tennis court on the blue priny is 6.25 cm what it the actual length of the tennis court
Step-by-step explanation:
so,
1cm : 4m
that means the factor is 1/400 (as 1 m = 100 cm).
also to remember : 1 m² = 100cm×100cm = 10,000 cm²
the area of a rectangle is
length × width
if both dimensions are shortened by a factor (1/400) in our case :
length×1/400 × width×1/400 =
= length × width × 1/400² = length × width × 1/160,000
that means the area of the actual tennis court is
160,000 times the area of the blueprint picture :
160,000 × 16.25 = 2,600,000 cm² = 260 m²
we now know that the actual length of the tennis court is 400 times the length of the blueprint length :
400 × 6.25 = 2,500 cm = 25 m
Find the value of X round your answer to the nearest tenths
Answer:
x = 17.9
Step-by-step explanation:
[tex]tan40^{0} =\frac{15}{x}[/tex]
[tex]x=\frac{15}{tan40^{0} } =17.88[/tex]
rounded: 17.9
Hope this helps
The circumference of a circle is 71 π m. What is the area, in square meters? Express your answer in terms of π.
Brandon rolls a six sided die twenty times, and records the result in the table below. how many times did brandon roll above the average? 6 1 3 4 4 4 6 5 5 3 6 4 4 5 2 3 5 4 4 2 a. 14 b. 7 c. 5 d. 4
The average is the arithmetic mean of all the observations of a set of numbers. The number of times Brandon rolls above the average is 7.
What is average?The average is the arithmetic mean of all the observations of a set of numbers. it is found by dividing the sum of all the observations of the set by the number of observations in the set.
[tex]\rm{Average=\dfrac{Sum\ of\ observations}{Number\ of\ observations}[/tex]
In order to know the number of times Brandon rolls the dice above the average, we first need to calculate the average of the twenty rolls.
The average of the 20 times dice rolls,
[tex]\rm Average = \dfrac{6+1+3+4+4+4+6+5+5+3+6+4+4+5+2+3+5+4+4+2}{20}[/tex]
[tex]\rm Average = \dfrac{80}{20} = 4[/tex]
Thus, the average of the 20 rolls of the dice is 4.
Now, the number of times the result of the dice roll is above 4(x>4) is 7.
Hence, the number of times Brandon rolls above the average is 7.
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Post Falls High School in Idaho has 1160 students and is growing by 22 students per year. Richmond High School in Indiana has 1900 students and is shrinking by 15 students per year.
PLEASE ANSWER I NEED MY MATH GRADE UP PLEASE GUYS
The prism below is made of cubes which measure of an inch on one side. What is the volume?
Note: Figure is not drawn to scale.
A. 12 cubic in
B. 24 cubic in
C. 3 cubic in
D. 9/2 cubic in
PLS HELP
what is the length of side s of the square shown below ?
Answer:
[tex]\sqrt{2}[/tex] A.
Step-by-step explanation:
There's a few ways you can go about solving this, but the way I would go with is using sine law.
Sine law:
[tex]\frac{sinA}{a} = \frac{sinB}{b}[/tex]
in the equation above 'A' an angle, and 'a' would be the length of the side opposite to it. Same thing for B.
You are given the angle 90 degrees, and its opposite side length is 2.
You are also given 45 degrees from one of the corners but it doesn't tell you its side length.
There is one corner where it doesn't tell you the angle but you can figure it out using the law that the angles in a triangle must add up to 180 degrees.
So you subtract the other angles to find the angle of the bottom right angle.
180-90-45 = 45
The reason we want to find that angle, is so we can use sin law to find s.
Write down what you have so far:
[tex]\frac{sin90}{2} = \frac{sin45}{s}[/tex]
Now all you need to do is solve for s.
[tex]\frac{sin90*s}{2} = \frac{sin45}{1}[/tex]
sin 90 is 1.
[tex]\frac{1*s}{2} = sin45\\ \\s = 2*sin45\\\\[/tex]
Now since the answers available are in exact values, you can't just punch this in your calculator.
[tex]sin45 = \frac{\sqrt{2} }{2}\\ \\[/tex]
so,
[tex]s = 2*\frac{\sqrt{2} }{2} = \sqrt{2}[/tex]
What is the value of the y-intercept of the graph f(x)=138⋅1.9x?
Answer:
Step-by-step explanation:
The y-intercept is the point where the graph cuts the y axis - that is when x = 0.
f(x)=138⋅1.9x
ehen x = 0 f(x) = 0 so the y-intercept is at (0, 0).
Plss help asap!
what fraction represents numbers between 21 - 27?
Answer:
0.7778
Step-by-step explanation:
step 1
Address the input parameters and observe what to be found:
Input values:
The fraction = 21/27
What to be found:
Find the decimal expansion of fraction 21/27.
step 2
The numerator is smaller than the denominator of the fraction 21/27, so find how many 10s should be multiplied with both numerator and denominator. Since the number of digits are equal in both numerator and denominator, multiply 10 with both numerator and denominator of 21/27.
=21
27
x10
10
step 3
Rearrange the fraction as like the below:
=10 x 21
27
x1
10
=210
27
x1
10
step 4
Simplify the above expression further:
=210
27
x1
10
=189 + 21
27
x1
10
= (189
27
+21
27
) x1
10
= (7 + 21
27
) x 1
10
step 5
Repeat the step 2 to find the decimal equivalent for the fraction 21/27 in the above expression:
= (7 + 21
27
) x 1
10
= (7 + 0.778) x1
10
step 6
Simplify the above expression further:
= (7 + 0.778) x1
10
= 7.778 x1
10
=7.778
10
21
27
= 0.7778
Hence,
21/27 as a decimal is 0.7778
Find all solutions of the equation below.
7^5-3=7^5x-19
Answer:
7⁵-3=7⁵x- 19
Step-by-step explanation:
16807 - 3 = 7⁵x - 19
16804 = 7⁵x - 19
16804 = 16807x - 1
adding 19 on both sides
16804 + 19 = 16807x - 19 + 19
16823 = 16807x
x = 16823 / 16807
16823 upon 16807 is the x
A crate of pears that usually costs $50 is on sale for 10% off. What is the sale price for the crate of pears?
Sale price of the crate of pears after 10% discount on cost price $50 is equals to $45.
What is sale price?" Sale price is defined as the amount on which something is sold out."
Formula used
Sale price = Cost price - Discount amount
According to the question,
Cost price of the crate of pears = $50
Discount on sale price = 10%
Discount amount = 10% of $50
[tex]=\frac{10}{100}(50) \\\\= \$5[/tex]
Substitute the value in the formula of sale price we get,
Sale price = [tex]\$ ( 50 - 5)[/tex]
= $ 45
Hence, sale price of the crate of pears after 10% discount on cost price $50 is equals to $45.
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PLEASE HELP
If you have a graph of two lines, explain how to find the solution to the system of equations.
Each shows two lines that make up a system of equations. If the graphs of the equations intersect, then there is one solution that is true for both equations. If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.
What is the area of the triangle shown below?
m2
1/2 bxh
1/2 30 x 12
15 x12
=12
What is the slope of the line that passes through (-1, 3) and (-1, 8)?
due today
Answer:
Slope of the line is undefined
Step-by-step explanation:
(x₁, y₁) = (-1 , 3) and (x₂, y₂) = (-1 , 8)
The line is parallel to y-axis. The slope of the line parallel to y-axis is undefined.
The area of a rectangular picture frame is 93.5 square inches. The area formula for a rectangle is A = ℓw. Use the given numbers to write and solve an equation to find the width, w, of the picture frame.
Answer: w=8.5
Step-by-step explanation:
Just did it.
A week before an election 100 ople were asked who they planned to vote for or the people asked 45 said they planned to vote for
candidate and they planned to vote for candidate. The rest and they had not yet decided How many of the people that were asked
weet yetece who they plan tovorfor?
Answer:
the answer is c
Step-by-step explanation:
45% of 1500=675
38% of 1500=570
675+570=1245
1500-1245=255
HELP!!!! I can’t figure this out
Answer:
[tex]A.\,\orange{ \bold{ \frac{x - 3}{3x + 1} }}[/tex]
Step-by-step explanation:
[tex] \frac{x + 2}{ {x}^{2} + 5x + 6 } \div \frac{3x + 1}{ {x}^{2} - 9} \\ \\ = \frac{x + 2}{ {x}^{2} + 3x + 2x+ 6 } \div \frac{3x + 1}{ {x}^{2} - {(3)}^{2} } \\ \\ = \frac{\cancel{x + 2}}{ \cancel{{({x}+ 3)}} \cancel{(x+ 2) }} \times \frac{\cancel{( {x} + 3)}( {x} - {3)}}{3x + 1} \\ \\ = \purple{ \bold{ \frac{x - 3}{3x + 1} }}[/tex]
A board is 8 feet 10 inches long. How long is it in inches?
Answer:
106
Step-by-step explanation:
a foot is 12 inches so 8x12 would be 96 and if you add the other 10 inches that would be 106
solve for x. -5 + 5x = -(1 - 6x)
- 5 + 5x = - 1 + 6x
- 5 + 5 + 5x = - 1 + 5 + 6x
5x = 4 + 6x
5x - 6x = 6x - 6x + 4
- x = 4
x = - 4
Answer:
The answer is that x = -4.
Step-by-step explanation:
You first take away the parenthesis so it would look like this: -5+5x=-1+6x
Then, you add 5 to both sides of the problem: -5+5x+5=-1+6x+5
Then, you simplify it down: 5x=6x+4
You then subtract 6x from each side: 5x-6x=6x+4-6x
Then simplify again: -x=4
Then, divide both sides by -1: -x/-1 = 4/-1
Then simplify to get x = -4.
Find the volume of the solid. Use 3.14 for π.
Answer:
vol= 10366.3175in²Step-by-step explanation:
So this is a cylinder
formula: π r²hR= 8.75in
h=43.12in
So it will be = 3.14x8.75²x43.12
=> 3.14x76.5625x43.12
3.14x 3301.375
10366.3175in²i think it is correct
.
stay safe
.
have a nice TIME