Answer:
x = 5 , y = 15
Step-by-step explanation:
You can solve this using substitution.
Let the quantity of cheese wafers be denoted by x and the quantity of chocolate wafers denoted by y
2x + 1y = 25
x + y = 20
These two equations are the answer to part A, (remember to include the above prompt which says what x and y denote).
For part B I used substitution because it was more applicable to the question then addition or elimination.
ACTUAL WORK
Set 2x + 1y = 25 equal to x
x = 25 - y / 2
Replace x with y in the second equation
(25 - y / 2) + y = 20
And solve for y
y = 15
Since we know what y is we can replace y in the second equation and find what x is
x + 15 = 20
Solve for x
x = 5
Answer:
5 Cheese Wafers and 15 Chocolate Wafers
Step-by-step explanation:
Combine the radicals. 2√24+5√54 A) 53√6 B) 5√6 C) 19√6 D) 93√6
Answer:
The answer is option CStep-by-step explanation:
2√24 + 5√54
To combine the radicals first make sure the radicals have the same square root
That's
For 2√24[tex]2 \sqrt{24} = 2 \sqrt{4 \times 6} = 2 \times 2 \sqrt{6} [/tex][tex] = 4 \sqrt{6} [/tex]For 9√54[tex]5 \sqrt{54} = 5 \sqrt{9 \times 6} = 5 \times \sqrt{9} \times \sqrt{6} [/tex][tex] = 5 \times 3 \times \sqrt{6} [/tex][tex] = 15 \sqrt{6} [/tex]Since they have the same square root we can combine them
That's
[tex]4 \sqrt{6} + 15 \sqrt{6} = (4 + 15) \sqrt{6} [/tex]We have the final answer as
[tex]19 \sqrt{6} [/tex]Hope this helps you
Review what you know about products and sums represented by rectangular area models. [5 points] Use algebra tiles to multiply (x-1)(3x+2).
3x^2 - x - 2
What are some ways to solve an equation?
Different ways to solve equations. We have 4 ways of solving one-step equations: Adding, Substracting, multiplication, and division. If we add the same number to both sides of an equation, both sides will remain equal.
How do you evaluate an equation?
∫ y2+y−2dy ∫ y 2 + y − 2 d y∫ 2 1 y2 +y−2dy ∫ 1 2 y 2 + y − 2 d y∫ 2 −1 y2 +y−2dy ∫ − 1 2 y 2 + y − 2 d y= (x - 1)(3x + 2)
= 3x^2 + 2x - 3x - 2
= 3x^2 - x - 2
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Puzzle corner
Look Before You Leap!
See how long it takes you to work out the
following:
(1 x2)×(3 x 4)×(586)×(7 x 8) x (
9×0)
Answer:
0
Step-by-step explanation:
Notice that the last factor is null (9×0)
So the result will be null since any number that is multiplied by 0 equals 0.
Find the slope of the line that passes through the points (-8,-3) and (2, 3)
0
1
3/5
5/3
Answer:
The answer is
[tex] \frac{3}{5} [/tex]Step-by-step explanation:
To find the slope passing through two points we use the formula
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]Where
m is the slope
( x1 , y1) and ( x2 , y2) are the points
From the question the points are
(-8,-3) and (2, 3)
So the slope is
[tex]m = \frac{3 + 3}{2 + 8} = \frac{6}{10} = \frac{3}{5} [/tex]Hope this helps you
761.8 x 10^-8 Express the number in scientific notation. A) 7.618 x 10^-6 B) 7.618 x 10^-8 C) 7.618 x 10^2 D) 7.618 x 10^6
Answer:
[tex]\huge\boxed{A)\ 7.618\times10^{-6}}[/tex]
Step-by-step explanation:
The scientific notation:
[tex]a\cdot10^n[/tex]
where
[tex]1\leq a<10;\ n\in\mathbb{Z}[/tex]
We have
[tex]761.8\times10^{-8}[/tex]
We need to move the decimal point two places to the left.
[tex]\underbrace{(7.618\times10^2)}_{=761.8}\times10^{-8}=7.618\times(10^2\times10^{-8})[/tex]
use
[tex]a^n\cdot a^m=a^{n+m}[/tex]
[tex]=7.618\times10^{2+(-8)}=7.618\times10^{-6}[/tex]
Answer:
a
Step-by-step explanation:
WILL MARK BRAINLIEST!!!!20 POINTS!!!!URGENT!!!
Answer:
the firsts third and last one
Step-by-step explanation:
hope this helped
The amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of minutes and a standard deviation of minutes. Find the probability that a randomly selected athlete uses a stairclimber for (a) less than minutes, (b) between and minutes, and (c) more than minutes. (a) The probability that a randomly selected athlete uses a stairclimber for less than minutes is nothing. (Round to four decimal places as needed.) (b) The probability that a randomly selected athlete uses a stairclimber between and minutes is nothing. (Round to four decimal places as needed.) (c) The probability that a randomly selected athlete uses a stairclimber for more than minutes is nothing.
Answer:
Step-by-step explanation:
Let S be the sample space, n(S) = 60
a) Let A be the event that the selected athlete uses
s less than a minute, n(A) = 59
The probability that a randomly selected athlete uses less a minute, P(A) = n(A)/n(S) = 59/60 = 0.9833
b) 1 - 0.9833 = 0.0167
c) 1 - 1 = 0
pls help. A granola mix sells for $8.99 a pound. Tung wants to buy a bag of granola mix that weighs 7.8 pounds. The bag of granola mix will cost about $16. $17. $63. $72.
Answer:
about 72 dollars
Step-by-step explanation
"about" tells us to round our numbers. Therefore, 7.8 becomes 8. As each pound is $8.99, we multiply the two and get 71.92, which is "about" 72.
Answer:
$72
Step-by-step explanation:
To find the cost, multiply the price per pound by the number of pounds.
8.99(7.8)
= 70.12
This is closest to $72
Which is the simplified form of the expression ((2 Superscript negative 2 Baseline) (3 Superscript 4 Baseline)) Superscript negative 3 Baseline times ((2 Superscript negative 3 Baseline) (3 squared)) squared?
Answer:
[tex]\dfrac{1}{6561}[/tex]
Step-by-step explanation:
Given the expression [tex][(2^{-2})(3^{4})]^{-3} * [(2^{-3})(3^2)]^{2}[/tex], Using the laws of indices to simplify the expression. The following laws will be applicable;
[tex]a^m*a^n = a^{m+n}\\(a^m)^n = a^{mn}\\[/tex]
[tex]a^{-m} = 1/a^m[/tex]
Given [tex][(2^{-2})(3^{4})]^{-3} * [(2^{-3})(3^2)]^{2}[/tex]
open the parenthesis
[tex]= (2^{-2})^{-3}(3^{4})^{-3}* (2^{-3})^2(3^2)^2\\\\= 2^{-2*-3}* 3^{4*-3} * 2^{-3*2} * 3^{2*2}\\\\= 2^6 * 3^{-12} * 2^{-6} * 3^4\\\\collecting \ like \ terms\\\\= 2^6 * 2^{-6} * 3^{-12} * 3^4\\\\= 2^{6-6} * 3^{-12+4}\\\\= 2^0 * 3^{-8}\\\\= 1 * \frac{1}{3^8}\\ \\= \frac{1}{6561}[/tex]
What is the solution to 7 × p = -56? A. -49 B. -8 C. 8 D. 49
Answer:
-8
Step-by-step explanation:
Hello!
What we do to one side of the equation we do to the other side
7 * p = -56
Divide both sides by 7
p = -8
The answer is -8
Hope this helps!
Which equation can be used to find x, the length of the hypotenuse of the right triangle?
Answer:
[tex] \boxed{\sf {18}^{2} + {24}^{2} = {x}^{2}} [/tex]
To Find:
Length of hypotenuse of the right triangle i.e. x
Step-by-step explanation:
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.
[tex] \therefore [/tex]
[tex] \sf \implies {18}^{2} + {24}^{2} = {x}^{2} [/tex]
Answer:
18²+24²=x²
Step-by-step explanation:
to answer this question you must know Pythagorean theorem
a^ 2+b^2 =c^2
a and b stands for the sides with length 24 and 18 and c stands for the HYPOTENUSE . so the correct answer for the above question is 18²+24²=x²
The physician orders 1500 flu injections. There were 300 shots given in September, 450 shots given in October, and 665 shots given in November. What percentage of flu vaccine has been given?
Answer:
94.33
Step-by-step explanation:
add up all numbers then input into a percentage calculator
Percentage of flu vaccine has been given 94.33%
What is percentage?
Percentage is defined as ratio expressed as a fraction of 100.
The physician have total 1500 flu injections
300 shots given in September,
450 shots given in October,
and 665 shots given in November,
Total flu vaccine has been given = 300+450+665 = 1415
Percentage of flu vaccine has been given = (1415/1500)×100%
Percentage of flu vaccine has been given = 0.9433×100%
Percentage of flu vaccine has been given = 94.33%
Hence, percentage of flu vaccine has been given 94.33%
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(08.02)How many solutions are there for the system of equations shown on the graph? No solution One solution Two solutions Infinitely many solutions
Answer: Infinitely many solutions
Step-by-step explanation:
There are many solutions because the lines lies on top of each other.
i dont know the exact answer but its not
One solution
Two solutions
so its most likely
Infinitely many solutions
If a polygon has an area of 10 cm² and is dilated by a factor of 2, what will be the area of the dilated polygon?
Area depends on the product of sides,
so if the sides are shortened by a factor of 2, area will reduce by a factor of 4. (2×2)
new area = 10/4=2.5 cm²
New York City is a popular feild trip destination. This year the senior
class at High School A and the senior class at High School B both
planned trips there. The senior class at High School A rented and filled
8 vans and 4 buses with 220 students. High School B rented and filled 12 vans and 4 buses with 228 students. Every van had the same
number of students in it as did the buses. How many students can a
van carry? How many students can a bus carry?
Step-by-step explanation: look so if you have
shcool A its 8v+4b=12
and
School B: 12v+4b= 16
since both classes used 4 busses we can use elimination by subtracting the A class Equation from the b class equation to solve from v for its value Then, use either equation and the now found value for v to solve for b.
You should find part of the process to be
12v+4b-(8v+4b)=12-16 which shows the van holds only a few people even before continuing the solution.
Answer -4
HELP SOMEONE PLEASE!!!!! Factor completely 10x2 + 2x − 8. 2
(5x − 1)(x + 4) 2(5x − 4)(x + 1) 2(5x + 2)(x − 2) 2(5x − 2)(x + 2)
Answer:
2(5x - 4)(x + 1)
Step-by-step explanation:
10x^2 + 2x − 8 =
First, factor out the GCF of all terms which is 2.
= 2(5x^2 + x - 4)
5x^2 factors into 5x and x.
= 2(5x )(x )
-4 factors into -4 and 1, -1 and 4, and -2 and 2. Use the set of two factors in the proper positions that will give the middle term.
= 2(5x - 4)(x + 1)
Answer:
[tex]\large \boxed{2(5x-4)(x+1)}[/tex]
Step-by-step explanation:
[tex]10x^2 + 2x - 8[/tex]
Rewrite 2x as 10x - 8x.
[tex]10x^2 + 10x-8x - 8[/tex]
Factor out the two groups.
[tex]10x(x+1)-8(x+1)[/tex]
Take x+1 as a common factor.
[tex](10x-8)(x+1)[/tex]
Factor 10x - 8.
[tex]2(5x-4)(x+1)[/tex]
Brian invested his savings in two investment funds. The $8000 that he invested in Fund A returned a 4% profit. The amount that he invested in Fund B returned a 1% profit. How much did he invest in Fund B, if both funds together returned a 2% profit?
Answer: Brian invested $16000 in Fund B .
Step-by-step explanation:
Let x be the amount Brian invested in Fund B.
Given, The $8000 that he invested in Fund A returned a 4% profit. The amount that he invested in Fund B returned a 1% profit.
i.e. profit on Fund A = 4% of 8000 = 0.04 ×8000 = $320
Profit on Fund B = 1% of x = 0.01x
Together they earn 1% profit, i.e. Combined profit = 2% of (8000+x)
= 0.02(8000+x)
As per question,
Combined profit=Profit on Fund A+Profit on Fund B
[tex]\Rightarrow\ 0.02(8000+x) =320+0.01x\\\\\Rightarrow\ 0.02(8000) +0.02x=320+0.01x\\\\\Rightarrow\ 160+0.02x=320+0.01x\\\\\Rightarrow\ 0.02x-0.01x=320-160\\\\\Rightarrow\ 0.01x=160\\\\\Rightarrow\ x=\dfrac{160}{0.01}\\\\\Rightarrow\ x=16000[/tex]
Hence, Brian invested $16000 in Fund B .
What is the simplified expression for 22 • 2?
24
O 20
021
O 22
0 23
2^1 would be the answer.
2^2 x 2^3 is 32
2^4 is 16
32/16 is 2
2^1 is 2 so the answer is 2^1
Answer:
2¹
Step-by-step explanation:
When multiplying exponents of the same base, you can simply add the exponents together so 2² * 2³ = 2⁽²⁺³⁾ = 2⁵. When dividing exponents of the same base, you can simply subtract the exponents so 2⁵ / 2⁴ = 2⁽⁵⁻⁴⁾ = 2¹.
what do you think you’d like most about working as a forensic scientist? why
Answer:
i think its very interesting and pretty cool, because there is so much to learn and so much to explore
i wouldn't like the fact that you have to study so much though
Step-by-step explanation:
Pls answer I really need help
Brainlist and thank you will be the reward thank you so much!!!
Answer:
0.667 ✅Step-by-step explanation:
This is best solved using a proportion.
The formula is soy/vinegar = soy/vinegar where one of these is a variable.
Here we have:
[tex]\frac{150}{100} = \frac{1}{x}[/tex]
Now, we solve this by cross multiplying.
150x = 100
Dividing both sides by x, we get x = 2/3 or about 0.667.
Checking:
[tex]\frac{150}{100} = \frac{1}{0.667}[/tex]
1.5 = 1.5 ✅
I'm always happy to help :)draw the graph of linear equation 5y = 3x + 18 on a cartesian plane. From the graph check weather (-2,4) is the solution of the linear equation or not PLS URGENT ANSWER
Answer:
The point (-2, 4) is not a solution of the linear equation, 5·y = 3·x + 18
Please find attached the required graph of the linear equation 5·y = 3·x + 18 written in the form y = 3/5·x + 18/5
Step-by-step explanation:
The given equation is 5·y = 3·x + 18, from which we have;
y = 3/5·x + 18/5
To draw the graph, we generate for vales of y corresponding to values of x as follows;
x, y
-6, 0
-5, 0.6
-4, 1.2
-3, 1.8
-2, 2.4
-1, 3
0, 3.6
1, 4.2
2, 4.8
3, 5.4
4, 6
5, 6.6
6, 7.2
7, 7.8
8, 8.4
9, 9
10, 9.6
11, 10.2
12, 10.8
13, 11.4
14, 12
15, 12.6
16, 13.2
Therefore, when y = 0, x = -6, when x = 0, y = 3.6, when x = -2, y = 2.4, when y = 4, x = -2, x = 6
Therefore, the point (-2, 4) is not a solution of the linear equation, 5·y = 3·x + 18
what is the coefficient of x in the equation of 32+2x=10
solve after finding the coefficient
Answer:
x= -11
Step-by-step explanation:
the coefficient is variable that appears before a number . bearing this in mind, the coefficient of x is therefore 2 .
the value of x is:
>32+2x=10
>2x=10-32
>2x= -22
>x= -11
Answer:
Step-by-step explanation:
Coefficient of x = 2
32 + 2x = 10
Subtract 32 from both side
32 + 2x -32 = 10 - 32
2x = - 22
Divide both sides by 2
2x/2 = -22/2
x = -11
A set of circular cups are placed so that they are touching rim to rim, as close together as possible. It is not possible to fit more cups inside the group if the longest straight line is five cups long, how many cups are there altogether?
Answer:
The total number of cups in arranged in an hexagonal area = 19 cups
Step-by-step explanation:
The pack the most circles within an area, the arrangement with the densest packing is the hexagonal lattice structure similar to the bee's honeycomb as has been proved Gauss and Fejes Toth.
Therefore, we pack the circles in an hexagonal lattice structure in an assumed hexagonal area where we have;
The longest straight line is five cups the next on either side are four cups and the final line on either side has three cups
The total number of cups = 3 + 4 + 5 + 4 + 3 = 19 cups
The total number of cups = 19 cups.
Rebecca is saving money to purchase a laptop, which costs $1,099.51. She has already saved $354.20 and plans to continue
saving $50.60 per week. Which inequality could be used to find w, the number of weeks that Rebecca must save in order to
purchase the laptop?
OA $354.20 + $50.60w < $1,099.51
OB. $354.20w+ $50.60 $1,099.51
OC $354.20 + $50.60w< $1,099.51
OD. $354.20 + $50.60w $1,099.51
Answer:
354.20 + 50.60w ≥ 1099.51
Step-by-step explanation:
354.20 + 50.60w ≥ 1099.51
math now..!! Help..?
Answer:
2p + 12
2 (p = +6) + 12 = 20
Answer:
I think its 6
Step-by-step explanation:
because you have to add 9 and 3 together then you get 12 and you have to divide 2p with 12 and you'll get 6
The side of an Equileteral triangle is 12cm. What is its Area?
Answer:
A = 62.35 cm²
Step-by-step explanation:
Use the area formula A = [tex]\frac{\sqrt{3}a^2}{4}[/tex], where a is the side length.
Plug in the values:
A = [tex]\frac{\sqrt{3}(12^2)}{4}[/tex]
A = [tex]\frac{\sqrt{3}(144)}{4}[/tex]
A = 62.35 cm²
What is the width of the rectangle shown below?
4x + 3
A = 8x2 – 10x – 12
Answer:
2x-4Step-by-step explanation:
Area of a rectangle = Length * Width
Given parameters
Area A = 8x2 – 10x – 12
Length of the rectangle = 4x+3
Required
Width of the rectangle.
Substituting the given parameters into the formula
8x2 – 10x – 12 = (4x+3)*width
width = 8x2 – 10x – 12 /4x+3
S
Factorizing the numerator
8x² – 10x – 12
= 2(4x²-5x-6)
= 2(4x²-8x+3x-6)
= 2(4x(x-2)+3(x-2))
= 2(4x+3)(x-2)
Width = 2(4x+3)(x-2)/4x+3
Width = 2(x-2)
Width = 2x-4
Hence the width of the rectangle is 2x-4
Which equation represents the line that is perpendicular to y=3/4x+1 and passes through (-5,11)
Will give brainliest!!
Answer:
y = - [tex]\frac{4}{3}[/tex] x + [tex]\frac{13}{3}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{3}{4}[/tex] x + 1 ← is in slope- intercept form
with slope m = [tex]\frac{3}{4}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{4} }[/tex] = - [tex]\frac{4}{3}[/tex] , thus
y = - [tex]\frac{4}{3}[/tex] x + c ← is the partial equation
To find c substitute (- 5, 11) into the partial equation
11 = [tex]\frac{20}{3}[/tex] + c ⇒ c = 11 - [tex]\frac{20}{3}[/tex] = [tex]\frac{13}{3}[/tex]
y = - [tex]\frac{4}{3}[/tex] x + [tex]\frac{13}{3}[/tex] ← equation of perpendicular line
The equation of the line that passes through (-5, 11) and perpendicular to y = (3/4)x + 1 is
y = -2x + 1
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
y = (2/4)x + 1 is in the form of y = m(2)x + c
So,
m(2) = 2/4 = 1/2
The equation of the line y = m(1)x + c is perpendicular to y = (2/4)x + 1.
So,
m(1) x m(2) = -1
m(1) = -1/(1/2)
m(1) = -2
Now,
y = -2x + c passes through (-5, 11).
This means,
11 = -2 x (-5) + c
11 = 10 + c
11- 10 = c
c = 1
Thus,
The equation of the line is y = -2x + 1.
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Work out the value of angle x
======================================================
Explanation:
The given exterior angle 97 is adjacent to the interior angle 180-97 = 83. This is the base angle of the isosceles triangle. The other base angle is directly above it. The base angles are always opposite the congruent sides.
The missing interior angle (adjacent to the blue angle x) is unknown, so we'll call it angle y. This angle adds to the other two base angles (83 each) to get a sum of 180. Adding any three interior angles of a triangle always gets you 180
y+83+83 = 180
y+166 = 180
y = 180-166
y = 14
Angle x and y are supplementary. They form a 180 degree angle
x+y = 180
x = 180-y
x = 180-14
x = 166
As you can see, the base angles combine to form the exterior angle we're after. This is because of the remote interior angle theorem.
Maria has eight black marbles, fourteen clear marbles, and twelve blue marbles in a bag. If she picks two marbles at random, without replacement, what is the probability that she will select a blue marble first, then a clear marble?
Answer:
[tex]\boxed{0.15}[/tex]
Step-by-step explanation:
Part 1: Solve for the total amount of marbles
To solve for the probability of certain events, a population is needed to derive this information from. In order to find this population, add up the amounts of each marble.
8 + 14 + 12 = 34 marbles
Part 2: Determine the probabilities
Now, given the amounts of marbles, simply multiply the ratios of blue marbles to total marbles and the ratio of clear marbles to total marbles to get the combined probability.
[tex]\frac{12}{34}*\frac{14}{33} = \frac{28}{187} \approxeq 0.1497 \approxeq 0.15 * 100 = 15[/tex]
The probability of these events occurring simultaneously is 15%.
