The volume of the 0.3% concentration of sodium fluoride required to mix with 100mL of a strong toothpaste with a 1.1% concentration of sodium fluoride to create a blend with a 0.8% concentration of sodium fluoride is 60 mL.
What are mixtures?Mixtures refers to substances which are composed of two or more substances physically combined together.
The 1.1% concentration of sodium fluoride will form a mixture with the 0.3% concentration sodium fluoride.
Let the volume of the 0.3 % concentration toothpaste required be x.
Final volume of toothpaste = (100 + x) mL
Amount of mixture = 0.8 * (100 + x)
100 ml * 1.1 + x * 0.3 = 0.8 * (100 + x)
solving for x
110 + 0.3x = 80 + 0.8x
110 - 80 = 0.8x - 0.3x
30 = 0.5x
x = 60
Therefore, 60 mL of the 0.3% concentration of sodium fluoride is required.
In conclusion, the volume of the weaker solution of the sodium fluoride solution required is obtained from the method of mixtures.
Learn more about mixtures at: https://brainly.com/question/2331419
#SPJ1
Rewrit using factored form solve using zero product property
Answer:
Step-by-step explanation:
a. d^2 - 7d + 6 = 0
(d - 1)(d - 6) = 0
d - 1 = 0, d - 6 = 0 therefore:
d = 1, 6.
b, x^2 + 18x + 81 = 0
(x + 9)(x + 9) = 0
x = -9 multiplicity 2.
c u^2 + 7u - 60 = 0
(u + 12)(u - 5) = 0
u = -12, 5.
Simplify the expression to a single numerical value. a. 144 b. 432 c. 900 d. 5,184
The correct option is: (b)
=432.
What is simplification?By employing multiple processes, simplification refers to reducing the expression to a simpler form. Approximation is the process of making something less complicated and hence easier to accomplish or understand, or the object that arises from this process. The mathematical formula is simplified to its nearest value but is not exactly correct.
What is the simplified equation?Therefore, we must follow the order listed above when simplifying expressions. In the example before, we divide 8 by 4 and then add the result to 12 because, according to BODMAS, division (D) comes before multiples (M).
[tex]$3 \cdot 2^{3} \cdot 2 \cdot 3^{2}Calculate exponents $2^{3}: 8$$$=3 \cdot 8 \cdot 2 \cdot 3^{2}$$Calculate exponents $3^{2}: 9$$$=3 \cdot 8 \cdot 2 \cdot 9$$ $3 \cdot 8 \cdot 2 \cdot 9= 432$$$=432$$[/tex]
So. the value will be = 432
To know more about simplification visit:
https://brainly.com/question/1511685
#SPJ4
I understand that the question you are looking for is :
Simplify the expression to a single numerical value.
3*2^3*2*3^2
(a)144
(b)432
(c)900
(d)5,184
A set of eight cards were labeled as M, U, L, T, I, P, L, Y. What is the sample space for choosing one card?
S = {I, U, Y}
S = {M, L, T, P}
S = {I, L, M, P, T, U, Y}
S = {I, L, L, M, P, T, U, Y}
Question 2(Multiple Choice Worth 2 points)
(Sample Spaces LC)
A paper bag has five colored marbles. The marbles are red, green, blue, yellow, and orange. List the sample space when choosing one marble.
S = {1, 2, 3, 4, 5}
S = {red, blue, green, yellow}
S = (g, r, b, y, o}
S = (green, blue, yellow, orange}
Question 3(Multiple Choice Worth 2 points)
(Sample Spaces LC)
A four-part spinner is spun once.
spinner with four parts labeled W, X, Y, and Z
List the sample space for the experiment.
S = {X, Y, Z}
S = {W, Z, Z}
S = {W, Y, Y, Z}
S = {W, X, Y, Z}
Question 4(Multiple Choice Worth 2 points)
(Sample Spaces LC)
Which event will have a sample space of S = {h, t}?
Flipping a fair, two-sided coin
Rolling a six-sided die
Spinning a spinner with three sections
Choosing a tile from a pair of tiles, one with the letter A and one with the letter B
Question 5(Multiple Choice Worth 2 points)
(Sample Spaces MC)
Julia had a bag filled with gumballs. There were 2 lemon-lime, 3 watermelon, and 5 grape gumballs. What is the correct sample space for the gumballs in her bag?
Sample space = 2, 3, 5
Sample space = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Sample space = lemon-lime, watermelon, grape
Sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape
Question 6 (Essay Worth 4 points)
(Sample Spaces HC)
Part A: Create your own experiment with 5 or more possible outcomes. (2 points)
Part B: Create a sample space for a single experiment and explain how you determined the sample space. (2 points)
The correct answers to the sample space illustrated will be:
S = {I, L, L, M, P, T, U, Y}.
S = {g, r, b, y, o}.
S = {W, X, Y, Z}.
Flipping a fair, two-sided coin.
Sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape.
S = {Joy, Bob, Ben, Peter, John}
How to explain the probability?A paper bag has five colored marbles. The marbles are red, green, blue, yellow, and orange. The sample space when choosing one marble will be S = {g, r, b, y, o}.
A four-part spinner is spun once and the spinner with four parts labeled W, X, Y, and Z. The sample space for the experiment is S = {W, X, Y, Z}.
The event will have a sample space of S = {h, t} is the flipping a fair, two-sided coin.
The correct sample space for the gumballs in her bag will be sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape.
My experiment with 5 or more possible outcomes will be that a teacher wants to randomly give one of his give students a pack of chocolate.
The sample space for the experiment will be based on their names. This will be S = (Joy, Bob, Ben, Peter, John).
Learn more about sample space on:
brainly.com/question/10558496
#SPJ1
What is the equation for the line of best fit on the scatter plot below?
We've got a negative slope, but it doesn't look steep enough to go through 6 on the y-axis.
So, it's the last option:
y = - 1.25x + 5.75
Hope this helps!
Find the radius of convergence R, then determine the interval of convergence
By the ratio test, the series converges for all [tex]x[/tex], since
[tex]\displaystyle \lim_{k\to\infty} \left|\frac{(k+1)^2 x^{k+4}}{(k+1)!} \cdot \frac{k!}{k^2 x^{k+3}}\right| = |x| \lim_{k\to\infty} \frac{(k+1)^2 k!}{k^2 (k+1)!} = |x| \lim_{k\to\infty} \frac1{k+1} = 0 < 1[/tex]
Then the radius of convergence is R = ∞, and the interval of convergence is the entire real line, -∞ < x < ∞.
The radius of convergence R is ∞ and the interval of convergence is (-∞, ∞) for the given power series. This can be obtained by using ratio test.
Find the radius of convergence R and the interval of convergence:Ratio test is the test that is used to find the convergence of the given power series.
First aₙ is noted and then aₙ₊₁ is noted.
For ∑ aₙ, aₙ and aₙ₊₁ is noted.
[tex]\lim_{n \to \infty} | \frac{a_{n+1} }{a_{n} } |[/tex] = β
If β < 1, then the series convergesIf β > 1, then the series divergesIf β = 1, then the series inconclusiveHere aₙ = (n²/n!) xⁿ⁺³ and aₙ₊₁ = ((n+1)²/(n+1)!) xⁿ⁺¹⁺³ = ((n+1)²/(n+1)!) xⁿ⁺⁴
Now limit is taken,
[tex]\lim_{n \to \infty} | \frac{a_{n+1} }{a_{n} } |[/tex] = [tex]\lim_{n \to \infty} | \frac{((n+1)^{2} /(n+1)!) x^{n+4} }{(n^{2} /n!) x^{n+3} } |[/tex]
= [tex]\lim_{n \to \infty} | \frac{((n+1)^{2} ) n!x^{n+4} }{(n+1)!(n^{2} ) x^{n+3} } |[/tex]
= [tex]\lim_{n \to \infty} | \frac{((1+1/n)^{2} ) x }{(n+1)} |[/tex]
= [tex]\lim_{n \to \infty} | \frac{ x }{(n+1)} |[/tex] = 0 < 1
Since the limit is less than 1 the series is converging.
We get that,
interval of convergence = (-∞, ∞)
radius of convergence R = ∞
Hence the radius of convergence R is ∞ and the interval of convergence is (-∞, ∞) for the given power series.
Learn more about power series here:
brainly.com/question/18763238
#SPJ1
(n - 1)!, where n = 4
Answer:
6
Step-by-step explanation:
Original Equation
(n-1)!
Plug in 4 as n
(4-1)!
Subtract
(3)!
Rewrite using definition of factorial: [tex]a! = a*(a-1)*(a-2)....*1[/tex]
3! = 3*2*1
You don't really have to write the 1, since it doesn't change the value
6
In what kind of an event does a choice made for one decision affect the choices available for
the other decisions?
Let's say you want to go on a vacation this summer because you finally saved enough money for it. While at the store to buy more hairbands (you just can't seem to figure out where they all went) you see something that you have been wanting for ages. The item is a bit on the more expensive side but you don't know when you will see it again. You decide to buy the item but you had to use some of the money planned for your trip to pay for it. But because you bought the item you now can't do all the activities you wanted on your trip.
The choice of buying the item affected your choices available on your trip.
Answer:
dependent events
Step-by-step explanation:
A 3.0-kg ball moving eastward at 4.0 m/s suddenly collides with and sticks to a 5.0-kg ball moving northward at 3.0 m/s. what is the magnitude of the momentum of this system just after the collision?
Magnitude of the momentum of this system just after the collision = 19.2Kgm/s
What is law of conservation of momentum?Law of conservation of momentum states that the total momentum after the collision must be equal to the total momentum before the collision.
The momentum of each ball is given by:
p = mv
where m is the mass of the ball and v its velocity.
The momentum of ball 1 is:
p = mv
= (3.0 kg)(4.0 m/s)
= 12.0 kg m/s in the eastward direction
The momentum of ball 2 is:
p = mv
= (5.0 kg)(3.0 m/s)
= 15.0 kg m/s in the northward direction
The two momenta are in perpendicular directions, so the magnitude of the total momentum can be found as:
[tex]p = \sqrt{p1^{2} +p2^{2} }[/tex]
[tex]p = \sqrt{12^{2} +15^{2} }\\p = \sqrt{144 + 225} \\p = \sqrt{369}\\ p = 19.2 kgm/s[/tex]
and due to the law of conservation of the momentum, this is also equal to the total momentum after the collision.
To learn more about law of conservation of momentum from the given link
https://brainly.com/question/12773641
#SPJ4
Ram sold to Shyam an article with 20% profit. Shyam sold same article for Rs. 504 with 5% profit to Ghanashyam. How much did it cost for Ram?
please do this with solutions quickly!!
Answer:
Rs 400 is the cost of an article for Ram.....
Step-by-step explanation:
X - cost of an article for Ram
120% = 1.2
1.2*X - Ram’s selling price
5% = 0.05
1.2*X*0.05 - Shyam selling price
1.2*X*0.05 = 504
X = Rs 400 is the cost of an article for Ram
Hope it Helps!!!!
Find an equation for the conic that satisfies the given conditions. parabola, focus (−8, 0), directrix x = 2
The equation of the given parabola is y2=−20(x+3)
A parabola is a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.
In general in a parabola, if we have
(y−n)2=4p(x−m),
then the vertex is (m,n)
The axis of symmetry is y=m
The focus is (p+m,n)
The directrix is x=m−p.
Hence, for the given case
p+m=−8
n=0
m−p=2
⇒n=0
m=−3
p=−5
So, the answer will be y2=−20(x+3)
For more information about parabola, visit
https://brainly.com/question/4061870
#SPJ4
What is the sign of b/c
Answer:
Negative.
Step-by-step explanation:
b is above zero. So, it is positive.
c is below zero. So, it is negative.
A positive divided by negative number results in negative.
Answer:
B. negative
Step-by-step explanation:
-2 is negative. That's why.
round off square root of 120 to the nearest whole number?
Answer:
11
Step-by-step explanation:
for this question we can look at the whole answer for the square root of 120 which equals 10.9544511501
[tex]\sqrt{120} = 10.9544511501[/tex]
now looking at our answer (10.9544511501) we want to find the nearest WHOLE NUMBER. in the current answer the whole number is 10, followed by many decimals.
10.9544511501
but to find the nearest whole number we have to round the place value BEFORE our whole number. (in this case the 9)
10.9544511501
we can now look at this highlighted section of our equation and think... is 10.9 closer to 11 or 10. well logically, to get to 11 from 10.9 we only have to go up by 0.1, rather than to get to 10, where you have to subtract 0.9.
10.9 + 0.1 = 11
10.9 - 0.9 = 10
But to make it easier, remember the rule:
the place value one place to the RIGHT of what you're rounding to, is what determines the new number. (in this case the .9)
and as any number 5 or above rounds up, we can say that our new number, rounded to the nearest whole number equals 11
10.9 rounded to the nearest whole number = 11
2. A football team plays 28 games and wins 4 out of every 7 games played. No match ended in a draw. (b) Calculate the win - loss ratio of this football team. ( I know the answer is 4:3 but I don't know the way work )TY.
Answer:4:3
Step-by-step explanation: We can first calculate the wins. 24/7 is 4 and 4x4 = 16. So, they won 16 games and lost the rest. 28-16 = 12. 16:12 is equal to 4:3.
PLEASE HELP IM STUCK
The number of outcomes possible from flipping each coin is 2, therefore;
The expression that can be used to find the number of outcomes for flipping 4 coins is: 2•2•2•2How can the expression for the number of combinations be found?The possible outcome of flipping 4 coins is given by the sum of the possible combinations of outcomes as follows;
The number of possible outcome from flipping the first coin = 2 (heads or tails)
The outcomes from flipping the second coin = 2
The outcome from flipping the third coin = 2
The outcome from flipping the fourth coin = 2
The combined outcome is therefore;
Outcome from flipping the 4 coins = 2 × 2 × 2 × 2
The correct option is therefore;
2•2•2•2
Learn more about finding the number of combinations of items here:
https://brainly.com/question/4658834
#SPJ1
Use theorem 9. 11 to determine the convergence or divergence of the p-series. 1 1 6 32 1 6 243 1 6 1024 1 6 3125. .
The given series is diverges according to the P Test.
According to the statement
we have given that the a series and we have to find that the those series is a converges or diverges.
So, For this purpose, we know that the
P-series test to say whether or not the series converges.
So, The given series is
[tex]1 + 1/\sqrt{32} + 1/\sqrt[3]{243 } + 1/\sqrt[4]{1024} + 1/\sqrt[5]{3125}[/tex]
And then
The value of P becomes P = 5/6 < 1 when we find it using the p series test.
Hence, the p-series diverges
Because according to the p series test, The series converges if, and only if, the power satisfies p>1.
And diverges if, and only if, the power satisfies p<1.
So, The given series is diverges according to the P Test.
Learn more about Convergence and Divergence here
https://brainly.com/question/4730059
Disclaimer: This question was incomplete. Please find the full content below.
Question:
Use Theorem 9.11 to determine the convergence or divergence of the p-series. 1 + 1/32 squareroot + 1/243 squareroot 3 + 1/1024 squareroot 4 + 1/3125 squareroot 5.
#SPJ4
find the surface area of composite figure. use 3.14 for π. round to the nearest tenth
Answer:
334 in²
Step-by-step explanation:
The total surface area of the composite figure is the sum of the total area of the bottom cuboid and the lateral area of the top cuboid.
Total cuboid areaThe area of a cuboid is given by the formula ...
A = 2(LW +H(L+W))
For the bottom cuboid, the area is ...
A = 2((9 in)(7 in) +(5 in)(9 in +7 in)) = 2(63 in² +5(16) in²) = 286 in²
Lateral areaThe lateral area of a cuboid is the product of its perimeter and height. The perimeter is the sum of side lengths, or twice the sum of length and width.
LA = Ph = (2(l +w))h
LA = 2(5 in +3 in)(3 in) = 48 in²
Total composite areaThe total surface area is the sum of the lateral area of the top cuboid and the total area of the bottom cuboid:
SA = (48 in²) +(286 in²) = 334 in²
The surface area of the composite figure is 334 square inches.
__
Additional comment
The exposed area of the bottom cuboid is its total area less the area of the very top face.
The exposed area of the top cuboid is its lateral area plus the area of the very top face.
When we add these two exposed areas together, we find the area of the very top face is both subtracted and added from the sum of the total bottom area and the lateral top area. We skipped that step of adding and subtracting, because its net effect is zero.
20 points please help me I'm desperate and I will mark brainlyist
Answer:
(a) 48, 52, 54
(b) 6
(c) b, c
Step-by-step explanation:
The sample mean is the mean of the sample. The range of sample means is the difference between the largest and smallest. As with all sampling processes, more data gives a better estimate.
(a)The sample means are calculated in the attachment. For the different samples, they are ...
485254(b)The range of the sample means is the difference between the largest and the smallest:
range = 54 -48 = 6
(c)More data is better, and the closer the estimates are to each other, the better confidence they offer. The true statements are ...
A single sample mean will tend to be a worse estimate than the mean of the sample means.The closer the range of sample means is to zero, the more confident they can be in their estimate.Find the output, y, when the input, x, is -5.
The output, y, when the input, x, is -5 is -2
How to determine the value of the output y?The input is given as:
-5
This means that
x = -5
This is so because x represents the input
From the graph, we have the following highlight
The line of the graph passes through the point x = -5
On the graph;
When x = -5, the value of y is -2
This means that the output, y, when the input, x, is -5 is -2
Read more about functions at:
https://brainly.com/question/2328150
#SPJ1
Which point is a solution to the system of inequalities graphed here? y ≤ 2x 2 y ≥ -5x 4
The point that is a solution to the system of inequalities is (5, 0)
How to determine the points on the solution?The system of inequalities is given as:
y ≤ 2x + 2
y ≥ -5x + 4
Next, we test the given options.
From the list of options, we have
(x, y) = (5, 0)
Substitute (x, y) = (5, 0) in y ≤ 2x + 2 and y ≥ -5x + 4
y ≤ 2x + 2
0 ≤ 2 * 5 + 2
0 ≤ 12 -- this is true
y ≥ -5x + 4
0 ≥ -5 * 5 + 4
0 ≥ -21 -- this is true
Since both results are true, then it means that the point that is a solution to the system of inequalities is (5, 0)
Read more about system of inequalities at:
https://brainly.com/question/24372553
#SPJ1
Complete question
Which point is a solution to the system of inequalities graphed here? y ≤ 2x + 2
y ≥ -5x + 4
A. (1,6)
B. (-6,0)
C. (0,5)
D. (5,0)
Enter the correct answer in the box. in triangle abc, the side lengths are ab = 13, ac = 21, and bc = x. write a compound inequality that represents the range of possible values for x.
The range of possible values should be (7,34), i.e 7 < x < 34.
The answer must be more noteworthy than 7, else the two sides are less than or rise to to the third. That triangle is outlandish. The reply must moreover be less than 34, since at that point the two other sides would rise to the third, making an impossible triangle.
By the property of triangle, Sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
To prove above propert, let us assume a ΔABC
extend AB to D in such a way that AD=AC.
In ΔDBC, as the angles opposite to equal sides are always equal, so,
∠ADC=∠ACD
so,
∠BCD>∠BDC
As the sides opposite to the greater angle is longer, so,
BD>BC
AB+AD>BC
Since AD=AC, then,
AB+AC>BC
Hence, sum of two sides of a triangle is always greater than the third side.
To learn more about triangles from the given link
https://brainly.com/question/2644832
#SPJ4
Answer:
7 < x < 34
Step-by-step explanation:
On a certain day, the temperature in Bismarck, North Dakota, was below 4∘F. Write an inequality to describe the possible temperatures. Let t represent the temperature.
The inequality to describe the possible temperature in Bismarck, North Dakota given that t represent temperature is t < 4°F
InequalityThe inequality signs are;
Greater than >Less than <Equal to =Greater than or equal to ≥Less than or equal to ≤Let
Temperature = tTemperature in Bismarck, North Dakota, was below 4∘F.Below in inequality sign means less than <So
t < 4°F in Bismarck, North Dakota
This means, temperature in Bismarck, North Dakota is less than 4°F
Therefore, t < 4°F is the inequality to represent temperature in Bismarck, North Dakota.
Learn more about inequality:
https://brainly.com/question/25275758
#SPJ1
A tape diagram. There are 65 students out of 100 students who ride the bus. There are question mark students out of 800 students who ride the bus.
65% of the 800 students at North High School ride the bus. How many students ride the bus?
Answer:
800÷100 = 8
65×8=520
[tex]\frac{520}{800}[/tex]
another way:
100%-65%=35%
35% = 0.35
800×0.35= 280
800-280=520
another way:
65% = 0.65
0.65×800=520
Hope it helped! :)
Mar18/Q9 - V2
2^p=1\8^4
Find the value of p.
Answer:
-12
Step-by-step explanation:
2^p = ⅛⁴
⅛ x ⅛ x ⅛ x ⅛ = 1/4096
2^p = 4096
log base 2 of 1/4096 = -12
Find an equation for the conic that satisfies the given conditions. ellipse, foci (±2, 0), vertices (±5, 0)
The equation of the ellipse having foci (±2,0) and vertices (±5,0) is [tex]x^{2} /4+y^{2} /21=1[/tex].
Given the foci of ellipse is (±2,0) and vertices (±5,0).
We are required to find the equation of ellipse having foci (±2,0) and vertices (±5,0).
Equation is the relationship between two or more variables that are expressed in equal to form. Equation of two variables looks like ax+by=c.
Equation of ellipse is as under:
[tex]x^{2} /a^{2} +y^{2} /b^{2} =1[/tex],where a is the semi major axis.
We have been given that a=5, c=2.
We know that [tex]c^{2} =a^{2} -b^{2}[/tex]
We have to find the value of b.
b=[tex]\sqrt{a^{2} -c^{2} }[/tex]
=[tex]\sqrt{5^{2} -2^{2} }[/tex]
=[tex]\sqrt{25-4}[/tex]
=[tex]\sqrt{21}[/tex]
Using the values of a and b in the equation [tex]x^{2} /a^{2} +y^{2} /b^{2} =1[/tex]
[tex]x^{2} /(2)^{2} +y^{2}/\sqrt{21} ^{2} =1[/tex]
[tex]x^{2} /4+y^{2} /21=1[/tex]
Hence the equation of the ellipse having foci (±2,0) and vertices (±5,0) is [tex]x^{2} /4+y^{2} /21=1[/tex].
Learn more about ellipse at https://brainly.com/question/16904744
#SPJ4
2. G.CO.9 Look at the diagram below showing two parallel lines being cut
by two transversals. If m24 = 70 and m412 = 130, which of the following
statements are true? SELECT ALL THAT APPLY.
The statements that are true regarding the angles formed by the transversal and parallel lines are:
A. m∠1 = 70°.
B. m∠2 = 110°
C. m∠6 = 70°.
E. m∠9 = 50°
H. m∠16 = 130°
How to Find the Angles Formed by a Transversal and Parallel Lines?Given the following angle measures formed when two parallel lines ( being cut by two transversals:
m∠4 = 70° m∠12 = 130°Using relevant theorems, let's determine which of the statements are true:
Angles 4 and 1 are vertical angles, therefore they are congruent based on the vertical angles theorem.
m∠4 = m∠1
m∠1 = 70°.
m∠2 = 180 - m∠4 [linear angles theorem]
m∠2 = 180 - 70
m∠2 = 110°
m∠6 = m∠4 [base on the alternate interior angles theorem]
m∠6 = 70°.
m∠9 = 180 - m∠12 [based on the linear angles theorem]
m∠9 = 180 - 130
m∠9 = 50°
m∠16 = m∠12 [based on the corresponding angles theorem]
m∠16 = 130°
The statements that are true are:
A. m∠1 = 70°.
B. m∠2 = 110°
C. m∠6 = 70°.
E. m∠9 = 50°
H. m∠16 = 130°
Learn more about transversal and parallel lines on:
https://brainly.com/question/24607467
#SPJ1
Solve each pair of simultaneous equations by elimination method.
a) 2x+3y-1=0
5x+2y+3=0
Answer:
x = -1
y = 1
Step-by-step explanation:
PART I: Find the y-valueGiven expressions
1) 2x + 3y - 1 = 0
2) 5x + 2y + 3 = 0
Add 1 on both sides of the 1) equation:
2x + 3y - 1 + 1 = 0 + 1
2x + 3y = 1
Subtract 3 on both sides of the 2) equation:
5x + 2y + 3 - 3 = 0 - 3
5x + 2y = -3
Current System
1) 2x + 3y = 1
2) 5x + 2y = -3
Multiply 2.5 on both sides of the 1) equation
(2.5) 2x + (2.5) 3y = (2.5) 1
5x + 7.5y = 2.5
Current System
1) 5x + 7.5y = 2.5
2) 5x + 2y = -3
Subtract 2) equation from 1) equation
(5x + 7.5y) - (5x + 2y) = 2.5 - (-3)
Get rid of the parenthesis
5x + 7.5y - 5x - 2y = 2.5 + 3
Combine like terms
5x - 5x + 7.5y - 2y = 5.5
0 + 5.5y = 5.5
5.5y = 5.5
Divide 5.5 on both sides
5.5y / 5.5 = 5.5 / 5.5
[tex]\boxed{y=1}[/tex]
PART II: Find the x-valueSubstitute the y-value back to one of the equations to find the x-value
2x + 3y - 1 = 0
2x + 3(1) - 1 = 0
Combine like terms
2x + 3 - 1 = 0
2x + 2 = 0
Subtract 2 on both sides
2x + 2 - 2 = 0 - 2
2x = -2
Divide 2 on both sides
2x / 2 = -2 / 2
[tex]\boxed{x=-1}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
A star system with more than 2 but less than a million stars. which type of star system is pictured?
The star system is pictured is open cluster
What is Open cluster?A type of star cluster known as an open cluster is composed of up to a few thousand stars that are around the same age and originated from the same massive molecular cloud. Within the Milky Way galaxy, more than 1,100 open clusters have been found, and it is believed that there are many more.
What is solar system?The Sun and the things that circle it make up the gravitationally bound solar system. It was created 4.6 billion years ago when a massive interstellar molecular cloud collapsed because to gravity. The Sun is the system's primary mass source, while Jupiter is home to the majority of the system's leftover mass.
To know more about Open cluster visit:
https://brainly.com/question/9881073
#SPJ4
I understand that the question you are looking for is :
| Will mark brainliest | Which type of star system is pictured? |
A. globular cluster
B. open cluster
C. binary
Answer:
B
Step-by-step explanation:
open cluster
A 2-gallon container of laundry detergent costs $10.24. What is the price per fluid ounce?
Answer:
$0.04
Step-by-step explanation:
The cost per ounce is found by dividing the cost by the number of ounces.
SolutionIn 2 gallons, there are 2×128 fl.oz. = 256 fl.oz. Then the cost per ounce is ...
cost/ounces = $10.24/(256 fl.oz) = $0.04 /fl.oz.
The cost of the laundry detergent is $0.04 per fluid ounce.
__
Additional comment
Keeping the units with the numbers in a calculation can give you confidence that the calculated result has the units you want it to have.
A train traveled 1/5 of the distance between two cities in ¾ hour. at this rate, how many hours will it take the train to travel the entire distance between these two cities?
Answer:
3 3/4 hour
Step-by-step explanation:
(3/4) ÷ (1/5) = (3*5) / (4*1)
= 15/4 hour
15/4 = 12/4 + 3/4 = 3 + 3/4 hour
= 3 3/4 hour
What is the value of x?
w
t
105°
80°
Answer:
x = 75°Step-by-step explanation:
Opposite angles in a cyclic quadrilateral are supplementary.
Applicationx° = 180° -105°
x° = 75°
__
The value of the other angle is similarly found:
w° = 180° -80°
w° = 100°
__
Additional comment
This result comes from the inscribed angle theorem. That theorem tells you the measure of the inscribed angle is half the measure of the intercepted arc.
The opposite angles of a cyclic quadrilateral intercept the circle at the same two points, dividing the total 360° circle into two parts. Each angle has a measure equal to half its corresponding arc, so the total of the two angles is half the total of the two arcs: 360°/2 = 180°. The angles are supplementary.
