Step-by-step explanation:
Because 1. x =(5-√73)/4=-0.886and the other one is 2. x =(5+√73)/4= 3.386
Final answer:
The positive solution to the equation 2x² + 25 = 73 is x = √24, which is approximately 4.9.
Explanation:
The student is asking for the positive solution to the equation 2x² + 25 = 73. To solve this, we first isolate the quadratic term by subtracting 25 from both sides of the equation, resulting in 2x² = 48. Then, we divide both sides by 2, simplifying to x² = 24. Taking the square root of both sides gives us two solutions, x = √24 and x = -√24. Since we're seeking the positive solution, we take the positive square root, which yields x = √24 or about 4.9.
Trial 1, H H T; trial 2, H T T; trial 3, H H T; trial 4, H H H; trial 5, H H T; trial 6, H H T; trial 7, T T T; trial 8, H H T; trial 9, H T T; trial 10, H H H; trial 11, H H T; trial 12, T T T; trial 13, T T T; trial 14, H T T; trial 15, H T T; trial 16, T T T; trial 17, H H T; trial 18, H T T; trial 19, H T T; trial 20, H T T.
On a nearby pond, black and white ducks are swimming in groups of three. Use the table to find the experimental probability of two white ducks and one black duck swimming together. Tails up represents white ducks and heads up represents black ducks.
Answer:
7/20
Step-by-step explanation:
The probability is 7/20.
What is probability?Probability is a branch of mathematics that deals with the occurrence of a random event.
The hazard that a given event will arise. The ratio of the variety of results in an exhaustive set of similarly probable results that produce a given occasion to the overall number of feasible results.
possibility = the number of methods of reaching achievement. the total number of possible outcomes.
explanation:
Tails up represents white ducks
and heads up represents black ducks
probability of two white ducks number tails from the table = 7
total sample = 20
Hence probability = 7/20
The possibility is the branch of mathematics regarding the incidence of a random event, and four major styles of opportunity exist: classical, empirical, subjective, and axiomatic. the possibility is synonymous with possibility, so you should say it is the possibility that a particular event will show up.
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i need help asap, we are out of school so i can't ask my teacher
Answer:
1 and 6
2 and 5
3 and 8
4 and 7
Step-by-step explanation:
vertical angles: each of the pairs of opposite angles made by two intersecting lines.
Ms. Omar runs the school tennis club. She has a bin of tennis balls and rackets
For every 5 tennis balls in the bin, there are 3 tennis rackets. Draw a model to
show the ratio of tennis balls to tennis rackets
write the following ratios
tennis balls to tennis rackets
tennis balls to total pieces of tennis equipment
Answer:
Draw a model ⇒ See the attached figure
Tennis balls to tennis rackets ⇒ 5 : 3
Tennis balls to total pieces of tennis equipment ⇒ 5 : 8
Step-by-step explanation:
Let the number of tennis balls ⇒ x
Let the number of tennis rackets ⇒ y
The general form represents the situation is ⇒ y = mx
Where m is the slope
Given: For every 5 tennis balls in the bin, there are 3 tennis rackets.
So, when x = 5 ⇒ y = 3
So, 3 = m * 5⇒ m = 3/5 = 0.6
∴ y = 0.6 x
See the attached figure which represents a model to show the ratio of tennis balls to tennis rackets.
Tennis balls to tennis rackets = 5 to 3 or 5 : 3
Total pieces of tennis equipment = 5 + 3 = 8
Tennis balls to total pieces of tennis equipment = 5 to 8 or 5 : 8
Cher is giving $330 to her grandchildren. She has 10 grandchildren
and each grandchild is going to receive the same amount of money.
How much will Cher give to each grandchild?
Answer:
$33 for each grandchild.
Step-by-step explanation:
If Cher has $330 to give to 10 grandkids equally you have to devide.
So you would do $330 divided by 10 (number of grandchildren), which equals $33. So each child gets $33.
Which of the following is closest to the volume of the shoe box? Here are the measurements 11 cm, 8.8 cm, and 18.4cm.
Answer:
1,782 CM
Step-by-step explanation:
Solve the following system,
x2 - y = 3
X-Y = -3
Answer:
[tex] x = 6 \\ y = 9[/tex]
Step-by-step explanation:
[tex]2x - y - (x - y) = 3 - ( - 3) \\ 2x - y - x + y = 6 \\ x = 6[/tex]
[tex]2x - y = 3 \\ 2 \times 6 - y = 3 \\ 12 - y = 3 \\ - y = 3 - 12 \\ - y = - 9 \\ y = 9[/tex]
[tex] x - y = - 3 \\ 6 - 9 = - 3 \\ - 3 = - 3[/tex]
hope this helps you,! have a nice day!!
The system of equations is solved by substituting the expression for y from the linear equation into the quadratic equation, factoring the resulting quadratic, and solving for the two values of x, which are then used to find the corresponding y values, yielding solutions (3, 6) and (-2, 1).
Explanation:To solve the system of equations given by
x2 - y = 3
x - y = -3
we observe that the second equation can immediately give us a value for y in terms of x. We can add 3 to both sides to isolate y:
y = x + 3
Next, we can substitute this expression for y into the first equation:
x2 - (x + 3) = 3
This simplifies to: x2 - x - 6 = 0
We can then solve this quadratic equation for x. A possible method is factoring, which, if the quadratic factors neatly, is often quicker than using the quadratic formula. The factored form is:
(x - 3)(x + 2) = 0
Setting each factor equal to zero gives us two solutions for x:
x = 3 or x = -2
Substituting these back into the equation y = x + 3 gives us the corresponding y values:
For x = 3: y = 3 + 3 = 6
For x = -2: y = -2 + 3 = 1
Thus, we have two solutions for the system: (3, 6) and (-2, 1).
Matt earned $162 this week working 9 hours. Matt wants to buy a new video game system for $342. How many hours does Matt need to work in all to buy the video game system? Explain how you know.
Answer:
19 hours
Step-by-step explanation: he needs to work 19 hours because if you divide the sum of money(162$) he got from working 9 hrs you get that he makes 18$ per hour then divide that by the sum of money that he needs(342$)
Matt earns $18 per hour and needs to work a total of 19 hours to afford a $342 video game system.
Explanation:Matt earned $162 this week by working 9 hours. This means that Matt earns $18 per hour (since 162 ÷ 9 = 18). To find out how many total hours Matt needs to work to buy a new video game system that costs $342, we divide the total cost of the video game system by his hourly wage. So, $342 ÷ $18 = 19 hours. Therefore, Matt needs to work a total of 19 hours to afford the video game system.
Louise sold 414 soft pretzels. If she sold them in groups of 18 soft pretzels, how many groups did she sell?
Answer:
23 groups :)
Step-by-step explanation:
Answer:
23
Step-by-step explanation:
Ok so heres the deal: You want to somehow take all 414 of those delicious pretzels and put them into x groups of 18. To do that you would divide 414 by the number of groups (x).
414/x=18
To solve this you just have to get x by itself.
So, multiply both sides by x.
414=18x.
Now divide by 18
414/18=x
23=x
how to solve and graph this inequality 8-u>4
Answer:
u < 4
Step-by-step explanation:
Step 1: Subtract 8 from both sides
8 - u - 8 > 4 - 8
-u > -4
Step 2: Divide both sides by -1
-u / -1 > -4 / -1
Since you divide by a negative, you flip the sign.
u < 4
Answer: u < 4
This system has one solution.
y=8x+9y=x2+4x+13
What is the y-coordinate of the solution?
Enter your answer in the box.
Answer:
25
Step-by-step explanation:
When the equations intercect, the y-value is 25. (2,25)
Answer:
25
Step-by-step explanation:
WHAT WOULD THIS BE? I DONT UNDERSTAND IT
Answer:
The answer would be x=7.3 cm
Step-by-step explanation:
Since you are using the angle of 20 degrees and you have the measure of 10 cm for its adjacent side, solving for x would mean you would use tan.
20=x/10
10*20tan=x
200tan=x
7.279404......=x
But when you do 200 tan on the calculator, you have to make sure you press the equal sign after.
what is the decimal of 3 and 2 thirds
Answer: 3.2
Step-by-step explanation:
There are three whole, and 2 last.
Answer:3.667
Well, you divide 11 and 3 and round it.
Question 5b) please, what have i done wrong?
2(x+3)(x+4)/(x+1)(x-5) x (x+1)/4(x+3)
At the denominator you have
(x-5)×4=4x-20.
But:
2(x+4)/(4(x-5))=(x+4)/2/(x-5)
Answer:
see explanation
Step-by-step explanation:
Given
[tex]\frac{2(x+3)(x+4)}{(x+1)(x-5)}[/tex] × [tex]\frac{(x+1)}{4(x+3)}[/tex]
Cancel the common factors (x + 1), (x+3) on the numerator/ denominator
and cancel 2 and 4 on the numerator/ denominator by 2
= [tex]\frac{x+4}{2(x-5)}[/tex]
Is -2/9 rational,irrational,integer, or etc?
Answer:
rational
Step-by-step explanation:
hope this helps!
Find the slope of the line that passes through (-99, -25) and (-98, -62).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
-37
Step-by-step explanation:
Slope = y2 - y1/x2 - x1
Given
x1 = -99
y1 = -25
x2 = -98
y2 = -62
Therefore
Slope = -62 -(-25) /-98 -(-99)
Negative negative becomes positive
= -62 + 25 /-98 + 99
= -37/1
= -37
Henri conducts an experiment to determine who likes peanut butter more: boys or girls. He has 25 girls and 25 boys taste some peanut butter and then rate it on a scale of 1 - 10 with 1 being cannot stand and 10 being tastes delicious. He finds that the girls had a mean of 7 with a range of 9 and the boys had a mean of 8 with a range of 5. Which statement is true? A) On average, boys like peanut butter more than girls did. B) The person who rated peanut butter the worst was a boy. C) Boys varied more in how they liked peanut butter than the girls did. D) There is not enough information to know if any of the above are true.
Answer:
I think that the answer is option A
Answer:
a
Step-by-step explanation:
Factor the GCF: 12x2y + 6x2y3 – 9xy? (4 points)
3x^2y(4x2 + 2xy - 3)
3xy(4x + 2xy - 3y^2)
3xy(4x^2 + 2xy – 3y^2)
3x^2y(4x^3y – 2x^2y^2 - 3xy^3)
The greatest common factor (GCF) of the expression 12² + 6²³ − 9 is 3. So, factored form is c) 3xy (4x² + 2xy – 3y²).
To factor out the greatest common factor (GCF) from the expression
12² + 6²³ − 9, we need to identify the highest common factor among the terms.
First, let's list the factors of each term:
12² can be factored into 3 × 2 × 2 × × ×
6²³ can be factored into 3 × 2 × × × × ×
9 can be factored into 3 × 3 × ×
The highest common factor among these terms is 3.
Now, we divide each term by 3:
12² ÷ 3 = 4
6²³ ÷ 3 = 22
9 ÷ 3 = 3
So, the factored expression becomes 3 (4² + 2² −3). This is the result of factoring out the GCF 3 from the given expression.
Complete Question:
Factor the GCF: 12x2y + 6x2y3 – 9xy?
a) 3x²y (4x² + 2xy - 3)
b) 3xy (4x + 2xy - 3y²)
c) 3xy(4x² + 2xy – 3y²)
d) 3x²y(4x³y – 2x²y² - 3xy³)
For which value of x is the relation not a function (5,2), (x,1), (8,6), (9,3)
Answer:
x=5, 8, 9
Step-by-step explanation:
in a function, one x value must be paired with one and only one y value, this means there cannot be two points where x values are the same, however the y values can repeat.
if x = 5, 8, or 9, the relation is not a function because there are 2 same x values.
Mary earned scores of 88, 91, 75, and 72 on four science tests. Determine her score on the
fifth test if her average for the five tests was 81.
о.
o
o
o
Answer:
Mary's score on the fifth test was 79.
Step-by-step explanation:
Mary's 1st score = 88Mary's 2nd score = 91Mary's 3rd score = 75Mary's 4th score = 72Mary's 5th score = xMary's average score for the five tests = 81Let's solve for x, this way:
Mary's average score for the five tests = (Mary's 1st score + Mary's 2nd score + Mary's 3rd score + Mary's 4th score + Mary's 5th score)/5
Replacing with the values given:
81 = (88 + 91 + 75 + 72 + x)/5
81 * 5 = 326 + x
405 = 326 + x
- x = 326 - 405
x = 79
What is 2.25% of 24 please help
The given sum is based on the concept of percentage.0.54 is 2.25[tex]\%[/tex] out of 24.
Percentage is a way of expressing a fraction or proportion out of 100. It is represented by the symbol "%". The word "percent" comes from the Latin phrase "per centum", which means "per hundred."
Percentages are commonly used to describe ratios, rates, or proportions in various fields such as mathematics, finance, statistics, and everyday life. They allow us to compare quantities or express relative changes easily.
To find 2.25[tex]\%[/tex] of 24, multiply 24 by 2.25[tex]\%[/tex] (or 0.0225):
2.25[tex]\%[/tex] [tex]\times[/tex] 24 = 0.0225 [tex]\times[/tex] 24
= 0.54.
Therefore, 2.25[tex]\%[/tex] of 24 is 0.54.
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which postulate proves these two triangles are congruent
Answer: nonenot congruent
Step-by-step explanation:
Write an equation of each line that passes through the following points in slope-intercept form:
1. A (8, –1) and B (–4, 17)
2. C (–19, 31) and D (1, –9)
Answer:
1. y = -3/2 x +11
2. y = -2 x -7
Step-by-step explanation:
Slope intercept form is y = mx+b
1. A (8, –1) and B (–4, 17)
First we need to find the slope
m = (y2-y1)/(x2-x1)
m = (17--1)/(-4-8)
=(17+1)/(-4-8)
=18/-12
Dividing top and bottom by 6
=-3/2
Given the slope
y = -3/2 x+b
Using the point (8,1) we can find b
-1 = -3/2(8) +b
-1 =-12 +b
Add 12 to each side
-1+12 = -12+12 +b
11 =b
The equation is y = -3/2 x +11
2. C (–19, 31) and D (1, –9)
First we need to find the slope
m = (y2-y1)/(x2-x1)
m = (-9-31)/(1--19)
=(-40)/(1+19)
= -40/20
=-2
Given the slope
y = -2 x+b
Using the point (1,-9) we can find b
-9 = -2(1) +b
-9 =-2 +b
Add 2 to each side
-9+2 = -2+2 +b
-7 =b
The equation is y = -2 x -7
Calculate the number of moles of K3PO4 in 6.49 X 1024 K3PO4 formula units.
Answer:
10.78moles
Step-by-step explanation:
Avogadro's hypothesis gives us a background understanding that 1mole of any substance contains 6.02x10^23 atoms.
Now, If 1 mole of K3PO4 contains 6.02x10^23 atoms,
Then Xmol of K3PO4 will contain = 6.49x10^24 atoms i.e
Xmol of K3PO4 = 6.49x10^24/6.02x10^23 = 10.78moles
To find the number of moles of K3PO4 in 6.49 x 10^24 formula units, divide the number of formula units by Avogadro's number, resulting in 10.78 moles of K3PO4.
Explanation:To calculate the number of moles of K3PO4 in 6.49 x 1024 formula units, we use Avogadro's number, which is 6.022 x 1023 formula units per mole. This is the key conversion factor for converting between the number of formula units and the number of moles.
First, we have the given number of formula units of K3PO4:
6.49 x 1024 formula units of K3PO4To convert this to moles, we divide by Avogadro's number:
Number of moles = (6.49 x 1024 formula units) / (6.022 x 1023 formula units/mole)
= 10.78 moles of K3PO4
This calculation shows that there are 10.78 moles of K3PO4 in 6.49 x 1024 formula units of K3PO4.
cot(x)=-3. find sin(x)
Answer:
sin(x)=1/[tex]\sqrt10[/tex]
Step-by-step explanation:
The trigonometric identities involve trigonometric functions. Here we will be using Trigonometric identity
sin²x = 1 /( 1+cot²x )
now cot(x)= -3
⇒ cot²x= (-3)²
⇒ cot²x= 9
sin²x= 1/( 1+9)
⇒ sin²x = 1/10
taking under root on both the sides we get
√sin²x=[tex]\sqrt1[/tex]/[tex]\sqrt10[/tex]
⇒ sin(x)=± 1/[tex]\sqrt10[/tex]
Find the mean of this set of numbers:
10, 10, 7, 12, 11
Answer:
u just take the sum of all numbers divide by the number of numbers (5)
I need help with this question please
Answer:
Step-by-step explanation:
√14 cannot be rewritten as the ratio of two integers and thus is irrational.
Similarly, √99 is irrational; √99 = √9√11 is irrational even though √9 is not.
Carpenters are installing hinges. They have 371 screws. Each hinge needs 3 screws. How many hinges can they install?
Answer:
Carpenters can install about 123 hinges.
Step-by-step explanation:
Since each hinge requires 3 screws. Divide 371 by 3.
= 123.666667
Answer:
123
Step-by-step explanation:
[tex]\lim_{n \to \infty} a_n \pi \beta[/tex][tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \alpha \leq x^{2} \sqrt{x} x^{2}[/tex]that's how I got it
[tex]\lim_{n \to \neq \geq \leq x^{2} x^{2}[/tex]
Maddy is carrying a 5 liter jug of sports drink that weighs 7.5 kg. She wants to know how many kilograms a 2 liter jug of sports drink would weigh (w). She assumes the relationship between volume and weight is proportional. What is the weight of the 2 liter jug
Answer:
if a 5 liter jug is 7.5 kg, The 2 liter jug weighs 3 kg
Step-by-step explanation:
7.5 / 5 = 1.5
1.5 x 2 = 3
Answer:
3kg
Step-by-step explanation:
w/2 = 7.5/5
w = 7.5/5 * 2
w = 15/5
w = 3
What property would justify the following statement?
If a = b and b = c, then a = c.
Answer:
It is the transitive property of equality
Answer: Transitive Property of Equality
Step-by-step explanation: The transitive property of equality states that if a = b and b = c, then a = c.
For example, if we're given the segment shown in the image provided and we know that the length of segment WX = XY and the length of segment XY = YZ, then based on the transitive property, he length of segment WX = YZ.
Solve each pair of equations by substituting
2x + y = 3
4x + 3y = 1
Answer:
the value of x and y is 4 and -5 respectively.
Step-by-step explanation:
from the equation we say let;
2x + y = 3 .............. equation 1
4x + 3y = 1.............. equation 2
from equation 1
2x + y = 3 .............. equation 1
y = 3 - 2x................ equation 3
Substitute for y in equation 2
4x + 3y = 1.............. equation 2
we have,
4x + 3(3- 2x) = 1
4x + 9 -6x = 1
we have to collect the like terms
9-1 = 6x -4x
8 = 2x
divide both sides by 2
8/2 = 2x/2
4 = x
therefore x = 4
put x = 4 in equation 3
y = 3 - 2x................ equation 3
y = 3 - 2(4)
y = 3 -8
y = -5
therefore the value of x and y is 4 and -5 respectively.
to check if your answer is correct, put the value of x and y in any of the equations.
2x + y = 3 .............. equation 1
2(4) + (-5) = 3
8 -5 = 3
3 = 3......................... proved