You just have to isolate the y term for both equations so the first one would be y=31-5x because you have to subtract x from both sides.
The second one would be y=3+3x and all of that over 4 because to get the y isolated, you have to add 3x to both sides and then divide by 4 to get 4 y to just be y.
Meg cycles 6.2 km every morning. How many feet are in 6.2 km, given that 1 mile= 1.609 km and 1 mile= 5280ft
Answer:
There are 20345.556... feet in 6.2 km.
Step-by-step explanation:
Given that, 1 mile = 1.609 km and 1 mile = 5280 ft.
That means we can say, 1.609 km = 5280 ft.
So, 1 km = [tex](\frac{5280}{1.609})ft = 3281.541... ft[/tex]
Now, for converting 6.2 km into feet, we will just multiply 6.2 by 3281.541... ft.
Thus, 6.2 km = [tex](6.2 \times 3281.541...)ft = 20345.556... ft[/tex]
So, there are 20345.556... feet in 6.2 km.
What type of number cannot be written as a fraction p and q where p and q are interfere and q is not equal to zero?
The definition of a rational number is that it can be written in form [tex]\frac{p}{q}[/tex]. If it cannot be written in that form then it is not a rational number (which makes it an irrational number)
Answer: irrational number
The height, in feet, of an arrow shot from a bow in an upwards direction, is modeled by the function h(t) = -16t2 + 96t + 5, where t represents the time in minutes.
Given function: h(t) = -16t^2 + 96t + 5, where t represents the time in minutes.
We need to find the interval for which the arrow is going up.
The arrow is going up would be the values of time t =0 when it start and when it went to highest point.
Given function is a quadratic function and it represents a parabolic shape.
The highest point on the parabola is a vertex point.
Therefore, we need to find the x-coordinate of the vertex.
We know, formula for x-coordinate of the vertex is
[tex]\frac{-b}{2a}[/tex]
For the given quadratic a= -16 and b=96.
Plugging values of a and b in formula, we get
[tex]\frac{-96}{2(-16)}=\frac{-96}{-32} = 3.[/tex]
Therefore, after 3 seconds arrow would be at maximum height.
Therefore, the interval for which the arrow is going up is [0,3].
What is the product of 6+5i and 4+7i?
Enter your answer, in standard form, in the box.
______
The answer to this question is the product is 12i
Answer: The required product is [tex]-11+62i.[/tex]
Step-by-step explanation: We are given to find the product of the following two complex numbers :
[tex]z_1=6+5i,~~~z_2=4+7i.[/tex]
We will be using the following property :
[tex](a+b)(c+d)=a(c+d)+b(c+d).[/tex]
Also, we will use the fact that [tex]i=\sqrt{-1},~~i^2=-1.[/tex]
The product of the given complex numbers is
[tex]z_1z_2\\\\=(6+5i)(4+7i)\\\\=6(4+7i)+5i(4+7i)\\\\=24+42i+20i+35i^2\\\\=24+62i-35\\\\=-11+62i.[/tex]
Thus, the required product is [tex]-11+62i.[/tex]
What is the solution for this inequality?
-4x < 28
A.
x > -7
B.
x < 7
C.
x < -7
D.
x > 7
Terry sees an offer about a refurbished phone which is 35% off the original price the new price is £78 how much was the phone before the discounted price
part/whole=0.65
78/whole=0.65
whole =78/0.65 =120 £
Answer:
The price before discount would be $120
Step-by-step explanation:
The actual price of the phone is 100%-35% = 65% of the original price of the phone.
So by rule of three
If 65% of the price is $78, the total price of the phone would be:
[tex]Total price = \frac{74}{0,65} \\\\Total price = 120[/tex]
Sal has a small bag of candy containing three green candies and two red candies. While waiting for the bus, he ate two candies out of the bag, one after the other, without looking. What is the probability that both candies were the same color?
A.
2/5
B.
3/100
C.
8/25
D.
3/5
Answer:
A. 2/5
Step-by-step explanation:
3/5*2/4+2/5*1/4
6/20+2/20
8/20 = 2/5
Answer:
Option A
Step-by-step explanation:
Given that Sal has a small bag of candy containing three green candies and two red candies.
He ate two candies one after the other.
The probability that both candies were the same color has to be calculated.
The probability that both candies were the same color = P(both are red or both are green)
= P(both are red)+P(both are green)
Total no of ways to draw 2 candies out of 5 = 5C2 = 5(4)/2 = 10
No of ways of drawing 2 red candies = 2C2 =1
No of ways of drawing 2 green candies = 3C2 =3
Hence required prob =(1+3)/10 = 2/5
Which ordered pair makes both inequalities true?
y > –3x + 3
y > 2x – 2
(1,0)
(–1,1)
(2,2)
(0,3)
Answer:
All options are wrong.
Step-by-step explanation:
We have y > –3x + 3 and y > 2x – 2
Option A - (1,0)
y > –3 x 1 + 3 = 0
We have y = 0, which is not greater than 0.
Option A is not correct.
Option B - (–1,1)
y > –3 x -1 + 3 = 6
We have y = 1, which is not greater than 6.
Option B is not correct.
Option C - (2,2)
y > –3 x 2 + 3 = -3
We have y = 2, which is greater than -3.
y > 2 x 2 – 2 = 2
We have y = 2, which is not greater than 2.
Option C is not correct.
Option D - (0,3)
y > –3 x 0 + 3 = 3
We have y = 3, which is not greater than 3.
Option D is not correct.
All options are wrong.
Four times the difference of a number and 5 is the same as 5 increased by four times the number plus five times the number
The value of expression is,
x = - 5
Here;
The written expression is;
''Four times the difference of a number and 5 is the same as 5 increased by four times the number plus five times the number.''
We have to solve this expression.
What is Mathematical expression?
The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.
Now,
Let a number is 'x'.
Then, The mathematical expression is written as;
4* ( x - 5 ) = 5 + (4*x) + (5*x)
We can solve as;
4* ( x - 5 ) = 5 + (4*x) + (5*x)
4x - 20 = 5 + 4x + 5x
- 20 - 5 = 4x + 5x - 4x
- 25 = 5x
x = -5
Hence, The value of expression is,
x = - 5
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@pinkfloyd @taskmasters PLEASE HELP IM STUCK ONE QUESTION??/
Use the figure to answer the question that follows:
Segments UV and WZ are parallel with line ST intersecting both at points Q and R respectively
When written in the correct order, the two-column proof below describes the statements and reasons for proving that corresponding angles are congruent:
Statements Reasons
segment UV is parallel to segment WZ Given
Points S, Q, R, and T all lie on the same line. Given
I m∠SQT = 180° Definition of a Straight Angle
II m∠SQV + m∠VQT = 180° Substitution Property of Equality
III m∠SQV + m∠VQT = m∠SQT Angle Addition Postulate
m∠VQT + m∠ZRS = 180° Same-Side Interior Angles Theorem
m∠SQV + m∠VQT = m∠VQT + m∠ZRS Substitution Property of Equality
m∠SQV + m∠VQT − m∠VQT = m∠VQT + m∠ZRS − m∠VQT
m∠SQV = m∠ZRS Subtraction Property of Equality
∠SQV ≅ ∠ZRS Definition of Congruency
Which is the most logical order of statements and reasons I, II, and III to complete the proof?
The correct logical order for the statements I, II, and III in the proof is: I. Definition of a Straight Angle, III. Angle Addition Postulate, and II. Substitution Property of Equality. This order supports the conclusion that corresponding angles, created by the transversal intersecting parallel lines, are congruent.
To complete the two-column proof that demonstrates the congruence of the corresponding angles when segments UV and WZ are parallel and line ST intersects both at points Q and R respectively, we need to place statements and reasons I, II, and III in the most logical order. This should allow us to show
corresponding angles are congruent, which is the ultimate aim of the proof.
The correct order of statements and reasons to complete the proof is:
Definition of a Straight Angle (I): We know that the angle measure of a straight line is 180°, hence m∠SQT = 180°.
Angle Addition Postulate (III): Based on the postulate, we can express m∠SQV + m∠VQT as equal to the measure of angle SQT because the two angles combine to form the straight angle, therefore m∠SQV + m∠VQT = m∠SQT.
Substitution Property of Equality (II): By substituting the equal values established in statements I and III, we get m∠SQV + m∠VQT = 180°.
After arranging the statements and their corresponding reasons, the proof logically demonstrates that the congruent angle pairs are a result of transversal ST intersecting parallel lines UV and WZ.
Tell the numbers that are odd and prime 2,14,23,24,25,31,45
Odd numbers are those numbers that gives a fraction when divided by 2
Prime numbers are those that can be divided only by 1 and the number itself.
Odd numbers are therefore : 23, 25, 31 and 45
Prime numbers are therefore: 2, 23 and 31
How is the divisibility rule for 7 more complicated then the rules for 2,3,5 and 10?
Final answer:
The divisibility rule for 7 is more complex than the rules for 2, 3, 5, and 10 due to the lack of a simple pattern or quick digit check, requiring multiple steps and manipulations of the number.
Explanation:
The divisibility rule for 7 is more complicated than the rules for 2, 3, 5, and 10 because it does not follow a simple pattern or involve a quick check of a number's last digit or sum. The rules for divisibility by 2, 3, 5, and 10 are straightforward: a number is divisible by 2 if its last digit is even, by 3 if the sum of its digits is divisible by 3, by 5 if its last digit is 0 or 5, and by 10 if it ends in 0.
The rule for divisibility by 7 requires more steps and cannot be easily performed in one's head. The process typically involves subtracting or adding multiples of 7 from different segments of the number, which often makes it more difficult for students to use effectively without practice or further understanding of the method. Complicated rules for divisibility by 7 prove the point that while mathematical rules are universally valid, some rules are inherently more complex than others.
Which of the following fractions is equivalent to -84/-90 in the least common terms?
14/15
(-)14/15
42/45
(-)42/45
The fraction equivalent to -84/-90 in the least common terms is 14/15, as both the numerator and the denominator can be divided by the common factor 6, resulting in a simplified positive fraction.
To find which fraction is equivalent to -84/-90 in the least common terms, we need to simplify the fraction by canceling out any common factors in the numerator and the denominator. We observe that both numbers are divisible by 6. When we divide the numerator and the denominator by 6, we get:
-84 / -90 = (-84 / 6) \/ (-90 / 6) = 14 / 15
Since a negative divided by a negative results in a positive number, we eliminate the negative signs and get the fraction in its least common terms as 14/15.
Ming took a cab across town. His fare was \$22$22dollar sign, 22, and he leaves an 18\%18%18, percent tip.
Answer:
$25.96
Step-by-step explanation:
We have been given that Ming took a cab across town. His fare was $22, and he leaves an 18% tip.
To find the total amount by Ming for cab ride will be equal to 22 plus 18% of 22.
[tex]\text{Total amount paid by Ming for the cab ride}=22+(\frac{18}{100}*22)[/tex]
[tex]\text{Total amount paid by Ming for the cab ride}=22+(0.18*22)[/tex]
[tex]\text{Total amount paid by Ming for the cab ride}=22+3.96[/tex]
[tex]\text{Total amount paid by Ming for the cab ride}=25.96[/tex]
Therefore, Ming paid a total amount of $25.96 to the cab driver.
On a number line, the distance from zero to -9 is 9 units.
Which equation demonstrates this concept?
A.
0 + 9 = 9
B.
|-9| = -9
C.
|-9| = 9
D.
92 = 81
Answer:
C. |-9| = 9
Step-by-step explanation:
Distance is always non-negative. Distances in a negative direction are made positive by the use of the absolute value function. The distance from 0 to -9 is one such distance.
Each section of a race is 2/5 mile.the race has 44 sections.which expression tells how many miles long the entire race is?
answer is equal to 2X44/5mile=17.6mile
Each section of a race is 25 mile.
The race has 4 sections.
Which expression tells how many miles long the entire race is?
Answer:
4×2/5
Aiden is a taxi driver. M(n) models Aiden's fee (in dollars) for his n^th drive on a certain day.What does the statement M(8)<M(4)M, mean
M(n) denotes Aiden's fee (in dollars) for his n^th drive on a certain day.
Then:
M(8) is Aiden's fee for his 8th drive;M(4) is Aiden's fee for his 4th drive.M(8)<M(4) means that 8th drive was less expensive than 4th drive.
Airbags are manufactured by Aces (A), Best (B), and Cool (C) at rates of 57%, 26% and 17%, respectively. Airbags occasionally kill (K) passengers when they deploy in accidents. Airbags made by Aces, Best, and Cool do not kill people at rates of 99%, 96%, and 87%, respectively. One airbag is randomly selected for testing.
If an airbag kills a passenger, calculate the probability that the airbag was manufactured by Cool. (Round to the nearest ten-thousandth.)
Air bag manufactured by Aces(A)=57%
So, Probability [tex]P(A)=\frac{57}{100}[/tex]
Air bag manufactured by Best (B) =26%
So, Probability [tex]P(B)=\frac{26}{100}[/tex]
Airbag manufactured by Cool(C)=17%
So, Probability [tex]P(C)=\frac{17}{100}[/tex]
Airbags made by Aces, Best, and Cool do not kill people at rates of 99%, 96%, and 87%, respectively.
Let K be the event which kill people.
Probability of Air bag made by A which kill people [tex]P(K/A)=\frac{1}{100}[/tex]
Probability of Air bag made by B which kill people [tex]P(K/B)=\frac{4}{100}[/tex]
Probability of Air bag made by C which kill people [tex]P(K/A)=\frac{13}{100}[/tex]
If an airbag kills a passenger, calculate the probability that the airbag was manufactured by Cool
Using Baye's theorem:
[tex]P(C/K)=\frac{P(K/C)P(C)}{P(K/A)P(A)+P(K/B)P(B)+P(K/C)P(C)}[/tex]
Substitute the values of probabilities into formula
We get,
[tex]P(C/K)=\frac{0.17\times 0.13}{0.57\times 0.01+0.26\times 0.04+0.17\times 0.13}[/tex]
Now we calculate it and get probability
So, [tex]P(C/K)=0.5785[/tex]
So, 57.85% of passenger kills if the airbag was manufactured by Cool.
Marissa is an event organizer for a charity group. She is organizing a five-hour dinner event being held to raise funds for the charity. The following list shows the costs for hosting the event. Facility Rental: $150 per hour of event Linens: $2 per attendee Food: $20 per attendee Table Decorations: $3 per attendee Musical Entertainment: $1,800 (flat fee) Cleaning Fee: $250 (flat fee) The total cost of the event, with n attendees, is represented by the given expression. Which statement best describes the constant in this expression?
A constant is a number that stays the same no matter what any outside variables are. In this case, the variables are the number of hours of the event and the number of attendees. However, it states in the problem that the event will be 5 hours so that becomes known; the only thing that might change is the number of attendees so you can eliminate any cost that will be affected by that. You are left with Facility Rental, Musical Entertainment, and Cleaning Fee. Furthermore, you can be sure that Musical Entertainment and Cleaning Fee must be included in the constant because they are described as "flat rates", which means they do not change.
The answer is D) It is the total cost for entertainment, facility rental, and cleaning.
Hope this helps!
The statement that best describes the constant in the expression
25n + 2,800 is:
It is the cost per person for food, linens, and food decorations.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Facility Rental = $150 per hour of the event
Linens = $2 per attendee
Food = $20 per attendee
Table Decorations = $3 per attendee
Musical Entertainment = $1,800
Cleaning Fee = $250
The total cost of the event.
= 25n + 2,800
Where n is the number of attendees.
Now,
25 is the total cost per attendee for food, linens, and table decorations.
Thus,
The constant in the expression is 25 which is the cost per attendee for food, linens, and table decorations.
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Alicia is making cupcakes for a party she is having and wants to make sure everyone gets at least one cupcake. The recipe calls for 1 of a teaspoon of salt for every batch and each batch makes 21 cupcakes. If 2 alicia is having a party with 84 people attending, how many teaspoons of salt will alicia use?
[tex]\frac{84}{21}=4[/tex]
Therefore you need 4 batches of cupcakes if you want every person to get one cupcake.
This means you multiply the amount of salt per batch by the number of batches, to get the total amount of salt you need.Each batch contains 1 teaspoon of salt for 21 cupcakes. Multiply: [tex]4\text{ batches of cupcakes}\times1\text{ teaspoon of salt}=4\text{ teaspoons salt}[/tex] for the whole thing.Use the drop-down menus to complete each equation so the statement about its solution is true.
no solutions:
7-5+3x-1 = __x + __
one solution:
7-5+3x-1 = __x +__
infinitely Many Solutions
7−5+3x−1=__ x +__
FILL IN THE BLANKS PLEASE :)) (will try to make you brainlist if correct!)
First, let's simplify the expression: 7 - 5 + 3x - 1 ⇒ 3x + 1 (slope=3, y-intercept = 1)
Next, let's understand what they are asking for:
no solutions means same slope but different y-intercepts
Answer: 3x + _______ (the blank can be anything except 1)
one solution means different slopes
Answer: ________x + _______ (the first blank can be anything except 3, the second blank can be anything)
infinitely many solutions means same slope and same y-intercept
Answer: 3x + 1
Answer:
1.3x+9
2.1x+4
3.3x+1
Step-by-step explanation:
You want to estimate the mean weight loss of people one year after using a popular weight-loss program being advertised on TV. How many people on that program must be surveyed if we want to be 95% confident that the sample mean weight loss is within 0.25 lb of the true population mean? Assume that the population standard deviation is known to be 10.6 lb.
Answer:
At least 6907 people.
Step-by-step explanation:
Population std deviation = sigma= 10.6
Since population std deviation is known, we can use normal probability table to get sample size from confidence interval.
The sample mean weight loss is within 0.25 lb of the true population mean.
Hence margin of error < 0.25
Margin of error = z critical (std dev/n) where n = sample size
Z critical for 95% = 1.96
Hence 0.25 >1.96(10.6)/sq rt n
Simplify to get
sq rt n > 1.96(10.6)/0.25 = 83.104
Square both the sides to get
n > 83.104 square = 6906.27
i.e. sample size should be atleast 6907.
Find the Area and Perimeter!
Area of a triangle is 1/2 x base x height.
base = 12
Height = x+6
Area = 1/2 * 12 * x+6
Area = 1/2 * 12x * 72
Area = 6x + 36
Perimeter is the sum of the 3 sides:
x-7 + 12 + 2x+5
3x -2 + 12
3x+10
The last choice is the correct answer.
A small company plans to invest in a new advertising campaign. There is a 20% chance that the company will lose $5,000, a 50% chance of a break even, and a 30% chance of a $10,000 profit. Based ONLY on this information, what should the company do? A) The expected value is $2,000.00, so the company should proceed with the campaign. B) The expected value is $4,000.00, so the company should proceed with the campaign. C) The expected value is −$2,000.00, so the company should not proceed with the campaign. D) The expected value is −$3,000.00, so the company should not proceed with the campaign.
A small company plans to invest in a new advertising campaign.
There is a 20% chance that the company will lose $5,000 ,
50% chance of a break even, and a 30% chance of a $10,000 profit
So the expected value from the advertisement campaign is calculated as - 20% of 5000 + 0% of 5000 + 30% of 10,000
= -1000 + 0 + 3000
= 2000
The expected value from the advertisement campaign is $2000.
So the Company must go ahead with the campaign.
Answer : Option A
Hope it helps.
Thank you ..!!
what is the base 8 representation of the number 11100111(2)
A) 231(8)
B) 329(8)
C) 347(8)
D) 385(8)
Remark
You could convert base two to base 10 and then convert base 10 to base 8. That's the long way. The procedure below is the short way.
Step One
Write the base 2 number in groups of 3 starting from the right and going left
11 100 111
Step Two
Convert the base 2 numbers in groups of 3 to base 8. The largest result will be a 7
11 = 2*1 + 1 = 2 + 1 = 3
100 = 1*2^2 = 4
111 = 1*2^2 + 1*2 + 1 = 7
Step Three
Read the answer going down.
347 is the answer
Answer
347(8) = C
Answer:
Option C)347(8) is correct. Below is the explanation for changing the base 2 number to the base 8
Step-by-step explanation:
Given:
11100111(2)
To find:
Number with base 8.
Let's convert the given base 2 number to a base 10 number or an integer. Then convert it to a base 8 number.
11100111(2) = 1* [tex]2^{7}[/tex]+1* [tex]2^{6}[/tex]+1*[tex]2^{5}[/tex] + 0*[tex]2^{4}[/tex] +0*[tex]2^{3}[/tex] +1* [tex]2^{2}[/tex]+1*[tex]2^{1}[/tex] +1*[tex]2^{0}[/tex]
Simplify it
=128 +64+32 +0+0+4+1+1
=231
Now, change this integer 231 to a base 8 number ( I have attached a file for this)
We get an answer of 347(8). Option C is correct!
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The area of a rectangle is 117117117 square meters. The width is 999 meters.
Area = 117 m² width = 9 m
Area (A) = length (L) x width (w)
117 = L * 9
117 = 9L
[tex]\frac{117}{9} = \frac{9L}{9}[/tex]
13 = L
Answer: length = 9 m
Answer:
117/9=13
13*9=117
So, the length is 13 since L*W=area.
:)
F the quadratic formula is used to solve 2x 2 = 8x - 3, what are the solutions?
x = 2 ± [tex]\frac{1}{2}[/tex]√10
express the equation in standard form : ax² + bx + c = 0 ( a ≠ 0 )
then x = ( - b ±√( b² - 4ac) ) / 2a
given 2x² = 8x - 3, then
2x² - 8x + 3 = 0 ( in standard form )
with a = 2, b = - 8, c = 3
x = (8 ±√(64 - 24) )/4 = (8 ±√40) / 4 = (8 ± 2√10) / 4
x = 2 ± [tex]\frac{1}{2}[/tex]√10
A recipe includes 6 cups of flour and three fourths cup of butter butter. Write the ratio of the amount of flour to the amount of butter butter as a fraction in simplest form.
To express the ratio of flour to butter from a recipe as a fraction in simplest form, start by setting it up as a fraction and then multiply by the reciprocal of the denominator. In this case, a recipe with 6 cups of flour and three-fourths cup of butter simplifies to a ratio of 8:1.
Explanation:To find the ratio of the amount of flour to the amount of butter as a fraction in simplest form, we start by writing the amounts given in the recipe as a fraction. There are 6 cups of flour and three-fourths (3/4) cup of butter. The initial ratio is therefore:
6 cups of flour / (3/4) cup of butter
To simplify, we can multiply both the numerator (the top part of the fraction) and the denominator (the bottom part of the fraction) by the reciprocal of the denominator:
6 / (3/4) = 6 × (4/3) = 24/3 = 8
So, the simplest form of the ratio of flour to butter is 8:1.
In 2015 there were approximately 33,500 firearm fatalities. How many deaths per hour
Take away 32 from the product of 6 and a number