The pair of equations has one solution and the solution is (30/11, 20/11).
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
The coordinates on one line are (2, 6) and (5, 0)
Here, m=(0-6)/(5-2)
= -2
Substitute m=-2 and (2, 6) in y=mx+c, we get
6=-2(2)+c
c=10
So, the equation of a line is y=-2x+10 -----(i)
The coordinates on another line are (0, 2) and (6, 6)
Here, m= (6-2)/(6-0)
= 2/3
Substitute m=2/3 and (0, 2) in y=mx+c, we get
2=2/3(0)+c
c=0
So, the equation is y=2/3 x -----(ii)
Substitute equation (ii) in (i), we get
2/3 x=-2x+10
2x/3 +3x =10
11x=30
x=30/11
Substitute x=30/11 in equation (ii), we get
y =2/3 × 30/11
y= 20/11
So, the solution is (30/11, 20/11)
Therefore, the pair of equations has one solution and the solution is (30/11, 20/11).
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What is the slope of the line passing through the points (9,7) and (4,-3)?
Answer:
2
Step-by-step explanation:
slope = m = (difference in y)/(difference in x)
m = (-3 - 7)/(4 - 9)
m = -10/(-5)
m = 2
Double the quotient of q and r
Answer:
(q/r)*2
Step-by-step explanation:
divide q and r, then multiply the result
The result of doubling the quotient of q and r is equal to 2 times the value obtained by dividing q by r.
To double the quotient of q and r, you would perform the following mathematical operation:
Double the quotient of q and r = 2 * (q / r)
In this expression, "q" and "r" are variables representing two numerical values. To get the result, you would divide "q" by "r" and then multiply the quotient by 2.
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Complete Question:
Write the expression for the below statement:
Double the quotient of q and r.
A coin is tossed twice. Let H represents heads, T represents tails, and the combination of the two letters represent the outcome of both tosses (e.g., if the coin landed heads on the first toss and tails on the second, we'd represent that with HT). Which of the following sets includes all possible outcomes of both tosses?
Answer:
{HH, HT, TH, TT}
Step-by-step explanation:
The set of all possible outcomes in tossing a coin twice is;
{HH, HT, TH, TT}
In the first toss the coin may land Heads. In the second toss the coin may land Heads or Tails. This can be represented as;
HH, HT
Heads in the first and second tosses. Heads in the first toss followed by a Tail in the second toss.
In the first toss the coin is also likely to land Tails. In the second toss the coin may land Heads or Tails. This can be represented as;
TH, TT
Tails in the first toss followed by a Head in the second toss. Tails in the first and second tosses.
Combining these two possibilities will give us the set of all possible outcomes in tossing a coin twice is;
{HH, HT, TH, TT}
A display of gift boxes has 1 box in the top row, 3 boxes in the next row, 5 boxes in the next row, and so on. There are 7 rows in all. How many gift boxes are in the display? Question 19 options: 64 boxes 47 boxes 36 boxes 49 boxes
Answer:
36 boxes
Step-by-step explanation:
For this case we have to increase two boxes each time we go to the next row. So:
1 row: 1
2 row: 3
3 row: 5
4 row: 7
5 row: 9
6 row: 11
7 row: 13
Adding the number of boxes we have:
[tex]1 + 3 + 5 + 7 + 9 + 11 + 13 = 49[/tex]
There are 49 boxes!
Answer:
Option D
1/5 can paint covers 1 wall how many with walls with 2 cans
Answer:
10
Step-by-step explanation:
1/5*10=2 cans so 1*10 is 10 walls
Kristen has $16.26 for a buffet. There is an entrance fee of $5.31 with a $2.96 charge for every pound of crab legs ordered. This situation is modeled by the equation 2.96p + 5.31 = 16.26, where p represents the number of pounds of crab legs ordered. How many pounds of crab legs can Kristen eat at the buffet? (round to the nearest tenth of a pounds of crab legs ordered)
Answer:
Step-by-step explanation:
8 pounds
Answer:
8 pounds
Step-by-step explanation:
a fish tank is shaped like a rectangular prism. It has a length of 5 feet, a width of 2 feet, and a height of 3 feet. what is the volume of the fish tank?
Answer:
30 ft
Step-by-step explanation:
It is 30 because to find the volume of a rectangular prism, you do
length x width x height.
So, 5 x 2 x 3 = 30.
To find the volume of a rectangular prism, multiply its length, width, and height. Thus, the volume of the fish tank measuring 5 feet in length, 2 feet in width, and 3 feet in height is 30 cubic feet.
Explanation:The volume of a rectangular prism such as a fish tank can be calculated by multiplying its length, width, and height together. For a fish tank with a length of 5 feet, a width of 2 feet, and a height of 3 feet, the volume calculation would look like this:
Volume = Length × Width × Height
Volume = 5 ft × 2 ft × 3 ft
Volume = 10 ft × 3 ft
Volume = 30 ft³
Therefore, the volume of the fish tank is 30 cubic feet.
Ron is slicing 5 pizzas each pizza slice is 1/8 of the pizza. How many pizza slices will be there in all
Answer:
there would be 40 slices of pizza
Step-by-step explanation:
If 5 pizzas each have 8 slices you multiply 5 X 8 which equals 40 slices
Answer:
there would be 40 slices of pizza.
Step-by-step explanation:
What is 5/6÷3/8 in simplelest form
For this case we must simplify the following expression:
[tex]\frac {\frac {5} {6}} {\frac {3} {8}} =[/tex]
Applying double C we have:
[tex]\frac {5 * 8} {6 * 3} =\\\frac {40} {18} =[/tex]
Dividing numerator and denominator between 2:
[tex]\frac {20} {9}[/tex]
ANswer:
[tex]\frac {20} {9}[/tex]is the simplified form
how do i become smarter
Answer:
You become smarter by working hard in school to get good grades and to get good grades you have to put in work and study to get the grades you want and probably deserve.
Step-by-step explanation:
Help and please show work
Answer:
5 unitsStep-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
We have the points (1, 2) and (-3, 5). Substitute:
[tex]d=\sqrt{(-3-1)^2+(5-2)^2}=\sqrt{(-4)^2+3^2}=\sqrt{16+9}=\sqrt{25}=5[/tex]
How do i find quartiles, 1,2 and 3
Lower quartile=25% of total frequency/numbers in the data set
Median=50% of total frequency/numbers in the data set
Upper quartile=75% of total frequency/numbers in the data set
Hope this helps:)
Answer:
see explanation
Step-by-step explanation:
To obtain the quartiles arrange the data in ascending order
38, 47, 54, 60, 67, 68, 76, 77, 84, 89
Q₂ is the median
The median is the middle value in the data set. If there is no exact middle value then it is the average of the 2 values either side of the middle
Q₂ = [tex]\frac{67+68}{2}[/tex] = 67.5
Q₁ is the lower quartile and is the middle value of the data to the left of the median
Q₁ = 54
Q₃ is the upper quartile and is the middle value of the data to the right of the median
Q₃ = 77
Maria wrote the equation log(x/2)+log(20/x2) What is the solution to Maria’s equation?
Answer:
log x - log 2 + log 20 - 2 log x
Step-by-step explanation:
We need to solve the equation:
[tex]log(\frac{x}{2}) + log(\frac{20}{x^2})[/tex]
We know that log(x/y) = log x - log y and
log(x^2) = 2logx
Solving we get:
[tex](log x - log 2) + (log20 - log x^2)\\(log x - log 2) + (log20 - 2 log x)[/tex]
The solution is:
log x - log 2 + log 20 - 2 log x
Answer:
The solution to Maria's equation is x=5/4
Expand the expression (5x + 3)2, and write the result in standard form.
Expand
2 × 5x + 2 × 3
Simplify 2 × 5x to 10x
10x + 2 × 3
Simplify 2 × 3 to 6
= 10x + 6
The expanded expression in standard form for the given equation is [tex]\(25x^2 + 30x + 9\).[/tex]
To expand the expression [tex]\((5x + 3)^2\)[/tex], we use the distributive property, which states that for any real numbers [tex]\(a\), \(b\), and \(c\):[/tex]
[tex]\((a + b)^2 = a^2 + 2ab + b^2\).[/tex]
In this case,[tex]\(a = 5x\)[/tex] and[tex]\(b = 3\)[/tex]. Substituting these values into the formula, we get:
[tex]\[(5x + 3)^2 = (5x)^2 + 2(5x)(3) + 3^2\][/tex]
Now, let's compute each term:
1.[tex]\( (5x)^2 = 25x^2 \) (since \((a)^2 = a \times a\)).[/tex]
2. [tex]\(2(5x)(3) = 30x\) (by multiplying \(2ab\) where \(a = 5x\) and \(b = 3\)).[/tex]
3. [tex]\(3^2 = 9\).[/tex]
Now, summing up all the terms, we get:
[tex]\[ (5x + 3)^2 = 25x^2 + 30x + 9 \][/tex]
So, the expanded expression in standard form is [tex]\(25x^2 + 30x + 9\).[/tex]
Complete question:
Expand the expression (5x + 3)2, and write the result in standard form.
a water sprinkler sprays water outward in a cirular pattern what area will be watered if the the radius of the spray from the sprinkler is 18ft write an exact answerin terms of pie/3.14
Answer:
circle area = PI * radius^2
circle area = 3.14 * 18^2
circle area = 1,017.36 square feet
Step-by-step explanation:
water sprinkler sprays water outward in a cirular pattern what area will be watered if the the radius of the spray from the sprinkler is 18ft write an exact answerin terms of pie/3.14 answer equal 324ñ²ft
One cell phone plan charges $20 per month plus $0.15 per minute used. A second cell phone plan charges $35 per month plus $0.10 per minute used. Write and slice an equation to find the number of minutes you must talk to have the same cost for both calling plans.
Answer:
300 minutes
Step-by-step explanation:
Let
x----> the numbers of minutes used
y ---> the cost per month
we know that
First cell phone plan
y=0.15x+20 ---> equation A
Second cell phone plan
y=0.10x+35 ---> equation B
equate the equation A and equation B
0.15x+20=0.10x+35
Solve for x
0.15x-0.10x=35-20
0.05x=15
x=15/0.05
x= 300 minutes
Find the cost y
y=0.15(300)+20 =$65
That means
For x=300 minutes
The cost for both calling plans is y=$65
What is the constant to
I take it the constant in this case it'll just be the coefficient, thus
[tex]\bf -\cfrac{2a^3}{7}\implies \stackrel{\stackrel{constant}{\downarrow }}{-\cfrac{2}{7}}a^3[/tex]
Work for 77.28 divided by 4.0
Answer:
19.32
Step-by-step explanation:
if 77.28 divided by 4.0 do long division and once you do that check yourself to see if you are correct
I hope I helped you guys! :)
Answer:
19.32
Step-by-step explanation:
Calculate the mean of this data set.
Answer:
The mean of the data set is 5.
Step-by-step explanation:
Add the numbers in the data set:
6+3+16+12+21+8+9
= 75
Then divide by the amount of values in the data set:
75/15
=5
The mean of this given data set is 15.
What is the mean of this data set?Given:
A data set is given in the image.Find:
The mean of the given data set.Solution:
A mean is the average of a data set.
We find the mean by adding all numbers together and then dividing the sum of the numbers by the number of numbers.
Now, a summation of number = 2+4+4+7+2+6+7+4+8+2+3+6+9+4+7 = 75
Now, there are total of 15 data given.
Therefore, mean = 75/15 = 5.
Hence, the mean of the given data set is 15.
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At the beginning of each school year, Madison Middle School orders new shirts for the entire student body. Each student receives
one shirt. Each shirt is the same price, s, and the school orders enough for n students. Which equation represents the
proportional relationship between P, the total price of the shirts, and the number of students?
NEED DONE NOW!!! WILL MARK BRAINLIEST
The equation representing the price of the shirt s, the number of students n and P is Option A.
sn = P
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of students be = n
Let the cost of each shirt be = s
The equation will be ,
So , the total cost of the shirt P = number of students x cost of each shirt
Total cost of the shirt P = n x s
So , the equation representing the proportional relationship is
P = ns
sn = P
Hence , The equation representing the price of the shirt s, the number of students n and P is Option A.
sn = P
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A member of congress is interested in
whether her constituents favor a proposed
gun-control bill. Her staff reports that 361
letters on the bill have been received and
323 of these oppose the bill. What is the
sample size?
A. 684
B. 38
C. 361
D. 323
Answer:361
Step-by-step explanation:
The sample size in this scenario is defined by the total number of letters received by the member of Congress, regardless of their stance on the bill. Therefore, the sample size is 361.
Explanation:In statistics, the term 'sample size' refers to the number of observations or measurements used in a study or experiment. In this particular case, the member of Congress is interested in the views of her constituents on a proposed gun-control bill. The total number of letters received - regardless of whether those letters support or oppose the bill - forms the sample size.
In this context, the total number of letters is 361, so option C is the correct answer. It doesn't matter how many of these letters were in favor or against the bill; all of them constitute the sample. The number of letters opposing the bill (323) is a part of the total sample, not the sample size itself.
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Please help I will mark brainliest!!! (10 points)
Answer:
A: 700
B: 6400
C: 50
Step-by-step explanation:
A: You can multiply by 5
B: You can just multiply by 20.
C: Every 10% is 5, because 15(30%)/3 is 5. 5 times 10 is 50.
Answer:
a. h = 700
b. j = 6400
c. g = 50
Step-by-step explanation:
Translate each statement into an equation and solve the equation. Remember that to change a percent to a decimal, you divide the percent by 100, which is the same as moving the decimal point two places to the left. Also, a percent of a number means a percent times the number.
a. 20% of h is 140
20% * h = 140
0.2h = 140
Divide both sides by 0.2
h = 700
b. 5% of j is 320
5% * j = 320
0.05j = 320
Divide both sides by 0.05
j = 6400
c. 30% of g is 15
30% * g = 15
0.3g = 15
Divide both sides by 0.3
g = 50
Use the Distributive Property to write each expression as an equivalent algebraic expression.
(7 + a)3
Answer:
21 + 3a
Step-by-step explanation:
3 (7+a)
distribute 3 into parentheses:
21 + 3a
The distributive property states that one should simplify the expression by multiplying each term inside the parentheses by the term outside of them:
3*7=21
3*a=3a
21+3a
Hope this helps!!
What is the least common multiple of the two denominators 6/8 and 4/32
The least common multiple (LCM) of the denominators 6/8 and 4/32 is 12.
Explanation:The least common multiple (LCM) of two numbers is the smallest number that is divisible by both numbers.
To find the LCM of the denominators 6/8 and 4/32, we need to find the LCM of 6 and 4.
The LCM of 6 and 4 is 12.
Therefore, the LCM of 6/8 and 4/32 is 12.
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To find the LCM of the denominators 8 and 32, we prime factorize them, identify the highest power of each prime number, and multiply these together. The LCM of 8 and 32 is 32.
To find the Least Common Multiple (LCM) of the denominators from the fractions 6/8 and 4/32, follow these steps:
Identify the denominators: 8 and 32.
Prime factorize each denominator:
8 = 2 × 2 × 2 (2³)32 = 2 × 2 × 2 × 2 × 2 (2⁵)Identify the highest power of each prime number that appears in the factorizations. Here, the highest power of 2 is 2⁵.
Multiply the highest powers of all the primes together to find the LCM: LCM = 2⁵ = 32.
So, the LCM of the denominators 8 and 32 is 32.
Terri wrote the equation using slope-intercept form for the line that passes through the points (4, 6) and (–2, 3).
Which best describes Terri’s first error?
In step 1, the slope of the line should be 1/2.
In step 2, she should have substituted the point (4, 6).
In step 3, she should have subtracted 4 from both sides of the equation.
In step 4, the m and b values should be switched.
Answer:
Step 1 is incorrect.
Step-by-step explanation:
The slope = difference of y values / difference of x values so Step 1 is incorrect. The slope is (6-3)/ ((4 - (-2)) = 1/2. He worked out x differences / y differences.
Answer: A: In step 1, the slope of the line should be 1/2.
Which of the following statements shows a characteristic of a statistical question?
Answer:
For a question to be statistical it has to have a specific population, room for a clear response, and a variability in the data.
An example of a statistical question is, "What is the typical amount of time it takes for a piece of gum to lose its flavor?" This is statistical because it accounts for a clear response, population, and variability.
Answer:
The question asks for a quantitative response.
Step-by-step explanation:
I did the 8.01 test, C was the correct answer.
Good luck FLVS students
solve for x: 6(4x+5)=3(x+8)+3
Answer:
x=-1/7
Step-by-step explanation:
6(4x+5)=3(x+8)+3
Distribute
24x +30 = 3x+24 +3
Combine like terms
24x+30 = 3x +27
Subtract 3x from each side
24x-3x+30 = 3x-3x+27
21x +30 = 27
Subtract 30 from each side
21x +30-30 = 27-30
21x = -3
Divide each side by 21
21x/21 = -3/21
x = -1/7
Answer:
-1/7
-0.14
Step-by-step explanation:
The length of your classroom is about 3.5 x 10^2 inches. If the hallway is ten times as long as the classroom, what is the length of the hallway, expressed in scientific notation?
Answer:
3.5x10^3
Step-by-step explanation:
3.5x10^2 = 350
350x10 = 3500
3500 = 3.5x10^3
Which is true about the line whose equation is y + 3 = 0?
The slope is zero.
The y-intercept is 3.
The slope is 3.
The value of x always equals the value of y.
the value of x always equals zero
Answer:
The slope is zero.
Step-by-step explanation:
The y-int is -3, the slope can't be 3, and the value of x isn't equal to y, if it was the lines would be intersecting
Kyle needed about 1 liter of water to fill a container. Did Kyle most likely fill a small glass, a spoon, or a vase?
The answer is vase.
A spoon is less than 3 ounces for sure.
A small glass is 8 ounces or less.
A vase is probably a liter of more.
Good luck!