The equation of the line is y = [tex]\frac{5}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
Step-by-step explanation:
The form of the linear equation is y = mx + b, where
m is the slope of the line, [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] b is the y-intercept, to find b substitute x and y in the equation by the coordinates of any point on the line∵ A line passes through points ( [tex]\frac{2}{5}[/tex] , 5) and ( [tex]-\frac{2}{5}[/tex] , 4)
∴ [tex]x_{1}[/tex] = [tex]\frac{2}{5}[/tex] and [tex]x_{2}[/tex] = [tex]-\frac{2}{5}[/tex]
∴ [tex]y_{1}[/tex] = 5 and [tex]y_{2}[/tex] = 4
- Substitute them in the rule of the slope to find m
∵ [tex]m=\frac{4-5}{-\frac{2}{5}-\frac{2}{5} }[/tex]
∴ [tex]m=\frac{-1}{-\frac{4}{5}}=\frac{5}{4}[/tex]
- Substitute it in the form of the equation
∴ y = [tex]\frac{5}{4}[/tex] x + b
- To find b substitute x and y in the equation by the coordinates
of any point on the line
∵ Point ( [tex]\frac{2}{5}[/tex] , 5) lies on the line
∴ x = [tex]\frac{2}{5}[/tex] and y = 5
∴ 5 = [tex]\frac{5}{4}[/tex] ( [tex]\frac{2}{5}[/tex] ) + b
∴ 5 = [tex]\frac{1}{2}[/tex] + b
- Subtract [tex]\frac{1}{2}[/tex] from both sides
∴ [tex]\frac{9}{2}[/tex] = b
∴ y = [tex]\frac{5}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
The equation of the line is y = [tex]\frac{5}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
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9 goes into 300 how many times
Answer:
300/9 = 33.33 repeating
Step-by-step explanation:
9 can go into 300, 33 times with a remainder of 3.
some body please help me!!!!!!
Surface area of a cube = 486 square inches
Solution:
Given each side of a cube = 9 inches
Net of a cube has 6 squares.
Area of square = side × side
Area of 1 square = 9 × 9 = 81 square inches
Surface area of a cube = Area of 6 squares
= 6 × (side × side)
= 6 × 81
= 486 square inches
Hence, surface area of a cube is 486 square inches.
3/?= 2/1.25 can you answer this for me please
Answer:
3/15/8=2/1.25
Step-by-step explanation:
Answer:
see attached work shown
I need the answer please ;/
Answer:Q
Step-by-step explanation: EF is a segment. k is not uppercase. and MN is a line. So only Q could work.
Hardcover books cost $8 and paperbacks cost $3. John buys 15 books for $70. How many of each book type did he buy?
Answer:
10 paperback and 5 hardcover books
Step-by-step explanation:
Please see attached picture for full solution.
Let's check:
total cost= 10(3) + 5(8)= $70 ✓
You could also try to solve the question by assuming John bought all paperback books first instead of all hardcover books. The answer should be the same.
-4 times a number plus 29
Answer:
-4x + 29
Step-by-step explanation:
Nathan has 80 us stamps,64 Canadian stamps,and 32 Mexican stamps. He wants to put the same number of stamps on each page. Each page will have stamps from only one country. What's the greatest number of stamps that he can put on each page?
Answer:
The greatest number of stamps that Nathan can put on each page = 16.
Step-by-step explanation:
Given:
Nathan has:
80 US stamps
64 Canadian stamps
32 Mexican stamps
The stamps need to put on a page such that each page has same number of same country stamps on each page.
To find the greatest number of stamps he can put on each page.
Solution:
In order to find the greatest number of stamps Nathan can put on each page, we will find the G.C.F. of the three numbers.
The numbers are:
[tex]80,64,32[/tex]
We will list down the prime factors of each number.
[tex]80=2\times 2\times 2\times 2\times 5[/tex]
[tex]64=2\times 2\times 2\times 2\times 2\times 2[/tex]
[tex]32=2\times 2\times2\times 2\times 2[/tex]
The G.C.F can be given as = [tex]2\times 2\times 2\times 2[/tex] = 16
Thus, the greatest number of stamps that Nathan can put on each page = 16.
. If the perimeter of a rectangle is 18x + 4 what is the length of the missing side?
2X-3
Answer:
Step-by-step explanation:
Let the length b y
Width = 2x - 3
Perimeter = 18x + 4
And
Perimeter = 2(l + w)
18x + 4 = 2(y + 2x - 3)
Dividing through by 2
9x + 2 = y + 2x - 3
Making y as subject
y = 9x - 2x + 2 + 3
y = 7x + 5
The missing side is 7x + 5
Kara spends $16 on tubes of paint and paint brushes. A tube of paint costs $3 and a paint brush costs $.50. Kara purchases twice as many brushes as tubes of paint. How many tubes of paint and how many brushes did she buy?
Answer: 3(4) + .5(8) = 16
Step-by-step explanation:Replace b with 2p in the 1st equation
3p + .50(2p) = 16
3p + 1P = 16
4p = 16
p = 16/4
p = 4 tubes of pain
then
b = 2(4)
b = 8 brushes
Kara bought 4 tubes of paint and 8 brushes, given the total cost of $16, the price per tube of paint is $3, and the price per brush is $.50.
Explanation:The question is asking how many tubes of paint and brushes Kara bought if she spent a total of $16, each tube of paint costs $3, each brush costs $0.50, and the number of brushes is twice the number of tubes of paint. To solve this problem, we can denote the number of paint tubes as x and the number of brushes as 2x.
So we set up the equation considering the total amount spent: $3x + $0.50(2x) = $16. This simplifies to:
$3x + $1x = $16 $4x = $16 x = 4
So, she bought 4 tubes of paint and 2 times that number of brushes, which is 8 brushes.
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solve the equation 1/3m+6m-9/3m=3m-3/4m
The correct answer is option B, as the solution of the equation:
[tex]\frac{1}{3 m}+\frac{6 m-9}{3 m}=\frac{3 m-3}{4 m}[/tex] is [tex]\frac{23}{15}[/tex]
Solving this type of equation containing the fractions involves the mathematical operations like finding a common denominator, combining the fractions, eliminating the fraction denominators, cancelling common terms, distributing, adding/subtracting to both sides, simplifying, and dividing both sides by the same factor.
The Steps of calculation are as follows:
Let's verify the answer:
We had the equation:
[tex]\[\frac{1}{3m} + \frac{6m - 9}{3m} = \frac{3m - 3}{4m}\][/tex]
And we simplified it to:
[tex]\[\frac{6m - 8}{3m} = \frac{3m - 3}{4m}\][/tex]
Next, we cross multiplied:
[tex]\[4m(6m - 8) = 3m(3m - 3)\][/tex]
[tex]\[24m^2 - 32m = 9m^2 - 9m\][/tex]
We then brought all terms to one side:
[tex]\[24m^2 - 9m^2 - 32m + 9m = 0\][/tex]
[tex]\[15m^2 - 23m = 0\][/tex]
Factoring out m:
[tex]\[m(15m - 23) = 0\][/tex]
So, either m = 0 or 15m - 23 = 0.
If 15m - 23 = 0, then [tex]\(m = \frac{23}{15}\)[/tex].
Therefore, the correct answer is: b. [tex]\frac{23}{15}$[/tex].
7x+14=7(x+2)
[tex]7x + 14 = 7(x + 2)[/tex]
Answer:
The equation has infinitely many solutionsx ∈ REach real number is the solution of this equation.Step-by-step explanation:
[tex]7x+14=7(x+2)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\7x+14=(7)(x)+(7)(2)\\\\7x+14=7x+14\qquad\text{subtract}\ 7x\ \text{from both sides}\\\\7x-7x+14=7x-7x+14\\\\14=14\qquad\bold{TRUE}\\\\\bold{CONCLUSION}\\\text{The equation has infinitely many solutions}[/tex]
Aaden is packing boxes into a carton that is 8 inches long, 8 inches wide, and 4 inches tall. The boxes are 2 inches long, 1 inch wide, and 1 inch tall. How many boxes will fit into the carton?
Answer:
first multiply length×width×height,of the carton
8×8×4=256
then multiply length×width×height for boxes
2×1×1=2
divide 256 by 2
256÷2=128
Fast answer pls. No stupid answers
First one.
y = -2x + 3
5x - (-2x + 3) = 11
y = -2x + 3
5x + 2x - 3 = 11
//
7x = 14
x = 2
y = - 2(2) + 3 = - 4 + 3 = - 1.
One x, one solution.
Find the perimeter of the polygon
Answer:
The perimeter of the polygon is 48 cm.
Step-by-step explanation:
Given: [tex]\angle B \cong \angle D[/tex]
To find the perimeter of the polygon, we need to find the lengths of the AB, BC, CD and DA
Since, [tex]\angle B \cong \angle D[/tex] and to find the length, from circle theorem, "Two tangents from an external point to a circle are always equal in length".
From this statement we shall conclude,
The length of [tex]AB=5+6=11[/tex]
The length of [tex]BC=6+7=13[/tex]
The length of [tex]CD=7+6=13[/tex]
The length of [tex]DA=6+5=11[/tex]
Thus, the perimeter of the polygon is
[tex]\begin{aligned}\text {Perimeter} &=A B+B C+C D+D A \\&=11+13+13+11 \\&=48 \mathrm{cm}\end{aligned}[/tex]
Hence, the perimeter of the polygon is 48 cm.
What is the arc length of the semicircle
Answer:
The arc length of the semicircle is half the circumference of the full circle
[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=11 \end{cases}\implies C=2\pi (11)\implies C=22\pi \\\\\\ \stackrel{~\hfill \textit{a semicircle has half of that}}{C=\cfrac{22\pi }{2}\implies C=11\pi \implies C\approx 34.56}[/tex]
Which property of multiplication is shown?
g • h = h • g
Commutative property of multiplication
My explanation is attached in the image provided.
One Direction makes $46,000 per show. How much money do they make after 100 shows?
Step-by-step explanation:
$46,000×100=$4,600,000
To find the total earnings from 100 shows for One Direction making $46,000 per show, multiply the earnings per show by the number of shows to get $4,600,000.
The total earnings from 100 shows for One Direction can be calculated by multiplying the earnings per show by the number of shows.
Given that they make $46,000 per show, the total earnings after 100 shows would be $46,000 x 100 = $4,600,000.
Therefore, One Direction would make $4,600,000 after 100 shows.
The total weight of a fully loaded coal truck is 4 tons. The ratio of the weight of the truck to the weight of the coal is 7:5. What is the weight of the truck and the coal?
Answer:
Step-by-step explanation:
total weight is 4 tons.
ratio of weight of truck to weight of coal is 7:5....added = 12
so 7/12 of the total weight is the truck's
and 5/12 of the total weight is the coal
7/12 of 4 tons = 7/12 * 4 = 28/12 = 2 1/3 tons <== weight of truck
5/12 of 4 tons = 5/12 * 4 = 20/12 = 1 2/3 tons <== weight of coal
Antonio has $350 to spend on skis. Sales tax is 6%. Decide if each description of a price and discount, plus sales tax, represents a pair of skis that Antonio can purchase with the money he has .
Choose Yes or No for each description
a. 25% off $450 Yes or No
b. 20% off $385 Yes or No
c. $20 off $360 Yes or No
d. 15% off $380 Yes or No
e. $10 off $340 Yes or No
Answer:
False
Step-by-step explanation:
I need help solving these problems--Images down below.
On the long word problem, I was given hints:
X=Less than 5 weeks
Y=Less than 200
- Use substitution instead of graphing.
Answer:
all work is pictured and shown
You roll a number cube two times. How many outcomes are possible? Please explain work.
The total number of possible outcomes when rolling a six-sided number cube twice is 36. This is calculated by multiplying the 6 possible outcomes from the first roll with the 6 possible outcomes from the second roll.
When you roll a six-sided number cube two times, you create a series of possible outcomes that can be categorised by understanding that each roll is independent of the other. On the first roll, you have 6 possible outcomes (1, 2, 3, 4, 5, or 6), and for the second roll, regardless of what the first number was, you again have 6 possible outcomes. To find the total number of outcomes possible when rolling a cube twice, you multiply the number of outcomes for each event. So, we calculate the total outcomes with 6 (for the first roll) times 6 (for the second roll), which equals 36 possible outcomes.
This means that rolling two dice can lead to one of thirty-six different combinations, where the first number of the pair corresponds to the result of the first roll and the second number to the result of the second. For instance, if you first roll a 4 and then a 3, one possible outcome is (4,3).
It is important to note that when calculating probabilities for specific sums of the two dice, such as the probability of rolling a seven, the outcomes are not all equally likely. If we consider the sum of the dice, rolling a two is less likely than rolling a seven because there's only one combination (1,1) for a sum of two, while there are six combinations (1,6; 2,5; 3,4; 4,3; 5,2; 6,1) for a sum of seven.
Which number sentence is true?
BRAINLIEST GETS 15 POINTS !!!
A. –39.6 ÷ 4.8 = 8.25
B. –39.6 ÷ (–4.8) = –8.25
C. 39.6 ÷ –4.8 = 8.25
D. –39.6 ÷ (–4.8) = 8.25
Answer:
the answer in D
Step-by-step explanation:
i just took the test and it was correct :)
The correct answer is option D. -39.6 ÷ (- 4.8) = 8.25
Canceling out is a mathematical process used for removing subexpressions from a mathematical expression when this removal does not change the meaning or the value of the expression because the subexpressions have equal and opposing effects.
Conclusion: The plus and minus signs, + and −, are mathematical symbols used to represent the notions of positive and bad, respectively. in addition, + represents the operation of addition, which results in a sum, while − represents subtraction, resulting in a difference.[1] Their use has been extended to many other meanings, more or less analogous. Plus and minus are Latin terms meaning "more" and "less", respectively.
When you see the other option you will find even after the cancelation of the minus sign the end results have either a faulty positive or negative sign.
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How do i solve the problem 7+7+7=3×
Answer:
x=7
Step-by-step explanation:
7+7+7=3*?
7+7+7 is basically 3 sevens, which is equivalent to 3*7 or 7*3. So x=7.
Answer:
x=7
Step-by-step explanation:
7+7+7=3x
14+7=3x
21=3x
x=21/3
x=7
What is an example of response bias
Answer with Explanation:
"Response Bias" refers to a pattern consisting of incorrect responses. Sometimes the question's way of wording may contribute to such kind of bias in responses. One question that could lead to a response bias is asking with the use of leading questions.
For example, "You don't want classes to start any earlier, do you?"This kind of question unduly favors the other option. Thus, the response would be biased.
Another situation which may lead to a response bias is the lack of privacy when answering survey questions. The respondent will feel pressured while being monitored, thus leading to a biased response. They will also choose the option that they think are socially acceptable.
Another example is providing respondents a scale of 1-5, when it comes to restaurant service. It becomes natural for them to choose the extremes, which are 1 and 5. These responses are mostly affected by a person's culture.
The handford high school basketball team scored 79, 68, 86, 91 and 72 points in their first five games. What was the average number of points scored in these five games?
Answer: 79.2 points
Step-by-step explanation: The word "average" is the same as the word "mean" so to find the average of the points scored in their first 5 games, we want to add up all the points and divide them by the number of games they played which is 5 games.
Let's begin by adding the numbers.
79 + 68 + 86 + 91 + 72
Adding these numbers, we get a sum of 396.
This will be divided by how many games they played which is 5.
396 ÷ 5 = 79.2
This means that the average number of points scored is 79.2 points which could round down to 79 points but don't round unless the problem asks.
If a lb of beef cost $4.25, how much would 1 1/4 lb cost?
Step-by-step explanation:
$4.25×1 1/4=$4.25/1×5/4=$21.25/4=$5.25
Answer:it would cost 5.25
Step-by-step explanation:
A 100-gram sample of a radioactive isotope decays at a rate of 6% every week. How much of the sample will be left one year from now?
4 grams sample will be left after 1 year
Step-by-step explanation:
The decay function for percentage decay is given by:
[tex]y =a (1-r)^x[/tex]
Here,
a is the initial value
r is the rate
x is the number of time periods
Given
Initial value = 100 grams
Rate = 6% = 0.06
Time = 1 year = 52 weeks
Putting the values in the formula
[tex]y = 100 (1-0.06)^{52}\\y = 100(0.94)^{52}\\y = 4.00\ grams[/tex]
Hence,
4 grams sample will be left after 1 year
Keywords: Decay, percentage
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Simplify this expression.
1 + 4.25n + 32p – 3 + (–2p) + 54n
A. 5.5n – 12p – 2
B. 9.5n + 1.5p – 2
C. 94n − 1.5p − 4
The correct expression to simplify is:
[tex]1+4.25n + 3/2p -3+(-2p)+5/4n[/tex]
Answer:
[tex]5.5n-1/2p-2[/tex]
Explanation:
1. Given expression:
[tex]1+4.25n + 3/2p -3+(-2p)+5/4n[/tex]
2. Group like terms:
[tex](1-3)+(4.25n+5/4n)+(3/2p-2p)[/tex]
3. Simplify:
1 - 3 = - 24.25n + 5/4n = 4.25n + 1.25n = 5.5n3/2p - 2p = 1.5p - 2p = - 0.5p = - 1/2p[tex]-2+5.5n-1/2p=5.5n-1/2p-2[/tex]
how many days in one week?
Answer:
7 , Monday, Tuesday, Wednesday, Thursday, Friday, then you have you r weekend Saturday, Sunday, then you restart the week . :)
Step-by-step explanation:
Answer:
7 days in 1 week
Step-by-step explanation:
Count the days. (Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday)
Find the cosine of T.
Answer:
c o s t = x \displaystyle P: \text{cos}t=x P:cost=x.
Step-by-step explanation:
The cosine of t is equal to the x-coordinate of point P