Equation of line passing through (2, -2) and parallel to 2x+3y = -8 is [tex]y=\frac{-2 x}{3}+\frac{-2}{3}[/tex]
Solution:Need to write equation of line parallel to 2x+3y=-8 and passes through the point (2, -2)
Generic slope intercept form of a line is given by y = mx + c
where "m" = slope of the line and "c" is the y - intercept
Let’s first find slope intercept form of 2x+3y=-8 to get slope of line
[tex]\begin{array}{l}{2 x+3 y=-8} \\\\ {=>y=\frac{-2 x-8}{3}} \\\\ {\Rightarrow y=-\frac{2}{3} x-\frac{8}{3}}\end{array}[/tex]
On comparing above slope intercept form of given equation with generic slope intercept form y = mx + c,
[tex]\text {for line } 2 x+3 y=-8, \text { slope } m=-\frac{2}{3}[/tex]
We know that slopes of parallel lines are always equal
So the slope of line passing through (2, -2) is also [tex]m=-\frac{2}{3}[/tex]
Equation of line passing through [tex](x_1 , y_1)[/tex] and having slope of m is given by
[tex]\left(y-y_{1}\right)=\mathrm{m}\left(x-x_{1}\right)[/tex]
[tex]\text { In our case } x_{1}=2 \text { and } y_{1}=-2[/tex]
Substituting the values in equation of line we get
[tex](y-(-2))=-\frac{2}{3}(x-2)[/tex]
[tex]\begin{array}{l}{\Rightarrow y+2=\frac{-2 x+4}{3}} \\\\ {=>3(y+2)=-2 x+4} \\\\ {=>3 y+6=-2 x+4} \\\\ {3 y=-2 x-2}\end{array}[/tex]
[tex]y=\frac{-2 x}{3}+\frac{-2}{3}[/tex]
Hence equation of line passing through (2 , -2) and parallel to 2x + 3y = -8 is given as [tex]y=\frac{-2 x}{3}+\frac{-2}{3}[/tex]
Please help with b..
Answer:
First side: 12 feet, second side: 16 feet
Step-by-step explanation:
We know that the second side is 4 feet longer than the first side. If the first side is x, then the second side is x+4
b) The total amount of the border is 28 feet, so we can say that first side+second side=28, or
x+(x+4)=28
2x+4=28
2x=24
x=12 feet is the first side
x+4 = 16 feet is the second side
We can check that 12 feet + 16 feet = 28 feet as stated by the problem
What is the answer to this?
Answer:
7^-12 or 1/7^12
Step-by-step explanation:
To divide exponents with the same base, subtract the second exponent from the first.
So:
7^-5/7^7 = 7^-5-7 = 7^-12
You can also write 7^-12 as 1/7^12.
Andy received a 25% discount on the book he bought at the book sale if he paid 17.40 what was the original price for the book
Answer:
$21.75
Step-by-step explanation:
Add 25% then subtract to get back to $17.40
4) Mark rented a bike from Jose's Bikes. It
cost $10 plus $6 per hour. If Mark paid
$22, then he rented the bike for how many
hours?
Answer: 2hrs
Step-by-step explanation:
paid 10 dollars at first and then 6 every hour he rode
so let x represent the # of hour rented
6x+10=22
x=2hrs
if 20%of a length is 23cm. what the complete lenght
Answer:
The complete length is 115 cm.
Step-by-step explanation:
Given:
If 20%of a length is 23 cm.
Now, to find the complete length.
Let, the complete length be [tex]x[/tex].
So, according to question:
20% of [tex]x[/tex] = 23 cm
[tex]\frac{20}{100} \times x=23[/tex]
[tex]0.20\times x=23[/tex]
[tex]0.20x=23[/tex]
Dividing both sides by 0.20 we get :
[tex]x=115[/tex]
Therefore, the complete length is 115 cm.
To find the complete length when 20% is 23 cm, divide 23 cm by 0.20 to get 115 cm as the total length.
If 20% of a length is 23 cm, we want to find out what the complete length is. To do so, we recognize that 20% is the same as saying 20 per 100 or 0.20 in decimal form. If 0.20 of the length is 23 cm, it means that 23 cm represents 0.20 of the total length. We can set up the equation like this:
0.20 * Total Length = 23 cm
To find the Total Length, we divide both sides of the equation by 0.20:
Total Length = 23 cm / 0.20
Total Length = 115 cm
Therefore, the complete length is 115 cm.
Choose the correct statement about the graph of x - 1 ≤ 2
A.) Closed circle on 1 and all the numbers to the left shaded
B.) Open circle on 3 and all numbers to the left shaded
C.) Open on 1 and all numbers to the right shaded
D.) Closed circle on 3 and all the numbers to the left shaded
Answer:
B.) Open circle on 3 and all numbers to the left shaded
Describe a relationship modeled by the function f(x) = 4x3 − 72x2 + 320x
Answer:
A relationship modeled by the function f(x) = 4x³ - 72x² + 320x is the volume of a right prism whose dimensions are 4 times a desired length, 10 units less that such desired length, and 8 units less than the same desired length.Explanation:
To find a relationship modeled by the given function it is recommendable to factor it.
The function is:
[tex]f(x)=4x^3-72x^2+320x[/tex]The first step to factor it is to extract common factor 4x:
[tex]f(x)=4x(x^2-18x+80)[/tex]The second step is to factor the quadratic trinomial.
That is made by writting it as a product of two binomials, for which the two constant terms add up - 18 and their product is 80. Those terms are -10 and - 8; so the two factors are (x - 10) and (x - 8), and the factored form is:
[tex]f(x)=(4x)(x-10)(x-8)[/tex]Then, a relationship modeled by that polynomial is the volume of right prism whose dimensions are 4 times a desired length, 10 units less that such desired length, and 8 units less than the same desired length.
x is the desired (unknown) length 4x is 4 times the desired lengthx - 10 is 10 less than the desired lengthx - 8 is 8 less than the desired lengthThus, the volume of the prism is the product of the three factors:
Volume = (4x)(x-10)(x-8)x=3y – 10
x 2y - 5 Solve by subst8tution
Answer:
x=5, y=5. (5, 5).
Step-by-step explanation:
x=3y-10
x=2y-5
--------------
3y-10=2y-5
3y-2y-10=-5
y-10=-5
y=-5+10
y=5
x=2(5)-5=10-5=5
In order to buy an authentic Wookie mask,, Dale invests $6000 in an account at 9.5% interest compounded continuously. The mask costs $12000. How long will it take until Dale car
buy this mask? Round your answer to the nearest hundredth.
years
It will take 7.30 years until Dale can by his mask
Step-by-step explanation:
Compound continuous interest can be calculated using the formula:
[tex]A=Pe^{rt}[/tex] , where
A is the future value of the investment, including interestP is the principal investment amount (the initial amount)r is the interest rate in decimalt is the time the money is invested forDale invests $6000 in an account at 9.5% interest compounded continuously. The mask costs $12000. We need to find how long will it take Dale until can buy this mask
∵ Dale invests $6000
∴ P = 6000
∵ The interest rate is 9.5% ⇒ compounded continuously
∴ r = 9.5% = 9.5 ÷ 100 = 0.095
∵ The mask costs $12000
∴ A = 12000
Substitute these values in the formula above
∵ [tex]12000=6000e^{0.095t}[/tex]
- Divide both sides by 6000
∴ [tex]2=e^{0.095t}[/tex]
- Insert ㏑ for both sides
∴ [tex]ln(2)=ln(e^{0.095t}[/tex])
- Remember that [tex]ln(e^{n})=n[/tex]
∴ [tex]ln(2)=0.095t[/tex]
- Divide both sides by 0.095
∴ t = 7.29628611
∴ t = 7.30 ⇒ to the nearest hundredth year
It will take 7.30 years until Dale can by his mask
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It will take Dale 7.64 years to save enough money to buy the mask we can use the method of compound interest.
To find how long it will take Dale to save enough money to buy the mask, we can use the following formula for compound interest:
A = P * e^(rt)
where:
A is the final amount
P is the principal amount
r is the interest rate
t is the time in years
We know that A = $12000, P = $6000, and r = 9.5%. We need to solve for t.
12000 = 6000 * e^(0.095t)
e^(0.095t) = 2
ln(2) = 0.095t
t = ln(2) / 0.095
t = 7.64
Therefore, it will take Dale 7.64 years to save enough money to buy the mask.
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A neighborhood garden is 3/4 acre in size. It is divided into plots that are each 1/8 acre. How many 1/8-acre plots are there in the neighborhood garden?
Use the models below to help you.
A. 1
B. 4
C. 6
D. 7
Answer:A
Step-by-step explanation:The answer is A because if you divide the numbers equally, then you will get 1
The number of 1/8-acre plots in a 3/4-acre garden is 6.
Explanation:The question is about dividing the total area of a garden into smaller plots and finding out how many plots there will be. Here, the total size of the garden is given as 3/4 acre and each plot is 1/8 acre in size. To find out how many 1/8-acre plots make 3/4 of an acre, we perform a division: 3/4 divided by 1/8. This is the same as multiplying 3/4 by the reciprocal (the 'flipped' fraction) of 1/8, which is 8/1. So, the calculation is 3/4 * 8/1 = 24/4 = 6. Therefore, there are 6 1/8-acre plots in a 3/4-acre garden.
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What is m∠LNM?
m∠LNM = °72
Answer:
72 degrees
Step-by-step explanation:
Congruent supplements Theorem.
The symbol m∠LNM denotes the measure of the angle formed by points L, N, M. The 'm' stands for measure, '∠' denotes an angle, and LNM are the points forming the angle. In this context, m∠LNM is 72 degrees.
Explanation:The term m∠LNM refers to the measure of angle LNM. In mathematical notation, the symbol '∠' is often used to denote an angle, and LNM refers to the points forming the angle. For instance, if you have a triangle or any other polygon, and points L, N, and M are three vertices (corners) of the shape, then ∠LNM would be the angle at vertex N, formed by the intersection of line segments LN and NM. Given that m∠LNM is said to be 72°, this indicates that the measure of angle LNM is 72 degrees.
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Simplify the expression -4b+8c+12-8b-2c+6
Answer:
-6(2b-c-3)
Step-by-step explanation:
Collect like terms
-12b+6c+12+6
Add the 2 numbers on right
-12b+6c+18
Factor -6 out of expression
-6(2b-c-3)
Answer:
2.03
Step-by-step explanation:
I am a multiple of 5, but not a
multiple of 10. My units and hundreds
digits are the same. The sum of my
three digits is 11.
Answer:
515
Step-by-step explanation:
If it's a multiple of five and not ten, that would be the units digit must be 5. Hundreds=units. 11-10=1. So the answer is 515
The number is a multiple of 5 but not 10, with the units and hundreds digits being the same and their sum being 11. Therefore, the number is 505.
Explanation:This question can be solved by analyzing the given clues. The number is a multiple of 5 but not 10, so it cannot end in 0. The units and hundreds digits are the same, meaning they both have to be a single digit number. Additionally, the sum of the three digits is 11.
Since the units and hundreds digits are the same, and their sum is 11, they both must be equal to 5. Thus, the number is 505.
9(2x + 1) – 4(x – 6) = 6(2x + 1) + 5(x – 6)
What does x equal and why??
Answer:
x = 19Step-by-step explanation:
[tex]9(2x+1)-4(x-6)=6(2x+1)+5(x-6)\\\\\text{use the distributive property:}\ a(b+c)=ab+ac\\\\(9)(2x)+(9)(1)+(-4)(x)+(-4)(-6)=(6)(2x)+(6)(1)+(5)(x)+(5)(-6)\\\\18x+9-4x+24=12x+6+5x-30\\\\\text{combine like terms}\\\\(18x-4x)+(9+24)=(12x+5x)+(6-30)\\\\14x+33=17x-24\qquad\text{subtract 33 from both sides}\\\\14x+33-33=17x-24-33\\\\14x=17x-57\qquad\text{subtract}\ 17x\ \text{from both sides}\\\\14x-17x=17x-17x-57\\\\-3x=-57\qquad\text{divide both sides by (-3)}\\\\\dfrac{-3x}{-3}=\dfrac{-57}{-3}\\\\x=19[/tex]
Shanley would like to give $5 gift cards and $4 teddy bears as party favors. Shanley has $124 to spend on party favors. Enter an inequality to find the number of gift cards x and teddy bears y Shanley could purchase. Give one solution to the inequality.
The inequality is:
[tex]5x+4y \leq 124[/tex]
Give one solution to the inequality:
Let x = 5 and y = 10
[tex]65\leq 124\,\,\,true[/tex]
Step-by-step explanation:
Cost of Gift cards= $5
Cost of Teddy bear = $4
Total money to spend on party = $124
The required inequality is:
Let no of gift cards= x
and no of teddy bears = y
The inequality is:
[tex]5x+4y \leq 124[/tex]
Give one solution to the inequality:
Let x = 5 and y = 10
then, the solution will be:
[tex]5x+4y \leq 124\\5(5)+4(10)\leq 124\\25+40\leq 124\\65\leq 124\,\,\,true[/tex]
Keywords: Solving inequalities
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Answer:
The inequality is 5x + 4y < and the line under the sign 124
(10,9)
Step-by-step explanation:
I NEED HELP FAST what is y+1=5/6(x-2) in standard form?
Answer:
[tex]\large\boxed{5x-6y=16}[/tex]
Step-by-step explanation:
The standard form of an equation of a line:
[tex]Ax+By=C[/tex]
We have the equation in the point-slope form. Convert:
[tex]y+1=\dfrac{5}{6}(x-2)\qquad\text{multiply both sides by 6}\\\\6y+6=6\!\!\!\!\diagup^1\cdot\dfrac{5}{6\!\!\!\!\diagup_1}(x-2)\\\\6y+6=5(x-2)\qquad\text{use the distributive property}\\\\6y+6=(5)(x)+(5)(-2)\\\\6y+6=5x-10\qquad\text{subtract 6 from both sides}\\\\6y+6-6=5x-10-6\\\\6y=5x-16\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\-5x+6y=5x-5x-16\\\\-5x+6y=-16\qquad\text{change the signs}\\\\\boxed{5x-6y=16}[/tex]
Jesse has made 120 cookies for the sale
and has one more day to bake. Jesse's
pan allows her to bake 20 cookies per
batch.
Jesse can use the equation of the
function to predict the total number of
cookies:
y=120 + 20(x). However, she prefers to
use a table.
Use the equation tool to complete the table. y=120+20(x)
Answer:
280
Step-by-step explanation:
Answer:280
Step-by-step explanation:
From 240 to 260 you add 20 each time so 260 plus 20 will give us the answer (280)
If f(x) = 2x + 25, then f(3) =
Answer:
31
Step-by-step explanation:
given f(x) = 2x + 25,
f(3) =2(3) + 25
= 6 + 25
= 31
Answer:
Step-by-step explanation:
if the variables x and y have a strong positive correlation, what generally happens to y as x increases? what if x and y have a strong negative correlation?
If there is a strong positive correlation between "x" and "y" then when "x" increases, "y" tends to increase
If variables x and y have strong negative correlation then as "x" increases in value, "y" will decrease; similarly, if "x" decreases in value, "y" will increase
Solution:1) If the variables x and y have a strong positive correlation, what generally happens to y as x increases?
Let us first understand about strong positive correlation
Given that "x" and "y" has strong positive correlation
Correlation coefficients are used to measure the strength of the relationship between two variables.
Positive correlation:
Positive correlation is a relationship between two variables in which both variables move in tandem—that is, in the same direction. A positive correlation exists when one variable decreases as the other variable decreases, or one variable increases while the other increases.
When one variable moves higher or lower, the other variable moves in the same direction with the same magnitude.
Therefore if there is a strong positive correlation between "x" and "y" then when "x" increases, "y" tends to increase
2) What if x and y have a strong negative correlation?
Negative correlation is a relationship between two variables in which one variable increases as the other decreases, and vice versa.
Negative correlation is a relationship between two variables whereby they move in opposite directions.
If variables x and y have strong negative correlation then as "x" increases in value, "y" will decrease; similarly, if "x" decreases in value, "y" will increase
I need answers to 4 and 5!!!
Answer:
4. B
5. C
Step-by-step explanation:
4.
We can say the 5 angles of the Pentagon PQRST equals 540 degrees.
We see that Angle P and Angle T are 90 degrees each.
R is given as 100
Q and S are same, let it be "x"
Now we can write an equation:
P + Q + R + S + T = 540
90 + x + 100 + x + 90 = 540
Solving for x, we get:
2x + 280 = 540
2x = 540 - 280
2x = 260
x = 260/2
x = 130
Angle Q is equal to x, so that is 130
Correct answer is B
5.
When 2 parallel lines are cut by transversal, the corresponding angles are equal.
The 60 degree angle given and the angle adjacent (beside) to angle x are same. So we can say that is equal to 60 degrees as well.
This 60 degree angle and x form a straight line. The degree measure of a straight line (or a straight angle) is 180 degrees. Thus we can write:
60 + x = 180
Now, we solve for x:
60 + x = 180
x = 180 - 60
x = 120
The correct answer is C
50% of what number is 284?
I believe 50% of 284 =142
Answer:
284/50*100 = 586 or simply double 284
Step-by-step explanation:
Factor 1/10 out of 1/10x-7/10
Answer:
[tex]\large\boxed{\dfrac{1}{10}x-\dfrac{7}{10}=\dfrac{1}{10}(x-7)}[/tex]
Step-by-step explanation:
[tex]\dfrac{1}{10}x=\left(\dfrac{1}{10}\right)(x)\\\\\dfrac{7}{10}=\left(\dfrac{1}{10}\right)(7)\\\\\dfrac{1}{10}x-\dfrac{7}{10}=\left(\dfrac{1}{10}\right)(x)-\left(\dfrac{1}{10}\right)(7)=\left(\dfrac{1}{10}\right)(x-7)[/tex]
Greta reads 1 1/2 pages per minute when she reads her homework assignment. At this rate, how long does it take Greta to read 60 pages?
Answer:
40 minutes
Step-by-step explanation:
60 pages / (1 1/2 pages/ minute)
= 60 / 3/2 minutes
= 40 minutes
Answer:
330 minutes
Step-by-step explanation:
11/2 times 60/1
so basically just do 60 times 11 equals
660 then divided by 2 equals 330
so she will read 60 pages in 330 minutes, I hope I did it right
I think I'm wrong
For the data in the table, find the line of best fit, rounding values to three places if necessary. A) y = 4.88 + 0.625x B) y = 4.98 + 0.725x C) y = 4.88 + 0.525x D) y = 4.98 + 0.425x
Answer: y = 4.88 + 0.525x
The equation of the line of best fit for the data shown in the picture is y=0.894x+0.535
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
We have a data in the table:
Let's suppose the equation for the line is:
y = mx + c
Where m is the slope of the line and c is the y-intercept.
The value of m is given by:
[tex]\rm m = \frac{S_{xy}}{S_{xx}} }[/tex] and
[tex]\rm S_{xy} = \sum_{i=1}^{n}x_iy_i-\frac{(\sum_{i=1}^{n}x_i)(\sum_{i=1}^{n}y_i)}{n}[/tex]
[tex]\rm S_{xx} = \sum_{i=1}^{n}x_i^2-\frac{(\sum_{i=1}^{n}x_i)^2}{n}[/tex]
From the table(data is not mentioned we have assumed the data) the values of [tex]\rm \sum_{i=1}^{n}x_iy_i= 415[/tex], [tex]\rm {\sum_{i=1}^{n}x_i= 44[/tex], [tex]\rm {\sum_{i=1}^{n}y_i= 42[/tex],
[tex]\rm {\sum_{i=1}^{n}x_i^2= 438[/tex], and n = 5.
[tex]\rm S_{xy}= 415-\frac{44\times42}{5} \Rightarrow 45.4\\\\\rm S_{xx}= 438- \frac{44^2}{5} \Rightarrow 50.8[/tex]
[tex]\rm m = \frac{45.4}{50.8} } \Rightarrow 0.8937 \approx0.894[/tex]
For c we have to calculate the means of x and y for this:
[tex]\rm \bar{x} = \frac{\sum x}{n} \Rightarrow \frac{44}{5} \Rightarrow8.8[/tex]
[tex]\rm \bar{y} = \frac{\sum y}{n} \Rightarrow \frac{42}{5} \Rightarrow8.4[/tex]
Now, put the above values in the equation of a line to find the value of c
8.4 = (0.894)(8.8)+c
c = 0.5328 ≈ 0.535
Now the line is y = 0.894x+0.535
Thus, the line of best fit for the data shown in the picture is y=0.894x+0.535
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what is the value of x is in the solution set of 8x-6>12+2x?
Answer:
see explanation
Step-by-step explanation:
Given
8x - 6 > 12 + 2x ( subtract 2x from both sides )
6x - 6 > 12 ( add 6 to both sides )
6x > 18 ( divide both sides by 6 )
x > 3
Any value of x greater than 3 will be in the solution set
Which simplified expression matches the set of tiles shown?
-x² – x+2
x² - x + 2
-x²+x+2
x2+x+2
Algebra tiles are a useful tool to simplify expressions. Depending on their shape and decoration, they represent different parts of the expression. Review your tiles and match them to the four given expressions carefully.
Explanation:The question pertains to Algebra and specifically, matching a simplified algebraic expression to a set of tiles. The exact matching algebraic expression cannot be determined as the set of tiles isn't provided in the question but here's how you would approach this kind of problem:
If you're using algebra tiles, squares typically represent x², rectangles portray x, and small squares depict constants like 2. The color or decoration of a tile may indicate a positive or negative value. For example, a square with '- ' could mean '-x²'.
So if you've got a square with '- ', a rectangle without a decoration, and two small plain squares, your expression should be '-x² - x + 2'. If the rectangle had a '-', your expression would be '-x² + x + 2' instead.
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The set of tiles shown represents the expression x² - x + 2.
Explanation:The set of tiles shown represents the expression x² - x + 2.
To match the tiles to the simplified expression, look at the coefficient and exponent of x on each tile. The first tile has an exponent of 2 and a coefficient of 1. The second tile has an exponent of 1 and a coefficient of -1. The third tile has an exponent of 0 and a coefficient of 2. Therefore, the simplified expression that matches the set of tiles is x² - x + 2.
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(-20)/4=
What’s the answer ?
Answer:
-5
Step-by-step explanation:
A negative number divided by a positive number will be negative.
20/4 is 5.
(5x4=20)
Therefore (-20)/4 = (-5)
a total of 677 tickets were sold for the school play they were either adult tickets or student tickets there were 73 fewer students tickets than adult tickets how many adult tickets were sold
Answer:
375 adult tickets and 302 student tickets
Step-by-step explanation:
s+a=677
a=s+73
s+s+73=677
2s+73=677
2s=604
s=302
a= 375
Final answer:
Explanation on finding the number of adult tickets sold for a school play when the total number of tickets sold and the relationship between adult and student tickets are known.
Explanation:
The total number of tickets sold for the school play was 677.
Let x be the number of adult tickets sold.
It is given that there were 73 fewer student tickets than adult tickets, so the number of student tickets sold would be x - 73.
Therefore, x + (x - 73) = 677.
Solving this equation, we find that 2x - 73 = 677, 2x = 750, x = 375.
So, 375 adult tickets were sold.
(3j +11) +(8j-7) how do you find the sum
Answer:
11j + 4
Step-by-step explanation:
Disregard parentheses in this situation.
3j + 11 + 8j - 7
Add the j's
11j + 11 - 7
11j + 4
Which expressions are equivalent to 36 y - 18 x - 108 y + 54 so that you correct answers
For this case we must find an expression equivalent to:
[tex]36y-18x-108y + 54[/tex]
We add similar terms:
[tex]36y-108y-18x + 54 =[/tex]
Different signs are subtracted and the sign of the major is placed:
[tex]-72y-18x + 54[/tex]
Thus, an equivalent expression is:
[tex]-72y-18x + 54\\-18x-72y + 54[/tex]
Answer:
[tex]-18x-72y + 54[/tex]
Final answer:
To find equivalent expressions, we combine like terms in the given expression 36y - 18x - 108y + 54.
Explanation:
To find expressions equivalent to 36y - 18x - 108y + 54, we can combine like terms.
First, combine the y terms: 36y - 108y = -72y.
Next, combine the x terms: -18x.
Combining the constants, we have: 54.
Putting it all together, the equivalent expression is: -18x - 72y + 54.