Answer:
6x - 7y = -11
Step-by-step explanation:
To write the equation of a line when given two points, calculate the slope and substitute it into the point slope form of a line. From this form of the equation, you can simplify and convert to the standard form.
First, find the slope using the formula.
[tex]m = \frac{y_2-y_1}{x_2-x_1} =\frac{2--1}{\frac{1}{2} --3} =\frac{3}{\frac{7}{2}} = \frac{6}{7}/tex]
Substitute m = 6/7 and the point (-3,-1) into the point slope form [tex](y-y_1) = m(x-x_1)[/tex].
[tex]y--1=\frac{6}{7}(x--3)\\y + 1 = \frac{6}{7}(x+3)\\7y + 7 = 6(x + 3)\\7y + 7 = 6x + 18\\-6x + 7y + 7 = 18\\-6x + 7y = 11\\6x - 7y = -11[/tex]
To convert to standard form, multiply the equation by 7. This means each term is multiplied by 7 to clear the denominator. Then multiply using the distributive property. You will now need to move terms across the equal sign. Begin by subtracting 6x from both sides. Then subtract 7 from both side. Lastly, multiply the equation by -1 since the leading coefficient in standard form cannot be negative.
Out of 6700 students of a school only 90% passed. Find how many students passed?
Answer:
6030 students passed.
Step-by-step explanation:
First: We must convert all percentages to decimals:
So, why do we need to convert all percentages to decimals. Well, you don't have to. It's just that it's easier to work with decimals than percentages. So I'll bold out all of the percents in this problem:
Out of 6700 students of a school only 90% passed. Find how many students passed?
So how do we convert that to a decimal. Well...
A: We have to take out the percent sign:
90
B: We have to move the decimal point 2 spaces to the left:
0.90
Now that we have our percent displayed as a decimal, we need to multiply it by the total number of students to find the fraction of people that passed.
So 0.90 [or 0.9] multiplied by 6700
[tex]0.9*6700 = 6030[/tex]
So, out of the 6700 students, 6030 passed.
Topic: Percentages
I need help with 9 please
Answer:
12
Step-by-step explanation:
Treat the less than or equal too sign as you would a normal equal sign.
Add 27 to -15 so that x is less than or equal to 12
solve the equation -7+2q=4
Regroup terms
2q - 7 = 4
Add 7 to both sides
2q = 4 + 7
Simplify 4 + 7 to 11
2q = 11
Divide both sides by 2
q = 11/2
One angle is 36 degrees. What is the measure of its complement?
Answer:
54
Step-by-step explanation:
90-36=54 degrees. The complement of an angle is 90- the angle
Round each number to the nearest... 100; 387,530
To round 387,530 to the nearest hundred, we leave the hundreds digit unchanged because the tens digit is 3, which is less than 5. The rounded number is therefore 387,500.
To round the number 387,530 to the nearest hundred, we look at the tens digit, which is 3.
The rounding rule states that if the digit to the right of the rounding place is less than 5, you do not change the rounding digit. If it is 5 or more, you round up. Since the tens digit is 3, it is less than 5, hence we do not round up.
The hundreds digit is 5, and because we do not round up, 387,530 rounded to the nearest hundred is 387,500.
Remember, rounding off to a certain place involves looking at the digit immediately to the right of the place you are rounding to.
Deciding whether to round up or keep the original number the same is based on whether this digit is less than or equal to 4, or 5 and above respectively.
The product of 17 and 1.27
Answer:
1.27 x 17 = 21.59 Product means multiply
Step-by-step explanation:
Answer:
21.59
Step-by-step explanation:
17 x 1.27 = 21.59
21.59/17=1.27
What number is the same as 10^-5
Answer:
0.00001
Step-by-step explanation:
1
______
100000
hope this helps
help me please asap!
Answer:
[tex](x^2-9)(x^2+9)\\(x-3)(x+3)(x^2+9)[/tex]
Step-by-step explanation:
To factor the expression, factor as a difference of squares. Find the square root of each term and write it in this form (x+a)(x-a).
[tex]x^4 - 81\\(x^2 - 9)(x^2 + 9)[/tex]
Factor x² - 9 as a difference of squares.
[tex](x^2-9)(x^2+9)\\(x-3)(x+3)(x^2+9)[/tex]
This is the most factored form because a sum of squares cannot be factored.
Does anyone know how to tell whether a number in bold is a solution? 35 points
Plz help!!!!!!!!!!!!!
Answer:
the third one
Step-by-step explanation:
-b to start is -(-6) which is 6
needs the plus and minus
the first expression is the whole numerator
Answer: [tex]\bold{c)\quad x=\dfrac{6\pm \sqrt{(-6)^2-4(3)(8)}}{2(3)}}[/tex]
Step-by-step explanation:
[tex]3x^2-6x+8=0\quad \rightarrow \quad a=3,\ b=-6,\ c=8\\\\\text{Quadratic formula is: }x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-6)\pm \sqrt{(-6)^2-4(3)(8)}}{2(3)}}\\\\\\x=\dfrac{6\pm \sqrt{(-6)^2-4(3)(8)}}{2(3)}[/tex]
what is the value of x
Answer:
The answer to your question is that x is equal to 50.
Simplify the expression -2.5f+0.8f-13-5
To simplify we can collect like terms so we get -1.7f-18 :)
help subtract (xsquared +43x10)-(10xsquared-5x+10 express the answer in standard form
Answer:
[tex]\large\boxed{(x^2+43x+10)-(10x^2-5x+10)=-9x^2+48x}[/tex]
Step-by-step explanation:
[tex](x^2+43x+10)-(10x^2-5x+10)\\\\=x^2+43x+10-10x^2-(-5x)-10\\\\=x^2+43x+10-10x^2+5x-10\qquad\text{combine like terms}\\\\=(x^2-10x^2)+(43x+5x)+(10-10)\\\\=-9x^2+48x[/tex]
evaluate i^31 please help
ANSWER
[tex] {i}^{31} = - i[/tex]
EXPLANATION
We want to evaluate
[tex] {i}^{31} [/tex]
Use indices to rewrite the expression as:
[tex] = {i}^{30} \times i[/tex]
We know that
[tex] {i}^{2} = - 1[/tex]
So we rewrite the expression to obtain;
[tex] = ({ {i}^{2}) }^{15} \times i[/tex]
This gives us;
[tex]= {( - 1) }^{15} \times i[/tex]
This simplifies to
[tex] = - 1 \times i[/tex]
[tex] = - i[/tex]
Add. Simplify the answer and write the answer as a mixed number if appropriate 1/9 + 5/6
Final answer:
To add fractions 1/9 and 5/6, find the least common denominator, which is 18, and then add the numerators of the equivalent fractions with the same denominator. The sum is 17/18, a simplified fraction.
Explanation:
To add fractions with different denominators, you must first find a common denominator. For the fractions 1/9 and 5/6, the least common denominator is 18. Multiply each fraction by a form of 1 that will give them this new denominator without changing their value.
For 1/9, you multiply it by 2/2 to get 2/18. For 5/6, you multiply it by 3/3 to get 15/18. Now that the fractions have the same denominator, you can add the numerators together: 2/18 + 15/18 equals 17/18. Since 17/18 is less than 1, it is already simplified and there is no mixed number to write.
if f={(2,3),(5,7),(3,3),(5,4),(9,1)} what is the range
[tex]\bf \stackrel{\textit{range is always the set of y-coordinates}}{f=\{(2,\stackrel{\downarrow }{3}),(5,\stackrel{\downarrow }{7}),(3,\stackrel{\downarrow }{3}),(5,\stackrel{\downarrow }{4}),(9,\stackrel{\downarrow }{1})\}}\qquad \qquad \{3,7,3,4,1\}\implies \{3,7,4,1\}[/tex]
Answer:
{3, 7, 3, 4, 1}
Step-by-step explanation:
The set of ordered pairs in the mapping below can be described as which of the following?
x----y
0 - 8
3 - 2
6 - -1
(1) a relation only
(2) a function only
(3) both a relation and a function
(4) neither a relation nor a function
Answer:
"(3)"
Step-by-step explanation:
Relation is a mapping between x-values and y-values. Xs are the domain and Ys are the range.
Given x values (0,3,6) and y-values(8, 2, -1), this is a relationship, so it is a relation.
To check whether a relation is a function or not, we simply see if each unique x value is paired with a unique y value.
Is there any y value that is same for x-values? NO! All are different. So this is a function as well!
Answer choice (3) is right.
Answer: (3) both a relation and a function
Step-by-step explanation:
Relation : It is the relation established between two set of values
Function : It is a kind of relation, where only output exist for e ach input.
Generally x values presents input values and y values represents the output values.
The given table :
x - y
0 - 8
3 - 2
6 - 1
Here, each x value is related to a y-value , so its a relation.
Also, there only one unique y-value for each x-values, thus its a function.
Hence, the set of ordered pairs in the mapping below can be described as both a relation and a function.
12 = g - 56
(Solve for g)
Answer:
G=68
Step-by-step explanation:
First get G by it's self
By adding 56 on both sides
12 plus 56 equals 68
G=68
I Hope this helps you
A parking lot in a shape of a trapezoid has an area of 12,052.1 square meters.the lean the of one base is 82.4 meters and the length of the other base is 108.6 meters.what is the height of the parking lot?
Answer:
126.2 meters
Step-by-step explanation:
A trapezoid's area is found using the formula A = 1/2 (a+b)h where a and b are the two bases. Substitute A = 12,052.1, a = 82.4 and b=108.6. Then solve for h.
A = 0.5(a+b)h
12,052.1 = 0.5(82.4 + 108.6)*h
12,052.1 = 0.5(191)h
12,052.1 = 95.5h
126.2 = h
7 square root of 75 simplify
7√75 = 7√25√3 = 35√3.
The simplification of the expression 7 * square root of 75 is 35 * square root of 3. This is achieved by factoring 75 into prime factors and finding pairs of those factors to take out from under the square root.
Explanation:To simplify the expression 7 * square root of 75, we first need to break down 75 into a product of prime factors:
75 = 5*5*3.
Since the square root of a number is the factor that, when squared, equals the original number, we can take out a pair of 5s from the square root:
Square root of 75 = 5 * square root of 3.
Finally, multiply this by 7 to get:
7* square root of 75 = 7 * 5 * square root of 3 = 35 * square root of 3.
Learn more about Square Root here:https://brainly.com/question/1540542
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Jeremiah has a batting average of 0.312 this baseball season. Express his average as a fraction in lowest terms.
312/1,000
39/125
13/50
13/42
There is not much that can be done to figure out how to write 0.312 as a fraction, except to literally use what the decimal portion of your number, the .312, means. Since there are 3 digits in 312, the very last digit is the "1000th" decimal place. So we can just say that .312 is the same as 312/1000.
Jeremiah's batting average of 0.312 can be expressed as the fraction 312/1,000, which can be further reduced to its simplest form 39/125 by dividing by their greatest common divisor, which is 8.
Explanation:To express Jeremiah's batting average of 0.312 as a fraction in lowest terms, we need to start by expressing it as a fraction out of 1,000, which gives 312/1,000. From there, we divide both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor to reduce it to its simplest form. The greatest common divisor of 312 and 1,000 is 8. If we divide 312 by 8, we get 39, and if we divide 1,000 by 8, we get 125. Therefore, the fraction in its simplest terms is 39/125.
Expressing decimals as fractions is a common task in Mathematics and it's a handy skill for dealing with real-world data, like a baseball player's batting average.
Learn more about Converting Decimals to Fractions here:https://brainly.com/question/2362378
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The sum of 1 and 3 times a number is 22
A. X= 4
B. X= 6
C. X= 7
D. X= 9
What is the mode of the data set?
Fifth Grade Jump Distance
2|0
3|2 4 6
4|0 2 4 8
5|5
6|5
2|0 = 20 inches
The data set is
20
32, 34, 36
40, 42, 44, 48
55
65
We can see that each value only shows up one time. Therefore there is no mode. To have a mode, we need to have a value show up more than once, and it must be the most frequent value. For example, the set {1,2,3,3,4} has a mode of 3 since it shows up twice, the most of any value in that set. However we don't have that occur for the data set your teacher gave you.
Final Answer: There is no mode for this data setAnswer:
no mode i just got it right
Step-by-step explanation:
Plz help
simplify (2x+1) (3x+4)
[tex](2x + 1)(3x + 4) \\ = 2x(3x + 4) + 1(3x + 4) \\ = 6 {x}^{2} + 8x + 3x + 4 \\ = 6 {x }^{2} + 11x + 4[/tex]
The function g is defined by g(x)=ax−7, where a is a constant. Find a, if the graph of g passes through the point ( 1/3 ,−2).
Answer:
a = 15
Step-by-step explanation:
The graph of function g(x) is described by g(x)=ax−7, or y = ax−7.
y = g(x)=ax−7 passes through (1/3, -2). We can subst. -2 for y and 1/3 for x to determine the value of the coefficient a:
-2 = g(1/3) = a(1/3) - 7
Solve for a. First, add 7 to both sides: 5 = a(1/3).
Next, multiply both sides by 3: 15 = a, or a = 15.
A rectangle prism has a length of 3 1/2 inches a width of 5 inches and height of 1 1/2 inches what is the volume
Answer:
Step-by-step explanation: I hope that helps you.
Analyze the sequence 243, 162, 108, 72,…
Answer: You multiply 1.5 each time.
Step-by-step explanation:
72*1.5=108
108*1.5=162
162*1.5=243
And so on and so forth.... Hope it helped!
243 = 3x3x3x3x3
162 = 3x3x3x3x2
108 = 3x3x3x2x2
72 = 3x3x2x2x2
The next two numbers in the sequence would be
48 = 3x2x2x2x2
32 = 2x2x2x2x2
The jacket is on sale for $36 which Is 80% of the original cost. What is the original price of the Jacket?
Part,whole and percent
Answer:
$45
Step-by-step explanation:
To find the discount price, you make the discount a decimal and multiply, like so
.8x=36
then divide and your answer is 45
The student body at a high school was surveyed about sports participation. The table below shows the data by grade level.
The number of students who are in 9th grade and play two or more sports is a
'marginal frequency'
'Joint frequency'
The number of students who are in the 11th grade is a
'marginal frequency'
'joint frequency'
The percentage of the student body that plays one sport is a
'marginal relative frequency'
'joint relative frequency'
The percentage of the student body that are in 12th grade and do not play a sport is a
'marginal relative frequency'
'joint relative frequency'
Marginal frequency:
The number in the end column or row - "Total".
Joint frequency:
The ratio of the frequency in a particular category and the total number of data values.
Basically, the values that aren't in the final row or column - "Total".
The number of students who are in 9th grade and play two or more sports is a joint frequency.
This is only asking for the students in 9th grade who play two or more sports.
The number of students who are in the 11th grade is a marginal frequency.
This is asking for the total number of students in 11th grade.
The percentage of the student body that plays one sport is a marginal relative frequency'.
This is asking for the total number of students who play 1 sport.
The percentage of the student body that are in 12th grade and do not play a sport is a joint relative frequency.
This is only asking for the students in 12th grade and don't play sports.
Answer:
The answer is D on edge
The teacher passed out math books.The length is 10 inches and the width is 8 inches.What is the perimeter of each book?
Answer: The perimeter of each book is: " 36 in. " .
__________________________________________________
Step-by-step explanation:
__________________________________________________
Note that the given units are all in "inches (in.)" .
Use the formula for the "perimeter of a rectangle" ;
{which happens to work for a "square" as well;
since a "square" is a rectangle.}.
__________________________________________________
This is based on the assumption that the book is shaped like a
"rectangle" (or "square" —which is a rectangle).
__________________________________________________
The formula for the Perimeter of a rectangle is:
P = 2 L + 2 w ;
in which:
P = the perimeter of the rectangle;
for which we shall solve; [in "inches (in.)" ] ;
L = the length of the rectangle = 10 in. (given) ;
w = the width of the rectangle = 8 in. (given) .
___________________________________________________
Now, plug the given values for the "length (L)" and the "width (w)" ;
as follows:
___________________________________________________
P = (2 * 10 in.) + (2 * 8 in.) ;
P = (20 in.) + (16 in.) ;
P = 36 in.
___________________________________________________
Answer: The perimeter of each book is: " 36 in. " .
___________________________________________________
Hope this helps!
Best wishes in your academic pursuits
— and within the "Brainly" community!
___________________________________________________