Answer:
y = -2x - 14Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m\ -\ \text{slope}\\b\ -\ \text{y-intercept}[/tex]
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\k\ ||\ l\iff m_1=m_2[/tex]
[tex]\text{We have the equation of a line in the standard form.}\\\text{Convert it to the slope intercept from:}\\\\3x-6y=-2\qquad\text{subtract }\ 3x\ \text{from both sides}\\\\-6y=-3x-2\qquad\text{divide both sides by (-6)}\\\\y=\dfrac{-3}{-6}x+\dfrac{-2}{-6}\\\\y=\dfrac{1}{2}x+\dfrac{1}{3}\to m_1=\dfrac{1}{2}[/tex]
[tex]\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{2}}=-1\cdot\dfrac{2}{1}=-2.\\\\\text{Put the value of a slope and the coordinates of the point (-3, -8)}\\\text{ to the equation of a line:}\\\\-8=-2(-3)+b\\\\-8=6+b\qquad\text{subtract 6 from both sides}\\\\-14=b\to b=-14\\\\\text{Finally:}\\\\y=-2x-14[/tex]
The table shown below gives the approximate number of pieces of mail handled by the United States Postal Service for different years.
How many more pieces of mail were handled by the United States Postal Service in 1995 than in 1965?
Express your answer in scientific notation.
Answer:
Step-by-step explanation:
Answer:
1.08×10^11
Step-by-step explanation:
1.08 times 10 to the power of 11
Answer:
1.08×10^11
Step-by-step explanation:
25/18 divided by 5/3
Answer:
0.09259259
Step-by-step explanation:
The value of expression 25/18 divided by 5/3 would be; 0.09259259
Since Division can be interpreted as equally dividing the number that is being divided into total x parts, x is the number of parts the given number is divided.
We need to find the expression of 25/18 divided by 5/3.
A negative divided by a negative is positive, then;
25/18 ÷ 5/3
25/18 x 3/5
75/ 90
Therefore, The value of expression 25/18 divided by 5/3 would be; 0.09259259
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Order -2.96,-2 11/12,and 2.95 from least to greatest
Answer:
-2.96 , -2 11/12, 2.95
Step-by-step explanation:
A book sold 39,200 copies in its first month of release. Suppose this represents 8.7% of the number of copies sold to date. How many copies have been sold to date?
Round your answer to the nearest whole number.
Answer: 450574.7126 which rounds up to 450575
Step-by-step explanation: Do cross multiplication
100 X
----- x ---------
8.7 39200
100 x 39200 = 3920000/ 8.7 = 450574.7
TO CHECK ANSWER
450574.7216 x 8.7% ( convert to decimal .087) = 39200
A surveyed was conducted at Holy Spirit High school where 50 students were randomly
chosen and asked whether they liked apples or bananas. Of the 50, 36 students said they
like apples, 30 students like bananas and 5 students do not like either apples or bananas.
How many students like both apples and bananas?
Answer:
26
Step-by-step explanation:
50 students were asked, and only 5 said that they did not like apples or bananas.This means that 45 students like either apples or bananas, or both of them. We will call these 45 students, the group of "45".We also know that, between these 45 students there are 36 who like apples and 30 that like bananas. This imply that, 45-36=9 students do not like apples, and 45-30=15 students do not like bananas.Then, there are 15 students within the group of "45" that do not like bananas, and 9 students within the group of "45" that do not like apples. This means that 9+15=24 students within the group of "45" only like bananas or apples. The rest of them, 45-24= 26 like both apples and bananas.Use Pascal’s Triangle to determine the third term of the expansion of (x + 3)4.
Answer:
In the Pascal Expansion of [tex](x+3)^4[/tex] the third term is [tex]54x^2[/tex].
Step-by-step explanation:
Here, the given expression is given as [tex](x+3)^4[/tex]
Now, by the PASCAL'S TRIANGLE EXPANSION:
[tex](a + b)^4 = 1(a)^4 + 4(a)^3b + 6(a)^2b^2 + 4(a)b^3 + 1b^4\\= 1 + 4b + 6a^2 + 4b^3 + b^4.[/tex]
Substituting a = x and b = 3, we get:
[tex](x + 3)^4 = 1(x)^4 + 4(x)^3(3) + 6(x)^2(3)^2 + 4(x)(3)^3 + 1(3)^4\\= x^4 + 12x^3 + 54x^2 + 108x+ 81[/tex]
In the given expansion, the third term is [tex]54x^2[/tex].
Hence, in the Pascal Expansion of [tex](x+3)^4[/tex] the third term is [tex]54x^2[/tex].
Final answer:
The third term is 6 times x squared times 3 squared, which simplifies to 54x².
Explanation:
To use Pascal's Triangle to determine the third term of the expansion of (x + 3)⁴, we first need to look at the row of Pascal's Triangle that corresponds to the exponent 4. This is the fifth row if we start counting from 0 and it reads 1, 4, 6, 4, 1. We use these coefficients for each term of the expansion, which follows the pattern (a + b)ⁿ = C(n,0)*aⁿ + C(n,1)*a⁽ⁿ⁻¹⁾b + C(n,2)*a⁽ⁿ⁻²⁾b² + ... + C(n,n)*bⁿ, where C(n,k) is the binomial coefficient from Pascal's Triangle.
So, the third term in the expansion is given by the third coefficient (counting from 0) from the row, which is 6, multiplied by x raised to power 4 - 2 times 3 squared. Therefore, the third term is 6x²·3², which simplifies to 54x².
The measure of arc LM is °. The measure of angle MBL is °. The measure of angle MNL is °.
Answer:
Measure of arc LM is 116
Measure of angle MBL is 58
Measure of angle MNL is 64
Step-by-step explanation:
took the test
Answer:
The answers are: 116, 58, 64
Step-by-step explanation:
Find the value of x in each case. Give reasons to justify your solutions!
BRAINLY SHALL BE GIVEN
L, M ∈
KN
1. m ∠KLP+m∠PLM = __180___
2. _3x____+m∠PLM = _180_____ Substitution
3. m∠PLM = _______ Algebra
4. m∠PMN=m∠P+m∠______ _______________
5. ____2x+72__ = _____x_+180°−3x Substitution
6. x= ___27___ Algebra
Answer:
x=27°
Step-by-step explanation:
we know that
The Triangle Exterior Angle Theorem, states that: An exterior angle of a triangle is equal to the sum of the opposite interior angles
step 1
Find the measure of angle PLM
we know that
m∠PLM+m∠LPM=m∠PMN ----> by Triangle Exterior Angle Theorem
we have
m∠LPM=x°
m∠PMN=2x+72°
substitute
m∠PLM+x=2x+72°
m∠PLM=2x-x+72°
m∠PLM=x+72°
step 2
Find the measure of angle x
we know that
3x+m∠PLM=180° ----> by supplementary angles (form a linear pair)
we have
m∠PLM=x+72° (see step 1)
substitute
3x+x+72°=180°
4x=180°-72°
4x=108°
x=27°
Answer:
By the given diagram,
PLM is a triangle,
K and N are points on line MN,
m∠KLP = 3x, m∠P = x, m∠PMN = 2x + 72°
We need to give the reasons in the steps of finding the value of x.
For this we have to know the following properties :
Linear pairs: Adjacent angles which are supplementary.
Subtraction property of equality : We can subtract a number or expression in both sides of an equation.
i.e. a = b ⇒ a + c = b + c
Exterior angle theorem : exterior angle formed by extending the side of a triangle is equal to the sum of its non-adjacent angles.
Thus, the steps of finding value of x are as follow,
1. m∠KLP+m∠PLM = 180° ( linear pairs )
2. 3x +m∠PLM = 180° ( Substitution)
3. m∠PLM = 180° - 3x ( Subtraction property of equality)
4. m∠PMN=m∠P+m∠PLM ( Exterior angle theorem )
5. 2x + 72° = x + 180° - 3x ( Substitution)
6. 2x + 72° = 180° - 2x ( Solving )
2x = 180° - 2x - 72°
2x + 2x = 108°
4x = 108°
x = 27°
Scale on the blue print drawingOf a house show 6 cm represents 3 m what number of centimeters on the blueprint represents actual distance of 27 m
Answer:
54 cm on the blueprint represents actual distance of 27 m.
Step-by-step explanation:
Scale on the blue print drawing of a house show 6 cm represents 3 m.
So, the proportion is [tex]\frac{6}{300} = \frac{1}{50}[/tex] {Since, 3 m = 300 cm.}
Hence, the original dimensions of the house is reduced in the ratio [tex]\frac{1}{50}[/tex] in the blue print drawing.
Then, 27 m i.e. 2700 cm will be represented in the drawing by [tex]2700 \times \frac{1}{50} = 54[/tex] cm.
Therefore, 54 cm on the blueprint represents actual distance of 27 m. (Answer)
Which function represents the graph of y=10(4)x ? PLEASE HELP! :)
f
g
h
j
Answer:
The answer is g.
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
Slope: 40
y-intercept: 0
x : 0, 0
y : 0, 0
Hope this helps!
Answer:
Answer:
The answer is g.
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
Slope: 40
y-intercept: 0
x : 0, 0
y : 0, 0
Hope this helps
Step-by-step explanation:
This was tuff but i managed to get the answer ur welcome
What is 10/12 written as a fraction in its simplest form
Answer:
Step-by-step explanation:
10/12 divide by 2= 5/6
please help solve with steps:
x + 3/4 = - 1/8
Answer:
x = - [tex]\frac{7}{8}[/tex]
Step-by-step explanation:
Given
x + [tex]\frac{3}{4}[/tex] = - [tex]\frac{1}{8}[/tex]
Multiply through by 8 to clear the fractions
8x + 6 = - 1 ( subtract 6 from both sides )
8x = - 7 ( divide both sides by 8 )
x = - [tex]\frac{7}{8}[/tex]
Answer:
x = -7/8
Step-by-step explanation:
x + 3/4 = - 1/8
Subtract both sides:
x + 3/4 - 3/4 = -1/8 - 3/4
x = -1/8 - 3/4
x = -7/8
Can I get some help on this please? This is part 1 I will post part 2 later.
Thanks! Will mark Brainliest!
Answer:
-2/3 (fixed it)
Step-by-step explanation:
Mt. Everest is 29,029 feet above sea level. The Dead Sea is 1,411 feet below sea level. What is the difference between the elevations?
A) −27,618 feet
B) −30,440 feet
C) 27,618 feet
D) 30,440 feet
Answer:
The correct answer is A)-27,618 feet because -29,029 Subtract by -1,411 is -27,618 far from each other
The answer is D the other guy is wrong, trust me I just got that question wrong lol
What is y+4=9 what is y?
Answer:
[tex]y = 5[/tex]
Step-by-step explanation:
Subtract the 4 from 9
please help: i need to translate a phrase into a two step expression.
Five more than the product of 10 and Maliks height. Use m to represent Maliks height.
Answer: y = 10m + 5
Step-by-step explanation:
Let m be Malik's height , the product of 10 and Malik's height means 10 multiplied by Malik's height, which is 10 x m , which will be
10m.
5 more than the product of 10 and Malik's height means that a particular function is more than the product of 10 and his height by 5. Let that function be y , then
y = 10m + 5 is the expression
TO TRANSMIT INFORMATION ON THE INTERNET, LARGE FILES ARE BROKEN INTO PACKETS OF SMALLER SIZES. EACH PACKET HAS 1,500 BYTES OF INFORMATION. AN EQUATION RELATING PACKETS TO BYES OF INFORMATION IS GIVEN BY B=1,500P REPRESENTS THE NUMBER OF PACKETS AND B REPRESENT THE NUMBER OF BYTES OF INFORMATION.
A. HOW MANY PACKETS WOULD BE NEEDED TO TRANSMIT 30,000BYTES OF INFORMATION
B. HOW MUCH INFORMATION COULD BE TRANSMITTED IN 30,000 PACKETS
Answer:
A. It would be needed 20 packets to transmit 30,000 bytes of information.
B. 45'000,000 (45 million) of bytes could be transmitted in 30,000 packets.
Step-by-step explanation:
1. Let's review the data given to us for solving the question:
Size of each packet of information = 1,500 bytes
Number of packets = P
Number of bytes of information = B
2. Let's answer the questions:
A. How many packets would be needed to transmit 30,000 bytes of information?
P = 30,000 ÷ 1,500
P = 20
It would be needed 20 packets to transmit 30,000 bytes of information
B. How much information could be transmitted in 30,000 packets?
B = 30,000 * 1,500
B = 45'000,000
45'000,000 (45 million) of bytes could be transmitted in 30,000 packets.
On a coordinate plane, parallelogram A B C D has points (3, 6), (6, 5), (5, 1), and (2, 2).
What is the area of parallelogram ABCD?
13 square units
14 square units
15 squa
Answer:
13
Step-by-step explanation:
7. Use mental math
28% of 100
Answer:
28/100 x 100= 28
Answer:
28% divided by 100 = 28
Brainly please?
Help!!! Solve for x!! Pls!!!
Answer:
57
Step-by-step explanation:
The bottom line of the triangle is 180 degrees. Therefore, 2y + 4y - 36 has to equal 180. So, once you solve this linear equation, you will find that y equals 36. A triangle's angles always equal a total of 180 degrees. So, x + 51 + 2y has to equal 180, as well. Since we know y, substitute in 36 for 2y. Now the equation is 51 + 72 + x = 180. Solve for x. X is 57.
Answer:
57°
Step-by-step explanation:
The angles that are at the bottom middle are on a straight line, so they must add up to 180°. In order to determine y, use the equation 180 = 2y + 4y -36. After solving for y, you should be left with 36 = y. Now, we can fill in the bottom right angle in the left triangle. This would be 36 times 2, or 72. In triangles, all angles always add up to 180°, so, we can use the equation 180 = x + 51 + 72. Once solved for x, this will leave you with 57 = x, our final answer.
63. What is the equation in point-slope form
of the line through the points (10,3) and
(12, 11)? (MAFS.912.F-BF.1.1)
Answer:
y-3=4(x-10)
Step-by-step explanation:
Point Slope Form: y-y1=m(x-x1)
Where m=slope and (x1, y1) is a point on the line.
m=(y2-y1)/(x2-x1)=(11-3)/(12-10)=8/2=4
So the slope is 4,
y-3=4(x-10)
How do you round to 630 to the nearest hundred
Answer: Here we will tell you what 630 is rounded to the nearest hundred and also show you what rules we used to get to the answer.
Remember, we did not necessarily round up or down, but to the hundred that is nearest to 630.
First, 630 rounded to the nearest hundred is: 600
When rounding to the nearest hundred, like we did with 630 above, we use the following rules:
A) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.
B) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.
C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.
Step-by-step explanation:
Rounding 630 to the nearest hundred results in 600.
To round the number 630 to the nearest hundred, consider the tens digit of the number.
In this case, the tens digit is 3.
If the tens digit is 5 or greater, you round up to the next hundred.
If the tens digit is 4 or less, you round down to the current hundred.
Since the tens digit in 630 is 3, which is less than 5, you round down.
Therefore, rounding 630 to the nearest hundred results in 600.
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5) Jon gets paid $4 for every 3 hours he works. How much will he get paid if he works
30 hours?
Answer:
$40
Step-by-step explanation:
3 hours x 10= 30 hours
$4 x 10= $40
15 people gather for a hot dog eating contest. in the past, eight of these contestants have eaten 37 hot dog during the competition. three at 43, three ate 47 and one ate 49. what is the expected number of hot dogs eaten by a randomly chosen contestant today?
Answer:
41
Step-by-step explanation:
Given that 15 people gather for a hot dog eating contest. in the past, eight of these contestants have eaten 37 hot dog during the competition. three at 43, three ate 47 and one ate 49.
From the information given we prepare table as follows
No of hot dogs eaten X Frequency f X*f
37 8 296
43 3 129
47 3 141
49 1 49
Total 15 615
Expected value of X
= Mean value one person can take = [tex]\frac{615}{15} \\=41[/tex]
the expected number of hot dogs eaten by a randomly chosen contestant today is 41
The arithmetic sequence 1, 3, 5, 7, 9, . . . represents the set of odd natural numbers. What is the explicit rule for the sequence? ak = ____ +____ (k - 1)
Answer:
The explicit rule is Ak = 1 + 2 * (k - 1)
Step-by-step explanation:
1. Let's review the information provided to us for finding the explicit rule for the sequence.
The arithmetic sequence 1, 3, 5, 7, 9, . . . represents the set of odd natural numbers.
2. Let's find the solution:
Ak = 1 + 2 * (k - 1)
For k = 1 ⇒ Ak = 1 + 2 * (1 - 1) = 1 + 2 * 0 = 1 + 0 = 1
For k = 2 ⇒ Ak = 1 + 2 * (2 - 1) = 1 + 2 * 1 = 1 + 2 = 3
For k = 3 ⇒ Ak = 1 + 2 * (3 - 1) = 1 + 2 * 2 = 1 + 4 = 5
For k = 4 ⇒ Ak = 1 + 2 * (4 - 1) = 1 + 2 * 3 = 1 + 6 = 7
For k = 5 ⇒ Ak = 1 + 2 * (5 - 1) = 1 + 2 * 4 = 1 + 8 = 9
For k = 6 ⇒ Ak = 1 + 2 * (6 - 1) = 1 + 2 * 5 = 1 + 10 = 11
For k = 7 ⇒ Ak = 1 + 2 * (7 - 1) = 1 + 2 * 6 = 1 + 12 = 13
Answer:
1st: 1+(k-1)2
2nd: 399
3rd: C
4th: 40,000
explanation:
just did it :)
Cousin Hector drove 1,851 miles to the reunion. He lives in Mexico and drove 747 miles through that country to the United States border. How many miles did he drive in the United States?
Answer:
1104 miles
Step-by-step explanation:
Say he lives in a place in Mexico which is at a distance of a miles from the Mexico-America border point and the reunion is at b miles from the same border point, in America.
So the total distance travelled is ( a + b ) miles
( this is just sum of distance travelled in Mexico + that in America )
Given , a=747 and a+b=1851
that implies:
747 + b = 1851
So, b = 1104 miles.
Therefore he has travelled 1104 miles in America,
Find the slope of the line that goes through the given points.
(7,2) and (5,2)
Answer: 0
Step-by-step explanation:
describes a horizontal line
so slope = 0
Answer:
0/2
Step-by-step explanation:
you have to subtract the x's and then then the y's, y is always on top. So, y=2-2/ x= 7-5 making 0/2 When the 0 is on the "top" of the fraction, that would mean that the two y-values are the same.
a 36 ft tree cast a shadow of 17ft. how long will the shadow be for a 22 ft tree?
Check the picture below.
What is the diameter of the circle?
12 inches
А)
6 inches
B
24 inches
C
26 inches
48 inches
Answer:
The diameter of the circle is B) 24 inches.
Step-by-step explanation:
The value given (12 inches) is the radius of the circle. The diameter of a circle is equal to 2 * radius. 2 * 12 = 24.
The diameter of the circle is 24 inches.
Option B is the correct answer.
We have,
The diameter of a circle is a line segment that passes through the center of the circle and connects two points on its circumference.
It is the longest chord of the circle and divides the circle into two equal halves.
The diameter is commonly denoted by the symbol "d" and is related to the radius of the circle (denoted by "r") by the equation:
d = 2r
Now,
r = 12 inches
So,
d = 2r = 2 x 12 inches
d = 24 inches
d = 24 inches
Thus,
The diameter of the circle is 24 inches.
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A survey of all beings on planet Tott found that 12 beings preferred
hab juice to all other juices. If 40 beings were surveyed altogether,
what percent of them preferred hab juice?
Answer:
4.8
12 x 40
100
= 4.8
Step-by-step explanation:
The percentage of beings that preferred hab juice, is 30% of beings preferring hab juice.
The question is asking to find the percentage of beings that preferred hab juice out of a total of 40 surveyed on planet Tott. To do this, we use the basic formula for percentage:
Percentage = (Part / Whole) * 100
In this case, 12 beings out of 40 preferred hab juice. So we have:
Percentage = (12 / 40) * 100 = 0.3 * 100 = 30%
Therefore, 30% of the beings surveyed preferred hab juice.