Identify the slope and y-intercept of each of the following lines. Then graph each line.
y + 3 = 2 (x + 4)
Answers
Answer:
Below!
Step-by-step explanation:
1. Determining the y-intercept of the line:
The provided equation is in point slope form. To determine the slope and the y-intercept, we need to convert the equation to slope intercept form. Once it is converted to slope intercept form, the constant will be the y-intercept of the line. Start out by simplifying the distributive property on the R.H.S.
[tex]\implies y + 3 = 2 (x + 4)[/tex]
[tex]\implies y + 3 = (2x + 8)[/tex]
Now, open the parenthesis on the R.H.S
[tex]\implies y + 3 = 2x + 8[/tex]
If we take a look at the formula of slope intercept form (y = mx + b), we can see that "y" is isolated on the L.H.S. Thus, we need to subtract 3 both sides to isolate the y-variable.
[tex]\implies y + 3 - 3 = 2x + 8 - 3[/tex]
[tex]\implies y = 2x + 5[/tex]
We can see that the only constant in the equation is 5.
Therefore, 5 is the y-intercept.
2. Determining the slope of the line:
To determine the slope of the line, let's compare the formula with the equation obtained.
[tex]\implies (y = 2x + 5) \ = \ (y = mx + b)[/tex]
Thus, we obtain the following:
y = y2 = m (Slope)x = x 5 = b (Y-intercept)Thus, 2 is the slope of the line.
3. Plotting the line on the coordinate plane:
To graph the line on a coordinate plane, plot the y-intercept on the graph. The y-intercept is ALWAYS plotted on the y-axis.
Thus, the y-intercept plotted on graph is (0, 5).
Furthermore, plot a second point on the graph to draw a straight line through those points.
Determining the second point of the line:
If the slope of the line is 2, it means that the run (x) is 1 and the rise (y) is 2. Thus, we can add 1 to the x-coordinate of the y-intercept and 2 to the y-coordinate of the y-intercept.
⇒ (0, 5) ⇒ x = 0; y = 5 ⇒ Second point: x = 0 + 1; y = 5 + 2⇒ Second point: x = 1; y = 7⇒ Second point: (1, 7)Then, plot these points on the coordinate plane. Keep in mind that plot the x coordinate first, then the y-coordinate next. Once the coordinates are plotted, draw a line from the x-coordinate and another line from the y-coordinate. Finally, use your ruler and draw a line that passes through those two points. Your obtained graph is the graph of the line.
Comapre to slope intercept form y=mx+b
Slope=m=2Y intercept=b=5Related Questions
Which statement describes the expression 20+ ½ x (4 + 6) ?
A. Half of 4 added to six, Plus 20
B. The sum of 4 and 6 plus half of 20
C. Half the sum of 4 and 6 added to 20.
D. The sum of 4 and 6 plus 20 divided by 2
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Find the measure of <1
Please answer ASAP!!!!
Answers
The area of a parallelogram is given by the formula A=bh. The area of the parallelogram is 85 sq. Units. Find it’s base and height.
Answers
Answer:
the height is 5 and the base is 17.
Step-by-step explanation:
X + 1 is the height and 4x + 1 is the base, so we can substitute this into an equation:
( x + 1 ) (4x + 1) = 85
{apply the distributive law}
4x² + x + 4x + 1 =
4x² + 5x + 1 = 85
Take 85 to the other side by -85 each side:
4x² + 5x + 1 - 85 = 85 - 85
4x² + 5x - 84 = 0
{Now we have a quadratic equation}
The roots are either -5.25 or 4. X must be 4 since it must be positive as it is a side length.
Substitute x into the base and height to get the answers.
X + 1 = 4 + 1 = 5
4x + 1 = 16 + 1 = 17
Therefore the height is 5 and the base is 17.
Tell wether the angles are complementary or supplementary. Then find the value of X
Answers
Answer:
The angles are Complementary Angles.
x = 55°
Step-by-step explanation:
the angles are Complementary Angles, because when added, together they form a 90° angle.
•to find the value of x, we form the equation :
⇒90° = x° + (x - 20)°
⇒90 = x + x - 20
⇒90 = 2x - 20
•shifting the 2x to the left side and the 90 to the right side
⇒2x = 90 + 20
⇒2x = 110
•shifting the 2 to the right side
⇒x = 110/2
⇒x = 55° Answer...
hope that helps...
Drag each pair of rates to the correct location on the table.
Identify the pairs of rates as equivalent or not equivalent
hand
18/3 and 9/1
20/5 and 3/1
36/6 and 6/1
32/4 and 8/1
35/7 and 5/1
100/10 and 5/1
Answers
1/8 is in it 3/2 if that is it
Which statement about the function is true? the domain of the function is all real numbers less than or equal to −2. the domain of the function is all real numbers less than or equal to 9. the range of the function is all real numbers less than or equal to −2. the range of the function is all real numbers less than or equal to 9.
Answers
The statement which is true about the function is the range of the function is all real numbers less than or equal to 9.
What is domain and range of function?
The Domain of a function is the set of all the possible input values which are valid for that function.
Range of a function is the set of all the possible output values which are valid for that function.
The function shown in the graph can be given as,
[tex]f(x)=-x^2-4x+5[/tex]
The one coordinate point of this equation is -2, 9, which is shown in the graph. At the value of x as -2, the value of f(x) is 9,
[tex]f(-2)=-(-2)^2-4(-2)+5\\f(-2)=-4+8+5\\f(-2)=9[/tex]
Here, the input value is -2 and the output value is 9. The domain for this function is all real number, but the range of this function is (-∞,9).
Hence, the statement which is true about the function is the range of the function is all real numbers less than or equal to 9.
Learn more about the domain and range of the function here;
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Answer:
its literally D bro on edge
Step-by-step explanation:
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
only question 5 parts a and b PLEASE HELP!!
Answers
Answer:
slope = 3/2
the plant grows 3 centimeters every 2 weeks
Step-by-step explanation:
1. Find two numbers that...
a. multiply to -40 and add to -6.
b. multiply to -40 and add to 6.
c. multiply to -36 and add to 9.
d. multiply to -36 and add to -5.
If you get stuck, try listing all the factors of the first number.
Answers
Answer:
a. +34 b. +46 c. +45 d. +31
Step-by-step explanation: use a number line
What is the length of the missing leg? If necessary, round to the nearest tenth
Answers
Answer: 48
Step-by-step explanation:
For what value of x does 3 superscript 2 x baseline = 9 superscript 3 x minus 4?
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Equations are expressions separated by equal sign. The value of x that make the expression equal is 2
Equation and expressionsGiven the equation expressed as:
3^2x = 9^3x - 4
This can be further simplified as:
3^2x = 3^2(3x-4)
2x = 2(3x - 4)
x = 3x - 4
x - 3x = -4
-2x = -4
x = 2
Hence the value of x that make the expression equal is 2
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Answer: its 2
Step-by-step explanation: just took test on chrome 2022, and got 100%
divide. give the quotient and remainder 295/4
Answers
Answer:73 and remainder of 3
Step-by-step explanation:
295/4=73 and a remiander of 3
Answer:
The quotient is 73 and the remainder is 3
Step-by-step explanation:
295/4 = 73.75 you can take 73 for the quotient. Then do 295 - 73*4 = 3 to calculate the remainder.
Think it likes 12/4 = 3 => 12 - 3*4 = 0
Which of the following is a geometric series? 0.1 0.3 0.5 0.7 1 3 9 27 19 17 15 13 0.4 0.9 1.5 2.2
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Geometric series have the same ratio. The series which is a geometric series is 1, 3, 9, 27.
What is a geometric series?A series of numbers is a geometric series if the quotient of any two consecutive numbers is the same.
A series of numbers is a geometric series if the quotient of any two consecutive numbers is the same.
A.) 0.1 0.3 0.5 0.7
To check if the series is geometric series, find the quotient.
[tex]r_1=\dfrac{0.3}{0.1} = 3\\\\r_2 = \dfrac{0.5}{0.3} = 1.66[/tex]
Since the ratio is different this is not a geometric series.
B.) 1 3 9 27
To check if the series is geometric series, find the quotient.
[tex]r_1=\dfrac{3}{1} = 3\\\\r_2 = \dfrac{9}{3} = 3[/tex]
Since the ratio is the same this is a geometric series.
C.) 19 17 15 13
To check if the series is geometric series, find the quotient.
[tex]r_1=\dfrac{17}{19} = 0.8947\\\\r_2 = \dfrac{15}{17} = 0.8823[/tex]
Since the ratio is different this is not a geometric series.
D.) 0.4 0.9 1.5 2.2
To check if the series is geometric series, find the quotient.
[tex]r_1=\dfrac{0.4}{0.9} = 0.4444\\\\r_2 = \dfrac{0.9}{1.5} = 0.6[/tex]
Since the ratio is different this is not a geometric series.
Learn more about Geometric Series:
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Answer:
its b 1 + 3 + 9 + 27
Step-by-step explanation:
Abby used the law of cosines for trianglekmn to solve for k. k2 = 312 532 – 2(31)(53)cos(37°) triangle k n m is shown. the length of k n is 53, the length of n m is k, and the length of k m is n. law of cosines: a2 = b2 c2 – 2bccos(a) what additional information did abby know that is not shown in the diagram? manglek = 37° and n = 31 manglek = 37° and k = 31 manglen = 37° and n = 31 manglen = 37° and k = 31
Answers
Answer:
(A) mK = 37° and n = 31.
Step-by-step explanation:
The following are A of ed.
help! (answers needed fast and will give brainliest)
Answers
Answer:
13/20
Step-by-step explanation:
Note that:
Difference is the same meaning as subtract.
Given:
1 ¼ - ⅗
We first have to change 1 ¼ into a improper fraction:
1 ¼ = 5/4
5/4 - ⅗
Since the denominator are different we have to find common denominator.
25/20 - 12/20
Subtracting: 25 - 12 = 13
13/20
Hence, the different of these fractions is 13/20
Kavinsky
△ACE, B is the midpoint of AC and D is the midpoint of EC.
Answers
Answer:
See below
Step-by-step explanation:
[tex]1.\:\:\overline{BD}||\overline{AE}[/tex]
(By Midsegment theorem)
[tex]2.\:\:m\angle 1=48\degree\implies m\angle 4=48\degree [/tex]
([tex]\angle 1\: \&\:\angle 4[/tex] are alternate angles)
[tex]3.\:\:m\angle 3=25\degree\implies m\angle 2=25\degree [/tex]
([tex]\angle 2\: \&\:\angle 3[/tex] are vertical angles)
[tex]4.\:\:\overline {AE}=17\: cm\implies BD = 8.5\: cm [/tex]
(By midsegment theorem: [tex]BD=\frac{1}{2}AE[/tex]
[tex]5.\:\: BD=\frac{1}{2}AE\\\\\implies (3x+10)=\frac{1}{2}\times (12x+2)\\\\\implies 2(3x +10) = 12x+2\\\\\implies 6x +20= 12x+2\\\\\implies 6x - 12x = 2-20\\\\\implies -6x =-18\\\\\implies x =\frac{-18}{-6}\\\\\implies x = 3\\\\\implies \overline{BD}= (3\times 3 + 10)\\\\=(9+10)\\\\\implies \overline{BD}= (9 + 10)\\\\\implies \huge{\purple{\overline{BD}=19}}[/tex]
Find the missing length of the triangle.
a= in.
Answers
Answer:
9 in.
Step-by-step explanation:
a^2 + 5.6^2 = 10.6^2
a^2 + 31.36 = 112.36
Subtract 31.36 from both sides
a^2 = 81
Squart Root both sides
a = 9 inches
Answer:
a = 11.9883 in
Step-by-step explanation:
Sides:
a = 5.6 in
b = 11.9883 in
c = 10.6 in
Angles:
A = 27.8476 °
B = 90 °
C = 62.1524 °
Other:
P = 28.1883 in
s = 14.0942 in
K = 29.68 in2
r = 2.10584 in
R = 5.99416 in
SAS is Side, Angle, Side
Given the size of 2 sides (c and a) and the size of the angle B that is in between those 2 sides, you can calculate the sizes of the remaining 1 side and 2 angles. Use The Law of Cosines to solve the remaining side.
Law of Cosines
If a, b and c are the lengths of the legs of a triangle opposite to the angles A, B and C respectively; then the law of cosines states:
a^2 = c^2 + b^2 - 2bc cos A, solving for cos A, cos A = ( b^2 + c^2 - a^2 ) / 2bc
b^2 = a^2 + c^2 - 2ca cos B, solving for cos B, cos B = ( c^2 + a^2 - b^2 ) / 2ca
c^2 = b^2 + a^2 - 2ab cos C, solving for cos C, cos C = ( a^2 + b^2 - c^2 ) / 2ab
Solving, for example, for an angle, A = cos^-1 [ ( b^2 + c^2 - a^2 ) / 2bc ]
help pls!!!! ASAPPPPPP
Answers
Answer:eht sistep 2 and step 4 is the correct answer
Step-by-step explanation:
Mr.Santino needs A total of 406 Forks restaurant. He currently has 302 forks. If each cell has 12 forks which is the minimum number of sets of forks you should buy?
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PLEASE HELP 20 POINTS!
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Answer:
Step-by-step explanation:
I’m very confused please help:)
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Answer:
b=20°, c=160°
Step-by-step explanation:
b=20° [vertically opposite angle]
c+b=180° [angle at same line ]
c=180° - 20°
c = 160°
Which is the equation of a hyperbola with directrices at x = ±2 and foci at (6, 0) and (−6, 0)? x squared over 12 minus y squared over 24 equals 1 x squared over 12 minus y squared over 48 equals 1 y squared over 12 minus x squared over 24 equals 1 y squared over 48 minus x squared over 12 equals 1
Answers
The equation of a hyperbola with directrices at x = ±2 and foci at (6, 0) and (−6, 0) is y squared over 48 minus x squared over 12 equals 1.
What is the equation of hyperbola?The equation of the hyperbola is the equation which is used to represent the hyperbola in the algebraic equation form, with the value of center point in the coordinate plane and foci.
The standard form of the equation of the hyperbola can be given as,
[tex]\dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=r^2[/tex]
Here (h,k) is the center of the hyperbola, (b) is the transverse axis, and (a) is the conjugate axis.
The foci of the hyperbola is,
[tex](h,k\pm c)[/tex]
The directrix is,
[tex]y=k\pm \dfrac{a^2}{c}[/tex]
A hyperbola is given with directrices at x = ±2 and foci at (6, 0) and (−6, 0). Thus, the directrix is,
[tex]y=k\pm \dfrac{a^2}{c}\\\pm 2=k\pm \dfrac{a^2}{c}\\\dfrac{a^2}{6}=2\\a^2=12\\[/tex]
It is known that,
[tex]a^2+b^2=c^2\\[/tex]
Put the value of a and c,
[tex](12)+b^2=6^2\\b^2=36-12\\b^2=24[/tex]
The value of center is (0,0). Thus, the equation of hyperbola is,
[tex]\dfrac{(y-0)^2}{24^2}-\dfrac{(x-0)^2}{12^2}=1\\\dfrac{y^2}{24^2}-\dfrac{x^2}{12^2}=1[/tex]
Thus, the equation of a hyperbola with directrices at x = ±2 and foci at (6, 0) and (−6, 0) is y squared over 48 minus x squared over 12 equals 1.
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Sean asked 10 of his classmates the amount of their weekly allowance. He recorded the information in this table. $15 $15 $22 $14 $12$24 $16 $25 $15 $15 Match the measures with their values. 13 12 22 15 7 third quartile interquartile range first quartile range
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The interquartile range = Third quartile - First quartile = 22 - 15 = 7
The range = 25 - 12 = 13
What is the Interquartile Range (IQR) and Range ofa Data?Range = largest data value - the least data value
Interquartile range = Q3 - Q1
Given the following weekly allowance of Sean's classmates as, 15, 15, 22, 14, 12, 24, 16, 25, 15, 15:
Third quartile (Q3) = 22
First quartile (Q1) = 15
Interquartile range = 22 - 15 = 7
Range = 25 - 12 = 13
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what is the slope of a line
(a) where the line crosses at the y-axis
(b) the amount the line rises on the y-axis over the amount it moves horizontally on the x-axis
(c) where the line crosses at the x-axis
(d) where the line begins
Answers
Answer:
the answer is (b), because
Step-by-step explanation:
rise over run
Answer:
B
because I
saw someone else say it was b
Step-by-step explanation:
I'm smart
HELP ME
Gia collected data on the weights, in ounces, of five newborn puppies. The weights are shown in the list below.
5, 6, 7, 11, 11
Which statement regarding the mean, median, and range of the weights of the puppies is true?
Group of answer choices
The median is greater than the mean, and the range is 6.
The mean is greater than the median, and the range is 6.
The median is greater than the mean, and the range is 11
The mean is greater than the median, and the range is 11.
Answers
Answer:Mean is greater than the median and the range is 6
Step-by-step explanation: Mean is the average 5+6+7+11+11/5 = 8
Mode is the number occurring most 11
Median is the middle number 7
Range is the highest -lowest 11-5=6
Answer: Mean is greater than the median and the range is 6.
help pleaseeeeee will ark brainliest
Answers
Answer:40
Step-by-step explanation:
Your correct and final answer for this question is 40
(✿◕‿◕✿) Pls mark me Brainiest (✿◕‿◕✿)
A circle is centered at (7,8). The point (11,8) is located on the lip of the circle. Write the equation for this circle.
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The center of the circle is (7,8) and the equation of the given circle is (x- 7)^2 + (y - 8)^2 = 16
How to determine the equation of the circle?The given parameters are:
Center (a,b) = (7,8)
Point (x,y) = (11,8)
Calculate the radius (r) using:
[tex]r = \sqrt{(x- a)^2 + (y - b)^2}[/tex]
So, we have:
[tex]r= \sqrt{(11- 7)^2 + (8 - 8)^2}[/tex]
Evaluate the expression
[tex]r = 4[/tex]
The circle equation is then calculated using:
[tex](x- a)^2 + (y - b)^2 =r^2[/tex]
So, we have:
[tex](x- 7)^2 + (y - 8)^2 = 4^2[/tex]
Evaluate the exponent
[tex](x- 7)^2 + (y - 8)^2 = 16[/tex]
Hence, the equation of the given circle is (x- 7)^2 + (y - 8)^2 = 16
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Is 10/12 greater less or equal to 3/8 also it's the same question for 1/7 4/11 and 2/6 5/8
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Answer:
10/12 is greater and for the second one, 4/11 is greater and 5/8 is greater
Help me on this inequality please!
Answers
Answer:
w ≤ 5
Step-by-step explanation:
-2w ≥ -10
-2w / -2 ≥ -10 / -2
The -2 cancels each other out and -10 divided by -2 is 5. When divding an inequality by a negative number you MUST flip the sign.
w ≤ 5
Jose is starting a word-processing business out of his home. He plans to charge $15 per hour. He anticipates his monthly expenses to be $490 for equipment rental, $45 for materials, and $65 for phone usage. What is the minimum number of hours he must work in a month to make a profit of at least $600?
Answers
Answer:
80
Step-by-step explanation:
profit = revenue - expenses
revenue = $15 per hour = $15 * number of hours (n) = $15 * n
expenses = $490 + $45 + $65 = $600
we want profit to be 600 or more
15 * n - 600 = profit
profit ≥ 600
15 * n - 600 ≥ 600
add 600 to both sides to isolate the variable and its coefficient
15 * n ≥ 1200
divide both sides by 15 to isolate the variable
n ≥ 80
Jose must therefore work 80 or more hours, for a minimum of 80
Translate the point A (-3,4) right 5 up 1
Answers
Answer:
(2,5)
Step-by-step explanation:
-3+5=2 and 4+1=5