Equation for the line in point-slope form is 5x + 6y = 6.
What is point slope form?The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.
Given Data
P(6, -3)
y =1/2 x + 2
When the equation has been solved for y, the line in slope intercept form with slope = m = 1/2 = the coefficient of the x term is represented by the equation y= (1/2)x + 2. 2 represents the y coordinate of the location (0, 2) where the line intersects the y axis as the y intercept.
So, the points are (6,-3) and (0,2)
Formula
y₂ - y₁ = m(x₂ - x₁)
slope of the line (m) = [tex]\frac{x-x}{y-y}[/tex]₁¹
m= [tex]\frac{2-(-3)}{0-6}[/tex]
m = -[tex]\frac{5}{6}[/tex]
Equation
y- (-3) = -[tex]\frac{5}{6}[/tex](x- 6)
y +5 = -[tex]\frac{5}{6}[/tex]x + 6
y + 5 = -[tex]\frac{5+36 }{6}[/tex]
6y + 30 = -5x + 36
5x + 6y = 6
Equation for the line in point-slope form is 5x + 6y = 6.
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for which values of (A) the system has at least one solution
Answer
The values of a that ensures that the system has at least one solution is
a > (21/127)
Explanation
We are told to find the values of a that ensures that the system has at least one solution. The system of equations include
3 (a - 5x) < 1 + x
2 - (x/2) > 3 + 5 (x - a)
To do this, we need to solve the expressions
3 (a - 5x) < 1 + x
3a - 15x < 1 + x
We can rewrite this as
1 + x > 3a - 15x
x + 15x > 3a - 1
16x > 3a - 1
Divide both sides 16
[tex]\begin{gathered} \frac{16x}{16}>\frac{3a-1}{16} \\ x>\frac{3a}{16}-\frac{1}{16} \end{gathered}[/tex]We then solve the second one. But to do this, let's multiply through by 2
2 - (x/2) > 3 + 5 (x - a)
4 - x > 6 + 10 (x - a)
we can rewrite as
6 + 10 (x - a) < 4 - x
6 + 10x - 10a < 4 - x
10x + x < 10a - 6 + 4
11x < 10a - 2
Divide both sides by 11
[tex]\begin{gathered} \frac{11x}{11}<\frac{10a-2}{11} \\ x<\frac{10a}{11}-\frac{2}{11} \end{gathered}[/tex]The two solutions are
x > (3a/16) - (1/16)
x < (10a/11) - (2/11)
To find a lasting solution, we need the inequality sign to be the same, so, we need to multiply through one of the equations by -1
x > (3a/16) - (1/16)
-x < (-3a/16) + (1/16)
So, the system of equations become
-x < (-3a/16) + (1/16)
x < (10a/11) - (2/11)
We can then add the two equations
-x + x < (-3a/16) + (1/16) + (10a/11) - (2/11)
0 < (-3a/16) + (10a/11) + (1/16) - (2/11)
0 < -0.1875a + 0.9091a + 0.0625 - 0.1818
0 < 0.7216a - 0.1193
Rewrite
0.7216a - 0.1193 > 0
0.7216a > 0.1193
Divide both sides by 0.7216
(0.7216a/0.7216) > (0.1193/0.7216)
a > 0.1653
a > (21/127)
Hope this Helps!!!
need help assap look in the picture
Answer:
8
Step-by-step explanation:
To find the perimeter, you must add the lengths of all sides.
In this question the perimeter is given, which is 63.
63 = 12 + 12 + 3x + 2x + 1 + x + 2
1. Add the numbers
63 = 12 + 12 + 3x + 2x + 1 + x + 2
12 + 12 + 1 + 2 = 27
63 = 27 + 3x + 2x + x
2. Combine Like Terms
63 = 27 + 3x + 2x + x
x = 1
3x + 2x + 1x = 6x
63 = 27 + 6x
3. Move Variable to the left
63 = 27 + 6x
63 = 6x + 27
4. Subtract 27 from both sides, the opposite of adding 27
63 = 6x + 27
63 - 27 = 6x + 27 - 27
36 = 6x
5. Divide by the same factor, the opposite of multiplying 6
36 = 6x
36/6 = 6x/6
6. Cancel out the 6s but leave the x
36/6 = 6x/6
x = 6
So, now that we know that x = 6 we can solve the expression, x + 2, to find out the length of the side BC.
6 + 2 = 8
ill give brainliest if i can have help, i am having trouble turning on axis, can someone explain? (refer to image somewhere lol)
Answer:
a=2,-2 b=-5,-1 c=-1,-2
Step-by-step explanation:
you just put the shape the opisite way
The ratio of 1.2 to 29 is the same as the ratio of 4.8 to
Answer:
116
Step-by-step explanation:
Given the ratio 1.2 : 29, you want x in the equivalent ratio 4.8 : x.
SetupEquivalent ratios can be written as a proportion:
1.2/29 = 4.8/x
SolutionMultiplying by 29x, we have ...
1.2x = 29(4.8)
Dividing by 1.2 gives ...
x = 29(4.8/1.2) = 29(4) = 116
The ratio is the same as 4.8 to 116.
__
Additional comment
A proportion like this can be written 4 ways. The solution takes only one step if the unknown is in the numerator.
[tex]\dfrac{1.2}{29}=\dfrac{4.8}{x},\quad\dfrac{29}{1.2}=\dfrac{x}{4.8},\quad\dfrac{1.2}{4.8}=\dfrac{29}{x},\quad\dfrac{4.8}{1.2}=\dfrac{x}{29}[/tex]
An investment grows by 4% per year for 5 years. By what percent does it increase over the 5-year period?
Give a formular on how to calculate growth rate
Answer:
Straight-line percent change method example
Growth rate = (489 - 402) / 402. Absolute change = 87 (489 - 402) Growth rate = 0.2164 (87 / 402) Percent change = 21.64% (0.2164 x 100)
magine,... L Free Games Online. Online Voice Recon What is the circumference of a circle with a radius 5 square un 50 m square units quare units
The distance around a circle is known as the circumference, by definition.
Flan- servers 10 people; $10.85 per person 1/8 teaspoon salt.1(12 fluid once) 1 teaspoon vanilla1/4 cup brown sugar
Filling with the information given, we have:
Multiply the original recipe by 10 (Since we have to serve 10 people)
New recipe:
Salt: 1/8 x 10 = 10/8 = 5/4 (Multiplying fractions and simplifying)
5/4 = 1 1/4 ( Converting the fraction to a mixed number)
Evaporated milk : 1 x 10 = 10 cans.
Vanilla: 1 x 10 = 10 teaspoons.
Brown sugar: 1/4 x 10 = 10/ 4 = 5/2 (Multiplying fractions and simplifying)
5/2 = 2 1/2 (Converting the fraction to a mixed number)
The values of the new recipe are:
Salt: 1 1/4
Evaporated milk: 10 cans
Vanilla: 2 1/2 teaspoons
Brown sugar: 2 1/2 cups
How many points of intersection are there between the graphs of the two hyperbolas?
The graphs of the hyperbola have zero point of intersection.
What is the point of intersection?The point of intersection is the point where two or more functions meet.
The given parameters;
3x² – 4y² + 4x – 8y +4= 0
3x² + y² + 4x – 3y +4= 0
To find the points of intersection, we simply equate both equations.
So;
3x² – 4y² + 4x – 8y +4= 3x² + y² + 4x – 3y +4
Now Cancel out the common terms
y² - 3y = - 4y² - 8y
Collect like terms;
y² + 4y²= 3y - 8y
5y² = - 5y
Divide through by 5
y² = -y
Divide through by y
y = -1
Hence, the graphs of the hyperbola have zero point of intersection.
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Solve the inequality for x.21 > x+2Simplify as much as posible.
The given inequality is 21>x+2.
The inequality can be solved as,
[tex]\begin{gathered} 21>x+2 \\ 21-2>x \\ 19>x \\ x\in(-\infty,19). \end{gathered}[/tex]Thus, the above expression gives the required solution for the inequality.
if once taxi fare was $7.65 how many miles did he travel in the taxi a taxi company charges $2.25 for the first mile and then $0.20 per mile for additional mile or f equals $2.25 + $0.20(m -1) where f is the fair and m is Adam's number of miles
Answer:
28 miles
Explanation:
The equation that describes the relationship between the fare and the number of miles is:
f = 2.25 + 0.20(m - 1)
Where f is the fare and m is the number of miles.
So, if the taxi fare was $7.65, we can replace f by 7.65. Then:
7.65 = 2.25 + 0.20(m - 1)
Therefore, we can calculate the number of miles by solving the equation for m. So, subtracting 2.25 from both sides:
7.65 - 2.25 = 2.25 + 0.20(m - 1) - 2.25
5.4 = 0.20(m - 1)
Dividing by 0.20, we get:
[tex]\begin{gathered} \frac{5.4}{0.20}=\frac{0.20(m-1)}{0.20} \\ 27=m-1 \end{gathered}[/tex]Finally, add 1 to both sides:
27 + 1 = m - 1 + 1
28 = m
So, he travels 28 miles in the taxi
Rita, Goran, and Kareem have a total of $93 in their wallets. Rita has $7 more than Goran. Kareem has 2 times what Rita has. How much do they have in their wallets?
Goran has $18 in his wallet. Rita has $25 and Kareem has $50 in his wallet.
What is basic algebra?Algebra is a branch of mathematics that helps translate real-world problems or situations into mathematical formulas. Mathematical operations like addition, subtraction, multiplication, and division as well as variables like x, y, and z are needed to construct a valid mathematical expression. Coordinate geometry, calculus, and trigonometry are just a few of the mathematics topics that involve algebra. A simple algebraic equation is 2x + 4 = 8. Algebraic expressions are the result of performing operations on variables and constants, such as addition, subtraction, multiplication, division, etc.
Let the amount Goran have = X
Then, the amount Rita have= x+7
Then, Kareem has the amount = 2(x+7)
According to question
The total money three of them have = $93
Therefore,
x+x+7+2(x+7) = 93
2x + 7 + 2x + 14 = 93
4x+21= 93
4x= 93-21
4x= 72
x= 18
So,
Goran has $18 in his wallet
Rita have $ 18 +37= $25 in her wallet
Kareem has 2 × 25 = $50 in his wallet
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-8 + 12x+7x+12= A19x4 B 24x-1 C 5x+20 D 5x+4
Given the expression:
-8 + 12x + 7x + 12
Let's simplify the expression.
To simplify the expression, combine all like terms.
We have:
-8 + 12x + 7x + 12
= 12x + 7x + 12 - 8
Add 12x and 7x
= 19x + 12 - 8
Add 12 and -8
= 19x + 4
ANSWER:
19x + 4
m multipled by the square of n
Answer:
mn²
Step-by-step explanation:
the square of n is n² and m multiplied by this is
mn²
(a)A circle has a radius of 12cm. If the radius is increased by a factor of 7, how's many times larger will the circle's circumference be? (b)What is the scale factor of the circumference of a circle with a radius of 3 when compared to the original circle? Write your answer as a decimal to the nearest hundredth.
The circumference of a circle is found using the formula,
[tex]C=2\pi r[/tex]Where
C is the circumference
r is the radius
A circle has radius 12 cm, so its circumference is
[tex]\begin{gathered} C_1=2\pi r \\ C_1=2\pi(12) \\ C_1=24\pi \end{gathered}[/tex]When the radius (12 cm) is increased by a factor of 7, we mean the radius is 7 times the original, so, the new radius is
[tex]7\times12=84[/tex]So, the circumference of this circle will be >>>>
[tex]\begin{gathered} C_2=2\pi r \\ C_2=2\pi(84) \\ C_2=168\pi \end{gathered}[/tex]To find how many times larger this circumference is of the previous one, we divide,
[tex]\frac{C_2}{C_1}=\frac{168\pi}{24\pi}=7_{}[/tex]Answer7(b)Using the circumference formula, we can find the circumference of this circle,
[tex]\begin{gathered} C=2\pi r \\ C=2\pi(3) \\ C=6\pi \end{gathered}[/tex]The original circle had a circumference of 24π
The question basically asks "how many times is the circumference of this circle compared to the circumference of the original circle?"
Of couse, it will be less than 1 since this circle is smaller than the original one.
So,
[tex]\begin{gathered} \frac{6\pi}{24\pi} \\ =\frac{1}{4} \end{gathered}[/tex]So, the scale factor is 1/4, or 0.25
Answer0.25please help me again )))))))))
Answer: -14/5, -2.25, 1 1/4, 3/2
Step-by-step explanation:
Answer:
-14/5, -2.25, 1 1/4, 3/2
Step-by-step explanation:
I double-checked, and I believe it's correct.
P.S, if I could get Brainliest, it'd mean a lot to me! Thanks!
Selena was comparing the flying seeds of different birds in science class. which of the three words why faster why?select the correct response 1. the blue jay Five Spices because it's rate is 20 m/s2. the Cardinal flies fast is because it's right is 10 m/s3.the robin Place passes because it's rate is 15 m/s4.they all fly at a rate of 10 m/s
Selena was comparing the flying seeds of different birds in science class.
Which of the three words why faster why?
Select the correct response
1. the blue jay Five Spices because it's rate is 20 m/s
2. the Cardinal flies fast is because it's right is 10 m/s
3. The robin Place passes because it's rate is 15 m/s
4.they all fly at a rate of 10 m/s
____________________________
The slope, in this case, expresses the variation of the distance with respect to time (that is, the speed).
Comparing the slopes
Blue Jay's Flight
slope 10 m/s
__________________
Robin's Flight
slope = (y1-y2)/ (x1-x2)
Selecting the points (x, y)
Point 1 (2, 30)
Point 2 (6, 90)
slope = (90- 30) m / (6-2 )s
=(60)/ 4
= 15 m/s
_______________________________
Answer
3. The robin Place passes because it's rate is 15 m/s
_______________________________
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Multiple choice triangle. im pretty sure its pythagorean theorem but please let me know
To solve this triangle, we cannot use either the Pythagorean Theorem or the Law of Cosines. We need more information.
Conversely, we can use SOHCAHTOA, in the sense that we can use the SOH part of this (Sine = opposite side over hypotenuse), that is, we can use angle 33 as the reference angle, and we have a right triangle here. Then, using trigonometric ratios, we can use:
[tex]\sin (\theta)=\frac{opp}{hyp}\Rightarrow\sin (33)=\frac{x}{29}\Rightarrow x=29\cdot\sin (33)\Rightarrow x=15.7945[/tex]We also can use the Law of Sines to solve it:
[tex]\frac{x}{\sin(33)}=\frac{29}{\sin(90)}\Rightarrow\frac{x}{\sin(33)}=\frac{29}{1}\Rightarrow x=29\cdot\sin (33)\Rightarrow x=15.7945[/tex]Therefore, we can solve this triangle using both Law of Sines and SOHCAHTOA. (We can select two options: c and d.)
Find the volume of the solid to the nearest unit. 13 A 6 A drawing not to scale 3 O 546 ft 3 O 1092 ft 3 O 273 ft 3 O 422 ft
Volume = Area of the base * height
Area of the base = (7 * 6) / 2
Area of the base = 42/2
Area of the base = 21ft^2
Volume of the prism = 21 * 13
Volume of the prism = 273 ft^3 The thi
In a city in Ohio, the sales tax rate is 7.5%. If you buy a blanket for $22.00 and a pillow for $8.00, what is your total bill of the blanket and pillow including tax?
A fisher finder shows a large fish at 13 ft below the surface and a smaller fish 4 ft below surface. what is the expressions that are equivalent to the distance between the fish
Answer:
Distance = 9 ft
Explanation:
We can represent the position of the large fish with the number -13 because it is 13ft below the surface. In the same way, we can represent the position of the smaller fish with the number -4.
Then, the distance between the fish will be the absolute value of the difference between their positions. So, the expressions that are equivalent to the distance between the fish are:
| - 13 - ( - 4) | = | - 13 + 4| = 9
or
| -4 - (- 13) | = | - 4 + 13 | = 9
Therefore the distance between the fish is 9 ft
Rachel earns $27 per hour at work. She worked 936 hours last year. How much did Rachel earn from working last year?
Answer: $25,272 is the answer hope it helps.
Answer:
25,272 dollars in total
i need help with this question
Answer:
58.29 cm^2
Step-by-step explanation:
The area of a trapezium is calculated with the following formula:
[tex] \frac{a + b}{2} \times h[/tex]
(a: base, b: base, h: height)
[tex] \frac{ 7 + (10.4)}{2} \times (6.7) \\ \\ \frac{17.4}{2} \times (6.7)[/tex]
get rid of fraction by dividing (17.4) with 2
(17.4)÷2 = 8.7 multiply this with height
(8.7) × (6.7) = 58.29
The area of the given trapezium is 58.29 cm².
What is a trapezium?In American and Canadian English, a quadrilateral with at least one pair of parallel sides is referred to as a trapezoid. A trapezium is a term used for a trapezoid in British and other varieties of English. These two terms were transposed due to a typo in Charles Hutton's mathematical dictionary.So, the area of the trapezium:
Formula: (a+b)/2 × hWhere, a = 7, b = 10.4 and h = 6.7.Solve as follows:
(a+b)/2 × h(7 + 10.4)/2 × 6.717.4/2 × 6.78.7 × 6.758.29 cm²Therefore, the area of the given trapezium is 58.29 cm².
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A 45 kg skydiver has a speed of 25 m/s at an altitude of 950 meters above the ground. Determine the
kinetic energy possessed by the skydiver.
The kinetic energy possessed by the skydiver is 14, 062. 5 Joules
What is kinetic energy?Kinetic energy of an object is defined as the energy possessed by an object due to its motion.
It is also described as the work that is required to accelerate a body of mass from rest to its given velocity.
The formula for calculating kinetic energy is expressed as;
Kinetic energy = 1/2 mv²
Where;
m is the mass of the objectv is the velocity of the objectNow, substitute the values
Kinetic energy = 1/2 (45)(25)²
Find the square
Kinetic energy = 1/2 (45)(625)
Find the product
Kinetic energy = 1/2(28125)
Find the quotient
Kinetic energy = 14, 062. 5 Joules
Hence, the value is 14, 062. 5 Joules
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(b) The area of a rectangular pool is 8075 m².If the length of the pool is 95 m, what is its width?Width of the pool: ]m
The area of a rectangle is:
[tex]A=wl[/tex]where w is the width and l is the length. Plugging the values we have and solving for w:
[tex]\begin{gathered} 8075=95w \\ w=\frac{8075}{95} \\ w=85 \end{gathered}[/tex]Therefore the width is 85 meters.
What are the coordinates of the point? Responses (−2, 4) begin ordered pair negative 2 comma 4 end ordered pair (4, −2) begin ordered pair 4 comma negative 2 end ordered pair (−4, −2) begin ordered pair negative 4 comma negative 2 end ordered pair (2, 4) begin ordered pair 2 comma 4 end ordered pair A coordinate grid with a dot placed in the second quadrant. The dot is to the left of positive 4 on the y axis and above negative 2 on the x axis Skip to navigation
The coordinates of the point are (-2,4)
A coordinate grid has two lines perpendicular to each other referred to as the Axis, labeled a bit like number lines. The horizontal axis is ordinarily called the x-axis. The vertical axis is ordinarily called the y-axis. The origin is the point where the x- and y-axis meets. The numbers on a coordinate lattice are utilized to find points. Each point can be identified by a requested combination of numbers; that's, a number on the x-axis called an x-coordinate, and a number on the y-axis called a y-coordinate. The requested sets are composed in enclosures (x-coordinate, y-coordinate).
For the given point, the x-coordinate is -2 on the negative x-axis, and y - coordiante is 4 on the positive y-axis.
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Which number is greater than 555,621,000?A.5.0 x 10*6B.6.2 x 10*7C.5.55621 x 10*7D.9.99 x 10*6
Given:
[tex]555,621,000[/tex]Consider the individual options and compare them with the given number.
A.
[tex]5.0\times10^9[/tex][tex]\text{Use }10^9=1,000,000,000.[/tex][tex]5.0\times10^9=5.0\times1,000,000,000[/tex][tex]5.0\times10^9=5,000,000,000[/tex]We know that
[tex]5,000,000,000>555,621,000[/tex]This option is correct.
B.
[tex]6.2\times10^7[/tex][tex]\text{Use }10^7=10,000,000.[/tex][tex]6.2\times10^7=6.2\times10,000,000[/tex][tex]6.2\times10^7=62,000,000[/tex]We know that
[tex]62,000,000<555,621,000[/tex]This option is not correct.
C.
[tex]5.55621\times10^7[/tex][tex]\text{Use }10^7=10,000,000.[/tex][tex]5.55621\times10^7=5.55621\times10,000,000[/tex][tex]5.55621\times10^7=55,562,100[/tex][tex]55,562,100<555,621,000[/tex]This option is not correct.
D.
[tex]9.99\times10^6[/tex][tex]\text{Use }10^6=1,000,000.[/tex][tex]9.99\times10^6=9.99\times1,000,000[/tex][tex]9.99\times10^6=9,990,000[/tex][tex]9,990,000<555,621,000[/tex]This option is not correct.
Final answer:
[tex]5.0\times10^9\text{ is greater than 555,621,000.}[/tex]Option A is correct.
A car travels for 15km in a city at a Certain speed-Dutside the city it travels 72km at twice its former speed. If the total travelling time is 1hour 8minutes find the average speed .
If the total traveling time is 1 hour 8 minutes f the average speed is 45 km/h.
This is a problem from time and distance. We can solve this equation by following a few steps.
Let's assume the car travel in the city for t minutes and the average speed is v.
According to the question, the car travel outside the city for, (68- t) minutes as 1 hour 8 minutes is equal to 68 minutes.
Therefore, the average speed (v) in the city = 15/t km/minute as v = s/t where v represents the speed, t represents the taken time and s represents the distance.Hence, the speed outside the city = 72/(68- t) km/minute.As per the question, Outside the city, it travels at twice its former speed v.
Now, we can form an equation, 2 (15/t) = 72/(68- t).
Let's simplify the given equation. 30/t = 72/(68- t)
Or, 72t = 30(68- t) [cross multiplication]
Or, 72t = 2040 - 30t
Or, 102t = 2040 [add with +30t both sides]
Or, t = 2040/102
Or, t = 20 [dividing by 102 both sides]
Therefore we can conclude that the average speed ( km/h) is (15×60) / 20 = 45 km/h.
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The net of a square pyramid is shown below. What is the surface area of the pyramid?
Answer:
qt 456u8u64t3544
Step-by-step explanation:
for wicks watchful warships x
Supposed that you purchased an old property for $120,000. You decide to mark
up the value by 40% before you put it on the market. If your real estate agent
charges 5.5% commission on the sale, how much did you make on the sale?
Answer:
158,760$
Step-by-step explanation:
120,000$ + 40%=168,000$-5.5%=158,760$