Hint :- The point slope form of the line is [tex] m(x-x_1) = y - y_1[/tex] , where [tex](x_1,x_2)[/tex] is the point and [tex] m [/tex] is the slope of the line .
Solution :- The given point is [tex](2,-1)[/tex] and the slope is 3 . On using the point slope form of the line, we have ;
[tex]\implies m(x-x_1)=y-y_1[/tex]
Substitute ,
[tex]\implies 3(x -2) = y -(-1) [/tex]
Simplify ,
[tex]\implies 3x -6=y+1 [/tex]
Add -1 and -y to the both sides ,
[tex]\implies \boxed{3x -y -7=0 }[/tex]
Find the area of the following kite:
Answer:
[tex]48 cm^2[/tex]
Step-by-step explanation:
Each of the small triangles are right, so we can add up all the small triangle's areas to find the total area.
The 4-by-10 triangle: The area is [tex]4*10/2=40/2=20[/tex].
The other 4-by-10 triangle has the same side lengths and hence the same area, so the area is [tex]20[/tex].
The 4-by-4 triangle: The area is [tex]4*4/2=8/2=4[/tex].
The other 4-by-4 triangle has the same area, [tex]4[/tex].
The total area is [tex]20+20+4+4=\boxed{48} cm^2[/tex].
A 20 foot ladder is set against the side of a house so that it reaches up 16 feet. If Christian grabs the ladder at its base and pulls it 2 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 14 ft.) Round to the nearest tenth of a foot.
Answer:
14.2
Step-by-step explanation:
The ladder forms a right angles triangle,
We have,
h=20
p=16
b=x
Using pythogorean theorem,
b=√(20^2-16^2)
√144
b=12
Now,
Since, she pulls it 2 cm,
b=x+2
b=14
p=?
Using pythogorean theorem,
p=√(20^2-14^2)
√204
p=14.2828568571
Rounding to the nearest tenth,
p=14.2
The side of the ladder will reach up is 14.3 feet.
What is trigonometric Ratios?"Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. It is with respect to any of its acute angles are known as the trigonometric ratios of that particular angle".
For the given situation,
Hypotenuse, h = 20 feet
Perpendicular, p = 16 feet
Base = b
By Pythagoras theorem,
[tex]h^{2} = p^{2} + b^{2}[/tex]
⇒[tex]20^{2} = 16^{2}+b^{2}[/tex]
⇒[tex]b^{2} = 400-256[/tex]
⇒[tex]b^{2}=144[/tex]
⇒[tex]b=\sqrt{144}[/tex]
⇒[tex]b=12[/tex]
The ladder at the house is pulled 2 feet farther.
So, base = [tex]12+2[/tex]
⇒[tex]b=14[/tex]
Now, the side of the ladder will reach up
[tex]p^{2} = h^{2}-b^{2} \\[/tex]
⇒[tex]p^{2}=20^{2}-14^{2} \\[/tex]
⇒[tex]p^{2}=400-196[/tex]
⇒[tex]p^{2}=204[/tex]
⇒[tex]p=\sqrt{204}[/tex]
⇒[tex]p=14.28[/tex]
⇒[tex]p=14.3[/tex] (rounded off to nearest tenth)
Hence we can conclude that the side of the ladder will reach up is 14.3 feet.
Learn more about trigonometric ratios here
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solve by substitution.
5x-3y=-4
x+y=-4
Answer:
x=-2,y=-2
Step-by-step explanation:
x+y=-4
x=-4-y--(3)
substitute (3) in (1)
5(-4-y) -3y=-4
-20-5y-3y=-4
-8y=16
y=16/-8
y=-2
substitute y in (3)
x=-4-(-2)
x=-2
Subtract.
-3-6-(-1)
Plot the solution on the number line.
Answer:
-8
Step-by-step explanation:
Start by putting a dot on the number line at -3. As we are to subtract 6, start at -3 and move 6 units to the left, arriving at -9. Finally, recognizing that -(-1) = +1, move 1 unit to the right from -9, ending up at -8.
Does the graph represent a function? Why or why not?
Answer:
This graph does represent a function because when you do the vertical line test, none of the x-values intercept more than once.
Step-by-step explanation:
Hope this helps!
Solve for y.
7v + 25 = 5(v + 7)
Simplify your answer as much as possible.
Answer:
v = 5
Step-by-step explanation:
Distribute on the left:
5 ( v + 7 )
( 5 x v ) + ( 5 x 7 )
5v + 35
7v + 25 = 5v + 35
Subtract 5v from each side:
2v + 25 = 35
subtract 25 from each side:
2v = 10
Divide each side by 2:
v = 5
what is 5 pounds to 35 pounds division
Answer: it would be 7
Step-by-step explanation:
Because 35 divided by 5 is 7
+5 when
2. What is the value of f(x)=2x +
X=4?
A А.
2
el ind
B 7
C 9
D 13
Answer:
B. 7
Step-by-step explanation:
[tex] \frac{1}{2} \times 4 + 5 = 7 \\ sub \: in \: 4 \: into \: the \: equation[/tex]
solve the inequality. 1/3b + 1 < -6
Answer:
b<-21
Step-by-step explanation:
1/3b+1<-6
1/3b<-7
*3 *3
b<-21
Answer:
b < - 21
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] b + 1 < - 6 ( subtract 1 from both sides )
[tex]\frac{1}{3}[/tex] b < - 7 ( multiply both sides by 3 to clear the fraction )
b < - 21
Simplify the expression 3/2(5/3)−1 1/4+1/2 . Given the answer as a simplified fraction.
The simplified expression is a/b .
Answer:
3/2(5/3) - 1 1/4 + 1 1/2
= 11/4
Step-by-step explanation:
8.
Look at the triangle below. Which of the following statement is true?
Q
7
6
R
5
A
B.
ZPis the smallest angle.
ZQis the largest angle.
ZR is the largest angle.
ZR is the smallest angle.
C.
D.
Answer:
b
Step-by-step explanation:
what is 523,278,and 351 .Estimate the total
Answer:
Your weight...
Step-by-step explanation:
I need the answers, fast!
Answer:
-5/8, 1/3, -3/2
Step-by-step explanation:
1.
-7/8+1/4
-7/8+2/8
(-7+2)/8
-5/8
2.
-19/3+20/3
1/3
3.
2-7/2
(4-7)/2
-3/2
1-
-7/8+1/4
-7/8+2/8
(-7+2)/8
-5/8
2-
IN THE FIGURE BC IS PARALLEL TO AD. AREA OF TRIANGLE ABC IS 100 cm². WHAT IS THE AREA OF TRIANGLE BCD
Answer:
150 cm2
Step-by-step explanation:
double of triangle abc is 200
this is in middle of both
Triangle JKL, with vertices J(2,-4), K(6,-5), and L(4,-2). What is the area, in square units, of triangle JKL?
Answer:
i bleve it is 43
Step-by-step explanation:
I COULD WRONG !!!!!! SORRRY
His CD collection went from 25 disks to 22 disks
Answer:
i-that doesn't help
Step-by-step explanation:
Please answer this question correctly, and include work within your answer.
Answer: 11.9 and 12.5
Step-by-step explanation:
|x - 12.2| = 0.3 is telling us that x must be either 12.2 + 0.3 or 12.2 - 0.3.
Longest is (12.2 + 0.3) = 12.5
Shortest is (12.2 - 0.3) = 11.9
you have 120 cows and 90% of them are female how many female cows do you have
Answer: 108
Step-by-step explanation:
If 90% are female, that means that female = 90% of 120, or 90/100 x 120
90/100 x 120 = 108, meaning that there are 108 female cows.
For BRAINILY please help I need to pass this class
Answer:
Angle D is the largest angle on this triangle! (74.261°) I hope you pass your class! : )
D= 74.261°
E= 42.184°
F= 63.554°
Largest to smallest - D, F, E
the product of a number and -3 increased by 8 is no less than 35
Answer:
-3x + 8 ≥ 35, hopefully that answers your question since you didn't really specify what you wanted your answer to be
A student writes the equation for a line that has a slope of -6 and passes through the point (2, –8).
y -(-8) = -6(x - 2)
y -(-8) = -6x + 12
y -(-8) + 8 = -6x + 12 + 8
y = -6x + 20
Explain why the work is not correct.
Answer:
The student should subtract 8 from each side not add 8
Step-by-step explanation:
Point slope form is
y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line
y - -8 = -6(x -2)
y+8 = -6(x-2)
Distribute
y+8 = -6x+12
Subtract 8 from each side
y+8-8 = -6x+12-8
y = -6x+4
The student should subtract 8 from each side not add 8
Answer:
y -(-8) = -6(x - 2)
y -(-8) = -6x + 12
y -(-8) + 8 = -6x + 12 + 8 (this step is incorrect as minus into minus is plus therefore when taking 8 to the right hand side we must subtract it from the left hand side
y = -6x + 20
the correct equation would be : y= -6x+4
413,405,397… find the 41st term
Answer:
it is the frst tow numbrs 41
Step-by-step explanation:
Help me pls and thx and have a nice day
Answer: the answer should be the last one
Step-by-step explanation:
pamelia is 9 years younger than jiri. The sum of their ages is 55. What is Jiris age?
Answer: 32
Step-by-step explanation: since Jiri is 9 years older, you set an equation where x (Pamelia age) + 9. So the equation is 55= x + (x+9). You subtract 9 from both sides, then divide 46 by 2 to find the Pamelia age. To find Jiri’s age, add 9 to 23 (Pamelia age).
find the value of a + 1a
Answer:
2a
Step-by-step explanation:
a+1a is the same as a+a=2a
QUICK QUESTION: did I do this right?
Answer:
Yup looks correct
Step-by-step explanation:
Lol I verified using the calculator :)
An office space in a city measures 38.4 feet by 43 feet and costs $22.50 per square foot. What is the selling price for the office space?
1 book/5 days is it a unit rate
Answer: No, it is not a unit rate
Explanation:
A unit rate is when the time value in the denominator is 1. So it would need to be "1 day" instead of "5 days" for it to be a unit rate. The term "unit" means "one".
To convert to a unit rate, we simply compute 1/5 = 0.20 to see that the unit rate is 0.20 books per day. This is the same as saying "0.20 books every 1 day", but I think the phrasing "books per day" is more common.
help please i dont know how to do this
PLEASEEEE HELPPPPPPPPPP
Answer:
-1/2, +1/4, -1/8, +1/16, -1/32, +1/64
Step-by-step explanation:
multiplying a negative by a negative makes it a positive. Multiplying a positive by a negative makes it a negative. The order will be negative, positive, negative, positive, negative, positive, etc.
Hope this helps!
Answer the answer is the third one