Answer:
y = -5x + 16
Step-by-step explanation:
Equation of line in slope intercept form is
y = mx + c where
m = slope of line and c is y intercept.
Given that slope of line is -5
hence we can use m = -5 then
equation of line will be y = -5x + c
this line passes though (2,6), hence
we put y = 6 and x = 2 in the equation y = -5x + c, to find c
y = -5x + c
=> 6 = -5*2 + c
=> 6 = -10 + c
=> c = 6+10 = 16
Thus, equation of line is y = -5x + 16 (i.e fourth option)
How do you figure out the area of a triangle?
General formula for area of triangle is [tex]A=\frac{h_bb}{2}[/tex].
Where:
[tex]h_b[/tex] is height of triangle perpendicular to base side of triangle.[tex]b[/tex] is the length of base side of triangle.Multiplying [tex]h_b[/tex] and [tex]b[/tex] results in rectangle, dividing that by 2 gives you area of a triangle.
Hope this helps.
Answer:
Area of Triangle = [tex]\frac{1}{2} (Base)(Height)[/tex]
Step-by-step explanation:
The area of a triangle can be found out by the following formula:
Area of Triangle = [tex]\frac{1}{2} (Base)(Height)[/tex]
Please help me I would appreciate it
Answer:
m<1= 50 degrees
m<2= 130 degrees
m<3= 50 degrees
m<4= 130 degrees
m<5= 40 degrees
m<6= 30 degrees
Step-by-step explanation:
All of the angles of triangles equal to 180 degrees, so you can solve all of the angles based on that info :)
Which of the following systems has equations that are dependent?
1. 2x + 2y = 6
4x + 4y = 4
2. 2x + 2y = 6
2x - 2y = 6
3. y = -x+3
y = -x-3
4. 2x+2y = 6
y = -x + 3
Question 6 Essay Worth 5 points)
(05.02) In the figure below, angle y and angle x form vertical angles. Angle x forms a straight line with the 50° angle and the 40° angle.
40
SO
Write and solve an equation to determine the measure of angle y.
I
The value of y will be 90°. The sum of angle of the two right angle is 180°. The property of the adjacent angle is used.
How can we find the solution to an equation?We do same operations on both the sides so that equality of both expressions doesn't get disturbed.
Solving equations generally means finding the values of the variables used in it for which the considered equation is true.
Sometimes we can find such value, and sometimes it is not possible at all, or sometimes, there are an infinite number of solutions.
The angles subtended by a circle is 360°, then;
The equation is found as;
[tex]\rm 40^0+50^0+x+y+z=360^0 \\\\ x+y+z=270^0[/tex]
The sum of angle of the two right angle is 180°;
x°+40°+50°=180°
x=90°
y+50°+40°=180°
Y=90°
Hence, the value of y will be 90°.
Learn more about solving equations here:
https://brainly.com/question/18015090
#SPJ2
Create a word problem that this Part-To-Whole Ratio can represent, 6:10
Step-by-step explanation:
Question formulation: A boy has a bag of red and blue PET caps, 60 red caps and 40 blue caps, which amount to a total of 100 caps. what is the ratio of the red caps to the total caps in the bag?
Answer
Given
red caps= 60
blue caps= 40
total caps= 60+40= 100
ratio of red to total caps= red:total = 60:100
= 60/100= 6/10
= 6:10
Simplify. a - {4b - [a - (5b - c) + 3c - (a - b - 9c)]}
Answer:
a - 8b + 13c
Step-by-step explanation:
a - (4b -( a - 5b + c + 3c -(a - b - 9c)))
a - (4b - (-5b + c + 3c + b + 9c)))
a - (4b - (-4b + 13c)))
a - (4b + 4b - 13c)
a- (8b - 13c)
Is the graph increasing, decreasing, or constant?
A. Decreasing
B. Constant
C. Increasing
Answer:
A: the graph is decreasing
The graph is decreasing because the slope is negative. Then the correct option is A.
What is increasing and decreasing of function?If the value of y increases as the value of x increases, then increasing function.
And if the value of y decreases as the value of x increases, then decreasing function.
In the graph, as the value of x increases, the value of y decreases.
The graph is decreasing because the slope is negative.
Then the correct option is A.
More about the increasing and decreasing of function link is given below.
https://brainly.com/question/14330051
#SPJ5
Helppppppppppppppppppppppppp!
10. (2x10^-3)^3= ? Explanation please
Answer: 0.000000002
Step-by-step explanation:
Evaluation of (2x10^-3)^3 will be achieved by using the law of indices or exponent.
(A^x)^y = A^xy
Therefore,
(2x10^-3)^3= 2x10^-9
Convert the number in standard form back to normal number form
2×10^-9 = 0.000000002
Therefore,
(2x10^-3)^3 = 0.000000002
Can someone help me please!!?
Answer:
Step-by-step explanation;
1. 41%=0.41=K
2. 23%=0.23=F
3. 98%=0.98=D
4. 67%=0.67=E
5. 34%=0.34=A
6. 12%=0.12=G
7. 48%=0.48=B
8. 76%=0.76=J
A. 3/10=0.3
B. 1/2=0.5
C. 1/4=0.25
D. 5/5=1
E. 2/3=0.67
F. 1/3=0.33
G. 1/10=0.1
H. 3/4=0.75
I. 9/10=0.9
J. 4/5=0.8
K. 2/5=0.4
The length of a rectangle is represented by the function L(x) = 2x. The width of that same rectangle is represented by the function W(x) = 8x2 − 4x + 1. Which of the following shows the area of the rectangle in terms of x?
Answer: (L. W)(x) = 16x^3 - 8x^2 + 2x
Step-by-step explanation:
The Area of a rectangle is calculated thus:
Area (A) = Width(W) × Length(L)
Given that:
Length = L(x) = 2x
Width = W(x) = 8x2 − 4x + 1
A = L(x) * W(x) = (2x) * (8x2 − 4x + 1)
Factorizing L(x) * W(x)
L(x) * W(x) = (L . W)(x)
(L . W)(x) = (2x) * (8x2 − 4x + 1)
(L . W)(x) = 16x^3 - 8x^2 + 2x
[tex]\frac{\sec\left(x\right)}{\cos\left(x\right)}-\frac{\sin\left(x\right)}{\csc\left(x\right)\cos^{2}\left(x\right)}[/tex]Use the basic identities to change the expression to one involving only sines and cosines. Then simplify to a basic trig function.
Answer:
1
Step-by-step explanation:
First, convert all the secants and cosecants to cosine and sine, respectively. Recall that [tex]csc(x)=1/sin(x)[/tex] and [tex]sec(x)=1/cos(x)[/tex].
Thus:
[tex]\frac{sec(x)}{cos(x)} -\frac{sin(x)}{csc(x)cos^2(x)}[/tex]
[tex]=\frac{\frac{1}{cos(x)} }{cos(x)} -\frac{sin(x)}{\frac{1}{sin(x)}cos^2(x) }[/tex]
Let's do the first part first: (Recall how to divide fractions)
[tex]\frac{\frac{1}{cos(x)} }{cos(x)}=\frac{1}{cos(x)} \cdot \frac{1}{cos(x)}=\frac{1}{cos^2(x)}[/tex]
For the second term:
[tex]\frac{sin(x)}{\frac{cos^2(x)}{sin(x)} } =\frac{sin(x)}{1} \cdot\frac{sin(x)}{cos^2(x)}=\frac{sin^2(x)}{cos^2(x)}[/tex]
So, all together: (same denominator; combine terms)
[tex]\frac{1}{cos^2(x)}-\frac{sin^2(x)}{cos^2(x)}=\frac{1-sin^2(x)}{cos^2(x)}[/tex]
Note the numerator; it can be derived from the Pythagorean Identity:
[tex]sin^2(x)+cos^2(x)=1; cos^2(x)=1-sin^2(x)[/tex]
Thus, we can substitute the numerator:
[tex]\frac{1-sin^2(x)}{cos^2(x)}=\frac{cos^2(x)}{cos^2(x)}=1[/tex]
Everything simplifies to 1.
Find CE. Please explain step by step!
Answer:
30
Step-by-step explanation:
We know that BD = 20 + 5 = 25. Let's call the point where BD and CE intersect point A. Therefore, ΔBAC ≅ ΔBAE by HL (BC = BE = 25 because they are radii, BA and AB are congruent because of the reflexive property). We can use Pythagorean Theorem to find CA. We can write CA² + 20² = 25² so CA = 15 and since CA = AE = 15 and CE = CA + CE, CE = 15 + 15 = 30.
Answer:
Step-by-step explanation:
BE=BC=25 in
trg BCE isosceles so CE=2✓25^2-20^2
=2"✓625-400=2*✓225=2*15
CE=30
I need help plz 6.2(a+5)-2a+1.2
Answer:
4.2a+32.2Solution,
[tex]6.2(a + 5) - 2a + 1.2 \\ = 6.2 \times a + 6.2 \times 5 - 2a + 1.2 \\ = 6.2a + 31 - 2a + 1.2 \\ = 6.2a - 2a + 31 + 1.2 \\ = 4.2a + 32.2[/tex]
Hope this helps.
Good luck on your assignment...
he graphed line shown below is y = 3 x minus 1. On a coordinate plane, a line goes through (0, negative 1) and (1, 2). Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions? y + 1 = 3 x y = negative 3 x + 1 y = 3 x + 1 y minus 3 x = negative 3
Answer:
y + 1 = 3x
Step-by-step explanation:
The graphed line is y = 3x - 1
The options given to us are
y + 1 = 3x
y = -3x + 1
y = 3x + 1
y - 3x = -3
Consider the first equation:
y + 1 = 3x
Substitute (0,-1) into the equation:
-1 + 1 = 3(0)
0=0
Substitute (1,2) into the equation:
2+1 = 3(1)
3 = 3
Thus the equation holds true for the given points.
Rearrange the equation
y + 1 = 3x
y = 3x - 1
As it is the same equation which was initially graphed, both of these lines will be same and overlap each other, resulting in infinite number of solution
Answer:
its a
Step-by-step explanation:
a
Marlene brought a can of polyurethane varnish that was stored at 40°F into her shop, where the
temperature was 74°F. After 2 hours, the temperature of the varnish was 58°F. If the varnish must be
68°F for best results, then how much longer must Marlene wait until she uses the varnish?
Please show explanation:(
Answer:
1 hour and 6 minutes
Step-by-step explanation:
A temperature difference of 58-40 = 18°F was obtained in 2 hoursA temperature difference of 68-40 = 28°F will be obtained in x hoursThe next proportion must be satisfied:
18 °F / 28 °F = 2 hours / x hours
x = 2*28/18
x = 3.1 hours in total
Given that she has already waited 2 hours, she must wait 3.1 - 2 = 1.1 extra hours. 1 hour is equivalent to 60 minutes, then 0.1 hours is equivalent to 0.1*60 = 6 minutes.
What is the value of f(6) in the function below?
f(x) = 2x
HELP ASAP PLS
Answer:
f(6) = 64
Step-by-step explanation:
f(x) = 2^x
Let x = 6
f(6) = 2^6
= 2*2*2*2*2*2
= 64
Answer:
B. 64
Step-by-step explanation:
[tex]f(x)=2^x[/tex]
Plug x as 6 and solve.
[tex]f(6)=2^{(6)}[/tex]
[tex]f(6)=2^6[/tex]
[tex]f(6)=2 \times 2 \times 2 \times 2 \times 2 \times 2[/tex]
[tex]f(6)=64[/tex]
Which of the following polynomials is in standard form?
O A. F(X) = 10+2x2 + x - 4x-9x?
B. F(x)=-9x2 - 4x + x + 2x2 +10
O C. F(X) = 10-9x2 - 4x+2x2 + x
OD. F(x) = x* -9xº + 2x2 - 4x +10
Answer:
Step-by-step explanation:
None of these are in standard form. In standard form the powers of x are arranged in descending order, which is not the case here. Also, all terms containing the same power of x (such as x - 4x - 9x) should be simplified into ONE term with ONE coefficient.
Should I use SAS (side angle side) or SSS (side side side) to see if the triangles are congruent? AND WHY?
Need Help Please I'm Out Of Time ;( The point (-2, 7) is graphed on a coordinate plane. The point is located 2 units ______ the origin and 7 units ______ the origin 1st Blank Choices: A. Above B. To The Left Of C. Below D. To The Right Of 2nd Blank Choices: A. Above B. To The Left Of C. Below D. To The Right Of
Answer:
Left, Up
Step-by-step explanation:
Since -2 is to the left of 0 on the x-axis, we are moving left 2 units.
Since 7 is above 0 on the y-axis, we are moving up 7 units.
Answer:
The point (-2, 7) is graphed on a coordinate plane. The point is located 2 units left of the origin and 7 units up the origin 1st Blank
A sporting goods company is planning to manufacture a commemorative lacrosse
ball to demonstrate the importance of lacrosse to Canadian culture. The ball has a
diameter of 10 cm. Determine the dimensions of the cylinder which will package
the lacrosse ball so that it has a maximum volume and minimum surface area.
Calculate the volume and surface area of this cylinder.
Answer:
Volume of this cylinder = 785.71 Cm³
Surface area of this cylinder = 157.14 Cm²
Step-by-step explanation:
Given:
Height of cylinder = 10 Cm
Radius of cylinder = 10 / 2 = 5 Cm
Find:
Volume of this cylinder.
Surface area of this cylinder
Computation:
Volume of this cylinder = πr²h
Volume of this cylinder = (22/7)(5)²(10)
Volume of this cylinder = 785.71 Cm³
Surface area of this cylinder = 2πr(h+r)
Surface area of this cylinder = 2(22/7)(5)(10+5)
Surface area of this cylinder = 2(22/7)(5)(15)
Surface area of this cylinder = 157.14 Cm²
halppp :3 Which equation can be used to calculate the area of the shaded triangle below? plss help <3
Answer:
1/2[6×10)=30
Step-by-step explanation:
A= 1/2bh
1/2×6×10=30
1/2(10×6)=30
Answer:
0.5(10x6)=30
Step-by-step explanation:
To the nearest tenth of a square centimeter, what is the
surface area of the cone if the radius of its base is 5 cm and
its height is 12?
Work Shown:
SA = surface area of cone
SA = pi*r^2 + pi*r*sqrt(r^2 + h^2)
SA = pi*5^2 + pi*5*sqrt(5^2 + h^2) ... plug in r = 5
SA = pi*5^2 + pi*5*sqrt(5^2 + 12^2) ... plug in h = 12
SA = pi*25 + pi*5*sqrt(169)
SA = 25pi + 5pi*13
SA = 25pi + 65pi
SA = 90pi .... exact surface area in terms of pi
SA = 282.743338823081 .... see note below
SA = 282.7
note: this is the approximate surface area. I used the calculator's stored value of pi, rather than something like pi = 3.14; that way the surface area is as accurate as possible. Your teacher may want you to use pi = 3.14 though, which is why its a good idea to ask and clarify.
A person places $26300 in an investment account earning an annual rate of 3.8%, compounded continuously. Using the formula V=Pe∧{rt}, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 19 years.
Answer:
V = $ 54135.92
Step-by-step explanation:
The formula for compounding continuously is given as:
V = P(e)^rt
V = Amount of money in the bank after 19 years
P = Principal amount initially invested = $26300
e = base of natural log
r = Interest rate = 3.8% = 0.038
t = time in years = 19
We have to calculate the value of V. Substitute all values into the given formula:
V = P(e)^rt
V = (26300)(e)^(0.038 · 19)
V = (26300)(2.718)^(0.722)
V = (26300)(2.0584)
V = $ 54135.92
Answer:
54139.76
Step-by-step explanation:
I need help with this sum
Hello there! :)
Answer:
D. [tex](\frac{3 }{2}, 2)[/tex]
Step-by-step explanation:
Use the midpoint formula to solve:
[tex](x_{m}, y_{m} ) = (\frac{x_{1}+x_{2} }{2}, \frac{y_{1}+y_{2}}{2})[/tex]
Plug in the points shown:
[tex](\frac{0+3 }{2}, \frac{4+0}{2})[/tex]
Simplify:
Midpoint coordinates at [tex](\frac{3 }{2}, 2)[/tex]
I have some red , blue, and green marbles. I have 5 less blue marbles than 4 times the red marbles. I have 3 more green marbles than 2 times the number of red marbles. All together I have 61 marbles. How many red , blue, and green marbles do I have? PLEASE ANSWER! I"LL GIVE CORRECT ANSWER AS THE BRAINLIEST ANSWER! I NEED HELP
Answer:
You have 9 red marbles, 21 green marbles, and 31 blue marbles.
Step-by-step explanation:
Let r equal the number of red marbles
Let b equal the number of blue marbles
Let g equal the number of green marbles.
"I have 5 less blue marbles than 4 times the red marbles."
4r-5=b
"I have 3 more green marbles than 2 times the number of red marbles."
2r+3=g
" All together I have 61 marbles."
r+b+g=61
Substitute the b and g for 4r-5 and 2r+3
r+(4r-5)+(2r+3)=61
5r-5+2r+3=61
5r+2r-5+3=61
7r-2=61
7r=63
r=9
2r+3=g
2(9)+3=g
21=g
4r-5=b
4(9)-5=b
36-5=b
b=31
You have 9 red marbles, 21 green marbles, and 31 blue marbles.
Let me know if this helps :)
Answer:
There are 9 red, 21 greens and 31 blues
Step-by-step explanation:
Set up equations
Let
R=# red
G=# green
B=# blue
I have 5 less blue marbles than 4 times the red marbles.
B=4R-5 .............(1)
I have 3 more green marbles than 2 times the number of red marbles.
G=2R+3..............(2)
All together I have 61 marbles.
R+G+B=61 ..................(3)
Solution:
substitute (1) & (2) in (3)
R + 2R+3 + 4R-5 = 61
Simplify
7R = 61+2 = 63
R = 63/7 = 9 ..........(4)
Substitute (4) in (1)
B = 4R-5 = 4(9) - 5 = 36-5 = 31
Substitute (4) in (2)
G = 2R+3 = 2(9) + 3 = 18+3 = 21
A credit card balance is $452.18. Find the new balance after these things happen: two items costing $26.45 and $15.90 are returned; three items costing $3.17, $16.42 and $57.71 are purchased; and a payment of $100 is made.
Answer:
the anwser is 232.33
Step-by-step explanation:
i added all of the things that happened and then toke that number and subtracted that from the main number.
hope this helps
Tara takes her pulse in order to determine her resting heart rate, measured in beats per minute ( bpm ) (bpm)left parenthesis, start text, b, p, m, end text, right parenthesis. She takes it for three minutes, and makes the following chart of the results. We'll assume that Tara's heart rate is constant over the three-minute period.
Answer:
Let x represent the number of minutes.
Lets y represents the number of beats.
Now consider the graph, when the time is equal to 1 min, the total beats are 60. We can say that this point can be taken in a coordinate plane as (1,60).
Similarly, when time is equal to 2 mins, total beats are 120, and when time is equal to 3 mins, total beats are equal to 180 mins. So the these points on the coordinate plane can be represented as (2,120) and (3,180)
Plot all the three points, and draw a line which joins them and extend the line. The line shows the proportionality relation between both values
Answer:
0,0 1,60
Step-by-step explanation:
x=1
y=60
graph
Maria is making a stained glass window using glass tiles. Each tile is 1/4 inch by 1/4 inch. The window is 14 inches wide by 20 inches long.. How many glass tiles will Maria need to make her stained glass window?
answer choices
4,480
2,240,
1,120
280
Answer:
4,480
Step-by-step explanation:
In the above question, we are told that the measurements of the stained glass windows Maria intends to make is 14 inches wide by 20 inches long.
Step 1
We find the area of the window
Length × Width ( Breadth)
= 20 × 14 = 280 square inches
Step 2
The tiles that she intends to use has the following measurements
1/4 inch by 1/4 inch
The Area of these glass tiles = 1/4 × 1/4 = 1/16 square inches.
Step 3
Finally to calculate the number of tiles that she would required to make the stained glass window =
Area of the window ÷ Area of the glass tiles
= 280 square inches ÷ 1/16 square inches
= 4,480
Therefore, Maria would be needing 4,480 glass tiles to make her stained glass window.
Dolve the equation
11q-6=3q+8q
Answer:
no solution
Step-by-step explanation:
Simplifying
11q + -6 = 3q + 8q
Reorder the terms:
-6 + 11q = 3q + 8q
Combine like terms: 3q + 8q = 11q
-6 + 11q = 11q
Add '-11q' to each side of the equation.
-6 + 11q + -11q = 11q + -11q
Combine like terms: 11q + -11q = 0
-6 + 0 = 11q + -11q
-6 = 11q + -11q
Combine like terms: 11q + -11q = 0
-6 = 0
Solving
-6 = 0
Couldn't find a variable to solve for.
This equation is invalid, the left and right sides are not equal, therefore there is no solution.