Answers
Answer:
Area of triangle ABC = 10
Option C is correct.
Step-by-step explanation:
We need to find area of triangle ABC
We are given A(2,1) B(4,7) and C(6,3)
The formula used to find [tex]Area \ of \ triangle=\frac{1}{2}base\times height[/tex] ABC is:
In the given triangle base= AC and height = BC
First we need to find the distance between A and C and B and C
The formula used to find distance between AC [tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have [tex]x_1=2, y_1=1, x_2=6, y_2=3[/tex]
Putting values and finding distance
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(6-2)^2+(3-1)^2}\\Distance=\sqrt{(4)^2+(2)^2}\\Distance=\sqrt{16+4}\\Distance=\sqrt{20}[/tex]
find distance between BC [tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have [tex]x_1=4, y_1=7, x_2=6, y_2=3[/tex]
Putting values and finding distance
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(6-4)^2+(3-7)^2}\\Distance=\sqrt{(2)^2+(4)^2}\\Distance=\sqrt{4+16}\\Distance=\sqrt{20}[/tex]
So, We have height = [tex]\sqrt{20}[/tex] and base = [tex]\sqrt{20}[/tex]
Finding area of triangle
[tex]Area \ of \ triangle=\frac{1}{2}base\times height\\Area \ of \ triangle=\frac{1}{2}\sqrt{20} \times \sqrt{20} \\Area \ of \ triangle=\frac{1}{2}\times 20\\Area \ of \ triangle=10[/tex]
So, Area of triangle ABC = 10
Option C is correct.
Related Questions
Please do quick
Estimate the amount of the tip by rounding the bill to the nearest dollar before calculating.
20% tip on a bill of $59.82
Answers
Answer:
$12
Explanation: 60 x .2= 12 + 60= $72
What is the line of reflection
Answers
Answer:
x=y
Step-by-step explanation:
Evaluate the function when x = 5: h(x) = 3x + 5
Answers
Answer:
h(x)=20
Step-by-step explanation:
x=5
3(5)+5
15+5
20
Hope this helps!
Answer:20
Step-by-step explanation:
Hello!
So first you want to plug in 5 to all of the x
h(5) = 3(5) + 5
No you want to do 3(5)
3(5) = 15
h(5) = 15 + 5
Now you add 15 + 5
15 + 5 = 20
h(5) = 20
So your answer is 20
Triangle PQR is shown below. Its original lengths are multiplied by 2.5. What are the new side lengths of P’Q’R’?
17, 8, 15
Answers
Answer:
17 will change to 42.5
8 will change into 20
and
15 will change into 37.5
Step-by-step explanation:
Multiply them all by 2.5
Answer:
A 37.5 cm x 20 cm x 42.5 cm
Step-by-step explanation:
Its 37.5 cm x 20 cm x 42.5 cm
NEED HELP ASAP PLEASE WILL GIVE BRAINLIEST
Review the diagram.
On a coordinate plane, a rectangle sits on the x-axis. A horizontal vector is 30 degrees from a vector labeled 40 pounds, and is 45 degrees from a vector labeled 35 pounds.
Two students are pulling an object with ropes. One student pulls with a force of 40 pounds at an angle of 30° above the ground, and the other student pulls with a force of 35 pounds at an angle 45° above the ground. What is the direction of the resultant force?
approximately 37.33° above the ground
approximately 42.27° above the ground
approximately 47.73° above the ground
approximately 53.13° above the ground
Answers
Answer: A. approximately 37.33° above the ground
Step-by-step explanation:
edge2020
The correct solution to the problem is that the direction of the resultant force will be approximately 37.33° from the horizontal above the ground.
What is Vector and how do we do component of a Vector ?In a coordinate plane there are two axis one is x axis and the second one is y axis.If a vector is lying in the coordinate plane then no matter what is its direction, we can always divide it in two components which are x component and y component for easier calculations.If the magnitude of the vector is R, then the magnitude of the X component along x axis will be R cos θ and the magnitude of the Y component along y axis will be R sin θ.We can find the final resultant magnitude and direction of the vector from the components by adding the the components.How to solve this question ?For 30° Vector of 40 pounds :-
If we divide it in components it will become
40 cos 30° Î + 40 sin 30° Ĵ
40 × ( √3 / 2 ) Î + 40 × ( 1 / 2 ) Ĵ
34.64 Î + 20 Ĵ ( approximately )
For 45° Vector of 35 pounds :-
If we divide it in components it will become
35 cos 45° Î + 35 sin 45° Ĵ
35 × ( 1 / √2 ) Î + 35 × ( 1 / √2 ) Ĵ
24.75 Î + 24.75 Ĵ ( approximately )
Now adding both vectors
( 24.75 + 34.64 ) Î + ( 24.75 + 20 ) Ĵ ( approximately )
59.39 Î + 44.74 Ĵ ( approximately )
Now Using formula of Tan θ to find the value of θ
( Tan θ = Perpendicular / Base )
Tan θ = 44.74 / 59.39
Tan θ = 0.75 ( approximately )
θ = Tan⁻¹ (0.75) ( approximately )
θ = 36.87° ( approximately )
We are calculated the value of θ as 36.87° which is approximate value as we used a lot of approximations while calculating and, the closest option given is 37.33° which is again an approximate value.
So we can say that the correct answer to this problem is The direction of the resultant force will be approximately 37.33° from the horizontal above the ground.
Learn more about Vectors here:
https://brainly.com/question/25705666
#SPJ2
What is the area of the triangle bounded by the line 3x+2y=12 and the x- and y- axes?
Answers
Answer:
12
Step-by-step explanation:
If x=0, then the y axis is 6
If y=0, then the x axis is 4
The base is 4 and the height is 6
4 x 6 / 2 = 12
WILL GIVE BRAINLIEST!!!!!!!!!
Use the value of y (y=4) for part b to correctly find the measures of AX and BD and list each step for each.
Use the figure below:
Answers
Answer:
So BD= 2*(y+4) -> 2*(4+4) = 16
and AX is the same lenght as BX so: AX = y+4 -> 4+4 = 8
Step-by-step explanation:
hope that helped
Let f (x) = 8x^2 + 4 and g(x) = -x^2+ 12x + 10. Which statements below are true for f (x) · g(x)? Select all that apply.
A.The constant term is 40.
B.The leading term is 8x^4.
C.The x term has a coefficient of 12.
D.The x^2 term has a coefficient of -76.
E.The x^3 term has a coefficient of 96.
F.The resulting polynomial has degree 4.
Answers
Answer:
Option A, E ,F are correct
Step-by-step explanation:
f(x).g(x)=(8x^2+4)(-x^2+12x+10)
=(-8x^4+96x^3+80x^2-4x^2+48x+40)
= -8x^4+96x^3+76x^2+48x+40
Leading term is -8x^4. The x term has coefficient 48. The x^2 term has coefficient +76
Write the standard form of 2 (4x - 1)(2x + 5)
Answers
Answer:
16x^2+36x-10
Step-by-step explanation:
2 (4x - 1)(2x + 5)
=2(8x^2-2x+20x-5)
=2(8x^2+18x-5)
=16x^2+36x-10
Calculate the quotient below and give your answer in scientific notation. 0.00065/5*10^-2
Answers
Answer:
1.3x10^-6
Step-by-step explanation:
Use a calculator.
0.00065/5 will give you 0.00013 which can be written as 1.3x10^-4 and multiply that by 10^-2, you will add the exponents -4+-2 and get -6 as your new exponent, ending with 1.3x10^-6
Answer:
The one above is incorrect, the answer is:
1.3 x 10-2
consider function g.
which function could be the inverse of function g?
A.
B.
C.
D.
Answers
Answer:
D
Step-by-step explanation:
Here, we want to select which of the options that could actually be the inverse of function g
The function that could actually be an inverse is that function in which we have a reversal of values
What we mean in this case is that the x values take up the f(x) values while the f(x) values take up the x values
With respect to this question, the option that fits this description is;
Option D
Answer: For Plato users
Step-by-step explanation:
The correct answer is B .
Just flip the x and y
Jordan is using a number line to model the division expression Negative 24 divided by 12. What should be a step in his work?
Answers
Answer:
-24/12= -2
Step-by-step explanation:
Answer:
Its B
Step-by-step explanation:
If I'm wrong please tell me
Write the sentence as an inequality: Sixteen is no more than the product of 4 and x
Answers
Your sentence:
16 < 4x
(BRAINLIEST FOR QUICKEST)
Write the following using algebraic notation, using the letter x for any unknown numbers.
I think of a number add seven and then divide by five.
Answers
Answer:
[tex]\frac{x+7}{5}[/tex]
Step-by-step explanation:
Add 7 to x gives x + 7 then divide this by 5, that is
[tex]\frac{x+7}{5}[/tex]
The lenngths of the sides of the triangle are in the extended ratio 8:9:10. The primeter of the triangle is 108 cm.What are the lengths of the sides?
The lengths of the sides of the triangle in cm are____?
Answers
Answer:
The lengths of the sides of the triangle in cm are 32 cm, 36 cm and 40 cm
Step-by-step explanation:
The lengths of side of the triangle are in ratio 8:9:10
Perimeter of triangle = 108 cm
We need to find length of sides of triangles.
The formula used is: [tex]Perimeter \ of \ triangle = Sum \ of \ all \ sides \ of \ triangle\\[/tex]
The length of side of triangle can be expressed as:
First side= 8x
Second Side =9x
Third Side=10x
So, finding x and then calculate length of each side
[tex]Perimeter \ of \ triangle = Sum \ of \ all \ sides \ of \ triangle\\\\108=8x+9x+10x\\108=27x\\x=\frac{108}{27}\\x=4[/tex]
So, value of x = 4
The length of sides of triangle will be found by putting value of x at each side.
First side= 8x = 8*4 = 32 cm
Second Side =9x= 9*4= 36 cm
Third Side=10x = 10*4=40 cm
So, The lengths of the sides of the triangle in cm are 32 cm, 36 cm and 40 cm
E
(5x + 9)
(30-3x)
A
Find the value of angle DFE
Angle BFC=Angle DFA=Angle EFA + Angle DFE
Solve for x, then use substitution for 27+2x
5x+9=30-3x+27+2x
Everything is on the picture
Answers
9514 1404 393
Answer:
43°
Step-by-step explanation:
Following the instructions is generally useful.
5x +9 = 30 -3x +27 +2x
6x = 48 . . . . add x-9
x = 8 . . . . . . .divide by 6
27 +2x = 27 +2(8) = 43 . . . . substitute into the expression for angle DFE
angle DFE = 43°
2. A 5-foot-tall fencepost casts a 7.25-foot shadow at the same time that a nearby
gazebo casts a 36.25-foot shadow. How tall is the gazebo?
Answers
Answer:
I think the answer is 25 feet
Step-by-step explanation:
5 / 7.25 = .6896551724
.6896551724 x 36.25 = 25
Define and give examples of x-intercept
Answers
(3,6) in that ordered pair, 3 would be the domain
Answer:
Definition: The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
Example: From the graph, describe the x and y-intercepts using point notation. The graph crosses the x-axis at x = 1 and x = 3, therefore, we can write the x-intercepts as points (1,0) and (–3, 0). Similarly, the graph crosses the y-axis at y = 3. Its y-intercept can be written as the point (0,3).
An online store sells only two types of bandanas: cotton bandanas and silk bandanas. Cotton bandanas cost $7 each, and silk bandanas cost $11 each. Mrs. Tran spent a total of $93 on bandanas at this store. How many cotton bandanas did Mrs. Tran buy
Answers
Given :
An online store sells only two types of bandanas: cotton bandanas and silk bandanas. Cotton bandanas cost $7 each, and silk bandanas cost $11 each.
Mrs. Tran spent a total of $93 on bandanas at this store.
To Find :
How many cotton bandanas did Mrs. Tran buy.
Solution :
Let, number of cotton and silk bandanas buys are x and y respectively.
So, 7x + 11y = 93
x = (93 - 11y)/ 7
Putting y = 1 , x = 82/7 ( not possible since x can only be positive integer )
Putting y = 4 , x = 7
Therefore, Mrs . Tran will buy 7 cotton bandanas.
Hence, this is the required solution.
what is the product of (3a2b7)(5a3b8)
Answers
Answer:
5040a^2b^2
Step-by-step explanation:
(3a2b7)(5a3b8)
(42ab)(120ab) multiply everything inside each parenthensis
42ab * 12ab remove parenthesis
5040a^2b^2 multiply
find the slope (m) and y -intercept (b) of the equation in standar form 2x-3y=6
Answers
Answer:
m = [tex]\frac{2}{3}[/tex] , b = - 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
Given
2x - 3y = 6 ( subtract 2x from both sides )
- 3y = - 2x + 6 ( divide all terms by - 3 )
y = [tex]\frac{2}{3}[/tex] x - 2 ← in slope- intercept form
with slope m = [tex]\frac{2}{3}[/tex] and y- intercept b = - 2
Answer:
y- intercept is (0, -2)
slope is 2/3
Step-by-step explanation:
find 2 points on the line:
2x-3y=6
1/2*(6+3y) =x
if y is 2, x is 6 ((6,2))
if y is 4, x is 9 ((9, 4))
y-intercept is when x = 0.
0-3y=6
y=-2
slope is (y2-y1)/(x2-x1): choose y2 and the corresponding x-coordinate is x2. then the others are the 1's. let's use 4 as y2 which means:
x2 = 9
x1 = 6
y1 = 2
then plug in and solve.
(4-2)/(9-6)
= 2/3
m = 2/3
Hope this helps!
PLS HELP ME I NEED THIS FASTTT ON SHOW ALL YOUR WORK
List the values for a, b and c in the following quadratic equation.
3x^2 + 6x = 7
Use your preferred method to solve the following quadratic equation for n. Please show ALL work to receive credit.
6n^2-18n -18=6
Use your preferred method to solve the following quadratic equation for n. Please show ALL work to receive credit.
x^2 + 8x = 10
Answers
Answer:
I tried my best so I hope this helps :)
(look at the screenshots for the work I don't feel like typing it out)
Step-by-step explanation:
1.) the solution is [tex]x=\frac{-3+\sqrt{30}}{3}\\[/tex], [tex]x=-\frac{3+\sqrt{30}}{3}[/tex]
2.) the solution is [tex]n=4,\:n=-1[/tex]
3.) the solution is [tex]x=-4+\sqrt{26},\:x=-4-\sqrt{26}[/tex]
Try using Symbolab, I use it all the time it gives the correct answer and it gives good explanations.
x = 7 - 2y
2x + y = 5
Answers
2(7-2y) = 5
14 - 4y = 5
-4y = -9, y = 9/4
2x + 9/4 = 5
8x + 9 = 20
8x = 11, x = 11/8
Final answer: x = 11/8, y = 9/4
Line g has a slope of–7/3. Line
h is parallel to line g. What
is the slope of line
h?
Answers
Answer:
-7/3
Step-by-step explanation:
Since the lines are parallel, the slopes would have to be the same
What is the slope of a line that connects points (5,8) and (10,12)
Answers
Answer:
4/5
Step-by-step explanation:
12-8=4
10-5=5
4/5 is the slope
what is x for 4(x+2) = 16 ?
Answers
Answer:
x=2
Step-by-step explanation:
4(x+2) = 16
Divide each side by 4
4/4(x+2) = 16/4
x+2 = 4
Subtract 2 from each side
x+2-2 =4-2
x =2
Answer:
x is 2
Step-by-step explanation:
parenthesis first ok ... 2 plus 2 is 4 ok?
and then 4 times 4 is 16 and the numbers haveta equal 16 so there u go mate x equals 2 yall
hope this helps
have a great day
im brooke btw
what is x in 9x + 89 = 161
Answers
Answer:
The answer is x=8
Step-by-step explanation:
hope that helps
9x+89=161
9x+89−89=161−89
9x=72
9x/9=72/9
x=8
Answer:
x = 8
Step-by-step explanation:
We just need to solve for x!
Here is a step-by-step process:
9x + 89 = 161
Subtract 89 from both sides
9x = 72
Divide both sides by 9
x = 8
The school track is 7/8 of a mile in length. Den ran 1/4 of a mile. How much more will he need to run to go all the way around the track?
Answers
Answer:
5/8
Step-by-step explanation:
1/4=2/8
7/8-2/8=5/8
Plz help it’s due soon I made it extra points
Answers
Answer:
the answer is D
Step-by-step explanation:
It shows both numbers of the graph.
M(-2,0), and N(-1, 2)
Use the function f (x) = 2x^2 – 5.
(Look at picture)
Answers
Answer:
C
Step-by-step explanation:
By the definition of an inverse function, if:
[tex]f(a)=b\text{ then } f^{-1}(b)=a[/tex]
Therefore, the domain of the original function will be the range of the inverse function.
And the range of the original function will be the domain of the inverse function.
We have the original function:
[tex]f(x)=2x^2-5[/tex]
With the domain:
[tex]-\infty<x<\infty[/tex]
Since the domain of the original function is such, then the range of the inverse function is also the same as above.
So, the range of the inverse function is also:
[tex]-\infty< f^{-1}(x)< \infty[/tex]
So, our answer is
C.
Notes:
A, B, and E would automatically be incorrect since we never use ”or equal to” when using the infinity symbol. This is because we can never “equal” infinity.