What are the area and the perimeter of a polygon with vertices( 1,-2), (1,5) (7,2)
Answers
Answer: P=7+3√5+2√13 units S=21 quadratic units
Step-by-step explanation:
[tex]A(1,-2)\ \ \ \ B(1.5)\ \ \ \ C(7,2)\\[/tex]
The perimeter of a triangle
[tex]|AB|=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2} \\|AB|=\sqrt{(1-1)^2+(5-(-2))^2} \\|AB|=\sqrt{0^2+(5+2)^2}\\|AB|=\sqrt{0+7^2}\\ |AB|= \sqrt{7^2} \\|AB|=7[/tex]
[tex]|BC|=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2} \\|BC|=\sqrt{(7-1)^2+(2-5)^2}\\ |BC|=\sqrt{6^2+(-3)^2}\\ |BC|=\sqrt{36+9}\\ |BC|= \sqrt{45} \\|BC|=\sqrt{9*5}\\ |BC|=3\sqrt{5}[/tex]
[tex]|AC|=\sqrt{(x_C-x_A)^2+(y_C-x_A)^2}\\ |AC|=\sqrt{(7-1)^2+(2-(-2)^2} \\|AC|=\sqrt{6^2+(2+2)^2}\\ |AC|=\sqrt{36+4^2}\\ |AC|=\sqrt{36+16} \\|AC|=\sqrt{52}\\ |AC|=\sqrt{4*13} \\|AC|=2\sqrt{13} \\[/tex]
[tex]Thus,\\\\P_{ABC}=|AB|+|BC|+|AC|\\\\P_{ABC}=7+3\sqrt{5}+2\sqrt{13}\ units[/tex]
The area of a triangle
Taking A as the first vertex, we find:
[tex]\displaystyle\\Find\ |\overline{AB}*\overline{AC}|\\\left|\begin{array}{cc}x_A-x_C&y_A-y_C\\x_B-x_C&y_B-y_C\\\end{array}\right|=\\\\\left|\begin{array}{ccc}1-7&-2-2\\1-7&5-2\\\end{array}\right| =\\\\\left|\begin{array}{ccc}-6&-4\\-6&3\\\end{array}\right| =\\\\|(-6)*3-(-6)*(-4)|=\\\\|-18-24|=\\\\|-42|=\\\\42\\\\S_{ABC}=\frac{1}{2} |\overline{AB}*\overline{AC}|\\\\S_{ABC}=\frac{1}{2}(42)\\\\S_{ABC}=21 \ quadratic\ units[/tex]
Related Questions
A recipe requires 1 2/3 cups of sugar. If Mrs.Marina is going to make one and one half of the recipe, then how much sugar does she need
Answers
5/3 + 5/6
10/6 + 5/6
she needs 15/6 or 2 3/6 or 2 1/2 cups of sugar
Mrs. Marina requires 5/2 or 2.5 cups of sugar to make one and one half of the recipe.
What is proportion ?
A proportion is an equation based on the equality of two ratios.
Here it is given that :
A recipe requires 1 (2/3) cups of sugar.
That is 1 recipe requires = 1(2/3) cups of sugars
= 5/3 cups of sugar
Now, Marina is going to make one and one half of the recipe and to find the sugar he needed we simply multiply 1(1/2) both the sides :
1 recipe requires = 5/3 cups of sugar
1(1/2) recipe requires = (5/3) x 1(1/2) cups of sugar
3/2 recipe requires = (5/3) x (3/2) cups of sugar
3/2 recipe requires = 5/2 cups of sugar or 2.5 cups of sugar.
Therefore, Mrs. Marina requires 5/2 or 2.5 cups of sugar to make one and one half of the recipe.
Read more about ratio at:
https://brainly.com/question/17869111
#SPJ5
Consider the line y=6×-7
what is the slope of a line parallel to this line?
what is the slope of a line perpendicular to this line?
Answers
Answer:
The slope of a line parallel to this line will be: 6
The slope of the perpendicular line will be: -1/6
Step-by-step explanation:
We know the slope-intercept form
[tex]y=mx+b[/tex]
Here,
m is the slope b is the y-interceptGiven the equation
[tex]y=6x-7[/tex]
Thus, the slope of the line is: 6
The slope of a line parallel to the line:
We have already determined that the slope of the line is: 6
We know that the parallel lines have the same slope.Thus, the slope of a line parallel to this line will be: 6
The slope of a line perpendicular to the line:
We have already determined that the slope of the line is: 6
As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line.
Thus, the slope of the perpendicular line will be:
[tex]\frac{-1}{6}\:\:[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}[/tex]
[tex]=-\frac{1}{6}[/tex]
Therefore, the slope of the perpendicular line will be: -1/6
evaluate 5x-[21-(3-11)x] when x=-2
Answers
Answer:
-15
Step-by-step explanation:
(5)(−2)−(21−(3−11)(−2))
=−15
HAve a wonderful day Brainliest Please.
Can someone help me Plz
Answers
Answer:
A
Step-by-step explanation:
Please give brainliest
ASAP PLZ HELP I MARK BRIANLIST IF U GIVE ME RIGHT ANSWER
Answers
Answer:
[tex]d = \sqrt{13}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra II
Distance Formula: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point A (-2, 1)
Point B (1, -1)
Step 2: Find distance d
Substitute: [tex]d = \sqrt{(1+2)^2+(-1-1)^2}[/tex]Add/Subtract: [tex]d = \sqrt{(3)^2+(-2)^2}[/tex]Exponents: [tex]d = \sqrt{9+4}[/tex]Add: [tex]d = \sqrt{13}[/tex]WILL BRAINLIST
45 points
Drag each tile to the correct box. Not all tiles will be used.
Simplify the expression by arranging the steps in sequence, based on the order of operations,
Answers
31. EF, given E(8, -3), (2, -5)
Domain
Range
Answers
Answer:
I think the domain would be the x values and range would be the y values in the given 2 points.
Domain : [2 , 8]
Range : [-5 , -3]
I hope you get this right.
1.When 2 is added to three times a number, the result was 17. The number isRequired to answer.
Answers
Answer:
3x+2=17
Step-by-step explanation:
Solve for
30 = 5(x + 5)
Answers
Answer:
x=1
Step-by-step explanation:
Trust me on this one
Answer:
x = 1
Step-by-step explanation:
Let's do this quickly and easily,
30 = 5(x + 5)
30 = 5x + 25
5x = 30 - 25
x = 5/5
x = 1
Hope it helps!<3
could someone explain? i will give brainliest thank you
Answers
Answer:
A
Step-by-step explanation:
Using the sine ratio on the right triangle on the right to find x
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{70}[/tex] ( multiply both sides by 70 )
70 × sin30° = x , thus
x = 35
-----------------------------------------------
Using the sine ratio on the right triangle on the left to find y
sin42° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{y}[/tex] = [tex]\frac{35}{y}[/tex] ( multiply both sides by y )
y × sin42° = 35 ( divide both sides by sin42° )
y = [tex]\frac{35}{sin42}[/tex] ≈ 52.3 ( to the nearest tenth ) → A
Answer:
y = 52.3.
Step-by-step explanation:
Consider the larger triangle on the right:
sin 30 = x / 70
x = 70 sin 30 = 70 * 0.5
= 35.
So, considering the small triangle:
Sin 42 = 35/y
y * sin 42 = 35
y = 35 / sin 42
y = 52.3.
Long division of 39486400 by 575???
Answers
WILL GIVE U EXTRA POINTS BY BRAINLIEST
need help asap
Answers
Answer:
(-2,4)
Step-by-step explanation:
If you drew a vertical line that went right through x = 1. This would be our line of reflection. Point is three unit to the right of that line. So, D' would be three unit to the left of the line. That would be at the point (-2,4)
pls answer all the parts of this
Answers
Answer:
A. 360
B. 780
C. 350
Step-by-step explanation:
Times the time by the speed
10. What is the measure of angle C?
A. 25°
B. 30°
C. 60°
D. 75°
Answers
Answer:
D
Step-by-step explanation:
x + 5 + 3x + C = 180 All triangles have 180 degrees.
4x + 5 + C = 180
But C must be equal to 3x. Notice the markings on the lets of the triangle.
4x + 5 + 3x = 180
7x + 5 = 180 Subtract 5 from both sides
7x = 180 - 5
7x = 175
x = 25
But angle C = 3x
C = 3*25
C = 75
HELPPP PLEASE!!
Solve for d:
3d-17 = 46
A. 15 1/3
B. 21
C. 5 2/3
D. 9 2/3
Answers
Explanation:
3d-17=46
+17 +17
3d = 63
63/3 = 21
show your solution find the 6 and 7 term
Answers
Answer:
1/6 and 1/7
Step-by-step explanation:
The sequence is 1 decreasing by 1/10 as it goes.
Help for BRAINLIEST! Find the missing coordinates of the points in the diagram
Answers
Answer:
(2, 2[tex]\sqrt{3}[/tex]) and (4,0)
Step-by-step explanation:
Let x be half of the triangles length
3x = 6
x = 2
so B should be (2, 2[tex]\sqrt{3}[/tex])
and D should be (4, 0)
If someone drove 640 miles in 4 hours how would you determine they would travel in 12?
Answers
Answer:
Step-by-step explanation:
if someone drove 640 miles in 4 hours,
, it means that they drove 640/4=160 miles per hour
in 12 hours
160*12=1920
or
640............................4 h
640*3.........................4*3 hours
which give syou the same answer
1920.............................12 hours
Answer:
1,920 miles
Step-by-step explanation:
640 divided by 4 = 160
160 x 12 = 1,920
Answer this please!!Subtracting a number is the same as adding its opposite Use this understanding to complete each of the equations below
Answers
A hot tub pump circulates 3.9 cubic feet of water per minute.how many cubic inches of water does it circulate each second
Answers
Answer:
0.78 cubic inches/sec
Step-by-step explanation:
you take 3.9 cubic feet and multiply it by 12 to convert it into inches and you get 46.8 cubic inches. then you divide by 60 to convert minutes to second and you get 0.78. hope that helps
Answer:
1123.2 cubic inch per second
Step-by-step explanation:
3.9 feet^3 = per minute
? = second
39 = 60 sec
? = 1 sec
39/60 =0.65 feet cubic
1 cubic foot = 1728 cubic inch
0.65 feet cubic = ?
0.65 * 1728
= 1123.2 cubic inch
Determine the intercepts of the line
Answers
Answer:
The y-intercept is 2
Step-by-step explanation:
In the image you can see the line going through the 2.
Explanation:
As you can see the line pass through the x-axis at point -7
m-
GET
17.
xm+ xy
(b) fa x = 2, y = 3, m= 4 n= 1 45 m-n
xm-nxymn
मान पत्ता लगाउनुहोस्।
If x = 2, y = 3, m = 4 and n= 1, find the value of
xm+nxy
Ans:
xm-nxym
m-n
+10
m + n.
Answers
Answer:
[tex]xm+nxy=14[/tex]
Step-by-step explanation:
Given that x = 2, y = 3, m = 4 and n= 1.
Putting all the given values to get the value of xm+nxy.
So, the value of [tex]xm+nxy=2\times 4 + 1\times 2 \times 3=14[/tex]
Hence, [tex]xm+nxy=14[/tex].
Rashad has 24 almonds and 32 walnuts for making snack bags. He wants to make as many snack bags as possible and wants each bag to have the same amount of almonds and walnuts. What is the greatest number of snack bags he could make? HURRY I NEED THIS FAST
Answers
Answer:
24 maximum
Step-by-step explanation:
Unless theres extra information we can't see, it is 24, because you can't have a snack bag with half an almond.
Answer:
the answer is 24 with each one with 4 bags, hope you can answer in time
A bouncing toy reaches a height of 64 inches at its first peak, 48 inches at its second peak, and 36 inches at its third peak. Which explicit function represents the geometric sequence of the heights of the toy?
f(x) = 48(Five-sixths) Superscript x minus 1
f(x) = 48(three-fourths) Superscript x minus 1
f(x) = 64(three-fourths) Superscript x minus 1
f(x) = 64(Five-sixths) Superscript x minus 1
Answers
Answer:
The correct option is;
f(x) = 64(three-fourths)Superscript x minus 1
Step-by-step explanation:
The first peak height that the bouncing toy reaches = 64 inches
The second peak height that the bouncing toy reaches = 48 inches
The third peak height that the bouncing toy reaches = 36 inches
Therefore, given that the sequence has a common ratio, r = 48/64 = 36/48 = 3/4
The first term of the sequence, a = The first peak height reached = 64
The xth term of the geometric sequence with general form, xth term = ar⁽ˣ⁻¹⁾
The xth term of the geometric sequence, f(x), is therefore, given as follows;
[tex]f(x) = 64 \times \left(\dfrac{3}{4} \right) ^{(x - 1)}[/tex]
The correct option is;
f(x) = 64(three-fourths)Superscript x minus 1
Step-by-step explanation:
The first peak height that the bouncing toy reaches = 64 inches
The second peak height that the bouncing toy reaches = 48 inches
The third peak height that the bouncing toy reaches = 36 inches
Therefore, given that the sequence has a common ratio, r = 48/64 = 36/48 = 3/4
The first term of the sequence, a = The first peak height reached = 64
The xth term of the geometric sequence with general form, xth term = ar⁽ˣ⁻¹⁾
The xth term of the geometric sequence, f(x), is therefore the correct answer is C
Select all the ratios that are equivalent to 9:6.
A 6:9
B 3:2
C 13:10
D 5:2
E 18:12
Answers
Answer:
B and E
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
9:6 reduced is 3:2
Please help!
For what value of x must ABCD be a parallelogram?
x=?
Answers
Answer:
[tex]x=3[/tex]
Step-by-step explanation:
For a shape to be a parallelogram, the angles that are across from one another have to be equal.
We can now find x by making both equations equal to each other and solving.
[tex]11x+1=13x-5[/tex]
Solve.
[tex]11x+1=13x-5\\6=2x\\x=3[/tex]
What is the result of adding these two equations? 50-y=6 -2x +y = 8
Answers
Answer:
48x = 14
General Formulas and Concepts:
Algebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define Systems
50x - y = 6
-2x + y = 8
Step 2: Solve for x
Elimination
Combine 2 equations: 48x = 14
The graph below represents which system of inequalities?
Answers
Answer:
c
Step-by-step explanation:
The variable b varies directly as the square root of c. If b = 100 when c = 4, which equation can be used to find other combinations of b and c
a. b=25c
b. b√c=50
c. b=200c
d. b=50√c
Answers
Hope this helps!
Use the formula to solve the problem. Round to the nearest hundredth.
Volume of a sphere: V = 4/31tr3
Surface area of a sphere: A = 4rtr2
Find the volume of a sphere with a radius of 1 inch.
_____cubic in.
Answers
Answer:
Volume of sphere = 4.186 cubic inches
Step-by-step explanation:
Radius of sphere = r = 1 inch
Volume of sphere = ?
The formula used is: [tex]Volume\:of\:sphere=\frac{4}{3}\pi r^3[/tex]
Putting value of radius and π and finding volume:
[tex]Volume\:of\:sphere=\frac{4}{3}\pi r^3\\Volume\:of\:sphere=\frac{4}{3}\times 3.14\times (1)^3\\Volume\:of\:sphere=\frac{4}{3}\times 3.14\times (1)^3\\Volume\:of\:sphere=4.186 \:cubic\:in[/tex]
So, Volume of sphere = 4.186 cubic inches