Answer:
see explanation
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, - 6) and (x₂, y₂ ) = (0, 2)
m = [tex]\frac{2+6}{0-4}[/tex] = [tex]\frac{8}{-4}[/tex] = - 2
---------------------------------------
Find the midpoint using the midpoint formula
M =( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
= [tex]\frac{4+0}{2}[/tex] , [tex]\frac{-6+2}{2}[/tex] ) = (2, - 2 )
-----------------------------------------------
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]
----------------------------------------------
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = [tex]\frac{1}{2}[/tex] , thus
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (2, - 2) into the partial equation
- 2 = 1 + c ⇒ c = - 2 - 1 = - 3
y = [tex]\frac{1}{2}[/tex] x - 3 ← equation of perpendicular bisector
Answer:
-2(2, -2)1/2y= 1/2x - 3Step-by-step explanation:
Points given: (4, -6) and (0, 2)
Slope intercept form of the line going through the given pints:
y= mx+b
m= (y2-y1)/(x2-x1)= (2+6)/(0-4)= -2 slope is -2y= -2x+b ⇒ -6= -2*4+b ⇒ b= 8-6= 2 ⇒ y= -2x+2
Mid point= (x1+x2)/2, (y1+y2)/2= (4+0)/2, (-6+2)/2= (2, -2)The slope of the perpendicular bisector is the negative reciprocal of the line segment which it is dividing:
m'= -1/m= -1/-2= 1/2Equation of perpendicular bisector:
y= 1/2x+bIt passes through the mid point: (2, -2), so
b= y - 1/2x= -2 - 1/2*2= -2 -1= -3So the equation of perpendicular line:
y= 1/2x - 3solve it (3+2) ^2 -7 =
Answer:
18
Step-by-step explanation:
PEMDAS
(3+2)=5
5^2=25
25-7=18
WILL GIVE BRAINLIEST ANSWER TO WHOEVER IS ABLE TO FULLY AND CORRECTLY ANSWER THIS QUESTION. Consider and trapezoid in the following image and use them to answer the questions below. is a right triangle and trapezoid is isosceles. Do NOT use the law of cosines, use our knowledge from the content of this course. a. Describe how to find the lengths of segments and . Show your answers for this question. Explain how you can be confident your calculations are correct. b. Describe how to find the angle measures of and . Explain how you can be confident your calculations are correct. c. Are there any segments or angles you can’t calculate based solely on the information in the image? Why? d. If we drew a median into trapezoid and the given measurement of that median was 21.425, would that change your answer for part c of this question?
This is an isosceles trapezoid, because the two angles are supplementary on the right side.
y is 25 based on the Pythagorean theorem
w is sqrt (850)=29.15
z must be 15
Making a right triangle to look at the altitude
cos 59=a/15, so a is 7.73 between the right corner and the edge of x
That means x is 29.15-2(7.73)=13.69
=============
The median should be half way between 13.69 and 29.15
That is half their sum, or half of 42.84 or 21.42
That doesn't change the answer above
Once I know the trapezoid is isosceles, the angles at the base have to be 59d and the angles at the top 121d.
please mark brainliest!
I just need help with it all I don't know really what to do
Answer:
Step-by-step explanation:
How to estimate 55 percent of 64?
Answer: 35.2
Step-by-step explanation: To estimate 55 percent of 64, you could round the 55 to 50 percent, and just find half of 64, which is 32. After this, because you only have 5 percent left over, you can take the number you got from 50% of 64 and move the decimal over one place to make it 3.2. Just add that number to 32 and you’ll get your answer.
PLEASE HURRY IM TIMED ASAP WILL MARK BRAINLIEST
Which of the following are solutions to x > 5? (Check all that apply.)
8
5.2
5
0
6.7
82
Answer:
8,5.2,6.7,82 sorry i had to hurry up
Answer:
8
5.2
6.7
82
Step-by-step explanation:
all that are bigger than 5
(would really, reallly appreciate the brainliest)
it’s due at 9am please help whoever helps first gets a brainliest and everyone gets a thank you
Answer:
Step-by-step explanation:
10) 4x+12
11) 7x+28
12)2x+16
13)9x+54
14)3x+33
15) 5x+35
16) 6x+24
17)8x+72
18) 4x+20
When the boat has traveled 7 meters, the height
of the barnacle is approximately:
-1 m
-0.657 m
0.657 m
1 m
Answer:
-0.544m
Step-by-step explanation:
The height of the barnacle is approximately is, 0.657 meters.
What is Algebra?
Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
Graph y = sin(x)
Boat travel= 7m
Now,
Let y be the height of the barnacle and x be the distance the boat has traveled
i.e, x = 7 meters
to find the height y :
Substitute the value of x =7 meters in [1] we have;
y = sin(7)
≈0.657.
Therefore, by algebra the answer will be 0.657 meters.
More about the Algebra link is given below.
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ACORDING OT THE IMAGE, WHATS THE ANSWER????
HURRY 30 POINTS BRAINLIEST!!!
Answer:
231 cubed centimeters
Step-by-step explanation:
Find the area of the base of the pyramid
18 x 7=126 divided by 2= 63 cm
Next, make sure to the remember the formula is [tex]V=\frac{1}{3} BH[/tex]
1/3(63)(11)=
21(11)=231
231 cubed centimeters is the answer.
Answer:
231 cubed centimeters
Step-by-step explanation:
The formula:
1/3(63)(11)=
21(11)=231
What is the total surface area of this prism?
Answer:
Step-by-step explanation:
let us calculate area of pentagon.
it consists of 5 isosceles triangles with base=5 cm
apothem h=3.6 cm
area of pentagon=5×1/2×5×3.6≈45 cm
area of 2 pentagons (top and bottom)=2×45=90 cm²
lateral area of 6 rectangles=2(10×5+10×5+10×5)=2(50+50+50)=300 cm²
Total surface area=90+300=390 cm²
what is the smallest prime that is a factor of the sum 51+ 1?
Answer:
the smallest prime factor of 52 is 2
Step-by-step explanation:
What is the smallest prime that is a factor of 52?
52 = 4*13, or 52 = 2*2*13. So the smallest prime factor of 52 is 2.
what is the area of this quadrilateral 30 square feet 12 square feet 42 square feet 36 square feet
Answer:
Step-by-step explanation:
The rectangle in the middle has an area of 30 because it is a 3x10.
The triangles each have an area of 6 because they are a 3x4 and the forumla to find it is .5(bh) which is .5(12)=6. There are 2 of them so the total area of the triangles add up to 12.
Add the area and get 42. 30+12=42
What is the solution to this equation?
х
5
= 30
O A. x= 35
B. x= 25
C. x = 150
O D. x = 6
Answer:
D
Step-by-step explanation:
if u said 5x=30 then its D
Answer:D
Step-by-step explanation:6 x 5 equals 30
Which is the graph of g(x) = 2x – 1 + 3? On a coordinate plane, an exponential function has a horizontal asymptote at y = 3 and crosses the y-axis at (0, 4). On a coordinate plane, an exponential function has a horizontal asymptote at y = negative 3 and crosses the y-axis at (0, negative 2) On a coordinate plane, an exponential function has a horizontal asymptote at y = negative 1 and crosses the y-axis at (0, 7). On a coordinate plane, an exponential function has a horizontal asymptote at y = negative 1 and crosses the y-axis at (0, negative 1).
The graph of g(x) is an exponential function that crosses the y-axis at y = 3.5, and a horizontal asymptote at y = 3.5
The function is given as:
[tex]g(x) = 2^{x - 1} + 3[/tex]
Set x = 0, to calculate the y-intercept
[tex]g(0) = 2^{0-1} + 3[/tex]
Simplify the exponent
[tex]g(0) = 2^{-1} + 3[/tex]
Express 2^-1 as decimal
[tex]g(0) =0.5 + 3[/tex]
Add 0.5 and 3
[tex]g(0) =3.5[/tex]
This means that the graph of g(x) is an exponential function that crosses the y-axis at y = 3.5
Also, the graph of g(x) has a horizontal asymptote at y = 3.5
Read more about exponential graphs at:
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Answer:
3 graph
Step-by-step explanation:
4x3 + 10x² - 6x?
Completely factored
Answer:
2x( 2x-1) (x+3)
Step-by-step explanation:
4x^3 + 10x² - 6x
Factor out 2x
2x( 2x^2 +5x -3)
Factor inside the parentheses
2x( 2x-1) (x+3)
Answer:
2x(2x-1)(x+3)
Step-by-step explanation:
4x³ + 10x² - 6x
4x³ = 2x²×(2x)10x² = 5x×(2x)6x = 3×(2x)here 2x is a common factor then we can pull it out:
4x3 + 10x² - 6x = 2x²×(2x) + 5x×(2x) - 3×(2x)
= 2x(2x² + 5x - 3)
= 2x(2x-1)(x+3)
2x² + 5x - 3 = (2x-1)(x+3) , here you can use the quadratic formula to find the roots.
Which expression represents a rational number?
StartFraction 5 Over 9 EndFraction + StartRoot 18 EndRoot
Pi + StartRoot 16 EndRoot
StartFraction 2 Over 7 EndFraction + StartRoot 121 EndRoot
StartFraction 3 Over 10 EndFraction + StartRoot 11 EndRoot
Answer:
[tex]\frac{2}{7}+\sqrt{121}[/tex]
Step-by-step explanation:
Given: expressions
To find: expression that denotes a rational number
Solution:
A number of the form [tex]\frac{p}{q}[/tex] where p and q are integers and [tex]q\neq 0[/tex] is said to be a rational number.
Sum of a rational and irrational number is irrational.
In [tex]\frac{5}{9}+\sqrt{18}[/tex], [tex]\frac{5}{9}[/tex] is a rational number and [tex]\sqrt{18}[/tex] is an irrational number
So, [tex]\frac{5}{9}+\sqrt{18}[/tex] is not a rational number.
In [tex]\pi+\sqrt{16}=\pi+4[/tex], [tex]\pi[/tex] is an irrational number and 4 is a rational number
So, [tex]\pi+\sqrt{16}[/tex] is not a rational number.
In [tex]\frac{2}{7}+\sqrt{121}=\frac{2}{7}+11=\frac{2+77}{7}=\frac{79}{7}[/tex], [tex]\frac{79}{7}[/tex] is a rational number
So, [tex]\frac{2}{7}+\sqrt{121}[/tex] is a rational number
In [tex]\frac{3}{10}+\sqrt{11}[/tex], [tex]\frac{3}{10}[/tex] is a rational number and [tex]\sqrt{11}[/tex] is an irrational number
So, [tex]\frac{3}{10}+\sqrt{11}[/tex] is not a rational number.
Answer:
2 / 7 + 12
Step-by-step explanation:
he is right i just took the test i just wanna help more ..
If 35 gms of pure drug are contained in 150 mls, how many grams are contained in 75 mls?
Answer:
17.5
Step-by-step explanation:
The ratio of "pure drug" to liquid is 35:150
Therefore to evaluate for 75 mls we get the ratio 75/2150 or simply 1/2
we can then multiply 35 by the ratio 1/2
35/2=17.5
State the answer
In 75 mls there are 17.5 grams of pure drug
The amount of the pure drug in 75 ml will be 17.5 grams.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
The ratio of the two proportional items will remain the same.
The amount of the drug is directly proportional to the contained liquid.
If 35 gms of the pure drug are contained in 150 ml.
Then the amount of the pure drug in 1 ml will be
⇒ 35 / 150
⇒ 0.2333 grams per ml
Then the amount of the pure drug in 75 ml will be
⇒ 0.2333 x 75
⇒ 17.5 grams
The amount of the pure drug in 75 ml will be 17.5 grams.
More about the ratio and the proportion link is given below.
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Please answer correctly !!!!!! Will mark brainliest !!!!!!!!!!
Answer:
Sakura spoke for 2 minutes in Hungarian and for 3 minutes in Polish
Step-by-step explanation:
So make the variables.
Hungarian = x
Polish = y
x and y are the amount of time she spent in minutes.
x + y = 5
150x + 270 = 190y
x = 5 - y
750 - 150y + 270 = 190y
1020 = 340y
y = 3
x = 2
1. John is building a miniature model of a building on campus. The dimensions of
the building are 95 ft x 80 ft x 30 ft. The model is 1/10th the dimensions of the
building. Sketch the model, then find the volume of the model.
Answer:
228 ft^2
Step-by-step explanation:
1/10 of the given dimensions are 9.5 ft by 8 ft by 3 ft.
The volume of the model is thus (9.5 ft)(8 ft)(3 ft) = 228 ft^2
Solve the following equations.
28÷x+4=11
Answer:
x=-28/3
28/x=1-4
28/x=-3
28=-3x
-28/3=x
switch them around and that's your answer.
Answer:
x = 4
Step-by-step explanation:
28÷x+4=11
28/x + 4 = 11
Subtract 4 from each side
28÷x+4-4=11-4
28 / x = 7
Multiply each side by x
28/x * x = 7x
28 = 7x
Divide each side by 7
28/7 = 7x/7
4 =x
Can someone please help me please only do if you know how to do geometry thank you thank you thank you
Answer:
AAA would be the answer
Step-by-step explanation:
The answer would be AAA because they both have equal angles. 90 and 45. Because they are vertical angles, where they intersect at S is also an congruent angle. Angle U is congruent to angle Q and so on.
Answer:
AAA
Step-by-step explanation:
Pls answer. i will mark u as branliest
Answer:
120°
Step-by-step explanation:
you can divide the shape into 4 triangles
each triangle is 180°
180 x 4 = 720
720 divided by the number of angles (6) is 120
Answer:
120
Step-by-step explanation:
360/3=120
An equivalent expression for sin x is?
(please answer with steps)
Answer:
b
Step-by-step explanation:
Using the trigonometric identity
sin2x = 2sinxcosx
That is the angle on the right side is half the angle on the left, thus
sinΘ = 2sin([tex]\frac{1}{2}[/tex] Θ )cos([tex]\frac{1}{2}[/tex]Θ ) → b
help this is for special right triangles 30-60-90
Answer:
y = 10, x = 10sqrt3
Step-by-step explanation:
30-60-90 right triangles follow the ratio of x:xsqrt3:2x
In this case, 2x = 20, so y = x = 10, and x = xsqrt3 = 10sqrt3
If you are curious as to how to find these ratios, I suggest noticing that the 30-60-90 triangle is really just half of an equilateral triangle.
Answer:
x = 10sqrt(3) = 17.3
y = 10
Step-by-step explanation:
The ratio of the lengths of the sides of a 30-60-90 triangle is
short leg : long leg : hypotenuse
1 : sqrt(3) : 2
The short leg is half the hypotenuse.
hypotenuse = 20
short leg = y = 20/2 = 10
The long leg is sqrt(3) times the short leg.
long leg = x = 10sqrt(3) = 17.3
Solve the following inequality:
-5.3 > 1 – 2(-5x - 1)
Answer:
Submit Answers
Answer:
X< -1.26
Step-by-step explanation:
Combine like terms and solve like any other two step equations
Answer:
X< -1.26
Step-by-step explanation:
In triangle ABC points M and N lie on sides AB and BC, respectively such that MN∥ AC . Segments AN and CM intersect at point K and AK = KC. Prove that △ABC is isosceles.
Answer:
Try this solution, it consists of two parts (MN=8).
Step-by-step explanation:
Prove that the diagonals of kite UVWX are
perpendicular
Step 1: Determine the slope of XV.
The slope of XV is
Step 2. Determine the slope of UW
The slope of UW is
Step 3. The slopes of the diagonals are
The diagonals of kite UVWX are
Answer:
The answer is the slope of XV is 1.
The slope of UW is -1
The slopes of the diagonals are negative reciprocals
The diagonals of kite UVWX are perpendicular
Step-by-step explanation:
Negative reciprocals in a kite create a perpendicular bisector. So the two lines share a midpoint so they are perpendicular.
One of the diagonal of a kite has a slope that is equal to the inverse
multiplied by (-1) of the other, therefore the diagonals are perpendicular
Reasons:
The proof that the diagonals of a kite are perpendicular is as follows;
The properties of a kite are;
The lengths of adjacent sides are equal
Therefore, taking the vertex at , U, as the origin, we have;
Coordinates of U = (0, 0)
Coordinates of V = (-a, b)
Coordinates of W = (0, c)
Coordinates of X = (a, b)
Step 1:
[tex]\displaystyle The \ slope \ of \ XV = \mathbf{ \frac{b - b}{x - (-x)} }=0[/tex]
The slope of XV is 0; XV is a horizontal line.
Step 2:
[tex]\displaystyle The \ slope \ of \ UW = \mathbf{\frac{c - 0}{0 - 0}} =\infty[/tex]
The slope of UW is infinity; UW is a vertical line.
Step 3:
The slope of the diagonals are; m₁ = 0, and m₂ = ∞
The above values satisfy the equation, [tex]\displaystyle m_2 = \mathbf{-\frac{1}{m_1}}[/tex]
Therefore;
The diagonals of kite UVWX are perpendicularLearn more about the characteristics of a kite here:
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Need help !!! If f(x) = 3x+10 and g(x) = 5x-3,find (f+g)(x)
Answer:
8x+7
Step-by-step explanation:
Use the given functions to set up and simplify
(f+g)(x)
Answer:
8x + 7
Step-by-step explanation:
(f+g)(x)= f(x) +g(x) = 3x + 10 + 5x - 3 = 8x + 7
On a coordinate plane, a triangle has points R (negative 3, 4), T (negative 1, negative 4), and S (negative 4, negative 2). What are the coordinates of the image of vertex R after a reflection across the y-axis? (–4, 3) (4, –3) (–3, –4) (3, 4)
Answer:
(3,4)
Step-by-step explanation:
if the original is (-3,4) and its a reflection over a vertical line that's the y-axis, the x would become opposite, which would mean -3 becoming 3.
Given the coordinate of vertex R(-3, 4). If reflected over the y-axis, the resulting coordinate will be (3, 4)
Images that are reflected are mirror images of each other. The coordinate (x, y) reflected over the y-axis will have the resulting coordinate at (-x, y).
Note that reflecting over the y-axis negates the x-coordinate point while the y-coordinate stays the same.
Given the coordinate of vertex R(-3, 4). If reflected over the y-axis, the resulting coordinate will be (3, 4)
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Luca is designing a propeller system that consists of 3 blades, each of which is identical. The blades are sectors of a circle that have radii of 4 inches and central angles of 20 . The blades are to be made from steel that weighs 16 grams per square inch. Determine the weight of the three blades together to the nearest gram.
Answer:
Total weight of blades = ~134gm
Step-by-step explanation:
Radius of circle, [tex]r[/tex] = 4 inches
Central angle of sector = [tex]20^\circ[/tex]
For finding the weight of blades, we need to find the area of blades.
Area of circle, A = [tex]\pi r^{2}[/tex]
We know that circle has a central angle of [tex]360^\circ[/tex].
We can use unitary method to find the area of sector with angle [tex]20^\circ[/tex].
Area of [tex]360^\circ[/tex] central angle = [tex]\pi r^{2}[/tex]
Area of [tex]1^\circ[/tex] central angle = [tex]\dfrac{\pi}{360} r^{2}[/tex]
Area of [tex]20^\circ[/tex] central angle = [tex]\dfrac{\pi}{360} r^{2} \times 20[/tex]
Putting value of r = 4 inches
Area of blade:
[tex]\dfrac{\pi}{360} \times 4^{2} \times 20\\\Rightarrow 2.79\ in^{2}[/tex]
We have 3 blades here, so area of 3 blades =
[tex]2.79 \times 3\\\Rightarrow 8.38\ in^{2}[/tex]
Weight of steel = 16 grams per square inch
Total weight of all 3 blades = 16 [tex]\times[/tex] 8.38 = ~ 134gm
in a box of chocolates, 1/5 of the chocolates contain nuts. the rest of the chocolates do not contain nuts. write down the ratio of the number of chocolates that contain nuts to the number of chocolates that do not contain nuts. give your answer in the form 1:n
Answer:
The ratio of the number of chocolates that contain nuts to the number of chocolates = 1:4
Step-by-step explanation:
The parameters given are;
Proportion of the box of chocolates that contain nuts = 1/5
Proportion of the box of chocolates that do not contain nuts = 1 - 1/5 = 4/5
Therefore, we have in a box of chocolates with five chocolates;
The number of chocolates that contain nuts = 1
The number of chocolates that do not contain nuts = 4
Which gives the ratio of the number of chocolates that contain nuts to the number of chocolates as 1:4.