Which point on the x-axis lies on the line that passes through point P and is perpendicular to line MN?
(0, 1)
(0, 4)
(1, 0)
(4, 0)
Answers
1. Points M and N have coordinates (-4,0) and (4,2), respectively.
Then vector [tex]\overrightarrow{MN}=(4-(-4),2-0)=(8,2)[/tex] is perpendicular to the neede line.
2. Write the equation of line that passes through the point P(2,-4) and is perpendicular to vector [tex]\overrightarrow{MN}=(8,2):[/tex]
[tex]8(x-2)+2(y+4)=0,\\8x-16+2y+8=0,\\8x+2y-8=0,\\4x+y-4=0.[/tex]
3. Find the point on x-axis, that lies on the perpendicular line.
When y=0, then 4x-4=0, x=1 and point (1,0) lies on perpendicular line.
Answer: correct choice is C.
Related Questions
Which is the best unit to use for measuring the length of an eyelash millimeters C centimeters B meters or D kilometers
Answers
The best unit for the measurement of length of eyelash is millimeters
A fundamental unit of measurement is a unit of measurement in which other units are derived from, it includes length often expressed as follows;
kilometers; for large distancesmeters for large lengths of objectscentimeters; for small distances or lengths of objectsmillimeters; for relatively small lengths, like keys, eyelashes etcThus, the best unit for the measurement of length of eyelash is millimeters
Learn more here: https://brainly.com/question/24161150
Christina can paint 420 square feet in 105 minutes. Which unit rate describes the scenario?
4 square feet per minute
square foot per minute
1 square foot per 4 minutes
1 square foot per minute
Answers
divide total sq ft x total minutes to get square feet per minute
420/105 = 4
so 4 sq ft per minute
The Fenton College Cougars made 40 field goals in a recent basketball game some 2 pointers and the rest 3 pointers. Altogether the 40 baskets counted for 89 points. how many of each type of field goal was made?
Answers
x + y = 40.....x = 40 - y
2x + 3y = 89
2(40 - y) + 3y = 89
80 - 2y + 3y = 89
-2y + 3y = 89 - 80
y = 9 <=== there were 9 three-point shots
x = 40 - y
x = 40 - 9
x = 31 <=== there were 31 two-point shots
There are 117 staff members in your school. 1/3 of them are going away for the Thanksgiving holiday. How many staff members are not traveling?
This was the main question but i didnt get how to solve it.. (wasnt sure if subtraction was thr right way)
Answers
117 - 39 = 78
78 staff members are not leaving for Thanksgiving.
Which is the better estimate of the weight of a football helmet
Answers
Probably 3 - 5 pounds.
Hope this helps :))
~Top
Rewrite 21/300 as a decimal.
Answers
What is the value of mc016-1.jpg?
-20
-4
4
20
the pic is the .jpg
Answers
(4-2)^3 -3*4 =
(4-2) = 2, 2^3 = 8
3*4 =12
so you have 8-12 = -4
Answer is -4
Explanation:
This question's it's about the order of operations. It stands for parenthesis, exponents, multiply, divide, add, and subtract. It can also go left too right. (PEMDAS)
First, do parenthesis.
[tex](4-2)=2[/tex]
[tex]2^3-3*4[/tex]
Then exponents.
[tex]2^3=2*2*2=8[/tex]
[tex]8-3*4[/tex]
Multiply left to right.
[tex]3*4=12[/tex]
Subtract left to right.
[tex]8-12[/tex]
[tex]12-8=4[/tex]
It change positive to negative sign.
Answer: → [tex]\boxed{=-4}[/tex]
*The answer must have a negative sign.*
Hope this helps!
Thank you!
-Charlie
A surveyor took the following measurements from two irregularly shaped pieces of land. Some of the lengths and angle measures are missing. Find all missing lengths and angle measures. Round lengths to the nearest tenth and angle measures to the nearest minute
Answers
To find angle D, we make use of the rule of Sines because we know the measure of the side opposite angle D and we also know the meansure another angle of the triangle with the measure of the side opposite the angle.
Thus, we find angle D as follows:
[tex] \frac{62}{\sin{D}} = \frac{51}{\sin{53^o}} \\ \\ \Rightarrow \sin{D}= \frac{62\sin{53^o}}{51}} \\ \\ = \frac{49.5154}{51} =0.9709 \\ \\ \Rightarrow D=\sin^{-1}{0.9709} \\ \\ =76.14^o=76^o8'[/tex]
Therefore, angle D is 76°8'
Part B:
To find angle E, recall that the sum of the angles in a triangle is 180°.
Thus, 53° + 76°8' + E = 180°
E = 180° - 53° - 76°8' = 50°52'
Therefore, angle E is 50°52'
Part C:
To find the measure of side e, we apply the cosine rule as follows:
[tex]e^2=51^2+62^2-2(51)(62)\cos{50^o52'} \\ \\ =2,601+3,844-2,098.85=3,991.25 \\ \\ \Rightarrow e=\sqrt{3,991.25}=63.18[/tex]
Therefore, the measure of side e is 63.2
Part D
To find angle G, we make use of the rule of Sines because we know the measure of the side opposite angle G and we also know the measure another angle of the triangle with the measure of the side opposite the angle.
Thus, we find angle G as follows:
[tex]\frac{80}{\sin{G}} = \frac{62}{\sin{49^o}} \\ \\ \Rightarrow \sin{G}= \frac{80\sin{49^o}}{62} \\ \\ = \frac{60.3768}{62} =0.9738 \\ \\ \Rightarrow G =\sin^{-1}{0.9738}=76.86^o=76^o52'[/tex]
Therefore, angle G is 76°52'
Part E:
To find angle H, recall that the sum of the angles in a triangle is 180°.
Thus, 49° + 76°52' + H = 180°
H = 180° - 49° - 76°52' = 54°14'
Therefore, angle H is 54°14'
Part F:
To find the measure of side a, we apply the cosine rule as follows:
[tex]a^2=80^2+62^2-2(80)(62)\cos{54^o14'} \\ \\ =6,400+3,844-5,798.10=4,445.90 \\ \\ \Rightarrow a=\sqrt{4,445.90}=66.68[/tex]
Therefore, the measure of side a is 66.7
Part G:
To find angle A, we make use of the rule of Sines because we know the measure of the side opposite angle A and we also know the measure another angle of the triangle with the measure of the side opposite the angle.
Thus, we find angle A as follows:
[tex]\frac{66.7}{\sin{A}} = \frac{30}{\sin{25^o54'}} \\ \\ \Rightarrow \sin{A}= \frac{66.7\sin{25^o54'}}{30} \\ \\ = \frac{29.1347}{30} =0.9712 \\ \\ \Rightarrow A =\sin^{-1}{0.9712}=76.21^o=76^o12'[/tex]
Therefore, angle A is 76°12'
Part H:
To find angle B, recall that the sum of the angles in a triangle is 180°.
Thus, 25°54' + 76°12' + B = 180°
B = 180° - 25°54' - 76°12' = 77°53'
Therefore, angle B is 77°53'
Part I:
To find the measure of side b, we make use of the rule of sines
Thus, we find side b as follows:
[tex]\frac{b}{\sin{77^o53'}} = \frac{30}{\sin{25^o54'}} \\ \\ \Rightarrow b= \frac{30\sin{77^o53'}}{\sin{25^o54'}} \\ \\ = \frac{29.3317}{0.4368} =67.15[/tex]
Therefore, the measure of side b is 67.2
To find the width of the river, use trigonometry and the tangent function. The width of the river is approximately 67.1 meters.
Explanation:To find the width of the river, we can use trigonometry. The surveyor measured an angle of 35° from the baseline to the tree on the opposite bank. We know the distance along the river is 100 m. Let's denote the width of the river as 'x'.
We can use the tangent function to solve for 'x'. The tangent of the angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is 'x' (the width of the river) and the adjacent side is 100 m (the distance along the river).
So, the equation becomes:
tan(35°) = x/100
To find the value of 'x', we can multiply both sides by 100:
x = 100 * tan(35°)
Using a calculator, we can find that x is approximately 67.1 m. Therefore, the width of the river is approximately 67.1 meters.
What is 5.8×2.4?
Show your work
What grade if u like this you will get 24 points
.
.
Answers
1. put 5.8*2.4 into a standard algorithm. which will look like this.
5.8
x 2.4
---------
232
+1160
--------
13.92 hope that helped
If you add 20% of a number to the number itself what percent of the result would you have to subtract
Answers
1/6 = 16.667%
Texaschic101
Help please
Answers
Obviously the mean and median aren't shown.
So in this case it would be the first one, since the second bar isn't including 9, so it wouldn't include 9, so we wouldn't know how many of 10-14 are 9s, so we don't know that.
So it would have to be the first one.
boa saved $179 a month. he saved $145 less than ada each month. how much would ada save in three and a half years?
Answers
three and a half years is 42 months
42 months times 324
13608
It says Boa's savings each month are "$145 less than Ada", so we need to add 179 to 145. 179+145 = 324.
Okay, so now we know the amount of Ada's savings per month, we need to find out how much money she would have in 3 and a half years. 12 months is equal to one year. A half a year is 6 months. Three whole years is 36 months, and 6 months added to that is 42 months.
Since $324 represents only one month, and we want 42 months, we need to multiply 324 by 42. 324*42 = $13608. $13608 is what Ada saved within 3 years and a half.
Find the limit, if it exists, or type dne if it does not exist.
a. \displaystyle\lim_{(x, y) \rightarrow (0, 0)} \frac{(x + 23y)^2}{x^2 + 529y^2} =
Answers
Suppose we choose a path along the [tex]x[/tex]-axis, so that [tex]y=0[/tex]:
[tex]\displaystyle\lim_{x\to0}\frac{x^2}{x^2}=\lim_{x\to0}1=1[/tex]
On the other hand, let's consider an arbitrary line through the origin, [tex]y=kx[/tex]:
[tex]\displaystyle\lim_{x\to0}\frac{(x+23kx)^2}{x^2+529(kx)^2}=\lim_{x\to0}\frac{(23k+1)^2x^2}{(529k^2+1)x^2}=\lim_{x\to0}\frac{(23k+1)^2}{529k^2+1}=\dfrac{(23k+1)^2}{529k^2+1}[/tex]
The value of the limit then depends on [tex]k[/tex], which means the limit is not the same across all possible paths toward the origin, and so the limit does not exist.
Which of these is equivalent to 3-23-2?
Answers
Answer:
-22
Step-by-step explanation:
This is a case of directed numbers. The numbers 23 and 2 carry negative signs like this:
- 23
- 2
Therefore, adding these negative numbers gives -23 - 2 = -25
Adding the sum to 3 gives: 3 - 25 = -22
Cell phones can weigh as little as 2 ounces. How many pounds can the cell phone weigh?
Answers
2/16= .125
.125 pounds
A cell phone weighing 2 ounces translates to 0.125 pounds, since there are 16 ounces in one pound.
Explanation:Cell phones can weigh as little as 2 ounces. The first step in determining how much a cell phone can weigh in pounds is to know the conversion factor between ounces and pounds. Since there are 16 ounces in one pound, you can divide the weight of the cell phone in ounces by 16 to convert it to pounds. For a cell phone that weighs 2 ounces:
Divide the weight in ounces by 16 to convert to pounds: 2 ounces ÷ 16 = 0.125 pounds.Therefore, a cell phone that weighs 2 ounces is equivalent to 0.125 pounds.
a 6-pack of capri-Suns costs $8.80 .How much would a 24-pack cost if the costs are proportional
Answers
in a 24-pack, there are 24 bottles, 24-pack.
so, if 6 bottles, cost 8.80, how much will it be for 24 bottles then?
[tex]\bf \begin{array}{ccll} bottles&price\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 6&8.80\\ 24&p \end{array}\implies \cfrac{6}{24}=\cfrac{8.80}{p}\implies p=\cfrac{24\cdot 8.80}{6}[/tex]
Write each equation in slope intercept form 5x+3y=30
Answers
In order to get x to the other side, you subtract it on both sides.
3y = -5x + 30
But in slope intercept form, y can’t have any number in front of it. To get rid of the number, divide both sides by 3
y = -5x/3 + 6
Jackie deposited $315 into a bank account that earned 1.5% simple interest each year.
If no money was deposited into or withdrawn from the account, how much money was in the account after 3 years?
Round your answer to the nearest cent.
Enter your answer in the box.
Answers
Answer: Its 329.18 just took a test.
8 Times 43 In expanded form
Answers
100×34 10×4 1×4 = 344 which is your answer. Hoped this helped! If you need any help just ask me! I am here to help!
Rosey
Can someone help me if anyone know. Please, thanks
Answers
Suppose θ is an angle in the fourth quadrant with cosθ=x/4. Find expressions for the other five trig functions in terms of x?
Answers
now, we know the angle is in the IV quadrant, that means, the cosine is positive and the sine is negative, or "x" is positive whilst "y" is negative.
[tex]\bf cos(\theta )=\cfrac{\stackrel{adjacent}{x}}{\stackrel{hypotenuse}{4}} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{4^2-x^2}=b\implies \stackrel{IV~quadrant}{-\sqrt{16-x^2}=b}\\\\ -------------------------------[/tex]
[tex]\bf sin(\theta)=\cfrac{-\sqrt{16-x^2}}{4} \qquad cos(\theta)=\cfrac{x}{4} \qquad % tangent tan(\theta)=\cfrac{-\sqrt{16-x^2}}{x} \\\\\\ % cotangent cot(\theta)=\cfrac{x}{-\sqrt{16-x^2}} \qquad % cosecant csc(\theta)=\cfrac{4}{-\sqrt{16-x^2}} \qquad % secant sec(\theta)=\cfrac{4}{x}[/tex]
now, for the cotangent and the cosecant, let's rationalize the denominator,
[tex]\bf cot(\theta)=\cfrac{x}{-\sqrt{16-x^2}}\cdot \cfrac{\sqrt{16-x^2}}{\sqrt{16-x^2}}\implies cot(\theta)=-\cfrac{x\sqrt{16-x^2}}{16-x^2} \\\\\\ csc(\theta)=\cfrac{4}{-\sqrt{16-x^2}}\cdot \cfrac{\sqrt{16-x^2}}{\sqrt{16-x^2}}\implies csc(\theta)=-\cfrac{4\sqrt{16-x^2}}{16-x^2}[/tex]
Each package of dried fruit contains 3/16 of a pound Mr. Lopez has 4 pounds of dried fruit How many packages can he fill
Answers
Final answer:
Mr. Lopez can fill 21 full packages of dried fruit, each containing 3/16 of a pound, with his 4 pounds of dried fruit.
Explanation:
The question asks how many packages of dried fruit Mr. Lopez can fill if each package contains 3/16 of a pound and he has 4 pounds of dried fruit. To answer this, we need to perform a division to find out how many 3/16 are in 4 pounds.
To solve this, we divide 4 pounds by 3/16 pounds per package:
4 ÷ (3/16) = (4/1) ÷ (3/16) = (4 × 16) / 3 = 64/3 = 21 with remainder 1.
Therefore, Mr. Lopez can fill 21 full packages of dried fruit and will have a little left over which is not enough to fill an additional full package.
A hair salon charges fixed rate of $25.00 for a haircut and then an additional $15.00 for any other services. Write a function to model cost of services there and then determine how many services you had if you were charged for $115.00
Answers
Answer:
f(x) = 15x + 25; f(6) = 115
Step-by-step explanation:
the flat rate of $25 will be the y-intercept and the slope will be $15. since u are charged $115, plug that in for f(x) and solve for x. so the right answer is
f(x) = 15x + 25; f(6) = 115
What is the molar solubility of magnesium fluoride in a solution that is 0.40 m f− ions? the ksp of mgf2 is 6.4 × 10−9. hints what is the molar solubility of magnesium fluoride in a solution that is ions? the of is . 8.0 × 10−9 8.0 × 10−5 1.6 × 10−8 4.0 × 10−8?
Answers
The molar solubility of magnesium fluoride in a solution with a concentration of 0.40 M fluoride ions is 0.80 M.
Explanation:The molar solubility of magnesium fluoride in a solution with a concentration of 0.40 M fluoride ions can be calculated using the solubility product constant (Ksp) of MgF2, which is 6.4 × 10-9.
First, write the dissolution equation for MgF2: MgF2(s) ⇌ Mg2+(aq) + 2F-(aq)
Since the stoichiometry of the dissolution equation is 1:2 between magnesium ions and fluoride ions, the molar solubility of MgF2 is twice the concentration of fluoride ions.
Therefore, the molar solubility of MgF2 in a solution that is 0.40 M fluoride ions is 2 × 0.40 M = 0.80 M.
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The complement of 17% is
Answers
Answer:
73%.
Step-by-step explanation:
Let x be the complement of 17%.
We are asked to find the complement of 17%.
We know that two angles are complementary when they add up-to 90 degrees. So we can set an equation as:
[tex]17\%+x=90\%[/tex]
[tex]17\%-17\%+x=90\%-17\%[/tex]
[tex]17\%-17\%+x=73\%[/tex]
Therefore, the complement of 17% is 73%.
The depths of water, at the edge of a pier, at different times of day, are represented by the table below. Which of the following functions best models the depths of the water?
Answers
Unfortunately, the two only ways to solve this problem are to either graph all the options or plug in time values for x and see which agrees the most with the tide chart. Both are time-consuming, but I chose to graph each one with a graphing application.
Plugging in a few values for x confirms that C is the best function.
12pm (x=0)
y = 4.75 * cos(0 - 2.08) + 7.65
y = 5.334
2pm (x=2)
y= 6.5
4pm (x=4)
y=12.4
It is not a perfect representation, but the shape of the graph and closeness to the points given is the best of the four options provided.
Take apart an addend to solve 35+27
Answers
35 + 27
= 32 + 3 + 27
= 32 + 30
= 62
Find three points that solve the equation , -5x-3y=-7
Answers
[tex]- \frac{7+5x}{-3} =y[/tex]
To make this really simple, we can make 7+5x equal to factors of -3. For example, -3*2=-6. If we have 7+5x=-6, we can subtract 7 to both sides to get -13=5x. Next, we can divide both sides by 5 to get x=-13/5. Since 7+5x=-6, we can plug that into
[tex]- \frac{7+5x}{-3} =y[/tex]
to get (-6)/(-3)=2=y. I challenge you to find the other two points on your own - good luck!
What is a transformation and 3 types of transformations.
Answers
There are four transformations
translation
rotation
reflection
dilation
translation, rotation and reflection do not change the shape or the size of the shape and are known as rigid motions
The four types:
Dilation: Change of size.
Rotation: A clockwise turn in each of the four quadrants in a graph.
Translation: Simply relocating the shape.
Reflection: Mirroring the shape across either the y or x axis.
Hope that helps!
Name the triangle with the following characteristics. Sides: 5 cm, 5 cm, 7 cm.
A. scalene triangle B. acute triangle C. isosceles triangle D. right triangle
HELP ASAP