Answer:
x = 5 unit
NM = 20 unit
OL = 20 unit
Step-by-step explanation:
Given:
LMNO is parallelogram
NM = x + 15
OL = 3x + 5
Find:
x and NM and OL
So,
NM = OL
x + 15 = 3x + 5
2x = 10
x = 5
So,
NM = x + 15 = 5 + 15 = 20
OL = 3x + 5 =3(5)+5 = 20
#5) What is the slope of the line that passes through the points (6, -8) and (4,10)?
A)1/3
B)-1/9
C) - 9
D) -1
To determine the height of the volcano Mount Saint Helens, a surveyor measured the angle of elevation to the top of the volcano to be 34.8°. She then moved 1000 feet closer to the volcano and measured the angle of elevation to be 40.4° Determine the height of Mount Saint Helens to the nearest foot.
Answer:
The height is 3791 ft.
Step-by-step explanation:
You need to make a drawing. Start with a vertical segment, 2 inches long, on the left side of the page. Label the top point A and the bottom point B. At the bottom endpoint, draw a longer horizontal segment, 4 inches long, to the right. Label the bottom right endpoint C. Connect A and C with a segment. Angle C is the original angle of elevation. On the bottom horizontal side, approximately 1 inch to the left of C, draw point D. Connect D and A with a segment. DA = 1000 ft. m<C = 34.8°. m<ABD = 40.4°. We are looking for AB, the height of the volcano.
We can work on triangle ADC.
m<C = 34.8°
Angles ADB and ADC are a linear pair, so m<ADC = 180° - 40.4° = 139.6°
m<DAC + m<ADC + m<C = 180°
m<DAC + 139.6° + 34.8° = 180°
m<DAC = 5.6°
Using the law of sines, we can find AC.
[tex] \dfrac{\sin A}{a} = \dfrac{\sin B}{b} [/tex]
[tex]\dfrac{\sin 5.6^\circ}{1000} = \dfrac{\sin 139.6^\circ}{AC}[/tex]
[tex]AC = \dfrac{1000\sin 139.6^\circ}{\sin 5.6^\circ}[/tex]
[tex] AC = 6642~ft [/tex]
Now we use triangle ABC. AC = hypotenuse. AB = opposite leg. <C is known angle.
[tex] \sin C = \dfrac{opp}{hyp} [/tex]
[tex]\sin 34.8^\circ = \dfrac{AB}{6642~ft}[/tex]
[tex]AB = 6642~ft \times \sin 34.8^\circ[/tex]
[tex] AB = 3791~ft [/tex]
Answer: The height is 3791 ft.
given AC with A(3,4) and C(-9,-2) if B partitions AC such that the ratio of AB to BC is 1:5 find the coordinates of B.
Answer:
The co-ordinates of B (1,3 )
Step-by-step explanation:
Step(i):-
Given A( 3,4) and C( -9, -2)
Given 'B' partition AC such that
B divides AC in the ratio is 1:5 internally
Section formula
[tex](\frac{mx_{2}+nx_{1} }{m+n} ,\frac{my_{2}_+ny_{1} }{m+n} )[/tex]
Step(ii):-
Given points are
A( 3,4) and C( -9, -2) and ratio 1 : 5
(x₁ , y₁) = ( 3,4) and (x₂, y₂) = (-9,-2)
m:n = 1 : 5
The co-ordinates of B
= [tex](\frac{1(-9)+5(3) }{1+5} ,\frac{1(-2)+5(4) }{1+5} )[/tex]
= [tex](\frac{6}{6} , \frac{18}{6} )[/tex]
= (1 , 3)
Final answer:-
The co-ordinates of B (1,3 )
the formula for the sum of the degree measures of the interior angles of a polygon is S=180(n-2) Solve for ,n, the number of sides of the polygon, in terms of S
NEED STEP BY STEP EXPLANATION
Answer:
n = (S + 360)/180Step-by-step explanation:
Given formula:
S = 180(n - 2)Solving for n:
S = 180(n - 2) ⇒ open parenthesisS = 180n - 360 ⇒ isolate n180n = S + 360 ⇒ divide both sides by 180n = (S + 360)/180[tex]S = 180(n - 2) \\ S = 180n - 360 \\ 180n =( S + 360) \\ n = \frac{(S+ 360)}{180} [/tex]
where, n =number of sides of polygon
S =sum of the degree measures of the interior angles of the polygon
Solve the equation 0.3 3=n
n=_____
Coffee costs $1.75 a pound. How much would 3.2 pounds of coffee cost?
Answer:
$5.60
Step-by-step explanation:
So each pound equals to $1.75 which means that we need to multiply by 3.2 because we're trying to find the number of money we'll spend on a certain amount of coffee. So if we multiply, we get 5.6. Though in context with the problem, it should be $5.60.
The sum of two numbers is 58. If there difference is 28, find both numbers
Answer:
y = 15
x = 43
Step-by-step explanation:
this is giving us a system of equations because we know two things:
x + y = 58
x - y = 28
take the second equation and format it where you have simplified it for one variable:
x = 28 + y
(we did this by adding y to both sides)
now substitute this new value of x into the first equation:
28 + y + y = 58
simplify this to get 2y = 30
divide both sides by 2: y = 15
now substitute your new value of y into the second equation:
x = 28 + 15
x = 43
Pls help and SHOW WORKINGS it due asap.
Answer:
C
Step-by-step explanation:
The x coordinate of the rest stop:
1/2 × (the sum of the x coordinates of the highschool and the stadium)
= 1/2 × (3+7)
= 1/2 × 10
= 5
The y coordinate of the rest stop:
- Same thing i did for the x coordinate, but use the y coordinates.
1/2 × (the sum of the y coordinates of the highschool and the stadium)
= 1/2 × (4 + 1)
= 1/2 × 5
=5/2
So the coordinate of the rest stop would be (5, 5/2).
Next for the distance, i used the pythagoras theory so it's like this:
a^2 + b^2 = c^2
Here you plot the highschool and the stadium on the coodinate plane, then connect the two dots to make a right triangle. The height of the triangle will be 3, and the base would be 4. So a=3, b=4 in the equation.
3^2 + 4^2 = c^2
9 + 16 + c^2
25 + c^2
c = 5
(Note that this isn't the real answer cuz at the end of the question it said that one UNIT equals 6.4 MILES.)
So the final answer is 5 × 6.4, which is 32. The answer is C.
PLLLZZZZZZ HELPPPP FASTTTTTT
Answer:
I think it's the y-function. Are there any choices to choose from?
Step-by-step explanation:
Answer:
They increase at the same rate
Step-by-step explanation:
If you look at linear function p, the equation is y=3x-6
Tara plans to rent a car for the weekend. The cost is $45 plus $0.15 for each mile she drives. Write an equation that represents this situation and describe the variables.
Answer:
y = 45 + 0.15x
Step-by-step explanation:
$45 is the initial cost
0.15 is the cost for each mile
we dont know the miles so miles is x, unknown
Hi. I need help with this question (see image). Please show workings.
Answer:
[tex]\frac{dy}{dx}[/tex] = 8(2x + 3)³
Step-by-step explanation:
Differentiate using the chain rule
Given
y = f(g(x)) , then
[tex]\frac{dy}{dx}[/tex] = f'(g(x)) × g'(x)
Here
f(x) = [tex](2x+3)^{4}[/tex] ⇒ f'(x) = 4(2x + 3)³
g(x) = 2x + 3 ⇒ g'(x) = 2
Thus
[tex]\frac{dy}{dx}[/tex] = 4(2x + 3)³ × 2
= 8(2x + 3)³
The coordinates of three vertices of a square A (-2 1/2 , 1 1/2), B (-2 1/2 -3), and C (2,1 1/2 when point D is placed on this square what will the perimeter of the square be?
Answer:
The perimeter of square will be 18 units
Step-by-step explanation:
We are given that the coordinates of three vertices of a square A (-2 1/2 , 1 1/2), B (-2 1/2 -3), and C (2,1 1/2 )
When point D is placed on this perimeter.
We have to find the perimeter of the square.
First we have to find the side of square by using the distance formula
Distance formula
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Coordinates of A=(-5/2,3/2)
Coordinates of B=(-5/2,-3)
Length of side AB=[tex]\sqrt{(-5/2+5/2)^2+(-3-3/2)^2}[/tex]
Length of side AB=[tex]\sqrt{0+(-9/2)^2}[/tex]
Length of side AB=9/2 units
Now, the perimeter of square=4 (side)
Using the formula
Perimeter of square=4(9/2)=18 units
Solve for f: ax+3b=2f
Final Answer: [tex]f = \frac{ax}{2} + \frac{3b}{2}[/tex]
Steps/Reasons/Explanation:
We will be trying to rewrite the equation. To do this we will move [tex]2f[/tex] to the left. Then, we will move [tex]ax + 3b[/tex] to the right.
Question: Solve for [tex]f[/tex]: [tex]ax + 3b = 2f[/tex].
Step 1: Rewrite the equation.
[tex]2f = ax + 3b[/tex]
Step 2: Divide each term by [tex]2[/tex] and simplify.
[tex]\frac{2f}{2} = \frac{ax}{2} + \frac{3b}{2}[/tex]
Step 3: Cancel out the common factor of [tex]2[/tex].
[tex]\frac{Cancel 2 f}{Cancel 2} = \frac{ax}{2} + \frac{3b}{2}[/tex]
Step 4: Divide [tex]f[/tex] by [tex]1[/tex].
[tex]f = \frac{ax}{2} + \frac{3b}{2}[/tex]
~I hope I helped you :)~
Question: How many solutions: x + 2y = 6 and 2x − 3y = 26
Answers/Answers to choose from:
One-Solution
Infinitely Many Solutions
Or No Solution
(Basically does the question have only one solution, infinitely many solutions, or does it have no solution) Please don't guess
Answer:
one-solution
Step-by-step explanation:
(x + 2y = 6)2
2x - 3y = 26
2x + 4y = 12
2x - 3y = 26
7y = -14
y = -2
x + 2(-2) = 6
x + -4 = 6
x = 10
Answer:
One-SolutionStep-by-step explanation:
It is two lines, if they intersect there is one solution, if parallel- no solution, if same lines- infinitely many solutions
Lets put them in slope-intercept form and compare:
x + 2y = 6 ⇒ 2y = -x + 6 ⇒ y = -1/2x + 32x - 3y = 26 ⇒ 3y = 2x - 26 ⇒ y = 2/3x - 26/3As we see the lines have different slopes, so they intersect which means one solution only.
I need help on this question.
Answer:
1410
Step-by-step explanation:
they said they would spend 3000 more than last year. it said this years budget is 4410.
please help me please
Answer:
change/original price X 100
22/88 X 100 = 25%
Q2
A car travels at 72 mph for 3 hours and 40 minutes.
How far has it travelled?
miles
[2]
8
Answer:
264 miles
Step-by-step explanation:
Let's convert 3 hours and 40 minutes into hours first.
Recall that 1 hour = 60 minutes.
Therefore 40 minutes = 40/60 hours = 2/3 hours.
The car travelled 3 and 2/3 hours in total.
Recall that distance = speed times time.
The car has travelled 72 x 3 2/3 miles = 264 miles.
Locate and label (4,5) and (4, -3), Draw the line segment between
the end points given on the coordinate plane. How long is the line
segment that you drew? Explain.
Given:
The two endpoints are (4,5) and (4,-3).
To find:
The line segment between the given endpoints and the length of the line segment.
Solution:
Plot the given point and connect them by and straight line segment as shown in the below graph.
The distance between (4,5) and (4,-3) is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]d=\sqrt{(4-4)^2+(-3-5)^2}[/tex]
[tex]d=\sqrt{(0)^2+(-8)^2}[/tex]
[tex]d=\sqrt{0+64}[/tex]
[tex]d=\sqrt{64}[/tex]
[tex]d=8[/tex]
Therefore, the length of the line segment is 8 units.
Lin and Elena have discovered they have so much in common. They each have a fish tank holding 20 units of water. Whose tank holds 20 gallons, and whose holds 20 cups?
Answer: a. Lin's tank hold 20 cups and Elena's tank hold 20 gallons; I know this because gallons are greater than cups.
Step-by-step explanation:
Gallons are greater than cups so the fish tank that will hold 20 gallons would have to be the bigger one which in this case is Elena's.
With cups being lesser in quantity than gallons, the fish tank that will hold 20 cups of water will definitely have to be the smaller one which in the case is Lina's.
Please help me with the questions please
Answer:
50,373 feet
Step-by-step explanation:
tan 15° = 13500 / x
.268 = 13500 / x
x = 50,373
Please help!!
Each pair of polygons is similar. Find the value of x.
Answer in fraction form: x = 55/4
Answer in decimal form: x = 13.75
Both forms are equivalent, but they say it in a slightly different way.
===========================================================
Work Shown:
AC/QY = CD/YW
(x+5)/15 = 5/4
4(x+5) = 15*5
4x+20 = 75
4x = 75-20
4x = 55
x = 55/4
x = 13.75
------------
Explanations:
The first step is possible because the polygons are similar. Similar figures have their corresponding sides be in the same proportion or ratio. Note how side AC has the double red angle (at point A) and a single red angle (point C). The side QY has the same idea in the same order. This is why AC corresponds to QY. The ratio AC/QY is the same as CD/YW.In the second step, I plugged in the expressions that the diagram shows. This is the substitution property.On step 3, I cross multiplied. The general format is A/B = C/D cross multiplies to A*D = B*C.-5 = -3(x + 11) HELPP
Answer: x=9 1/3
Step-by-step explanation:
-5=-3x-33
-5+33=-3x
28=-3x
3x=-28
x=28/3
x=9 1/3
Answer: X=-28/3
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
−5=−3(x+11)
−5=(−3)(x)+(−3)(11)(Distribute)
−5=−3x+−33
−5=−3x−33
Step 2: Flip the equation.
−3x−33=−5
Step 3: Add 33 to both sides.
−3x−33+33=−5+33
−3x=28
Step 4: Divide both sides by -3.
-3x/-3= 28/-3
X=-28/3
have a nice day :)
Identify the slope in the equation y=-7/3x +5 5 -5 7/3 -7/3
Answer:
-7/3
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
y = -7/3x + 5
Step 2: Break Function
Identify Parts
Slope m = -7/3
y-intercept b = 5
Which set of ordered pairs represents a function?
( Please help me with this as soon as possible )
Answer:
B
Step-by-step explanation:
i did the same test
4. Chrissy had 4 gallons of gas in her tank when she arrived at the
gas station. She pumped gas into her car at a rate of 0.3 gallon per
second. How many gallons of gas were in the tank after s seconds?
Solve: (a-7)(a+1) = 0
Answer:
0
Step-by-step explanation:
Answer:
a = −1 or a = 7
Step-by-step explanation:
Let's solve your equation step-by-step.
( a − 7 ) ( a + 1 ) = 0
Step 1: Simplify both sides of the equation.
a^2 − 6a − 7 = 0
Step 2: Factor left side of equation.
( a + 1 ) ( a − 7 ) = 0
Step 3: Set factors equal to 0.
a + 1 = 0 or a − 7 = 0
a = −1 or a = 7
Given f(x) = –x– 5, solve for a when f(x) = -3.
Answer:
-2
Step-by-step explanation:
f(x) = –x– 5
f(x) = -(-3)– 5
f(x) = 3– 5
f(x) = -2
Answer:
Answer is -2 because - * - = + 3-5=-2
plss help
7. (a) how many 3-digit positive numbers are there?
(b) how many 4-digit positive numbers are there?
Answer:
a) 900
b) 9,000
Step-by-step explanation:
Answer:
Step-by-step explanation:
A. a=100. an=999
an=a+n-1.d
Therefore answer will be 900.
B. 9000.
Read the ratio as a fraction in simplest form 3611 and 12 odd
Answer:
3611/12
Step-by-step explanation:
y = -x +2
7x + 4y = -1
What is the value of y for the solution to this system of equations?
Answer:
Hi! The correct answer is y = 5
Step-by-step explanation:
~Solve for the first variable in one of the equations, then substitute the result into the other equation~