The system of equation has an infinitely many solutions
How to solve the system of equations?The equations are given as:
2x + y = -3
-2y = 6 + 4x
Express 2x + y = -3 in slope-intercept form
y = - 3 -2x
Divide through by -2 in -2y = 6 + 4x
y = -3 - 2x
So, we have:
y = - 3 -2x and y = -3 - 2x
Both equations are the same.
This means that the system of equation has an infinitely many solutions
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Please help with this question
Answer:
4
Step-by-step explanation:
the second column and the second row so, the answer is 4
1. In a class of 24, 3 students were absent, What fraction of class is present
2. Karen taped a television show that lasted 1h 30mins. On the same tape she recorded another 2 shows that were 5/6h each. What time was still left on the 4h tape.
3. Steve ordered 12 lengths of timber, each 6m long. He cut 6 lengths into 1 1/2m pieces and the other 6 lengths into 3/4 pieces A. How many pieces together is this? B. Was there any waste?
Problem 1
Answer: 7/8 of the class is presentReason:
24 people total with 3 absent. So 24-3 = 21 are present
21/24 = (7*3)/(8*3) = 7/8
==========================================================
Problem 2
Answer: 50 minutes left on the tape.Work Shown:
1 hour = 60 min
(5/6)*(1 hour) = (5/6)*(60 min)
5/6 of an hour = 50 min
1 hr + 30 min = 60 min + 30 min = 90 min
The first show is 90 minutes. Add on two more shows that are 50 min each to get 90+50+50 = 190 minutes used up
4 hours = 4*60 = 240 min
240 - 190 = 50 min
There are 50 minutes left on the tape.
==========================================================
Problem 3
Answer: 72 pieces; not enough info to calculate the wasteExplanation:
1 1/2 = 1 + 1/2 = 1 + 0.5 = 1.5
6/(1.5) = 4
Each 6 meter board is cut into 4 equal pieces each 1.5 meters long
There are 6 boards this applies to which means so far that's 6*4 = 24 pieces
Now to the other 6 boards.
3/4 = 0.75
6/(0.75) = 8
Each of the other 6 boards are cut into 8 equal pieces of 0.75 meters each
That's another 6*8 = 48 pieces
In total there are 24+48 = 72 pieces
When cutting into wood, there always is a small sliver that is discarded. While small, these slivers do add up. So yes there is some waste. Unfortunately, we don't have enough info to calculate. We would need to know the width of the saw blade.
help its TIMED
WHICH OF THE FOLLOWING MAY BE TRUE ABOUT f(x)
All three are possible.
The table tells us that for certain x and y, we have f(x) < f(y) if x < y. There's also no evidence that f(x) = f(y) for some points x ≠ y in the interval, so f(x) could easily be monontonically increasing. (I is true)
If we assume f(x) is strictly increasing (which does not contradict the given table) on the entire interval, we have f'(x) > 0. A positive function can be strictly increasing. (II is true)
A function is concave up on an interval if its derivative is increasing on that interval. This follows from statement (II) if it happens to be true. (III is true)
(E)
if 13 sin θ=12 cos θ, find the value
From the given information, we have
[tex]13\sin(\theta) = 12\cos(\theta) \implies \dfrac{\sin(\theta)}{\cos(\theta)} = \dfrac{12}{13}[/tex]
In the expression of interest, divide through everything by [tex]\cos^2(\theta)[/tex] to get
[tex]\dfrac{2\sin(\theta)\cos(\theta)}{\cos^2(\theta) - \sin^2(\theta)} = \dfrac{2\frac{\sin(\theta)}{\cos(\theta)}}{1 - \frac{\sin^2(\theta)}{\cos^2(\theta)}}[/tex]
Then plugging in the given info, we get
[tex]\dfrac{2\sin(\theta)\cos(\theta)}{\cos^2(\theta) - \sin^2(\theta)} = \dfrac{2\times \frac{12}{13}}{1 - \left(\frac{12}{13}\right)^2} = \boxed{\dfrac{312}{25}}[/tex]
help the question is on the image.
Answer:
[tex]\boxed {tan\theta = \frac{2}{3}}[/tex]
Step-by-step explanation:
Let's derive a formula :
⇒ Area (triangle) × 3 = Area (square)
⇒ 1/2(bh) × 3 = a²
∴ But a = h (shown in diagram)
⇒ 3/2(bh) = h²
⇒ h = 3b/2
Now, taking tan θ :
⇒ tan θ = b/h
⇒ tan θ = b/(3b/2)
⇒ tan θ = 2b/3b
⇒ tan θ = 2/3
HELP ME!! FIND X AND Y.
Answer:
x = 26
y = 72°
Step-by-step explanation:
Finding x:Alternates angles are equal.(4x - 16)° = (3x + 10)°
Subtract 3x to both sides
4x - 3x - 16 = 10
x - 16 = 10
Add 16 to both sides
x = 10 + 16
x = 26
Finding y:Angles on a straight lines add up to 180 degrees.(4x - 16)° + y° = 180°
4x - 16 + y = 180
4(26) - 16 + y = 180
104 - 16 + y = 180
88 + y = 180
Subtract 88 to both sides
y = 180 - 88
y = 72°
[tex]\rule[225]{225}{2}[/tex]
The ratio of players to soccer balls at practice sessions is 5:2. How many soccer balls are needed for 20 players?
Answer:
8 soccer balls
Step-by-step explanation:
Since the ratio of players to soccer balls is 5:2, we can conclude that:
Players = 5 peopleSoccer balls = 2 ballsThe question asks to find how many soccer balls are needed for 20 players.
Multiply both players and soccer balls by 4, this will get:
Players = 20 peopleSoccer balls = 8 ballsHenceforth, 8 soccer balls are needed for 20 players.
How to subtract negative number from 1
when you subtract a negative number from any platitude number the equation changes to addition so you would add the value of the negative number to 1.
To subtract a negative number from one you will need to set it up like this
1- (-x) x equals the negative number you're talking about
so we use the method KCC (keep change change)
So we KEEP the positive one, CHANGE the subtraction sign in to a plus sign "+" then CHANGE the negative number to a positive
lets say the negative number is 2
1-(-2)
1+ (+2)
1+2 = 3
Population 422 increasing by 10 people per year. Write an equation to determine the population (y) after any number of years (x).
Answer:
y = 10x + 422
Step-by-step explanation:
Let f(r) = 42 - 5, find f(3).
(-2/3)^3 (Evaluate)
A: 8/9
B: 6/9
C: -8/27
D: 8/27
Answer:
C
Step-by-step explanation:
using the rule of exponents
[tex](\frac{a}{b}) ^{m}[/tex] = [tex]\frac{a^{m} }{b^{m} }[/tex] , then
[tex](\frac{-2}{3}) ^{3}[/tex]
= [tex]\frac{(-2)^{3} }{3^3}[/tex]
= [tex]\frac{-8}{27}[/tex]
= - [tex]\frac{8}{27}[/tex]
Definition:
[tex]a^2=a\cdot a\\\\a^3=a\cdot a\cdot a\\\\a^4=a\cdot a\cdot a\cdot a\\\vdots\\a^n=\underbrace{a\cdot a\cdot a\cdot...\cdot a}_{n}[/tex]
also
[tex]a^1=a\\\\a^0=1[/tex]
We have
[tex]\left(-\dfrac{2}{3}\right)^3=\left(-\dfrac{2}{3}\right)\cdot\left(-\dfrac{2}{3}\right)\cdot\left(-\dfrac{2}{3}\right)=-\dfrac{2\cdot2\cdot2}{3\cdot3\cdot3}=-\dfrac{8}{27}[/tex]
[tex]\huge\boxed{C:\ -\dfrac{8}{27}}[/tex]
Which formula can be used to describe the sequence? negative two-thirds, −4, −24, −144,...
Answer:
Step-by-step explanation:
The height of each story in a hotel is feet. The height is measured from the ceiling to the floor. The hotel has 2 underground levels that are used as banquet halls. Stephen is a waiter who works two levels below ground. At what elevation are Stephen’s feet? Assume the ground level of the hotel is at 0 feet.
A.
feet
B.
feet
C.
D.
feet
The coordinates of triangle LMN are shown. L(-1,4) M(-1, -3) V N (4, -1) What is the length of LM? Enter the answer in the box. unit(s) The coordinates of triangle LMN are shown . L ( -1,4 ) M ( -1 , -3 ) V N ( 4 , -1 ) What is the length of LM ? Enter the answer in the box . unit ( s )
Answer:
7
Explanation:
Use the distance formula to find the answer
Answer:
7 units
Step-by-step explanation:
since the x- coordinates of L and M are equal , both - 1 then the length of LM is the absolute value of the difference of the y- coordinates.
LM = | 4 - (- 3) | = | 4 + 3 | = | 7 | = 7
or
LM = | - 3 - 4 | = | - 7 | = 7
Which transformations could have taken place? Select two options.
The two options are R₀ 270 , R₀ 90 , Option C and D .
The complete question is attached in the image.
What are the two types of Transformations ?There are two types of transformations namely , Rigid Transformation and Non- Rigid Transformation
The rigid transformations do not change the shape and size of the preimage .
The non Rigid transformation do not change the shape but change the size of the preimage.
The rule rotating the origin , 270 degree is
(x,y) ----> (y , -x)
as (x,y) is (0,5)
Therefore after 270 degree transformation
(y,-x) is (5 , 0)
So, the clockwise rotation is 90 degree about origin
(x,y) ----> (y , -x)
as (x,y) is (0,5)
Therefore after 90 degree transformation
(y,-x) is (5 , 0)
Therefore the two options are R₀ 270 , R₀ 90 , Option C and D .
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Which expression is equal to the polynomial
below?
2x + 5x38x - 20
Ox³(2x + 5) + 4(2x - 5)
Ox³(2x + 5)- 4(2x + 5)
Ox³(2x-5)-4(2x - 5)
Ox³(2x + 5) + 4(2x + 5)
The expression 2x⁴ + 5x³ - 8x - 20 can be express as follows;
x³(2x + 5) - 4(2x + 5)
How to factorise an expression?2x⁴ + 5x³ - 8x - 20
Therefore,
2x⁴ + 5x³ - 8x - 20
x³(2x + 5) - 4(2x + 5)
Hence, the expression 2x⁴ + 5x³ - 8x - 20 can be express as follows:
2x⁴ + 5x³ - 8x - 20 = x³(2x + 5) - 4(2x + 5)
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The length of a rectangle is units greater than twice its width. If its width is w, which expression gives the perimeter of the rectangle in terms of w?
A.
2(w) + w
B.
w + w
C.
3w +
D.
6w + 5
The expression that gives the perimeter of the rectangle in terms of w is 6w+5 units.
Given that, the length of the rectangle is [tex]\frac{5}{2}[/tex] units greater than twice its width.
We need to determine the expression that gives the perimeter of the rectangle in terms of w.
Given, width = w units, then length= 2w + [tex]\frac{5}{2}[/tex] units.
What is the perimeter of the rectangle?The perimeter of the rectangle is the sum of all the sides of the rectangle.
That is, perimeter of a rectangle = 2 (length+width).
Now, perimeter of a rectangle = 2 (2w + [tex]\frac{5}{2}[/tex]+w)=6w+5 units.
Hence, the expression that gives the perimeter of the rectangle in terms of w is 6w+5 units.
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Fraction:
23
100
Decimal: 0.23
Percent: 30 %
Answer: Below is the correct data.
Fraction: [tex]\frac{23}{100}[/tex]
Decimal: 0.23
Percent: 23%
I hope this helps! Pls mark brainliest!! :)
URGENT!!! PLEASE HELP!!! Find x and y.
Answer:
x is 48 and y is 100
Step-by-step explanation:
Angle y = 100 degree
Angle x = 48 degree
Jaime makes the following claim.
An angle with a measure of π/3 radians in a circle with a radius of 3 inches is smaller than an angle with a measure of π/3 radians in a circle with a radius of 6 inches. This is because the radian measure is based on the length of the radius of the circle and a radius of 3 inches is smaller than a radius of 6 inches.
1. Review Jaime’s statement and what you know about angles and radians.
a. Explain whether you agree with Jaime’s statement or not.
b. Provide examples to support your whether you agree or disagree.
Jaime is incorrect, the angle does not depend on the radius of the circles.
Is Jaime correct?Remember that an angle that defines an arc on a circle, does not depend on the radius of the circle.
So, if we have an angle with a measure of π/3 radians in a circle with a radius of 3 inches and an angle with a measure of π/3 radians in a circle with a radius of 6 inches, these two angles are exactly the same thing.
The radius of the circle only has an impact on the length of the arc defined by the angle.
So Jaime is clearly incorrect.
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SOS help please ignore the answers I put they are wrong
The conversion to logarithm function will be that log3 27 = 3.
How to calculate the log?From the information given, we are to convert the exponential equation to logarithm function. This will be:
log 3 27
This will be log 3 3³
= 3 × log 3^3
= 3 × 1
= 3
Therefore, x = 3.
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I already worked on most of my question, although, I am just curious about how you would go about finding the fourth power of the square root of 50. Can someone please explain this in detail?
Answer:
(50^1/2)^4
Step-by-step explanation:
basically if I am comprehending your question correctly, the square root of 50 can also be written as 50^1/2
If you put 50^1/2 to the 4th power, it basically becomes (50^1/2)^4
what is the cos? trigonometry
Answer:
Cos, a abreviation of cosine is used in trigonometry, and it represents the ratio of the hyptenuse and the adjacent side of a right triangle (a triangle with a right/90 degree angle). The formula for evaluating cosine/cos is the length of the adjacent side of the triangle divided by length of the hypotenuse of the triangle. To be clear, the hypotenuse is the side of the triangle the 90 degrees is facing, and the adjacent side is the side across the hypotenuse.
Step-by-step explanation:
Answer:
A trigonometric function that for an acute angle is the ratio between the leg adjacent to the angle when it is considered part of a right triangle and the hypotenuse.
What is cos law?
The cos law or cosine law defines the relationship between the sides and the angles of the triangle. This law is also known as the law of cosine or cosine rule. According to this law,
c2 = a2 + b2 − 2ab cos α
Where a, b and c are the sides of the triangle.
Pls help quickly!!!
Find the coordinates of the vertex of the graph of the function.
y=3x^2-4x+3
Answer:
vertex = ( [tex]\frac{2}{3}[/tex], [tex]\frac{8}{3}[/tex] )
Step-by-step explanation:
given the equation of a parabola in standard form
y = ax² + bx + c ( a ≠ 0 )
then the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = 3x² - 4x + 3 ← is in standard form
with a = 3 , b = - 4 , then
x = - [tex]\frac{-4}{6}[/tex] = [tex]\frac{2}{3}[/tex]
substitute x = [tex]\frac{2}{3}[/tex] into the equation for corresponding y- coordinate of vertex
y = 3([tex]\frac{2}{3}[/tex] )² - 4([tex]\frac{2}{3}[/tex] ) + 3
= 3([tex]\frac{4}{9}[/tex] ) - [tex]\frac{8}{3}[/tex] + 3
= [tex]\frac{4}{3}[/tex] - [tex]\frac{8}{3}[/tex] + [tex]\frac{12}{3}[/tex]
= [tex]\frac{8}{3}[/tex]
vertex = ( [tex]\frac{2}{3}[/tex], [tex]\frac{8}{3}[/tex] )
The length of a rectangle is twice its breadth. If its length is decreased half of the 10 cm and the breadth is increased by half of the 10 cm cm, the area of the rectangle is increased by 5 sq cm, more than 70 sq cm. Find the length of the rectangle.
Also....any armies, stays and blinkss?
Since the length of this rectangle is twice its breadth, the length is equal to 40 cm.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
Area = Length × Width
Based on the information provided, we have:
Its length is decreased half of the 10 cm ⇒ (length - 5)Its breadth is increased by half of the 10 cm ⇒ (breadth + 5)Its area is increased by 75 cm ⇒ (area + 5)Substituting the parameters into the formula, we have:
LB + 75 = (L - 5)(B + 5)
2B² + 75 = (2B - 5)(2B + 5)
2B² + 75 = 2B(B + 5) - 5(B + 5)
2B² + 75 = 2B² + 10B - 5B - 25
5B = 75 + 25
5B = 100
B = 100/20
B = 20 cm.
For the length, we have:
L = 2B
L = 2 × 20
L = 40 cm.
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Choose the variable expression that matches this phrase.
the sum of the number of crew members on the tour boat and the 5
passengers.
A. 5-c
B. 5c
C. 5+ c
D. 5÷c
The sum of the number of crew members (c) on the tour boat and the 5 passengers is 5 + c. Then the correct option is C.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
The sum of the number of crew members (c) on the tour boat and the 5 passengers.
This can be written as in the form of the mathematical form.
⇒ 5 + c
Then the correct option is C.
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Selena is preparing for her eighth-grade graduation party. she must keep within the budget set by her parents. which is the best price for her to purchase ice cream? a. $3.99/ 24 oz carton b. $4.80/ one-quart carton c. $11.00 / one gallon tub d. $49.60/ five gallon tub
Answer:
Basically find the unit rate by doing 3.99/24 = $0.16625/1oz
1 quart = 32 ounces so 4.8/32 = $0.15/1oz
1 gallon = 153.722 ounces so 11/153.722 = 0.07
49.6/768.61 = 0.06
Step-by-step explanation:
D.
Solve by elimination
show your work
y = 3x + 10
y = 2x - 8
im giving brainlyest
Answer:
[tex]x=-18, y=-44[/tex]
Step-by-step explanation:
[tex]y=3x+10\\y=2x-8\\\\3x+10=y\\2x-8=y\\3x-y=-10\\2x-y=8\\\\-2(3x-y=-10)\\3(2x-y=8)\\\\-6x+2y=20\\6x-3y=24\\-y=44\\y=-44\\-44=3x+10\\-54=3x\\x=\frac{-54}{3} \\x=-18\\\\x=-18, y=-44\\[/tex]
CHECK
[tex]-44=3(-18)+10\\-44=-54+10\\-44=-44\\\\-44=2(-18)-8\\-44=-36-8\\-44=-44[/tex]
After how many seconds does the object reach its maximum height? 2 seconds 3 seconds 6 seconds 9 seconds
Answer:
3 seconds
proofi took the test
The object reaches its maximum height after 3 seconds.
The correct option is 3 seconds.
To find the time at which the object reaches its maximum height, we need to determine the vertex of the parabolic function[tex]h(t) = -16t^2 + 96t + 6[/tex] . The vertex form of a parabola is given by [tex]h(t) = a(t - h)^2 + k[/tex], where (h, k) represents the vertex.
In this case, a = -16, so the vertex is given by t = -b/2a. Plugging in the values, we get t = -96/(2 x (-16)) = 96/32 = 3 seconds.
Therefore, the object reaches its maximum height after 3 seconds.
Option B, 3 seconds, is the correct answer.
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The complete Question:
The function [tex]h(t) = -16t^2 + 96t + 6[/tex] represents an object projected into the air from a cannon. The maximum height reached by the object is 150 feet.
After how many seconds does the object reach its maximum height?
A. 2 seconds
B. 3 seconds
C. 6 seconds
D. 9 seconds
which statements could be an interpretation of the graph x intercept or y intercept
Answer:
If you attach the answers i can help you better
Step-by-step explanation:
Suppose ∠A and ∠B are complements, while ∠B and ∠C are supplements. If m∠A=3x+17, m∠B=55−x, and m∠C=67(x/3−1), then m∠A=44, m∠B=46, and m∠C=134. TRUE OR FALSE? Please show your work.
Answer:
TRUE
Step-by-step explanation:
Angle <A and angle <B are complementary, which means their sum must be = 90
Angle <B and angle <C are supplementary which means their sum must be = 180
Now let's see
m∠A=3x+17, m∠B=55−x, and m∠C=67(x/3−1)
first find the sum of A and B
3x + 17 + 55 - x = 90 add like terms
2x + 72 = 90 subtract 72 from both sides
2x = 18 divide both sides by 2
x = 9
TRUE OR FALSE is asked for
m∠A=44, m∠B=46, and m∠C=134
to find that we just replace c with 9 with every expression given for angles
m<A = 3x + 17
m<A = 3*9 + 17 = 44
m<B = 55 - x
m<B = 55 - 9 = 46
m<C = 134, we don't really need to calculate one by one since the angle are complementary and supplementary.
The answer is TRUE
The statement is true if A and ∠B are complements, while ∠B and ∠C are supplements.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
We have:
∠A and ∠B are complements, while ∠B and ∠C are supplements.
∠A + ∠B = 90 degree
3x + 17 + 55 - x = 90
2x = 18
x = 9
Angle ∠B and angle ∠C are supplementary:
∠B + ∠C = 180
55 -x + 67(x/3 - 1) = 180
x = 9
Put the value of x and find angles A, B, and C.
m∠A = 44
m∠B = 46
m∠C = 134
∠A + ∠B = 90
∠B + ∠C = 180
The above statement is true.
Thus, the statement is true if A and ∠B are complements, while ∠B and ∠C are supplements.
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