Answer:
Like terms are mathematical terms that contain the same variables. We combine like terms, because it simplifies algebraic expressions.
Closure property is the term for when you add or multiply two whole numbers together, and the result is always just a whole number. It is related to adding, subtracting, and multiplying polynomials, because when something is closed, the output will result in being the same type of object as the inputs.
Step-by-step explanation:
Like terms: When combining like terms, we add their coefficients. For instance, if we have 3y and 4y, we get 7y. That is because we added (3+4) to get 7, and plugged in the variable "y".
Closure property: Adding, subtracting, or multiplying two polynomials will output a polynomial.
Is -7=7 an infinite solution or no solutions for a system of equations?
Answer:
no solutions
Step-by-step explanation:
-7 does not equal 7, so there are no solutions.
Infinite solutions would be if it was two equal values, for example, 7 = 7.
The cost of the toy is expressed by the function y = 3x + 5, where x is the number of toys. If Peter bought 8 toys, find the cost of the toys.
Answer:
$29
Step-by-step explanation:
Substitute x with 8.
3(8) + 5 = 24+5 = 29
Answer: $29
Step-by-step explanation:
x = # toys
if the number of toys is 8
substitute 8 into x
y = 3(8) + 5
y = 24 + 5
y = 29
You are going on vacation with your family to the beach. You already spent $160 on
groceries for the week, and you know that each time you eat out you will spend another
$40. Does The relationship between the number of the Times eating out in the total budget represent a linear function?
Answer:$440, 9
Step-by-step explanation:
The relationship between the number of the times eating out in the total budget represent a linear function.
What is a linear function?"A linear functions are those whose graph is a straight line."
Given, I already spent $160 on groceries for the week.
Each time I eat out you will spend another $40.
Let, I eat 'x' times during vacation.
Therefore, the required function will be:
f(x) = 160 + 40x
Hence, the function is a linear function.
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What is the measure of the unknown angle?
image of a two hundred ninety seven degree angle and an unknown angle
60°
63°
64°
70°
Answer:
63
Step-by-step explanation:
A circle is 360 degrees
So, subtracting 297 from 360, we'd get 63 degrees
There are eight shirts in your closet, four
blue and four green. you randomly select
one to wear on monday and then a
different one on tuesday. you wear blue
shirts both days.
please show your work, just so i would also understand how to answer this question !!
Answer:
it is a 50 50 %chance so it is random this is called probability the probability of blue is half so it is by chance I chose blue
prove that x-y = √(x+y)^2-4xy?
Proved Below
[tex]\Longrightarrow x-y = \sqrt{(x+y)^2-4xy}[/tex]
[tex]\Longrightarrow x-y = \sqrt{x^2+2(x)(y)+ y^2-4xy}[/tex]
[tex]\Longrightarrow x-y = \sqrt{x^2+2xy-4xy+y^2}[/tex]
[tex]\Longrightarrow x-y = \sqrt{x^2-2xy+y^2}[/tex]
[tex]\Longrightarrow x-y = \sqrt{(x-y)^2}[/tex]
[tex]\Longrightarrow x-y =x-y[/tex]
Let's check
x-y=√(x+y)²-4xy
Solve RHS
√(x+y)²-4xy√x²+2xy+y²-4xy√x²+y²-2xy√(x-y)²x-yHence proved
This circle is centered at the origin, and the length of its radius is 8. What is
the circle's equation?
or +
5
8
5
OA. x+y=8
OB.x²2² +2²=8
OC. x + y = 64
OD. x² + y² = 64
4
Answer:
D
Step-by-step explanation:
x² + y² = 64, because when x is 0, y = ± 8, when y is 0, x = ± 8, that is the radius r
The equation of a circle with center at the origin and radius 8 is,
⇒ x² + y² = 64
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
This circle is centered at the origin, and the length of its radius is 8.
Since, The equation of a circle with center at the origin and radius r is,
⇒ x² + y² = r.
Hence, for this circle, the equation would be;
⇒ x² + y² = 8²,
or simplified,
⇒ x² + y² = 64
Thus, The equation of a circle with center at the origin and radius 8 is,
⇒ x² + y² = 64
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You are riding along a straight river from east to the west at speed of 160m/m. At a given time, you will see the bearing of a church on the other parallel road is N 70 degrees W, and 4 minutes later the bearing is N 56 degrees W. What is the width of the river? (Round your answer to two decimal points)
Using the given information, the width of the river is 505.96 m
Bearing and DistancesFrom the question, we are to determine the width of the river
Consider the given diagram,
Let F be the first position of the biker
S be the second position
and C be the position of the church
First, we will determine the distance covered from F to S
Speed = 160m/min
Time = 4 minutes
Using the formula,
Distance = Speed × Time
Distance covered = 160 × 4
Distance covered = 640 m
That is, /FS/ = 640 m
Now, consider ΔFSC
∠F = 90° - 70° = 20°
∠S = 90° + 56° = 146°
and ∠C = 180° - 20° - 146° = 14°
By the Law of Sines
[tex]\frac{/FC/}{sin\ S}= \frac{/FS/}{sin\ C}[/tex]
∴ [tex]\frac{/FC/}{sin\ 146^\circ}= \frac{640}{sin\ 14^\circ}[/tex]
[tex]/FC/ =\frac{640 \times sin \ 146^\circ}{sin \ 14^\circ}[/tex]
/FC/ = 1479.33 m
Now,
By SOH CAH TOA
[tex]cos \ 70^\circ = \frac{d}{/FC/}[/tex]
NOTE: d is the width of the river
∴ d = /FC/ × cos70°
d = 1479.33 × cos70°
d = 505.96 m
Hence, the width of the river is 505.96 m
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Which point is on the graph of f(x) = 3.4^x
O A. (1, 12)
OB. (0, 12)
O C. (12, 1)
O D. (0,0)
The point on the graph f(x) = 3.4ˣ is (0, 1)
None of the given options is correct.
What is a function?A function is a relationship between a number of inputs and outputs. A function is an association of inputs where each input is coupled with exactly one output. There is a range, co-domain, and domain for every function.
To determine which point is on the graph of f(x) = 3.4ˣ, we need to substitute the given x-coordinate into the function and see if we get the given y-coordinate.
Let's try each option:
A. (1, 12): f(1) = 3.4¹ = 3.4, so this point is not on the graph of f(x) = 3.4ˣ.
B. (0, 12): f(0) = 3.4⁰ = 1, so this point is not on the graph of f(x) = 3.4ˣ.
C. (12, 1): f(12) = 3.4¹² ≈ 108089.7, so this point is not on the graph of f(x) = 3.4ˣ.
D. (0, 1): f(0) = 3.4^0 = 1, so this point is on the graph of f(x) = 3.4ˣ.
Therefore, the point (0, 1) is on the graph of f(x) = 3.4ˣ. The answer is option D.
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pls help i dont understand .Thankkk uuu!!!!
whats the answer to this? I don't know how to do it but i need to factor it completely with whatever method gies with it.
Answer:
3x²y²(1 - 4xy²z)
Step-by-step explanation:
________________________________________
Factor 3 out of 12
Factor x² out of x³
Factor y² out of y⁴
you will get the GCF of 3x²y² and left with (1 - 4xy²z)
3x²y²(1 - 4xy²z)
________________________________________
Hoped this helped
The graph shows two lines, A and B:
Based on the graph, which statement is correct about the solution to the tC system of equations for lines A and B?
O (3, 4) is the solution to both lines A and B.
© (3, 4) is the solution to line A but not to line B.
O (0, 2) is the solution to both lines A and B.
O (0, 2) is the solution to line A but not to line B.
Answer:
the answer is (3,4) is the solution to line A but not to line b
Why is it important to keep the two sides of an equation balanced when solving? what other properties do we use to rewrite expressions and equations?.
"Law of conservation of Mass and Energy", is the reason for which it is important to keep the two sides of an equation balanced when solving.
The other properties that we should consider while rewriting the expressions of an equation is that we should not multiply or divide the expressions by zero on both the sides.
According to the law of conservation of mass, mass is neither generated nor destroyed during a chemical process. For instance, when coal is burnt, the carbon atom in it transforms into carbon dioxide. The carbon atom transforms from a solid to a gas, yet its mass remains constant. Similar to this, according to the law of conservation of energy, energy cannot be generated or destroyed. For instance, kinetic energy is converted to potential energy when a toy vehicle is rolled down a ramp and collides with a wall.
While rewriting expressions of an equation, we should not multiply or divide them by zero, as multiplying or dividing by zero makes two non-equal expressions equal (0 and ∞ respectively.
This is the reason why is it important to keep the two sides of an equation balanced, and that the expressions should not be multiplied or divided by zero.
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I also need help on 3 4 5 if some one can explain it will be really helpful
And I will give 65 points
The equation that shows the relationship between the variables are T = 0.112N, D = 54A and T = 62.5A
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let k represent the constant of proportionality
3) T = kN
28 = 250k
k = 0.112
i) T = 0.112N
ii) T = 0.112(300) = 33.6
iii) 98 = 0.0112N
N = 875
4) D = kA
270 = 5k
k = 54
i) D = 54A
ii) D = 54(4.5) = 243
iii) 324 = 54A
A = 6
5) T = kA
150 = 2.4k
k = 62.5
i) T = 62.5A
ii) T = 62.5(1.8) = 112.5
iii) 3(60) = 62.5A
A = 2.88
The equation that shows the relationship between the variables are T = 0.112N, D = 54A and T = 62.5A
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Which statements about the arcs and angles are true? select three options. ∠efd ≅ ∠egd ∠egd ≅ ∠ecd arc e d is-congruent-to arc f d marc e f = 60° marc f d = 120°
The true statements about the arcs and angles in circle C are:
∠EFD ≅ ∠EGD.Arc ED ≅ arc FD.m arc FD = 120°.How to analyze the arcs and angles?In Geometry, the sum of the measures of the interior angles in a quadrilateral is equal to 360°. Thus, we have:
m∠G + m∠GDC + m∠DCE + m∠GEC = 360°
60 + 90 + m∠DCE + 90 = 360
240 + m∠DCE = 360
m∠DCE = 360 - 240
m∠DCE = 120°.
Since ∠DFE is an inscribed angle that is subtended by arc DE, we have:
m∠DFE = m∠DCE
m∠DFE = 120
m∠DFE = 1/2 × 120
m∠DFE = 60°.
Therefore, ∠EFD ≅ ∠EGD.
From circle C, we can deduce that side ED is subtended by arc ED and side FD is subtended by arc FD (side ED ≅ side FD). Thus, arc ED ≅ arc FD and m arc FD is equal to 120°.
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Answer:
A C E
took quiz
What is the slope of the line that contains the points (-2, 7) and (2, 3)?
Answer:
The slope of the line is -1.
Step-by-step explanation:
SLOPE OF A LINE FORMULA
SLOPE = Y2 - Y1/ x2 - x1
m = Y2 - Y1/ x2 - x1
m = 3 - 7 / 2- (-2)
m = -4/4
m = -1
The slope of the line is -1.
What function is represented below?
HELP ASAP!!
Answer:
C
Step-by-step explanation:
(1/4)^x-2 is the answer
Please help with this question thanks!!
Answer:
(-1,4)
Step-by-step explanation:
Step 1) Change both equations to slope intercept form
3x+y=1 ---> y=-3x+1
5x+y=-1 ---> y=-5x-1
Step 2) Plot lines accordingly on graph
Lines intersect at (-1,4)
which of the following functions best describes this graph?
A.y=(x-1)(x-1)
B.y=x^2-5x+6
C. y=x^2-x+5
D. y=( x-3)(x+1)
Answer: y = (x-1)(x-1)
Step-by-step explanation:
There is pretty much no vertical shift so that immediately rules out B and C.
We can solve y = (x-1)(x-1) and get x = 1
The graph shows x = 1 as a zero, so we know this graph is correct.
Pls anyone answer
15 - 8 + - 9
Answer:
-2
Step-by-step explanation:
15-8+-9
bodmas
15-8=7
7-9
=-2
Put the following equation of a line into slope-intercept form, simplifying all fractions. 4x+4y=-28
Answer:
y=-x-7
Step-by-step explanation:
Slope-intercept form is y=mx+b
We have the equation 4x+4y=-28 and must put it into the form above. To do this first subtract 4x from both sides.
4x-4x+4y=-28-4x
This equals 4y=-4x-28. Now, divide 4 from both sides.
4y/4=-4x/4-28/4
y=-x-7
Hope this helps!
If not, I am sorry.
Examine the equation.
-2(-x + 9) = 2(x - 9)
2x 18 = 2x - 18
This equation has
Infinite solutions
One solution
No solution
Answer:
No solution
Step-by-step explanation:
What is the volume of the cone shown below?
A. 1344 cu. units
B. 504 cu. units
C. 4032 cu. units
D. 2016 cu. units
Work Shown:
r = 8 = radius
h = 63 = height
V = volume of the cone
[tex]V = \frac{1}{3}\pi*r^2*h\\\\V = \frac{1}{3}\pi*8^2*63\\\\V = \left(\frac{1}{3}*8^2*63\right)\pi\\\\V = \left(\frac{1}{3}*63*8^2\right)\pi\\\\V = \left(21*64\right)\pi\\\\V = 1344\pi\\\\[/tex]
Side note: You could write the symbol π as "pi" without quotes.
Jocelyn is training for a race by running several miles each day. she tracks her progress by recording her average speed in minutes per mile for each day since she started training. based on the information given, what could jocelyn expect to have for her average speed on the 9th day?
Finding the regression equation, her average speed on the 9th day should be expected to be of 6.92 minutes per mile.
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
Researching the problem on the internet, the values of x and y are given as follows:
Values of x: 1, 2, 3, 4, 5, 6.Values of y: 8.2, 8.1, 7.5, 7.8, 7.4, 7.5.Hence, using a calculator, the equation for the average minutes per mile after t days is given by:
V(t) = -0.15143t + 8.28
Hence, for the 9th day, t = 9, hence the estimate is:
V(9) = -0.15143(9) + 8.28 = 6.92 minutes per mile.
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Please help!
What is the first step in solving the function below?
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow C.\:factor \:\: out \:\: 2x [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 2 {x}^{3} - 18 {x}^{2} + 40x[/tex]
[tex]\qquad \tt \rightarrow \: 2x(x {}^{2} ) - 2x(9x) + 2x(20)[/tex]
[tex]\qquad \tt \rightarrow \: 2x( {x}^{2} - 9x + 20)[/tex]
Henceforth, The most efficient first step in factorising the given trinomial is to factor out 2x
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
suppose a triangle has sides a, b, and c and the angle opposite the side of length a is acute what must be true?
A. b2+c2>a2
B. a2+b2
C. b2+c2
D. a2+b2=c2
The true statement about the triangle is (a) b^2 + c^2 > a^2
How to determine the true inequality?The sides are given as:
a, b and c
The angle opposite of side length a is an acute angle
The above means that:
The side a is the longest side of the triangle.
The Pythagoras theorem states that:
a^2 = b^2 + c^2
Since the triangle is not a right triangle, and the angle opposite a is acute.
Then it means that the square of a is less than the sum of squares of other sides.
This gives
a^2 < b^2 + c^2
Rewrite as:
b^2 + c^2 > a^2
Hence, the true statement about the triangle is (a) b^2 + c^2 > a^2
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Find the equation of the line which:
passes through (3, 4) and is perpendicular to y=x+2
Answer:
y = -x + 7.
Step-by-step explanation:
General form:-
y = mx + c where m = slope. So:
y = x + 2 has a slope of 1.
The line perpendicular to it has slope -1/1 = -1
To find the required line we use the point-slope form with m = -1, x1 = 3 and y1 = 4.
y - y1 = m(x - x1)
y - 4 = -1(x - 3)
y - 4 = -x + 3
y = -x + 7.
Solve
A.
A bag has 18 marbles of three different colours.
There are twice as many red marbles as blue
ones.
There are two fewer green marbles than blue ones.
Form an equation to model this situation, and solve
to determine the number of each color marble in
the bag.
B.
The perimeter of a large triangle is 237 cm.
The lengths of the three sides are consecutive
integers, Form an equation to model this situation,
and solve to find the lengths of the three sides.
Answer:
5 blue marbles
10 Red marbles
3 Green marbles
Step-by-step explanation:
5 times 2 = 10
then 5-2 =3
Add 5+10+3
=18 Marbles in total
Write the next 3 numbers in each sequence.
Answer:
The next 3 numbers will be 1 3/4, 2, and 2 1/4
Step-by-step explanation:
The numbers in the sequence are increase by 1/4. So to find the next number in the sequence and 1/4 to the previous number. Don't foget to simplify your answers. Ex.) Rather than saying 2 2/4 you would say 2 1/2.
Cheryl mixes 350ml of cranberry juice with 2 litres of blueberry juice. Write the ratio of cranberry juice: blueberry juice in its simplest form. Find the ratio of 2/5 h to 250 S.
cranberry juice = 350 ml
blueberry juice = 2 liters = 2000 ml
Ratio of cranberry juice : blueberry juice = 350 : 2000 = 7 : 40
The simplest ratio is 7 : 40 or 7/40
