The best definition of the phrase "like terms" is as follows: terms that have identical variable parts.
What are like terms in algebra?Like terms is used to describe terms that contain the same variable which is raised to the same power.
Algebra is an aspect of mathematics that involves the system of computation using letters or other symbols to represent numbers.
For example; in the algebraic expression: x² + 3 - 2x², x² and 2x² are like terms because they are terms that have identical variable parts.
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Can somebody please help answer this word problem using grass method? And showing how u get the answer thanks!!!
WILL MARK BRAINLIEST FOR WHOEVER ANSWERS THIS !!! :DD
Answer:
0.25m or 1/4m
Step-by-step explanation:
Given Height of Dorsal Fin = 1/6 of Length of whale Sculpture,
and given length of whale sculpture = 1.5m or [tex]1\frac{1}{2} m\\[/tex]
Height of Dorsal fin on scuplture = [tex](\frac{1}{6})(1\frac{1}{2} )\\[/tex]
= [tex](\frac{1}{6} )(\frac{3}{2}) \\= \frac{3}{12} \\= \frac{1}{4}m or 0.25m[/tex]
The complex numbers $z_1$ and $z_2$ are such that $|z_1| = 5,$ $|z_2| = 13,$ and
\[13z_1 - 5z_2 = 27 - 99i.\]find $z_1 z_2.$
By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.
How to determine two complex numbers based on their norms and a given operation
In this question we must derive two complex numbers such that the following conditions are fulfilled:
a² + b² = 5² (1)
c² + d² = 13² (2)
13 · (a + i b) - 5 · (c + i d) = 27 - i 99 (3)
If we assume that a, b, c, d are integers, then we can suppose that (a, b) = (4, -3) and (c, d) = (5, 12) and we check if these values satisfy (3):
13 · (4 - i 3) - 5 · (5 + i 12)
52 - i 39 - 25 - i 60
27 - i 99
By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.
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Review the graph of 2x – 7 – 3 ≥ y.
On a coordinate plane, a curve goes through (0, negative 3) and increases up through (8.5, 0) and (10, 5). Everything below the line is shaded and is labeled 2 Superscript x minus 7 Baseline minus 3 greater-than-or-equal-to y.
What is the least integer value that satisfies the inequality 2x – 7 ≥ 3?
7
8
9
10
The least integer value that satisfies the inequality [tex]2^{x-7} - 3[/tex] ≥ y is 7.
What is Exponential function?
Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round.
Here, In the given function
Least possible value of 2ˣ⁻⁷ is 1
2ˣ⁻⁷ = 2⁰
On comparing both sides, we get
x-7 = 0
x = 7
Thus, The least integer value that satisfies the inequality 2ˣ⁻⁷-3≥ y is 7.
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Answer:
7
Step-by-step explanation:
edg 2022
is the statement 15=|-15| true
Answer:
Yes! |-15| = 15
Step-by-step explanation:
Many people think of absolute value (the two bars symbol around the -15) as ALWAYS POSITIVE.
You can also think of absolute value as a distance. If you move 15 units, it doesn't matter in what direction you go. 15 units travelled is 15 units.
Lastly, absolute value has a V-shaped graph, that is because its always positive.
Translate the shape A three squares right and one square up
What are the coordinates of the vertices of the image?
To better give a visual, I drew it out instead.
The attachment is the solution.
Answer:
(4, 5)
(4, 2)
(6, 2)
Step-by-step explanation:
add 3 in "x" and 1 in "y"
(1, 4) ⇒ (1+3, 4+1) = (4, 5)
(1 , 1) ⇒ (1+3 , 1+1) = (4, 2)
(3, 1) ⇒ (3+3, 1+1) = (6, 2 )
Hope this helps
Jamie is playing a card game. Jamie's score changes by -12 points for 8 turns in a row.
What is the total change in Jamie's score?
Answer:-96
Step-by-step explanation:The answer is -96
The length of one leg of an isosceles right triangle is 3 ft. What is the perimeter of the triangle?
O 3+3√2 ft
O 3+3√√3 ft
O 6+3-√√2 ft
O 6+3√√3 ft
Check the picture below.
The perimeter of the triangle with the given dimension of leg is 6+3√2.
What is Pythagoras theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
Using Pythagoras theorem
c² = a² + b²
where c is the hypotenuse.
Here, c² = 3² + 3²
c = 3√2
So, the perimeter of triangle is
= 3 + 3 + 3√2
= 6 + 3√2
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Simplify (8z - 10) ÷ (-2) + 5(z - 1).
OZ
OZ-1
Oz-2
Answer:
A) z
Step-by-step explanation:
(8z - 10) ÷ (-2) + 5(z - 1)
1. Rewrite:
[tex]\large \textsf{$\dfrac{(8x-10)}{-2}+5(z-1)$}[/tex]
2. Distribute 5
[tex]\large \textsf{$5(z-1)$}\\\\\large \textsf{$5(z)+5(-1)$}\\\\\large \textsf{$5z-5$}[/tex]
Now we have:
[tex]\large \textsf{$\dfrac{(8x-10)}{-2}+\large \textsf{$5z-5$}$}[/tex]
3. Reduce the fraction:
[tex]\large \textsf{$\dfrac{(8x-10)}{-2}+\large \textsf{$5z-5$}$}\\\\\large \textsf{$-4x+5+5z-5$}[/tex]
4. Combine like terms:
[tex]\large \textsf{$-4x+5+5z-5$}=\large \textsf{z}[/tex]
Final answer: z
Hope this helps!
Point RR lies on the directed line segment from L\left(-8,-10\right)L(−8,−10) to M\left(4,-2\right)M(4,−2) and partitions the segment in the ratio 33 to 55. What are the coordinates of point RR?
The coordinates of point R of the given line segment are (-3.5, -7)
How to partition a line segment?
We are given the coordinates;
L (-8,-10) to M (4,-2)
We are told that they are partitioned in the ratio 3 to 5.
Thus;
The coordinates of R divide directed line segment from L (-8,-10) to M (4,-2) in ratio 3:5will be :
x = [3(4) + 5(-8)]/(3 + 5)
x = -3.5
y = [3(-2) + 5(-10)]/(3 + 5)
y = -7
Thus, the coordinates of point R are (-3.5, -7)
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Meril Starts driving at 14 00
i need some help doing this
Bob's living room floor is a rectangle that measures 9 feet by 12 feet. what is the diagonal distance, in feet, across the floor.
Answer:
15
Step-by-step explanation:
For this question you would need to do a squared + b squared so 9x9 is 91 + 12x12 which is 144. you add the two up then find the square root of that which should make your answer 15
A family wants to make a 20% downpayment on a house that costs $20,000, which of the amount is the downpayment?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 20000}}{\left( \cfrac{20}{100} \right)20000}\implies 4000\qquad \impliedby downpayment[/tex]
55. a rubber ball is dropped from a height of 60 feet. if it rebounds approximately two-thirds the distance after each fall, use an infinite geometric series to approximate the total distance the ball travels.
The required total distance the ball travels, approximately, is 180 feet.
Let's denote the height of the first fall as a (initial height of 60 feet), and the distance covered during each rebound as r (two-thirds the distance of the previous fall).
The first fall distance (a) is 60 feet.
The first rebound distance (r) is (2/3) * 60 feet.
The total distance covered during the first fall and rebound cycle is:
60 + (2/3) * 60 = 60 + 40 = 100 feet.
Now, for the subsequent cycles, the ball will continue to fall and rebound in the same pattern:
Second fall distance = r * a
= (2/3) * 60
= 40 feet.
Second rebound distance = r*(2/3) * 60
= (2/3) * 40
= 80/3 feet.
The total distance covered during the second fall and rebound cycle is:
40 + (80/3) ≈ 66.67 feet.
The pattern will continue for the subsequent cycles.
To represent this as an infinite geometric series, we can write:
Total distance = [tex]a + (a * r) + (a * r^2) + (a * r^3) + ...[/tex]
Where:
a = 60 feet (height of the first fall)
r = 2/3 (rebound factor)
Using the formula for the sum of an infinite geometric series:
Total distance = a / (1 - r)
Total distance = 60 / (1 - 2/3)
Total distance = 60 / (1/3)
Total distance = 60 * 3
Total distance = 180 feet.
Therefore, the total distance the ball travels, approximately, is 180 feet.
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A car leaves its garage and travels for 30km on a bearing of 145, then 10 km on a bearing of 250 Calculate a) the distance travelled from the starting point b) the bearing of the starting point from the car.
The distance travelled from the starting point is 29 km , the bearing is 344 degree
The missing diagram is attached with the answer.
What is Bearing Angle ?It is the horizontal angle between the object and another object.
It is given that the car starts from point travels for 30km on a bearing of 145, then 10 km on a bearing of 250
(a) the distance travelled from the starting point
It can be understood from the diagram that
To determine the distance , b is to determined4
By applying Cosine rule
b² = a² +c²-2ac cos[tex]\rm \theta[/tex]
b² = 10² +30² - 2* 30*10 cos75
b² = 100+900 -600* 0.2588
b² = 100-155.2914
b² = 844.7
b = 29 km
Therefore the distance travelled from the starting point is 29 km.
(b) the bearing of the starting point from the car.
To determine the bearing ,
angle C has to be determined
By sine rule
sin C / c = sin B / b
sin C = sin 75 * 30 / 29
sin C = 0.9970
C = sin⁻¹ 0.9970
C = 85.59 degree
angle C = α +70 degree
α = 15.59 degree
Bearing = 70 + 20 + 9 0 + 90+74 = 244 degree
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What is the exact value of x
Answer:
The value of x is 30 degrees.
Step-by-step explanation:
We know that angle 1 is 60 degrees, and that angle two is a right angle (meaning 90 degrees.) 60+90 is equal to 150 degrees. 180 degrees - 150 degrees is equal to 30 degrees. I hope this helps! :)
[tex]~~~~~~\sin \theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\\\implies \sin 60^{\circ} = \dfrac{x}{8}\\\\\\\implies x = 8 \sin 60^{\circ}\\\\\\\implies x = 8 \cdot \dfrac {\sqrt3}2\\\\\\\implies x = 4\sqrt 3[/tex]
Find the equation to the line below.
Answer:
y=-1/1x
Step-by-step explanation:
First, let's take the slope of a line equation:
y=mx+b
Now, all we have to do is find the slope(m) and the y-intercept(b).
The line intercepts the y axis at 0, so b=0.
Next, find the slope.
The equation to FIND slope is rise/run, so we can solve that:
1/1=1, but since the line goes down, it's negative.
The slope is 1, so m=1.
Now, put that into m.
y=-1x+0, but we don't need 0, so the answer is y=-1x.
I'm confused I got an answer but got it wrong help please.
Answer:
[tex]y = \frac{2}{3}x -6[/tex]
Step-by-step explanation:
I'm just gonna assume you want the equation of the line
Standard slope-intercept form is [tex]y=mx+b[/tex] with [tex]m[/tex] being the slope [tex]\frac{rise}{run}[/tex] (aka [tex]\frac{y_1 - y_2}{x_1 - x_2}[/tex]) and [tex]b[/tex] being the y-intercept (the point where the line crosses the y-axis)
First we will find the slope using the 2 points on the line.
[tex]\frac{-2 - (-4)}{6-3} = \frac{2}{3}[/tex]
This means our slope ([tex]m[/tex]) is [tex]\frac{2}{3}[/tex].
Next we can find our y-intercept. The line crosses the y-axis at [tex](0, -6)[/tex] meaning the y-intercept ([tex]b[/tex]) is -6.
Finally we can plug in our values and find the equation of the line.
[tex]y = \frac{2}{3}x -6[/tex]
That might be the answer (i don't know the question)
- Kan Academy Advance
Anyone please help me, deadline is tomorrow.༎ຶ‿༎ຶ wahhhhhhhh huhuhu
mean is average, add all numbers and divide by quantity of numbers.
Median is the middle value, list the numbers from smallest to largest and find the middle number.
mode is the number that appears the most.
1. Mean = 6
Median = 5
Mode = 6
2. Mean = 86.1
Median = 86.5
Mode = 85
My sister needs help on this question and I am too lazy to figure this out please help ASAP
The question was: Which figure has exactly one line of symmetry?
Answer:
its the Pentagon, the other shaps have 2 lines if symmetry
solution for -2 1/3 divided by 4 2/3
Answer:
-0.5
Step-by-step explanation:
For f(x) = 2x+1 and g(x)=x^2-7, find (f+ g)(x).
OA. 2x²-15
OB.x²+2x-6
OC. 2x³-6
OD. x²+2x+8
Answer:
B
Step-by-step explanation:
(f + g)(x)
= f(x) + g(x)
= 2x + 1 + x² - 7 ← collect like terms
= x² + 2x - 6 ← in standard form
The value of (f + g)(x) is x² + 2x - 6.
What are arithmetical operations?Arithmetic operations are a set of four basic operations to be performed to add, subtract, multiply or divide two or more quantities. They include the study of numbers including order of operations which are useful in all the other parts of mathematics such as algebra, data handling, and geometry.
Given are two functions, f(x) = 2x+1 and g(x) = x²-7, we are asked to find
(f + g)(x),
So we know,
(f + g)(x) = f(x) + g(x)
Therefore,
(f + g)(x)
= f(x) + g(x)
= 2x + 1 + x² - 7
= x² + 2x - 6
Hence the value of (f + g)(x) is x² + 2x - 6.
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Horizontal stadia sights. Determine the error in distance if the uppermost portion of a 3. 0m long stadia rod is inclined 14 cm toward the observer and the rod intercept is 1. 75m on a horizontal sight
The error in the distance if the uppermost portion of a 3. 0m long stadia rod is inclined 14 cm toward the observer and the rod intercept is 1. 75m on a horizontal sight is 8.167cm.
What is Tangent (Tanθ)?The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
Tan(θ) = Perpendicular/Base
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
Given the uppermost portion of a that is 3.0m long stadia rod is inclined 14 cm toward the observer, therefore, the angle of inclination, θ can be written as
tan(θ)=0.14/3
θ = 2.672°
Also, the rod intercept is 1.75m, therefore, t the error in distance in the distance is,
tanθ=x/1.75
x = 1.75 tan(θ)
x = 1.75 × tan(2.672°)
x = 0.08167 m = 8.167 cm
Hence, the error in the distance if the uppermost portion of a 3. 0m long stadia rod is inclined 14 cm toward the observer and the rod intercept is 1. 75m on a horizontal sight is 8.167cm.
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Which of the following expressions is equivalent to the one shown below?
OA. 5.-11
OB. (-11)
14
OC.
(-11)
D. (-11)
145
The expression that is equivalent to (-11/15)⁵ is (-11)⁵/(15)⁵
Indices expressionGiven the expression as shown below
(-11/15)⁵
This expression means that we are to raise the value -11 and 14 raised to the power of 5 individually as shown:
(-11/15)⁵ = (-11)⁵/(15)⁵
Hence the expression that is equivalent to (-11/15)⁵ is (-11)⁵/(15)⁵
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What is the partial fraction decomposition, I know D is wrong
[tex]\dfrac{7x^2+14}{(x^2+3)^2}=\dfrac{7x^2+21-7}{(x^2+3)^2}=\dfrac{7x^2+21}{(x^2+3)^2}-\dfrac{7}{(x^2+3)^2}=\dfrac{7(x^2+3)}{(x^2+3)^2}-\dfrac{7}{(x^2+3)^2}=\\=\dfrac{7}{x^2+3}-\dfrac{7}{(x^2+3)^2}[/tex]
Katherine is landscaping her home with juniper trees and pansies. She wants to arrange 15 pansies around each of 8 trees. Each tree costs $20.75 and a six-pack of pansies costs $2.50. Explain how to write an expression to find Katherine’s final cost
The expression that signifies Katherine’s final cost F= P + T= $466
Calculation of final costThe number of pansies to be arranged around each tree = 15 pansies
The cost of pansies(P) = 15 × 8 × 2.50 = $300
The number of juniper trees available = 8
The cost of the trees available(T) = 8 × 20.75= $166
Therefore Katherine's final cost(F)= $300 + $166 = $466
The expression to find Katherine’s final cost = F= P + T
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A cylindrical vase is 10 centimeters in height. When
filled to the very top, it holds 125 cubic centimeters of
water. What is the radius of the vase, rounded to the
nearest tenth? Explain or show your reasoning.
The measure of the radius of the cylinder to the nearest tenth is 1.7cm
Surface area of a cylinderThe formula for calculating the surface area of a cylinder is expressed as:
S = 2πr(r+h)
Given the following
S=. 125cm²
h = 10cm
Substitute
125 = 2πr(r+10)
Expand
125 = 2(3.14)r² + 20(3.14)r
6.28r² + 62.8r - 125 = 0
Factorize
On factorizing, the measure of the radius of the cylinder will be 1.7cm
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Omg I can't work this one out, help!!
You can also check whether I did wrong on the other ones but help me on the last question
Answer:
a) 26 tickets
b) £5
c) chips, pastie and a soft drink
Step-by-step explanation:
Given:
Price of one ticket = £7.50Total available to spend = £200Part (a)
Greatest number of tickets = total available to spend ÷ cost of one ticket
= 200 ÷ 7.5
= 26.66666...
= 26 tickets
(We can't round up, as 27 tickets would cost £202.50)
Part (b)
Money left = Total available spend - cost of 26 tickets
= 200 - (26 × 7.50)
= 200 - 195
= £5
Part (c)
Cost of 3 items = £10 - change
= £10 - £4.70
= £5.30
One of the items can't be a burger, as £5.30 - £3.50 = £1.80
and £1.80 is not enough to buy 2 items.
If he buys chips, he has: £5.30 - £2.40 = £2.90 left to spend on the other 2 items.
Pastie + Soft Drink = £1.60 + £1.30 = £2.90
So he can buy: chips, pastie and a soft drink
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match the resulting values to the corresponding limits.
The correct solution to the limits of x in the tiles can be seen below.
[tex]\mathbf{ \lim_{x \to 9^+} (\dfrac{|x-9|}{-x^2-34+387}) }[/tex][tex]\mathbf{ = -\dfrac{1}{52} }[/tex][tex]\mathbf{ \lim_{x \to 8^-} (\dfrac{8-x}{|-x^2-63x+568|}) }[/tex][tex]\mathbf{=\dfrac{1}{79} }[/tex][tex]\mathbf{ \lim_{x \to 7^+} (\dfrac{|-x^2-17x+168| }{x-7}) }[/tex]= -31 [tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{|x-6| }{-x^2-86x+552}) }[/tex][tex]\mathbf{ =\dfrac{1}{98}}[/tex]What are the corresponding limits of x?The limits of x approaching a given number of a quadratic equation can be determined by knowing the value of x at that given number and substituting the value of x into the quadratic equation.
From the given diagram, we have:
1.
[tex]\mathbf{ \lim_{x \to 9^+} (\dfrac{|x-9|}{-x^2-34+387}) }[/tex]
So, x - 9 is positive when x → 9⁺. Therefore, |x -9) = x - 9
[tex]\mathbf{ \lim_{x \to 9^+} (\dfrac{x-9}{-x^2-34+387}) }[/tex]
Simplifying the quadratic equation, we have:
[tex]\mathbf{ \lim_{x \to 9^+} (-\dfrac{1}{x+43}) }[/tex]
Replacing the value of x = 9
[tex]\mathbf{ = (-\dfrac{1}{9+43}) }[/tex]
[tex]\mathbf{ = -\dfrac{1}{52} }[/tex]
2.
[tex]\mathbf{ \lim_{x \to 8^-} (\dfrac{8-x}{|-x^2-63x+568|}) }[/tex]
-x²-63x+568 is positive when x → 8⁻.Thus |-x²-63x+568| = -x²-63x+568
[tex]\mathbf{ \lim_{x \to 8^-} (\dfrac{1}{x+71}) }[/tex]
[tex]\mathbf{=\dfrac{1}{8+71} }[/tex]
[tex]\mathbf{=\dfrac{1}{79} }[/tex]
3.
[tex]\mathbf{ \lim_{x \to 7^+} (\dfrac{|-x^2-17x+168| }{x-7}) }[/tex]
x -7 is positive, therefore |x-7| = x - 7[tex]\mathbf{ \lim_{x \to 7^+} (\dfrac{-x^2-17x+168 }{x-7}) }[/tex]
[tex]\mathbf{ \lim_{x \to 7^+} (-x-24)}[/tex]
[tex]\mathbf{ \lim_{x \to 7^+} (-7-24)}[/tex]
= -31
4.
[tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{|x-6| }{-x^2-86x+552}) }[/tex]
x-6 is negative when x → 6⁻. Therefore, |x-6| = -x + 6[tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{-x+6 }{-x^2-86x+552}) }[/tex]
[tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{1}{x+92}) }[/tex]
[tex]\mathbf{ \lim_{x \to 6^-} (\dfrac{1}{6+92}) }[/tex]
[tex]\mathbf{ =\dfrac{1}{98}}[/tex]
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Read the excerpt from Black Boy.
The boys scattered, yelling, nursing their heads, staring at
me in utter disbelief. They had never seen such frenzy. I
stood panting, egging them on, taunting them to come on
and fight.
What is the connotative meaning of frenzy as it is used in this
excerpt?
-Negative; it describes a violent reaction based on
rage.
-Positive; it develops a sense of excitement.
-Negative; it suggests a complete mental breakdown.
-Positive; it emphasizes strength and courage
Answer:
Negative; it describes a violent reaction based on rage.
Step-by-step explanation: