To find the greatest common factor (GCF) between monomials, take each monomial and write it's prime factorization. Then, identify the factors common to each monomial and multiply those common factors together.
What is monomial?Monomial is defined as an expression that has a single non-zero term. It consists of different parts like the variable, the coefficient, and its degree. The variables in a monomial are the letters present in it. The coefficients are the numbers that are multiplied by the variables of the monomial. The degree of a monomial is the sum of the exponents of all the variables. Let us consider an expression 6xy2. The variables, the coefficient, and the degree of this monomial are shown in the table given below. Observe the table to learn the various parts of the monomial 6xy2.In algebra, a monomial is an expression that has a single term, with variables and a coefficient. For example, 2xy is a monomial since it is a single term, has two variables, and one coefficient. Monomials are the building blocks of polynomials and are called 'terms' when they are a part of larger polynomials. In other words, each term in a polynomial is a monomial.To learn more about coefficients refer to:
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Is 1 1/3 an irrational number?
In Mrs. Austin's science class, 37.5% of the students have compleated their science project. Of the remaining students, 40% have compleated only half of their science project. If there are 32 students in Mrs. Austin's science class, how many of these students have compleated half of their science project?
well, we know that 37.5% have finished it, that leaves unaccounted for 100% - 37.5% = 62.5%.
now, of those 62.5% fellows only 40% have finished only half of it, how many are those?
well, what's 62.5% of 32? what's 40% of that much?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{62.5\% of 32}}{\left( \cfrac{62.5}{100} \right)32}\implies 20 ~\hfill \stackrel{\textit{40\% of 20}}{\left( \cfrac{40}{100} \right)20}\implies \text{\LARGE 8}[/tex]
Teddy works part-time in the Sony Store. He has a base salary of $12.50/h plus a commission of 12% of the total sales he makes.
If Teddy works 10 hours and sells $1500 electronics, how much will he earn this week?
Answer: $305
Step-by-step explanation:
1) 12.50 multiplied by 10= 125
2) 12% of 1500 is 180
3) 125+180=305
Person A baked 4 1/2 Dozens of cookies for a bake sale.
Person B Baked 1 1/2 as many as Person A
Person C Baked 2 1/3 as many as Person B
How many cookies did each person bake? How many did they bake altogether?
Please also tell me how you got the answer, thanks.
This question is related to Fractions.
The cookies that each person bake will be:
A = 4 1/2 dozen cookies
B = 6 3/4 dozen cookies
C = 15 3/4 dozen cookies.
How to illustrate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.
Person A baked 4 1/2 Dozens of cookies for a bake sale. Person B Baked 1 1/2 as many as Person A. This will be:
= 1 1/2 × 4 1/2
= 6 3/4
Person C Baked 2 1/3 as many as Person B. This will be:
= 2 1/3 × 6 3/4
= 7/3 × 27/4
= 15 3/4
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A community theater performed a play each Saturday evening for 10 consecutive
weeks. The graph shows the attendance for the performances in weeks 1, 4, 6, and 10.
Describe the rates of change in attendance with respect to time.
Weeks 1-4:
Weeks 4-6:
Weeks 6-10:
300
250
200
150
100
50
y
Attendance
Play Attendance
(4, 230)-
(1,131)
(6,208)
(10,60)
Week of performance
0
0 1 2 3 4 5 6 7 8 9101112
The rates of change in attendance in week 1-4 is 33, week 4-6 is -11, week 6-10 is -37 people per week
What is rate of change of attendance?The rate of change in attendance with respect to time is calculated by taking the difference in attendance between two weeks and dividing by the number of weeks between those weeks. This is done to find the average rate of change in attendance per week. The formula used is:
[tex]Rate =\frac{Attendance at week 2 - Attendance at week 1}{week 2 - week 1}[/tex]
Weeks 1-4:
The rate of change in attendance with respect to time is 33 people per week. This can be calculated by taking the difference in attendance between weeks 1 and 4 (230-131) and dividing by the number of weeks between those weeks (4-1 = 3).
[tex]rate =\frac{230-131}{4-1}\\[/tex]
hence rate is 33 people per week
Weeks 4-6:
The difference in attendance between weeks 4 and 6 (230 - 208)
The number of weeks between those weeks (6-4 = 2).
[tex]rate =\frac{208-230}{6-4}[/tex]
Hence rate is -11 people per week
Weeks 6-10:
The difference in attendance between weeks 6 and 10 (60-208)
The number of weeks between those weeks (10-6 = 4).
[tex]rate=\frac{60-208}{10-6}[/tex]
Hence rate is -37 people per week
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Two parallel lines are crossed by a transversal.
Horizontal and parallel lines b and c are cut by transversal a. At the intersection of lines b and a, the bottom right angle is 50 degrees. At the intersection of lines c and a, the top left angle is y degrees.
What is the value of y?
The value of y is 130°
What are corresponding angles?The angles occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.
Given here:
Horizontal and parallel lines b and c are cut by transversal a. At the intersection of lines b and a, the bottom right angle is 50 degrees. At the intersection of lines c and a, the top left angle is y degrees.
Thus the angle adjacent to the 50-degree angle will be 130
but this angle corresponds to the angle y thus y=130 as corresponding angles are equal when a transversal intersects two parallel lines
Hence, The value of y is 130°
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Question 9 of 10
Which is the largest number?
OA. 5.8 x 10-3
B. 2.5 x 105
о C. 1.9 × 106
OD. 8.7 x 10²
On solving the provided question, we can say that F= The lifting force is 27135 0.003357*250*180*180 = F=27135, surface area
What is surface area and an illustration?The total area that all of a 3D object's faces cover is the surface area. The surface area of a cube is its surface area, for instance, if we are trying to determine how much paint is needed to paint it. Always expressed in square units.
The entire surface of a three-dimensional shape is referred to as its surface area. A cuboid with six rectangular faces has a surface area equal to the sum of the areas of each face. Alternatively, you can label the cuboid's length, width, and height (l, w, and h), then calculate its surface area (SA) using the formula: SA=2lw+2lh+2hw.
F= k*a*v^2
a= 250
v=190
30300=k*250*{190^2}
k= 0.03357
F= 0.003357*250*180*180
F=27135
The lifting force is 27135
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Can any1 help with this pls
Describe the transformation between these two lines.
Answer:
To get black from red ...
scale by a factor of 3reflect over the x-axisshift left 1 unitshift up 4 unitsStep-by-step explanation:
You want the know the transformation that is applied to the red graph to make it be the black graph.
ObservationWe note that the vertex of the black graph is (-1, 4), which is 1 unit left and 4 units up from the vertex of the red graph.
The black graph opens downward, and has a slope of ±3 compared to the slope of ±1 for the red graph. This means it has been reflected across the x-axis and scaled by a factor of 3.
TransformationThe reflection and scaling can both be accomplished by multiplying the function by -3. The translation is accomplished by adding 4 to the function value to shift it up 4 units, and adding 1 to the x-value to shift the graph left 1 unit.
The transformations applied to the red graph are ...
scale by a factor of 3reflect over the x-axisshift left 1 unitshift up 4 unitsAnusha starts from her home p goes to school S via Q, R. Find the total displacement made by her to go from her home to school.
The total displacement made by her to go from home to the school is given by the sum of the distances of P to Q, Q to R and then R to S.
How to obtain the total displacement?The total displacement is obtained as the distance that she walks to go to the school from her home.
The check-points that she passes to go to the school are given as follows:
P to Q.Q to R.R to S.Hence the total displacement is given by the sum of each of these distances.
These distances are calculated using the formula for the distance between two points, given as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In which [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of each point.
Missing InformationThe problem is incomplete, hence the answer is given in general terms.
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Write as an radical expression
U 2/5
Answer:
Step-by-step explanation:
An radical expression usually involves a radicand which is the number or expression inside the radical symbol √ and an index which is the number outside the radical symbol indicating the root, the radicand raised to the power of the reciprocal of the index.
But in the case of expression "U-2/5" it's not a radical expression as is. It's a fractional expression with variable U and a constant -2/5.
It can be written as √(U-2)/5 or U- √(2/5) if you want to express it as an radical expression.
Simplify the difference. (2w2 – 8w – 8) – (5w2 + 3w – 5)
Answer:
-3w2-11w-3
Step-by-step explanation:
take w2 and w as variables. you can substitute it as w2=y and w=X then expand brackets
2y-8x-8-5y-3x+5
note that the signed changed at the second part because it was expanded with the minus sign which is basically like -1, so it changes the signs
then you collect like terms:
2y-5y-8x-3x-8+5= -3y-11x-3
now put substitute back w2=y and w=X
-3w2-11w-3
if it won't be a problem solving with w2 and w, then you skip the substitution part and solve the same
For problems 1-3, use the information in the diagram to find the angle measure of in radians. Round your answer to the nearest ten-thousandth, if necessary.
Answer:
4.25 radians2.4 radians0.625 radiansStep-by-step explanation:
You want the angles associated with different arc lengths and radii.
AngleThe length of an arc is given by the formula ...
s = rθ . . . . . θ is the angle in radians, r is the radius
Solving for θ gives ...
θ = s/r
1.For s=17 in, r=4 in, ...
θ = (17 in)/(4 in) = 4.25 . . . . radians
2.For s=12 ft, r=5 ft, ...
θ = (12 ft)/(5 ft) = 2.4 . . . . radians
3.
For s=8.5 mm, r = 13.6 mm, ...
θ = (8.5 mm)/(13.6 mm) = 0.625 . . . . radians
(3,4) m=0
Formula
Y-y=m(x-x1)
Answer:
[tex]y1 = 4 \\ x1 = 3[/tex]
[tex]y - y1 = m(x - x1)[/tex]
[tex]y - 4 = 0(x - 3)[/tex]
[tex]y - 4 = 0[/tex]
[tex]y = 4[/tex]
Y intercept and slope
Answer: A y-intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system.
Slope - A number that describes both direction and steepness of the line.
Step-by-step explanation: If a line intersects the y-axis at point 5 then its y-intercept will be c= 5. As we denote y-intercept with c.
The slope is denoted by m.
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
Two equations that have the same solution as the given equation are;
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p – 400 – p
What is Multiplication property of equality?Both sides of an equation will remain equal, when both sides are
multiplied by the same amount.
The given equation: 2.3·p - 10.1 = 6.5·p - 4 - 0.01·p
Simplifying the above equation by collecting like terms gives;
2.3·p - 10.1 = 6.5·p - 0.01·p - 4 = 6.49·p - 4
2.3·p - 10.1 = 6.49·p - 4
Multiplying both sides of the original equation by 100 gives
100 × (2.3·p - 10.1) = 100 × (6.5·p - 4 - 0.01·p)
230·p - 1010 = 650·p - 400 - p
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Solve by factoring
-3x^2-11x+2=0
Answer:
x = -11, 2/3
Step-by-step explanation:
-3x^2-11x+2=0
-(3x^2+11x-2) = 0
3x^2 + 11x - 2 = 0
3x^2 + 33x - 22x - 2 = 0 ==> 33-22=11 and 33/11=3 and -22/11=-2
3x(x + 11) - 2(x + 11) = 0 ==> factor
(3x - 2)(x + 11) = 0
3x - 2 = 0 x + 11 = 0
3x = 2 x + 11 - 11 = 0 - 11
{ x = 2/3 x = -11 } ==> x = -11, 2/3
Simplify. -15 times the square root of y^2 if y>0
Answer:
-15y
Step-by-step explanation:
The square root of any squared number is always the number itself.
So in this case, it is -15y
Brainliest please. It'll help a lot.
Answer:
- 15y---------------------------------
Simplify the expression:
[tex]-15\sqrt{y^2}[/tex]We know the square root is never negative and since y is positive, we get:
[tex]-15\sqrt{y^2} =-15y[/tex]Find a formula for RN for the function f(x) = (5x)² on [-1, 5] in terms of N.
Could you please show the work? I was able to get the area but can't exactly figure out what they want for the formula.
Compute the area under the graph as a limit.
lim RN=1050
Therefore , R(N) = 100 + 400 (N+1)(2N+1) + 800 x N2 N3 and area are the formulas for R(N) for the function f(x) = (5x)2 on [1, 5] and the function f(x) = (5x)2 in terms of N. R(N) = 767(approx) (approx).
What is function?Each x value in the domain has one but only one y value range, according to the rule of a function. Definition. If there is only one and only one value of x variable such that f(x) = y, then the function is one-to-one.
Here,
In the given question, we have to find a formula for R(N) for the function f(x) =(5x)^2 on [1, 5] in terms of N.
The given function is f(x)=(5x)^2 on [1, 5].
Ax = (5-1)/N
Ax = 4/N
X = 1+iAx
X = 1+i4/N
f(x) = 25X^2
f(x) = 25(1+i4/N)^2
f(x) = 25(1+i8/N+16/N^2 i^{2})
R(N) = 1ƒ(X) Ax
Now putting the value of f(x) and Ax
R(N)==1 [25 (1+ &i + 16i2)]
R(N) = 1001 (1 +Ni + 16i2)
N100 (1+i+12)N
100 (N += i +122)+16 N(N+1)(2N+1)(+1)(2N+1)
R(N)=100 (N + √2/ N(N+1) x 100
R(N) =2/6× N + 100 × 5 × N(N+1) + 100 x 2
[tex]\lim_{n \to \infty}[/tex] R(N) = 100 + 400 + 800/3
[tex]\lim_{n \to \infty}[/tex] R(N) = 766.67
[tex]\lim_{n \to \infty}[/tex] R(N) = 767(approx)
Therefore , the solution of the given problem of function comes out to be [tex]\lim_{n \to \infty}[/tex] R(N) = 767(approx).
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Pls help fractions pls and sm else
Answer:
Step-by-step explanation:
(49/72)-(13/14)
-125/504
A tree that is 30 tall casts a 40 shadow. What is the distance from the top of the tree to the end of the shadow?
The distance from the top of the tree of height 30 tall to the end of the shadow is 50.
What is distance?Distance is the length between two point.
To calculate the distance from the top of the tree to the end of the shadow, we use the formula below.
Note: The tree and the shadow form a right angle.
Formula:
a = √(b²+c²)................. Equation 1Where:
a = Distance of from the top of the tree to the end of the shadowb = Height of the treec = Length of the shadowFrom the question,
Given:
b = 30 c = 40Susbtitute these values into equation 1
a = √(30²+40²)a = √(900+1600)a = √2500a = 50Hence, the distance from the top of the tree to the end of the shadow is 50.
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What is the value of f(x) = –x2 + 3 when x = 1?
Solve 0.5(-2+ 4d) - 2d=-13 for d.
O Infinite solutions
O No solution
O d=-11
O d = 1.375
Answer:
(b) No solution
Step-by-step explanation:
You want the solution to 0.5(-2+ 4d) - 2d = -13.
SimplifiedEliminating the parentheses using the distributive property, we have ...
-1 +2d -2d = -13
Collecting terms gives ...
-1 = -13 . . . . . false
No value of d will make this true. There is No Solution.
An Item costs $450 Before tax. and the sales tax is $31.50
Find the sales tax rate. Write your answer as a percentage
The tax rate of an Item that costs $450 Before tax. and the sales tax is $31.50 is 7%
What is tax rate?The tax rate is the percentage of an income or an amount of money that has to be paid as tax.
To find the tax rate of $31.50 from $450
The formula is
Amount taxed/Principal amount x 100
= $31.50/$450 x100
=$3150/450
=7%
Hence, the tax rate is 7%
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June is buying a sweater using a coupon offering a 30% discount on items over $99. If the discounted price is $91, how much was the original price of the sweater?
Answer: 130
Step-by-step explanation:
The original price of the sweater is $303.
What is discount?A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.
Given that, June is buying a sweater using a coupon offering a 30% discount on items over $99.
The discounted price is $91
Let the original price of the sweater be x.
So, 30% of x=91
30/100 ×x=91
0.3x=91
x=91/0.3
x=$303
Therefore, the original price of the sweater is $303.
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1/950/18/4
Write an equation and solve for b using the diagram
below. YOU MUST WRITE THE EQUATION IN
ORDER TO GET CREDIT.
40°
(6b+ 2)°
OLIC
One possible equation is (6b+2)+40 = 90
That equation solves to b = 8
======================================================
Explanation:
The angles (6b+2) and 40 degrees combine to form a right angle, aka 90 degree angle. This is because the upper angle is 90 degrees, so the remaining portion is 180-90 = 90.
So (6b+2)+40 = 90 is one possible equation.
Let's solve for b.
(6b+2)+40 = 90
6b+42 = 90
6b = 90-42
6b = 48
b = 48/6
b = 8
---------------
A slight alternative.
The angles (6b+2), 40, and the 90 degree angle form a straight line.
The three angles add to 180
(6b+2)+(40)+(90) = 180 is another possible equation
6b+132 = 180
6b = 180-132
6b = 48
b = 48/6
b = 8
In an acid-base titration, a base or acid is gradually added to the other until they have completely neutralized each other. Because acids and bases are usually colorless (as are the water and salt produced in the neutralization reaction), pH is measured to monitor the reaction. Suppose that the equivalence point is reached after approximately 100 mL of a NaOH solution have been added (enough to react with all the acetic acid present) but that replicates are equally likely to indicate from 95 to 104 mL to the nearest mL. Assume that volumes are measured to the nearest mL and describe the sample space. (a) What is the probability that equivalence is indicated at 100 mL? (b) What is the probability that equivalence is indicated at less than 100 mL? (c) What is the probability that equivalence is indicated between 98 and 102 mL (inclusive)?
Neglecting the fractional points and taking the whole number values for volume, the probability of getting equivalence point at 100 ml is 1/10. The probability of getting less than 100 ml is 1/2.
What is probability?The probability is the measurement of the chance of an event to happen. It is determined based on the total possibilities and criteria.
Given that the experiment trials got the values from 95 to 104. From 95 to 104, there are 10 numbers. Thus, the volume of the acid can be any of these 10.
Thus, total possibility = 10.
probability of getting 100 = 1/10
There are 5 volumes which are less than 100 here, [95, 99]. Thus, the probability = 5/10 = 1/2.
There are 5 values between 98 and 102 including these two values.
Hence, probability of getting these range = 5/10 = 1/2.
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Jayda has a vegetable garden. 2/3 of the garden is made up of tomato plants. 4/5 of the tomato plants are beefsteak tomatoes. What portion of the garden is made up of beef steak tomatoes?
a) The portion of the garden is made up of beef steak tomatoes is 8.
b) he Equation for beef steak tomatoes is 4/5 x (portion of tomatoes).
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
Portion of Garden have Tomatoes = 2/3
and, 4/5 of the tomato plants are beefsteak tomatoes.
a) The total section in model is 15.
so, Tomatoes in the garden = 2/3 x 15
= 10
and, the portion of the garden is made up of beef steak tomatoes
= 10 x 4/5
= 8 portion.
b) The Equation for beef steak tomatoes
= 4/5 x (portion of tomatoes)
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Please someone help me !!
Answer: $26.81
Step-by-step explanation: the tank holds 16.5 gallons. Meaning, half of the tank is 8.25 gallons. Multiply that by the cost of the gas, 3.25, and you get 26.81
From a rock ledge, the angle of elevation to the top of a tree is 22°. The angle of depression to the base of the tree is 12°.
a) Find the height of the rock ledge, to
the nearest metre.
b) Find the height of the tree, to the
nearest metre.
The height of the rock ledge will be 20.35 meters.
The height of the tree will be 58.75 meters
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The angle of elevation to the top of a tree is 22°.
And, The angle of depression to the base of the tree is 12°.
Now,
Let the height of the rock ledge = x
So, By figure, we get;
⇒ tan 12° = x / 96
⇒ x = 96 × tan 12°
⇒ x = 20.35 meters
And, Let total height of the tree = x + y
= 20.35 + y
Hence, By figure, we get;
⇒ tan 22° = y / 96
⇒ y = 96 × tan 22°
⇒ y = 96 × 0.40
⇒ y = 38.4 meter
Thus, The height of tree = 38.4 meters + 20.35 meters
= 58.75 meters
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To find:-
The height of the rock ledge.Height of the tree .Answer:-
Part A :-
Here we can see that the distance between the rock ledge and the base of the tree is 96m . Also the angle of elevation to the top of the tree from the rock is 22° .
Firstly, we can see that,
[tex]\implies \angle CAD =\angle EDA = 12^o\\[/tex]
This is so because they are alternate interior angles .
Now , in ∆ADE ,
[tex]\implies \tan\theta =\dfrac{p}{b}=\dfrac{AE}{ED}\\[/tex]
[tex]\implies \tan 12^o =\dfrac{AE}{96m} \\[/tex]
[tex]\implies AE = 96\tan12^o m \\[/tex]
[tex]\implies AE = 96 (0.21)m \\[/tex]
[tex]\implies AE = 20.16 \ m \\[/tex]
Hence the height of the rock ledge is 20.16 m.
_______________________________________
Part B :-
Now in ∆ACB , we have;
[tex]\implies \tan\theta =\dfrac{BC}{AC} \\[/tex]
[tex]\implies \tan 22^o =\dfrac{BC}{96m} \\[/tex]
[tex]\implies BC = 96\tan 22^o \ m \\[/tex]
[tex]\implies BC = 96(0.4) m \\[/tex]
[tex]\implies BC = 38.4 \ m \\[/tex]
Now the total height of the tree will be = BC + AE
[tex]\implies h_{tree}= BC + AE \\[/tex]
[tex]\implies h_{tree}=38.4\ m + 20.16 \ m =\boxed{58.56\ m} \\[/tex]
Hence the height of the tree is 58.56m.
and we are done!