The greatest common factor for the given expression is 5z.
What is GCF?
The greatest common factor, which is the product of two or more numbers, is the largest number (GCF). A natural number is created by dividing them by the biggest number (factor). There are a few factors that both share once all the number's factors have been identified. The greatest common factor is the one with the largest number among the common factors. The highest common factor is another name for the GCF (HCF). The highest number that is a factor of all the numbers is known as the greatest common factor of two or more numbers.
Given, the first expression is: y₁ = 70x³z = 5z.14x³ -(i)
Also, the second expression is: y₂ = 45y4z² = 5z.36yz -(ii)
Comparing (i) and (ii), the greatest common factor for y₁ and y₂ is 5z.
Thus, the greatest common factor for the given expression is 5z.
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Rationalizing factor of cube root 5
Answer:
You cube your answer that is the numerator and denominatorTo prove that △LMN ~ △XYZ by the SAS similarity theorem, it also needs to be shown that
For both triangles to be proven to be similar to each other by the SAS similarity theorem, it also needs to be shown that: A. angle N ≅ angle Z.
What is the Side-angle-side Similarity Theorem (SAS)?The side-angle-side similarity theorem (SAS) states that two triangles can be proven to be similar to each other if two pairs of corresponding sides of the two triangles are proportional to each other and one pair of corresponding angles of the two triangles are congruent to each other.
In the image given, we know that in both triangles:
XZ/LN = 6/2 = 3
ZY/NM = 9/3 = 3
Therefore:
XZ/LN = ZY/NM = 3
This means that the two triangles have two pairs of corresponding sides that are proportional to each other.
Thus, we also need to show that both triangles have a pair of congruent included angles before we can prove both triangles are similar to each other.
Thus, what needs to be shown is: A. angle N ≅ angle Z.
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Stephanie ran 5 3/4 miles in one hour if she ran at the same pace how far would she be able to run in 2.5 hours
Answer:
14.375 or 14 3/8
Step-by-step explanation:
5.75*2.5=answer
Answer 5 3/4
Step by step explanation:
So her speed is 5 3/4 mph.
So you just calculate 5 3/4 x 2.5 and you get 14 3/8
I hope this helps
Help 5 star and thanks to the best answer
The value of the smiley face provided in the question is 908.
What is the value of the smiley face ?The first step is to determine the value of each of the shapes.
The value of the rectangle would be determined first. Using the third given equation, let r represent the value of one rectangle.
(4 x r) + (2 x r) - (3 x r) = 15
4r + 2r - 3r = 15
3r = 15
r = 15 / 3 r
r = 5
The next step is to determine the value of the triangle. The second equation would be used. Let t represent the value of the triangle.
(3 x 5) + (4 x t) = 47
15 + 4t = 47
4t = 47 - 15
4t = 32
t = 32 / 4
t = 8
Finally, the value of the star would be determined. Let the value of the star be represented with s. Using the first equation:
5 + (3 x 8) - s = 17
5 + 24 - s = 17
29 - s = 17
s = 29 - 17
s = 12
Now, the value of the smiley face can be determined:
12 x (8 + 12 - 5) + 8(8 . 12 - 5)
12 x (15) + 8(91)
180 + 728 = 908.
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Question 1 of 25
f(x) = 2x³ + 7x²
g(x) = 3x - 2
Find (f - g)(x).
-
4x - 5
A. (f g)(x) = 2x³ +7x²-x-3
OB. (f-g)(x) = 2x³ + 7x² - 7x - 7
c. (f- g)(x) = 2x³ +7x² - 7x - 3
OD. (f-g)(x) = 2x³ +7x²-x-7
The answer of the given function is [tex](f-g)(x) = 2x^3+7x^2-7x-3[/tex]. So the answer is C option.
What does f(x) mean?
f(x) is a function that can be named to avoid repeatedly writing it out. The function's name is f, and we are providing the variable x to it.
And g(x) also has a similar meaning.
The given question is a quadratic equation problem.
Given: f(x)= 2x³+7x²-4x-5
And g(x)= 3x-2
To find: (f-g)(x) we have to simply subtract the above to equations
That is [tex](f-g)(x)[/tex] = 2x³+7x²-4x-5-(3x-2)
On opening the brackets we get;
[tex](f-g)(x)[/tex]= [tex]2x^3+7x^2-4x-5-3x+2[/tex]
[tex]= 2x^3+7x^2 -7x - 3[/tex] { here we subtracted and added the like terms together}.
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The area of a rectangle ABCD is 9cm².
Show that x² + 5x = 3
We can show that x² + 5x = 3 given the dimensions of the rectangle that has an area of 9 cm² as explained below.
How to Find the Area of a Rectangle?To find the area of a rectangle, use the formula given below:
Area of a rectangle = (length)(width).
Given the parameters:
Area of rectangle ABCD = 9 cm²Length of the rectangle = BC = (x + 3) cmWidth of the rectangle = AB = (x + 2) cmTo show that x² + 5x = 3, plug in the values into the formula for the area of a rectangle:
(x + 3)(x + 2) = 9
Apply the distributive property of equality
x(x + 2) + 3(x + 2) = 9
x² + 2x + 3x + 6 = 9
Combine like terms:
x² + 5x + 6 = 9
Add -6 to both sides of the equation
x² + 5x + 6 - 6 = 9 - 6 [subtraction property of equality]
x² + 5x = 3
Thus, if the area of the rectangle with the given dimensions is 9 cm², then we can show that, x² + 5x = 3 as explained above.
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£N is shared between three people in the ratio 2:3:7 The largest share is £540 more than the smallest share. Calculate the value of N.
If £N is shared between three people in the ratio 2:3:7 The largest share is £540 more than the smallest share. the value of N is 1296.
Value of NLet x represent the sharing unit
Hence,
2x :3x :7x
so
7x = 2x + 540
7x - 2x = 540
5x =540
Divide both side by 5x
x = 540/5
x = 108
Sharing unit
2x = 2 ×108
= 216
3x = 3 × 108
= 324
7x = 7 × 108
= 756
Value of N = 216 + 324 +756
Value of N = 1296
Therefore we can conclude that the value of N is 1296.
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please help me figure out this problem i don’t know if i did it right
Answer:
Explanation:
Given:
[tex]\cos x\text{ =}\frac{\sqrt[]{15}}{4}[/tex]We must remember that:
[tex]\cos (2x)=2\cos ^2x-1[/tex]Since the value of cos x is given, we plug in the value into 2cos^2x-1. So,
[tex]\begin{gathered} 2\cos ^2x-1 \\ =2(\frac{\sqrt[]{15}}{4})^2-1 \\ \text{Simplify} \\ =2(\frac{15}{16})-1 \\ \text{Calculate} \\ =\frac{7}{8} \end{gathered}[/tex]Therefore, the exact value of cos 2x is 7/8.
the time it takes me to wash the dishes is uniformly distributed between 12 minutes and 20 minutes. what is the probability that washing dishes tonight will take me between 14 and 16 minutes?
The probability that washing dishes will take time between 14 and 16 minutes is equal to 25%.
This type of probabilty can be termed a uniform probability in which all the outcomes or results are equally likely.
The lower limit can be represented as a and in this problem is 12 minutes and the upper limit can be considered b and in this problem is 20 minutes.
The equation to find probability, in this case, can be given as:
P ( c ≤ X ≤ d ) = d - c / b - a
Here c = 14 and d = 16 as we have to find the probability that washing dishes will take between 14 and 16 minutes.
Therefore;
P ( 14 ≤ X ≤ 16 ) = 16 - 14 / 20 - 12 = 2 / 8 = 0.25
Converting it into percentage:
0.25 = 0.25 × 100 = 25%
Therefore, the probability that washing dishes will take her between 14 and 16 minutes is calculated to be 25%.
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Pointss!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
always remember (for your life) : the sum of all angles in a triangle is always 180°.
and the sum of all angles around a single point on one side of a line is also always 180°.
so,
180 = 65 + 51 + angle PSR
angle PSR = 180 - 65 - 51 = 64°
angle PST is the supplementary angle to angle PSR (that means together they have 180°), because of the principle of all angles around a single point (S) on one side of a line (TSR).
so,
180 = angle PST + angle PSR = angle PST + 64
angle PST = 180 - 64 = 116°
Answer:114
Step-by-step explanation:
the nth term of a sequence is givin by 3n2
position of the term that is the first one to have a value over 100
Position of 1083 is 19 in the sequence that is the first one with a value greater than 1000.
What is Sequence?
A list of numbers or objects in a special order is called sequence.
Given that;
The nth term of a sequence = 3n²
Now,
Let [tex]a_{n}[/tex] be the nth term.
Then, [tex]a_{n} = 3n^{2}[/tex]
Let m be the term which is the first term with a value greater than 1000.
Then, [tex]a_{m} > 1000[/tex]
Substituted the value of [tex]a_{m}[/tex] we get;
3m² > 1000
Divide by 3 we get;
m² > 1000/3
m² > 333.333
Take square root both side;
m > √333.33
m > 18.25
Thus, m = 19
So, 19th term is the first one with a value greater than 1000.
Hence, [tex]a_{19} = 3(19)^2 = 3 * 361 = 1083[/tex]
Thus, Position of 1083 is 19 in the sequence that is the first one with a value greater than 1000.
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Please answer the question
For given functions f(x) = 3x² - 8 and g(x)=5 - 2x - 2x², f(x) - g(x) = 5x² + 2x - 13
In this question, we have been given two functions f(x) = 3x² - 8 and g(x)=5 - 2x - 2x²
We need to find f(x) - g(x)
We need to subtract function g(x) from function f(x)
= f(x) - g(x)
= 3x² - 8 - (5 - 2x - 2x²)
= 3x² - 8 - 5 + 2x + 2x²
= 3x² + 2x² + 2x - 8 - 5
= (3 + 2)x² + 2x - (8 + 5)
= 5x² + 2x - 13
Therefore, for given functions f(x) = 3x² - 8 and g(x)=5 - 2x - 2x², f(x) - g(x) = 5x² + 2x - 13
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Introduction: Drag the concepts more commonly associated with each type of economy to the correct column. More public property Command economies Mixed market economies More private property Greater chance for higher income Larger wealth gap Less chance for higher income Smaller wealth gap
Command Economies -More Public Property, Smaller Wealth Gap ,Less chance for higher income
Mixed Market Economies- Larger Wealth Gap, Greater chance for
higher income, More private property
What is Meant by Economy?Economy: An economy encompasses all of the activities related to the production, consumption, and trade of goods and services in an entity, whether the entity is a nation or a small town. No two economies are identical. Each is formed according to its own resources, culture, laws, history, and geography
Command Economies Mixed Market Economies
More Public Property Larger Wealth Gap
Smaller Wealth Gap Greater chance for higher income
Less chance for higher income More private property
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Answer:
in the picture
Step-by-step explanation:
Solve for x
2x = -21
Give your answer as an
improper fraction in its simplest
form.
Answer: x = -21/2
Step-by-step explanation:
2x/2 = -21/2
x = -21/2
Divide both sides by 2.
-21 is not divisible by 2, so -21/2 is improper in simplest form.
A combination lock uses numbers between 1 and with repetition, and they must be selected in the correct sequence. Is the name of combination lock appropriate? why or why not?.
No, the combination lock is not appropriate. This is so as the repetition is allowed, neither permutation nor the combination rule holds true or valid.
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Brian is driving to Miami. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Brian has 69 miles to his destination after 15 minutes of driving, and he has 58.8 miles to his destination after 27 minutes of driving. How many miles will he have to his destination after 41 minutes of driving?
Brian will have 46.90 miles to his destination after 41 minutes of driving.
In the question ,
it is given that
Brian has 69 miles left to his destination after 15 minutes of driving
let x denotes the driving time ( in minutes)
and y denote the remaining distance ( in miles )
so the point is represented by (15,69)
and given that
Brian has 58.8 miles to his destination after 27 minutes of driving
so the second point is (27,58.8).
Since the relationship is given to be linear , hence it will represent a line .
the equation of line passing through the two points (15,69) and (27,58.8) is given by
(y-69)=(58.8-69)/(27-15) * (x-15)
y-69 = -10.2/12 * (x-15)
y-69 = -0.85(x-15)
y-69= -0.85x+12.75
y = -0.85x + 81.75
So , the linear relationship between remining distance and driving time is given by y = -0.85x + 81.75 .
to find miles will he have to his destination after 41 minutes of driving
Substituting x=41 we get
y = -0.85(41) + 81.75
y = -34.85 + 81.75
y = 46.90 .
Therefore , Brian will have 46.90 miles to his destination after 41 minutes of driving.
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Find the coordinates of the midpoint M
(-3, 2) and K(9, 2)
Answer:
(3,2)
Step-by-step explanation:
since -3 + 9 =6
6 ÷ 2 =3
2 + 2 = 4
4 ÷ 2 = 2
therefore (3,2)
Use elimination to solve for x and y: 2x-y =18
-2x-9y=2
Answer:
2x-y=18
-2x-9y=2
cancel 2x
add equation:
-y+(-9y)=20
-10y=20
y=-20/10
y = -2
input y in any equation:
2x-(-2)=18
2x+2=18
2x=18-2
2x=16
x= 8
Find the domain of the graphed function.
OA. -9≤x≤ 5
OB. 0≤x≤ 10
OC. x20
-10
D. x is all real numbers.
10-
-10-
PLEASE HURRY
The domain of the graphed function is option (D)
What is the domain of a graphed function?
In mathematics, the domain of a function is the set of inputs that the function accepts. It is also known as dom(f) or dom f, where f is the function.
The domain of the graphed function is option (D) x is all real numbers.
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What is the result of converting 0.5 cups to fluid ounces? (Remember that 1
cup = 8 fluid ounces.)
O A. 16 fluid ounces
OB. 2 fluid ounces
OC. 4 fluid ounces
O D. 8 fluid ounces
SUBT
Hellppp
Which describes the graph of y = −(x + 6)2 + 6?
A.Minimum at (6, 6)
B.Maximum at (−6, 6)
C.Maximum at (6, 6)
D.Minimum at (−6, 6)
Augustina has 2 posters with length x inches.
One poster has a width of x + 5 inches, and
the other has a width of x + 7 inches. Write an
expression to represent the area of wall that the
posters will cover.
Answer:
2x² + 12x
Step-by-step explanation:
Area of rectangle:Area of rectangle = length * width
Poster 1:
length = x inches
widht = (x + 5) inches
Area of poster 1 = x * (x + 5)
= x*x + x*5 {Distributive property}
= x² + 5x square inches
Poster 2:
length = x inches
width = (x + 7) inches
Area of poster =x *(x+ 7)
= x*x + x*7
= x² + 7x
Area of wall = area of poster1 + area of poster 2
= x²+ 5x + x² + 7x
= x² + x² + 5x + 7x {Combine like terms}
= 2x² + 12x
Answer:
[tex]2x^2+12x[/tex]
Step-by-step explanation:
Dimensions of Poster 1:
Length = x inchesWidth = (x + 5) inchesDimensions of Poster 2:
Length = x inchesWidth = (x + 7) inchesThe posters can be modeled as rectangles.
[tex]\boxed{\textsf{Area of a rectangle}=\sf length \times width}[/tex]
Therefore, the expressions for the area of each poster are:
[tex]\implies \textsf{Area of Poster 1}=x(x+5)[/tex]
[tex]\implies \textsf{Area of Poster 2}=x(x+7)[/tex]
Therefore, the expression that represents the area of the wall that the posters will cover is the sum of the expressions of the areas of the individual posters:
[tex]\begin{aligned}\textsf{Area of wall posters will cover}&=\textsf{Area of Poster 1}+\textsf{Area of Poster 2}\\& = x(x+5)+x(x+7)\\&=x^2+5x+x^2+7x\\&=x^2+x^2+5x+7x\\&=2x^2+12x\end{aligned}[/tex]
The lengths of the four sides of a quadrilateral (in feet) are consecutive even integers. If the perimeter is 9292 feet, find the value of the longest of the four side lengths.
The longest side of a quadrilateral with length of consecutive even integers is 26 feet.
How to find the side of a quadrilateral?The lengths of the four sides of a quadrilateral (in feet) are consecutive even integers.
A quadrilateral is a polygon with 4 sides.
Therefore, the sides are consecutive even numbers.
Hence,
smallest side = x
Therefore, perimeter is the sum of the whole sides of the quadrilateral.
x + x + 2 + x + 4 + x + 6 = 92
4x + 12 = 92
4x = 92 - 12
4x = 80
x = 80 / 4
x = 20
Therefore, the longest side of the quadrilateral is 20 + 6 = 26 ft.
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The quarterly dividend for Tiffany, a jewelry company, was $0.12
during the second quarter of 2008. What was the annual divider
for 2,000 shares?
Answer:
$960
Step-by-step explanation:
Quarterly Dividend Per Share = $0.12
Quarterly Dividend For 2000 shares = 0.12 x 2000 = $240
Since there are 4 quarters in a year, yearly dividend for 2000 shares at $0.12 per share
= $240 x 4 = $960
Write and solve multiplication equations
We need to solve the s varibale for the given equation:
[tex]\begin{gathered} s-12=20 \\ Add\text{ both sides 12} \\ s-12+12=20+12 \\ s=32 \end{gathered}[/tex]Hence, s=32
At the beginning of spring, Khalil planted a small sunflower in his backyard. When it was first planted, the sunflower was 5 inches tall. The sunflower then began to grow at a rate of 1 inch per week. How tall would the sunflower be after 6 weeks? How tall would the sunflower be after w weeks?
The sunflower would be 11 inches tall after 6 weeks and it would be (5+w) inches tall after w weeks .
In the question ,
it is given that
the height of the sunflower when it was planted = 5 inches
rate of growth of sunflower = 1 inch per week
let y represents the height of the sunflower after x weeks .
So , According to the question , the equation becomes
y = 5 + 1*x
to find the height after 6 weeks , substitute x=6
we get ,
y = 5 + 1(6)
y=5+6
y=11
height after 6 weeks will be 11 inches .
to find the height after w weeks , substitute x=w
we get ,
y = 5 + 1(w)
y=5+w
sunflower will be (5+w) inches tall
Therefore , the sunflower would be 11 inches tall after 6 weeks and it would be (5+w) inches tall after w weeks .
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Which of the following best describes the graph below?
A. It is not a function.
B. It is a one-to-one function.
C. It is a many-to-one function.
D. It is a function, but it is not one-to-one.
The correct option B. It is a one-to-one function; for the given graph.
What is termed as the one-to-one function?Each element of one set, say Set (A), is mapped with such a unique element of another set, say Set (B), where A as well as B are two different sets. It can also be written 1-1. In terms of function, if f(x) = f(y) implies that x = y, after which f is one to one.An injective function is a one-to-one function that maps each element of one set to each element of some other set.For the given question;
As, in the given graph for the function, for each value of the domain (the value of x), there is only one value of range (y).
Thus, the given graph shows the one-to-one function.
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100
Assessment Practice
27. Mr. Tran would like to buy a new sofa
that costs $934. He can pay the total all
at once, or he can make a $125 payment
each month for 8 months. How much
less does it cost to pay all at once? Write
equations to show how you solve. Tell
what your variables represent.
n
$125 $125 $125 $125 $125 $125 $125 $125
Each payment?
The issues are divided into groups according to the four mathematical operations: addition, subtraction, multiplication, and division (suitable for pupils in the second or third grade who have mastered decimal division). Here answer will be $66.
How to solve money word problems?These worksheets on money word problems expose pupils to practical issues and arithmetic applications. The issues are divided into groups according to the four mathematical operations: addition, subtraction, multiplication, and division (suitable for pupils in the second or third grade who have mastered decimal division).
Not all possible values of the domain may be covered by an operation's definition. For instance, it is impossible to square the roots of negative numbers or divide by zero in real numbers. An operation's domain of definition, also known as the active domain, is the set of values for which the operation is specified. However, the set of real values obtained by the operation is its codomain of definition, active codomain, image, or range. The set that contains the values created is referred to as the codomain. For instance, only non-negative numbers are produced by the squaring operation when applied to the real numbers; the set of real numbers is the codomain, but the non-negative numbers are the range.
Each month payment= $125
8 months payment= $125*8= 1000
cost of a car= $934
cost to pay all at once= $1000-$934
= $66
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Find the Area of the figure below, composed of a square and four semicircles. Rounded to the nearest tenths place
The Area of the figure ,composing of a square and four semicircles is 832.7 sq. units
The Length of the side of the square is 18 units which is also the diameter of the semicircle.
So, The Area of square is Length * Length = 18*18 = 324 sq. units
Now, the radius of semicircle = 0.5(diameter)= (0.5)*18 = 9 units
The area of semicircle = half of area of circle = (0.5)3.14(radius)(radius)
The area of one semicircle = (0.5)3.14(9)(9)
The area of one semicircle = 127.17
The Total area of figure consists of 4 semicircles and one square
So, Total area = 4(area of 1 semicircle) + area of square
Total area = 4(127.17) + 324
Total area = 832.68 sq. units
rounding off the total area = 832.7 sq. units
Therefore, the total area of the given figure is 832.7 sq. units.
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-5 + |1 - 8n| > 58
MUST SHOW EQUATION
The value of the inequality is n > 7. 75
What are inequalities?Inequalities are simply defined as mathematical relations that makes an unequal or unbalanced comparison between two elements or numbers and even for known mathematical expressions
They are frequently used in comparing two or more numbers on the number line and this is carried out on the basis of their magnitude or size.
What is absolute value?Absolute value can be defined as the value of a number irrespective of its direction from zero on the number line.
The absolute value of a number must take the positive sign.
It is represented with the symbol '| |'
Given the inequality:
-5 + |1 - 8n| > 58
find the absolute value
-5 + 1 + 8n > 58
collect like terms
8n > 58 + 4
8n > 62
Make 'n' the subject of formula by dividing both sides by 8
8n/8 > 62/8
n > 7. 75
Hence, the value is n > 7. 75
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