a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
where
a
=
7
and
b
=
3
x
.
(
7
+
3
x
)
(
7
−
3
x
)
Answer: -(3x - 7)(3x + 7)
Step-by-step explanation:
1. Rewrite the formula:
-[tex]9x^{2} + 49[/tex]
2. Factor -1 out of [tex]-9x^{2} + 49[/tex]
[tex]-(9x^{2} - 49)[/tex]
3. [tex]9x^{2} - 49 = (3x)^{2} - 7^{2}[/tex]
[tex]((3x)^{2} - 7^{2})[/tex]
4. Factor the difference of two squares. [tex](3x)^{2} - 7^{2} =[/tex]
[tex](3x-7)(3x+7)[/tex]
5. Add back negative:
Answer: [tex]-(3x-7)(3x+7)[/tex]
1.25x + 1.49 = 100.
The value of x comes to 78.808 after solving the given expression 1.25x + 1.49 = 100.
What are expressions?Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)A single term or a collection of terms can be used to create an algebraic expression. For instance, 4x and y are the two terms in the expression 4x + y.So, 1.25x + 1.49 = 100:
Now, solve as follows:
1.25x + 1.49 = 1001.25x = 100 - 1.491.25x = 98.51x = 98.51/1.25x = 78.808Therefore, the value of x comes to 78.808 after solving the given expression.
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How many lines of symmetry does the figure at the right have?
Lines of symmetry, a line that divides a figure into two mirror parts, for example:
As we can see, the only line of symmetry that we can draw in our figure is:
Answer: One
please show all work
The point that lies on the graph y = tanx is ([tex]\frac{4\pi }{3},\sqrt{3}[/tex]),([tex]\frac{\pi }{3},\sqrt{3}[/tex])
What is coordinate plane ?Two number lines combine to form a two-dimensional surface known as a coordinate plane. It is created when the origin, a point where the X- and Y-axes coincide, is crossed by a horizontal line. Points are located using the numbers on a coordinate grid. You can graph points, lines, and many other things using a coordinate plane. It serves as a map and provides clear directions between two points.The following is a definition of a coordinate plane: The intersection of the Y-axis, a vertical line, and the X-axis, a horizontal line, creates a coordinate plane, also referred to as a rectangular coordinate plane grid.
The point that lies on the graph y = tanx is ([tex]\frac{4\pi }{3},\sqrt{3}[/tex]),([tex]\frac{\pi }{3},\sqrt{3}[/tex])
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The ratio of the area between a small square of land and a large squareof land is 3: 7. Given that the total area of the two squares of land is4,000 m2, find the area of each square of land.
Given:
The ratio of the area between a small square of land and a large square
of land is 3: 7.
Total area of the two squares of land (in sq. meter) is 4000.
Required:
The area of each square of land.
Answer:
We have the ratio of the area between a small square of land and a large square of land is 3: 7.
Let
[tex]x^[/tex]be the area of the square of land.
Then their ratio is given by,
[tex]3x^:7x^[/tex]Also given that the total area of the two squares of land (in sq.meter) is
4,000.
The area of
Therefore,
[tex]\begin{gathered} 3x^+7x^=4000 \\ \Rightarrow10x^=4000 \\ \Rightarrow x^=400 \\ \end{gathered}[/tex]Therefore,the area of small square (in sq. meter) is,
[tex]3x=3(400)=1200[/tex]and the area of large square (in sq. meter) is,
[tex]7x=7(400)=2800[/tex]Final Answer:
The area of small and large square respectively (in sq. meter) is,1200 and 2800.
I need the answer ASAP
In order to rationalize the denominator of the fraction, we need to multiply the fraction by the conjugate of the expression in the denominator.
The conjugate is the same expression but with the signal between the numbers changed.
So we have:
[tex]\frac{4}{3+\sqrt[]{7}}=\frac{4}{3+\sqrt[]{7}}\cdot\frac{3-\sqrt[]{7}}{3-\sqrt[]{7}}=\frac{4(3-\sqrt[]{7})}{3^2-(\sqrt[]{7})^2}=\frac{12-4\sqrt[]{7}}{9-7}=\frac{12-4\sqrt[]{7}}{2}[/tex]So the new denominator of the fraction is 2, therefore the correct option is D.
A store sells juice in different sizes. Determine which size is the best buy and the unit price.8 oz $2.4024 oz $6.4864 oz $14.08
To determine which is the best buy, we need to first find the unit price of each
8 oz $2.40
Unit price
$2.40/8 = $0.3
1 oz = $0.3
24 oz $6.48
Unit price
$6.48/24 =$0.27
1 oz = $0.27
64 oz $14.08
Unit price
$14.08/64 =$0.22
From the above the best best buy is the one with the lowest price which is $0.22
The best buy is;
64 oz $14.08
and the unit rate is $0.22 per oz
The lines below are perpendicular. If the slope of the green line is ž, what isthe slope of the red line?maO A A. -O B.O c. - 3O D.1Nim
-3/2 (option A)
Explanation:The line of green and red are perpendicular.
For two lines to be perpendicular, the slope of one line will be the negative reciprocal of the second line.
slope of one line (green) = 2/3
slope of red line = negative reciprocal of green line
slope = 2/3
reciprocal of line = 3/2
negative reciprocal of the line = -3/2
The slope of the red line = -3/2 (option A)
Perform the given operations on the functions
21) f(x)=x² + 3x, g(x) = 2x + 2,
A. (f+g)(x)
B. (f- g)(x)
Answer:
see explanation
Step-by-step explanation:
A
(f + g)(x)
= f(x) + g(x)
= x² + 3x + 2x + 2 ← collect like terms
= x² + 5x + 2
B
(f - g)(x)
= x² + 3x - (2x + 2)
= x² + 3x - 2x - 2 ← collect like terms
= x² + x - 2
using the path method for multivariable limits, demonstrate that the limit doesn't exist:
[tex]lim_{(x,y) \to (1,1)} \frac{x y - x - y + 1}{x^2 + y^2 - 2 x - 2 y + 2}[/tex]
Demonstrating that the limit doesn't exist
What is Limits?
The value that a function approaches when the input approaches a certain value is known as a limit. Calculus and mathematical analysis are not possible without limits, which are used to define continuity, derivatives, and integrals.
The limit exists only if the value of the limit along every direction that leads to (1,1) is same.
So by calculating,
lim xy -x-y + 1 / x^2 + y^2 - 2x - 2y + 2
x->1
calculating the limit along the line x = 1
Similarly,
lim xy -x-y + 1 / x^2 + y^2 - 2x - 2y + 2
x->1
calculating the limit along the line y = 1
And the last limit you calculated is along line y=x.
To answer your question, the calculation of the limit along y=1 would not have been necessary. It is sufficient to demonstrate the absence of a limit by giving just two cases in which it appears to vary along several directions.
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Compute P9, 2 please help me solve this
Answer:
72
Step-by-step explanation:
Formula: P (n,r) = n! ÷ (n - r)!
n = Total number of objects in a set
r = The number of items you choose
!/Factorial = Product of all positive numbers less than or equal to the given positive number
9! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9
7! = 1 x 2 x 3 x 4 x 5 x 6 x 7
P (9,2) = 9! ÷ (9-2)!
362,880 ÷ 5,040 = 72
Only 1 and 9 please show work THANK YOU
Simplification of the given expression to single complex number are as follow :
1. 3i
2. 4i
3. 24
4. 15
5. 1 + √3 i
6. 2 + [tex]\sqrt{5}i[/tex]
As given,
Simplify the following expression to a single complex number,
1) [tex]\sqrt{-9}[/tex] = [tex]\sqrt{9}\sqrt{-1}[/tex] = 3i
where i is the complex number representing [tex]\sqrt{-1}[/tex]
2) √-16 = 4i
3) √-6 √-24
= √6 ×6 ×4
= 6 ×4
= 24
4) √-3 √-75
=√ 3×75
= √3 × 3 ×25
= 3 ×5
=15
5) [tex]\frac{2 +\sqrt{-12} }{2}[/tex]
= (2 + 2√-3) /2
= 1 + √3 i
6) [tex]\frac{4+\sqrt{-20}}{2}[/tex] = [tex]\frac{4+\sqrt{20}\sqrt{-1}}{2}[/tex] = [tex]\frac{4+(2\sqrt{5}\sqrt{-1})}{2}[/tex] = [tex]\frac{4+(2\sqrt{5}i)}{2}[/tex] = [tex]\frac{2(2+\sqrt{5}i)}{2}[/tex] = 2 + [tex]\sqrt{5}i[/tex]
where i is the complex number representing [tex]\sqrt{-1}[/tex]
Therefore, simplification of the given expression to single complex number are as follow :
1. 3i
2. 4i
3. 24
4. 15
5. 1 + √3 i
6. 2 + [tex]\sqrt{5}i[/tex]
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A contractor bought 8.2 ft2 of sheet metal. He has used 3.7 ft² so far and has $90 worth of sheet metal remaining. The equation 8.2x-3.7x = 90 represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?
By solving the equation, we get the cost of sheet metal =$20 per sq. feet
What is an equation?
An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign. Solving an equation with variables entails finding which variables' values make the equality true. The variables for which the equation must be solved are also known as unknowns, and the values of the unknowns that fulfill the equality are known as equation solutions. Identity equations and conditional equations are the two types of equations.
Given equation 8.2x-3.7x = 90
or, 4.5x = 90
or, x = 90/4.5 = 20
Hence, the cost of sheet metal is $20 per sq. feet
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Given f(x) = 8(12 − x) — 5, what is the value of f(-2)?
Answer:
f(2)=8(12-x)-5
=8(12-2)-5
f(2)=8(10)-5
=75
What are the coordinates of a point 4/5 of the way B to A
A(3,-4)
B(13,11)
[tex]\textit{internal division of a segment using a fraction}\\\\ B(\stackrel{x_1}{13}~,~\stackrel{y_1}{11})\qquad A(\stackrel{x_2}{3}~,~\stackrel{y_2}{-4})~\hspace{8em} \frac{4}{5}\textit{ of the way from B to A} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_2}{3}-\stackrel{x_1}{13}~~,~~ \stackrel{y_2}{-4}-\stackrel{y_1}{11})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment BA}}}{\left( -10 ~~,~~ -15 \right)} \\\\[-0.35em] ~\dotfill\\\\ \left( \stackrel{x_1}{13}~~+~~\frac{4}{5}(-10)~~,~~\stackrel{y_1}{11}~~+~~\frac{4}{5}(-15) \right) \\\\\\ (13~~ - ~~8~~,~~11~~ - ~~12)\implies {\Large \begin{array}{llll} (5~~,~~-1) \end{array}}[/tex]
The water pressure on a submerged object is given by P = 64d, where P is the pressure in pounds per square foot, and d is the depth of the object in feet.
a. solve the formula for d.
b. Find the depth of a submerged object if the pressure is 672 pounds per square foot.
60 and 274.
Step-by-step explanation:
Consider the expressions (2.4 x 10/8) and (9.2 x 10/6) Find the difference of the expressions.
Find the product of the expressions
The difference of the values is -12.9 while the product of the expression is 45.9
How to solve for the differenceWe have to solve for
2.4 x 10/8
= 2.4 x 1.25
= 3
(9.2 x 10/6)
= 9.2 x 1.667
= 15.3
The difference between the values wpuld be
3 - 15.3
= -12.3
The product of the expressions would be solved by
3 x 15.3
= 45.9
Hence we would say that the difference that is in the values that we have here is -12.9 while the product of these values is given as 45.9
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Can you give me two examples of a absolute value parent function
SOLUTION:
Step 1:
In this question, we are given the following:
Can you give me two examples of an absolute value parent function?
Step 2:
What is the parent function for absolute value?
An absolute value function is a function that contains an algebraic expression within absolute value symbols. Recall that the absolute value of a number is its distance from 0 on the number line.
Examples include:
1. The absolute value parent function, written as: f(x)=| x |, is defined as:f(x)={x if x>00 if x=0−x if x<0.
[tex]f(x)\text{ =}\lvert x\rvert[/tex], is defined as:
[tex]f(x)\text{ =}\lvert x\rvert[/tex][tex]\begin{gathered} f(x)\text{ =}\lvert x\rvert \\ \text{if x > 0, then f(x) = x} \\ \text{if x < 0, then f(x) = x} \end{gathered}[/tex]2. The second example of absolute value function is:
[tex]f(x)\text{ =}\lvert\sin x\rvert[/tex]Find the difference: 11/21 - 3/7
We will operate as follows:
[tex]\frac{11}{21}-\frac{3}{7}=\frac{2}{21}[/tex]List the first 6 common multiples of 8
List the first 6 common multiples of 12
The first six common multiples of 6 and 8 are :
24,48,72, 96, 120 and 144.
The first six common multiples of 12 and 18 are :
24, 36, 72, 108, 144, 216.
In order to resolve this, we shall use the multiples idea.
(A) The two numbers given are 6 and 8.
Six is the first multiple of which there are the following: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, and 144.
multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, and 144.
Therefore, common multiples are: 24, 48, 72, 96, 120 and 144.
(B) The two numbers given are 18 and 12.
The first few multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, and 240.
Similarly, the multiples of 18 are: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252, and 270.
Therefore, common multiples are: 24, 36, 72, 108, 144, 216.
Hence we get the required common multiples.
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solve for x. 7/13=x/48
Answer:
25.7
Step-by-step explanation:
7/13=x/48. By cross multiplication 13 x=326 = 25.7
how could you use a graph of a proportional relationship to find any ratio in the the proportional relationship why does this work?
It should be noted that when the graph of a relationship is a line that passes through the origin, then it is proportional.
How to illustrate the information?A connection is proportional if its graph is a line that goes through the origin. The ratio is not proportionate if it is not a line or ray that doesn't accomplish this. K = y/x is the equation for the proportionality constant. The equation for the slope of a straight line with respect to the origin is the same as this.
A relationship is proportionate if its graph is a line or ray that passes through the origin. It is not proportionate if the line or ray does not go through the origin. Additionally, something is not proportionate if it is not linear.
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3.5 divided by 85
answers:
at least 500/ at least 50/ at least 20/ at least 200
Ive looked up answers to this question in iready but everyone says the answer is 24?
The value of 3.5 divided by 85 will be 0.4118.
What is division?Division is one of the four basic arithmetic operations, or the process by which two numbers are added together to produce a new number. Multiplication, addition, and subtraction make up the remaining operations.
Division's opposite is multiplication. Dividend Divisor = Quotient + Remainder is a formula for calculating the division of two numbers.
The dividend in this situation refers to the number that is being divided. The divisor is the number that divides the number (dividend) into equal parts.
In this case, 3.5 ÷ 85 = 0.4118. This can be computed through the use of a calculator.
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There was a jar of cookies on the table. First Ken came along. He was hungry
because he missed lunch, so he ate half the cookies in the jar. Mary came in the
kitchen next. She didn't have dessert at lunch so she ate one third of the cookies
left in the jar. Karen followed her to the cookie jar and she took three fourths of
the remaining cookies. Susan ran into the kitchen, grabbed one cookie from the
jar and ran out again. That left one cookie in the jar. How many were in the jar to
begin with?
Answer:
There were 24 cookies in the jar at the beginning.
Step-by-step explanation:
There is 1 cookie left add the one susan took that is two. Two is 1/4 of 8. Eight is 2/3 of 12. Twelve is 1/2 of 24. 24 is the answer. You can also check it by going back.
7. Jill was 80th in a class of 200, whereas Nathan, who is in the same class, has a percentile rank of 80. Which student has the higher standing in the class?
The student that has the higher standing in the class is Jill
How to determine the student that has the higher standing in the class?The given parameters are:
Number of students = 200
Jill's position =80th
Nathan's position = Percentile rank of 80
The above means that
Nathan's position = 80 percentage of the number of students in the class
Substitute the known values in the above equation
So, we have the following equation
Nathan's position = 80 percentage of 200
Rewrite as
Nathan's position = 80 percentage * 200
Express as percentage
Nathan's position = 80% * 200
Express 80% as decimal
Nathan's position = 0.80 * 200
Evaluate the product
Nathan's position = 160
So, we have
Jill's position =80th
Nathan's position = 160th
By comparing the positions, 80th is greater than 160th
Hence, Jill has the higher standing in the class
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who can solve this equation 4x-6=x+9 ??
Answer:
x = 5
Step-by-step explanation:
Hello!
According to the question, what's the value of 4x-6=x+9
4x-6=x+9
Collect like terms
x - 4x = -6 - 9
-3x = -15
Divide both sides by the coefficient of x which is -3
-3x/-3 = -15/-3
x = 5
When checking
4x-6=x+9
(4)(5)−6 = 5+9
14=14
True
Simplify the fraction 112 144 as much as possible.
Answer:
7/9
Step-by-step explanation:
Answer:
7/9
Step-by-step explanation:
I took the quiz
Each pair of polygons is similar. Write a similarity statement for the polygons. Then, find the measure of x, the
measures of the indicated sides, and the scale factor.
CB and AB
D
2.4
729
2
610
E
2.6
F
C
3.6
A
72⁰
3x-0.6
2x
61 B
2
| ADEF - AABC;x=15;CB=39; AB=3; 3
2
ADEF-ACBA; x = 3; CB=3; AB=3.9; 3
2
ADEF-ACBA; x = 1; CB = 3.9; AB = 3; 3
3
ADBF - AABC;x=1.5; CB=3; AB=3.9; 2
Scale factor means ratio of the sides of the triangle then the measures of the indicated sides, and the scale factor of CB and AB exists ΔDEF - ΔABC; x = 1.5; CB = 3.9; AB = 3.
What is meant by scale factor?A scale factor is the amount by which an object is multiplied to produce a second object of different size but with the same appearance. The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
Each pair of given polygons are similar.
Similarity statement for the given polygons:
In ΔDEF and ΔABC,
∠D = ∠A (Angle)
∠E = ∠B (Angle)
Therefore, ΔDEF ΔABC (by AA similarity)
If two triangles are similar, then their sides are proportional.
[tex]$\Rightarrow \frac{D F}{A C}=\frac{D E}{A B}$[/tex]
[tex]$\Rightarrow \frac{2.4}{3.6}=\frac{2}{2 x}$[/tex]
By using cross multiplication, we get
⇒ 2.4 × 2x = 2 × 3.6
simplifying the above equation, we get
⇒ 4.8x = 7.2
⇒ x = 1.5
Therefore, the value of x = 1.5.
Substitute x = 1.5 in CB and AB,
CB = 3x – 0.6 = 3(1.5) – 0.6 = 3.9
AB = 2x = 2(1.5) = 3
Scale factor means ratio of the sides of the triangle.
⇒ DF/AC = 2.4/3.6 = 2/3
Therefore, the correct answer is option a) ΔDEF - ΔABC; x = 1.5; CB = 3.9; AB = 3.
The complete question is:
Each pair of polygons is similar. Write a similarity statement for the polygons. Then, find the measure of x, the measures of the indicated sides, and the scale factor.
[tex]$\overline{C B}$[/tex] and [tex]$\overline{A B}$[/tex]
a) ΔDEF - ΔABC; x = 1.5; CB = 3.9; AB = 3;
b) ΔDEF - ΔCBA; x=3 ; C B=3 ; A B=3.9 ; 2/3
c) ΔDEF - ΔCBA; x=1 ; C B=3.9 ; A B=3 ; 2/3
d) ΔDEF - ΔABC; x=1.5 ; C B=3 ; A B=3.9 ; 3/2
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The length of a ruler is 12 inches. There are approximately 25.4 millimeters in 1 inch.
The length of the ruler is approximately 304.8 millimeters .
Length is used to measure distance.
According to the International System of Quantities, length has the dimension of distance. In most measurement systems, length is represented by a base unit from which all other units are derived. The International System of Units (SI) system's fundamental unit of length is the metre.The longest dimension of an object is typically understood to be what is meant by length.However, this isn't always the case depending on the object's position.The length of a fixed object is referred to by a number of names, including height, also referred to as vertical length or vertical extension, and width, breadth, or depth.Given that there are approximately 25.4 millimeters in 1 inch.
Therefore the length of the ruler = 25.4 × 12 = 304.8 mm
Hence the length of the ruler is approximately 304.8 millimeters .
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Answer:
304.8
Step-by-step explanation:
12*25.4 = 304.8
Estimate 5.209 + 2.667 by rounding to the nearest whole number.
Answer:
I'm pretty sure it would be 8 though forgive me if I'm wrong
Given the function h(x) = x^2 – 7x + 6, determine the average rate of change of the function over the interval 3 < x < 7.hurry please need answer.
Answer:Explanation:
The average rate of change = 3
The average rate of change for a function f(x) is an intervale a < x < b can be calculated using the following equation:
[tex]\frac{f(b)-f(a)_{}}{b-a}[/tex]Therefore, the average rate of change of the function h(x) = x^2 – 7x + 6 in the interval 3 < x < 7 is:
[tex]\frac{h(7)-h(3)}{7-3}[/tex]Where h(7) and h(3) are equal to:
[tex]\begin{gathered} h(7)=7^2-7(7)+6 \\ h(7)=49-49+6 \\ h(7)=6 \\ h(3)=3^2-7(3)+6 \\ h(3)=9-21+6 \\ h(3)=-6 \end{gathered}[/tex]So, the average rate of change is:
[tex]\frac{6-(-6)}{7-3}=\frac{6+6}{4}=\frac{12}{4}=3[/tex]Therefore, the answer is 3.