Answer:
(a) 9a + 2
(b) a = 5
Step-by-step explanation:
Perimeter of a triangle = sum of sides
=
2a + 1 +
3a + 2 +
4a - 1
----------
9a + 2 Answer (a)
If perimeter = 47 , then 9a + 2 =47
Subtract 2 from both sides
==> 9a = 47 -2
9a = 45
a = 45/9
a = 5
Find the number of distinct permutations that can be formed from all the letters of each word (1) UNUSUAL.
The number of unique permutations that may be made from all of the letters in each word 210.
What is permutations?The number of alternative arrangements of such an object in different orders or sequences is referred to as its permutation. These are typically computed using factorials, as denoted by the symbol. Only natural numbers are utilized in factorials.
Assume we wish to find the number of various permutations of n objects, where p items are one type, q items are another, r items are yet another, and so on.
According to the given data:For the word 'UNUSUAL' there are 7 letters. Then there are 7! possibilities.
We have to divide this by the number of possibilities where letters would replace the same letters.
there are letter U repeated 3 time so 3!
= [tex]\frac{7!}{3!}[/tex]
= 210
the number of unique permutations that may be made from all of the letters in each word 210.
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The vertices of a figure are R(-7, - 5), S(-1,
- 2), and T(-1.
- 5. Find the coordinates of the
image after the figure rotates 90° counterclockwise about the origin. Then translates 3 units left and 8
units up.
The co-ordinates of the image after translation are R"(2,1),S"(-1,7) and T"(2,7).
A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction. A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.
When a point is rotated 90° counter clockwise, the co-ordinates of the point say A(x ,y) changes to A"(y,-x).
The given co-ordinates are: R(-7, - 5), S(-1,- 2), and T(-1.- 5 ).
So when this co-ordinates are translated by rotating 90° counterclockwise.
R(-7, -5) →R'(5,-7)
S(-1,- 2) →S'(2,-1)
T(-1.- 5) →T'(5,-1)
Now the figure is translated 3 units left and 8 units up the new co-ordinates is given by (x-3,y+8).
So when this co-ordinates are translated the new co-ordinates are:
R'(5,-7)→R"(2,1)
S'(2,-1)→S"(-1,7)
T'(5,-1)→T"(2,7)
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Unit 3: Parallel & Perpendicular Lines Homework 6: Slope Intercept & Standard Form y= -3 and x=-6
The slope Intercept and the standard form of the equation are y = -1/2x - 3 and x + 2y = -6
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the slope Intercept and the standard form of the equation?The given parameters are
y= -3 and x=-6
The above represent the y and the x intercepts
i.e.
y-intercept = -3
x-intercept = -6
A linear equation is represented as
y = mx + c
Where
c = y-intercept = -3
So, we have
y = mx - 3
At x-intercept = -6, we have
y = 0
So, we have
0 = m(-6) - 3
This gives
m = -1/2
So, we have
y = -1/2x - 3 --- slope-intercept form
Multiply through by 2
So, we have
2y = -x - 6
Rewrite as
x + 2y = -6 ----- standard form
Hence, the slope Intercept and the standard form of the equation are y = -1/2x - 3 and x + 2y = -6
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The price of a share of stock started the day at $20.
During the day it went down $13, up $2, down $8, and then up $5.
Which integer represents the price of a share at the end of the day?
A. 8
B. 20
C. 6
D. 5'
100 points if answered
Answer:
C. 6
Step-by-step explanation:
$20 - $13 + $2 - $8 + $5 =
= $7 + $2 - $8 + $5
= $9 - $8 + $5
= $1 + 5
= $6
what is the answer for 5 - ( -7) = 5 + _____
write as addition
please give explanation for this
The complete statement is 5 + 7
What is the commutative property of addition?The commutative property of addition is a mathematical rule stating that a change in the order or arrangement of the numbers being added does not affect the sum.
It is also important to note the following sign changes;
(-) (-) = +
(+) (+) = +
(-)(+) = -
(+)(-) = -
Given the expression;
5 - ( -7)
We know that the signs (-)(-) is equivalent to (+) sign
Substitute into the expression;
5 + 7
Thus, the complete statement is 5 + 7
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1. Clark rounded 4.359 to 4.36. He rounded to the nearest (tenths, hundredths, thousandths) Please circle.
Answer: to the nearest hundredth
I hope this helps!
A school has 1256 pupils write this number to the nearest 10 , 100 and 1000
The required solution of the number to the nearest 10 , 100 and 1000 is 1260, 1300, 1000.
What is rounded number?A number that is easily multiplied, divided, etc., and especially a number that ends in zero.
Given:
A school has 1256 pupils write this number to the nearest 10 , 100 and 1000
According to given question we have
⇒ Round off to 10 for 1256 is 1250 or 1260 but nearest to 1256 is 1260.
⇒ So, round off to the nearest 10 is 1260.
⇒ Round off to 100 for 1256 is 1200 or 1300 but nearest to 1260 is 1300.
⇒ So, round off to the nearest 100 is 1300.
⇒ Round off to 1000 for 1256 is 1000 or 2000 but nearest to 1256 is 1000.
⇒ So, round off to the nearest 1000 is 1000.
∴ The answer is 1260,1300,1000.
Therefore, the required solution of the number to the nearest 10 , 100 and 1000 is 1260, 1300, 1000.
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Which number gives you a rational sum when you add it to 4/7 ?
Use the Distributive Property to determine which of the following statements is equivalent to 4(8 – 1).
Answer: 4*8 - 4*1
Or you could write it as 4(8) + 4(-1)
The distributive property in general is a(b+c) = ab+ac. We multiply the outer term 'a' with each term inside.
Determine the function that satisfies the following conditions.
Find sin theta when cos theta= 0.319 and tan theta <0.
The value of sinФ = 0.139 for the given cosФ = 0.139 and tanФ > 0.
What is termed as the trigonometric equations?Trigonometry is a branch of mathematics that focuses on specific angle functions and their implementation to calculations. In trigonometry, there are 6 functions of an angle that are commonly used. A trigonometric equation is one that involves one or more unknown trigonometric ratios. It is expressed as sine(sin), cosine(cos), and tangent ratios (tan), A trigonometric equation is a formula that contains a variable and a trigonometric function. A trigonometric equation is, for example, sin x + 2 = 1.The given trigonometric function is-
cosФ = 0.139.
We know the relation of sin and cos functions.
sin²Ф + cos²Ф = 1
Thus,
sinФ = √(1 - cos²Ф)
Put the value of cosФ = 0.139
sinФ = √(1 - 0.139²)
sinФ = √0.981
sinФ = 0.139
Thus, the value of the trigonometric function sinФ = 0.139.
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(FUNCTIONS & RELATIONS/TRANSFORMATIONS)
f(x) = x² -2x - 1
Find the image of 3
and the image of -2
The image of 3 and the image of -2 are 2 and 7, respectively
How to find the image of 3 and the image of -2?The equation of the function is given as
f(x) = x^2 - 2x - 1
To determine the image of 3 and the image of -2, we set x to the following values
x = 3 and -2
Substitute x = 3 and -2 in the equation f(x) = x^2 - 2x - 1
So, we have
f(3) = (3)^2 - 2(3) - 1 = 2
f(-2) = (-2)^2 - 2(-2) - 1 = 7
Hence, the image of 3 and the image of -2 are 2 and 7, respectively
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40 POINTS!
Solve 2x^2 + x = 15.
x = −5 and x = 5
x = three over two and x = −5
x = 15 and x = −2
x = five over two and x = −3
Answer:
x = five over two and x = −3
Step-by-step explanation:
Let's solve your equation step-by-step.
2x2+x=15
Step 1: Subtract 15 from both sides.
2x2+x−15=15−15
2x2+x−15=0
Step 2: Factor left side of equation.
(2x−5)(x+3)=0
Step 3: Set factors equal to 0.
2x−5=0 or x+3=0
x=5/2 or x=−3
Please i need help desperately.
The minimum cost is $210.
Forgetting the situation for just a second, we can take a look atthe equation.
c(x)=x^2-40x+610
It is a parabola that opens upward and has a minimum value.
That minimum value will be the minimum cost of the taco stand.
The equation x=-b/2a gives you the axis of symmetry of theparabola. Basically, it goes right down the middle of the parabola,right through its minimum
In the equation c(x)=x^2-40x+610, a=1 and b=-40
x=-b/2a
x=-(-40/2(1)) = 20
So 20 tacos should be sold to achieve the minimum cost.
To find the cost, return to the original equation.
c(x)=x^2-40x+610
c(20)=(20)^2-40(20)+610 = 210
So the minimum cost is $210.
A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.
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The minimum cost of the function is $210.
A function is defined as the representation of a set of variables known as the domain which are mapped onto another set of variables called the range.
The most common function is of the form y = f(x) , where x is the independent variable and y is the dependent variable and f(x) is the function.
The given function is of the form:
c(x) = x² - 40 x + 610
To find the maximum or minimum point of the function we find the second degree derivative of the function.
c'(x)=2x -40
Now we find the second degree derivative.
c"(x) = 2 > 0 so we know that c(x) is minimum at x for c'(x)=0.
Therefore c'(x) = 0
or , 2x-40 = 0
or , x = 20
Now the minimum value of the function is
c(20) = 20² - 40 (20) + 610
or, c(20) = 400 - 800 + 610
or, c(20) = 210
Hence the minimum value of the function is $210.
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simplify the following absolutevalue expression |29|
Find the length of YZ if Y is between X and Z
Given: XY = 8a, YZ = 6a, XZ = 2a + 50
Answer:
25
Step-by-step explanation:
By the segment addition postulate,
[tex]XY+YZ=XZ \\ \\ 8a+6a=2a+50 \\ \\ 14a=2a+50 \\ \\ 12a=50 \\ \\ a=\frac{25}{6} \\ \\ \therefore YZ=6(25/6)=25[/tex]
Carlo is 3 2/3 years older than his sister if his sister us 18 5/6 years old how old is carlo
Answer:
[tex]\sf 22\dfrac{1}{2}\; years[/tex]
Step-by-step explanation:
[tex]\textsf{First convert all mixed fractions to improper fractions: }\\\\3\dfrac{2}{3} = \dfrac{3 \times 3 + 2}{3}= \dfrac{11}{3}\\\\18\dfrac{5}{6 } = \dfrac{18 \times 6 + 5}{6} = \dfrac{113}{6}[/tex]
Let Carlo's age be C
Carlo's age = sister's age + 11/3
[tex]\sf == > C = \dfrac{113}{6} +\dfrac {11}{3}\\\\\textsf{Multiply both sides by 6 to eliminate the denominator}\\\\\sf 6C = 6\cdot\dfrac{113}{6} + 6\cdot\dfrac {11}{3}\\\\[/tex]
[tex]\sf == > C = \dfrac{113}{6} +\dfrac {11}{3}\\\\\textsf{Multiply both sides by 6 to eliminate the denominator}\\\\\sf 6C = 6\cdot\dfrac{113}{6} + 6\cdot\dfrac {11}{3}\\\\\sf 6C = 113 + 22 = 135\\[/tex]
[tex]\textsf {Divide both sides by 6}\\\\\sf C = \dfrac{135}{6} \\\\\textsf {Reduce $\dfrac{135}{6}$ by dividing numerator and denominator by 3}\\\\== > C = \dfrac{135 \div 3}{6\div3} = \dfrac{45}{2}[/tex]
[tex]\textsf{So Carlo's age is $\dfrac{45}{2}$ or $22\dfrac{1}{2}$ years}[/tex]
What is the slope of(1,-19),(-2,-7)
Answer:
Step-by-step explanation:
slope = (y2-y1) ÷ (x2-x1)
= ((-7)-(-19)) ÷ ((-2) - (1))
= 12 ÷ -3
m = -4
pls help me with this:(. What is 532 divided by 46. Can you help?
Answer: 11.5652174
.
Hello I'm Ash I'm here to help you! <3
Answer:
11 Remainder 26
Step-by-step explanation:
The number 532 is called the numerator or dividend, and the number 46 is called the denominator or divisor.the quotient and remainder of 532 divided by 46 = 11 R 26The quotient of 532÷ 46 equals 11; the remainder (“ the number left over”) is 26.I hope this Helps!
Answered by:AshTheNeko <3
The party is at 3 pm in only 12 minutes the party starts. what time is it right now?
well, let's say is 3pm, now, let's take away 10 minutes, that means 2:50pm, now let's take away another 2 minutes, that's 2:48pm.
Draw trapezoid ABCD and diagonals AC and BD. Add point E(6, 2) at the intersection of
Coordinate Geometry Graph the points A(0, 0), B(3, 3), C(9, 3), and D(12, 0).
agonals AC and BD.
Find BE and CE. What do you notice?
Answer: AED and BEC are isosceles triangles
Definition: A quadrilateral having two and only two sides parallel is called a trapezoid.
Formula: distance between two points =√(x1-x2)^2-(y1-y2)^2
Given,
ABCD is a trapezoid
AC and BD are diagonals
E is the intersection of two diagonals
A(0,0), B(3,3), C(9,3), D(12,0), E(6,2)
distance between BE=√10
distance between CE=√10
BE=CE
Similarly, AE=DE
Therefore, AED and BEC are isosceles triangles
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Find the next two terms of the sequence:
5, 15, 45, 135, 405, 1215
The next two terms of the sequence are blank and blank
Answer:
3645, 10935
Step-by-step explanation:
1215*3 = 3645
3645*3= 10935
Write the equation in slope intercept form of the line that is parallel to the group in each equation and passes through the given point 7. y=-2x + 5; (3,-7)
Answer:
The equation in slope intercept form of the line that is parallel to the group in each equation and passes through the given point (3,-7) is y = -2/7x - 6.14
Step-by-step explanation:
It is given that the line that is parallel to the group in each equation and passes through the given point 7y= -2x + 5; (3,-7) and we need to write the equation in slope intercept form of the same line.
Now,
The slope of parallel lines is the same. By changing the equation to slope-intercept form, get the slope in the first line;
=> 7y= -2x + 5
=> y= -2/7x + 5/7
So, the slope = -2/7
Further,
Given the point and the knowledge that the second line would similarly have a slope of -2/7 and the point is (3, -7). With these numbers, we can construct an equation in the slope-intercept form and apply it to get the y-intercept;
=> y = mx + b
=> -7 = -2/7 × 3 + b
=> -7 + 2/7 × 3 = b
=> b = -6.14
Now, put the value of y-intercept back into the equation;
=> y = -2/7x - 6.14
Therefore, the equation in slope intercept form of the line that is parallel to the group in each equation and passes through the given point (3,-7) is y = -2/7x - 6.14
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Evaluate -2y^(3)+y^(2)-3y+4 when y=3
The value of the algebraic expression -2y³ + y² - 3y + 4, when y = 3 is evaluated as: -50.
How to Evaluate an Algebraic Expression?An algebraic expression contains a variable. To find the value or evaluate the algebraic expression, plug in the the value of the variable and solve accordingly.
Given the algebraic expression,
-2y³ + y² - 3y + 4, when y = 3
Substitute the value of y into the algebraic expression:
-2(3)³ + (3)² - 3(3) + 4
Evaluate the exponents in the expression:
-2(27) + 9 - 9 + 4
-54 + 9 - 9 + 4
Add together to get the value of the algebraic expression:
-54 + 0 + 4
-54 + 4
= -50
In summary, the value of the algebraic expression -2y³ + y² - 3y + 4, when y = 3 is evaluated as: -50.
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trains on two different routes at the same train station. Train on one route stop there every 9 minutes and trains on the other route stop there every 6 minutes
When the train on one route stop there every 9 minutes and trains on the other route stop there every 6 minutes, the time when they will stop at same time is 18 minutes.
How to illustrate the information?From the information, the train on one route stop there every 9 minutes and trains on the other route stop there every 6 minutes.
Therefore, the time when will they stop at same time will be the lowest common multiple for 9 and 6. This is 18. Therefore, 18 minutes is the appropriate answer.
Therefore, the the time when they will stop at same time is 18 minutes.
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Trains on two different routes at the same train station. Train on one route stop there every 9 minutes and trains on the other route stop there every 6 minutes. When will they stop at same time?
Big ideas math question
(xy^4)^3 simplify simplify simplify
Answer:
[tex]x^3y^{12}[/tex]
Step-by-step explanation:
[tex]\left(xy^4\right)^3\\\left(xy^4\right)^3=x^3\left(y^4\right)^3\\=x^3\left(y^4\right)^3\\=(y^4)^3\\=(y)^{4\times 3}\\= y^{12}\\= x^3y^{12}[/tex]
[tex]\textsf{Hi Brainy User, I'm Here to Help you!}[/tex]
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\textsf{By using the \textbf{Exponent Property}, we can simplify this.}[/tex]
[tex]\textsf{This is what it states:}[/tex]
[tex]\sf{(x^m)^n=x^{(m*n)}}[/tex]
[tex]\textsf{Multiply:}[/tex]
[tex]\sf{(xy^4)^3=x^3y^{3*4}=x^3y^{12}}[/tex]
[tex]\Large\overbrace{\underbrace{\boldsymbol{\rm{Reflection - RoSe}}}}^\star_\star[/tex]
Help pls I’ll mark brainliest
Answer:
its true, true, false, false
Step-by-step explanation:
a is true b is true c is false and d is false
PLEASE I REALLY NEED HELP ON THIS QUESTION OR I WILL FAIL PLEASE HELP!!!
A school district has paid a construction business 1.5 million to build a school, but still needs to pay the construction business 12.35 million for the total amount of work. How much will it cost to build the school?
PLEASE SHOW WORK!
Answer:
13.85 million $
Step-by-step explanation:
the man just add 12.35 and 1.5
therefore = 13.85 million $
Consider polynomial function f.
f(x) = (x - 1)²(x + 3)³(x + 1)
Use the equation to complete each statement about this function.
The zero located at x = 1has a multiplicity of 2, and the zero located at x = -3has a multiplicity of 1
The graph of the function will touch, but not cross, the x-axis at an x-value of
Reset
Next
Answer: somehow got that v
Step-by-step explanation:
f=
x6+8x5+17x4−8x3−45x2+27
x
A professor expects the education and health service industries to increase total employees by 14.8% from 2009 to 2016. Based on the employment graph below, approximately how many new jobs will the education and health service industries gain between 1/2009 and 1/2016?
Based on the number of people employed in education and health service industries in 2009, the number of new jobs that will be gained between 1/2009 and 1/2016 is b. 2,826,800 people.
How many jobs will be gained?The number of total jobs in 2016 can be found as:
= Number of jobs in education and health service industries x (1 + rate of increase)
= 19,200,000 x (1 + 14.8%)
= 19,200,000 x 1.148
= 22,041,600 people
The number of new jobs are:
= 22,041,600 people - 19,200,000
= 2,841,600 people
= 2,826,800 people approximate
Graph and options for the question are:
Education and Health Services - All Employees, 2000-2009 A line graph titled Education and Health Services, All Employees, 2000 to 2009, where the x-axis shows years and the y-axis shows all employees, in thousands. Line starts at 15,000 on January 2000, and increases gradually to 16,000 on January 2002, 17,200 on January 2005, 18,100 on January 2007, and 19,200 on January 2009.
a. 21,926,800
b. 2,826,800
c. 16,273,200
d. 1,790,600
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Answer:
b on edge
Step-by-step explanation: