The expression that is a factor of both x² - 9 and x² + 8x + 15 is (x + 3).
What is the common factor between the given polynomials?Given the polynomials in the question:
x² - 9
x² + 8x + 15
To find a factor that is common to both x² - 9 and x² + 8x + 15, we can factorize the two expressions and look for any common factors.
First, factorize x² - 9:
Using the difference of sqaure formula
a² - b² = ( a + b )( a - b )
x² - 9
x² - 3² = (x - 3)(x + 3)
Next, factorize x² + 8x + 15:
Using AC method
( x + 3 )( x + 5 )
From the factorizations, we can see that both expressions have a common factor of (x + 3).
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
The sum of the measures of the exterior angles of a convex 21-gon is 360°.
Given,
Convex 21- gon
Polygon is a plane figure with a finite number of straight line segments.
Convex polygons are those in which none of their interior angles are greater than 180°.
Now,
The sum of exterior angles of any regular polygon is 360°.
Hence,
The sum of the measures of the exterior angles of a convex 21-gon is 360°.
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50 Points! Multiple choice algebra question. Thank you!
The expression that is equivalent to the trigonometry ratio (sin²θ + cos²θ)/tan²θ is (a) cot²θ
How to determine the expression that is equivalent to the trigonometry ratioFrom the question, we have the following parameters that can be used in our computation:
The trigonometry ratio given as
(sin²θ + cos²θ)/tan²θ
In trigonometry,
sin²θ + cos²θ = 1
So, we have the following representation
(sin²θ + cos²θ)/tan²θ = 1/tan²θ
Evaluate the quotient
(sin²θ + cos²θ)/tan²θ = cot²θ
Hence, the expression that is equivalent to the trigonometry ratio is (a) cot²θ
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50 Points! Multiple choice algebra question. Photo attached.
The period of the function is given as follows:
C) 4.
How to obtain the period of the function?A periodic function is a function that has the behavior repeating in intervals over the domain.
Then the period of the function is defined as the difference between two points in which the function has the same behavior.
The function in this problem has the behavior repeating at these following points:
x = 0, x = 4, x = 8, ...
Hence the period is given as follows:
4 - 0 = 8 - 4 = 4.
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the area of a trapizoid is 150 square millimeters 7mm 16mm 13mm what is the trapezoids height
The height of the trapezoid is approximately 13.043 mm.
Understanding How to Solve TrapezoidTo find the height of a trapezoid, you can use the formula:
Area = 1/2 * (base1 + base2) * height
Given:
Area = 150 square millimeters
base1 = 7 mm , w
base2 = 16 mm
150 = 1/2 * (7 + 16) * height
150 =1/2 * 23 * height
Make height the subject of the formula
300 = 23 * height
height = 300 / 23
height = 13.043 mm (rounded to three decimal places)
Therefore, the height of the trapezoid is approximately 13.043 mm.
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task1 part b evaluate
The solution of expression ∫ (0 to 10) (x + 1) dx is,
⇒ 60
We have to given that,
Expression to solve,
⇒ ∫ (0 to 10) (x + 1) dx
Now, We can simplify as,
⇒ ∫ (0 to 10) (x + 1) dx
⇒ ∫ (0 to 10) (x) dx + ∫ (0 to 10) dx
⇒ (x² / 2)₀¹⁰ + ((x)¹⁰₀
⇒ 1/2 (10² - 0) + (10 - 0)
⇒ 1/2 × 100 + 10
⇒ 50 + 10
⇒ 60
Therefore, The solution of expression ∫ (0 to 10) (x + 1) dx is,
⇒ 60
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Identify the pairs of alternate exterior angles in the given figure.
A) ∠2 and ∠7; ∠1 and ∠8
B)∠3 and ∠6; ∠4 and ∠5
C) ∠3 and ∠5; ∠4 and ∠6
D) ∠1 and ∠7; ∠2 and ∠8
The pairs of alternate exterior angles in the given figure is Option D) ∠1 and ∠7; ∠2 and ∠8
Alternate exterior angles are a pair of angles formed by a transversal line intersecting two parallel lines and located on opposite sides of the transversal and on the exterior of the parallel lines. In other words, if two parallel lines are intersected by a third line (the transversal), then the pairs of angles on opposite sides of the transversal and outside the parallel lines are alternate exterior angles. These angles are congruent to each other.
In the given figure two parallel lines, which are crossed by a transversal line which forms angles.
Now according to the given figure
so, answer is Option D) ∠1 and ∠7; ∠2 and ∠8
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According to the table below, What is the domain of the data
Domain: {15, 17, 19, 21, 23}
Step-by-step explanation:The domain describes the x-values within a function.
Inputs
In a function, the inputs are the values that are plugged into a function, and the outputs are the resulting values. This means that the inputs represent the x-values and the outputs are the y-values. Since this is a function, each of the inputs has one output. So, each input is unique. We can use the input values to find the domain.
Domain
The domain of a data set is the x-values. Each x-value is one part of the domain. The domain is written as a list of values in numerical order with braces surrounding the values. Since the inputs represent the x-values, we can use the input values as the domain values. This means that the domain of the data is {15, 17, 19, 21, 23}.
The following transactions were completed by the company:
The company completed consulting work for a client and immediately collected $5,600 cash.
The company completed commission work for a client and sent a bill for $4,100 to be received within 30 days.
The company paid an assistant $1,450 cash as wages for the period.
The company collected $2,050 cash as a partial payment for the amount owed by the client in transaction b.
The company paid $720 cash for this period's cleaning services.
In accounting, the accounting equation is a fundamental principle that describes the relationship between a company's assets, liabilities, and equity. This equation is represented as Assets = Liabilities + Equity. Every financial transaction that a company undertakes has an impact on at least two of the components of the accounting equation.
Transaction Analysis:
a. The company completed consulting work for a client and immediately collected $5,600 cash earned.
This transaction increases both cash and revenue. There is no impact on liabilities or equity.
Accounts Affected:
Cash: +$5,600
Revenue: +$5,600
b. The company completed commission work for a client and sent a bill for $4,100 to be received within 30 days.
This transaction does not impact any account initially. Revenue will increase when payment is received.
Accounts Affected:
Accounts Receivable: +$4,100
Revenue: +$0
c. The company paid an assistant $1,450 cash as wages for the period.
This transaction decreases cash and increases expenses. There is no impact on liabilities or equity.
Accounts Affected:
Cash: -$1,450
Expenses: +$1,450
d. The company collected $2,050 cash as a partial payment for the amount owed by the client in transaction b.
This transaction increases cash and decreases accounts receivable. There is no impact on liabilities or equity.
Accounts Affected:
Cash: +$2,050
Accounts Receivable: -$2,050
e. The company paid $720 cash for this period's cleaning services.
This transaction decreases cash and increases expenses. There is no impact on liabilities or equity.
Accounts Affected:
Cash: -$720
Expenses: +$720
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Complete Question
The following transactions were completed by the company
a. The company completed consulting work for a client and immediately collected $5,600 cash earned.
b. The company completed commission work for a client and sent a bill for $4,100 to be received within 30 days.
c. The company paid an assistant $1,450 cash as wages for the period.
d. The company collected $2,050 cash as a partial payment for the amount owed by the client in transaction b
e. The company paid $720 cash for this period's cleaning services Required: Enter the impact of each transaction on individual items of the accounting equation. (Enter decreases to account balances with a minus sign.)
Can someone help me find the surface area of these 2 prisms?
Step-by-step explanation:
1) the 1-st prism is cube. Then its surface area can be calculated as:
A=5*5*6=150 [ft²];
2) A=[Perimeter of triange]*height+2*[Area_of_triangle];
according to the formula above height=3; Perimeter of triangle=9+12+15=36; Area of triangle=12*9*0.5=54;
Finally, A=36*3+2*54=108+108=216 [cm²].
The mean of a, 31, 42, 65, and b is 51. The greatest number is 67 more than the least number. What are the missing numbers? Please explain.
Answer:
a=25
b=92
Step-by-step explanation:
Because the average of the five numbers is 51, the sum of the five numbers is 255.
a+b+73+65=255
138+a+b=255
a+b=117
a+67=b
Therefore,
a=25
b=92
Feel free to tell me if I made a mistake! :)
At the farmers' market, Tom bought 11/12 of a pound of string beans and 1/2 of a pound of
lima beans. How many more pounds of string beans did Tom purchase?
Write your answer as a fraction or as a whole or mixed number.
pounds
Arizona license plates are designed so there
are three letters followed by four digits.
How many different license plates are
possible if letters and digits cannot be
repeated?
A. 175,760,000
B. 47,174,400
C. 78,624,000
D. 115,316,136
78,624,000 different license plates are possible if letters and digits cannot be repeated.
For the letters:
There are 26 letters in the English alphabet, and we need to choose three of them without repetition.
This can be calculated as a permutation of 26 letters taken 3 at a time:
P(26, 3) = 26! / (26 - 3)!
= 26! / 23!
= 26 x 25 x 24
= 15,600
For the digits:
There are 10 digits (0-9), and we need to choose four of them without repetition.
This can be calculated as a permutation of 10 digits taken 4 at a time:
P(10, 4) = 10! / (10 - 4)! = 10! / 6!
= 10 x 9 x 8 x 7
= 5,040
To find the total number of different license plates possible, we multiply the number of possibilities for the letters by the number of possibilities for the digits:
Total possibilities = P(26, 3) x P(10, 4)
= 15,600 x 5,040
= 78,624,000
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The first shelf of one bookcase is 2 inches off the ground. The second shelf is 1’5” above the first the third shelf is 1’3” above the second and the fourth shelf is 1’2” above the third. The top shelf is 1’4” above the fourth how high off the ground is the top shelf.
answer: 5'6"
step by step: 1'5"+2"=1'7"+1'3"=3'0"+1'2"=4'2"+1'4"=5'6"
A random survey of 495 adults found that 59 had dietes. Which of the following is a 98% confidence interval for the population proportion of adults with diabetes?
Answer:
{0.0853,0.1531}
Step-by-step explanation:
[tex]\displaystyle CI=\hat{p}\pm z\sqrt{\frac{\hat{p}\bigr(1-\hat{p}\bigr)}{n}}[/tex]
[tex]\displaystyle CI_{98\%}=\frac{59}{495}\pm2.326\sqrt{\frac{\frac{59}{495}\bigr(1-\frac{59}{495}\bigr)}{495}}\approx\{0.0853,0.1531\}[/tex]
A circle with circumference 72π is divided into 10 congruent sectors. Find the area of two sectors. Round to the nearest tenth
Can someone answer this question
Answer: 4th one is the correct one
Step-by-step explanation:
x^2 -5x + 29 = 8x -6
Answer:
Step-by-step explanation:
x²-5x+29=8x-6
x²-13x+35=0
[tex]x=\frac{13 \pm\sqrt{(-13)^2-4(1)(35)} }{2(1)} \\x=\frac{13 \pm\sqrt{169-140} }{2} \\x=\frac{13 \pm\sqrt{29} }{2}[/tex]
Three lines intersect to form six angles that measure in degrees in some of the angles are represented by expressions as shown in this. Based on the diagram write an algebraic equation that can be used to find the value of X show explain how you got your answer
1. The equation to be formed is 40 + 5x + 90 = 180
2. The value of x is 10
What is the sum of angles on a straight line?A straight line's total angles are always 180 degrees. Around the place where two lines join, they create four angles. The total of the angles on either side of a straight line, if those lines are straight and form one, is always 180 degrees.
We know that;
40 + 5x + 90 = 180 (Sum of angles on a straight line)
130 + 5x = 180
5x = 180 - 130
x = 50/5
x = 10
Thus the value of x is given as 10
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A triangle has sides with lengths of 13 meters, 18 meters, and 8 meters. Is it a right triangle?
Answer:
The Pythagorean Theorem describes the relationship among the three sides of a right triangle
[tex]a^{2} +b^{2} = c^{2} \\8^2+13^2=c^2=208 \\\sqrt{208}=14.4\\ 14.4 \neq 18[/tex]--> not a right triangle
In Algebra, a minus symbol [-] will represent two things, an operation of subtraction and a negative number, depending on where it's placed.
(a) True
(b) False
Answer:
It is true that in algebra minus symbol represent two things
Step-by-step explanation:
And it is true that it depend on where it placed such as
8-2 this minus indicate the substraction of two terms
-3 this show that the number has negative quantity
Please help with picture below
The complete statement should be If 3m = 7n, then m/n = 7/3. The proportion was obtained by solving for m, and then using the converse of the cross products property. Option B
What does the converse of the cross product property say?The converse of the cross products property states that if two ratios are equal, then the product of the means is equal to the product of the extremes.
To justify the answer, you solve for m/n in the original equation by dividing each side by 3n, which gives you m/n = 7/3.
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Type the correct answer in each box. Use numerals instead of words. Consider function h. h ( x ) = { 3 x − 4 , x < 0 2 x 2 − 3 x + 10 , 0 ≤ x < 4 2 x , x ≥ 4 What are the values of the function when x = 0 and when x = 4 ?
h(0)=
h(4)=
The value of function h (0) is,
h (0) = 10
And, The value of function h (4) is,
h (4) = 8
Given that;
The function is,
h (x) = { 3x - 4 , x < 0
= {2x² - 3x + 10, 0 ≤ x < 4
= { 2x , x≥ 4
Hence, The value of function h (0) is,
h (x) = 2x² - 3x + 10, 0 ≤ x < 4
h (0) = 2 (0) - 3 (0) + 10
h (0) = 10
The value of function h (4) is,
h (x) = 2x
h (4) = 2 (4)
h (4) = 8
Thus, The value of function h (0) is,
h (0) = 10
And, The value of function h (4) is,
h (4) = 8
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Find the y-intercept for the parabola defined by
this equation:
y=-4x^2-x+3
Answer:
y is 0,3
Step-by-step explanation:
To find the x-intercept, substitute in
0
for
y
and solve for
x
. To find the y-intercept, substitute in
0
for
x
Answer:
(0,3)
Step-by-step explanation:
Two methods:
Method 1: General method for any equation
Method 2: Method specific for parabolas in standard form
Method 1: General method for any equation
For any two-variable equation to be graphed, the y-intercept is the point where the graph crosses the y-axis. The y-axis is a vertical line through the origin (0,0).
Any y-intercept is on that line, and to get to that point starting from the origin, one can't travel left or right to get to the y-intercept point (without moving back to the y-axis). The only movement would be up or down.
Since no left-right movement will happen, the x-coordinate is zero.
For any two-variable equation, the x and y coordinates of any point on the graph are linked by the equation. If it is known that the x-value is zero, the y-value associated with that x-value is given by substituting zero into the equation everywhere there is an "x", and solving for "y".
[tex]y=-4x^2-x+3[/tex]
[tex]y=-4(0)^2-(0)+3[/tex]
Order of operations requires exponents before multiplication, or addition & subtraction...
[tex]y=-4(0)-(0)+3[/tex]
multiplication...
[tex]y=0-0+3[/tex]
addition & subtraction, from left to right...
[tex]y=3[/tex]
So, when the x-value is zero, the y-value is three. Therefore, the ordered pair representing that point is (0,3).
Method 2: Method specific for parabolas in standard form
The given equation is the equation for a parabola (as stated in the question), and it is given in "standard form": [tex]y=ax^2+bx+c[/tex], where a, b, and c are real numbers (and a isn't equal to zero, because then the x-squared term would be zero, and the equation would really just be a linear equation).
Note that for our equation, it is in standard form if we rewrite the equation to only use addition, [tex]y=-4x^2+-1x+3[/tex], where [tex]a=-4, ~b=-1 ~ \text{and}~c=3[/tex]
For a parabola in standard form, the y-intercept is always at a height of "c".
So, the y-intercept would be (0,3).
a librarian has weekends off and has 10 paid vacation days per year, including holidays that fall on weekends. If his salary is 32,500 per year, what is his pay per workday?
his pay per workday will be $127.45.
How to calculate interest?Thus, the formula for calculating simple interest is J = C i t, where J is interest, C is principal, i is interest rate, and t is time. That is, J represents the amount added to the initial value, the capital is the calculation basis, the interest rate is the percentage applied on the capital and time is the capitalization period.
Knowing that:
10 paid vacation days per yearsalary is 32,500 per yearThe total weekends in a year:
52 * 2 = 104 weekend days.
Total paid vacation days, including holidays that fall on weekends:
10 - 4 = 6 paid vacation days.
Total non-working days:
104 + 6 = 110 non-working days.
Total working days in a year:
365 - 110 = 255 working days.
Pay per workday = Annual salary / Total working days
= $32,500 / 255= $127.45
Therefore, the librarian's pay per workday is approximately $127.45.
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A submarine dives to a depth of 3775 m. It then climbs to a depth of 1395 m before descending one more time to a depth of 2890 m. How many meters in total has the submarine dived? What is the total distance (up and down) it has travelled? (Include the first descent in your calculations).
Step-by-step explanation:
3775 + 2890-1395 = total diving meters = 5270 m
Total movement = 3775 + ( 3775 - 1395 ) + (2890 - 1395 ) = 7650 m
PLS HELP ME, WILL GIVE BRAINLIEST!!!!!!!!!!!!!
sorry i was going to show work but my water spill on the paper. so answer is 556.05cm^2
1
The dimensions of a cube and a rectangular prism are shown below.
Cube
B
2x
3x
Rectangular Prism
4x
Which statement is true?
A The surface area of the rectangular prism is 24 times larger than the surface area of
the cube.
26
The surface area of the rectangular prism is times larger than the surface area of
the cube.
C The volume of the rectangular prism is 48 times larger than the volume of the cube.
D
8
The volume of the rectangular prism is 3 times larger than the volume of the cube.
The surface area of the rectangular prism is (26/3) times larger than the surface area of the cube.
Given data ,
Let the surface area of the cube be S₁
Let the surface area of the rectangular prism be S₂
Let the volume of the cube be V₁
Let the volume of the prism be V₂
On simplifying , we get
The side length of cube = x
So , surface area of cube = 6x²
The volume of cube = x³
And , the surface area of prism = 2 ( 12x² + 8x² + 6x² )
S₂ = 52x²
And , volume of prism = l x w x h
V₂ = ( 2x ) ( 3x ) ( 4x ) = 24x²
So , S₂ = ( 26/3 ) S₁
52x² = ( 26/3 ) ( 6x² )
52x² = 52x²
Hence , The rectangular prism's surface area is (26/3) times greater than the cube's surface area.
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The complete question is attached below :
The dimensions of a cube and a rectangular prism are shown below.
Which statement is true?
A The surface area of the rectangular prism is 24 times larger than the surface area of the cube.
The surface area of the rectangular prism is times larger than the surface area of the cube.
C The volume of the rectangular prism is 48 times larger than the volume of the cube.
D The volume of the rectangular prism is 3 times larger than the volume of the cube.
Intro
Nautilus Clothing's stock has a 50% chance of producing a 15% return, a 20%
chance of producing a 21% return, and a 30% chance of producing a -13% return.
Part 1
What is the stock's expected return?
A sales person starts working 40 hours per week at a job with 2 options for being paid . Option A is an hourly wage of $19. Option B is a commission rate of 8% on weekly sales.
How much does the sales person need to sell in a given week to earn the same amount with each option?
A. $9,500
B. $4,750
C. $760
D. $320
Given, Option A: Hourly wage is $19 and the salesperson works 40 hours per week. So, he will earn in a week [tex]\sf = 19 \times 40 = \$760[/tex]
Now, according to option b, he will get 8% commission on weekly sales.
Let. x = the amount of weekly sales.
To earn the same amount of option A, he will have to equal the 8% of x to $760
So, [tex]\sf \dfrac{8x}{100}=760[/tex]
Or, [tex]\sf 8x= 76000[/tex]
Or, [tex]\sf x= \dfrac{76000}{8}=9500[/tex]
the salesman needs to make a weekly sales of $9,500 to earn the same amount with two options.
need help on this math question
The expression which gives the number of months passed in terms of p is √300 -0.5p
Subject of formulaWe make t the subject of the formula in the expression
p = 600 - 2t²
subtract 600 from both sides in other to isolate 2t²
p - 600 = 600 - 2t² - 600
p - 600 = -2t²
Rearrange the equation
2t² = 600 - p
Divide both sides by 2 in other to isolate t²
2t²/2 = 600/2 - p/2
t² = 300 - 0.5p
Take the Square root of both sides in other to isolate t
√t² = √300 - 0.5p
t = √300 - 0.5p
Hence, the correct expression which gives the number of months t in terms of price p is t = √300 - 0.5p
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