The product or multiplication of the polynomials is given as
x² +11x + 24.
A result or product is produced by multiplication or a statement that lists the factors to be multiplied.
The commutative law of multiplication states that the product is independent of the sequence in which real or complex numbers are multiplied.The order of the factors often determines the outcome of multiplying matrices or the constituents of other associative algebras.For instance, multiplication in general and in matrices are non-commutative operations in other algebras.Additionally, two complex numbers can be multiplied to get a complex number. When we multiply two integers, we always get back an integer.Given (x+8) (x+3)
let us find the product :
= x² + 8x + 3x + 24
= x² +11x + 24
Let us now test the equivalency .
(x+8) (x+3) = (1+8)(1+3) = (9)(4) = 36
x² +11x + 24 = (1)² + 11(1) + 24 = 36
Hence we can see that the product is same in both the cases.
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plsssssszz answerrrrrr
I think this is one of those trick questions!
I'm going to say the answer is... 90°
because it states within the question that ∠A and ∠B are vertical angles
That is my educated guess. I hope it's helpful!
Pls let me know if my answer is incorrect.
14. “-4 times a number plus 29”
Answer:
It depends on what that number is but -4+29 is equal to 29-4; making the answer to -4+29=5.
Step-by-step explanation:
Identify all rays and lines in the picture below.
According to this definition given below, we identify all lines and rays as follows, EA, EB, EC, and ED are rays, and ED and BE are, Line.
A line is, it is actually difficult to give a good mathematical definition. Roughly, we can say that a line is an infinitely thin, infinitely long collection of points extending in two opposite directions. When we draw lines in geometry, we use an arrow at each end to show that it extends infinitely.
A line can be named either using two points on the line (for example, AB←→ ) or simply by a letter, usually lowercase (for example, line m ).
A line segment has two endpoints. It contains these endpoints and all the points of the line between them. You can measure the length of a segment, but not of a line.
___
A segment is named by its two endpoints, for example, AB.
A ray is a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray.
A ray is named using its endpoint first, and then any other point on the ray (for example, BA−→− ).
according to this definition, EA EB EC ED are rays, and ED, and BE are Line
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If an airplane can travel at 20,000 miles per hour, how many meters per second does it travel? Knowing that: 1 mi 1.609 km
Answer: 8,938 [tex]\frac{8}{9}[/tex] or 8,938.8889 meters per second
Step-by-step explanation:
To solve this problem, we will use a process called dimensional analysis (that you have probably done many times without realizing it).
What is dimensional analysis? Let's say you know there are 12 inches in a foot, and you want to know how many inches are in 2 feet. 12 * 2 = 24 inches in a foot, that's dimensional analysis!
Here is the process you would take to solve your problem:
➜ If we have the units [tex]\frac{hour}{hour}[/tex], they "cancel" out to become one. This way, we make sure we end up with the correct units, [tex]\frac{meters}{second}[/tex].
➜ We take units we know, such as 3,600 seconds in an hour, and multiply them by the original value until we end up with the measurement we want.
[tex]\displaystyle 20,000\; \frac{miles}{hour}*\frac{1 \;hour}{3,600\; seconds} *\frac{1,609\;meters}{1\;mile}=\frac{20,000*1*1,609\;meters}{3,600\;seconds} =\frac{32,180,000\;meters}{3,600\;seconds} = 8,938.89\; \frac{meters}{second}[/tex]
In other words;
8,938.89 meters per second
find the value of 9^-1/2
Applying the negative exponent rule, the value of 9^-1/2 is calculated as: 1/3.
What is the Negative Exponent Rule?If a number has a negative exponent, i.e. a^-1/2, it can be rewritten and expressed as:
a^-1/2 = 1/a^½
1/a^½ can also be rewritten or expressed as:
1/a^½ = 1/√a
Thus, we would apply the negative exponent rule to find the value of the expression, 9^-1/2 as explained below:
9^-1/2 = 1/9^½
Rewrite 1/9^½ as 1/√a
1/9^½ = 1/√9
Take the square root of 9
1/√9 = 1/3
This implies that, the value of the expression, 9^-1/2 is 1/3.
In conclusion, applying the negative exponent rule, the value of 9^-1/2 is determined as: 1/3.
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A retail clothing store offers customers an opportunity to open up a credit card during checkout. one location of the retail clothing store states that the number of credit cards, a, that are opened t months since january can be modeled by the function a(t) = 20 4t. the number of credit cards opened at another location, b, is defined by the function b(t) = 25 − t. what is an expression that can be used to determine the total amount of credit cards opened at the two locations? (a − b)(t) = −5 5t (a − b)(t) = −5 3t (a b)(t) = 45 5t (a b)(t) = 45 3t
An expression that can be used to determine the total amount of credit cards opened at the two locations is: (a + b) (t) = 45 + 3t.
Given,
Number of credit cards opened at location a = a (t) = 20 + 4t
Number of credit cards opened at location b = b (t) = 25 - t
Hence,
Total amount of credit card:
(a + b) (t) = (20 + 4t) + (25 - t)
(a + b) (t) = 20 + 4t + 25 - t
(a + b) (t) = 45 + 3t
Therefore an expression that can be used to determine the total amount of credit cards opened at the two locations is: (a + b) (t) = 45 + 3t.
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help help help guys HELP
Slope can be described as rise/ run, change in the dependent variables relative to the change in the independent variables and Δy / Δx.
How to find the accurate expression of the slope?The slope of a line is a number that describes both the direction and the steepness of the line.
The slope of a line is the change in y coordinate with respect to the change in x coordinate.
Therefore, slopes can be described as follows:
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Nayeli went to the grocery store and bought bottles of soda and bottles of juice. each bottle of soda has 25 grams of sugar and each bottle of juice has 15 grams of sugar. nayeli purchased 5 more bottles of soda than bottles of juice and they all collectively contain 205 grams of sugar. write a system of equations that could be used to determine the number of bottles of soda purchased and the number of bottles of juice purchased. define the variables that you use to write the system.
The system of equations are:
25s + 15j = 205
s - j = 5
Where:
s = number of soda bought
j = number of juice bottles bought
What are the system of equations?In order to determine the number of bottles of soda and juice bought, two sets of equations would need to be formed based on the information provided in the question. The equations would be solved simultaneously.
Grams of sugar in the soda bottle + grams of sugar in the juice bottle = total grams of sugar
difference in the number of bottles bought
25s + 15j = 205
s - j = 5
The methods that can be used to solve the simultaneous equations :
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Can you guys help me with my math homework? I'll be asking more q's after they get answered. THX!!!
Answer:
y = 22.5x
Step-by-step explanation:
Using the scale 1:22.5
then the actual length is y = 22.5x
Marta paid $53 for 4 tickets to see a ballet. each ticket cost the same amount. what was the cost each ticket for the ballet?
The cost of each ticket for the ballet is $13.25.
What is cost price?The cost price or simply the cost in retail systems represents the particular value that corresponds to the unit price paid. In some stock market theories, this value is utilized to establish the value of stock holdings and is used as a key determinant of profitability.
There are numerous ways to calculate cost pricing, however it all relies on the kind of query we are asking. For instance,
If a selling price and profit are provided, then,
Cost price = Selling price (SP) − profit
If a selling price and loss are provided, then,
Cost price =Selling price + loss
In the given question,
The total amount that Marta paid is $53
=> amount = $53
and total number of tickets = 4
Now, the cost of each ticket = Total amount / number of tickets
= $53 / 4
= $ 13.25
Hence, the cost each ticket for the ballet is $13.25.
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Samantha is following a blueprint to build an addition to her house. The kitchen countertop will be 8.75 feet long. The scale of the blueprint is 1 centimeter = 1.75 feet. What is the length of the countertop on the blueprint?
The length of the countertop on the blueprint is 5 cm.
What is defined as the scale?Scale is a ratio that reflects the relation between the size of a model and the actual dimensions of a figure or object. It aids in the representation of real-world objects on paper with relatively tiny dimensions. Scale is primarily employed in maps as well as blueprints for building construction.For the given question;
The length of kitchen countertop = 8.75 feet.
The scale used in blueprint is 1 centimeter = 1.75 feet.
Thus, use the unitary method.
1.75 feet -----> 1 cm.
Divide both side by 1.75.
1 feet ------>1/1.75 cm
Multiply both side by 8.75.
8.75 feet ---> 8.75/1.75 cm
8.75 feet ------> 5 cm.
Therefore, the the length of a countertop for the blueprint is found as 5 cm.
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Marie can type 25 labels in 10 mins. How many can
she type
in one hour?
Step-by-step explanation:
her ratio is therefore 25/10, which can be also written as 5/2, because ratios are just a special form of fractions.
to find how many labels she can type in 1 hour, we need to find the rehashing between 10 minutes and 1 hour.
1 hour = 60 minutes.
60 minutes = 6 × 10 minutes.
so, to find the equivalent ratio based on 1 hour, we need to multiply the denominator (bottom part) by 6.
and to keep the ratio value we need to multiply the numerator (top part) by the same number :
25/10 × 6/6 = 150/60
and since the ratio is always telling us how many labels can be typed per unit of time, we see,
she can type 150 labels in 1 hour (60 minutes)
convert 3100 fluid ounces to milliliters. round your answer to the nearest whole number
Answer:
91678 milliliters
Step-by-step explanation:
hope this is helpful! stay safe, and have a blessed day! :)
Interest Suppose you deposit $ 2000 in a savings account that pays interest at an annual rate of 4 % . If no money is added or withdrawn from the account, answer the following questions.
d. How many years will it take for the account to contain $ 3000 ?
It will take 10.3 years for the account to contain $3000.
The formula to be used is given as follows :
A(t) = a ( 1 + r )^t (1)
where, A(t) = future value
a = principal amount or amount initially deposited.
r = annual interest rate
t = time
According to the question we have been given that
a = $2000
r = 0.04
A(t) = $3000
putting the required values in equation (1) we get
3000 = 2000(1+0.04)^t
1.5 = (1.04)^t
Taking log both sides we get
log(1.5) = t log(1.04)
0.176 = t *0.017
t = 10.3 years.
Thus it takes 10.3 years for the account to contain $3000.
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convert 87.65 to base 8
The answer is 127.5146314631
What is 87.65 decimal in octal? 87.65 from decimal to octal is 127.5146314631. Here we show you how to write 87.6510 in octal and how to convert 87.65 from base-10 to base-8.
To convert decimal number 87.65, we convert its integer and fraction part individually and then add them to get the equivalent octal number, as below:
To convert integer 87 to octal, follow these steps:
Divide 87 by 8 keeping notice of the quotient and the remainder. Continue dividing the quotient by 2 until you get a quotient of zero.
Then just write out the remainders in the reverse order to get the equivalent octal number.
87 / 8 = 10 with remainder 7
10 / 8 = 1 with remainder 2
1 / 8 = 0 with remainder 1
Here is the answer to 87 decimal to octal number:
127
For converting decimal fraction 0.65 to octal number, follow these steps:
Multiply 0.65 by 8 keeping notice of the resulting integer and fractional part. Continue multiplying by 8 until you get a resulting fractional part equal to zero (we calcuclate upto ten digits).
Then just write out the integer parts from the results of each multiplication to get equivalent octal number.
0.65 × 8 = 5 + 0.2
0.2 × 8 = 1 + 0.6
0.6 × 8 = 4 + 0.80000000000001
0.80000000000001 × 8 = 6 + 0.40000000000009
0.40000000000009 × 8 = 3 + 0.20000000000073
0.20000000000073 × 8 = 1 + 0.60000000000582
0.60000000000582 × 8 = 4 + 0.80000000004657
0.80000000004657 × 8 = 6 + 0.40000000037253
0.40000000037253 × 8 = 3 + 0.20000000298023
0.20000000298023 × 8 = 1 + 0.60000002384186
Here is the answer to 0.65 decimal to octal number:
0.5146314631
Therefore, decimal number 87.65 converted to octal is equal:127.5146314631
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Factories (a + b)³-3a²b(a + b)
Answer:
(a+b) (a+2ab+b2−3a2b)
Step-by-step explanation:
You are driving a car when a deer suddenly darts across the road in front of you. Your brain registers the emergency and sends a signal to your foot to hit the brake. The car travels a reaction distance D , in feet, during this time, where D is a function of the speed r , in miles per hour, that the car is traveling when you see the deer, given by D(r)=11 r+5/10 . Find the inverse and explain what it represents. Is the inverse a function?
The inverse of the given equation is r = (10D - 5)/11 which represents the reaction speed of the car in terms of the reaction distance.
The car travels a distance of D feet, where D is a function of the speed r miles/hour given by D(r) = (11r + 5)/10
D = (11r + 5)/10
⇒ 10D = 11r +5 (multiply by 10 on both sides)
⇒ 10D - 5 = 11r (subtracting 5 on both sides)
⇒ (10D - 5)/11 = r (dividing by 11 on both sides)
Therefore, the inverse of the given equation is r = (10D - 5)/11.
Inverse represents the speed of the car (miles/hour) in terms of the reaction distance D.
The inverse is also a function, which represents the reaction speed of the car in terms of the reaction distance.
Therefore. the inverse of the given equation is r = (10D - 5)/11 which represents the reaction speed of the car in terms of the reaction distance.
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PLease help!!!! 3( - 4y - 5) = 8y + 25, Show your work please!!
Answer:
y = -2
Step-by-step explanation:
Given equation:
[tex]3(-4y-5)=8y+25[/tex]
Distribute:
[tex]\implies 3 \cdot -4y - 3 \cdot 5=8y+25[/tex]
[tex]\implies -12y - 15=8y+25[/tex]
Add 15 to both sides:
[tex]\implies -12y - 15+15=8y+25+15[/tex]
[tex]\implies -12y =8y+40[/tex]
Subtract 8y from both sides:
[tex]\implies -12y-8y =8y+40-8y[/tex]
[tex]\implies -20y =40[/tex]
Divide both sides by -20:
[tex]\implies \dfrac{-20y}{-20} =\dfrac{40}{-20}[/tex]
[tex]\implies y =-2[/tex]
Now we have to,
→ solve for the required value of y.
Let's solve the problem,
→ 3(-4y - 5) = 8y + 25
→ -12y - 15 = 8y + 25
→ -12y - 8y = 25 + 15
→ -20y = 40
→ y = -40/20
→ [ y = -2 ]
Hence, the value of y is -2.
Use the properties of logarithms to evaluate each expression.
log₄48- 1/2 log₄9
Using the properties of logarithm the value of the expression is [tex]log_{4} 48 - \frac{1}{2}log_{4} 9 = 2[/tex]
A logarithm is the power to which a number must be raised in order to get some other number.
According to the question we have been given the expression as
= [tex]log_{4} 48 - \frac{1}{2}log_{4} 9[/tex]
The properties of logarithm that we are going to use are :
[tex]log(\frac{x}{y} ) = logx - logy[/tex] and [tex]log_{a} a = 1[/tex]
Also we can see that the base are same so we can use the property of logarithm in the given equation and we know that √2304 = 48. Thus replacing 48 by √2304.
Now solving this step by step using the properties of logarithm we get
[tex]=log_{4} \sqrt{2304} - \frac{1}{2} log_{4} 9 \\=\frac{1}{2} log_{4} 2304 - \frac{1}{2} log_{4} 9\\= \frac{1}{2} [log_{4} 2304 - log_{4} 9]\\= \frac{1}{2} [log_{4} (2304/9)]\\= \frac{1}{2} log_{4} 256\\= \frac{1}{2} log_{4} (4^{4} )\\= 2 * log_{4} 4\\= 2*1\\= 2[/tex]
Hence using the properties of logarithm the value of the expression is
[tex]log_{4} 48 - \frac{1}{2}log_{4} 9 = 2[/tex]
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what is the square of -3
Answer:
The square of -3 is 9
Step-by-step explanation:
(-3)^2=9
Solve each equation by factoring. Check your answers.
x²-8 x+15=0
The factors of equation are 5 and 3.
Rewriting the equation -
x² - 8x + 15 = 0
ax² + bx + c = 0
Factorizing the equation such that -
Sum of factors is equal to middle expression (b) (8x in this case)Product of factors is equal to the numeral values (a and c) (15 in this case)The suitable factors that can be used for solving the expression are 5 and 3.
x² - 5x - 3x + 15 = 0
x(x - 5) -3 (x - 5) = 0
(x - 5) (x - 3) = 0
(x - 5)= 0
x = 5
(x - 3) = 0
x = 3
Hence, the two factors of expression are 5 and 3.
To check the factors, we will keep each value of x to see if Left Hand Side is equal to Right Hand Side or not
When x = 5
x² - 8x + 15 = 0
5² - 8×5 + 15 = 0
25 - 40 + 15 = 0
-15 + 15 = 0
0 = 0
When x = 3
x² - 8x + 15 = 0
3² - 8×3 + 15 = 0
9 - 24 + 15 = 0
- 15 + 15 = 0
0 = 0
Since for both factors Left Hand Side is equal to Right Hand Side, thus, 5 and 3 are correct factors of the equation.
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If x= -2, the value of the expression 3x² - 5x +1/x is
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{3x^2 - 5x + 1}{x}}\\\\\mathsf{= \dfrac{3(-2)^2 - 5(-2) + 1}{-2}}\\\\\mathsf{= \dfrac{(3)(4) - (5)(-2)+1}{-2}}\\\\\mathsf{= \dfrac{12 - (5)(-2)+1}{-2}}\\\\\mathsf{= \dfrac{12 - (-10) + 1}{-2}}\\\\\mathsf{= \dfrac{12 + 10 + 1}{-2}}\\\\\mathsf{= \dfrac{22 + 1}{-2}}\\\\\mathsf{= \dfrac{23}{-2}}\\\\\mathsf{-11 \dfrac{1}{2}}\\\\\\\\\huge\text{Thus, your answer should be: \boxed{\mathsf{-11\dfrac{1}{2}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Find the center, vertices, and foci of the ellipse with equation x squared divided by 9 plus y squared divided by 25 = 1
Answer:
Center: (0,0)
Vertices: (0,-5), (0,5)
Foci: (0,-3) (0,3)
Step-by-step explanation:
f(x)=10 x-10 . Find each value.
(f ⁰ f⁻¹)(-10)
The inverse function returns the original value for which the output of a function was given.
The value of f(x) = 10x - 10 is -110.
What is the inverse formula?The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x. A function that is made up of its inverse returns the original value.
An inverse in mathematics is a function that serves to "undo" another function. That is, if f(x) produces y, then putting y into the inverse of f yields x. Invertible functions are those that have an inverse, which is denoted by f1.
Lett the function be F(x) = 10x - 10
To differentiate with respect to X
F⁻¹(x) = 10
F( f⁻¹(x)) = F(10)
F( f⁻¹(x)) = -10x -10
Substitute the value of X = 10, then we get
F( f⁻¹(x)) = -10(10)-10
simplifying the above equation, we get
F( f⁻¹(x)) = -100-10
F( f⁻¹(x)) = -110
Therefore, the value of (f ⁰ f⁻¹)(d) = -110.
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Please help me out please please please
The surface area is the sum of the area of the surfaces. The surface area of the box is 360x^2 - 216x
Surface area of a box.
The formula for calculating the surface area of a box is expressed according to the equation:
Surface area = 2(lw + wh +lh)
Given the following parameters
length = 6x
width = 12x - 9
height = 6x
Substitute
Surface area = 2(6x(12x-9) + (12x-9)(6x) +(6x)(6x))
Expand
Surface area = 2(72x^2-54x) + (72x^2-54x) + 36x^2)
Surface area = 2(180x^2-108x)
Surface area = 360x^2 - 216x
Hence the surface area of the box is 360x^2 - 216x
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the sum of three is 131 the second of three numbers is seven more than twice the first the third number is 12 less then the first what equation can be used to solos this problem
Answer:
4x - 5 = 131 where x is the first number.
Step-by-step explanation:
Let the first number be x.
Seconder number = 2x + 7.
Third number = x - 12.
So, the equation is :-
x + 2x + 7 + x - 12 = 131
4x - 5 = 131
4x = 136
x = 34
First number = 34, second = 2(34) + 7 = 75 and third number = 34-12 = 22.
Evaluate each logarithm.
log₅(-25)
log₅(-25) is undefined
Logarithms are another notation for exponents in mathematics. The logarithm of a number whose base is equal to another number.A logarithm is the reciprocal of a power. For example, if 10² = 100 then log₁₀ 100 = 2. The natural logarithm is called the base e logarithm. The natural logarithm is represented by ln or loge. where 'e' represents Euler's constant, which is approximately equal to 2.71828. For example, the natural logarithm of 78 is written ln 78. The natural logarithm determines how much "e" must be multiplied to get the desired output.Since the logarithmic function y = logₐ(x) is the inverse of the exponential function,
As the base is positive so x must also be positive
The logarithm of the real base of negative numbers is undefined.
Hence, log₅(-25) is undefined
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Read each question. Then write the letter of the correct answer on your paper.Let g(x)=x-3 and h(x)=x²+6 . What is h(1)xg(1) ?
We get the value of h(1) × g(1) as - 14 for the functions g (x) = x - 3 and h (x) = x² + 6.
We are given the two functions as:
g (x) = x - 3 and h (x) = x² + 6
Now, we will first find h (1)
h (1) = (1)² + 6
h(1) = 1 + 6
Add them, we get:
h (1) = 7
Now, we will find g (1):
g (1) = 1 - 3
g (1) = - 2
Now we will find the expression h(1) × g(1):
h(1) × g(1) = 7 × ( - 2 )
h(1) × g(1) = - 14
Therefore, we get the value of h(1) × g(1) as - 14 for the functions g (x) = x - 3 and h (x) = x² + 6.
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Suppose you invest $ 500 in a savings account that pays 3.5 % annual interest. How much will be in the account after five years?
Amount $593.84 will be in the account after five years.
According to the question we have been given that the
amount invested initially = $500
annual interest rate = 0.035
Time = 5 years.
The formula for the future value is given as
[tex]FV = a(1 + r)^{t}[/tex] (1)
where , FV = future value
a = amount invested initially
r = annual interest rate
t = time
putting the required values in equation (1) we get
[tex]FV = 500 (1 + 0.035)^{5} \\FV = 500 ( 1.035)^{5}[/tex]
FV = 500*1.188
FV = $ 593.84
Thus, $593.84 will be the amount in the account after five years.
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Use compass and straightedge moves to construct the angle bisector for angle ABC. In other words, create a ray that divides angle ABC into 2 congruent angles.
Answer:
Step-by-step explanation:
Draw a line in the middle of the compass slightly slanted like this /with an on top of the line indicating 2 congruent angles being created.