The factorization of 21+39 is 3(7+13)
What is factorization of expression?The process of finding two or more expressions whose product is the given expression is called the factorization of algebraic expressions. Thus, the factorisation of algebraic expressions is the reverse process of multiplication.
to factorize, we find a common factor between the two terms
The common factor between 21 and 39 is 3 .
3 in 21 is 7 and 3 in 39 is 13
therefore 21+39 can be written as 3(7+13)
we can therefore be say that 21+39 = 3(7+13) and 3 is the missing number in the question
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Mr. Cortez is building a brick boarder the bricks are 1 ft. How many bricks does he need to buy? Use 3.14 for pi
The number of bricks needed to border the circular pool is 6.28r.
What are the circumference and diameter of a circle?The circumference of a circle is the distance around the circle which is 2πr.
The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.
Given, Mr. Cortez is putting a brick border around his circular pool.
So, He is boarding the circumference of the circular pool which has a distance of 2πr.
Now, The bricks are 1 foot in length.
Therefore, The number of bricks needed is,
= 2πr/1.
= 2πr.
= 6.28r.
According to the radius number of bricks can be determined.
Q. Mr. Cortez is putting a brick border around his circular pool. The bricks are 1 foot in length. How many bricks does Mr. Cortez need to buy to build the border? Use 3.14 for π.
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You decide to invest in government bonds to save money for your eventual wedding. You have an
initial investment of $7,000 and when you choose to invest for 14 years you get a 10% rate
of return. What will be the value of your investment at maturity?
y = a(1+r)²
Round off to the nearest whole number
(don't forget to change your rate to a decimal percentage)
The value of your investment at maturity at a 10% rate of return will be,
$8470.
What is compound interest?Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.
We know the formula for compound interest is,
A = P(1 + r/100)ⁿ.
Where, A = amount, P = principle, r = rate, and n = time in years.
Given, An initial investment of $7,000 and when you choose to invest for 14 years you get a 10% rate of return.
We know, 10% = 10/100 = 0.1.
Therefore, The value of your investment at maturity will be,
y = 7000(1 + 0.1)².
y = 7000(1.1)².
y = 7000×1.21.
y = 8470.
So, The value of the maturity will be $8470.
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let a . find the third column of without computing the other two columns.
The third column of the matrix is:
[tex]\begin{bmatrix}1 \\5 \\7\end{bmatrix}[/tex]
The third column of a matrix can be calculated without computing the other two columns by using the formula:
A_{ij} = (A_{i1} - A_{i2}) \times \frac{j - 1}{2} + A_{i2}
Where A_{ij} is the element in the ith row and jth column of the matrix, A_{i1} is the element in the ith row and 1st column of the matrix and A_{i2} is the element in the ith row and 2nd column of the matrix.
To calculate the third column of a matrix, we will first calculate the difference between the first two columns. For example, if we have the following matrix:
[tex]\begin{bmatrix}1 & 4 & ? \\7 & 2 & ? \\3 & 8 & ?\end{bmatrix}[/tex]
The difference between the first two columns is 3 (4 - 1 = 3). Now we can use the formula to calculate the third column. For the first row, we have A_{11} = 1, A_{12} = 4, and j = 3 (the third column). Plugging these values into the formula, we get:
A_{13} = (1 - 4) \times \frac{3 - 1}{2} + 4 = 1
For the second row, we have A_{21} = 7, A_{22} = 2, and j = 3 (the third column). Plugging these values into the formula, we get:
A_{23} = (7 - 2) \times \frac{3 - 1}{2} + 2 = 5
For the third row, we have A_{31} = 3, A_{32} = 8, and j = 3 (the third column). Plugging these values into the formula, we get:
A_{33} = (3 - 8) \times \frac{3 - 1}{2} + 8 = 7
Therefore, the third column of the matrix is:
[tex]\begin{bmatrix}1 \\5 \\7\end{bmatrix}[/tex]
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1. (10 pts) use the definition of big o notation to find the constants c, no which show that t(n) is o(f(n)). a. ()= 32 4, ()= 52
use the definition of big o notation to find the constants c, no which show that t(n) is o(f(n)) then 5^n+25 is not = 5^n
The main purpose of the computational complexity is to categorize the algorithms about their show. And we can represent the T(n), which is the time function with the help of the big O notation, for showcasing an algorithm runtime complexity. As an example,
T(n) = O(n3)
proves that the algorithm has the cubic time complexity.
Now let's define Bio O, and from here we will get our answer. For any function which is monotonic in nature, f(n) and g(n) from the +ve integers to the +ve integers, we assume that f(n)= O(g(n)) when exist a c>0 which is the constant, and n0 greater than 0, such that
f(n) < c * g(n), for each n>=n0
i) if O (5^n)= 4^n + 25
O (f) should be = (20^n)/f + 25
Then constant
O(5^n)= (20^n)/(5^n) + 25 = (20/5)^n +25=4^n+25
ii) O (4^n)=(20^n)/(4^n) + 25 = (20/4)^n +25=5^n+25
And 5^n+25 is not = 5^n
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complete question is
Use the definition of O (f) to show that 4^n + 25 is O (5^n) (ii) show that 5^n is not O (4^n)
suppose →=→×→ and is the angle between → and → where when they are drawn with their tails at the same point. it is know that is not equal to 90°. which of the following is false?
None of the following statements are false. The angle between → and → is not equal to 90°.
Given that →=→×→ and is the angle between → and → where when they are drawn with their tails at the same point, and it is known that is not equal to 90°, none of the following statements are false.
Given that → and → are two vectors drawn with their tails at the same point, and →=→×→ is the angle between them, and it is known that is not equal to 90°, none of the following statements are false:
1. The angle between → and → is not equal to 90°.
2. The angle between → and → is greater than 90°.
3. The angle between → and → is less than 90°.
4. The angle between → and → is equal to 0°.
5. The angle between → and → is not equal to 180°.
The complete question is :
Given that →=→×→ and is the angle between → and → when they are drawn with their tails at the same point, it is known that is not equal to 90°. Which of the following is false?
A. The angle between → and → is not 90°.
B. The angle between → and → is equal to 90°.
C. The angle between →=→×→ is not 90°.
D. The angle between →=→×→ is equal to 90°.
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Gavin buys 36 packets of raisins. Each packet of raisins costs £0.35.
Work out the total cost of all the packets that Gavin buys.
Answer: I'm not sure if it's right but I got 12.6
Step-by-step explanation: Multiplication
A baeball team play in a tadium that hold 44000 pectator. With the ticket price at $11 the average attendance ha been 19000. When the price dropped to $8, the average attendance roe to 22000. Aume that attendance i linearly related to ticket price. What ticket price would maximize revenue?
Answer:
$8 because the ticket would be affordable.
solve 14A and 14B please
The slope of the graph is 1 and the y-intercept is -273.15. The slope presents the ratio between Celcius and Kelvin temperature and y-intercept shows the difference between both scales.
Based on the given graph:
(273.15, 0)
(0, -273.15)
m ?
y-intercepts?
slope:
m = y₂ - y₁
x₂ - x₁
m = -273.15 - 0
0 - 273.15
m = 1
y-intercept --> x = 0
x = 0 is when y = -273.15
The graph represents the relationship between temperature in Celcius scale and Kelvin scale.
The slope shows that both Celcius and Kelvin have equal ratio in measuring temperature. However, the y-intercepts shows that both scales have different zero points. The same temperature will be 273.15 lower in value under Kelvin scale than Celcius.
Then:
0°C = -273.15K
0K = 273.15°C
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A survey of statistics undergraduate at prosperity university completed a survey that asked for their verbal and math sat scores. They wanted to predict the verbal score based on the math score. The value of r-squared was 12. 78%. The least squares regression equation is yhat = 383. 3 + 0. 3489x. Find r.
The coefficient of determination (r-squared) provides an indication of how well the regression model fits the data and the value of r is 0.3574
In this example, the r-squared value is 12.78%, which means that 12.78% of the variation in verbal SAT scores can be explained by the variation in math SAT scores. The least squares regression equation is yhat = 383.3 + 0.3489x, where yhat is the predicted verbal score and x is the math score.
The coefficient of correlation (r) provides a measure of the strength of the linear relationship between two variables. In this example, the coefficient of correlation (r) can be calculated from the coefficient of determination (r-squared) as follows: r = √r-squared = √12.78% = 0.3574. This indicates that there is a weak linear relationship between verbal and math SAT scores.
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A wolf can run 110 m in 6. 3 seconds. A Tiger can run 85 m in 4. 2 seconds. Compare
their unit speeds to determine which animal is faster. Round to the nearest whole
unit.
Tiger speed? Wolf speed?
Which one is faster ?
Acceleration versus time graph for four objects are shown below. All axes have the same scale. Which object had the greatest change in velocity during the interval ?
The slope of a velocity graph represents the acceleration of the object.
Why does slope make things go faster?
Gravity is what causes the change in speed on a slope. Objects accelerate (move faster) when traveling downhill, and decelerate (move slower) when moving uphill (slow down).
They will then continue moving at the same pace on a level surface, presuming there is little friction.
= area of graph is 1/2 t₀a₀.
= area is less than 1/2 t₀a₀.
= area is more than 1/2 t₀a₀.
So in option (d) change in velocity is greatest.
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GRAPHING EXPONENTIAL FUNCTIONS
Please show work I don’t understand how to do this
Solving the provided question, we can say that the given exponent is
[tex]32 = 2^{ 3x - 1 }[/tex] => 64 = [tex]2^{3x}[/tex] => [tex]2^{3(2)} = 2^{3x}[/tex] on comparing both side, we have x = 2
what are exponents?Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where
the given exponent is
[tex]32 = 2^{ 3x - 1 }[/tex]
64 = [tex]2^{3x}[/tex]
[tex]2^{3(2)} = 2^{3x}[/tex]
on comparing both side, we have
x = 2
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How much is 510 in meters?
510 is a quantity in the unit of feet and not in meters, so it can't be directly expressed as a quantity in meters.
How much is 510 in meters?To convert from feet to meters, you can use the following conversion factor:1 foot = 0.3048 metersFeet and meters are units of length used to measure distances and lengths.The conversion factor of 1 foot to 0.3048 meters is based on the definition of the meter as being equal to approximately 3.2808 feet.To convert from feet to meters, simply multiply the number of feet by the conversion factor of 0.3048.For example, 510 feet is equal to 510 x 0.3048 = 155.448 meters.It's important to note that this conversion factor is an approximation and may not be entirely accurate in all situations.For more precise conversions, it's best to use a conversion calculator or a reference guide that provides exact conversion factors.To learn more about meter refer:
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rewrite the quadratic equation in factored form
Answer:
(x - 7)(x + 8)
Step-by-step explanation:
x² + x - 56
Multiples of 56 whose difference is 1: 7, 8
So, splitting the equation:
x² + 8x - 7x - 56
(x - 7)(x + 8)
The factored form of a quadratic expression is a way to rewrite the expression which shows the sums of products.
general form: [tex]y= a(x-r)(x-s)[/tex]
in which the parenthesis, when solved for will give the roots/x-intercepts of the equationwhen the a value is equal to zero:
find two numbers that sum to the middle term and when multiplied give you the product of the third term[tex]y=x^2+x-56[/tex]
find two numbers that are the sum of 1 and are the multiply to give you -56+8 and -7 create a sum of +1 and the product of -56[tex]y=(x+8)(x-7)[/tex]
how is calculus used in disasters
Answer: quantifies the economic devastation of natural and man-made disasters
El mundo cuenta con 6,974,400,000 de personas y si la población mundial aumenta en un 1. 2% anualmente ¿Cuántas personas aumentan en un año?
The population of the world after 1 year will be 6,974,400,000 + 1.2% of 6,974,400,000 = 7,058,092,800
What is percentage ?A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
By dividing the value by the entire value and multiplying the result by 100, one may get the percentage. The percentage calculation formula is (value/total value)100%.
The word "percentage" means "out of 100." In mathematics, percentages are used, together with fractions and decimals, to denote parts of a whole. The total is split into 100 equal pieces to calculate percentages.
Total population of the world is 6,974,400,000
The population is incresing at a 1.2% rate annually
The population of the world after 1 year will be 6,974,400,000 + 1.2% of 6,974,400,000 = 6,974,400,000 + 836928000 = 7,058,092,800
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What is the equation of the following line? Be sure to scroll down first to see all answer options. (8,2) (0, 0)
The equation of the line is y = 4x
How to determine the equation of the lineThe general equation of a line is expressed with the formula;
y = mx + c
Where the parameters are given as;
y is a point of the line on the y -axis of the graphx is a point of the line on the x -axis of the graphm is the slope of the line in the graphc is the intercept of the iine on the y -axis of the graphFrom the information given, we have the expression;
Slope, m = y₂ - y₁/x₂ - x₁
Substitute the values into the formula
Slope, m = 0 - 8/0 - 2
Subtract the values
Slope, m = -8/-2 = 4
For the intercept
0 = 4(0) + c
c = 0
Hence, the equation is y = 4x
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What is the equation of the line described below written in slope-intercept form?
the line passing through point (2, 2) and perpendicular to the line whose equation is y = x
y = x + 4
y = -x + 4
y = x - 4
The slope of the line perpendicular to y = x is -1. The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept. Substituting m = -1 and using the point (2, 2), we have:
y = -x + b
2 = -2 + b
b = 4
So the equation of the line passing through (2, 2) and perpendicular to y = x is:
y = -x + 4
Please Brainliest
PLEASE HURRY AND ANSWER ASAP FOR BRAINLIEST AND POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!! PLEASE ANSWER MY OTHER QUESTIONS TOO BECAUSE I ALWAYS GIVE THE RIGHT ANSWER A BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!
The function f(x) represents the number of texts sent this week, and g(x) represents the number of texts sent last week. Given f(x) = 6x + 8 and g(x) = 2x − 9, find (f − g)(x) to find how many more texts were sent this week than last week.
(f − g)(x) = 4x − 1
(f − g)(x) = 8x − 1
(f − g)(x) = 4x + 17
(f − g)(x) = 8x + 17
Answer:
(f − g)(x) = 4x + 17
Step-by-step explanation:
find (f − g)(x) = f(x) - g(x)
f(x) = 6x + 8 and g(x) = 2x − 9
6x + 8 - (2x − 9)
multiply the -1 to 2x − 9
6x + 8 - 2x + 9
Combine like terms
4x + 17
Answer: choice C
Step-by-step explanation:
Took exam on FLVS
In ΔFGH, f= 8.8 inches, m∠F=23° and m∠G=107°. Find the length of g to the nearest 10th of an inch
The value of length g is 21.56 inches
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
Therefore to find length g
f/sinF = g/sinG
8.8/sin23 = g/sin 107
8.8 × sin107 = g× sin 23
8.8 × 0.956 = g × 0.39
g = 8.8 × 0.956/0.39
g = 8.41/0.39
g = 21.56 inches
therefore the value of the length of g is 21.56 inches
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Answer:21.5
Step-by-step explanation:
solve for
secx = 1 - tanx
The required solution of the given trigonometric equation is given as x = 3π/2 + 2nπ.
What are trigonometric equations?These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
Here,
sec(x) = 1 - tan(x)
1/cosx = cosx - sinx / cosx [secx = 1 / cosx ; tanx = sinx / cosx]
cosx = 1 + sinx
1 + sinx - cosx = 0
1 + √2[sin{x - π/4}] = 0
sin{x - π/4} = -1/√2
x - π/4 = 5π/4 + 2nπ
x = 3π/2 + 2nπ
Thus, the solution of the given trigonometric equation is given as x = 3π/2 + 2nπ.
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Kate is filling out her income tax return. Her tax for last year is $973. Her employer withheld $712 in federal taxes. What is the difference between Kate’s tax and the amount withheld by her employer?
Therefore , the solution of the given problem of unitary method comes out to be $261 is the difference between kate's tax and amount with held by employer.
What exactly is a unitary method?After establishing the size of a little slice, multiply the quantity by two to complete a task utilizing unitary technique. Simply expression, the unit technique serves to isolate a programmed thing from a certain set or sets of sets. For example, the price of 40 pens is 400 pounds ($1.01) or Rs. It's possible that one country will have total control over the method employed to do this. Almost every living creature has a distinctive quality. It can equally integrate and reciprocate (mathematics, algebra).
Here,
Given :
=> tax for last year is $973
=> employed with held is $712
the difference between Kate's tax and amount with held is:
=> 973 - 712
=> $261.
Thus , $261 is the difference between kate's tax and amount with held by employer.
Therefore , the solution of the given problem of unitary method comes out to be $261 is the difference between kate's tax and amount with held by employer.
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In Activity 1. 3
For the second set of values：
a. Which among the missing components can be solved using the given？
b. How will you solve the next missing component？
The Pythagorean Theorem can be used to solve for the missing sides of a triangle when given two other sides
a. The missing components that can be solved using the given values are the missing sides of the triangle (side b and side c).
b. To find the missing side, we can use the Pythagorean Theorem, which states that a^2 + b^2 = c^2, where a and b are the two sides of the triangle, and c is the hypotenuse. Therefore, we can solve for c by taking the square root of (a^2 + b^2).
The Pythagorean Theorem can be used to solve for the missing sides of a triangle when given two other sides. To do this, we take the square root of the sum of the squares of the two given sides, which gives us the length of the hypotenuse.
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How can the study of mathematical logic help you in your everyday life?
The study of mathematical logic help you in your everyday life in the following way.
Mathematical logic is a branch of mathematics that deals with the principles of reasoning and makes statements based on deductive reasoning.
It is not just a subject that helps you ace your math exams but also a useful tool in your everyday life.
Understanding the basic principles of logic can help you make better decisions, solve problems more effectively, and communicate your ideas more clearly.
Logic helps you analyze information, evaluate arguments and make informed decisions.
In everyday life, you often encounter situations where you have to make choices based on information that is incomplete or ambiguous.
Furthermore, logic can also help you improve your critical thinking skills. By understanding how to reason and argue logically, you can more easily identify and evaluate flawed arguments, understand the relationships between different ideas and reach more accurate conclusions.
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22 VA-Geometry IC (Year)
Determining Truth Values
Suppose statement p is true but statement q is false. Which of these compound statements are true? Check all that
apply.
О р^g
Opvq
Op-q
9-P
Op-q
q-p
If statement p is true but statement q is false, then the following compound statements are true -
Option B: p ∨ q
Option D: q → p
What is compound statement?
A compound statement is a collection of two or more statements joined together using terms like "or," "and," "if then," and "only if." Each component statement of a compound statement can be determined to be true or untrue with clarity.
If the truth value of the statement p is 'True' and truth value of statement q is 'False',
p ∧ q → False [Conjunction of both the statements will be true only when both the statements are True]
p ∨ q → True [Disjunction of two statements will be false only when both the statements are false]
(p → q) → False [p is same as q]
(q → p) → True [Implication of both the statements is false only when p is true and q is false otherwise true]
(p ↔ q) → False [Bi-conditional statements are true if and only when both the statements are true]
(q ↔ p) → False [Bi-conditional statements are true if and only when both the statements are true]
Therefore, the compound statements p ∨ q and (q → p) is true.
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Wayne plays multiple instruments in a rock band. He also composes the songs. He takes 36 weeks to write the songs for an album of 12 songs. If you assume he takes an equal amount of time to compose each song and graph this relationship with the number of weeks on the x-axis and the number of songs on the y-axis, what is Wayne's unit rate for composing a song?
the unit rate for composing a song will be 3 weeks per song.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given, Wayne plays multiple instruments in a rock band. He also composes the songs. He takes 36 weeks to write the songs for an album of 12 songs.
He took 36 weeks to compose 12 songs.
Since,
Unit rate: Divide total weeks by total songs.
Thus,
Unit Rate = 36 / 12 = 3 weeks per song.
Therefore, the unit rate for composing a song will be 3 weeks per song.
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The one about the triangle
Answer: I split it up and got 4.
Step-by-step explanation: You will have to split it up into equal pieces.
Answer:
Step-by-step explanation:
The sum of the interior angles of a triangle is 180 degrees
Bernard borrows a sum of money from the bank which charges a compound interest of 4. 2% per annum, compounded quarterly. Given that Bernard had to pay $96. 60 in interest payments at the end of the first year, find the original sum of money borrowed, giving your answer correct to the nearest dollar.
(answer : $2264 )
The original sum of money borrowed would be $ 2246.51.
What is meant by Future Value?A financial concept called future value (FV) determines the worth of an asset by using projected factors like future interest rates or cashflows. An investor could find it interesting to know how much, given a projected rate of return, their investment might be in five years. Future value is the idea that an investment will be worth more in the future if its current value is multiplied by anticipated growth.
Interest = $ 96.60
Interest is compounded 6 times in a year; n = 6
time = 1 year ; Rate of interest (r) = 4.2 %
Interest = Future Value - Principal Value
Future Value = Principal [tex]$\cdot\left(1+\frac{r}{100 \times n}\right)^{n \cdot t}$[/tex]
Substituting this value in equation (1), We get
Interest = Principal [tex]$\cdot\left(1+\frac{r}{100 \times n}\right)^{n \cdot t}-$[/tex]Principal
96.60 = Principal [tex]$\left[\cdot\left(1+\frac{4.2}{100 \times 6}\right)^{6 \cdot 1}-1\right]$[/tex]
Principal = $ 2246.51
Therefore, the original sum of money borrowed would be $ 2246.51.
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The area of a hexagon is the space that is enclosed by all six sides of the hexagon.
True
False
It is true that The area of a hexagon is the area enclosed within its six sides. It is measured in square units such as m2, cm2, yard2,in2, etc. A hexagon is a two-dimensional closed shape that has six sides and six angles.
What is a six-sided shape's area?The area of a hexagon is calculated using the formula Area = (33 s2)/2, where s is the length of one of the regular hexagon's sides. The area of a hexagon can also be calculated using the apothem by using the formula Area of hexagon = (1/2) a P, where an is the apothem's length and P is the hexagon's perimeter.
There are six lines of symmetry in regular hexagons. The midpoints of its two opposite sides are joined by three lines, and the diagonals are joined by three more lines. This denotes the existence of "mirror symmetry" in a regular hexagon.
A regular hexagon is a regular polygon with six sides. determine the regular hexagon's side length, Apply the formula for the hexagon's surface area (33 s2)/2 to calculate the area, where s is the hexagon's side length.
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Arianna practices the piano 665 minutes in 5 weeks. If t represents the total time she practices for any number of days, d, write a proportional equation for t in terms of d that matches the context.
Answer:
The proportional relation for t in terms of d is:
t = (53 min/day)*d.
Step-by-step explanation: