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.
The decimal 105.7 becomes 1,057 when multiplied by 10. The same number becomes 10.57 when multiplied by 0.10. Explain why.
-Multiplying by 10 makes the number
(Type whole numbers or decimals.)
by a factor of Multiplying by 0.10 makes the number
by a factor of
Suppose that $2000 is invested at a rate of 3.4% compounded quarterly. Assuming that no withdrawals are made, find the total amount after 4 years. Do not round any intermediate computations and round your answer to the nearest cent.
Given data:
The amount invested ( principal) is
[tex]P=\text{ \$2,000}[/tex]The interest rate given is
[tex]r=3.4\%[/tex]The number of years is
[tex]t=4\text{ years}[/tex]The number of times compounded is quarterly
A quarterly event happens four times a year, at intervals of three months.
[tex]n=4[/tex]Concept:
The formula to calculate the amount compounded is given below as
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{Where,} \\ A=\text{amount} \\ P=\text{principal} \\ r=\text{rate} \\ n=\text{ number of times compounded} \\ t=\text{ number of years} \end{gathered}[/tex]By substituting the values above in the formula, we will have
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=2,000(1+\frac{3.4}{400})^{4\times4} \end{gathered}[/tex]By solving the equation above, we will have
[tex]\begin{gathered} A=2,000(1+\frac{3.4}{400})^{4\times4} \\ A=2,000(1+0.0085)^{16} \\ A=2000(1.0085)^{16} \\ A=2,290.05 \end{gathered}[/tex]Hence,
The final answer = $2,290.05
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The shape shown below is made from a triangle and a rectangle.
a) Work out the area of the triangle.
b) Work out the area of the whole shape.
OLA
O
4 cm
3 cm
10 cm
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7 cm
Not drawn accurately
Answer
Raining now â
(a) The area of the triangle = 6 cm squares
(b) The area of the whole shape = 76 cm squares
The shape given is formed by a triangle and a rectangle.
First we need to find the area of the triangle.
Height of the triangle = 3 cm
Base of the triangle = 4 cm
Area of the triangle = 1/2 x base x height
= 1/2 x 4 x 3
= 6 cm squares
Area of the whole shape = Area of the triangle + Area of the rectangle
Length of the rectangle = 10 cm
Width of the rectangle = 7 cm
Area of the rectangle = length x width
= 10 x 7
= 70 cm squares
Therefore, area of the whole shape = 6 + 70
= 76 cm squares
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I’m pretty sure it is option (C).
Given:
[tex]n+0=7[/tex]Find the property.
Sol:
The additive identity property is:
[tex]\begin{gathered} a+0=a \\ \\ 0+a=a \end{gathered}[/tex]So use the Additive Identity property.
5. Betty wants to mail a package. The flat rate for mailing a package is $20, plus $3 per
pound. Write an expression that can be used to determine the total cost of mailing a package
that weighs p pounds.
If Betty spent $56 to mail her package, how many pounds did it weigh?
1. The mathematical expression that can be used to determine the total cost of mailing a package weighing p pounds is f(Tc) = 20 + 3p.
2. Since Betty spent $56 to mail her package, the weight in pounds of the mail must be 12 pounds.
What is a mathematical expression?A mathematical expression is a statement containing numbers, variables, and an arithmetic operation.
Flat (fixed) rate for mailing a package = $20
Variable mailing rate per pound = $3
Expression to model the total cost:
Let Tc = total cost
p = number of pounds
Tc = 20 + 3p
If Betty spent $56 to mail her package, the number of pounds, using the mathematical expression above:
Tc = 20 + 3p
56 = 20 + 3p
56 - 20 = 3p
36 = 3p
p = 12
Check:
Tc = 20 + 3p
56 = 20 + 3 (12)
56 = 20 + 36
56 = 56
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Wat is 3 times 4? cause i don’t know what it could be
Answer:
13
Step-by-step explanation:
3X4=12
Isaiah is measuring 3 1/2 inches using a ruler marked in 1/8 inch increments. Which of the following below is the total number of eighths that Isaiah will need to count out to make his measurement? Hint: turn 3 1/2 into an improper fraction with a denominator of 8.
A.24
B.28
C.30
D.36
If Isaiah is measuring 3 1/2 inches using a ruler marked in 1/8 inch increments. The total number of eighths that Isaiah will need to count out to make his measurement is B.28.
Total numberWe would be making use of the given hint to determine the total number of eight.
The hint is to use 3 1/2 into an improper fraction with a denominator of 8.
Hence,
Converting 3 1/2 to improper fraction
3 1/2 = 7/ 2 inches
Now let determine the total number with a denominator of 8.
= 7 × 4 / 2 ×4
= 28 /8
Therefore the correct option is B.
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please can someone help… A cuboid with a volume of 924 cm' has dimensions
4 cm, (x + 1) cm and (x + 11) cm.
Show clearly that x2 + 12x – 220 = 0
By substitute values in formula for volume of cuboid we get;
x² + 12x – 220 = 0
What is mean by Volume?
Volume of cuboid is defined as the amount of space occupied by the sides of cuboid in three-dimensional space.
Given that;
A cuboid with a volume of 924 cm' has dimensions,
4 cm, (x + 1) cm and (x + 11) cm.
Since, Volume of cuboid = Length x width x height
After substitute we get;
Volume of cuboid = 4 × (x + 1) × (x + 11)
924 = 4 (x² + 11x + x + 11)
924 = 4 (x² + 12x + 11)
Divide 4 both side;
231 = x² + 12x + 11
x² + 12x + 11 - 231 = 0
x² + 12x - 220 = 0
Thus, By the formula of volume of cuboid we get;
x² + 12x - 220 = 0
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Twelve skateboards have 48 wheels what is the value of the ratio of skateboards wheel in simplest form
The value of the ratio of skateboards wheel in its simplest form is 1:4.
What is the ratio?The ratio refers to the numerical relationship between two variables.
Ratios show the quantity of one variable contained in another.
Ratios are expressed in fractions, decimals, or percentages. They can also be written using the ratio symbol (:).
The total number of skateboards = 12
The total number of wheels = 48
The ratio value of skateboards wheels = 48:12
= 4:1 or 1:4
Thus, we can conclude that for every skateboard, there must be 4 wheels, given their ratio values.
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Si la suma de un número y 5 se multiplica por 3, el resultado es igual a 7 veces el número
disminuido en 13. Halla el número.
We construct an equation and calculate that number as 7 .
The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions. The word equation and its cognates can have slightly different meanings in different languages. For instance, in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign, whereas in French, an equation is defined as containing one or more variables.
The equation's solutions are the values of the unknown variables that satisfy the equality, which are often referred to as the variables for which the equation must be solved.
let the number be x .
9 times the number is = 9x
5 times the number added to 3 is
(x + 3) × 5
Now let us set up an equation and find that number :
(x + 3) × 5 = 9x - 13
Simplifying the given equation we get :
5 (x + 3) = 9x - 13
5x + 15 = 9x - 13
5x - 9x = - 13 - 15
- 4x = - 28
x = - 28/-4
x = 7
Hence the required number calculated from the equation is 7 .
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Disclaimer: The complete question is :
If the sum of a number and 3 is multiplied by 5 , the result is equal to 9 times the number decreased by 13. Find the number
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You deposit $400 each month into an account earning 4% interest compounded monthly. a) How much will you have in the account in 30 years?
Answer:
$14540
Step-by-step explanation:
you are earning 4 dollars per 400 dollars per month. there are 12 months in a year. 400 * 12*30 = 144000. 144000 divided by 400 is 360.
360 times 4 is 1440.
Would you classify 121 as a perfect square, perfect cube, both, or neither?Choose the correct answer below.O A. The number is a perfect square because = 121.OB. The number is a perfect cube because= 121OC. The number is both a perfect square and a perfect cube because= 121 and= 121OD. The number is neither a perfect square nor a perfect cube because there is no integer thatcan be squared to get 121 and no integer that can be cubed to get 121.
To know if a number is a perfect sqare of a perfect cube you:
perfect sqare
determine if its sqaure root is an integer. If is not an interger, then the number is not a perfect sqare
[tex]\sqrt[]{121}=11[/tex]perfect cube
determine if its Cube root is an interger. If is not an interger then the number is not a perfect cube
[tex]\sqrt[3]{121}=4.94[/tex]Then so, 121 is a perfect cube, because is the result of (11*11)
121 is not a perfect cube
The length of the batter's box on a softball field is 1 ft more than twice the width. The area of the batter's box is 78 ft2. Find the length and width of the rectangular batter's box.
The length and width of the rectangular box are 13 ft and 6 ft respectively.
How to find the length and width of a rectangle?The length of the batter's box on a softball field is 1 ft more than twice the width.
The area of the batter's box is 78 ft².
The length and width of the rectangular batter's box can be found as follows:
Therefore,
area of a rectangle = lw
where
l = lengthw = widthTherefore,
area of the rectangular box = 78 ft²
l = 1 + 2w
Hence,
78 = (1 + 2w)w
78 = w + 2w²
2w² + w - 78 = 0
Hence,
w = 6 and w = -13 /2
we can only use positive values.
Therefore,
width = 6 ft
length = 2(6) + 1 = 13 ft
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4) On average, Aliah drinks of a 6 ounce glass of water in hour. How much water does she
drink in an hour?
Answer: 60
Step-by-step explanation:6x10=60
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I need help with this please
SOLUTION:
[tex]\begin{gathered} 4^6X4^{-8} \\ 4^{6+(-8)} \\ 4^{6-8} \\ 4^{-2} \\ \frac{1}{4^2} \end{gathered}[/tex]А с 5 Find the missing side C 4 9 3 6.4 41
Use the pythagorean theorem to find side C
[tex]\begin{gathered} C=\sqrt[]{5^2+4^2} \\ C=\sqrt[]{25+16} \\ C=\sqrt[]{41} \\ C=6.4 \end{gathered}[/tex]The right answer is 6.4
Stocks and bonds both have costs, risk, and (interest or returns) associated with them. Bonds offer an interest payment through a ( coupon date or maturity date), while stocks may offer(dividends or interest) that will grow until it is sold.
Select the correct answer for the blanks
Stocks and bonds both have costs, risks, and returns associated with them. Bonds offer an interest payment through a maturity date while stocks may offer dividends that will grow until it is sold.
How to illustrate the information?Over the long term, stocks have the highest potential for growth for investors. Investors who have chosen to hold onto stocks for an extended length of time have typically been rewarded with robust, profitable returns. However, stock prices fluctuate both up and down.
An IOU-like debt security called a bond. Bonds are issued by borrowers to attract capital from investors ready to extend a loan to them for a specific period of time. When you purchase a bond, you are making a loan to the issuer, which could be a corporate, government, or municipality.
A dividend is a payment made by a corporation to its shareholders that is decided by the board of directors. Dividend payments are frequently made quarterly and might take the form of cash payments or stock reinvestments.
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Create a table that represents the transformation of f given by g.
g(x) = 3f(x)
The table which represents the transformation of function f given by g(x) = 3f(x) is:
x - 3 - 1 1 3
f(x) - 5 - 1 3 7
g(x) = 3f(x) - 15 - 3 9 21
When a function is transformed, the graph's curve of the parent function either "moves to the left/right/up/down," "expands or compresses," or "reflects."
A table for every value of x and its corresponding value of f(x) is given as:
x - 3 - 1 1 3
f(x) - 5 - 1 3 7
Now the transformed function g is given as:
g(x) = 3f(x)
Therefore, the table that represents the transformation of f given by g will be:
x - 3 - 1 1 3
f(x) - 5 - 1 3 7
g(x) = 3f(x) - 15 - 3 9 21
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If a car factory checks 380 cars and 11 of them havedefects, how many will have defects out of 1260 cars?
Answer:
Explanation:
Let x represent the number of defective cars.
Assuming that number of defective cars are uniformly distributed in the total number of cars, we can go ahead and solve for x by setting up proportion as shown below;
[tex]\begin{gathered} \frac{11}{380}=\frac{x}{1260} \\ 380x=13860 \\ x=\frac{13860}{380} \\ x=40 \end{gathered}[/tex]Please help :)..................................
Answer:
(d) Domain: {x|x∈ℝ} and range: {y|y∈ℝ}
Step-by-step explanation:
You want the domain and range of the relation shown in the graph.
GraphThe graph shows a line. The arrows on the end of it mean that it extends to infinity in both directions (up and left; down and right).
DomainThe domain is the horizontal extent. It includes all real numbers (from -∞ to +∞).
RangeThe range is the vertical extent. It includes all real numbers (from -∞ to +∞).
Domain: {x|x∈ℝ} and range: {y|y∈ℝ}
if the gradient of a line is 3, what is the gradient of the line which is perpendicular to A
16. Fill in the left side of the two-column proof (4 points).
Given:
32 = 2x + 4y; x = 2
y = 7
Prove:
32 = 2x + 4y; x = 2
Given
Substitution Property
Subtraction Property of Equality
Division Property of Equality
Symmetric Property of Equality
The left side of the two-column proof should be filled as follows:
Statements Reasons_______________
32 = 2x + 4y; x = 2 ⇒ Given
32 = 2(2) + 4y ⇒ Substitution Property
32 - 4 = 4 + 4y - 4 ⇒ Subtraction Property of Equality
28/4 = 4y/4 ⇒ Division Property of Equality
7 = y, y = 7 ⇒ Symmetric Property of Equality
What is the division property of equality?The division property of equality states that when both sides (left and right) of an algebraic expression or equation are divided by the same (common) real number that isn't equal to zero (0), the quotients would always remain equal.
What is the subtraction property of equality?The subtraction property of equality states that the two (2) sides of an algebraic expression or equation would still remain equal even when the same number has been subtracted from both sides of an equality.
In conclusion, it has been proven that y is equal to 7 by using the two-column proof.
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How much 36% acid solution should be added to 8% acid solution to make 196mL of a 10% acid solution?
Answer:
[tex]x = \frac{196}{13} [/tex]
How does finding the prime factorization of a group of numbers help
you to find their GCF
Take the prime factorization of both numbers to find the GCF. Then list the characteristics that they share. If they have more than one of the same factor (for example, two 2's), write them both down. Then multiply the factors they share.
What is prime factorization?A positive integer's prime factors are the prime numbers that divide it exactly. Finding these numbers is known as integer factorization or prime factorization. According to the fundamental theorem of arithmetic, every positive integer has a unique prime factorization.
What is GCF?The GCF (Greatest Common Factor) of two or more numbers is the greatest number among the given numbers' common factors. The greatest common factor (GCF) of two natural numbers x and y is the largest possible number that divides both x and y without leaving any remainder. GCF can be calculated in three ways: division, multiplication, and prime factorization.
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2 tablets 3 times per day 14 day supply 15 tablets needed per bottle. How many bottles are needed
6 bottles are needed.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
given:
2 tablets 3 times per day
so, total tablets = 6 tablets
Total days = 14
so, total tablets in 14 days = 14 x 6 = 96
and, tablets per bottle= 15
Then, the number of bottles required = 96 /15 =6.4
Hence, 6 bottles are needed.
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Write the sentence as an inequality. The temperature is not more than 82F.
1) Let's call Temperature by T
Since the temperature is not more than 82 F, then we exclude any value above 82º F, and we include 82.
T≤82
5y – 3 = 6y + 3
solve y
Answer: y = −6
Step-by-step explanation:
Answer:
5y−3=6y+3
Step 1: Subtract 6y from both sides.
5y−3−6y=6y+3−6y
−y−3=3
Step 2: Add 3 to both sides.
−y−3+3=3+3
−y=6
Step 3: Divide both sides by -1.
−y
−1
=
6
−1
y=−6
Step-by-step explanation:
brainliest please?
Please help I don’t understand this .
Step-by-step explanation:
cook time = 65 min + 11 min + 60 seconds + 30 seconds
= 65 min + 11 min + 1.5 minute
cook time = 77.5 minutes or: 1 hour, 17 minutes and 30 seconds.
For food to be ready by 4PM:
4PM - 1 hour, 17 minutes and 30 seconds = when to put food in
put food in = 2:42:30 PM
Pat has 3 times as many dimes as nickels. In all she has $1.40. How many coins of each does she have?
Answer:
Step-by-step explanation:
d=3n
0.10d+0.05n=1.40
0.10(3n)+0.05=1.40
0.3n+0.05n=1.40
0.35n=1.40
n=4
d=3(4)
d=12
12(0.10)+.05(4)=1.40
1.40=1.40
Use the information provided to find the vertex form equation of each parabola:-2x^2 + 36x -171
The vertex form of a parabola is expressed as
y = a(x - h)^2 + k
where
a is the leading coefficient
h and k are the horizontal and vertical coordinates of the vertex.
Recall, the general expression for a quadratic equation is
y = ax^2 + bx + c
By comparing with the given equation,
a = - 2, b = 36, c = - 171
The formula for the x coordinate of the vertex is
x = - b/2a
x = - 36/(2 * - 2) = - 36/- 4 = 9
Substituting x = 9 into the equation, we have
y = - 2(9)^2 + 36(9) - 171
y =