The quadratic function of h (x) in vertex form will be;
⇒ h(x) = (x + 2)² − 3
What is substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The values of x and h (x) for the quadratic function is given as;
x = -3, -2, -1, 0, 1, 2, 3,
h (x) = -2, -3, -2, 1, 6, 13, 22
Now,
Let the quadratic function is,
h (x) = ax² + bx + c
Substitute x = -3 and h (x) = -2 in above quadratic function we get;
h (x) = ax² + bx + c
- 2 = a × (-3)² + b × -3 + c
- 2 = 9a - 3b + c
And, Substitute x = -2 and h (x) = -3 in above quadratic function we get;
h (x) = ax² + bx + c
- 3 = a × (-2)² + b × -2 + c
- 3 = 4a - 2b + c
And, Substitute x = -1 and h (x) = -2 in above quadratic function we get;
h (x) = ax² + bx + c
- 2 = a × (-1)² + b × -1 + c
- 2 = a - b + c
After solving we get;
a = 1 , b = 4 and c = 1
Substitute all the values in above quadratic equation, we get;
h (x) = ax² + bx + c
h (x) = 1 × x² + 4x + 1
h (x) = x² + 4x + 1
h (x) = x² + 4x + 4 - 4 + 1
h (x) = (x + 2)² - 3
Thus, The quadratic function of h (x) in vertex form will be;
⇒ h(x) = (x + 2)² − 3
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Exit ticket: Joehamster eats 12 muffin morsels every sixth day, 24 celery sticks every 8th oday, and 18 cookies every 10th day. After how many days will he eat all three food items on the same day?
In order to calculate after how many days all three food items will be eaten in the same day, we need to calculate the least common multiple (LCM) between the periods of 6 days, 8 days and 10 days.
First, let's factorize each number:
[tex]\begin{gathered} 6\to2\cdot3 \\ 8\to2\cdot2\cdot2 \\ 10\to2\cdot5 \end{gathered}[/tex]Then, let's multiply the factors using the maximum number of time they appear in a number, that is, number 2 three times, number 3 one time and number 5 one time:
[tex]2\cdot2\cdot2\cdot3\cdot5=120[/tex]So after 120 days all three food items will be eaten on the same day.
Characterize the slope of the line in the graph
A. Positive
B. Negative
C. Zero
D. Undefined
The slope of the line in the graph is undefined.
The line in the graph is a straight vertical line whose slope can be found.
The characteristics of a vertical line can be used to find the slope of the vertical line given.
A vertical line has same x-co-ordinate but will have different y-co-ordinates.
Slope of a line is the change in y-co-ordinates divided by change in x-co-ordinates.
That is, slope = change in y-co-ordinates/ change in y-co-ordinates
But here, change in x-co-ordinates is zero since the x-co-ordinates are same for the vertical line given in the graph.
So slope = change in y-co-ordinates/ 0
This is undefined.
So the slope of the line in the graph is undefined.
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PLEASE HELPPPPP
Which graph represents the same relation as the set
♦
5
4
3
2-
1
--5-4-3-2-1₁ 1 2 3 45
-2+
-3
4 9
st²
•
t{(-3,2).(5.5).(3.3).(3.-2)}?
X
Answer: I think it’s t{(-3,2).(5.5).(3.3).(3.-2)}
Step-by-step explanation:
Eyesight is key m’lady
The first graph represents the same relation as the set {(-3,2).(5.5).(3.3).(3.-2)}
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The given relation is {(-3,2).(5.5).(3.3).(3.-2)}
We have to find the graph which represents the relation of the set
A binary relation on a set may, or may not, hold between two given set members.
The first number in the ordered pair represents the x coordiantes
The second number in the ordered pair represents the y coordiantes
When we match the ordered pairs with the given graphs
The first graph matches with the given relation
Hence, the first graph represents the same relation as the set {(-3,2).(5.5).(3.3).(3.-2)}
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hopt shipping company charges a
flat fee of $9 Plus an additional
$0.18 per pound to ship a package.
Gespil shipping company
flat fee of $10 plus an additional
$0.10 per pound. How many pounds
would a package weigh
that cost the same at
both companines?
Answer:
Hopt: 10 Gesplil; 6
Step-by-step explanation:
8. Find the value of x if xsin45º. cos45°. tan60° = tan² 45° - cos²60⁰
The study of the correlations between triangles' side lengths and angles is known as trigonometry. x= 0.11
What is trigonometry?The study of the correlations between triangles' side lengths and angles is known as trigonometry. The field was created in Hellenistic era in the third century BC as a result of the use of geometry in astronomical research. While Indian mathematicians produced the earliest tables of values for trigonometric ratios (also known as trigonometric functions), such as sine, the Greeks concentrated on chord calculation.
Trigonometry has been used historically in the fields like geodesy, surveying, celestial mechanics, and navigation.
Trigonometry has a wide variety of identities. In order to simplify an expression, identify a more practical version of an expression, or solve an equation, trigonometric identities are frequently employed to rewrite trigonometrical expressions.
xsin45º. cos45°. tan60° = tan² 45° - cos²60⁰
x0.7*0.70*1.73 =1*1-0.5*0.5
x = [tex]\frac{0.7*0.70*1.73}{1*1 - 0.5*0.5}[/tex] = 0.11
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Levi is 5 feet, 9 inches tall. How many centimeters tall is Levi? (1 inch = 2.5 centimeters)
Answer:
175.259 cm
Step-by-step explanation:
The probability that Gavyn wins in a raffle is given by the expression
p. Write down an expression for the probability that Gavyn does not win.
Explanation:
Let's replace p with something like 0.72
Pick any number between 0 and 1.
This says he has a 72% chance to win
1-p = 1-0.72 = 0.28
and he has a 28% chance of not winning.
For more information, check out "probability complement".
what is a four sided shape that has two parallel sides: can be cut into two triangles with a diagonal line through opposite corners?
The four sided shape that has two parallel sides: can be cut into two triangles with a diagonal line through opposite corners is a parallelogram.
What is a parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposite or facing sides are of equal length, and its opposite angles are of equal measure.
The parallelogram is divided into two congruent triangles by each diagonal. The total of the squares of a parallelogram's sides equals the sum of the squares of its diagonals. It is also known as parallelogram law.
A parallelogram is a two-dimensional geometrical shape with two parallel sides. It is a four-sided polygon (sometimes known as a quadrilateral) with parallel sides that are equal in length. The sum of a parallelogram's neighboring angles equals 180 degrees.
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HELP ME PLEASE!!! due tonight
Answer:
y=1x-5
Step-by-step explanation:
Use rise/run
Answer:
[tex]y=x-5[/tex]
Step-by-step explanation:
Just look at the slope and the y-intercept.
The y-intercept is b, and it's -5. The slope is 1, so it is x.
Properties of equality can be used to justify steps in solving an equation.
ANSWER:
4x-1=27
or,4x=27+1
or, x=28/4
or, x=7
Solve for v.
V =
Blank 1:
Answer:
v=60
Step-by-step explanation:
3v=180
v=60
:]
A map ratio is 1:50 000. Two villages
are 8km apart. How far apart are they
on the map?
Answer: they should be 2cm apart
Step-by-step explanation: This means that 1 cm on the map represents an actual distance of 50 000 cm (or 500 m or 0.5 km). We saw above that if a map has a scale of 1 : 50000, then 1 cm on the map is 50000 cm in real life.
What is -8.64 / -0.024?
Let's first write both numbers in their fraction form:
[tex]\begin{gathered} -8.64=-\frac{864}{100} \\ -0.024=-\frac{24}{1000} \end{gathered}[/tex]then, we can write the division like this:
[tex]-8.64\frac{\cdot}{\cdot}-0.024=-\frac{864}{100}\frac{\cdot}{\cdot}(-\frac{24}{1000})[/tex]Now, given the general rule for the division of fractions, we have:
[tex]\begin{gathered} \frac{a}{b}\frac{\cdot}{\cdot}\frac{c}{d}=\frac{a\cdot d}{b\cdot c} \\ b,d\ne0 \end{gathered}[/tex]also notice that we are dividing two negative numbers, then our final result will be positive according to the law of signs. Then, we have in this case:
[tex]-\frac{864}{100}\frac{\cdot}{\cdot}(-\frac{24}{1000})=\frac{864\cdot1000}{24\cdot100}=\frac{864\cdot10}{24}=\frac{8640}{24}=360[/tex]therefore the final result is 360
Write the equation of the line that is perpendicular to y = 1 and goes through (4, −9).
FOR PERPENDICULAR LINES WHEN THEIR GRADIENTS ARE MULTIPLIED THEY GIVE -1
BUT IF WE ARE TO CHECK IN THE LJNE y=1 the gradient is 0
there is no number when multiplied with 0 that will give us -1 it means that the gradient of the line perpendicular to the given one will also be 0
when we substitute in the general equation y=mx+c together with the points
[tex] - 9 = (0)(4) + c \\ c = - 9[/tex]
IT MEANS THE EQUATION OF THE NEW EQUATION WILL BE
[tex]y = - 9[/tex]
HOPE THIS HELPS
help !
Select the correct answer.
What is the measure of an angle that is the complement of angle R? R 80
Answer: B: 10
Step-by-step explanation:
complementary angles are two angles that add up to 90 degrees
At a carnival it costs $34.92 for 12 tickets. Write an equation that can be used to express the relationship between the total cost (t) and the number of tickets(n) you buy.
The equation that can be used to express the relationship between total cost and tickets is t = $2.91n.
What is the total cost?The first step is to determine the cost of one ticket. The cost of one ticket can be determined by dividing the total cost of the ticket by the total number of tickets. Division is the operation that is used to determine the quotient of two or more numbers.
Cost of one ticket = $34.92 / 12 = $2.91
The equation that can be used to determine the total cost would have this form:
Total cost = cost per ticket x number of tickets
t = $2.91 x n
t = $2.91n
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a package container 72 plastic cups 17.99
Approximately, the unit cost of the plastic cups is $0.25
Here, we want to get the unit rate of the plastic cups
By unit rate, we mean the price of 1
From the question, the total 72 costs $17.99
The cost of one is thus;
[tex]\frac{17.99}{72}\text{ = 0.25}[/tex]seven distinct pieces of candy are to be distributed among three bags. the red bag and the blue bag must each receive at least one piece of candy; the white bag may remain empty. how many arrangements are possible?
Using combination, there are 1932 arrangments possible.
A combination is a mathematical approach that counts the number of potential configurations in a box containing objects, regardless of their order.
In combinations, we can select items in any order. In combinations, the order doesn’t matter.
The combination formula of given as: n! / r!(n-r)!
Each candy would be distributed in three different ways if there were no limits on how many candies might fit in a bag. 3⁷ different ways to distribute the sweets in this scenario. However, only empty blue and red bags count in this scenario.
There are 2⁷ methods to distribute candy if the red bag is left empty.
Similarly, for the blue bag.
Hence there are 2⁷ +2⁷ – 1 ways to distribute candy such that either blue or red bag is empty.
The total amount of circumstances and ways to deliver the sweets
= 3⁷ – (2⁷ + 2⁷ -1)
= 1932
Therefore, there are a total of 1932 arrangements possible.
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a computer password is required to be 8 characters long. how many passwords are possible if the password requires 1 letter(s) followed by 7 digits (numbers 0-9), where no repetition of any letter or digit is allowed?
There will be 15724800 computer passwords possible with 1 letter followed by 7 digits without any repetition of letters or digits.
It is given to us that -
A computer password is required to be 8 characters long
The computer password requires 1 letter(s) followed by 7 digits
The 7 digits are from numbers 0-9.
It is also mentioned that there will be no repetition of any letter or digit
We know that,
The total number of English alphabets = 26 (from a-z)
The total number of digits = 10 (from 0-9)
Since it is given that the computer password has
1 letter followed by 7 digits without any repetition of any letters or digits
So, the number of computer passwords that are possible can be -
[tex]26*10*9*8*7*6*5*4\\= 15724800[/tex] (1 letter and 7 digits with no repetition)
Thus, 15724800 computer passwords are possible that contains 1 letter followed by 7 digits where no repetition of any letter or digit is allowed.
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(9x-26) (4x+43) (2x-12)
The value of the expression given as (9x-26) (4x+43) (2x-12) is 72x³ + 134x² -5642x + 13416
How to evaluate the expression?From the question, the expression is given as
(9x-26) (4x+43) (2x-12)
Next, we evaluate the expression in pairs
So, we have
(9x-26) (4x+43) (2x-12) = (9x-26) (4x+43) (2x-12)
Evaluate the first two factors
So, we have
(9x-26) (4x+43) (2x-12) = (36x² + 387x - 104x - 1118) (2x-12)
Evaluate the like terms in the expression
So, we have
(9x-26) (4x+43) (2x-12) = (36x² + 283x - 1118) (2x-12)
Evaluate the first two factors
So, we have
(9x-26) (4x+43) (2x-12) = (72x³ - 432x² + 566x² - 3396x - 2246x + 13416)
Evaluate the like terms
So, we have
(9x-26) (4x+43) (2x-12) = (72x³ + 134x² -5642x + 13416)
Remove the bracket
(9x-26) (4x+43) (2x-12) = 72x³ + 134x² -5642x + 13416
Hence, the solution is 72x³ + 134x² -5642x + 13416
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Simplify the equation. Show your work.[tex]-i^3^2[/tex]
[tex]{\Large \begin{array}{llll} i^4=1 \end{array}} \\\\[-0.35em] ~\dotfill\\\\ -i^{32}\implies -i^{4\cdot 8}\implies -(i^4)^8\implies -(1)^8\implies \text{\LARGE -1}[/tex]
Solve the equation 3 sinx+3 = 1 for 0°
The value of x after solving the equation 3sinx+3 = 1 for 0° is -46.455.
First, take the equation 3sinx+3 = 1. This is a first order linear equation with a single variable, x. To solve this equation find the value of x.
First subtract three from both LHS and RHS part. The equation becomes
3sinx+3-3 = 1-3,
which is equal to,
3sinx = -2. now divide both LHS and RHS by 3 and the equation becomes, (3sinx)÷3 = -2÷3 solving this we get the equation as sinx = -2÷3.
now take the sine to the LHS we get the equation as,
x = [tex]sin^{-1}[/tex](-2÷3)
so by solving this, the final answer for x is,
x = -46.455
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When 6 times a number is increased by 11 the result is 16 less than 9 times the number. Find the number
Answer:
The number is 9
Step-by-step explanation:
6n + 11 = 9n -16 Subtract 6n from both sides of the equation
11 = 3x -16 Add 16 to both sides of the equation
27 = 3n Divide both sides of the equation by 3
9 = n
is -1/3-4/5 positive,negative,or zero
The fraction expression given as -1/3-4/5 is a negative number
How to categorize the number?The fraction expression is given as
-1/3 - 4/5
From the above expression, we observe that:
The numbers are fractionsThe numbers are negative numbersThe sum of two negative numbers will result in another negative number
This means that the value of -1/3 - 4/5 is a negative expression
Solving further, we have:
-1/3 - 4/5
Evaluate the expression
-1/3 - 4/5 = -17/15
See that 17/15 is negative
Hence, -1/3 - 4/5 is negative
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x = 8.27 rounded to the nearest tenth
Answer:
x = 8.3
Step-by-step explanation:
We look at the final place of the decimal to round, in this case the thousandths place (underlined)
8.27
If the final place of the decimal is greater than or equal to 5, we round up the decimal to the left, otherwise we round down.
Because 7 > 5, round 2 up to 3, therefore giving 8.3
Answer:
Your answer is 8.3!
Step-by-step explanation:
Step 1: Locate and underline the tenths place (2) then look at the digit to the right (7):
8.27
Step 2: In this case, the digit to the right (7) is 5 or above. So, we add 1 to the tenth place (2). The digit(s) after the (2) are replaced by zeros (or dropped). Thus, we get 8.3 as the answer.
In short: 8.27 rounded to the nearest tenth is 8.3.
Find the slope and y-intercept of the following equations :
3x-4y = 12
Percents
Progress:
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your and
Solve this problem, and identify the percent, amount, and base.
What percent of 60 is 45?
O Percent = 75, Amount = 60, Base = 45
O Percent = 45, Amount =27, Base = 60
O Percent = 75, Amount = 45, Base = 60
Percent 60, Amount = 27, Base = 45
Submit
Hold
The correct option is- Percent = 75, Amount = 45, Base = 60 for the movement of the progress bar.
What is termed as the progress bar?In math, bar notation is a simple method for expressing a repeating number by drawing a line over the number which repeats. Learn regarding infinity, when figures go on forever, and when to use bar notation by exploring the definition as well as examples of bar notion.For the given question,
The movement of the progress bar could be uneven due to questions can be worth more or less (including zero) due-
Type of problemThe individual capacityThe amount of something is stated in terms of a fraction of a hundred. The ratio can be expressed as a fraction of 100.
Base = 60 and the Amount is the 45.
Let the % will be x;
x% of 60 =45
60x =45
x=45/60
x=0.75
To obtain the percentage value, multiply it by 100 as follows:
% x = 0.75 × 100
% x = 75
Thus, the percentage of 60 is 45 will become 75%.
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A box is in the shape of a right rectangular prism made from cardboard has dimensions of 18 inches, by 12 inches, by 8 inches, as shown in the diagram below. find the volume of the box and show your calculations and use appropriate units
Volume of the rectangular prism = 1,728 in³
Explanation:Volume of the rectangular prism = width × height × length
width = 12 in
length = 18 in
height = 8 in
Volume of the rectangular prism = 12 in × 8 in × 18 in
Volume of the rectangular prism = 1,728 in³
suppose that a current recipe yields 30 servings (2 ounces each) and the desired recipe yields 30 servings (5 ounces each). what is the recipe conversion factor?\
Conversion factor [tex]= \frac{final serving}{initialserving}[/tex][tex]=\frac{5}{2} =2.5[/tex]
The recipe conversion factor is 2.5
solve for t
275,000 = 300 1-(1 + .038/12 ) ^(-12t)/(.038/12)
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
The value of t exists [tex]$t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$$[/tex].
What is meant by an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Expressions have the following structure: (Number/variable, Math Operator, Number/variable).
Given: [tex]$275000=\frac{3001-\left(1+\frac{0.038}{12}\right)^{(-12 t)}}{\left(\frac{0.038}{12}\right)}$$[/tex]
Multiply both sides by 0.038 / 12, we get
[tex]$275000 \cdot \frac{0.038}{12}=\frac{3001-\left(1+\frac{0.038}{12}\right)^{-12 t}}{\frac{0.038}{12}} \cdot \frac{0.038}{12}$$[/tex]
Simplifying the above equation, we get
[tex]$\frac{5225}{6}=3001-\left(1+\frac{0.038}{12}\right)^{-12 t}$$[/tex]
Add [tex]$\left(1+\frac{0.038}{12}\right)^{-12 t}$[/tex] to both sides
[tex]$\frac{5225}{6}+\left(1+\frac{0.038}{12}\right)^{-12 t}=3001-\left(1+\frac{0.038}{12}\right)^{-12 t}+\left(1+\frac{0.038}{12}\right)^{-12 t}$$[/tex]
Simplifying the above equation, we get
[tex]$\frac{5225}{6}+\left(1+\frac{0.038}{12}\right)^{-12 t}=3001$$[/tex]
Subtract 5225 / 6 from both sides
[tex]$\frac{5225}{6}+\left(1+\frac{0.038}{12}\right)^{-12 t}-\frac{5225}{6}=3001-\frac{5225}{6}$$[/tex]
Simplify
[tex]$\left(1+\frac{0.038}{12}\right)^{-12 t}=\frac{12781}{6}$$[/tex]
By using exponent rules, we get
[tex]$-12 t \ln \left(1+\frac{0.038}{12}\right)=\ln \left(\frac{12781}{6}\right)$$[/tex]
Solve [tex]$-12 t \ln \left(1+\frac{0.038}{12}\right)=\ln \left(\frac{12781}{6}\right): \quad t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$[/tex]
[tex]$t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$$[/tex]
Therefore, the value of t exists [tex]$t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$$[/tex].
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