Answer:
Step-by-step explanation:
We will have to convert this to vertex form.
First we add y to both sides.
y = 3x^2 + 9x - 3
The vertex form is y = a(x – h)^2 + k
y = 3(x^2 + 3x) - 3
We need to complete the square now, and half if 3 is 1.5, and 1.5^2 is 2.25, so we add 2.25 inside the parentheses but we have to be careful, because if we subtract 2.25 from outside the parentheses it wouldn't work because the 2.25 inside the parentheses is being multiplied by 3, so we have to subtract 2.25*3=6.75 from the outside.
y=3(x^2 + 3x + 2.25) - 9.75
we can simplify this now to
y=3(x + 1.5)^2 - 9.75
and now this is vertex form. From here it is incredibly easy to get the vertex. Just take the x value required to make the total in the parentheses zero, so in this problem it would be -1.5 (Because (-1.5+1.5)^2 is zero) and then you have your x coordinate. From there we just take k, which in this problem is -9.75, and it is the y value of our vertex.
In conclusion, the vertex is (-1.5. -9.75)
1 inch is to 9 miles as ? inches is to 81 miles.
Please help me with this question please I need help asap
Answer:
You can travel 112.5 on a full tank of gas.
Step-by-step explanation:
500/60 = 8 [tex]\frac{1}{3}[/tex]
You can travel 8 [tex]\frac{1}{3}[/tex] miles on one gallon of gas.
Your tank holds 13 1/2 gallons.
8 [tex]\frac{1}{3}[/tex] x 13 [tex]\frac{1}{2}[/tex]
[tex]\frac{25}{3}[/tex] x [tex]\frac{27}{2}[/tex] 3 and 2 share a common factor of 3 so I cross canceled.
[tex]\frac{25}{1}[/tex] x [tex]\frac{9}{2}[/tex] = [tex]\frac{225}{2}[/tex] = 112.5
Answer:
your answer is 1,245 gas
Kendyl ate 4 pieces of the banana. Adison ate 2
pieces of the banana. They ate the entire
panana. What fraction represents the WHOLE
banana?
Answer:
Whole banana = 6/6
Step-by-step explanation:
Given information,
→ Kendyl ate 4 pieces.
→ Adison ate 2 pieces.
Now the total number of pieces,
→ 4 + 2
→ 6 banana pieces
Fractional representation is,
→ Kendyl = 4/6
→ Adison = 2/6
→ Whole banana = 6/6 = 1
Hence, the answer is 6/6.
1 and2.Select all that apply of the following terms: acute,right,obtuse,adjacent,vertical,complementary,supplementary.
1 and2.Select all that apply of the following terms: acute,right,obtuse,adjacent,vertical,complementary,supplementary.
The statement that apply to the given terms are:
rightadjacentsupplementaryHow can the angles be analysed?The facts to be noted :
An Angle in the figurecan be regarded as right angle which is 90°
∠2 can be seen as 90° since they are vertically opposite angles are equal
Both ∠1 and ∠2 altogether will give us 180° which can be seen as Linear Pair Then ∠1 = 90°.
Hence, we can deduce that :
They are Right angles ( measure of both angles are 90)
They are Adjacent angles (there is common arm and a common vertex)
They are Supplementary angles (sum of both angles is 180°)
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Match the term with its definition.
Identical, equal or the same.
A property of having two
equal length sides.
Lines that never intersect.
add to 180°
To divide or split into two equal parts.
Lines or segments that
intersect at 90°
add to 90°
1. Bisect
2. Perpendicular
3. Supplementary
4. Isosceles
5. Complimentary
6. Parallel
7. Congruent
16^2x-5 > 64 ^2x-3 solve for x Exponential equation and inequalities
Solving for x in the exponential equation and inequalities gives the value of
x < -1/2How to find the value of xpower or exponents as used in mathematics are number written on top of a base number. The power says how many times the base number multiplies itself.
For the given problem,
16²ˣ ⁻ ⁵ > 64 ²ˣ ⁺ ³
finding a common base
4²⁽²ˣ ⁻ ⁵⁾ > 4³⁽²ˣ ⁺ ³⁾
equating the bases
2(2x - 5) > 3(2x - 3)
4x - 10 > 6x - 9
4x - 6x > 10 - 9
-2x > 1
x < -1/2
the value of x in the inequality is -1/2
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how do i solve 3x+2y=10, 3x-y=4 in substitution? please help i will mark you brainliest
Step-by-step explanation: you times 3 by 2, which equals 6. And then you times 2 by 2 which gives you 4, and then you get 10. For the second one you do 3 times 2 which is 6 minus 2 ad it's 4.
sorry if it's wrong, st my school we do things very different that lots of other schools.
Answer:
i believe the answer is 2,2
Step-by-step explanation:
slove for the variable in one of the equations, I usually do the bottom but don't think it matters. Then add the final product back into the top one to get the final answer.
Please Solve, and Explain
Answer:
The triangle ABC was dilated with a scale factor of 3.
Take the unknown variable's previous value (4) and multiply it by 3.
You should get an answer of 12.
Hope this helps.
On a piece of paper, use a protractor to construct a triangle with angle measures of 60 degrees and 80 degrees. Select from the drop-down menu to correctly classify the triangle. A triangle with angle measures of 60 degrees and 80 degrees Is triangle.
Answer:80 pieces
Step-by-step explanation:
Graph the line that represents a proportional relationship between d and t with the property that an increase of 6 units in t corresponds to an increase of 7 units in d
What is the unit rate of change of d with respect to t (That is, a change of 1 unit in t will correspond to a change of how many units in d?)
The graph of the line of the proportional relationship is added as an attachment
The unit rate is 7/6
How to graph the line of the proportional relationshipFrom the question, we have the following parameters that can be used in our computation:
An increase of 6 units in t This corresponds to an increase of 7 units in dThis means that
d : t = 7 : 6
Express as fraction
So, we have
d/t = 7/6
Multiply both sides by t
d = 7t/6
So, the equation is d = 7t/6
This also means that the unit rate is 7/6
See attachment for the graph
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PLEASE HELP ME! URGENT!
The numeric values for each expression in this problem are given as follows:
a. g(g(g(1))) = 1.
b. f(f(f(2)) = 1.
c. f(f(g(2))) = 2.
d. g(f(g(4))) = 2.
How to obtain the numeric value for each expression?The numeric value for each expression is obtained using the compositions, and also the numeric values given from the tabke,
As an example, from the table, we have that when x = 1, g(x) = 4, hence:
g(1) = 4.
Hence:
g(g(g(1))) = g(g(4)) = g(3) = 1.
The circle symbol represents composition, meaning that the expressions are similar to item a.
Thus the numeric value in item b is obtained as follows:
f(f(f(2)) = f(f(4)) = f(5) = 1.
The numeric value in item c is obtained as follows:
f(f(g(2))) = f(f(5)) = f(1) = 2.
The numeric value in item d is obtained as follows:
g(f(g(4))) = g(f(3)) = g(6) = 2.
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round 6.07 x 3.29 to the nearset whole.number
Answer:
20
Step-by-step explanation:
6.07 *3.29=19.9703
since rhe number after decimal is greater than 5
so we can add 1 to the real number
that's why whole number is 19+1=20
what is the value of 32,538 divided by 10 to the third
Answer:
32.538
Step-by-step explanation:
[tex]\frac{32538}{1000}[/tex] move the decimal point that is at the end of the number 3 places to the left.
How many three letters code words can be constructed from the first nine letters of the Greek alphabet if no repetition are allowed
Answer:
504
Step-by-step explanation:
There are 9 choices for the first letter, 8 choices for the second letter, and 7 choices for the third letter, for a total of 987 = 504 three-letter code words that can be constructed from the first nine letters of the Greek alphabet without repetition.
Write these numbers in order of size. Start with the smallest number. 3.7 5.62 0.7 14.3
Answer: 0.7, 3.7, 5.62 and 14.3.
Step-by-step explanation: Write all numbers in ascending order.
According to the rules of tennis, a regulation ball "shall have a bounce of more than 53 inches and less than 58 inches when dropped 100 inches upon a concrete base."
Which number sentence reflects the bounce height restrictions for tennis balls?
A. 53 inches < bounce height <58
B. 53 inches > bounce height >58 inches inches
C. 53 inches ≤ bounce height ≤58
D. 53 inches ≤ bounce height ≤58 inches inches
The number sentence inequality that reflects the bounce height restrictions for tennis balls is given as follows:
A. 53 inches < bounce height < 58 inches.
How to construct the number sentence inequality?To construct the number sentence inequality, we must look at the restrictions for the bounce height of the tennis balls.
The restrictions are given as follows:
More than 53 inches.Less than 58 inches.The inequality that symbolizes the first restriction is given as follows:
bounce height > 53 inches.
The inequality that symbolizes the second restriction is given as follows:
bounce height < 58 inches.
Hence the compound inequality that involves the two restrictions is given as follows:
53 inches < bounce height < 58 inches.
Meaning that the correct option for this problem is given by option A.
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A broken rectangular window needs to be replaced. It measures 24 1/2 inches by 9 1/2 inches. How much glass is needed, in square inches, to replace the window?
The window measures 24 1/2 inches by 9 1/2 inches, so the area of the window is 24.5*9.5 = 230.25 square inches. Therefore, 230.25 square inches of glass are needed to replace the window
6. Complete the two-column proof.
Given: 3x + 4 = 10 Prove: x = 2
3x + 4 = 10 __?___
3x = 6 __?___
x = 2 ___?___
Answer:
see explanation
Step-by-step explanation:
given
3x + 4 = 10 ( subtract 4 from both sides )
3x = 10 - 4 = 6 ( divide both sides by 3 )
x = 6 ÷ 3 = 2
thus x = 2 is proven
Determine the truth value of each of the following implications.
a. If 3 + 4 = 12, then 3 + 2 = 6
b. If 3 + 3 = 6, then 3 + 6 = 9
c. If 3 + 3 = 6, then 3 + 4 = 9
d. If Fidel V. Ramos was the twelfth president of the Republic of the Philippines. Then 2 + 3 = 5
Answer:
Step-by-step explanation:
A: false
B: true
C: true
D: false
Ernie has another account at the bank that pays 2½% simple interest. How
much interest will he earn in 8 years on an initial deposit of $250?
Answer:
$50
Step-by-step explanation:
To find the amount of interest earned in 8 years, we can use the formula:
interest = principal * rate * time
where "principal" is the initial deposit, "rate" is the interest rate, and "time" is the number of years the interest is compounded.
Plugging in the values from the problem, we get:
interest = $250 * 2.5% * 8 years
interest = $250 * 0.025 * 8
interest = $50
So Ernie will earn $50 in interest in 8 years on his initial deposit of $250.
Subscribe to EvilMrGui Remastered if this was correct.
6-2x=3 please help me
Answer:
x = 3/2
Step-by-step explanation:
6 - 2x = 3
-2x = -3
x = 3/2
I hope this helps!
Match the pairs of equivalent expressions. ( - 14 + 3 2 b ) − ( 1 + 8 2 b ) 4 b + 13 2 ( 5 + 2 b ) + ( 2 b + 3 2 ) 8 b − 15 ( 7 2 b − 3 ) − ( 8 + 6 b ) - 5 2 b − 11 ( - 10 + b ) + ( 7 b − 5 )
The pairs of equivalent expressions are matched as follows:
(-14 + 3b/2) - (1 + 8/2b) and -15 - 5b/2.(5 + 2b) + (2b + 3/2) and 4b + 13/2.(7b/2 - 3) - (8 + 6b) and -5b/2 - 11.(-10 + b) + (7b - 5) and 8b - 15.What are equivalent expressions?Equivalent expressions are expressions that are equal when both are simplified.
For the first expression, we have that:
(-14 + 3b/2) - (1 + 8/2b)
-14 + 3b/2 - 1 - 8/2b
Combining the like terms:
-15 - 5b/2.
For the second expression, we have that:
(5 + 2b) + (2b + 3/2)
5 + 2b + 2b + 3/2
10/2 + 4b + 3/2
4b + 13/2.
For the third expression, we have that:
(7b/2 - 3) - (8 + 6b)
7b/2 - 3 - 8 - 6b
7b/2 - 11 - 12b/2
-5b/2 - 11.
For the fourth expression, we have that:
(-10 + b) + (7b - 5)
-10 + b + 8b - 5
8b - 15.
Missing InformationThe problem is given by the image shown at the end of the answer.
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what is the domain and range of y= square root of x-7-1
For the function: y = √(x - 7) - 1
The domain is D: [7, ∞) and the range is R: [1, ∞)
How to find the domain and range of the function?
Remember that the for a function y = f(x), the domain is the set of the possible inputs (possible values of x) while the range is the set of the possible outputs (possible values of y).
Here we want to find the domain and range of the function:
y = √(x - 7) - 1
First, we will find the domain, remember that the argument of a square root must be zero or larger, then the minimum of the domain is the value of x such that:
x - 7 = 0
x = 7
The domain is:
D: [7, ∞)
The square root is an increasing function, then the minimum of the range is given by evaluating the function in the minimum of the domain:
f(7) = √(7 - 7) - 1
f(7) = 1
Then the range is:
R: [1, ∞)
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Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the solution to this system of inequalities in the coordinate plane.
3y2x + 12
2x + y ≤ - 5
The Graph C shows the solution to this system of inequalities in the coordinate plane.
What are system of inequalities?When mathematical expressions are compared, with non-strict equality, then such mathematical statements are called mathematical inequalties.
A collection of inequalities for which we consider common solution for all inequalities is called a system of inequalities.
We are given that
3y > 2x + 12
2x + y ≤ - 5
Therefore, solving it;
x < 3(y - 4) / 2
y > 2 (x + 6) / 2
2x + y< -5
x> -5
So,
x < 3(y - 4) / 2
Here it shows dotted ascending line attached through x=-6
This means x=--6 and y = 0
This x>-5 shows boundary dotted vertical line through -5
Which means x = -5 y = 0
If it had been x ≥ -5 it would have been solid boundary line.
The vertices of both show (-5,1) so the correct option is C.
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Graph the inequality on the axes below y>-5/4x-2
The graph of the inequality:
y > (-5/4)*x - 2
Can be seen in the image at the end.
How to graph the inequality?Here we want to graph the following inequality:
y > (-5/4)*x - 2
To graph the inequality, we first need to draw the line:
y = (-5/4)*x - 2
With a dashed line (because the points on the line are not solutions) and then shade all the region above that dashed line.
To graph that line you need to find two points on the line and then connect them.
To find the points, we need to evaluate the line in two values of x.
if x = 0.
y = (-5/4)*0 - 2
y = -2
So we have the point (0, -2)
if x = 4
y = (-5/4)*4 - 2
y = -5 - 2
y = -7
So we have the point (4, -7)
Now we can graph the inequality, you can see the image below.
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If a success is defined as getting a 6 on a six-sided die, what is P( x < 4) if the dice is rolled 20 times
The probability of rolling a number less than 4 on a six-sided die, when rolled 20 times, is 0.5.
What is probability?Probability is the mathematical study of outcomes in uncertain situations. It is used to describe the likelihood of an event occurring, and it can be expressed as a number between 0 and 1. Probability is used to quantify the uncertainty associated with any given event. It helps us understand how likely it is that something will happen, and it can be used to make predictions about future events. Probability theory is a cornerstone of modern statistics and is widely used in fields such as finance, economics, and science.
This is because there are four possible outcomes when rolling a six-sided die, and two of those outcomes are numbers less than 4: 1 and 2. The probability of rolling a number less than 4 is therefore 2/4, or 0.5. This probability holds true regardless of how many times the die is rolled, as long as it is a fair and unbiased die.
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Use the properties of exponents to rewrite this expression.
What is the value of the rewritten expression when ?
A.
B.
C.
D.
The value of the expression Illustrated as (2a⁴)²/a^0a^5 is C. -500
What is the value of the exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number
From the information (2a⁴)²/a^0a^5
We know ( xy) ^z = x^z y^z
(2a^4)^2 = 2^2 a^4^2
and x^y^z =x^(y*z) so a^4^2 = a^(4*2) = a^8
(2a^4)^2 = 4 a^8
We know that a^0 = 1
4 a^8/1 a^5
We know x^y / x^z = x^ ( y-z)
4 a^( 8-5)
4 a^3
Let a = -5
4 ( -5) ^3
4 ( -125)
= -500
The correct option is C.
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I need help solving this
Answer:
C. {15, 16, 17, 18, ..., 165}
Step-by-step explanation:
Natural numbers are a set of numbers that occurs commonly and obviously in nature.
As such, it is a whole, non-negative number.
The set is denoted with letter N, starts from "0" and continues to the infinity.
The natural numbers between 14 and 166 would start with 15 and goes on until 165 so, the option C is the correct answer.
Last weekend, the movie theater in Wildgrove issued 8,060 tickets to comedies. This weekend, it issued 15,314 tickets to comedies. What is the percent of increase in the number of comedy ticket issued per weekend?
The percent increase in the number of comedy tickets issued per weekend, given the number of tickets issued, can be found to be 90 %
How to find the percentage increase ?To find the percentage increase, you need to find out the increase in the number of tickets issued between last weekend and this weekend. This difference would then be found as a percentage of the number of tickets sold last weekend.
The increase in tickets sold for comedies is therefore:
= This weekend tickets - Last weekend tickets
= 15, 314 - 8, 060
= 7, 254 tickets
The percentage increase is:
= Increase in tickets sold / Total tickets sold last weekend x 100 %
= 7, 254 / 8, 060 x 100 %
= 0. 90 x 100 %
= 90 %
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[(-5) - {4^2- (-5) }] • (4 - 3)
the answer is -26
please show me how to get that answer?
The value of the numerical expression [(-5) - {4²- (-5) }] · (4 - 3) will be negative 26.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The numerical expression is given below.
⇒ [(-5) - {4²- (-5) }] · (4 - 3)
Simplify the expression, then we have
⇒ [(-5) - {4²- (-5) }] · (4 - 3)
⇒ [(-5) - {16 + 5}] · (1)
⇒ [(-5) - 21]
⇒ - 26
The value of the numerical expression [(-5) - {4²- (-5) }] · (4 - 3) will be negative 26.
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