Answer:
Step-by-step explanation:
410/25 = 16.4 gallons of gas
16.4*$3.40 = $55.76
mangleR = 120° and mangleS = 100°. Find mangleT. The diagram is not drawn to scale.
Find the value of t; log3y=2 and log3ty=6
Answer: [tex]10^4[/tex]
Step-by-step explanation:
Assuming we are using the common log (base 10),
[tex]\log 3ty=6\\\\\log 3y +\log t=6\\\\2+\log t =6\\\\\log t=4\\\\t=10^4[/tex]
A design consists of the capital letter E. What kind of symmetry would be shown in the design? Explain.
The kind of symmetry that would be shown in the design is an axial symmetry.
What is an axial symmetry?It should be noted that an axial symmetry simply means a symmetry around an axis.
In this case, the capital letter E has an acid of symmetry. Therefore, an axial symmetry is appropriate.
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The roots of the quadratic function describing the relationship between number of products produced and
overall profit margin are x = 0 and 26. The vertex is (13, -50).
The vertex is a minimum at (13, -50). The company actually loses money on their first few products as it
costs them more to make them, but once they hit 26 items they break even again.
The worst case scenario is that they produce
first root tells us that the profit will be 0 when
Check
items, as they will have a profit of
products are sold.
dollars.
In Economics, profit can be defined as a measure of the amount of money generated when the selling price is deducted from the cost price of a good or service, which is usually provided by producers.
This ultimately implies that, all producers of any product generally work to maximize their profits and make them as large as possible, in order to enable them break even and successful.
Based on the information provided, we can logically deduce that this function has its roots at x = 0 and x = 26 and its vertex is a minimum. Thus, this quadratic function which describes the relationship between the number of products produced and the overall profit margin is an increasing function:
0 < x < 26, f(x) < 0, which implies a negative profit is generated when between 0 and 26 items are produced.x > 26, f(x) > 0, which implies a positive profit is generated when more than 26 items are produced.x is equal to 26 is the break even point.Therefore, once they hit 26 items they break even again. The worst case scenario is that they produce 13 items, as they will have a profit of -50 dollars because the minimum point is at (18, -35). Also, the first root tells us that the profit will be 0 when 0 products are sold.
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please help im failing what is the answer
The general-form equation of the circle is:
A. [tex]x^2 + y^2 - 8x - 8y + 23 = 0[/tex]
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
This circle has center at (4,4), hence:
[tex]x_0 = 4, y_0 = 4[/tex]
The radius is of 3 units(distance of A and B from the center), hence the equation is:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
[tex](x - 4)^2 + (y - 4)^2 = 3^2[/tex]
We expand the equation to find the general form, hence:
[tex]x^2 - 8x + 16 + y^2 - 8y + 16 = 9[/tex]
[tex]x^2 + y^2 - 8x - 8y + 23 = 0[/tex]
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Determine whether AB and CD are parallel, perpendicular, or neither. A(-3, 2), B(5, 1), C(2, 7), D(1, -1)
Answer:
perpendicular
Step-by-step explanation:
We'll find the slope of both lines and see what it tells us.
If the slopes are the same, the lines are parallel. If the slopes are opposite sign and flipped (negative reciprocals) then they are perpendicular.
The slope is y-Y on top of a fraction and x-X on the bottom.
Slope of AB:
m = 2-1 / -3 -5
= 1/-8 = -1/8
Slope of CD:
m = 7- -1 / 2-1
= 8/1 = 8
Since the slopes are -1/8 and 8, the lines are perpendicular, because they are opposite sign and flipped (negative reciprocals)
One month Kevin rented 2 movies and 5 video games for a total of $30. The next month he rented 8 movies and 3 video games for a total of $35. Find the rental cost for each movie and each video game. Rental cost for each movie: s Rental cost for each video game
Answer:
M = $2.5; V = $5
Step-by-step explanation:
We need to set up a system of equations to find the price for both movies (M) and video games (V).
We can use 2M + 5V = 30 and 8M + 3V = 35
We can use elimination:
[tex]-4(2m+5v=30)\\8m+3v=35\\\\-8m - 20v = -120\\8m+3v=35\\-17v=-85\\v=5\\\\2m+5(5)=30\\2m+25=30\\2m=5\\m=5/2 ;m=2.5[/tex]
8 cm
Find h.
9 cm
h = √[?] cn
Answer:
[tex]\sqrt{65}[/tex], so [?] = [65]
Step-by-step explanation:
This is a classic Pythagorean Theorem problem :)
We are given a right triangle with 2 sides, so all we have to do is plug it into the formula a² + b² = c², or in simple terms: the square of one side plus the square of the other equals the square of the hypotenuse.
line h is going to bisect the diameter of the circle (8) so one side will be 4. We're given 9 as our hypotenuse, so:
(4)² + (h)² = (9)².
16 + h² = 81
h² = 81 - 16, h² = 65, h = [tex]\sqrt{65}[/tex].
For what values of x is the expression below defined?
√x+3 ➗√1-x
A. 3≤x≤1
B. 3>x>1
C. -3
D. 3> x≤-1
Answer: [tex]-3 \leq x < 1[/tex]
Step-by-step explanation:
[tex]\sqrt{x+3} \geq 0 \longrightarrow x \geq -3\\\\\sqrt{1-x} > 0 \longrightarrow 1-x > 0 \longrightarrow x < 1\\\\\therefore -3 \leq x < 1[/tex]
A ______ function is a specific type of function that represents the relationship between two variables, usually x and y. The graph of this function is a line.
the answer choices are
dependent
independent
parallel
slope
perpendicular
rate
scale
y
change
linear
What is the completely factored form of f(x) = x3 – 2x2 – 5x + 6?
f(x) = (x + 2)(x – 3)(x + 6)
f(x) = (x + 2)(x – 3)(x – 6)
f(x) = (x – 2)(x + 3)(x – 1)
f(x) = (x + 2)(x – 3)(x – 1)
Answer:
The last option, (x+2)(x-3)(x-1)
Step-by-step explanation:
The completely factored form of f (x) = x³ - 2x² - 5x + 6 is,
⇒ f (x) = (x - 1) (x - 2) (x - 3)
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
Function is,
⇒ f (x) = x³ - 2x² - 5x + 6
Now, We can factor the function as;
Since, 1 is a root of function as it satisfy the function.
So, One factor is,
⇒ (x - 1)
Find another roots as;
(x - 1) ) x³ - 2x² - 5x + 6 ( x² - x - 6
x³ - x²
----------
- x² - 5x
- x² + x
-------------
- 6x + 6
- 6x + 6
------------
0
Hence,
⇒ f (x) = x³ - 2x² - 5x + 6
⇒ f (x) = (x - 1) ( x² - x - 6 )
⇒ f (x) = (x - 1) ( x² - 3x - 2x - 6)
⇒ f (x) = (x - 1) ( x (x - 3) - 2 (x - 3))
⇒ f (x) = (x - 1) (x - 2) (x - 3)
Hence, The completely factored form of f (x) = x³ - 2x² - 5x + 6 is,
⇒ f (x) = (x - 1) (x - 2) (x - 3)
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9
What is the price of a two year bond with a 9% annual coupon and a yield to maturity of 8%?
97.51
102.53
101.78
105.25
The price of a two-year bond is 101.78 and the correct option is C.
Given that a 9% annual coupon and a yield to maturity of 8%.
Simple yield is the amount of interest received by a bond issuer divided by the current market price of the associated bond.
Implicit Face value, FV=$100
Time, N=2 years
Coupon, C=(9/100)×$100=9
The yield of maturity, r=8%=0.08
Now, we will find the bond price using the formula
Price of bond = C× [1-{1/ (1+r)ⁿ}/r] +M/ (1+r)ⁿ
Substitute the values in this formula, we get
Price of bond=9×[1-{1/(1+0.08)²}/0.08]+100/(1+0.08)²
Price of bond=9×[1-{1/(1.08)²}/0.08]+100/(1.08)²
Price of bond=9×[1-{1/1.1664}/0.08]+100/1.1664
Price of bond=9×[(1-0.857)/0.08]+85.73
Price of bond=9×[0.143/0.08]+85.73
Price of bond=9×1.7875+85.73
Price of bond=16.0875+85.73
Price of bond=101.78
Hence, the price of a two-year bond with a 9% annual coupon and a yield to maturity of 8% is 101.78.
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what is the inverse of the function f(x)=x/5-2
Answer:
[tex]\huge\boxed{\sf f^{-1}(x)=5x+10}[/tex]
Step-by-step explanation:
Given function:[tex]\displaystyle f(x)=\frac{x}{5} -2[/tex]
Put f(x) = y
[tex]\displaystyle y=\frac{x}{5} -2[/tex]
Swap x and y
[tex]\displaystyle x = \frac{y}{5} -2[/tex]
Now, solve for y
[tex]\displaystyle x = \frac{y}{5} -2[/tex]
Add 2 to both sides
[tex]\displaystyle x + 2 =\frac{y}{5}[/tex]
Multiply 5 to both sides
[tex]5(x+2)=y[/tex]
Distribute
[tex]5x + 10 =y[/tex]
Put y = f⁻¹(x)
[tex]\boxed{f^{-1}(x)=5x+10}[/tex]
[tex]\rule[225]{225}{2}[/tex]
The graph of f(x) = x3 + x2 – 9x – 9 is shown.
Based on the graph, what are the solutions of x3 + x2 – 9x – 9 = 0?
x = –1, 3
x = –3, –1
x = –3, –1, 3
x = –9, –3, –1, 3
Answer:
the third option, x = –3, –1, 3
Step-by-step explanation:
Please help ASAP!
What is the measure of arcXY shown in the diagram below?
Applying the angles of intersecting secants theorem, the measure of arc XY is: 32°.
How to Apply the Angles of Intersecting Secants Theorem?According to the angles of intersecting secants theorem, m∠XZY = 1/2(arc VW - arc XY).
Plug in the values:
39 = 1/2(110 - arc XY)
2(39) = 110 - arc XY
78 = 110 - arc XY
78 - 110 = - arc XY
-32 = - arc XY
Arc XY = 32°
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A rental car company charges $20 per day to rent a car and $0.10 for every mile driven. Addison wants to rent a car, knowing that:
She plans to drive 100 miles.
She has at most $80 to spend.
Considering the definition of an inequality, the inequality that can be used to determine x is 20x + 10≤ 80
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values called unknowns, in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
This caseA rental car company charges $20 per day to rent a car and $0.10 for every mile driven.
Addison wants to rent a car, knowing that:
She plans to drive 100 miles.She has at most $80 to spend.On the other hand, x represents the maximum number of days Alyssa can afford to rent for while staying within her budget.
Then, the inequality that can be used to determine x is:
20x + 0.1×100≤ 80
So:
20x + 10≤ 80
In summary, the inequality that can be used to determine x is 20x + 10≤ 80
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Which of the following rational functions is graphed below?
Answer:
D
Step-by-step explanation:
As the function approaches a certain x-value, it makes a very sharp turn and doesn't touch the axis as you can see in the graph. It does that because if the x-value is applied to the function, it would make it undefined. In this case, the graph is approaching x = -3 and x = +7 since at those points, the lines for the graph change suddenly. You would look for a function that if x is -3 or 7, it makes the y-value undefined.
Another way to easily do this would be to substitute values that are in front of the value that the graph is avoiding like 6 or 8 for 7 and -2 and -4 for -3. You can see if the y-values that would output from substituting those numbers are correct.
25 POINTS, QUICKLY PLEASE!
1. Which system is represented in the graph?
A. y > x2 + 4x – 5, y > x + 5
B. y < x2 + 4x – 5, y < x + 5
C. y ≥ x2 + 4x – 5, y ≤ x + 5
D. y > x2 + 4x – 5, y < x + 5
2. Which type of function describes f(x)?
A. Exponential
B. Logarithmic
C. Rational
D. Polynomial
Answer:
1) y > x² + 4x - 5, y > x + 5
2) Rational
Step-by-step explanation:
For a parabola, if the shade is inside the curve then the value of y will be greater or equal to:
For a line, if the shade is above it then the value of y will be greater or equal to:
Therefore, since parabola doesn't have solid curve (--- graph) then the inequality is ">"
Therefore, the inequality for parabola is y > x² + 4x - 5
For a line, it does not have solid graph so the inequality is ">"
Therefore, the inequality for line is y > x + 5
-----------
The graph of function describes the shape of rational function. It cannot be exponential as exponential only has one curve. It cannot be logarithm for same reason as exponential. It cannot be polynomial as polynomial is continuous function but the graph is discontinuous at specific point x = 0.
That being said, all choices except rational are all continuous function by default but rational function isn't and since the graph is discontinuous then we can say that it's rational function.
how do you find the area and perimeter
area is multiplication
perimiter is adding the numbers on each side, for example, if the right side is 7, the left side will be 7. Add them and it will givey ou 14
Multiply.
x²+3x+2
x 2x²+3x-1
OA. 2x¹ +9x² + 12x² + 3x-2
OB. 2x¹ +9x2 - 2
OC. 3x2 + 6x +1
OD. 2x¹ +21x² + 3x-2
The multiplication of the expression (x² + 3x + 2) (2x² + 3x + 1) is 2x⁴ + 9x³ + 14x² + 9x + 2
Multiplication(x² + 3x + 2) (2x² + 3x + 1)
= 2x⁴ + 3x³ + x² + 6x³ + 9x² + 3x + 4x² + 6x + 2
collect like terms= 2x⁴ + 3x³ + 6x³ + x² + 9x² + 4x² + 3x + 6x + 2
= 2x⁴ + 9x³ + 14x² + 9x + 2
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What is lcm of 3,6,9
Answer:
lcm of 3,6,9 is 18
A cash deposit box has five-dollar and ten-dollar bills in it totaling $450. There are eight times as many five-dollar bills as ten-dollar bills. How many bills are in the box?
Answer:
81
Step-by-step explanation:
What is the classification of each system?
Answer:
inconsistentconsistent independentconsistent dependentStep-by-step explanation:
Consistent Independent = exactly ONE solution
Consistent Dependent = INFINITELY many solutions
Inconsistent = NO solution
The equation of line / is y=3x/a +5, where a is a positive constant. If the value of a in this equation is doubled, then the resulting equation will represent a line whose slope is how many times the slope of line / ?
The resulting equation will represent a line whose slope is 1/2 times the slope of the line
How to determine the slope of the new line?The equation of the line is given as:
y = 3x/a + 5
The constant a is a positive constant.
So, when the value of a in the equation is doubled, we have:
y = 3x/2a + 5
A linear equation is represented as
y = mx + b
Where m represents the slope.
So, we have:
m1 = 3/a
m2 = 3/2a
Substitute m1 = 3/a in m2 = 3/2a
m2 = 1/2 * m1
Hence, the resulting equation will represent a line whose slope is 1/2 times the slope of the line
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) Explain why the expression x2 + (p + q )x + pq leads to the need to determine integers that add to b and have a product c when factoring a trinomial of the form x2 + bx + c.
The reason why the expression x² + (p + q)x + pq leads to the need to determine integers that add to b and have a product c is because they follow the FOIL Technique
How to factorize Quadratic Equations?We want to explain why x² + (p + q)x + pq leads to the need to determine integers that add to b and have a product c.
Now, using the FOIL Technique we can say that the factors are;
(x + p)(x + q)
Expanding this gives;
x² + px + qx + pq
⇒ x² + (p + q)x + pq
Now, applying that to the trinomial; x² + 6x + 8, we can say that;
p + q = 6, and pq = 8
Thus, solving simultaneously gives;
p = 2 and q = 6.
Thus;
x² + 6x + 8 = (x + 2)(x + 6)
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What are the values of a₁ and r of the geometric series?
2-2+2-2+2
O
a₁ = 2 and r=-2
O a₁ = -2 and r = 2
O
a₁ = -1 and r = 2
a₁ = 2 and r=-1
Answer:
Step-by-step explanation:
Therefore, the values of
a
1
and r are 2 and -1, respectively.
The values of a₁ and r of the geometric series are 2 and -1 respectively.
What is Geometric Sequence?Any term divided by the preceding term is a constant in a geometric series. The common ratio of the sequence is the name given to this constant. Any term in the sequence can be divided by the prior term to determine the common ratio.
We have the series 2, -2, 2, -2, ......
Here, The first term is 2.
and, the Common Ratio = -2 / 2
= 2/(-2)
= -1
So, the first term is 2 and r is -1.
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will give brainliest!!
Answer:
[tex]\huge\boxed{\sf n = 49}[/tex]
Step-by-step explanation:
Given expression:[tex]x^2-14x+n[/tex] ---------------(1)
We need to solve it using the following formula:
[tex]a^2-2ab+b^2=(a-b)^2[/tex]
Writing the middle term in the expression as 2ab
[tex](x)^2-2(x)(7)+n[/tex]
Form the expression, we come to now that
b = 7So, the we can write the expression as:
[tex](x)^2-2(x)(7)+(7)^2\\\\x^2-14n+49[/tex]
Comparing expression (1) with the above expression, we get:
n = 49[tex]\rule[225]{225}{2}[/tex]
60 POINTS IF CORRECT AND BRAINLIEST ANSWER FOR COMPLETE ANSWER
1. The solution to the first percent puzzle is as follows:
75% 66²/₃ 11¹/₉
33¹/₃% 25% 22¹/₅% 3⁷/₁₀%
50% 37¹/₂% 33¹/₃% 5¹/₂%
50% 37¹/₂% 33¹/₃% 5¹/₂%
2. The solution to the second percent puzzle is as follows:
10% 90%
50% 5% 45%
50% 5% 45%
What is a percent puzzle?A percent puzzle is a puzzle that engages students to practice working with percentages.
The percent puzzle involves a matrix format, in which students multiply the column percent by the row percent to find the percent they must put in the missing boxes to complete the puzzle.
The multiplication results for the missing boxes can be either stated in decimals, fractions, or a combination.
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The difference of four times a number and seven is 21
Answer: 4n - 7 = 21, n = 7
Step-by-step explanation:
A difference indicates subtraction of two terms. Four times a number indicates that a number of any value has to be multiplied by 4.
Hence, the equation that is represented by the question is
[tex]4x - 7 = 21[/tex]
We can also solve this equation (i.e., find the value of x that makes this equation true).
Adding 7 to both sides, we get
[tex]4x - 7 + 7 = 21 + 7[/tex]
Since the -7 and 7 add to 0, the equation becomes
[tex]4x = 28[/tex]
To get x by itself, we can divide both sides by 4, making the equation
[tex]x=7[/tex]
Hence, x must be 7 to make the equation true, or 7 is a solution to the equation.
the sum of a number increased by three and the number decreased by seven
Answer is (n + 3) + (n - 7)
Simplified to 2n - 4
Using “n” for number