Equation for a rational function is 10(x2 + 7x + 12) / (x2 + 11x + 30) = 0.
What is Rational Function?
Any function that can be expressed mathematically as a rational fraction—an algebraic fraction in which both the numerator and the denominator are polynomials—is referred to as a rational function. The polynomials' coefficients don't have to be rational numbers; they can be found in any field K.
So this will be a rational function with the vertical asymptotes given by the denominators:
(x + 5) and (x + 6).
The x-intercepts will be provided by the numerator,
which will be:
a(x + 3)(x + 4)
The letter an is a constant.
Given that (0,4) is the y intercept, we have:
4 = a(0+3)(0+4) / (0+5)(0+6)
4= 12a / 30
12a = 120
now,
a = 120/12,
a = 10,
and a = 1.
Now,
a(x+3)(x+4) / (x+5)(x+6) = 0
10 (x^2 + 7x + 12) / (x^2 + 11x + 30) = 0
Hence, We have the following equation for a rational function:
10 (x2 + 7x + 12) / (x2 + 11x + 30) = 0.
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When you purchase a T.V., the size refers to the diagonal measurement of the screen. If
the 46 inch TV has a square screen, what is the approximate length and width? Round
your answer to the nearest tenth.
TV Dimensions (Diagonal) Screen Width
46 inch TV 40.1 inches + Bezel
A TV's screen size is determined by measuring the panel diagonally from one corner to the other. The TV's bezels and other exterior surfaces are not included in this. There are numerous models in a certain size group.
What does diagonal screen size mean?A screen's size is often determined by the diagonal, or the distance between its opposite corners, which is typically measured in inches. To distinguish it from the "logical image size," which characterizes a screen's display resolution and is measured in pixels, it is also often referred to as the physical image size.
Start at the top-left corner and measure diagonally down to the bottom-right corner using a measuring tape. Do not include the bezel (the plastic, metal, or glass edge), if any, when measuring the screen alone.
because the units are too large to be offered by furlongs and fathoms. Since the United States does not use the metric system, while television was being invented, American engineers used the units they were most accustomed to.
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What is the value of 3-(-2) how can I solve this questions
Explanation:
[tex]\text{Given: }3-\mleft(-2\mright)[/tex]To find the value od 3-(-2), we will multiply the sign at the outer with the inner
[tex]undefined[/tex]I apologize about the quality the shaded region is the trapezoid part not the square in the middle
First, find the area of the trapezoid.
Area of a trapezoid = 0.5 ( sum of bases ) x height
bases = 15in, 8in
height = 8in
A 1 = 0.5 (15 + 8 ) x 8 = 92 in 2
Then, subtract the area of the rectangle:
Area of a rectangle = lenght x width
L = 5
W= 3
A2 = 5 x 3 = 15 in 2
Area of the shaded region = A1 - A2 = 92 - 15 = 77 in2
HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST
The rational number - 91 / 200 is a number between the decimal numbers - 0.45 and - 0.46.
How to determine a rational number between two decimal numbers
In this problem we find two decimal numbers, of which we need to find a rational number between these numbers. Please notice that the decimal numbers are also rational numbers. First, we transform each decimal number into rational numbers:
- 0.45 = - 45 / 100
- 0.46 = - 46 / 100
Second, find a possible rational number between the two ends by the midpoint formula:
x = (1 / 2) · (- 45 / 100) + (1 / 2) · (- 46 / 100)
x = - 45 / 200 - 46 / 200
x = - 91 / 200
Then, the rational number - 91 / 200 is a number between - 0.45 and - 0.46.
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The mayor of a town proposes to fence off a triangular area of a building that includes two sides of the building as shown below.Which distance, in feet could be the length of the proposed fence line?100280220130
Solution
Using triangle inequality
The triangle inequality states that the sum of the lengths of any two sides of a triangle is greater than the length of the remaining side.
The fence line is the longest size
100, 130 can't be the answer
[tex]200+70=270[/tex]280 can't be the answer be ause the triangle inequality says it should be less than the sum
[tex]Z<\text{ X +Y}[/tex]Therefore, the correct answer is 220
3
Drag each tile to the correct box.
Place the parallelograms in order from least area to greatest area.
3 cm
4 cm
6 cm
3 cm
4 cm
5 cm
4 cm
3 cm
----
4 cm
Submit Test
}
The least area of the parallelogram will be 12cm² and the greatest area will be 20cm².
What will be the area of the parallelogram?The area of a parallelogram is simply calculated thus:
= Base × Height
The least area will be:
= Base × Heights
= 3cm × 4cm
= 12cm²
The greatest area of the parallelogram will be:
= Base × Height
= 4cm × 5cm
= 20cm²
Note that the figures are gotten from the. information given.
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The question is in the picture, couldn’t fit the last graph so sent it in a separate picture
Explanation:
Concept:
To figure out if a graph is a function, we will use the vertical line test below
The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.
From the first graph we can see that the vertical line cuts the points at on intersection
The Second graph is given below as
Its has two intersections on both sides of the graph
The third graph is given below as
It has two intersections on the ride hand side of the graph
The Fourth graph ios given below as
Its has two intersection on the right hand side of the graph
In conclusion,
A graph is said to be a function if one value of x has a separate value of y
Therefore,
The final answer is
The FIRST OPTION is the correct answer
In the diagram below of triangle DEF, G is a midpoint of DE and H is a midpoint of EF. IfGH = 50 -- 87, and DF = 9x + 0, what is the measure of GH? E H D F
GH = 18
Explanations:From the diagram:
DF = 9x + 0
GH = 50 - 8x
Since G is a midpoint of DE and H is a midpoint of EF, using the midpoint theorem:
DF = 2GH
9x + 0 = 2 (50 - 8x)
9x = 100 - 16x
9x + 16x = 100
25x = 100
x = 100/25
x = 4
Substituting the value of x into GH = 50 - 8x
GH = 50 - 8(4)
GH = 50 - 32
GH = 18
A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 12.5 ft by 13.5 ft by 13 ft. The container is entirely full. If, on average, its contents weigh 0.18 pounds per cubic foot, and, on average, the contents are worth $7.18 per pound, find the value of the container’s contents. Round your answer to the nearest cent.
The volume of a right rectangular prism is given by
[tex]V=\text{height}\times length\times width[/tex]From the given information, we know that
[tex]\begin{gathered} \text{ height=13.5 ft} \\ \text{ length=13 ft} \\ \text{width = 12.5 ft} \end{gathered}[/tex]So, the volume is given by
[tex]V=13.5\times13\times12.5ft^3[/tex]which gives
[tex]V=2193.75ft^3[/tex]Now, since the content weigh 0.18 pound per cubic foot and worth $7.18 per pound, the value of the container is given by,
[tex]\text{ Value=}2193.75\times0.18\times7.18[/tex]Therefore, by rounding to the nearest cent, the answer is:
[tex]\text{Value}=\text{ \$2835.20}[/tex]Which of the following is a perfect cube?118481
From the options given we will have that a perfect cube is:
[tex]1^3=1\ast1\ast1=1[/tex]So, 1 is the perfect cube.
I need to know The answer to this word problem
Given:
The little cheese 8 in $ 7.
The big cheese 10 in $ 9.
The cheese monster 12 in $ 12.
Required:
To find the ratio of little cheese, big cheese and cheese monster.
Explanation:
(1)
The crust to prize ratio for little cheese is,
[tex]\begin{gathered} 8:7=1:? \\ \\ =\frac{7}{8} \\ \\ =0.875 \end{gathered}[/tex](2)
The crust to prize ratio for big cheese is,
[tex]\begin{gathered} 10:9=1:? \\ \\ =\frac{9}{10} \\ \\ =0.9 \end{gathered}[/tex](3)
The crust to prize ratio for cheese monster cheese is,
[tex]\begin{gathered} 12:12=1:? \\ \\ =\frac{12}{12} \\ \\ =1 \end{gathered}[/tex](4)
The cheese monster is the best pizza for him.
Final Answer:
The crust to prize ratio for little cheese is = 0.875
The crust to prize ratio for big cheese is = 0.9
The crust to prize ratio for cheese monster cheese is = 1
The cheese monster is the best pizza for him.
Solve the equation-3 + a = 13a = ???
ANSWER
a = 16
EXPLANATION
To solve for a we have to add 3 on both sides of the equation:
[tex]\begin{gathered} -3+3+a=13+3 \\ a=16 \end{gathered}[/tex]Victoria, Cooper, and Diego are reading the same book for theirlanguage arts class. The table shows the fraction of the bookeach student has read. Which student has read the leastamount? Explain your reasoning.
Given:
Completion of reading in fractions:
[tex]\text{Victoria}=\frac{2}{5};\text{Cooper}=\frac{1}{5};\text{Diego}=\frac{3}{5}[/tex]Since the denominators,
[tex]\text{The least value of the three given values is }\frac{1}{5}[/tex]Therefore, Cooper has read the least amount.
If y varies directly with x and y = 48 when x = -4, write the equation that represents this direct variation relationship12 345
Answer
The equation that represents the direct variation relationship between y and x is
y = -12x
Explanation
We are told that y varies directly with x.
y = 48 when x = -4.
We are then told to write the equation that represents this direct variation relationship.
In mathematical terms, y varies directly with x is written as
y ∝ x
If we introduce a constant of variation, k, we can then write this relationship as
y = kx
To now fully write this relationship, we need to solve for k.
y = 48 when x = -4.
y = kx
48 = k × -4
48 = -4k
-4k = 48
Divide both sides by -4
(-4k/-4) = (48/-4)
k = -12
We can then put in the value of k obtained
y = kx
y = -12x
The equation given is
3y = 10x
Recall that variation is represented as
y ∝ x
And written as
y = kx
So, we can convert 3y = 10x into this form and establish the direct variation and obtain the value of k.
3y = 10x
Divide both sides by 3
(3y/3) = (10x/3)
y = (10x/3)
which is similar to y = kx
k = (10/3)
So, option A is correct.
Hope this Helps!!!
How would you use the Pythagorean Theorem to find the missing length in the triangle shown? Find the missing length.
The given triangle is a right angle triangle. The pythagorean theorem is expressed as
hypotenuse^2 = one leg^2 + other leg^2
From the diagram,
hypotenuse = AB = c
one leg = BC = 9
other leg = AC = 12
By applying the pythagorean theorem, we have
[tex]\begin{gathered} c^2=9^2+12^2\text{ = 81 + 144} \\ c^2\text{ = 225} \\ c\text{ = }\sqrt[]{225} \\ c\text{ = 15} \end{gathered}[/tex]The missing length is 15 cm
Devonte is growing a rose. Today the rose is 5 cm high. The rose grow$ 1.5 cm per day. Write a linear equation that represents the helght of the rose (y) after (2) days. How tall will the rose be after 20 days?
The equation of a line in slope-intercept form, is:
[tex]y=mx+b[/tex]Where m represents the slope of the line (rate of change), and b represents the y-intercept of the line (initial value).
Since the rose grows 1.5 cm per day, then the rate of change is 1.5:
[tex]m=1.5[/tex]Since today the rose is 5cm high, then the initial value is 5:
[tex]b=5[/tex]Then, the height of the rose after x days is:
[tex]y=1.5x+5[/tex]To find the height of the rose after 20 days, substitute x=20:
[tex]\begin{gathered} y=1.5(20)+5 \\ =30+5 \\ =35 \end{gathered}[/tex]Then, the height of the rose after 20 days is 35 cm.
the cash register do ducks $250 from a $25 Coffee Cafe gift card for every medium coffee with a customer buys an equation is written to calculate the total amount on the gift card what is the meaning of the Y intercept in the equation
The equation can be represented by
y= 25 - 2.5x
by comaprison with y = mx + c
c = 25 ( note tha c means y-intercept)
This 25 represents the initial value of the gift card
The correct answer is option d
Consider the following sets
U = {1,2,3,4,5,6,7,8,9,10,11,12,13}
A= {1,2,3,4,7}
B = {3,4,5,6}
Find the set (A U B)’
The elements in the set (A u B)' are is {8,9,10,11,12,13}
How to determine the value of the set?The definitions of the sets and the elements are given as
Universal Set, U = {1,2,3,4,5,6,7,8,9,10,11,12,13}Set A= {1,2,3,4,7}Set B = {3,4,5,6}The set to calculate is represented by the notation
(A u B)'
Start by calculating the set A u B
This means that we combine the sets A an B without repetition
So, we have
A u B = {1, 2, 3, 4, 5, 6, 7}
Next, we calculate (A u B)'
This represents the sets in U that are not in A u B
So we have
(A u B)' = {8,9,10,11,12,13}
Hence, the value of the set is {8,9,10,11,12,13}
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Use the remainder theorem to find P(-2) for P(x) = x³ + 3x² +9,Specifically, give the quotient and the remainder for the associated division and the value of P(-2).QuotientRemainder =P(-2)=
Answer:
Quotient:
[tex]x^2+x-2[/tex]Remainder:
[tex]13[/tex]P(-2):
[tex]13[/tex]Step-by-step explanation:
Remember that the remainder theorem states that the remainder when a polynomial p(x) is divided by (x - a) is p(a).
To calculate the quotient, we'll do the synthetic division as following:
Step one:
Write down the first coefficient without changes
Step two:
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
Step 3:
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
Step 4:
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
Now, we will have completed the division and have obtained the following resulting coefficients:
[tex]1,1,-2,13[/tex]Thus, we can conlcude that the quotient is:
[tex]x^2+x-2[/tex]And the remainder is 13, which is indeed P(-2)
Give the first four terms of the geometric sequence for which A1 = -7 and r = -4.07 7 7 74, 16, 64, 256 -7,28, -112, 448 -7, -11, -15, -1928. -112, 448. - 1792
Given:
[tex]\begin{gathered} firstterm(a_1\text{) = -7} \\ \text{common ratio (r) = -4} \end{gathered}[/tex]Required: First four terms
The nth term of a geometric sequence :
[tex]a_{n\text{ }}=a_1\text{ }\times r^{n-1}[/tex]Hence, we can obtain the next four terms by substituting
[tex]\begin{gathered} \text{when n = 1, a}_1\text{ = -7} \\ n=2,a_2\text{ =-7 }\times(-4)^{2\text{ - 1}} \\ a_2\text{ = -7 }\times\text{ -4} \\ =\text{ 28} \\ \\ \text{when n =3, a}_3\text{ = -7 }\times(-4)^{3\text{ -1 }} \\ a_3\text{ = -7 }\times\text{ 16} \\ =\text{ -112} \\ \\ \text{when n = 4, a}_4\text{ = }-7\text{ }\times(-4)^{4-1} \\ a_4\text{ = -7 }\times\text{ -64} \\ =\text{ 448} \end{gathered}[/tex]Mr. Alvarez is laying square paver blocks in sections in rows that look like steps.Section 1 has 3 rows that look like steps, the section is 6 blocks wide, and the bottom step is 8 blocks long. Section 2 has 4 rows that look like steps, the Section is 8 blocks wide, and the bottom step is 10 blocks long. Each Section after that is 2 blocks wider and 2 blocks longer.Drag the numbers to complete the table. Numbers may be used once, more than once, or not at all.
12
14
36 blocks
56 blocks
108 blocks
Explanation:The length of section 1 = 8
The length increases by 2 uits as the section increases
Section 2 length of block = length of section 1 + 2 =
= 8 + 2
length of block = 10
Section 3 length of block = length of section 2 + 2
= 10 + 2
length of block = 12
Section 4 length of block = length of section 3 + 2
= 12 + 2
length of section = 14
Number of blocks needed:
if the blocks are counted,
For section 1 there are 6 rows . So we count the total number of blocks on each of them
= 4 + 4 + 6 + 6 + 8 + 8
Section 1 = 36 blocks
For section 2, we count the number of blocks on each row
= 4 + 4 + 6 + 6 + 8 + 8 + 10 + 10
section 2 = 56 blocks
For sectoion 3: The length and width increases by 2 respectively
previous length + 2 = 10 + 2 = 12
Due to the increase we would have two length of 12
= 4 + 4 + 6 + 6 + 8 + 8 + 10 + 10 + 12 + 12 = 80
Already given = 80
For section 4: The length and width increases by 2 respectively
previous length + 2 = 12 + 2 = 14
The increase causes an addition of two length of 14 blocks
Total blocks = 4 + 4 + 6 + 6 + 8 + 8 + 10 + 10 + 12 + 12 + 14 + 14
Total blocks for Section 4 = 108
help meeeeeeeeeeee pleaseee
The solution of the composite function is as follows:
(f + g)(x) = 9x + 1(f - g)(x) = -7x - 17 (f. g)(x) = 8x² - 55x - 72(f / g)(x) = x - 8 / 8x + 9How to solve composite function?Composite functions are when the output of one function is used as the input of another.
In other words, a composite function is generally a function that is written inside another function.
Therefore, the composite function can be solved as follows:
Therefore,
f(x) = x - 8
g(x) = 8x + 9
Hence,
(f + g)(x) = f(x) + g(x) = x - 8 + 8x + 9 = 9x + 1
(f - g)(x) = f(x) - g(x) = x - 8 - ( 8x + 9 ) = x - 8 - 8x - 9 = -7x - 17
(f. g)(x) = f(x) . g(x) = (x - 8)(8x + 9) = 8x² + 9x - 64x - 72 = 8x² - 55x - 72
(f / g)(x) = f(x) / g(x) = x - 8 / 8x + 9
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Soue se compound inequality and give your answer in intentel notation- 10 AND-80-72-1
S= (-4, 1 ]
1) Solving that compounded inequality
4x +6 > -10 and -8x+7 ≥ -1
2) Let's start by 4x +6 > -10
4x +6 > -10 Subtracting 6 from both sides
4x > -10-6
4x > -16 Dividing both sides by 4
x > -4
And with -8x+7 ≥ -1
-8x+7 ≥ -1 Subtract 7 from both sides
-8x ≥ -1 -7
-8x ≥ -8 Multiply by -1
8x ≤ 8
x ≤ 1
3) Graphing the solution interval:
So the solution is the interval S= (-4, 1 ] not including x= -4 and including the value x = 1
Solving a present makes your problem using a system of linear equations
Answer:
Explanation:
Find the value of x in the triangle shown below.42
Since we are dealing with a right triangle, we can use the Pythagorean theorem, shown below
[tex]H^2=L^2_1+L^2_2[/tex]In our case, H=4, L_1=2, L_2=x; then,
[tex]4^2=2^2+x^2[/tex]Solving for x,
[tex]\begin{gathered} \Rightarrow x^2=16-4 \\ \Rightarrow x^2=12 \\ \Rightarrow x=\sqrt[]{12}=\sqrt[]{4\cdot3} \\ \Rightarrow x=2\sqrt[]{3} \end{gathered}[/tex]The answer is x=2sqrt(3)
What transformation would cause the change from ABC to A'B'C'?
Answer:
D. 1/4
Explanation:
When the coordinates of A, B, and C are multiplying by 1/4 we get A', B', and C'.
For example,
[tex]\frac{1}{4}\times A(-8,4)=A^{}(-\frac{8}{4},\frac{4}{4})[/tex][tex]\therefore A(-8,4)\rightarrow A^{\prime}(-2,1)[/tex]The same goes for B and C.
Hence, the transformation that gives us A'B'C' from ABC is Choice D DIlation using k = 1/4.
You buy a new commercial stove for $9,000 and estimate that it will enable you to deliver 20 additional meals per night at an average price of $20. Assuming 25% food cost and no additional costs to using the new stove, how long will it take the stove to pay for itself?
Assuming 25 % food cost and no additional costs to using the new stove, The time it will take the stove to pay for itself is 30 days.
Determining the number of daysProfits per meal = $20 - ( 0.25 x20)
Profits per meal = $20 -$5
Profits per meal = $15
Profits for 20 meals = $15 x 20
Profits for 20 meals =$300
Now let determine the number of days
Number of days =$9000 / $300 days
Number of days =30 days
Therefore we can conclude that 30 days is the days that it will take.
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Pic attached of problem. Answer must be with proper number of significant figures
Answer:
1310 cubic feet per minute
Explanation:
Let x represent the value in cubic feet per minute
Note that;
1 cubic meter per second = 2118.87997 cubic feet per minute
Given 0.618 cubic meter per second, to be able to solve for x, we'll go ahead and set the proportions as seen below;
[tex]\frac{1\text{ cubic meter per second}}{0.618\text{ cubic meter per second}}=\frac{2118.87997\text{ cubic f}eet\text{ per minute}}{x\text{ cubic f}eet\text{ per minute}}[/tex]Let's go ahead and cross-multiply;
[tex]\begin{gathered} x=2118.87997\times0.618 \\ x=1309.46782146cfm \\ x=1310\text{cfm (to 3 significant figures)} \end{gathered}[/tex]4. Sales tax in a certain state is 5%. If the sales tax on a new boat was $400, what was the selling price of the boat?
Sales tax percentage = 5% = 5/100 = 0.05 (decimal form)
Sales tax amount = $400
Multiply the selling price of the boat (x) by the sales tax percentage in decimal form. That expression must be equal to 400.
0.05x = 400
Solve for x:
x = 400/ 0.05
x= $8,000
Hi how do I graph these? I don't understand how I'm supposed to graph fractions?
To plot in the plane points with fraction number coordinates (x or y) you can rewrite the fractions as decimal numbers:
[tex]\begin{gathered} \frac{-5}{2} \\ \\ -5\text{ divided into 2} \\ \\ -\frac{5}{2}=-2.5 \\ \\ \\ \\ \\ \frac{-1}{4} \\ \\ -1\text{ divided into 4:} \\ -\frac{1}{4}=-0.25 \end{gathered}[/tex]Then, you have the next coordinates;
(- 2.5, 2) and (1, -0.25)
And the next graph:
Use a line to link the points
