Rationalize the denominator and simplify the expression below. Show all steps and calculations to earn full credit. You may want to do this work by hand and upload an image of that written work rather than try to type it all out. \frac{8}{1- \sqrt[]{17} }
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The Solution:
The given expression is
[tex]\frac{8}{1-\sqrt[]{17}}[/tex]Rationalizing the expression with the conjugate of the denominator, we have
[tex]\frac{8}{1-\sqrt[]{17}}\times\frac{1+\sqrt[]{17}}{1+\sqrt[]{17}}[/tex]This becomes
[tex]\frac{8(1+\sqrt[]{17})}{1^2-\sqrt[]{17^2}}[/tex][tex]\frac{8+8\sqrt[]{17}}{1-17}=\frac{8(1+\sqrt[]{17})}{-16}=-\frac{1+\sqrt[]{17}}{2}[/tex]Thus, the correct answer is
[tex]-\frac{1+\sqrt[]{17}}{2}[/tex]Related Questions
The length of a rectangle is 9 inches more than the width. The perimeter is 34 inches. Find the length I need both length and the width of the rectangle
Answers
The perimeter is the sum of the side lengths of a polygon. Now, let it be:
• l,: the length of the rectangle
,• w,: the width of the rectangle
Considering the information given and the previous definition, we can write and solve the following system of equations.
[tex]\begin{cases}l=9+w\Rightarrow\text{ Equation 1} \\ l+w+l+w=34\Rightarrow\text{ Equation 2}\end{cases}[/tex]We can use the substitution method to solve the system of equations.
Step 1: We combine like terms in Equation 2.
[tex]\begin{cases}l=9+w\Rightarrow\text{ Equation 1} \\ 2l+2w=34\Rightarrow\text{ Equation 2}\end{cases}[/tex]Step 2: We substitute the value of l from Equation 1 into Equation 2.
[tex]\begin{gathered} 2l+2w=34 \\ 2(9+w)+2w=34 \end{gathered}[/tex]Step 3: We solve for w the resulting equation.
[tex]\begin{gathered} \text{ Apply the distributive property on the left side} \\ 2\cdot9+2\cdot w+2w=34 \\ 18+2w+2w=34 \\ \text{ Add similar terms} \\ 18+4w=34 \\ \text{ Subtract 18 from both sides} \\ 18+4w-18=34-18 \\ 4w=16 \\ \text{ Divide by 4 from both sides} \\ \frac{4w}{4}=\frac{16}{4} \\ w=4 \end{gathered}[/tex]Step 4: We replace the value of w in Equation 1.
[tex]\begin{gathered} \begin{equation*} l=9+w \end{equation*} \\ l=9+4 \\ l=13 \end{gathered}[/tex]Thus, the solution of the system of equations is:
[tex]\begin{gathered} l=13 \\ w=4 \end{gathered}[/tex]AnswerThe length of the rectangle is 13 inches, and the width of the rectangle is 4 inches.
Can the numbers 12, 6, 6 be used to form the sides of a triangle? Why or why not?
Enter your answer and also a 2-3 sentence explanation that describes how you determined your answer.
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Using the numbers 12, 6, 6, the triangle can not be formed.
The given numbers are 12, 6 and 6.
What is the triangle inequality theorem?The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.
Here, 6 + 6 = 12 but not greater than 12
Therefore, using the numbers 12, 6, 6, the triangle can not be formed.
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First try was incorrect Fill in the blank. Constant: a number that is next to a variable.
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A number that is right next to a variable. For instance,
[tex]5x+6[/tex]the number 6 is a constant.
A student at a junior college conducted a survey of 20 randomly selected full-time students to determine the relation between the number of hours of video game playing each week. X, and grade-point average, y. Shefound that a linear relation exists between the two variables. The least-squares regression line that describes this relation is ý = -0.0579x + 2.9408(Round to the nearest hundredth as needed.)(Part b) Interpret the slope.For each additional hour that a student spends playing video games in a week, the grade-point average will decrease by 0.0579 points, on average.(Part c) if appropriate, interpret the y-intercept.A. The grade-point average of a student who does not play video games is 2.9408.B. The average number of video games played in a week by students is 2.9408.C. It cannot be interpreted without more information.
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exactly For sentence A "The grade-point average of a student who does not play video games is 2.9408" we can verify as follows:
That means this sentence "The grade-point average of a student who does not play video games is 2.9408" is true.
For sentence B "The average number of video games played in a week by students is 2.9408" is not exactelly correct because the average number of hours of video game played is not specified.
For sentence C "It cannot be interpreted without more information" let's look over an illustration.
We can see, we can interpret the y-intercept as the moment where x = 0 which means when the student does not play a video game. So this sentence is false.
I mean the correct sentence is sentence A.
Can yoy help me with number 3? I do not understand the question.
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The law of sines states that:
[tex]\frac{\sin\alpha}{a}=\frac{\sin\beta}{b}=\frac{\sin \gamma}{c}[/tex]where alpha is the opposite angle to side a, beta is the opposite angle to side b and gamma is the opposite angle to side c.
For the triangle given we notice that:
Angle x is opposite to side 2.5.
Angle 28° is opposite to side 3.
Therefore the expression to find x is:
[tex]\frac{\sin x}{2.5}=\frac{\sin 28}{3}[/tex]Find the area of the shaded part of the figure if a=6, b=7, c=4. (I need help on this)
Answers
To obtain the area(A) of the shaded part of the figure, we will sum up the area of the triangle and the area of the rectangle.
Let us solve the area of the triangle(A1) first,
The formula for the area of the triangle is,
[tex]A_1=\frac{1}{2}\times base\times\text{height}[/tex]where,
[tex]\begin{gathered} base=b=7 \\ height=a=6 \end{gathered}[/tex]Therefore,
[tex]A_1=\frac{1}{2}\times7\times6=21unit^2[/tex]Hence, the area of the triangle is 21 unit².
Let us now solve for the area of the rectangle(A2)
The formula for the area of the rectangle is
[tex]A_2=\text{length}\times width[/tex]Where,
[tex]\begin{gathered} \text{length}=b=7 \\ \text{width}=c=4 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} A_2=7\times4=28 \\ \therefore A_2=28\text{unit}^2 \end{gathered}[/tex]Hence, the area of the rectangle is 28unit².
Finally, the total area of the shaded area is
[tex]\begin{gathered} A=A_1+A_2=21+28=49 \\ \therefore A=49unit^2 \end{gathered}[/tex]Hence, the area of the shaded part is 49unit² (OPTION A).
Please help me with this word problem quickly, work is needed thank you!
Answers
Given:
Sheila can wash her car in 15 minutes. Bob takes time twice as long to wash the same car.
Required:
Find the time they take both together.
Explanation:
Sheila can wash her car in 15 minutes.
Work done by sheila in a minute =
[tex]\frac{1}{15}\text{ }[/tex]Bob takes time twice as long to wash the same car. He washes the car in 30 minutes.
Work done by Bob in a minute
[tex]=\frac{1}{30}[/tex]If they work together let them take time x per minute.
[tex]\frac{1}{15}+\frac{1}{30}=\frac{1}{x}[/tex]Solve by taking L.C. M.
[tex]\begin{gathered} \frac{2+1}{30}=\frac{1}{x} \\ \frac{3}{30}=\frac{1}{x} \\ \frac{1}{10}=\frac{1}{x} \\ x=10\text{ minutes.} \end{gathered}[/tex]If they work together they will take 10 minutes.
Final Answer:
Sheila and Bob wash the car together in 10 minutes.
A. Find the zeros in state the multiplicity of each zeroB. Write an equation expressed as the product of factors, of a polynomial function for the graph Using A leading coefficient of 1 or -1 and make the degree of F a small as possible.C. Use both the equation in part B and graph to find the Y intercept
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Given the graph of a polynomial function:
We will find the following:
A. Find the zeros and state the multiplicity of each zero
The zeros of the function are the points of the intercept between the x-axis and the graph of the function
as shown, there are 3 points of intersection (3 zeros)
x = -1, multiplicity = 3
x = 1, multiplicity = 2
x = 2, multiplicity = 1
B. Write an equation expressed as the product of factors, of a polynomial function for the graph Using A leading coefficient of 1 or -1 and make the degree of F as small as possible.
Form A, the factors of the function will be:
(x+1), (x-1), and (x-2)
The equation of the function will be:
[tex]f(x)=(x+1)^3(x-1)^2(x-2)[/tex]C. Use both the equation in part B and graph to find the Y-intercept
The y-intercept is the value of (y) when (x = 0)
So, substitute with x = 0
So,
[tex]y=(0+1)^3\cdot(0-1)^2\cdot(0-2)=-2[/tex]So, the answer will be: y-intercept = -2
Which equation, written in the form of y = x + b, represents the table of values?
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Let:
[tex]\begin{gathered} (x1,y1)=(2,7) \\ (x2,y2)=(5,10) \end{gathered}[/tex][tex]\begin{gathered} x=2,y=7 \\ 7=2m+b \\ ---------------- \\ x=5,y=10 \\ 10=5m+b \\ ---------- \\ Let\colon \\ 2m+b=7_{\text{ }}(1) \\ 5m+b=10_{\text{ }}(2) \\ (2)-(1) \\ 5m-2m+b-b=10-7 \\ 3m=3 \\ m=1 \end{gathered}[/tex]Replace m into (1):
[tex]\begin{gathered} 2(1)+b=7 \\ 2+b=7 \\ b=7-2 \\ b=5 \end{gathered}[/tex]Answer:
[tex]y=x+5[/tex]A woman transit in her room tour, which got 40 miles per gallon on the highway and purchased a new car which is 28 miles per gallon. What is the percent of decrease in mileage
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The percent of decrease in mileage is 30%.
How to calculate the percentage?From the information, the woman transit in her room tour, which got 40 miles per gallon on the highway and purchased a new car which is 28 miles per gallon. The decrease will be:
= 40 - 28 = 12 miles per gallon.
The percentage decrease will be:
= Decrease in mileage / Initial mileage × 100
= 12/40 × 100
= 3/10 × 100
= 30%
This illustrates the concept of percentage.
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4. McKenzie wants to determine which ice cream option is the best choice. The chart below gives the description and prices for her options. Use the space below each item to record your findings. Place work below the chart. A scoop of ice cream is considered a perfect sphere and has a 2-inch diameter. A cone has a 2-inch diameter and a height of 4.5 inches. A cup, considered a right circular cylinder, has a 3-inch diameter and a height of 2 inches. a. Determine the volume of each choice. Use 3.14 to approximate pi. b. Determine which choice is the best value for her money. Explain your reasoning. (That means some division, you decide which.) $2.00 $3.00 $4.00 One scoop in a сир Two scoops in a cup Three scoops in a cup Half a scoop on a cone filled with ice cream A cup filled with ice cream (level to the top of the cup)
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McKenzie wants to determine which ice cream option is the best choice.
Part (a)
Volume of Scoop:
A scoop of ice cream is considered a perfect sphere and has a 2-inch diameter.
The volume of the sphere is given by
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]Where r is the radius.
We know that radius is half of the diameter.
[tex]r=\frac{D}{2}=\frac{2}{2}=1[/tex]So, the volume of a scoop of ice cream is
[tex]V_{\text{scoop}}=\frac{4}{3}\cdot3.14\cdot(1)^3=\frac{4}{3}\cdot3.14\cdot1=4.19\: in^3[/tex]Therefore, the volume of a scoop of ice cream is 4.19 in³
Volume of Cone:
A cone has a 2-inch diameter and a height of 4.5 inches.
The volume of a cone is given by
[tex]V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h[/tex]Where r is the radius and h is the height of the cone.
We know that radius is half of the diameter.
[tex]r=\frac{D}{2}=\frac{2}{2}=1[/tex]So, the volume of a cone of ice cream is
[tex]V_{\text{cone}}=\frac{1}{3}\cdot3.14\cdot(1)^2\cdot4.5=\frac{1}{3}\cdot3.14\cdot1^{}\cdot4.5=4.71\: in^3[/tex]Therefore, the volume of a cone of ice cream is 4.71 in³
Volume of Cup:
A cup, considered a right circular cylinder, has a 3-inch diameter and a height of 2 inches.
The volume of a right circular cylinder is given by
[tex]V=\pi\cdot r^2\cdot h[/tex]Where r is the radius and h is the height of the right circular cylinder.
We know that radius is half of the diameter.
[tex]r=\frac{D}{2}=\frac{3}{2}=1.5[/tex]So, the volume of a cup of ice cream is
[tex]V_{\text{cup}}=3.14\cdot(1.5)^2\cdot2=3.14\cdot2.25\cdot2=14.13\: in^3[/tex]Therefore, the volume of a cup of ice cream is 14.13 in³
Part (b)
Now let us compare the various given options and decide which option is the best value for money
Option 1:
The price of one scoop in a cup is $2
The volume of one scoop of ice cream is 4.19 in³
[tex]rate=\frac{4.19}{\$2}=2.095\: [/tex]Option 2:
The price of two scoops in a cup is $3
The volume of one scoop of ice cream is 4.19 in³
[tex]rate=\frac{2\cdot4.19}{\$3}=2.793\: [/tex]Option 3:
The price of three scoops in a cup is $4
The volume of one scoop of ice cream is 4.19 in³
[tex]rate=\frac{3\cdot4.19}{\$4}=3.1425[/tex]Option 4:
The price of half a scoop in a cone is $2
The volume of one scoop of ice cream is 4.19 in³
The volume of one cone of ice cream is 4.71 in³
[tex]rate=\frac{\frac{4.19}{2}+4.71}{\$2}=\frac{2.095+4.71}{\$2}=\frac{6.805}{\$2}=3.4025[/tex]Option 5:
The price of a cup filled with ice cream is $4
The volume of a cup is 14.13 in³
[tex]rate=\frac{14.13}{\$4}=3.5325[/tex]As you can see, the option 5 (a cup filled with ice cream) has the highest rate (volume/$)
This means that option 5 provides the best value for money.
Therefore, McKenzie should choose "a cup filled with ice cream level to the top of cup" for the best value for money.
The graph shows the projections in total enrollment at degree granting institutions from Fall 2003 to Fall2012The linear model, y= 0.2145x + 15.79, provides the approximate enrollment, in millions, between the years 2003 and 2012, where x = 0 corresponds to 2003, x = 1to 2004, and so on, and y is in millions of students.(a) Use the model to determine projected enrollment for Fall 2008.The projected enrollment for Fall 2008 is millions.(Type an integer or decimal rounded to the nearest tenth as needed.)
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In order to find the projected enrollment for 2008, we need to use the value of x equal to 5, because x represents the number of years after 2003.
Then, using the linear model with x = 5, we have:
[tex]\begin{gathered} y=0.2145\cdot5+15.79\\ \\ y=1.0725+15.79\\ \\ y=16.8625 \end{gathered}[/tex]Rounding to the nearest tenth, we have y = 16.9.
Why might It be more useful to have a square root in simplest form rather than a large number under the root or the approximate Value?
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Problem
Why might It be more useful to have a square root in simplest form rather than a large number under the root or the approximate Value?
Solution
One possible answer is that if we have the square root in the simplest form we can simplify expression add, subtract and multiply/divide by other quantities. Also with the simplification is easire to understand the value of interest.
-1010The graph of the equation y - 272. 2 is shown. Which equation will shift the graph up 3 units?A)ya 2x²y=2x-1y=2x²-3D)y = 2(x+3)²
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f(x) + 3, translates f(x) 3 units up
In this case, the function is y = 2x² - 2.
Applying the above rule, we get:
y = 2x² - 2 + 3
y = 2x² + 1
Determine the angle of rotation of the conic section given by: 32x2 +50xy + 7y2 = 100 (round your answer to the nearest tenth of adegree).
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The formula to obtain the angle of rotation is as follows:
[tex]\cot 2\theta=\frac{A-C}{B}[/tex]Compare the given equation to the general equation of a conic.
[tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex]Thus, the values of A, B, and C are as follows.
[tex]\begin{gathered} A=32 \\ B=50 \\ C=7 \end{gathered}[/tex]Substitute the values into the equation.
[tex]\begin{gathered} \cot 2\theta=\frac{32-7}{50} \\ \cot 2\theta=\frac{25}{50} \\ \cot 2\theta=\frac{1}{2} \end{gathered}[/tex]Find the value of the θ.
[tex]\begin{gathered} \frac{1}{\tan 2\theta}=\frac{1}{2} \\ \tan 2\theta=2 \\ 2\theta=\tan ^{-1}(2) \\ 2\theta\approx63.4349 \\ \theta\approx31.7 \end{gathered}[/tex]Please help me I need the answer asap.
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Therefore the right answer is option D = 1. The values of the variables will be obtained when the system of linear equations is solved; this is referred to as the solution of a linear equation.
What are linear equations?An equation with the form Ax+By=C is referred to as a linear equation. It consists of two variables combined with a constant value that exists in each of them. The values of the variables will be obtained when the system of linear equations is solved; this is referred to as the solution of a linear equation. If an equation has the formula y=mx+b, with m representing the slope and b the y-intercept, it is said to be linear.A two-variable linear equation can be thought of as a linear relationship between x and y, or two variables whose values rely on each other (often y and x) (usually x).Hence,
The correct Option is D = 1
Given
[tex]x^2+x-1\\[/tex] = 0
[tex]\frac{1-x}{2x^2} +\frac{ x^2}{2x-2}[/tex] = ?
From [tex]x^2+x-1\\[/tex] = 0
[tex]x^2 = 1-x[/tex]
Therefore,
[tex]\frac{1-x}{2x^2} +\frac{ x^2}{2x-2}[/tex] = [tex]\frac{x^2}{2x^2} + \frac{x^2}{2(x-1)}[/tex]
[tex]\frac{1}{2} + \frac{x^2}{2(x-1)}[/tex]
[tex]\frac{1}{2} + \frac{1}{2}[/tex]
= 1
Therefore the right answer is option D = 1
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Can some one help and explain pls
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There, on the hypotenuse, is the longest side. Therefore, 12 might be viewed as C if we consider the Pythagorean theorem, which states that A squared plus B squared equals C squared. The hypotenuse is this. The hypotenuse squared is equal to the C squared.
What is the formula a2 b2 c2 used for?The Pythagorean Theorem describes the relationship among the three sides of a right triangle. In any right triangle, the sum of the areas of the squares formed on the legs of the triangle equals the area of the square formed on the hypotenuse: a2 + b2 = c2.
Consolidate terms multiplied into a single fraction.
i) c + -2/3(2/3c).2
c - 2/3(2/3c).2
c - 2/3 . 2c/3.2
c -4/3 . 2c/3
c + -4.2c / 3.3
c /9.
II)-5u.3(-2)u + -3/5
Add up the numbers.
30uu + -3/5
= 30u² + -3/5
= 3/5(50u² -1).
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A biologist wants to determine the effect of a new fertilizer on tomato plants. What would be the control?All PlantsPlants not treated with the Fertilizer.The FertilizerPlants treated with the Fertilizer.
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Remember that the control variable does not change in the experiment or in any study.
So the control here will be all the plants because you can not control the type of the plant.
Answer:b
Step-by-step explanation:
write the equation for a quadratic function in vertex form that opebs down shifts 8 units to the left and 4 units down .
Answers
STEP - BY STEP EXPLANATION
What to find?
Equation for a quadratic equation.
Given:
Shifts 8 unit to the left.
4 units down
Step 1
Note the following :
• The parent function of a quadratic equation in general form is given by;
[tex]y=x^2[/tex]• If f(x) shifts q-units left, the f(x) becomes, f(x+q)
,• If f(x) shift m-units down, then the new function is, f(x) -m
Step 2
Apply the rules to the parent function.
8 units to the left implies q=8
4 units down implies m= 4
[tex]y=(x+8)^2-4[/tex]ANSWER
y= (x+8)²- 4
Which of the following best describes terms that have the same degree in the same radicand? A. like rational termsB. like fractional termsC. like radical termsD. like polynomial terms
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Two radical expressions are called like terms if they have the same degree and the same radicand.
So, like radical terms, best describes terms that have the same degree and the same radicand.
Like radicals are those, that have the same root number and radicand.
So, the correct answer is option C.
Which list orders the numbers from least to greatest?
[tex]\pi \: 4.3 \: 3.6 \: 13 \: \sqrt{19} [/tex]
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Answer:
[tex]\pi[/tex], 3.6, 4.3, [tex]\sqrt{19}[/tex], 13
Step-by-step explanation:
[tex]\pi[/tex]≈ 3.14 This is an approximation because [tex]\pi[/tex] never repeats or terminates.
[tex]\sqrt{19}[/tex] This is also a number that never repeats or terminates. If you put this in your calculator, I estimated it to
4.359
Using this information, I put the numbers in order.
# 3 symbols of inequalities and the coordinate system...hello I'm a 7th grader can u please help me with my math summer package and explain it in a way that a 7th grader can understand it
Answers
Given: A grocery store is located at the origin (0,0). Madison lives 3 blocks west of the grocery store, and Gavin lives 5 blocks west of the grocery store.
Required: To determine the coordinates of Madison's house and Gavin's house and the distance between the grocery store and madison's and Gavin's house. Also, write inequalities for the distance.
Explanation: Let the graph represents the directions as follows-
Then, the direction west lies on the negative x-axis. So, according to the question, Madison lives 3 blocks west of the grocery store, and Gavin lives 5 blocks west of the grocery store. This can be represented as follows-
Here, M represents Madison's house, and G represents Gavin's house. Now the distance from the grocery store to Madison's house is 3 blocks and to Gavin's house is 5 blocks.
Gavin lives at a greater distance from the store. Let d(M) represent the distance of Madison's house from the store and d(G) represent the distance of Gavin's house from the store. Then-
[tex]\begin{gathered} 0Final Answer: Coordinates of Madison's house=(0,-3).Coordinate of Gavin's house=(0,-5)
Distance from the grocery store to Madison's house=3 unit blocks.
Distance from the grocery store to Gavin's house=5 unit blocks.
Inequalities are-
[tex]\begin{gathered} 0\lt d(M))\leqslant3 \\ 0\lt d(G))\leqslant5 \end{gathered}[/tex]
Question 6 of 1
For f(x)-3x+1 and g(x)=x²-6, find (f-g)(x).
A. -x²+3x+7
OB.x²-3x-7
O C. 3x²-17
OD. -x²+3x-5
Answers
-x² + 3x + 7 is value of function .
What is function in math?
An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.f(x) = 3x + 1
g(x) = x² - 6
Then,
According to the' question :-
(f - g)(x) = f(x) - g(x)
= 3x + 1 - (x² - 6)
= 3x + 1 - x² + 6
= -x² + 3x + 7
Hence,
Option 1st : -x² + 3x + 7 is Correct.
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A scale drawing of a rectangular park is 4 inches wide and 8 inches long. The actual park is 320 yards long. What is the perimeter of the actual park, in square yards?
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Given:
• Width of scale drawing = 4 inches
,• Length of scale drawing = 8 inches
,• Length of actual park = 320 yards
Let's find the perimeter of the actual park.
Let's first find the width of the actual park.
To find the width of the actual park, we have:
[tex]\begin{gathered} \text{ width of actual = }\frac{\text{ length of actual}}{\text{ length of scale}}*\text{ width of scale} \\ \\ \\ \text{ width of actual = }\frac{320}{8}*4 \\ \\ \text{ width of actual = 40 * 4 = 160 yards} \end{gathered}[/tex]The width of the actual park is 160 yards.
Now, to find the perimeter of the actual park, apply the formula do perimeter of a rectangle:
P = 2(L + W)
Where:
P is the perimeter
L is the length = 320 yards
W is the width = 160 yards
Thus, we have:
P = 2(320 + 160)
P = 2(480)
P = 960 yards
Therefore, the perimeter of the actual park is 960 yards.
ANSWER:
960 yards
(2.4 × 10^3) × (3 × 10^n) = 7.2 × 10^9
Answers
Answer:
n = 6
Step-by-step explanation:
(2.4 × 10^3) × (3 × 10^n) = 7.2 × 10^9
First lets solve the parentheses:
(2.4 × 1000) × ( 3 × 10^n) = (7.2 × 1000000000)
2.4 × 1000 = 2400 so...
2400 × (3 × 10^n ) = 7200000000
Next lets divide:
7200000000/2400 = 3000000
So now we have...
(3 × 10^n ) = 3000000
Even though we just divided we have to divide again so...
3000000/3 = 1000000
then to get the answer of n we have to figure out how many times to the power of 10 do we get 1000000.
one easy but time consuming way is
dividing it by ten till you get to one and you would get the same answer. You choose to do that way then that works for your.
There are also other way to figure that out but your teacher teaches you an easier way to figure it out.
I am asked to graph f(x) = (- 1/x-2) -1
Answers
Answer
[tex]f(x)=-\frac{1}{x-2}-1[/tex]Decide whether the word problem represents a linear or exponential function. Circle either linear or exponential. Then, write the function formula.
Answers
a. The given table is
Notice, the value of x increases at equal intervals of 1
Also, the value of y increases at an equal interval of 3
This means for the y values the difference between consecutive terms is 3
Also, for the x values, the difference between consecutive terms is 1
Hence, the table represents a linear function
The general form of a linear function is
[tex]y=mx+c[/tex]Where m is the slope
From the interval increase
[tex]m=\frac{\Delta y}{\Delta x}=\frac{3}{1}=3[/tex]Hence, m = 3
The equation becomes
[tex]y=3x+c[/tex]To get c, consider the values
x = 0 and y = 2
Thi implies
[tex]\begin{gathered} 2=3(0)+c \\ c=2 \end{gathered}[/tex]Hence, the equation of the linear function is
[tex]y=3x+2[/tex]b. The given table is
Following the same procedure as in (a), it can be seen that there is no constant increase in the values of y
Hence, the function is not linear
This implies that the function is exponential
The general form of an exponential function is given as
[tex]y=a\cdot b^x[/tex]Consider the values
x =0, y = 3
Substitute x = 0, y = 3 into the equation
This gives
[tex]\begin{gathered} 3=a\times b^0 \\ \Rightarrow a=3 \end{gathered}[/tex]The equation become
[tex]y=3\cdot b^x[/tex]Consider the values
x =1, y = 6
Substitute x = 1, y = 6 into the equation
This gives
[tex]\begin{gathered} 6=3\cdot b^1 \\ \Rightarrow b=\frac{6}{3}=2 \end{gathered}[/tex]Therefore the equation of the exponential function is
[tex]y=3\cdot2^x[/tex]c. The given table is
As with (b) above,
The function is exponential
Using
[tex]y=a\cdot b^x[/tex]When
x = 0, y = 10
This implies
[tex]\begin{gathered} 10=a\cdot b^0 \\ \Rightarrow a=10 \end{gathered}[/tex]The equation becomes
[tex]y=10\cdot b^x[/tex]Also, when
x = 1, y =5
The equation becomes
[tex]\begin{gathered} 5=10\cdot b^1 \\ \Rightarrow b=\frac{5}{10} \\ b=\frac{1}{2} \end{gathered}[/tex]Therefore, the equation of the exponential function is
[tex]y=10\cdot(\frac{1}{2})^x[/tex]I need help please there are two parts when we are done with part one the next part shows :) now can I get help
Answers
The months in which the income was greater than the expenses are:
June, July and August
Rafael is buying ice cream for a family reunion. The table shows the prices for different sizes of two brands of ice cream.
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the correct answer is that the small size of the brand Cone dreams, because the price of each pint in it will be $2.125 =4.25/2, and if we calculate the price per pint with the other options it would be the minimum of all of them.
Devon is 30 years old than his son, Milan. The sum of both their ages is 56. Using the variables d and m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.How old is Devon?
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Let's set d as the age of Davon and m as the age of Milan.
Devon is 30 years old than his son Milan, it is represented by the equation:
[tex]d=m+30\text{ Equation (1)}[/tex]The sum of both ages is 56, the equation that represents the situation is:
[tex]d+m=56\text{ Equation (2)}[/tex]To find Devon's age, in equation 1, solve for m in terms of d:
[tex]m=d-30[/tex]Now, replace in equation 2 and solve for d:
[tex]\begin{gathered} d+(d-30)=56 \\ 2d-30=56 \\ 2d=56+30 \\ 2d=86 \\ d=\frac{86}{2} \\ d=43 \end{gathered}[/tex]Devon is 43 years old.
