Solve the inequality below to determine and state the smallest possible value of x in the solution set. - 7(x + 4) + 3x < 8x - 2(2x - 2)
Answers
given the inequality :
- 7(x + 4) + 3x < 8x - 2(2x - 2)
so,
-7x - 28 + 3x < 8x - 4x + 4
combine like terms:
-7x + 3x - 8x + 4x < 28 + 4
-8x < 32
Divide both sides by -8
Do not forget to flip the inequality sign
so,
x > -4
so, The solution is the interval ( -4 , ∞ )
On the number line the solution will be :
The smallest possible interger of x = -3
Related Questions
Pep Boys Automotive paid $208.50 for a pickup truck bed liner. The original selling price was $291.90, but this was marked down 35%. If operating expenses are 28% of the cost, find the absolute loss
Answers
Step 1: State the given in the question
THe following were given:
[tex]\begin{gathered} \text{Amount Paid (}A_{\text{paid}})=208.50 \\ (Originalsellingprice)SP_{ORIGINAL}=291.90 \\ \text{Marked Percentage=35\%} \\ \text{Operating expenses=28\%} \end{gathered}[/tex]Step 2: State what is to be found
We are to find the absolute loss
Step 3: Calculate the selling price
Please note that the selling price is the marked down price
The marked down price would be
[tex]\begin{gathered} P_{\text{MARKED DOWN}}=(100-35)\text{ \% of original selling price} \\ P_{\text{MARKED DOWN}}=65\text{ \% of }SP_{ORIGINAL} \\ P_{\text{MARKED DOWN}}=\frac{65}{100}\times291.90=189.74 \end{gathered}[/tex]The selling price is the marked down price which is $189.74
Step 4: Calcualte the operating expenses
Please note that the cost price is amount paid. Therefore, the operating expenses would be as calculated below:
[tex]\begin{gathered} E_{\text{OPEARATING}}=28\text{ \% of Amount Paid} \\ E_{\text{OPERATING}}=28\text{ \% of }A_{\text{paid}}=\frac{28}{100}\times208.50 \\ E_{\text{OPERATING}}=0.28\times208.50=58.38 \end{gathered}[/tex]Hence, the operating expenses is $58.38
Step 5: Calculate the total cost price
The total cost price is the addition of the cost price and the operating expenses. This is as calculated below:
[tex]\begin{gathered} C_{\text{TOTAL COST PRICE}}=E_{OPERATING}+A_{PAID} \\ C_{\text{TOTAL COST PRICE}}=58.38+208.50=266.88 \end{gathered}[/tex]Hence, the total cost price is $266.88
Step 6: Calculate the absolute loss
The absolute loss is the difference between the total cost price and the marked down price (or the actual selling price). This is as calculated below:
[tex]\begin{gathered} L_{\text{ABSOLUTE LOSS}}=C_{TOTAL\text{ COST PRICE}}-P_{MARKED\text{ DOWN}} \\ L_{\text{ABSOLUTE LOSS}}=266.88-189.74=77.14 \end{gathered}[/tex]Hence, the absolute loss is $77.14
4. Adam had $200. He spent $75 on clothes and $55 on a video game. Then his Momgave him $20 more dollars. How much money does Adam have now?
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Adam had $200
He spent $75 on clothes and $55 on video game
The total money spent by Adam is
[tex]=75+55=\text{ \$130}[/tex]The amount left with Adam is
[tex]=200-130=\text{ \$70}[/tex]Then his mom gave him $20
The total amount of money Adam have now is
[tex]=70+20=\text{ \$90}[/tex]Hence, the answer is $90
Graph the set {x|x2-3} on the number line.Then, write the set using interval notation.
Answers
Given,
The expression is,
[tex]\lbrace x|x\ge-3\rbrace[/tex]Required:
The graph of the line.
The interval notation is [-3, infinity).
The line of the inequality is,
Hence, the graph of the line is obtained.
8. A boy owns 6 pairs of pants, 8 shirts, 2 ties, and 3 jackets. How many outfits can he wear to school if he must wear one of each item?
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It is given that the boy owns 6 pairs of pants, 8 shirts, 2 ties, and 3 jackets.
It is also given that he must wear one of each item.
Recall the Fundamental Counting Principle:
The same is valid for any number of events following after each other.
Hence, the number of different outfits he can wear by the counting principle is:
[tex]6\times8\times2\times3[/tex]Evaluate the product:
[tex]6\times8\times2\times3=288[/tex]The number of different outfits he can wear is 288.
Boden's account has a principal of $300 and a simple interest rate of 3.5%. Complete the number line. How much money will be in the account after 4 years, assuming Boden does not add or take out any money?
Answers
formula for simple intrest
A= p(1+rt)
= 300(1+ 3.5 * 4)
=300( 15)
4500
after 4 years he has $4500
I am studying for the big test tomorrow and just need someone to go through this sheet I made with me.Sorry
Answers
SOLUTION
Let us solve the simultaneous equation
[tex]\begin{gathered} -2x-y=0 \\ x-y=3 \end{gathered}[/tex]using elimination
To eliminate, we must decide which of the variables, x or y is easier to eliminate. The variable you must eliminate must be the same and have different sign. Looking above, it is easier to eliminate y because we have 1y above and 1y below. But to eliminate the y's, one must be +y and the other -y. So that +y -y becomes zero.
So to make the y's different, I will multiply the second equation by a -1. This becomes
[tex]\begin{gathered} -2x-y=0 \\ (-1)x-y=3 \\ -2x-y=0 \\ -x+y=-3 \end{gathered}[/tex]So, now we can eliminate y, doing this we have
[tex]\begin{gathered} -2x-x=-3x \\ -y+y=0 \\ 0-3=-3 \\ \text{This becomes } \\ -3x=-3 \\ x=\frac{-3}{-3} \\ x=1 \end{gathered}[/tex]Now, to get y, we put x = 1 into any of the equations, Using equation 1, we have
[tex]\begin{gathered} -2x-y=0 \\ -2(1)-y=0 \\ -2-y=0 \\ \text{moving -y to the other side } \\ y=-2 \end{gathered}[/tex]So, x = 1 and y = -2
Using substitution, we make y or x the subject in any of the equations. Looking at this, It is easier to do this using equation 2. From equation 2,
[tex]\begin{gathered} x-y=3 \\ \text{making y the subject we have } \\ y=x-3 \end{gathered}[/tex]Now, we will put y = x - 3 into the other equation, which is equation 1, we have
[tex]\begin{gathered} -2x-y=0 \\ -2x-(x-3)=0 \\ -2x-x+3=0 \\ -2x-1x+3=0 \\ -3x+3=0 \\ -3x=-3 \\ x=\frac{-3}{-3} \\ x=1 \end{gathered}[/tex]So, substituting x for 1 into equation 1, we have
[tex]\begin{gathered} -2x-y=0 \\ -2(1)-y=0 \\ -2\times1-y=0 \\ -2-y=0 \\ y=-2 \end{gathered}[/tex]Substituting x for 1 into equation 2, we have
[tex]\begin{gathered} x-y=3 \\ 1-y=3 \\ y=1-3 \\ y=-2 \end{gathered}[/tex]Now, for graphing,
In the given figure, find the mesure of angle BCD
Answers
Since the sum of angles in a triangle is 180°, it follows that;
[tex]\begin{gathered} 4x+3x+2x=180 \\ 9x=180 \\ \text{ Divide both sides of the equation by }9 \\ \frac{9x}{9}=\frac{180}{9} \\ x=20 \end{gathered}[/tex]Since line segment AB is parallel to the line segment CD, it follows from the Corresponding angles theorem that:
[tex]\begin{gathered} \angle{B}=\angle{BCD} \\ \text{ Therefore:} \\ \angle{BCD}=4x \\ \text{ Substitute }x=20\text{ into the equation} \\ \angle{BCD}=4\times20=80 \end{gathered}[/tex]Therefore, The req
Can you please help me solve this question. Thank you
Answers
Answer:
0.4384 < p < 0.5049
Explanation:
The confidence interval for the population proportion can be calculated as:
[tex]p^{\prime}-z_{\frac{\alpha}{2}}\sqrt[]{\frac{p^{\prime}(1-p^{\prime})}{n}}Where p' is the sample proportion, z is the z-score related to the 95% level of confidence, n is the size of the sample and p is the population proportion.
Now, we can calculate p' as the division of the number of voters of favor approval by the total number of voters.
[tex]p^{\prime}=\frac{408}{865}=0.4717[/tex]Additionally, n = 865 and z = 1.96 for a 95% level of confidence. So, replacing the values, we get:
[tex]\begin{gathered} 0.4717-1.96\sqrt[]{\frac{0.4717(1-0.4717)_{}}{865}}Therefore, the confidence interval for the true proportion is:
0.4384 < p < 0.5049
What is the meaning of estimate
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The meaning of estimate is approximately calculating an answer to check its accuracy.
Approximate calculation:
Approximate value means the value that is close to this number, less than it, as close as possible, and with a requested level of precision.
For example, the approximate value of π is 3.14
Given,
Here we have the word estimate.
Now, we have to find the meaning of it.
Estimate value means to find a value that is close enough to the right answer, usually with some thought or calculation involved.
For example, let us consider Alex estimated there were 10,000 sunflowers in the field by counting one row then multiplying by the number of rows. Here we doesn't have the exact value instead of that we take the approximate value to identify the number. This process is called estimation.
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A small publishing company is planning to publish a new book. Let C be the total cost of publishing the book (in dollars). Let be the number of copies of the book produced. For the first printing, the company can produce up to 100 copies of the book. Suppose that C = 10N + 700 gives C as a function of N during the the correct description of the values in both the domain and range of the function. Then, for eachchoose the most appropriate set of values.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
C = 10N + 700
Step 02:
functions:
C = total cost
N = number of copies
Domain:
number of copies produced
{0, 1, 2, 3, .... 100}
Range:
cost of publishing book (in dollars)
{700, 710, 720, 730, ... 1700}
That is the full solution.
Use the given conditions to write an equation for the line.Passing through (−7,6) and parallel to the line whose equation is 2x-5y-8=0
Answers
For a line to be parallel to another line, the slope will be the same
1st equation:
[tex]\begin{gathered} 2x\text{ - 5y - 8 = 0} \\ \text{making y the subject of formula:} \\ 2x\text{ - 8 = 5y} \\ y\text{ = }\frac{2x\text{ - 8}}{5} \\ y\text{ = }\frac{2x}{5}\text{ - }\frac{8}{5} \end{gathered}[/tex][tex]\begin{gathered} \text{equation of line:} \\ y\text{ = mx + b} \\ m\text{ = slope, b = y-intercept} \end{gathered}[/tex][tex]\begin{gathered} \text{comparing the given equation and equation of line:} \\ y\text{ = y} \\ m\text{ = 2/5} \\ b\text{ = -8/5} \end{gathered}[/tex]Since the slope of the first line = 2/5, the slope of the second line will also be 2/5
We would insert the slope and the given point into equation of line to get y-intercept of the second line:
[tex]\begin{gathered} \text{given point: (-7, 6) = (x, y)} \\ y\text{ = mx + b} \\ 6\text{ = }\frac{2}{5}(-7)\text{ + b} \\ 6\text{ = }\frac{-14}{5}\text{ + b} \\ 6\text{ + }\frac{14}{5}\text{ = b} \\ \frac{6(5)\text{ + 14}}{5}\text{ = b} \\ b\text{ = }\frac{44}{5} \end{gathered}[/tex]The equation for the line that passes through (-7, 6) and parallel to line 2x - 5y - 8 = 0:
[tex]\begin{gathered} y\text{ = mx + b} \\ y\text{ = }\frac{2}{5}x\text{ + }\frac{44}{5} \end{gathered}[/tex]Please look at the image below. By the way this is my homework.Use the definition of congruence to decide whether the two figures are congruent. Explain your answer. Give coordinate notation for the transformations you use.
Answers
Congruent Shapes
Two congruent shapes have the same size and shape, which means all of their side lengths are equal and all of their internal angles are congruent (have the same measure),
All of the rigid transformations map the original figure to a congruent figure. One of the transformations is the reflection.
The image shows two shapes SRQP and EDCB. They seem to have the same shape and size, but it must be proven by finding the appropriate transformation used.
Comparing the corresponding vertices we can find that out. For example, the coordinates of S are (-6,4) and the coordinates of E are (4,4). The x-coordinate of the midpoint between them is
xm = (-6+4)/2 = -1
Now analyze the points P(-8,2) and B(6,2). The x-coordinate of the midpoint is:
xm = (-8+6)/2 = -1
For the points R(-4,-6) and D(2,-6):
xm = (-4+2)/2 = -1
For the points Q(-9,-4) and D(8,-4):
xm = (-9+8)/2 = -0.5
Since this last pair of corresponding points don't have the same axis of symmetry as the others, the shapes don't have the same size and angles, thus they are not congruent
For both shapes to be congruent, the coordinates of Q should have been (-10,-4)
On the Richter Scale, the magnitude R of an earthquake of intensity I is given by the equation in the image, where I0 = 1 is the minimum intensity used for comparison. (The intensity of an earthquake is a measure of its wave energy). Find the intensity per unit of area I for the Anchorage Earthquake of 1989, R = 9.2.
Answers
we have the formula
[tex]R=\log _{10}\frac{I}{I_0}[/tex]we have
R=9.2
I0=1
substitute in the given equation
[tex]\begin{gathered} 9.2=\log _{10}\frac{I}{1} \\ 9.2=\log _{10}I \\ I=10^{(9.2)} \\ \end{gathered}[/tex]I=1,584,893,192.46
Which expression has a negative value
Answers
Answer:
bottom one
Step-by-step explanation:
A rectangular athletic field is twice as long as it is wide if the perimeter of the athletic field is 360 yards what are its dimensions. The width isThe length is
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Step 1. We will start by making a diagram of the situation.
Since the length of the rectangle is twice the width, if we call the width x, then the length will be 2x as shown in the diagram:
Step 2. One thing that we know about the rectangle is its perimeter:
[tex]\text{Perimeter}\longrightarrow360\text{yd}[/tex]This perimeter has to be the result of the sum of all of the sides of the rectangle:
[tex]x+x+2x+2x=360[/tex]Step 3. Solve the previous equation for x.
In order to solve for x, the first step is to combine the like terms on the left-hand side:
[tex]6x=360[/tex]The second step to solve for x is to divide both sides of the equation by 6:
[tex]\frac{6x}{6}=\frac{360}{6}[/tex]Simplifying:
[tex]x=60[/tex]Step 4. Remember from the diagram from step 1, that x was the width of the rectangle:
[tex]\text{width}\longrightarrow x\longrightarrow60yd[/tex]and the length was 2x, so we multiply the result for the with by 2:
[tex]\text{length}\longrightarrow2x=2(60)=120\longrightarrow120yd[/tex]And these are the values for the width and the length.
Answer:
The width is 60yd
The length is 120yd
GI and JL are parallel lines.which angles are alternate interior angles?
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In the given figure,
[tex]GI\text{ }\parallel\text{ }JL[/tex]The pair of alternate interior angle is,
[tex]\angle LKH\text{ and }\angle GHK[/tex]what should the height of the container be so as to minimize cost
Answers
Lets make a picture of our problem:
where h denotes the height of the box.
We know that the volume of a rectangular prism is
[tex]\begin{gathered} V=(4x)(x)(h) \\ V=4x^2h \end{gathered}[/tex]Since the volume must be 8 cubic centimeters, we have
[tex]4x^2h=48[/tex]Then, the height function is equal to
[tex]h=\frac{48}{4x^2}=\frac{12}{x^2}[/tex]On the other hand, the function cost C is given by
[tex]C=1.80A_{\text{bottom}}+1.80A_{\text{top}}+2\times3.60A_{\text{side}1}+2\times3.60A_{\text{side}2}[/tex]that is,
[tex]\begin{gathered} C=1.80\times4x^2+1.80\times4x^2+3.60(8xh+2xh) \\ C=3.60\times4x^2+3.60\times10xh \end{gathered}[/tex]which gives
[tex]C=3.60(4x^2+10xh)[/tex]By substituting the height result from above, we have
[tex]C=3.60(4x^2+10x(\frac{12}{x^2}))[/tex]which gives
[tex]C=3.60(4x^2+\frac{120}{x})[/tex]Now, in order to find minum cost, we need to find the first derivative of the function cost and equate it to zero. It yields,
[tex]\frac{dC}{dx}=3.60(8x-\frac{120}{x^2})=0[/tex]which is equivalent to
[tex]\begin{gathered} 8x-\frac{120}{x^2}=0 \\ \text{then} \\ 8x=\frac{120}{x^2} \end{gathered}[/tex]by moving x squared to the left hand side and the number 8 to the right hand side, we have
[tex]\begin{gathered} x^3=\frac{120}{8} \\ x^3=15 \\ \text{then} \\ x=\sqrt[3]{15} \\ x=2.4662 \end{gathered}[/tex]Therefore, by substituting this value in the height function, we get
[tex]h=\frac{12}{2.4662^2}=1.9729[/tex]therefore, by rounding to the neastest hundredth, the height which minimize the cost is equal to 1.97 cm
Given the figure below, determine the angle that is a same side interior angle with respect to1. To answer this question, click on the appropriate angle.
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Same side interior angles are angles on the same side of the transversal line, inside the two lines intersected.
<5 is an interior angle, on the same side as <3.
On The left side of the bisector line.
45% of 240 is what number?
Answers
We are asked to determine the 45% of 240. To do that we need to multiply 240 by 45/100, that is:
[tex]240\times\frac{45}{100}=108[/tex]therefore, 45 percent of 240 is 108
factor bofe problems using synthetic division and list All zeros
Answers
Given:
[tex]f(x)=x^3-7x^2+2x+40;\text{ x -5}[/tex]Let's factor using synthetic division.
Equate the divisor to zero:
x - 5 = 0
x = 5
List all terms of the polynomial: 1, -7, 2, 40
Palce the numbers representing the divisor and dividend into a long division-like configuration
To factor using synthetic division, we have:
Therefore, the factored expression is:
[tex]\begin{gathered} 1x^2-2x-8 \\ \\ =x^2-2x-8 \\ \\ =(x-4)(x+2) \end{gathered}[/tex]The zeros are also the roots of the polynomial.
The zeros of a polynomial are all the x-values that makes the polynomial equal to zero,
To find the zeros, equate each afctor to zero:
(x - 4) = 0
x = 4
(x + 2) = 0
x = -2
Thus, the zeros are:
x = 4, -2
ANSWER:
[tex]\begin{gathered} (x-4)(x+2) \\ \\ \text{Zeros: 4, and -2} \end{gathered}[/tex]if (x + y) +61 = 2, what is x + y?
Answers
The question is given as
[tex](x+yi)+6i=2[/tex]To solve, we need to make (x + yi) the subject of the formula.
To do so, we move 6i to the right-hand side of the equation:
[tex]x+yi=2-6i[/tex]Therefore, OPTION A is correct.
Answer:
(x + yi)= 2-6i
Step-by-step explanation:
Complex numbers
(x + yi) +6i = 2
Subtract 6i from each side
(x + yi) +6i -6i = 2-6i
(x + yi)= 2-6i
fine the slope of every line that is parallel to the line on the graph
Answers
Every parallel line would have the same slope because the slope formula is Δy/Δx and the difference would be the same, so the slope for the line with the given points would be -1/6, or roughly 0.167.
What is parallel lines?Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a fixed minimum distance between them and no contact or intersection are said to be parallel.
What is slope?A line's steepness can be determined by looking at its slope. In mathematics, slope is determined by dividing the change in y by the change in x. Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.
Here the coordinates are (-6,0) and (0,-1)
ΔX = 0 – -6 = 6
ΔY = -1 – 0 = -1
Slope (m) =ΔY/ΔX
=-1/6
= -0.16666666666667
≈-0.167
The slope for the line with the given points would be -1/6, or roughly 0.167, because the slope formula is Δy/Δx and the difference would be the same for every parallel line.
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Which description is paired with its correct expression?
O seven less than the quotient of two and a number squared, increased by six;
Onine times the difference of a number cubed and three, 9(n²-3)
7-+8
O eight more than the quotient of a number squared and four, decreased by seven;
Otwice the difference of a number cubed and eight, 27³-8
8+/-7
Answers
Answer:
seven less than the quotient of two and a number squared increased by six
7 - (2/n²) + 6
nine times the difference of a number cubed and three; 9(n³-3)
eight more than the quotient of a number squared and four, decreased by seven; 8 + (4 /n²) - 7
twice the difference of a number cubed and eight; 2 n³- 8
Step-by-step explanation:
True or False: A power has two parts, a base and an exponent. True False
Answers
The said statement is true.
A power has two parts, a base and an exponent.
Example
[tex]2^3[/tex]The answer is TRUE
In the 1st generation, there are 6 rabbits in a forest. Every generation after that, the rabbit population triples. This sequence represents the numbers of rabbits for the first few generations: 6, 18, 54, What is the explicit formula for the number of rabbits in generation n?
Answers
You have the following sequence for the population of the rabbits:
6, 18, 54, ...
The explicit formula for the previous sequence is obtained by considering the values of n (1,2,3,..) for the first terms of the sequence.
You can observe that the explicit formula is:
a(n) = 6·3^(n - 1)
in fact, for n=1,2,3 the result is:
a(1) = 6·3^(1 - 1) = 6·3^0 = 6
a(2) = 6·3^(2 - 1) = 6·3^1 = 18
a(3) = 6·3^(3 - 1) = 6·3^2 = 6·9 = 54
which is consistent with the given sequence 6, 18, 54, ...
Answer the statistical measures and create a box and whiskers plot for the following set of data.
Answers
Solution
The picture below is the solution to the problem
Brief explanantion
From the data given, It is obvious that:
Minimum = 2
Maximum =
The total number of the data is 3, so the number 7th term is the median
Thus,
Median = 8
To find Q1
[tex]\begin{gathered} Q_1=\frac{1}{4}(n+1)th\text{ term} \\ Q_1=\frac{1}{4}(13+1)=\frac{14}{4}=3.5 \end{gathered}[/tex]Q1 is between the third and fourth term
Therefore, Q1 is
[tex]Q_1=0.5(4)+0.5(6)=5[/tex]Similarly, to find Q3
[tex]\begin{gathered} Q_3=\frac{3}{4}(n+1)th\text{ term} \\ Q_3=\frac{3}{4}(13+1)=3\times\frac{14}{4}=3\times3.5=10.5 \end{gathered}[/tex]Q3 is between the tenth and the eleventh term
Therefore, Q3 is
[tex]Q_3=0.5(11)+0.5(11)=11[/tex]Instructions: Find the missing length indicated.BII1600900X
Answers
From the diagram given in the question, we are asked to find the missing length indicated.
We can see from the diagram that the right triangles are similar, so the ratio of hypotenuse to short leg is the same for all.
So,
x/900 = (1600 + 900)/x
Let's cross multiply:
x² = 900(2500)
let's take square of both sides:
x = √(900) * √(2500)
x = 30(50)
x = 30 * 50
x = 1500
Therefore, the missing length is 1500
Find F as a function of x and evaluate it at x = 2, x = 5 and x = 8.
Answers
Given:
[tex]F(x)=\int_2^x(t^3+6t-4)dt[/tex]Find-:
[tex]F(x),F(2),F(5),F(8)[/tex]Sol:
[tex]\begin{gathered} F(x)=\int_2^x(t^3+6t-4)dt \\ \\ \end{gathered}[/tex]Use integration then:
[tex]\begin{gathered} F(x)=\int_2^x(t^3+6t-4)dt \\ \\ F(x)=[\frac{t^4}{4}+\frac{6t^2}{2}-4t]_2^x^ \\ \\ \\ F(x)=\frac{x^4}{4}+3x^2-4x-\frac{2^4}{4}-3(2)^2+4(2) \\ \\ F(x)=\frac{x}{4}^4+3x^2-4x-8 \end{gathered}[/tex]The function value at x = 2 is:
[tex]\begin{gathered} F(x)=\frac{x^4}{4}+3x^2-4x-8 \\ \\ F(2)=\frac{2^4}{4}+3(2)^2-4(2)-8 \\ \\ F(2)=4+12-8-8 \\ \\ F(2)=16-16 \\ \\ F(2)=0 \end{gathered}[/tex]The function value at x = 5
[tex]\begin{gathered} F(x)=\frac{x^4}{4}+3x^2-4x-8 \\ \\ F(5)=\frac{5^4}{4}+3(5)^2-4(5)-8 \\ \\ F(5)=156.25+75-20-8 \\ \\ F(5)=203.25 \end{gathered}[/tex]Function value at x = 8
[tex]\begin{gathered} F(x)=\frac{x^4}{4}+3x^2-4x-8 \\ \\ F(8)=\frac{8^4}{4}+3(8)^2-4(8)-8 \\ \\ F(8)=1024+192-32-8 \\ \\ F(8)=1216-40 \\ \\ F(8)=1176 \end{gathered}[/tex]Solve the system of two linear inequalities graphically,4x + 6y < 24(x22Step 1 of 3 : Graph the solution set of the first linear inequality.AnswerKeypadKeyboard ShortcutsThe line will be drawn once all required data is provided and will update whenever a value is updated. The regions will be added once the line is drawn.Enable Zoom/PanChoose the type of boundary line:Solid (-) Dashed (--)Enter two points on the boundary line:10-5Select the region you wish to be shaded:
Answers
Answer:
To solve the system of two linear inequalities graphically,
[tex]\begin{gathered} 4x+6y<24 \\ x\ge2 \end{gathered}[/tex]For step 1,
Draw a line 4x+6y=24
Since the given equation has less than sign, the required region will not include the line, Hence we draw the dashed line for the line 4x+6y=24.
Since we required redion is 4x+6y<24, the points bellows the line satisfies the condition hence the required region is below the line,
Similarly for the inequality,
[tex]x\ge2[/tex]It covers the region right side of the line x=2,
we get the siolution region as the intersecting region of both inequality which defined in the graph as,
Dark blue shaded region is the required solution set for the given inequalities.
Question 8 of 10What is the slope of the line described by the equation below?y=-x+ 8A. 8B. 1OOOC. -8O D.-1SUBMIT
Answers
We have the following equation
y = -x + 8
this equation is writen in slope intercept form
y = mx + b
where m is the slope
From the above, we can see that the slope is m = -1