Answers
Given:
[tex]4x-39>-43and8x+31<23[/tex]Solve the inequality separately,
[tex]\begin{gathered} 4x-39>-43 \\ 4x>-43+39 \\ 4x>-4 \\ x>-1 \end{gathered}[/tex]Also,
[tex]\begin{gathered} 8x+31<23 \\ 8x<23-31 \\ 8x<-8 \\ x<-1 \end{gathered}[/tex]As the given inequality give x > -1 and x < -1 it shows that there is no solution for the given inequality.
The graph is given as,
The red region shows the inequality 4x -39 > -43 and blue region shows 8x +31 < 23.
Answer: Option D.
Related Questions
You deposit 500$ in a savings account that earns 2.5 interest compounded yearly. Find the balance in the account after the given amount of time A. 1 yearB. 5 years C. 20 years
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In order to find the balance after the given time, use the following formula:
I = P(1 + r/n)^(t·n)
where
r: interes rate = 2.5% = 0.025
n: frequency = 1
t: time = 1, 5, 20
P: principal investment = 500
replace the previous values of the parameters into the formula for I:
A. 1 year:
I = $500(1 + 0.025/1)^(1·1) = $512.5
B. 5 years:
I = $500(1 + 0.025)^(5·1) = $565.7
C. 20 years
I = $500(1 + 0.025)^(20·1) = $819.3
which statement best describes the changes to the graph when the coefficient of x^2 is multiplied by 1/2?A. the parabola will get narrower.B. the parabola will get wider.C. the parabola will shift to the right by 1/2 unit.D. the parabola will shift to the left by 1/2 unit.
Answers
B. The parabola will get wider
Explanatiion:The graph for the function x² is shown in the question
The graph x² is multiplied by 1/2. The new function becomes 1/2 x²
Let us plot the graph of 1/2 x² to compare with the graph of x² that has already been given
The graph of 1/2 x² is plotted above
As shown, it is obvious from the graphs of 1/2 x² and x² that the graph of 1/2 x² is wider than the graph of x²
the sum of pi and 3/4 is a (n)_________ numberA. RationalB. NaturalC. WholeD. Irrational
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Remember that pi is an irrational number which means it has infinite decimal without a pattern.
If we add a number to pi we would still get an irrational number because the sum of a rational and an irrational won't give another type of number than an irrational.
Therefore, the right answer is D.a backyard sandbox shaped like a right rectangular prisms is 0.45 meters high 2 m 2.6 m long if the sand is the box is 0.25 m deep what volume of sand is the box?
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In order to determine the volume of the sand inside the box, take into account that the shape of the volume of the sand inside the box is the same that the rectangular prism. Then, you can use the folowing formula for the volume of the sand:
V = w·h·l
where w is the width, h the height and l the length. In this case, the height of the sand is 0.25m and the width and the length are the same of the box.
w = 2 m
l = 2.6 m
h = 0.25 m
replace the previous values of the parameters into the formula for V:
V = (2 m)(2.6 m)(0.25 m)
V = 1.3 m³
Hence, the volume of the sand inside the box is 1.3 m³
A pyramid has a square base of 120ft. On a side. The four slant faces are all congruent isosceles triangles with base angles 55 degrees. Find the height of the pyramid?
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Our first approach will be to get the slant height, i.e. the sides of the triangle. We can get this via the sine rule as:
We can get the side of the isosceles to be:
[tex]\begin{gathered} \frac{120}{\sin70}=\frac{x}{\sin 55} \\ x=\frac{120\sin 55}{\sin 70}=104.6ft \end{gathered}[/tex]Now we need to find the perpendicular height.
To do that, we need to find the length of the diagonal of the base. We will apply the Pythagoras theorem.
This is given as:
[tex]\begin{gathered} d=\sqrt[]{o^2+a^2} \\ \text{ Where:} \\ o=\text{opposite = length of base} \\ a=\text{adjacent = length of base} \end{gathered}[/tex][tex]\begin{gathered} d=\sqrt[]{120^2+120^2} \\ d=170\text{ ft} \end{gathered}[/tex]Next, we plot the triangle that will help us get our perpendicular height.
We now find h.
[tex]\begin{gathered} h=\sqrt[]{104.6^2-85^2} \\ h=60.96\text{ ft} \end{gathered}[/tex]The perpendicular height is 60.96 ft
my question:solve the equation or inequality.5t - 3 (7t + 1) < 93would the answer be 7 > -6?
Answers
Answer:
Explanation:
To solve the inequality for t, we first expand the left-hand side to get:
[tex]5t-21t-3<93[/tex]adding the like terms gives
[tex]-16t-3<93[/tex]adding 3 to both sides gives
[tex]-16t<96[/tex]At this point, we have to remember that dividing or multiplying an inequality by a negative number reverses its sign. So when we divide our inequality by -16, the inequality reverses sign and we get:
[tex]t>-\frac{96}{16}[/tex][tex]\boxed{\therefore t>-6.}[/tex]which is our answer!
given the function given the function f of x equals 5 (x + 4) ^ 3/2 which of the following represent its y-intercept
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Graph y=3/4x+2. i got the y intercept but i don’t know how to do the other point
Answers
ANSWER
EXPLANATION
Once we have the y-intercept we have to find another point - since two points are enough to draw a line. To find this other point we can use the slope of the line. We can write the slope of a line as:
[tex]m=\frac{\text{rise}}{\text{run}}[/tex]In this line rise = 3 and run = 4. This means that the other point is 4 units to the right of the y-intercept and 3 units up:
Mark this new point and draw a line through both points.
For the following pair of variables state the units that might be used to measure each variable. then state whether you believe that the two variables are correlated .if you believe they are correlated, state whether the correlation is positive or negative. explain your reasoningTo measure fertility rate for women the unit _ might be used. to measure life expectancy the unit _ might be used. what correlation if any is there between the variables?
Answers
Problem
For the following pair of variables state the units that might be used to measure each variable. then state whether you believe that the two variables are correlated .if you believe they are correlated, state whether the correlation is positive or negative. explain your reasoningTo measure fertility rate for women the unit _ might be used. to measure life expectancy the unit _ might be used. what correlation if any is there between the variables?
Solution
To measure fertility rate for women the number of births per 1000 women might be used.
To measure life expectancy the years might be used.
what correlation if any is there between the variables?
For this case we would expect that the correlation would be positive. With higher number of life expectancy years we would expect a higher number of births
A plane is 110 mi north and 189 mi east
Answers
ANSWER:
30.2°
STEP-BY-STEP EXPLANATION:
The angle x can be calculated by means of the tangent trigonometric ratio, which relates the opposite leg to the adjacent leg, just like this:
[tex]\begin{gathered} \tan x=\frac{\text{ opposite}}{\text{ adjacent }} \\ \text{ opposite = 110} \\ \text{ adjacent = 189} \end{gathered}[/tex]We substitute and calculate for x just like this:
[tex]\begin{gathered} \tan\:x\:=\:\frac{110}{189} \\ x=\tan^{-1}\left(\frac{110}{189}\right) \\ x=30.2\degree \end{gathered}[/tex]Therefore, the angle is 30.2°
A small office supply store sells paper clipsin packs of 100 and packs of 250. If thestore has 84 packs of paper clips in stocktotaling 12,300 paper clips, how manypaper clips would a customer buy if he buyshalf of the packs of 250 that the store hasin stock?
Answers
The first equation should represent the total number of packs, each with 100 or 250 paper clips
i,e. x + y = 84 (1)
The second equation should represent the total number of paper clips. Because x represents packs with 100 paper clips and y represents packs with 250 paper clips, the second equation is
100x + 250y = 12,300 (2)
Simplify the linear equation;
x + y = 84
x = 84 - y
Substitute the value of x = 84 - y in the equation (2);
100x + 250y = 12300
100(84 - y) + 250y = 12300
8400 - 100y + 250y = 12300
8400 + 150y = 12300
150y = 12300 - 8400
150y = 3900
y = 3900/150
y = 26
Substitute the value of y = 26 in the equation x = 84 - y
x = 84 - y
x = 84 - 26
x = 58
The store has 26 packs of 250 paper clips in stock.
The customer would buy 13 × 250 = 3,250 paper clips,
Answer : 3250
Fidn the x intercept(s) and the coordinates of the vertex for the parabola y=x^2-8x+12 if there is more then one x intercept esperate them with commas!
Answers
To calculate the x-intercepts we replace y=0 and solve for x
[tex]x^2-8x+12=0[/tex]where a is 1, b is -8 and c 12
so factor the expression using
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]replacing
[tex]\begin{gathered} x=\frac{-(-8)\pm\sqrt[]{(-8)^2-4(1)(12)^{}}}{2(1)} \\ \\ x=\frac{8\pm\sqrt[]{64-48}}{2} \\ \\ x=\frac{8\pm\sqrt[]{16}}{2} \\ \\ x=\frac{8\pm4}{2} \\ \\ x=4\pm2 \end{gathered}[/tex]so x have two solutions because there are two x-intercepts
[tex]\begin{gathered} x_1=4+2=6 \\ x_2=4-2=2 \end{gathered}[/tex]then the x-intercepts are 6 and 2, the corrdinates are
[tex]\begin{gathered} (6,0) \\ (2,0) \end{gathered}[/tex]Vertex
the vertex is a point (x,y) to calculate x we use
[tex]x=\frac{-b}{2a}[/tex]and replace
[tex]\begin{gathered} x=\frac{-(-8)}{2(1)} \\ \\ x=\frac{8}{2}=4 \end{gathered}[/tex]now replace x=4 on the equation of the parable to find y
[tex]\begin{gathered} y=x^2-8x+12 \\ y=(4)^2-8(4)+12 \\ y=16-32+12 \\ y=-4 \end{gathered}[/tex]the coordinate of the vertex is
[tex](4,-4)[/tex]Henry runs up 10 flights of stairs.Then, he runs down 10 flights of stairs.Does this situation represent additiveinverses? Explain.
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Problem
Henry runs up 10 flights of stairs. Then, he runs down 10 flights of stairs. Does this situation represent additive inverses? Explain.
solution
For this case we know that Henry runs up 10 stairs and thenhe goes down 10 stairs so for this case yes that represent additive inverses because the net operation is:
10 +(-10)=0
And he back againt to 0
Which graph shows the solution to this system of linear inequalities?y2 2x+3ys-2x-4
Answers
To solve this problem, we will graph the solution set of each inequality and the solution to the system will be the intersection of the solution sets.
Graph of the solution set of the first inequality:
Graph of the solution set of the second inequality:
The graph of the overlap of the solution sets is:
Answer: Option B.Suppose f(x) = x. Find the graph of f(x + 2).graph 1, 2, 3, or 4
Answers
Master Level2. Brandon is wrapping the present shown below. How many square centimeters ofwrapping paper will he need?Height: 7 cmWidth:10 cmLength: 22 cm
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Given the following:
Height = 7cm
Width = 10cm
length = 22cm
We were asked to find the number of square centimeters of wrapping paper Brandon will be needing.
To solve for this, we will be using the total surface formula.
Total surface formula (SA) = 2lw + 2lh + 2hw)
factoring out 2
SA = 2(lw + lh + hw)
lw = 22 x 10 = 220cm²
lh = 22 x 7 = 154cm²
hw = 7 x 10 = 70cm²
So,
SA =2(220 + 154 + 70)
SA = 2(644)
SA = 1288cm²
I don’t know if it’s maximum value or minimum value and the answer too
Answers
Answer:
The minimum value is 0
Step-by-step explanation:
If there is a negative sign in front of the x^2 it is always a maximum (-x^2 goes downwards)
If the x^2 is positive it always a minimum.
You have the correct ordered pair, the minimum value is equal to the y value.
Calculate the area of the region enclosed by the x-axis and the curve y(x)=−x^2−3x+4.(show a figure and detailed answer please)
Answers
Given that the region is enclosed by the x-axis and this curve:
[tex]y=-x^2-3x+4[/tex]You can graph the function using a Graphic Tool:
Noice that the area region you must calculate is:
Notice that it goes from:
[tex]x=-4[/tex]To:
[tex]x=1[/tex]Therefore, you can set up that:
[tex]Area=\int_{-4}^1(x^2-3x+4)-(0)dx[/tex]In order to solve the Definite Integral, you need to:
- Apply these Integration Rules:
[tex]\int x^ndx=\frac{x^{n+1}}{n+1}+C[/tex][tex]\int kf(x)dx=k\int f(x)dx[/tex]Then, you get:
[tex]=(\frac{x^3}{3}-\frac{3x^2}{2}+4)|^1_{-4}[/tex]- Evaluate:
[tex]=(\frac{1^3}{3}-\frac{3(1)^2}{2}+4)-(\frac{(-4)^3}{3}-\frac{3(-4)^2}{2}+4)[/tex][tex]Area\approx64.17[/tex]Hence, the answer is:
[tex]Area\approx64.17[/tex]Do you go to the movies at least twice a week?Yes No TotalMale 35 45 80Female 67 28 95Total 102 73 175Jasmine wants to find out how manystudents at her school go to themovies at least twice a week. Sheinterviews 175 students and recordstheir gender and a yes if they go atleast twice a week and no if they goless than twice a week. She displaysthe results in the table.What is the probability that a personwho does not go to the movies atleast twice a week is male (round tothe thousandth)?
Answers
We have to determine the probability that a person who does not go to the movies at least twice a week is male.
From the table , it is given that there are total 73 students who does not go to school atleast twice a week.
Also, the number of male students whod does not go to school atleast twice a week is, 45.
Therefore, the probability that a person who does not go to the movies at least twice a week is male is determined as.
[tex]P=\frac{45}{73}[/tex][tex]P=0.61643[/tex]Evaluate the expression when y= -4.y²-7y+2
Answers
Put y = -4 into the expression below:
[tex]y^2-7y+2[/tex]Hence,
[tex]\begin{gathered} y^2-7y+2=(-4)^2-7(-4)+2 \\ =16+28+2 \\ =46 \end{gathered}[/tex]Therefore, the value of the expression when y = -4 is 46
Write in standard form the equation of a line passing through the point (-3, 4) and having the slope m = 2.
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then the equation in standard form:
[tex]\begin{gathered} y=mx+b \\ y=2x+10 \end{gathered}[/tex]The box plots represent the length of 100 randomly sampled commercial breaks for two different television stations Length of Commercial Breaks Channel 1 Channel 2 20 40 60 140 160 80 100 120 Time (seconds) Which statement about the difference in the medians of the two data sets is true?
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Given data:
The length of the first commercial break is,
[tex]\begin{gathered} C_1=(120-90) \\ =30 \end{gathered}[/tex]The length of the second commercial break is,
[tex]\begin{gathered} C_2=(90-50) \\ =40 \end{gathered}[/tex]The expression for the diffrence compared to the first channel is,
2? + kI - 20limI-5I - 5Solve for k to make it exist?
Answers
Answer:
k = -1
Step-by-step explanation:
The limit will exist if:
One of the roots of the equation in the numerator is 5. This happens because if this happens, we can simplify with the denominator. So
Solving a quadratic equation:
In the following format:
ax² + bx + c = 0
The solution is given by:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this question:
x² + kx - 20 = 0
The solution is:
[tex]x=\frac{-k\pm\sqrt[]{k^2-4\ast1\ast(-20)}}{2}=\frac{-k\pm\sqrt[]{k^2-80}}{2}[/tex]Since we want x = 5.
[tex]\frac{-k+\sqrt[]{k^2+80}}{2}=5[/tex][tex]-k+\sqrt[]{k^2-80}=10[/tex][tex]\sqrt[]{k^2+80}=10+k[/tex][tex](\sqrt[]{k^2+80})^2=(10+k)^2[/tex][tex]k^2+80=100+20k+k^2[/tex][tex]k^2+80-100-20k-k^2=0[/tex][tex]-20-20k=0[/tex][tex]20k=-20[/tex][tex]k=\frac{-20}{20}=-1[/tex]k = -1
16. – 2y+5=-1IIs 3 the solution?
Answers
We plug the value given to see tif the equation holds:
[tex]\begin{gathered} -2(3)+5=-1 \\ -6+5=-1 \\ -1=-1 \end{gathered}[/tex]Since the equation holds then, 3 IS the solution.
What survey contains the best example of a sampling error
Answers
Answer:
The correct option is the second one: "a survey of high school students to determine the favorite type of doll"
This is a sampling error, because it's very unlikely that high school students have a favorite doll, and the results won't be very use
USH financial is a small bank that is examining it’s customers use of its website. The numbers of online transactions made per day during the past 8 days are as follows.
Answers
Given:
The number of online transaction made per day during tha past 8 days are given as follows
51, 57, 71, 57, 55, 62, 51, 65
Find:
we have to find Mean, Median and mode of the given data.
Explanation:
(a)Mean
Mean of the given data is
[tex]\begin{gathered} Mean=\frac{51+57+71+57+55+62+51+65}{8} \\ Mean=58.6 \end{gathered}[/tex]Therefore, Mean is 58.6
(b) Median
Write the given data values in ascending order as following
51
51
55
57 Now n = 8
57 n/2 = 4
62 Median = Average of 4th and 5th items
65 Median = (57 + 57)/2 = 57
71
Therefore, Median is 57
(c)Mode
We know, the Mode is the value or values that occur most frequently.
Since 51 occurs 2 times and 57 also occurs 2 times.
Therefore, there are two modes, which are 51 and 57
do the data in the table Represent a linear function?
Answers
Answer:
The correct option is the last one "no"
Explanation:
To see if the table represents a linear function, we can mark each point in the cartesian plane and connect them with a line. If all of the points lie in the line, then the table represents a linea
43)Solve the system 4x+2y=-3 4x-3y=22A. (7, –5)B. (7/4, –5)C. (7/4, 5)D. (4, –5)
Answers
Given,
The linear pair of equations are:
[tex]\begin{gathered} 4x+2y=-3 \\ 4x-3y=22 \end{gathered}[/tex]Required
The solution of the pairs of equations.
Taking the first equation as,
[tex]\begin{gathered} 4x+2y=-3 \\ 2y=-4x-3 \\ y=-2x-1.5 \end{gathered}[/tex]Substituting the value of y in second equation then,
[tex]\begin{gathered} 4x-3y=22 \\ 4x-3(-2x-1.5)=22 \\ 4x+6x+4.5=22 \\ 10x=17.5 \\ x=1.75 \\ x=\frac{7}{4} \end{gathered}[/tex]Substituting the value of x in first equation,
[tex]\begin{gathered} y=-2x-1.5 \\ y=-2(1.75)-1.5 \\ y=-3.5-1.5 \\ y=-5 \end{gathered}[/tex]Hence, the solution of the system is(7/4, -5).
(-79.2x + 80) +(74.5x -89y) in standard form
Answers
Ok, so:
We want to write (-79.2x + 80) +(74.5x -89y) in standard form:
So, -79.2x + 80 + 74.5x - 89y is equal to:
-4.7x - 89y + 80.
Then, -89y = 4.7x - 80
And finally, y = ((-4.7)/(89))x + 80/89
6,9x,y3,3I need to find a equation relating to x and y
Answers
Answer:
[tex]y=2x-3\rightarrow Slope-intercept\text{ form}[/tex]Step by step explanation:
As a first step to find the equation of the line, we need to calculate the slope.
The slope is represented by the following equation:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{where,} \\ \text{ (x}_1,y_1)and(x_2,y_2)_{}_{} \\ \text{are the points given} \end{gathered}[/tex]Then, the slope of the line would be:
[tex]\begin{gathered} m=\frac{9-3}{6-3} \\ m=\frac{6}{3} \\ m=2 \end{gathered}[/tex]Then, by the slope-point form of the line we can get slope-intercept form:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=2(x-3) \\ y=2x-6+3 \\ y=2x-3\rightarrow Slope-intercept\text{ form} \end{gathered}[/tex]