Solution:
Given the inequality:
[tex]|3x+3|+3>15[/tex]To solve the inequality,
step 1: Add -3 to both sides of the inequality.
Thus,
[tex]\begin{gathered} |3x+3|+3-3>-3+15 \\ \Rightarrow|3x+3|>12 \end{gathered}[/tex]Step 2: Apply the absolute rule.
According to the absolute rule:
[tex]\mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad \mathrm{or}\quad \:u\:>\:a[/tex]Thus, from step 1, we have
[tex]\begin{gathered} 3x+3<-12\text{ or 3x+3>12} \\ \end{gathered}[/tex][tex]\begin{gathered} when \\ 3x+3<-12 \\ add\text{ -3 to both sides of the inequality} \\ 3x-3+3<-3-12 \\ \Rightarrow3x<-15 \\ divide\text{ both sides by the coefficient of x, which is 3} \\ \frac{3x}{3}<-\frac{15}{3} \\ \Rightarrow x<-5 \end{gathered}[/tex][tex]\begin{gathered} when \\ 3x+3>12 \\ add\text{ -3 to both sides of the inequality} \\ 3x+3-3>12-3 \\ \Rightarrow3x>9 \\ divide\text{ both sides by the coefficient of x, which is 3} \\ \frac{3x}{3}>\frac{9}{3} \\ \Rightarrow x>3 \end{gathered}[/tex]This implies that
[tex]x<-5\quad \mathrm{or}\quad \:x>3[/tex]Hence, in interval notation, we have:
[tex]\left(-\infty\:,\:-5\right)\cup\left(3,\:\infty\:\right)[/tex]I need help question
Solution
- The first integral is bounded by the x-values of [6, 22]
- The second integral is bounded by the x-values of [6, 14]
- When we are asked to find the difference between the two integrals, since, they both begin at 6, it implies that, when the second integral is taken away from the first integral, there must be some extra x-values.
- The extra values are from 14 to 22.
- Thus, we have:
[tex]\int_6^{22}f(x)-\int_6^{14}f(x)=\int_{14}^{22}f(x)[/tex]Final Answer
[tex]\begin{gathered} b=22 \\ a=14 \end{gathered}[/tex]P is inversely proportional to Q. If P = 24 when Q = 3, then write the inverse variation equation that relates P and Q.
Inverse proportionality is when the value of one quantity increases with respect to a decrease in another, they behave opposite in nature.
It is represented by the following expression:
[tex]P=\frac{k}{Q}[/tex]Since P=24 when Q=3, we can substitute and solve for the constant k:
[tex]\begin{gathered} 24=\frac{k}{3} \\ k=24\cdot3 \\ k=72 \end{gathered}[/tex]Then, the equation that represents the inverse variation would be:
[tex]P=\frac{72}{Q}[/tex]Hi, could you help me figure out why I got 8 points off in this problem?
In triangle PQR
Construction: Draw PX perpendicular to QR where x lies on QR
Since:
PX perpendicular to QR
In the 2 triangles PXQ and PXR
given
proved up
PX = PX ------- common side in the 2 triangles
Triangle PXQ congruent to triangle PXR by the AAS theorem of congruency
As a result of congruency
PQ = PR ------- proved
In triangle XYZ, | XZ | = | YZ | ∆YXZ = 40⁰ and ∆XZY = (13x - 20)⁰. Find the value of x.
Given the triangle XYZ with the following parameters
[tex]\begin{gathered} |XZ|=|YZ| \\ \measuredangle YXZ=40^0 \\ \measuredangle XZY=(13x-20)^0 \\ \text{Therefore} \\ \measuredangle ZYX=40^0 \end{gathered}[/tex]The diagram of the triangle is shown below
To find the value of x, we will apply sum of interior angle of triangle theorem
[tex]\begin{gathered} 40^0+40^0+(13x-20)^0=180^0(\text{ sum of angles in a triangle)} \\ 80^0+13x-20^0=180^0 \\ 13x+60^0=180^0 \\ 13x=180^0-60^0 \\ 13x=120^0 \\ x=\frac{120^0}{13} \\ x=9.2308^0 \end{gathered}[/tex]Hence, the value of x is 9.2308°
A lighthouse beacon will illuminate to a distance of 12 km. If the lighthouse is located at (-5,2) on a grid, find the equation of the location of the furthest points lit the beacon.
Light house is located at (-5,2)
Lighthouese beacon will illuminate a distnce =12 km
Use the distance formula to find the equation :
Distance formula is expressed as :
[tex]\begin{gathered} (x-a)^2+(y-b)^2=c^2 \\ \text{where (a,b) \& (x,y) are the coordinates and c is the distance} \end{gathered}[/tex]Substitute the given values :
[tex]undefined[/tex]The diameter of a circle has endpoints P(-12, -4) and Q(6, 12).
ANSWER
[tex](x+3)^{2}+(y-4)^{2}=145[/tex]EXPLANATION
The equation of a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h, k) = center of the circle
r = radius of the circle
The center of a circle is the midpoint of the endpoints of the diameter of the circle. Hence, to find the center of the circle, we have to find the midpoint of the diameter:
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]where (x1, y1) and (x2, y2) are the endpoints of the diameter.
Hence, the center of the circle is:
[tex]\begin{gathered} M=(\frac{-12+6}{2},\frac{-4+12}{2}) \\ M=(\frac{-6}{2},\frac{8}{2}) \\ M=(-3,4) \end{gathered}[/tex]To find the radius of the circle, we have to find the distance between any endpoint of the circle and the center of the circle.
To do this apply the formula for distance between two points:
[tex]r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Therefore, the radius of the circle is:
[tex]\begin{gathered} r=\sqrt{(6-(-3))^2+(12-4)^2}=\sqrt{9^2+8^2} \\ r=\sqrt{81+64}=\sqrt{145} \end{gathered}[/tex]Hence, the equation of the circle is:
[tex]\begin{gathered} (x+3)^2+(y-4)^2=(\sqrt{145})^2 \\ (x+3)^2+(y-4)^2=145 \end{gathered}[/tex]The stock price for dgy was $38.21. In June. In July the stocked had in by 7 percent, but in August the price fell by 7 percent. What was the price of dgy stock in august . Round your answer to nearest cent , if necessary
The initial price is $38.21, and it got an increase of 7%, so the new price is the old one multiplied by 1.07:
[tex]38.21\cdot1.07=40.88[/tex]Then, the new price decreased by 7%, so let's multiply it by 0.93 (that is, 1 minus 0.07):
[tex]40.88\cdot0.93=38.02[/tex]So the price in August is $38.02.
I have a practice problem that I need help on.These are included in the problem as well Where did Arjun make errors?Explain his errors and the properties of logarithms that leads to the answer. State the correct answer.
Arjun applied the wrong laws of logarithms.
The question can be solved as shown below:
[tex]\log _7x+\log _7y+\log _7z[/tex]Step 1: Apply the addition rule of logarithm given as
[tex]\log _am+\log _an=\log _a(m\cdot n)[/tex]Thus, we have:
[tex](\log _7x+\log _7y)+\log _7z=\log _7(x\cdot y)+\log _7z[/tex]Step 2: Apply the subtraction rule of logarithm given as
[tex]\log _am-\log _an=\log _a(\frac{m}{n})[/tex]Thus, we have:
[tex]\log _7(x\cdot y)+\log _7z=\log _7(\frac{x\cdot y}{z})[/tex]Therefore, the correct answer is:
[tex]\log _7x+\log _7y+\log _7z=\log _7(\frac{xy}{z})[/tex]find the value of x
For supplementary angles, we can do the following equality
[tex]3x+4=x+70[/tex]What we have to do, is to clear "x" to find its value.
[tex]\begin{gathered} 3x-x=70-4 \\ 2x=66 \\ x=\frac{66}{2} \\ x=33 \end{gathered}[/tex]In conclusion, the value of x is 33
An observer for a radar station is located at the origin of a coordinate system. For the point given, find the bearing of an airplane located at that point. Express the bearing using both methods.(-8,0)
Given,
The coordinates of the point is (-8, 0).
There are two methods of bearing is:
Compass bearing
True bearing.
The figure of the point is,
The bearing of the point with respect to anticlockwise from north is,
[tex]\begin{gathered} \tan \theta=\frac{y}{x} \\ \tan \theta=\frac{0}{-8} \\ \theta=\tan ^{-1}0 \\ \theta=0^{\circ} \\ \text{Bearing from north=(90}^{\circ}-0^{\circ})=90^{\circ} \end{gathered}[/tex]The bearing of point from west is 0 degree and from anticlockwise north is 90 degree.
The true bearing is,
[tex]\begin{gathered} \theta=0^{\circ} \\ B=(360^{\circ}-90^{\circ}) \\ B=270^{\circ} \end{gathered}[/tex]Write the slope-intercept form of the equation of the line with the given characteristics. Perpendicular to y = -5x + 2 and passing through (3,-1).
The slope intercept form of a line can be expressed as,
[tex]y=mx+c[/tex]Here, m is the slope of the line and c is the y intercept.
Comparing the above equation with the given equation of a line y=-5x+2, we get
m=-5.
The slope of a line perpendicular to line with slope m is -1/m.
Hence, the slope of line perpendicular to y=-5x+2 is,
[tex]m_1=\frac{-1}{m}=\frac{-1}{-5}=\frac{1}{5}[/tex]The new line is given to be passing through point with coordinates (x1, y1)=(3, -1).
The point slope form of a line passing through point with coordinates (x1, y1)=(3, -1) and having slope m1 is,
[tex]\begin{gathered} y-y_1=m_1(x-x_1) \\ y-(-1)=\frac{1}{5}(x-3) \\ y+1=\frac{1}{5}x-\frac{3}{5} \\ y=\frac{1}{5}x-\frac{3}{5}-1 \\ y=\frac{1}{5}x-\frac{3-5}{5} \\ y=\frac{1}{5}x-\frac{8}{5} \end{gathered}[/tex]Therefore, the slope-intercept form of the equation of the line perpendicular to y = -5x + 2 and passing through (3,-1) is,
[tex]y=\frac{1}{5}x-\frac{8}{5}[/tex]Let the graph of f(x) be given below. Find the formula of f(x), a polynomial function, of least degree.
To detrmine the formula of the polynomial, we check for the roots on the graph:
when y = 0, x = -2
when y = 0, x = 4
We have two roots.
x = -2
x + 2 = 0
x = 4
x - 4 = 0
3rd factor is x = 0
Hence, we have two factors: x(x + 2) and (x - 4)
The polynomial function using the factors:
[tex]f(x)\text{ = ax(x + 2)(x - 4)}[/tex]Next, we find the value of a:
To get a , we pick a point on the graph. let the point be (0, -4)
substitute the point in the function above:
[tex]\begin{gathered} f(x)\text{ = y = -4, x = 0} \\ -4\text{ = a(0 + 2) (0 - 4)} \\ -4\text{ = a(2)(-4)} \\ -4\text{ = -8a} \\ a\text{ = -4/-8} \\ a\text{ = 1/2} \end{gathered}[/tex]The formula of the polynomial becomes:
[tex]f(x)\text{ = }\frac{1}{2}x(x\text{ }+2)(x-4)[/tex]Pls help with my hw pls
Which equation shows a proportional relationship? options: O y = x O y + 1 = 7x O y - 2 = x + 8 O x = y + 5
A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:
y = kx
for some constant k , called the constant of proportionality . This means that as x increases, y increases and as x decreases, y decreases-and that the ratio between them always stays the same.
From the given options, the baove property is satisfied by,
[tex]y=\frac{2}{3}x[/tex]Thus, the correct option is A.
Figure 2 is a scaled copy of Figure 1.B.Figure 1AsADMYColJFigure 2MYHKProIdentify the side in Figure 2 that corresponds to side BC in Figure 1.
Figure 1 was enlarged to figure 2
Hence the side |AB| is corresspounding to the side |PQ|
Garret is removing a hem from a skirt. It takes
Garret 5 min to remove 4 in. of the hem. He wants to
know how long it will take to remove 5 ft of the hem if
he continues to work at the same rate.
Lavar
How can Garret determine how long it will take to remove 5 ft of the hem?
Choose one option from each drop-down menu to answer the question.
It takes Garret Choose... min to remove 1 ft of hem.
He should multiply the number of minutes by Choose... to determine the number of minutes it will take to
remove 5 ft of hem.
It will take Choose.... min to remove 5 ft of hem.
It takes Garret Choose min to remove 1 ft of hem. He should multiply the number of minutes by Choose... to determine the number of minutes it will take to remove 5 ft of hem.
What is the unitary method?The unitary method is a technique used to determine the value of a single unit from the value of many units and the value of multiple units from the value of a single unit. We typically utilize it for math calculations. This approach will come in handy for topics involving ratio and proportion, algebra, geometry, etc. In the unitary technique, we always count the value of a unit or one quantity first before figuring out the values of more or fewer quantities. This method is referred to as the "unitary method" for this purpose.
There are two types of unitary methods because they result in two types of variations and those are given below:
Direct VariationIndirect VariationTo know more about the unitary method ,visit:
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I need the slope the y intercept is -2 and the x intercept is -1
The x intercept is the value of x when y = 0
Given that x intercept = - 1, the coordinate is (- 1, - 0)
The y intercept is the value of y when x = 0
Given that y intercept = - 2, the coordinate is (0, - 2)
Slope = (y2 - y1)/(x2 - x1)
x1 = - 1, y1 = 0
x2 = 0, y2 = - 2
Slope = (- 2 - 0)/(0 - - 1)
slope = - 2/1
slope = - 2
Solve the system by graphing:2x – y= -14x - 2y = 6Solution(s):
To find the solution of the system by graphing we need to plot each line in the plane and look for the intersection.
First we need to write both equations in terms of y:
[tex]\begin{gathered} y=2x+1 \\ y=2x-3 \end{gathered}[/tex]now we need to find two points for each of this lines. To do this we give values to the variable x and find y.
For the equation 2x-y=-1, if x=0 then:
[tex]y=1[/tex]so we have the point (0,1).
If x=1, then:
[tex]y=3[/tex]so we have the point (1,3).
Now we plot this points on the plane and join them with a straight line.
Now we look for two points of the second equation.
If x=0, then:
[tex]y=-3[/tex]so we have the point (0,-3)
If x=1, then:
[tex]y=-1[/tex]so we have the point (1,-1).
We plot the points and join them wiith a line, then we have:
once we have both lines in the plane we look for the intersection. In this case we notice that the lines are parallel; this means that they wont intersect.
Therefore the system of equations has no solutions.
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
the rriangle is 3 4 5 triangle so 5×5 is 25
in a recent year the annual salary of the governor of New York was 1790000 during the same year the annual salary of the governor of Tennessee was 940000 less write and solve an equation to find the annual salary of the government of Tennessee in that year
Step 1 : Let's review the information given to us to answer the problem correctly:
• Annual salary of the governor of New York = $ 1,790,000
,• Annual salary of the governor of Tennessee = $ 940,000
Step 2: Let x to represent the annual salary of the governor of New York
and let's find the ratio of the salary of the governor of Tennessee, as follows:
940,000/1,790,000 = 0.525
Step 3: Now, let's write the equation for calculating the salary of the governor of Tennessee for any given year, this way:
• 0.525x = Annual salary of the governor of Tennessee
,•
Step 4: If the salary of the governor of New York for the next year is 2,000,000, then we can calculate the salary of the governor of Tennessee, this way:
0.525x = 0.525 * 2,000,000 = 1,050,000
The annual salary of the governor of Tennessee woudl be 1,050,000
Ninas math classroom is 6 and 4/5 meters long and 1 and 3/8 meters wide. What is the area of the classroom?
The most appropriate choice for area of rectangle will be given by -
Area of classroom = [tex]4\frac{27}{40}[/tex] [tex]m^2[/tex]
What is area of rectangle?
Rectangle is a four sided figure whose parallel sides are equal and whose every angle is 90°
The total space taken by the rectangle is called area of the rectangle.
If the length of the rectangle be l and the breadth of the rectangle be b, then area of the rectangle is given by
Area = [tex]l \times b[/tex]
Here,
Length of classroom = [tex]6\frac{4}{5}[/tex] m = [tex]\frac{34}{5}[/tex] m
Width of classroom = [tex]1\frac{3}{8}[/tex] m = [tex]\frac{11}{8}[/tex] m
Area of classroom = [tex]\frac{34}{5} \times \frac{11}{8}[/tex]
= [tex]\frac{187}{40}[/tex]
= [tex]4\frac{27}{40}[/tex] [tex]m^2[/tex]
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could someone please help :(
Given from the number line:
D = -2 and F = 13
So, the distance DF = 13 - (-2) = 13 + 2 = 15
1) find E such that, DE : EF = 2 : 1
so,
so, x : (15 - x) = 2 : 1
x = 30 - 2x
3x = 30
x = 10
So, E = -2 + 10 = 8
=========================================================================
2) E is 4/5 of the distance from F to D
So, the distance from F = 4/5 * 15 = 12
So, E = 13 - 12 = 1
=====================================================================
3) the ratio of DE : EF = 2 : 3
So,
3x = 2 ( 15 - x)
3x = 30 - 2x
5x = 30
x = 30/5 = 6
E = -2 + 6 = 4
=================================================
4) E is 1/3 of the distance from D to F
So, the distance DE = 1/3 * 15 = 5
So, E = -2 + 5 = 3
=====================================================
As a summery:
1) E = 8
2) E = 1
3) E = 4
4) E = 3
Given the graph of f (x), determine the domain of f –1(x).
Radical function f of x that increases from the point negative 3 comma negative 2 and passes through the points 1 comma 0 and 6 comma 1
The domain of the function f(x) that has a range of [-2, ∞) is [-2, ∞)
What is the inverse of a function?The inverse of a function that maps x into y, maps y into x.
The given coordinates of the points on the radical function, f(x) are; (-3, -2), (1, 0), (6, 1)
To determine the domain of
[tex] {f}^{ - 1}( x)[/tex]
The graph of the inverse of a function is given by the reflection of the graph of the function across the line y = x
The reflection of the point (x, y) across the line y = x, gives the point (y, x)
The points on the graph of the inverse of the function, f(x), [tex] {f}^{ - 1} (x)[/tex] are therefore;
[tex]( - 3, \: - 2) \: \underrightarrow{R_{(y=x)}} \: ( - 2, \: - 3)[/tex]
[tex]( 1, \: 0) \: \underrightarrow{R_{(y=x)}} \: ( 0, \: 1)[/tex]
( 6, \: 1) \: \underrightarrow{R_{(y=x)}} \: ( 1, \: 6)
The coordinates of the points on the graph of the inverse of the function, f(x) are; (-2, -3), (1, 0), (1, 6)
Given that the coordinate of point (x, y) on the image of the inverse function is (y, x), and that the graph of the function, f(x) starts at the point (-3, -2) and is increasing to infinity, (∞, ∞), such that the range of y–values is [-2, ∞) the inverse function, [tex] {f}^{ - 1}( x)[/tex], which starts at the point (-2, -3) continues to infinity, has a domain that is the same as the range of f(x), which gives;
The domain of the inverse of the function, [tex] {f}^{ - 1}( x)[/tex], using interval notation is; [-2, ∞)
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Which transformations of quadrilateral PQRS would result in the imageof the quadrilateral being located only in the first quadrant of thecoordinate plane?
Given:
The quadrilateral PQRS is given.
The aim is to locate the given quadrilateral into first quadrant only.
The graph will be reflected across x=4 then the graph will not be located to the first quadrant.
in a public opinion poll 624 people from a sample of 1100 indicated they would vote for specific candidate how many votes can the candidate expect to receive from a population of 40000
Hello!
In a sample of 1100 people, the specific candidate got 624 votes. So, we can write it as 624/1100.
And if the total of voters is 40,000, how many votes this specific candidate will receive? We can write it as x/40,000.
Now, let's equal both fractions look:
[tex]\begin{gathered} \frac{624}{1100}=\frac{x}{40000} \\ \\ 1100x=624\times40000 \\ 1100x=24960000 \\ x=\frac{24960000}{1100} \\ \\ x\cong22691 \end{gathered}[/tex]Answer:Approximately 22691 votes.
Original cost $21.99 Markup 5%. What's the new price?
Explanation:
We have to find 5% of the original cost first:
[tex]21.99\times\frac{5}{100}=21.99\times0.05=1.0995[/tex]And then add it to the original price:
[tex]21.99+1.0995=23.0895[/tex]Since it's a price, we have to round this result to the nearest hundredth
Answer:
The new price is $23.09
Here are the exam scores for the 15 students in Mr. Kirk's statistics class:
72 75 75 78 81 83 85 89 90 90 90 91 95 95 98
Karen was at the 20th percentile of the distribution. What score did Karen earn on the exam?
(A) 75
(B) 78
(C) 81
(D) 83
Use the formula for compound amount:$14,800 at 6% compounded semiannually for 4 years
SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Write the formula for calculating compound amount
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A = final compounded amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
STEP 2: Write the given data
Semiannually means that n will be 2
[tex]P=14,800,r=\frac{6}{100}=0.06,n=2,t=4[/tex]STEP 3: Calculate the compound amount
[tex]\begin{gathered} A=14800(1+\frac{0.06}{2})^{2\times4}\Rightarrow A=14800(1+0.03)^{2\times4} \\ A=14800(1.03)^8 \\ A=14800\times1.266770081 \\ A=\text{\$}18,748.1972 \end{gathered}[/tex]Hence, the compounded amount after 4 years is $18,748.1972
Which expression is equivalent to 8 - (-5) ?O 8+50 -8 +(-5)O 8+-5O -5 +8
Answer:
The first option is correct
[tex]8+5[/tex]Explanation:
[tex]\begin{gathered} 8--5 \\ \\ 8+5 \\ \end{gathered}[/tex]Two negatives makes a positive.
The figure shows rectangle PQRS in the first quadrant of the coordinate plane?
The quadrants of a coordinate plane are:
Then, we can say that the rectangle PQRS is in the first quadrant.