The solution for the given inequality is −8<x<3 or 3<x<7.
The given inequality is (x+8)(x-3)²(x-7)³<0.
What is a inequality?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality can be solved as follows
Solve for x by simplifying both sides of the inequality, then isolating the variable.
Inequality Form: x+8<0
x<-8 (Subtract 8 on both the sides of the inequality)
(x-3)²<0
⇒ x-3<0
⇒ x<3 (Add 3 on both the sides of the inequality)
(x-7)³<0
⇒ x-7<0
⇒ x<7 (Add 7 on both the sides of the inequality)
Solution is −8<x<3 or 3<x<7
Therefore, the solution for the given inequality is −8<x<3 or 3<x<7.
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7. What is the value of z?t50°60°70°
Answer:
50 is next to 70 ,_(60) with the rest
Step-by-step explanation:
(50)_(60)+(70)
A lifeguard is sitting in an observation chair at a pool. The lifeguard's eye level is 6.2. feet fromground. The chair is 15.4 feet from a swimmer. Calculate the measure if an angle forms when thelifeguard looks down at the swimmer.
We can represent this situation with a triangle, as shown below:
We need to calculate the angle that forms between the line of sight of the Life Guard and the swimmer. For that, we will have to use the tangent relation.
[tex]undefined[/tex]Which of the following are remote interior angles of Z1? Check all that apply51613/241O A. 23I B. 25O C. 26hO D. 22O E. 24O F. 21
Given data:
The given figure of the triangle.
The remote interior angles of ∠1 are,
[tex]\angle4\text{ \& }\angle6[/tex]Thus, the options (C) and (E) are correct.
Convert the angle \frac{13\pi}{4} 413π radians to degrees.
1 rad x 180/pi =57.296 deg
so the answer is 744.845
Ashe worked 8 hours every day for 10 days. If she made $620 for those 10 days she worked. What is her pay per hour?
Answer:
$7.75 per hour
Step-by-step explanation:
10 days x 8 hours = 80 hours
$620/80 hours = $7.75 per hour
Answer:
$7.75 per hour
Step-by-step explanation:
8 x 10 =80
$620=80 hours
÷80 ÷80
$7.75=1 hour
What is the value of x in the geometric sequence x, 3, — ‚ .A. -27B. -9C. -1D. -3
Recall that in a geometric sequence, whenever we take one value of the sequence and divide it by the next number of the sequence, we would get a constant number unique to that sequence. If we take the first and second numbers and calculate the ratio, we get
[tex]\frac{x}{3}[/tex]if we do that with the second and third numbers, we get
[tex]\frac{3}{\text{ -}\frac{1}{3}}=\text{ -}\frac{3\cdot3}{1\cdot1}=\text{ -9}[/tex]this two numbers should be equal. So we get
[tex]\frac{x}{3}=\text{ -9}[/tex]if we multiply both sides by 3, we get
[tex]x=3\cdot\text{ -9= -27}[/tex]so option A is the correct option.
I'll give brainliest!
The square roots would not be between 9 and 10 is [tex]\sqrt{80}[/tex].
[tex]\sqrt[]{80}=8.944\\ \sqrt[]{90}=9.486\\ \sqrt[]{95}=9.746\\ \sqrt[]{88}=9.380[/tex]
What are square roots?
The opposite of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, whereas the square root of a number may be found by looking for a number that, when squared, yields the original value. It follows that a, a = b if "a" is the square root of "b." Every integer has two square roots, one of a positive value and one of a negative value because the square of any number is always a positive number. For instance, the square roots of 4 are both 2 and -2. However, the square root of a number is typically only expressed as the positive value.
The value of a number's power 1/2 is the number's square root. It is the number whose product by itself yields the original number, to put it another way. It is symbolized by the character "." The number behind the square root sign is referred to as the radicand, whereas the square root symbol itself is known as a radical.
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Use the graph of y=f(x) shown below to graph the function GAnd then choose the correct graph
Rule of dilation:
[tex](x,y)\rightarrow(4x,4y)[/tex]Find the coordinates of the points in g(x) following the rule above:
[tex]undefined[/tex]what is the sum?17.34 8.03+0.009
In order to add these numbers, first let's write all of them with the same number of decimal places:
17.34 = 17.340
8.03 = 8.030
0.009 = 0.009.
Then, let's add all algarisms that are in the same position in each number:
0 + 0 + 9 = 9
4 + 3 + 0 = 7
3 + 0 + 0 = 3
7 + 8 + 0 = 15 (5 plus 1 to next algarism)
1 + 0 + 0 (+ 1) = 2
So the final result is 25.379.
Simplify the complex rational expression. When typing your answer for the numerator and denominator be sure to type the term with the variable first with no spaces between characters. If an exponent is needed use the carrot key (^) by pressing shift and 6 at the same time.\frac{\left(\frac{2}{a}+\frac{7}{b}\right)}{b}The numerator is AnswerThe denominator is Answer
The given expression is
[tex]\frac{(\frac{2}{a}+\frac{7}{b})}{b}[/tex]To add 2 fractions we have to give them the same denominators
In the up part (numerator) we have 2 different denominators a and b
Then the common denominator of the 2 fractions must be the product of them
[tex]\frac{2}{a}+\frac{7}{b}=\frac{2b}{ab}+\frac{7a}{ab}=\frac{2b+7a}{ab}[/tex]Then the fraction will be
[tex]\frac{\frac{2b+7a}{ab}}{b}[/tex]Now, we will multiply the denominator of up by the denominator of the first fraction (ab x b)
[tex]\frac{\frac{2b+7a}{ab}}{b}=\frac{2b+7a}{b(ab)}[/tex]Multiply b by b to simplify, then
[tex]\frac{2b+7a}{b(ab)}=\frac{2b+7a}{ab^2}[/tex]The numerator is 2b + 7a
The denominator is ab^2
I need help graphing this piecewise function!
The piecewise function on the graph is,
f(x) = { 1 -3x ; if x ≤ 2
{ 4-x ; if x > 2
The graph of a piecewise function is given. The left function is defined on the interval x ≤ 2 and the right function is defined on the interval x > 2.
To find the functions we need two points on each function since both functions are straight lines.
First we will find the left function defined on x ≤ 2.
So the two points are (x₁, y₁) = (0,1) and (x₂, y₂) = (2, -5).
Now slope of the left function, m₁ = (y₂ - y₁)/(x₂ - x₁)
= -5 - 1/2 - 0
= -6/2
= -3
So the equation of the left function is,
y - y₁ = m(x-x₁)
⇒ y - 1 = -3(x-0)
⇒ y = 1 -3x
Thus the left function is f(x) = 1 -3x
Consider the right function.
The two points on the graph of the right function are (x₁, y₁) = (4,0) and (x₂, y₂) = (6, -2).
So slope of the second function, m₂ = (y₂ - y₁)/(x₂ - x₁)
= -2 - 0/6-4
= -2/2
= -1
Now equation for the right function is,
y - y₁ = m(x-x₁)
⇒ y - 0 = -1(x-4)
⇒ y = 4 -x
So the right function is f(x) = 4-x
Hence the piecewise function is,
f(x) = { 1 -3x ; if x ≤ 2
{ 4-x ; if x > 2
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How does slavery and oppression of other people impact you?
Slavery and oppression of other people impact others as it brings about discrimination and fear.
What is slavery?In the olden days, slavery was so lucrative that the Mississippi River valley produced more millionaires per capita than any other region of the country. With cash crops like tobacco, cotton, and sugar cane, the southern states of America developed into the country's economic engine.
In Africa, the slave trade had a terrible impact. A culture of lawlessness and violence was encouraged by the financial incentives provided to warlords and tribes to participate in the slave trade. Economic and agricultural development in a large portion of western Africa was virtually impossible due to depopulation and a persistent fear of enslavement.
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1/6 (x-3) = 1/3 (x+2)
The value of x in the equation given as 1/6(x - 3) = 1/3(x + 2) is 7
How to evaluate the equation?The equation is given as
1/6(x - 3) = 1/3(x + 2)
From the question, we can see that the equation is a linear equation with one variable
As a general rule: linear equations are equations that have constant average rates of change.
We start by multiplying both sides of the equation by 6
So, we have the following equation
6 * 1/6(x - 3) = 1/3(x + 2) * 6
Next, we evaluate the products
So, we have the following equation
x - 3 = 2x + 4
Next, we collect the like terms
So, we have the following equation
2x - x = 3 + 4
Evaluate the like terms in the above equation
x = 7
This means that the solution of the equation is 7
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A trapezoid has bases 4 and 12 and area of 40m^2 find the height
Step 1
State the formula for the area of a trapezoid
[tex]\begin{gathered} The\text{ area of a trapezoid=(}\frac{a+b}{2})\times height(h) \\ \text{Where a= base 1=4}m \\ b=\text{base 2=12m} \\ \text{The area of the trapezoid=40m}^2 \end{gathered}[/tex]Step 2
Find the height
[tex]\begin{gathered} 40=(\frac{4+12}{2})\times h \\ 40=\frac{16}{2}\times h \\ 80=16h \\ h=\frac{80}{16} \\ h=5m \end{gathered}[/tex]Hence, the height = 5m
8. (15 pts) Explain clearly why Graph A IS a function, while Graph B is NOT a function. (Youcan indicate where the graphs pass or fail and reference that in your explanation)
We can see two graphs and we need to determine the reason why graph A IS a function, and graph B is NOT a function.
To achieve that, we can proceed as follows:
1. A function is a relation in which for each element of the domain we have only (exactly) one element of the range.
2. The domain of a function is the values for x for which the function is defined, and the range is those values for y that result when the function takes values for x and after following the rule of the function (the values for which the function is defined).
3. To determine if a graph is a function, we can use the vertical line test. Given the above definitions, this test tells us that if a vertical line passes through a graph at more than a point, then the relation is NOT a function.
4. Now we can use the Vertical Line Test on each graph as follows:
Graph A:As we can see from the graph, the vertical line passes through only one point (one value for y associated to x). We can see that the open circle indicates that the function is not defined for the value while the solid circle indicates that the function is defined for that value.
For instance, for x = -1 the value of the function is y = 0 (and not y = -1 - see the open circle). We have a similar case for x = 1 (y = 1) (not y = 0).
Therefore, graph A IS a function.
Graph B
In this case, we can say that the vertical line passes through more than one point in most of the values. However, we can say that there are some values where the line passes through one point - from x = -3 to x = -2 (included) -, and for values greater than 2 (x>2).
However, since the vertical line test indicates that the line passes through more than a point (there are more than a value, y, for each x) then Graph B is NOT a function.
Therefore, in summary, we can say that using the method of the vertical line test, Graph A IS a function, while Graph B is NOT a function.
(d) Find the domain of function R. Choose the correct domain below.
Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.
During a weight loss challenge, Ms. Norris went from 190 pounds to 160 pounds. percent of weight did she lose?
the original weight is 190 pounds
the new weight is 160 pounds
so the percentage of weight loss is
[tex]=\frac{original\text{ weight - new weight}}{\text{original weight}}\times100[/tex][tex]\begin{gathered} =\frac{190-160}{190}\times100 \\ =\frac{30}{190}\times100 \\ =15.78 \end{gathered}[/tex]so she loss 15.78 per cent of the weight.
the following equation is used by scientists to relate the pressure, volume, amount and temperature of gas solve for r in terms of p,v,n and t
The equation is PV = nRT.
What is a ideal gas law?The calculations for the ideal gas law are comparison of the Pressure and Volume of gas based upon amount and temperature.
The basic formula is PV = nRT where
P = Pressure in atmospheres (atm)
V = Volume in Liters (L)
n = number of moles (mol)
R = the Ideal Gas Law Constant
T = Temperature in Kelvin (K)
The value of n is the amount of the gas measured as moles.
One may need to convert a mass to moles by dividing the given mass of the gas by the molar mass of the gas to get moles.
Hence, The equation is PV = nRT.
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Miriam buys the chair shown. The tax rate is . How much was the tax on the chair?
The tax on the chair is $7.50.
What is a tax?A tax is a mandatory financial charge or other sort of levy imposed by a governmental entity on a taxpayer in order to fund government spending and related public expenses.
The tax rate is the ratio at which a firm or individual is taxed in a tax system. A tax rate can be presented in numerous ways: statutory, average, marginal, and effective.
Let the cost of the chair be $150 and the assumed tax rate be 5%.
In this case, the tax on the chair will be:
= Tax rate × Cost of chair
= 5% × $150
= 0.05 × $150
= $7.50
Note that an overview was given as the information is incomplete.
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What value of x satisfies the equation 4x + 2 = 22?
A 3.5
B 5.0
C 6.0
D 7.5
Answer:
B
Step-by-step explanation:
4x + 2 = 22 ( subtract 2 from both sides )
4x = 20 ( divide both sides by 4 )
x = 5
The average number of babies born at a private hospital's maternity wing is 6 per hour. What is the probability that three babies are born during a particular 1-hour period in this maternity wing?
If the average number of babies born at a private hospital's maternity wing is 6 per hour. The probability that three babies are born during a particular 1-hour period in this maternity wing is 0.09.
How to find the Probability?Mean = 6 per hours
Number of babies = 3 babies
Hence,
Now let determine the probability
Let x represent the probability
Pr(X=3) = e^-6 × 6^3 ÷ 3!
Pr(X=3) =0 .535410 ÷ 6
Pr(X=3) = 0.089
Pr(X=3) =0.09 (Approximately)
Therefore we can conclude that 0.09 is the probability.
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You need a 55% alcohol solution. On hand, you have a 150mL of a 45% alcohol mixture. You also have 80% alcohol mixture. How much of the 80% mixture will you need to add to obtain the desired solution?
Let the equired amount of 80% alcohol mixture required be 'x' mL.
If C represents the concentration and V represents the correspon
during the winter olympics the us curling team scored 2 points more than the canadian team. the canadian curling team scored 4 points more than the norwegian team. altogether the three teams scored a total of 208 point. how many points did the canadian team scored?
Answer:
70 points
Step-by-step explanation:
u = US points
c = Canadian points
n = Norwegian points
u = c + 2
n = c - 4
208 = u + c + n
208 = ( c + 2 ) + c + ( c - 4 ) = 3c - 2
Isolate c:
208 = 3c - 2
210 = 3c
c = 70
Signs are placed at regular intervals along a mountain road to indicate altitude. At Grinbrir Lodge, the sign indicates an elevation of 876 meters. But 17 kilometers down the road, another sign indicates that the elevation is 672 meters. What is the average elevation change per kilometer traveled from the Lodge
Answer:
-12 m/km
Step-by-step explanation:
You want to know the average elevation change per kilometer given the elevation changes from 876 meters to 672 meters over a distance of 17 kilometers.
Rate of changeThe average elevation change per kilometer is found by dividing the elevation change by the number of kilometers. The elevation change is the difference between the ending elevation and the starting elevation.
rate of change = ((end elevation) -(start elevation))/(distance)
= (672 m -876 m)/(17 km) = (-204 m)/(17 km) = -12 m/km
The average elevation change is -12 meters per kilometer traveled from the lodge.
__
Additional comment
Expressing both dimensions in the same unit, we can find the average grade of the road to be ...
(-12 m)/(1000 m) = -0.012 = -1.2% . . . . . average grade of the road
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Solve for perimeter
Answer:
7x+9=8
Step-by-step explanation:
4-x+7x-1-8-5x+6x+13
=7x+8
:]
my daughter is working on expression problems. i cant remember how to do this...the problem is 12(3y+x)please help me tell her how to write and solve this.
EXPLANATION
Given the expression 12(3y+x).
Let's solve it:
Applying the distributive property:
12*3y + 12*x
Multiplying like terms:
36y + 12x
The answer is 36y + 12x
5. x^2+2x+1Factors:(__________________________)(_____________________)
Question: what are the factors of the expression:
[tex]x^2+2x+1[/tex]Solution:
Let the expression
[tex]x^2+2x+1[/tex]If we apply the quadratic equation:
[tex]\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]we get the zero of the polynomial
[tex]f(x)=x^2+2x+1[/tex]which is -1. Thus the polynomial can be factored in the following way
[tex]x^2+2x+1\text{ = (x+1)(x+1)}=(x+1)^2[/tex]then, we can conclude that the factors of the given polynomial are:
(x+1) and (x+1)
Estimate the total cost of the following items from your dorm room rounded individual cost to the nearest $10 round your answer to the nearest dollar no sense
First item= $159.55
Chair= $49.75
Cubes= $29.87
Lamp= $19.78
Rounding the individual cost to the nearest $10, we get:
First item= $160
Chair= $50
Cubes= $30
Lamp= $20
The total cost will be:
$160+$50+$30+$20= $260.
The answer is: $ 260.
Name
1) The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to
24 rings each day using up to 80 total man-hours of labor. It takes 4 man-hours to make one VIP ring and 2
man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the
company's profit, if the profit on a VIP ring is $40 and on an SST ring is $35?
Let V stand for the number of VIP rings made, S stand for the number of SST rings made.
State the Objective Function
Z=_
State the total ring constraint
State the man-hours constraint
Use the graph below to graph your constraints, label your Optimal Region points, and evalute them for the. Optimal solution using your
Z equation.
What is your Optimal Sales $'s.
How many VIP Rings
How many SST Rings
The combination that gives the most profit exists 12 VIP rings and 12 SST rings (900 / day).
How to maximize the company's profit, if the profit on a VIP ring is $40 and on an SST ring is $35?This is a linear programming problem.
The objective function is profit R, which has to be maximized. [tex]$R=40 \mathrm{~V}+35 S$[/tex]
being V: number of VIP rings produced, and S : number of SST rings produced.
The restrictions are
Amount of rings (less or equal than 24 a day): [tex]$V+S \leq 24$[/tex]
Amount of man-hours (up to 60 man-hours per day):[tex]$3 V+2 S \leq 60$[/tex]
The number of rings of each type exists a positive integer: [tex]$V, S \geq 0$[/tex]
We get 3 points, in which 2 of the restrictions exists saturated. In one of these three points lies the combination of V and S that maximizes profit.
The points and the values for the profit function in that point are:
Point 1: V=0 and S=24
[tex]$R=40 \mathrm{~V}+35 S=40 \cdot 0+35 \cdot 24=0+840[/tex]
R = 840
Point 2: V=12 and S=12
R = 40 V+35 S [tex]=40 \cdot 12+35 \cdot 12=480+420[/tex]
R = 900
Point 3: V=20 and S=0
R = 40 V+35 S [tex]=40 \cdot 20+35 \cdot 0=800+0 \\[/tex]
R = 800
The combination that gives the most profit exists 12 VIP rings and 12 SST rings (900 / day).
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The management of the UNICO department store has decided to enclose a 903 ft2 area outside the building for displaying potted plants and flowers. One side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing. If the pine board fencing costs $7/running foot and the steel fencing costs $4/running foot, determine the dimensions of the enclosure that can be erected at minimum cost.
The dimensions of the enclosure that can be erected at minimum cost are 21.25 feet by 42.50 feet
How to determine the dimensions of the enclosure that guarantees the minimum costFrom the question, the given parameters are
Area = 903 square feet
Shape = rectangle
From the question, we understand that:
One side of the area would be enclosed by the external wall of the store
If the dimensions of the area are Length (L) and Width (W), then we have
Area = LW
Perimeter = 2L + W
Rewrite as
A = LW
P = 2L + W
Substitute 903 for A in A = LW
LW = 903
Make W the subject
W = 903/L
Substitute W = 903/L in P = 2L + W
P = 2L + 903/L
Differentiate the equation
So, we have
P' = 2 - 903/L²
Set to 0
2 - 903/L² = 0
So, we have
903/L² = 2
This gives
L² = 903/2
Divide
L² = 451.5
Take the square roots
L = 21.25
Substitute L = 21.25 in W = 903/L
W = 903/21.25
Evaluate
W = 42.50
Hence, the dimensions of the enclosure are 21.25 feet by 42.50 feet
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