the domain refers to all possible values of x in the function.
since a negative time does not make sense, the smallest value of the domain is zero
on the other hand, the problem indicates that the model is considered accurate up to 100,000 years, therefore that would be the largest value of t
in conclusion, the domain of the function A(t) is
[tex]\lbrack0,100000\rbrack[/tex][ 0 , 100,000 ]
A system of equations is shown below. Solve for x.
y = x² - 6x + 4
y = x + 1
The value of x in the given quadratic equations is either -2.7 or -11.3.
What are quadratic equations?A quadratic equation is a second-degree algebraic equation in x. ax² + bx + c = 0, where a and b are coefficients, x is the variable, and c is the constant term, is the quadratic equation in its simplest form.
Given first equation, y = x²- 6x + 4 second equation, y = x +1
Put the value of y in the first equation to get
x + 1 = x² - 6x + 4
Solving this equation
x² - 7x + 3 = 0
Using quadratic formula,
x = - b ± [tex]\frac{\sqrt{(b^{2}- 4ac)}}{2a}[/tex]
x = - 7 ± [tex]\frac{\sqrt{(-7)^{2}- 4(3)}}{2}[/tex]
x = - 7 ± 4.3
Therefore in the given quadratic equations, the value of x can be either -2.7 or -11.3
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Enter the missing values in the area model to find 10(8y + 5)+510BoyAccording to the model above, 10(8y + 5) =Submit Answeatte
Note you have to use the value outside the bracket to multiply the inner value.
which graph represents the solution to -1/2m>7/11
The graph of the inequality:
(-1/2)*m > 7/11
Can be seen in the image at the end.
Which graph represents the solution for the inequality?Here we have the following inequality:
(-1/2)*m > 7/11
First, let's solve this for m, this means that we need to isolate the variable in one side of the inequality.
If we multiply both sides by -2, we get:
-2*(-1/2)*m < -2*(7/11)
Where the direction of the symbol changes because we are multiplying by a negative number.
m < -14/11
The graph of this will be an open circle at -14/11 and an arrow that goes to the left, like the one below.
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Find the lenghts of the sides of the rectangle ABCD shown on the coordinate plane. Suppose you double the length of each side. What would be the new coordinates of point C if the coordinate of point A stay the same
Looking at the diagram,
each small box represents one unit
The number of units from A to B is 4 units
The number of units from B to C is 3 units
Thus, the length of rectangle ABCD is 4 units and its width is 3 units.
The original coordinates are
A(0, 0)
B(0, 4)
C(3, 4)
D(3, 0)
If
3) Describe what ALL graphs of proportional relationships have in common
SOLUTION
What all graphs of proportional relationships have in common is a straight line.
This line is straight, no curves or bends. This straight line passes through the origin at an intersection of
[tex](0,0)[/tex]Hence, the answer is "A straight line that passes through the origin and goes at a constant rate".
Solve the following system of equations Detailed step by step
SOLUTION:
Step 1:
In this question, we are given the following:
[tex]\begin{gathered} 2\text{ x + y = 2 ------equation 1} \\ 4\text{ x + 3y =- 2--- -equation 2} \end{gathered}[/tex]Step 2:
The details of the solution are as follows:
The graphical solution for the two systems of equations are as follows:
CONCLUSION:
The solutions to the systems of equations are:
[tex]x\text{ = 4 , y = -6}[/tex]
Hello,Can you help me with the following word problem?A medical researcher needs 6 people to test the effectiveness of an experimental drug. If 13 people have volunteered for the test, in how many ways can 6 people be selected?This might be using the nCr formula
Solution:
Given that a medical researcher needs 6 people to test the effectiveness of an experimental drug. If 13 people have volunteered for the test, this implies that
[tex]\begin{gathered} total\text{ number of options in the set = 13} \\ number\text{ of oprions to be chosen = 6} \end{gathered}[/tex]To evaluate the number of people that can be selected, we use the combination formula expressed as
In this case,
[tex]\begin{gathered} n=13 \\ r=6 \end{gathered}[/tex]Thus, the question involves combination.
2. Using Vièta's theorem, find the solutions to the equation. a) x^2 - 3x + 2 = 0 b) x^2 + 2x - 15 = 0.
Given:
[tex]\begin{gathered} x^2-3x+2=0 \\ x^2+2x-15=0 \end{gathered}[/tex]Required:
We need to find the solution by Vièta's theorem.
Explanation:
Compare 1st equation with
[tex]ax^2+bx+c=0[/tex]we get
[tex]\begin{gathered} a=1 \\ b=-3 \\ c=2 \end{gathered}[/tex]Vièta's theorem is
[tex]\begin{gathered} x_1+x_2=-\frac{b}{a} \\ x_1x_2=\frac{c}{a} \end{gathered}[/tex][tex]\begin{gathered} x_1+x_2=3 \\ x_1x_2=2 \end{gathered}[/tex]now solve this equation and we get
[tex]\begin{gathered} x_1=1 \\ x_2=2 \end{gathered}[/tex]because addition of 1 and 2 is 3 and multiplication is 2
Now for 2nd equation
[tex]\begin{gathered} a=1 \\ b=2 \\ c=-15 \end{gathered}[/tex]apply Vièta's theorem
[tex]\begin{gathered} x_1+x_2=-2 \\ x_1x_2=-15 \end{gathered}[/tex]by this
[tex]\begin{gathered} x_1=3 \\ x_2=-5 \end{gathered}[/tex]because addition of 3 and -5 is -2 and multiplication is -15
Solve, graph and write the solution in interval notation: |2x−1|>5
Given: the inequality is,
[tex]|2x-1|>5[/tex]To solve the inequality,
[tex]\begin{gathered} |2x-1|>5 \\ -5<2x-1<5 \\ -5+1<2x<5+1 \\ -4<2x<6 \\ -\frac{4}{2}The graph will conntain a region -2The graph for the giev inequality is,
PLEASE GIVE ME THE ANSWER AND HOW YOU GOT IT IM BEGGING YOU I WILL GET KICKED OUT IF I DONT GET A GOOD SCORE ON THIS
By solving the given equations, the values of x are 7 and -7.
What are equations?A mathematical equation is a formula that uses the equals sign to express the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 = 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, |x| -7:
Now, solve for x as follows:
|x| -7Then,
x - 7 = 0 and -x - 7 = 0Which gives, x = 7 and x = -7Therefore, by solving the given equations, the values of x are 7 and -7.
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Answer:
see below
Step-by-step explanation:
All the given equation have mod function in them .We know that, if
[tex]\longrightarrow |x| = y \\[/tex]
then ,
[tex]\longrightarrow x =\pm y \\[/tex]
1) |k| = 8
[tex]\longrightarrow k =\pm 8 \\[/tex]
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2)|x| = 7
[tex]\longrightarrow x = \pm 7\\[/tex]
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3) |a+2| = 8
[tex]\longrightarrow a + 2 =\pm \\[/tex]
[tex]\longrightarrow a = 8-2 \ or \ -8-2\\[/tex]
[tex]\longrightarrow a = 6 , -10 \\[/tex]
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4) |8a|/10 = 2
[tex]\longrightarrow |8a| = 20 \\[/tex]
[tex]\longrightarrow 8a =\pm 20\\[/tex]
[tex]\longrightarrow a =\pm\dfrac{20}{8} \\[/tex]
[tex]\longrightarrow a = \pm\dfrac{5}{2} \\[/tex]
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5)|-m+9| = 13
[tex]\longrightarrow -m+9 =\pm 13\\[/tex]
[tex]\longrightarrow m -9 =\pm 13\\[/tex]
[tex]\longrightarrow m = 13-9\ or \ -13-9\\[/tex]
[tex]\longrightarrow m = 4 , -22\\[/tex]
____________________________
6)|7-5x|=27
[tex]\longrightarrow 7-5x =\pm 27 \\[/tex]
[tex]\longrightarrow 5x -7 =\pm 27\\[/tex]
[tex]\longrightarrow 5x = 27 +7 \ or \ -27+7 \\[/tex]
[tex]\longrightarrow 5x = 34 \ or -20 \\[/tex]
[tex]\longrightarrow x =\dfrac{34}{5}, -4\\[/tex]
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7)|2x+7|/5=5
[tex]\longrightarrow |2x+7|=25\\[/tex]
[tex]\longrightarrow 2x +7 =\pm 25 \\[/tex]
[tex]\longrightarrow 2x = 25-7 \ or \ -25-7\\[/tex]
[tex]\longrightarrow 2x = 18 \ or \ -32\\[/tex]
[tex]\longrightarrow x = 9 , -16 \\[/tex]
And we are done!
describe the center and spread of the data using the more appropriate status either the mean median range interquartile range or standard division
In a group of 80 animals, 32 are dogs. Dogs make upwhat percent of the animals in the group?A. 32.00B. 28.6C. 35.5D. 38.00E 40.00
Let's calculate the percentage of dogs in the animal group
[tex]\begin{gathered} P=\frac{32}{80} \\ P=0.40 \\ P=40\text{ \%} \end{gathered}[/tex]The answer would be 40%.
the net of a rectangular prism is shown below. the surface area of each face is labeled. which vakues represent the dimensions, in meters, of the rectangular prism.
The answer is 5, 9, 10
If the radius of a sphere increases from 3 feet to 9 feet, by how many cubic feet does the volume of the sphere increase? 967 ft3 A 1087 ft3 936 ft 0
The volume of a sphere is given by:
[tex]V=\frac{4}{3}\pi r^3[/tex]The original sphere, with radius r=3, has volume:
[tex]\begin{gathered} V=\frac{4}{3}\pi(3)^3 \\ =36\pi \end{gathered}[/tex]The second sphere, with radius r=9, has volume:
[tex]\begin{gathered} V=\frac{4}{3}\pi(9)^3 \\ =972\pi \end{gathered}[/tex]To find how much the volume increased we substract the first volume to the second one:
[tex]972\pi-36\pi=936\pi[/tex]Therefore the v
Solve for the unknown: 6(B+2) = 30
The unknown is B
[tex]6(B+2)=30[/tex][tex]\begin{gathered} 6B+12=30 \\ 6B+12-12=30-12 \\ 6B=18 \\ B=\frac{18}{6} \\ B=3 \end{gathered}[/tex]|x|=-5 why is there no solution?
Absolute value is the distance a number is from zero.
Because distance cannot be negative, an absolute value can never be a negative.
Therefore,
|x| = -5 has no solutions
Find y if the line through (1, y) and (8, 2) has a slope of 3.
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{y})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{y}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{1}}} ~~ = ~~\stackrel{\stackrel{m}{\downarrow }}{3}\implies \cfrac{2-y}{7}=3 \\\\\\ 2-y=21\implies -y=19\implies y=\cfrac{19}{-1}\implies y=-19[/tex]
what is the area of a circle with the radius of 10, then rounding the answer to the nearest tenth?
Given a circle with a radius = r = 10 in
The area of the circle is given by the following formula:
[tex]A=\pi\cdot r^2[/tex]Substitute with r= 10
so, the area will be:
[tex]A=\pi\cdot10^2=\frac{22}{7}\cdot10^2=\frac{22}{7}\cdot100=314.2857[/tex]Rounding the answer to the nearest tenth:
So, the answer will be area = 314.3 square inches
Identify the slope and y-intercept of the line y=−2x−1.
Given the equation of the line:
[tex]y=-2x-1[/tex]The given equation as the slope-intercept form: y = m * x + b
where m is the slope and b is the y-intercept
the y-intercept is the value of y when x = 0
By comparing the given equation with the slope-intercept form
So,
The slope = m = -2
The y-intercept = b = -1
the point of y-intercept = ( 0, -1 )
One Sunday night, the Celluloid Cinema sold $ 1,585.75 in tickets. If the theater sold a children's ticket for $ 7.7S and an adult ticket for $ 10.25, a) write an equation to represent this situation. b) If the theater sold 75 children's tickets, solve your equation to find the number of adult tickets.
Answer:
98 adult tickets
Explanation:
Part A
Let the number of children's ticket sold = c
Let the number of adult's ticket sold = a
Cost of a children's ticket = $7.75
Cost of an adult's ticket = $10.25
Total income from ticket sales = $1,585.75
An equation to represent this situation is:
[tex]7.75c+10.25a=1585.75[/tex]Part B
If the number of children's ticket sold, c = 75
Then:
[tex]\begin{gathered} 7.75c+10.25a=1585.75 \\ 7.75(75)+10.25a=1585.75 \\ 581.25+10.25a=1585.75 \\ 10.25a=1585.75-581.25 \\ 10.25a=1004.50 \\ \frac{10.25a}{10.25}=\frac{1004.50}{10.25} \\ a=98 \end{gathered}[/tex]The number of adult tickets sold by the cinema is 98.
2064 is divisible by 2, 4 and 8 true or false
Given these points please solve this problme.
The point that belongs to the solution set is A( 4, 4)
What are inequalities?Inequalities are defined as mathematical relations involving an unequal comparison between two numbers, elements or other arithmetic expressions.
They are mostly used to compare two numbers on the number line on the basis of their sizes.
Given the inequalities;
x + y > 63x - 5y ≤ 2Make 'x' the subject from equation 1, we have;
x > 6 - y
substitute the value into equation 2, we have;
3( 6 - y) - 5y ≤ 2
expand the bracket
18 - 3y - 5y ≤ 2
collect like terms
- 8y ≤ 2 - 18
- 8y ≤ -16
Make 'y' the subject of formula
y ≤ 2
Substitute the value in equation 3
x > 6 - 2
x > 4
Hence, the point is A( 4, 4)
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ABC is a right angle. What is the measusre of DBE?
According to the given diagram the sum of ABD, DBE and EBC must be 90. Use this information to find the measure of DBE:
[tex]\begin{gathered} 33+\measuredangle DBE+33=90 \\ \measuredangle DBE=90-33-33 \\ \measuredangle DBE=24 \end{gathered}[/tex]The measure of DBE is 24 degrees.
An exam has 2 papers each scored differently. one is out of 120 and another is out of 80. Maryam scores 65% on the first and 80% on the second. work Maryam's total percentage score for her exam.
Maryam's total percentage score on her exam is 71%.
What is the total percentage score?
Percentage is the ratio of an amount that is expressed as a number out of hundred. The sign that is used to represent percentage is %.
The first step is to determine the score on each paper.
Score on the first test = 65% x 120
(65 / 100) x 120 = 78
Score on the second test = 80% x 80
0.80 x 80 = 64
Total percentage score = (sum of scores / total score) x 100
Sum of scores = 64 + 78 = 142
Total score = 120 + 80 = 200
(142 / 200) x 100 = 71%
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The pentagonal prism below has a height of 13 units and a volume of 247 units ^3. Find the area of one of its bases.
• Volume of pentagonal prism = area of base x height
Volume = 247 unis^3
height = 13 units
Replacing:
V = A x h
A = V / h
A = 247/13 = 19 units^2
Help with these two questions please. Match the sentence with a word
EXPLANATION
Given that two angles form a linear pair, we can assevere that the postulate that applies is the Linear Pair Postulate.
The equation 3x + 2y = 120 models the number of passengers who can sit in a train car, where isthe number of adults and y is the number of children. Explain what the 2- and y-intercepts mean.
Explanation:
Given the equation that models the number of passengers who can sit in a car expressed as 3x + 2y = 120
x is the number of adults
y is the number of children
The x-intercept is the point where y is zero i.e. the number of adults when there is no number of children.
when y = 0
3x + 2(0) = 120
3x = 120
x = 120/3
x = 40
This means that there will be 40 adults if there are no children
The y-intercept is the point where x is zero i.e. the number of children when there is no number of adults.
when x = 0
3(0) + 2y = 120
2y = 120
y = 120/2
y = 60
This means that there will be 60children if there are no adults
Julie has a total of 16 chickens. If she has 4 times as many chickens as dogs, write and solve an equation to determine the number of dogs she has.
The equation that can be used to determine the number of dogs that Julie has =
4× (number of chicken) = 64
What is an equation?An equation is defined as the expression that shows a connection between two variables that are connected with an 'equal to' sign.
The number of chicken owned by Julie = 16 chickens
The number of dogs = X
But she has 4× (number of chicken) = X
That is 4 × 16 = X
X= 64
Therefore the number of dogs that Julie has = 64 dogs.
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-8(4 p -1)-7 p+8( p+1)
-31p + 16
Explanation:
-8(4 p -1) - 7p+8( p+1)
Open the bracket:
-8(4p) -8(-1) - 7p +8(p) +8(+1)
Simplify:
-32p + 8 - 7p + 8p + 8
Note: the multiplication of opposite sign gives negative number. While multiplication of same sign gives positive number
Collect like terms:
= -32p - 7p + 8p + 8 + 8
= -31p + 16
Professor Torres is stucked in a burning building. He is leaning to the window on the 5th floor which is 60feets above the ground. For stability, the firefighter have to place the bottom of their ladder 15feet from the wall of the building. How long does the ladder needs to be to reach the window on the 5th floor and save professor Torres? round to 2 decimal place
The situation forms the right triangle above:
Where x is the length of the ladder.
Apply the Pythagorean theorem:
c^2 = a^2 +b^1
where:
c = hypotenuse = longest side = x
A &b = the other 2 legs of the triangle
Replacing:
x^2 = 60^2 + 15^2
Solve for x
x^2 = 3,600 + 225
x^2 = 3,825
x =√3,825
x = 61.85 ft