Answer:
[tex]x \geq 0.5[/tex]
Step-by-step explanation:
Im assuming you want to know the value of x.
Let's use algebraic rules and solve for the intervals (values) of x. Shown below:
[tex]3.8-1.4x \geq 5.6-5x\\-1.4x+5x \geq 5.6 - 3.8\\3.6x \geq 1.8\\x \geq \frac{1.8}{3.6}\\x \geq 0.5[/tex]
Hence, x is greater than or equal to 0.5
Ifa-b=4 and a^2- b^2=3, what is the value of a+b?
Answer:
[tex]\large\boxed{a+b=\dfrac{3}{4}}[/tex]
Step-by-step explanation:
[tex]\text{Use}\ a^2-b^2=(a-b)(a+b).\\\\\text{We have}\ a-b=4\ \text{and}\ a^2-b^2=3.\\\\\text{Substitute:}\\\\3=4(a+b)\qquad\text{divide both sides by 4}\\\\\dfrac{3}{4}=(a+b)\to a+b=\dfrac{3}{4}[/tex]
four thrids times the sum of a number 8 is 24. what is the numver
Answer:
The number is 10
Step-by-step explanation:
Let the number be x.
four thirds times = 4/3
According to the statement:
four thrids times the sum of a number and 8 is 24
4/3 *(x+8)= 24
Move 3 to the R.H.S and Multiply 4 with the parenthesis.
4x+32=24*3
4x+32=72
Move constant to the R.H.S
4x=72-32
4x=40
Divide both the terms by 4
4x/4=40/4
x=10
Therefore the number is 10....
Final answer:
To solve the equation, which is four thirds times the sum of a number and 8 equals 24, we isolate the variable by dividing by four thirds and subtracting 8 from both sides, resulting in the number being 10.
Explanation:
The student's question is asking to solve an algebraic equation. Specifically, the equation is: four thirds times the sum of a number and 8 equals 24. To find the number, represented by a variable, we'll denote it as x and translate the statement into the following equation: (4/3) × (x + 8) = 24.
First, we need to divide both sides of the equation by 4/3 to isolate the sum on one side:
(x + 8) = 24 × (3/4)
(x + 8) = 18
Now, subtract 8 from both sides to solve for x:
x = 18 - 8
x = 10
The final answer is that the number is 10. This is obtained through a step-by-step explanation solving the initial equation.
Choose a system of equations with the same solution as the following system: 6x + 2y = −6 3x − 4y = −18
Final answer:
To find a system with the same solution, multiply one of the original equations by a constant and/or add the two original equations together to derive a new equation. An example is the alternative system 6x - 8y = -36 and 9x - 2y = -24, which shares the same solution as the original.
Explanation:
To find a system of equations with the same solution as the given system:
6x + 2y = −6
3x − 4y = −18
We must ensure that the alternative system is equivalent, meaning they share the same solution. A common technique is to multiply both sides of one or both of the equations by a constant to create new equations that have the same solutions. For example, we could multiply the second equation by 2:
3x − 4y = −18 becomes 6x − 8y = −36 after multiplying by 2.
Then, to avoid having the same equation, we could add the original second equation to the first one to get a different second equation:
6x + 2y + (3x − 4y) = −6 + (−18) becomes 9x − 2y = −24.
So, the alternate system that shares the same solution as the original would be:
6x − 8y = −36
9x − 2y = −24
Thirty cities were researched to determine whether they had a professional sports team, a symphony, or a children's museum of these cities, 15 had a professional
sports team 15 had a symphony, 13 had a children's museum, 8 had a professional sports team and a symphony, 7 had a professional sports team and a children's
museum 7 had a symphony and a children's museum, and 3 had all three activities Complete parts a) through e) below
Answer:
the way its set up its kind of confusingStep-by-step explanation:
Answer:
Step-by-step explanation:
cities were researched to determine whether they had a professional sports team, a symphony, or a children's museum. Of these cities, had a professional sports team, had a symphony, had a children's museum, had a professional sports team and a symphony, had a professional sports team and a children's museum, had a symphony and a children's museum, and had all three activities. Complete parts a) through e) below.
(2,5) and (3/2 ,2) find the slope of the line passing through the points.
Answer:
6
Step-by-step explanation:
To find the slope 'm' we use 2 points from the line, those are given in the statement:
[tex]x_{1} =2\\y_{1} =5\\\\x_{2} =3/2\\y_{2} =2[/tex]
[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1}}[/tex]
[tex]m=\frac{2 -5 }{3/2-2}}[/tex]
Finally m=6
What is the solution to the system of equations -x+2y+2z=0, -x-2y-2z=0, x-z=-1
Answer:
x = 0, y = 1, z = -1 ⇒ (0, 1, -1)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}-x+2y+2z=0&(1)\\-x-2y-2z=0&(2)\\x-z=1&(3)\end{array}\right\qquad\text{add both sides (1) and (2)}}\\\underline{\left\{\begin{array}{ccc}-x+2y+2z=0\\-x-2y-2z=0\end{array}\right}\\.\qquad-2x=0\qquad\text{divide both sides by (-2)}\\.\qquad x=0\\\\\text{Put it to (3):}\\\\0-z=1\\-z=1\qquad\text{change the signs}\\z=-1\\\\\text{Put the value of x and z to (1):}\\\\-0+2y+2(-1)=0\\2y-2=0\qquad\text{add 2 to both sides}\\2y=2\qquad\text{divide both sides by 2}\\y=1[/tex]
SOLVE y = 3x – 2 x – y = 4 BY USING SUBSTITUTION!! SHOW ALL WORK! HELPPP!
Answer:
(-1,-5)
Step-by-step explanation:
So we have the system:
y=3x-2
x-y=4.
We are asked to use substitution. Luckily, it is already setup for this because one of the equations has one of the variables solved for, namely the y=3x-2 equation. We are going to insert y=3x-2 into x-y=4 and solve for x.
x-y=4 (with y=(3x-2) ):
x-(3x-2)=4
Distribute:
x-3x+2=4
Combine like terms:
-2x+2=4
Subtract 2 on both sides:
-2x =2
Divide both sides by -2:
x =-1
Now if y=3x-2 and x=-1, then y=3(-1)-2=-3-2=-5.
So the solution is (-1,-5).
the postage required to mail a box depends on its weight
Jesse should use kilograms to weigh the package for postage.
Explanation:Jesse should use kilograms to weigh the package for postage. The books and documents in the box would likely weigh more than grams, so a larger unit of measurement is needed. Kilograms are a commonly used metric unit for measuring weight, and they are suitable for weighing the package accurately and determining the postage required.
7 × (–3) × (–2)2 = ?
Answer:
84
Step-by-step explanation:
Order of operations (Parentheses first, exponents next, then multiplication, etc.)
-3 * -2 = 6
Multiply
7 * 6 = 42
42 * 2 = 84
Answer:
84
Step-by-step explanation:
7 x (-3) x (-2) x 2 =
v
-21 x (-2) x 2 =
v
42 x 2 =
84
Write a function for (0,4)(1,8)
Firstly, find the slope.
Let m = slope
m = (8 - 4)/(1 - 0)
m = 4/1
m = 4
Now use the point-slope formula.
y - y_1 = m(x - x_1)
Pick one of the given points. I will use the point (0, 4) but you can certainly use (1, 8) if you'd like.
We now plug and chug.
y - 4 = 4(x - 0)
y - 4 = 4x
y = 4x + 4
Replace y with f(x).
f(x) = 4x + 4
Did you follow?
Answer:
f(x) = 4 x (2)^x
Step-by-step explanation:
A phere has a diameter of 12 ft. What is the volume if the sphere? Give the exact value in terms of pi
if the diameter of it is 12, its radius is half that or 6.
[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3} \begin{cases} r=radius\\ \cline{1-1} r=6 \end{cases}\implies V=\cfrac{4\pi (6)^3}{3}\implies V=288\pi[/tex]
Which number can each term of the equation be multiplied by to eliminate the decimals before solving?
5.6j – 0.12 = 4 + 1.1j
Answer:
100 is the number which can be multiplied to eliminate the decimals....
Step-by-step explanation:
Given:
Which number can each term of the equation be multiplied by to eliminate the decimals before solving
5.6j – 0.12 = 4 + 1.1j
Solution:
Notice that the constants and the coefficients in this equation contains decimal. All the numbers are in decimal up to tenth place except 0.12 which has decimal up to hundredth place.
Therefore, if we want to eliminate the decimal from 0.12 we have to multiply it by 100.
Thus the given equation will be multiplied by 100 to eliminate decimal from the terms.
100(5.6j – 0.12 = 4 + 1.1j)
By multiplying the equation by 100 we get:
560j - 12 = 400 + 110j
Thus 100 is the number which can be multiplied to eliminate the decimals....
Answer:
100
Step-by-step explanation:
Well, to answer this question, you have to find the number/coefficient that has the most numbers after a decimal point (not including trailing zeros), and then use the rule 10^(numbers after the decimal point) to see how to eliminate the decimals. So, 2 digits, 10^2=100
Explain how System 1 becomes equivalent to System 2.
System 1:
AX + By = C
LX + My=N
System 2:
(A + L)X + (8 + M)y = C+N
AX + By = C
A.The first equation in System 2 is the sum of the equations in System 1. The second equation in System 2 is the first equation in System 1.
B.The first equation in System 2 is the difference of the equations in System 1. The second equation in System 2 is the first equation in System 1.
C.The first equation in System 1 is the sum of the equations in System 2. The second equation in System 1 is the second equation in System 2.
D.The first equation in System 1 is the difference of the equations in System 2. The second equation in System 1 is the second equation in System 2.
Answer:
[tex]\left\{\begin{array}{ccc}(A+L)x+(B+M)y=C+N\\Ax+By=C\end{array}\right[/tex]
A.The first equation in System 2 is the sum of the equations in System 1. The second equation in System 2 is the first equation in System 1.Step-by-step explanation:
[tex]\underline{+\left\{\begin{array}{ccc}Ax+By=C\\Lx+My=N\end{array}\right}\qquad\text{add both sides of the equations}\\(Ax+Lx)+(By+My)=C+N\qquad\text{distributive}\\(A+L)x+(B+M)y=C+N[/tex]
Equivalent expressions are expressions that have the same value.
The true statement is: (a) The first equation in System 2 is the sum of the equations in System 1. The second equation in System 2 is the first equation in System 1.
The systems of equations are:
System 1
[tex]\mathbf{Ax + By = C}[/tex]
[tex]\mathbf{Lx + My = N}[/tex]
System 2
[tex]\mathbf{(A + L)x + (8 + M)y = C + N}[/tex]
[tex]\mathbf{Ax + By = C}[/tex]
When the equations of system 1 are added, we have:
[tex]\mathbf{Ax + Lx + By + My = C + D}[/tex]
Factor out x and y
[tex]\mathbf{(A + L)x + (8 + M)y = C + N}[/tex]
The above equation is the first equation of system 2.
While [tex]\mathbf{Ax + By = C}[/tex] is the second equation of the system
Hence, the true statement is (a)
Read more about systems of equations at:
https://brainly.com/question/13997560
Here are the heights in inches of 10 professional basketball players: 66, 74, 76, 77, 78, 79, 80, 80, 82, 84. The mean of these heights is 77.6 inches. Does this set have an outlier and, if so, how does removing it affect the mean?
The set has 66 as an outlier and removing it decreases the mean by about 1.3 inches.
The set has 66 as an outlier and removing it increases the mean by about 1.3 inches.
The set has 66 as an outlier and removing it decreases the mean by about 6.6 inches.
The set has no outliers.
Question 5
Here are 10 test scores: 50, 74, 76, 77, 78, 79, 80, 80, 82, 84. The mean of these scores is 76. How does removing the outlier 50 affect the mean?
The set has 50 as an outlier and removing it decreases the mean by about 10.
The set has 50 as an outlier and removing it decreases the mean by about 2.
The set has 50 as an outlier and removing it increases the mean by about 3.
The set has 50 as an outlier and removing it decreases the mean by about 6.
Answer:
Question 4: The set has 66 as an outlier and removing it increases the mean by about 1.3 inches.
Question 5: The set has 50 as an outlier and removing it increases the mean by about 3.
Step-by-step explanation:
Question 4:
Given heights are:
66, 74, 76, 77, 78, 79, 80, 80, 82, 84
The mean is: 77.6 inches
Removing 66 will make the mean increase to 78.9
So,
The set has 66 as an outlier and removing it increases the mean by about 1.3 inches.
Question 5:
50, 74, 76, 77, 78, 79, 80, 80, 82, 84
The mean is 76.
We can clearly see that 50 is an outlier as it is quite less than the given data.
Calculating mean after removing 50 will give us mean equal to 78.9
So the correct answer is:
The set has 50 as an outlier and removing it increases the mean by about 3.
100 + 20m when m= 5 1/4
Answer:
205
Step-by-step explanation:
100 + 20m
Let m = 5 1/4
Change this to an improper fraction
5 1/4 = (4*5+1)/4 = 21/4
100 + 20*21/4
100 + 5*21
100 + 105
205
What is the directrix of the parabola defined by 1/4(y 3)=(x-2)^2?
Answer:
[tex]y = - 3.0625[/tex]
Step-by-step explanation:
The given parabola has equation:
[tex] \frac{1}{4} (y + 3) = {(x - 2)}^{2} [/tex]
Or
[tex]{(x - 2)}^{2} = \frac{1}{4} (y + 3)[/tex]
We compare this to
[tex] {(x - h)}^{2} = 4p(y - k)[/tex]
[tex] \implies \: 4p = \frac{1}{4} [/tex]
[tex]p = \frac{1}{4} \div 4[/tex]
[tex]p = \frac{1}{4} \times \frac{1}{4} [/tex]
[tex]p = \frac{1}{16} [/tex]
The vertex of this parabola is (2,-3)
The directrix is p units below the y-value of the vertex
[tex]y = - 3 - \frac{1}{16} = - 3.0625[/tex]
Which of the following is the radical expression of a^4/9
For this case we must find an expression equivalent to:
[tex]a ^ {\frac {4} {9}}[/tex]
By definition of properties of powers and roots we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So, rewriting the expression we have:
[tex]\sqrt [9] {a ^ 4}[/tex]
Answer:
Option 4
Answer: OPTION 4.
Step-by-step explanation:
By definition, Radical expressions are those that use a root.
In this case you have this expression:
[tex]a^{\frac{4}{9}[/tex]
In order to find the radical expression of [tex]a^{\frac{4}{9}[/tex], it is important to remember that:
[tex]a^\frac{m}{n}=\sqrt[n]{a^m}[/tex]
Therefore, once you apply this, you get:
[tex]a^{\frac{4}{9}=\sqrt[9]{a^4}[/tex]
You can observe that it matches with the expression provided in Option 4.
Find the surface area of the right rectangular prisim
Answer:
46 units^2
Step-by-step explanation:
The formula for surface area of a rectangular prism is
SA = 2(lw +lh+wh) where l is length, w is width and h is height
SA = 2 (2.5* 4+ 2.5*2 + 4*2)
= 2 (10+5+8)
= 2( 23)
= 46 units^2
Answer:
46 units^2
Step-by-step explanation:
The formula for surface area of a rectangular prism is
= 2(lw +lh+wh) is the formula
= 2 (2.5* 4+ 2.5*2 + 4*2)
= 2 (10+5+8)
= 2( 23)
= 46
Step-by-step explanation:
Suppose the odds in favor of me being nice are given as 100:1. What is the probability that the next time we meet I will be nice?
the probabiltity is:
outcome/total possible outcomes
therefore, 100/101
The probability that the next time we meet I will be nice is [tex]\frac{100}{101}[/tex].
Given that,
Suppose the odds in favor of me being nice are given as 100:1.
Based on the above information, the calculation is as follows:
[tex]= 100 \div (100 + 1)\\\\= 100\div 101[/tex]
Therefore we can conclude that The probability that the next time we meet I will be nice is [tex]\frac{100}{101}[/tex].
Learn more: brainly.com/question/17429689
A data set that consists of many values can be summarized using the five-number summary. Arrange these five values in order from least to
greatest
Your answer would be:
Minimum < Q1 < Median < Q3 < Maximum
Your welcome!
Two equations are given below:
a − 3b = 16
a = b − 2
What is the solution to the set of equations in the form (a, b)?
(−2, −6)
(−7, −9)
(−11, −9)
(−12, −10)
Answer:
(-11,-9)
Step-by-step explanation:
b-2-3b=16
-2b-2=16
-2b=18
b= -9
a= -9-2
a=-11
Solve for x.
4x – 4 <8 AND 9x + 5 > 23
Answer:
[tex]\large\boxed{2<x<3\to x\in(2,\ 3)}[/tex]
Step-by-step explanation:
[tex](1)\\4x-4<8\qquad\text{add 4 to both sides}\\4x<12\qquad\text{divide both sides by 4}\\x<3\\\\(2)\\9x+5>23\qquad\text{subtract 5 from both sides}\\9x>18\qquad\text{divide both sides by 9}\\x>2\\\\\text{From (1) and (2) we have}\ 2<x<3[/tex]
Answer:
[tex]2<x<3[/tex]
Step-by-step explanation:
Given : Inequality [tex]4x-4<8[/tex] and [tex]9x+5>23[/tex]
To find : Solve for x?
Solution :
Inequality 1 - [tex]4x-4<8[/tex]
Add 4 both side,
[tex]4x<12[/tex]
Divide by 4 both side,
[tex]x<3[/tex]
Inequality 2 - [tex]9x+5>23[/tex]
Subtract 5 both side,
[tex]9x>18[/tex]
Divide by 9 both side,
[tex]x>2[/tex]
From Inequality 1 and 2,
[tex]x<3[/tex] and [tex]x>2[/tex]
or [tex]2<x<3[/tex]
If the sum of the zereos of the quadratic polynomial is 3x^2-(3k-2)x-(k-6) is equal to the product of the zereos, then find k?
Answer:
2
Step-by-step explanation:
So I'm going to use vieta's formula.
Let u and v the zeros of the given quadratic in ax^2+bx+c form.
By vieta's formula:
1) u+v=-b/a
2) uv=c/a
We are also given not by the formula but by this problem:
3) u+v=uv
If we plug 1) and 2) into 3) we get:
-b/a=c/a
Multiply both sides by a:
-b=c
Here we have:
a=3
b=-(3k-2)
c=-(k-6)
So we are solving
-b=c for k:
3k-2=-(k-6)
Distribute:
3k-2=-k+6
Add k on both sides:
4k-2=6
Add 2 on both side:
4k=8
Divide both sides by 4:
k=2
Let's check:
[tex]3x^2-(3k-2)x-(k-6) \text{ with }k=2[/tex]:
[tex]3x^2-(3\cdot 2-2)x-(2-6)[/tex]
[tex]3x^2-4x+4[/tex]
I'm going to solve [tex]3x^2-4x+4=0[/tex] for x using the quadratic formula:
[tex]\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\frac{4\pm \sqrt{(-4)^2-4(3)(4)}}{2(3)}[/tex]
[tex]\frac{4\pm \sqrt{16-16(3)}}{6}[/tex]
[tex]\frac{4\pm \sqrt{16}\sqrt{1-(3)}}{6}[/tex]
[tex]\frac{4\pm 4\sqrt{-2}}{6}[/tex]
[tex]\frac{2\pm 2\sqrt{-2}}{3}[/tex]
[tex]\frac{2\pm 2i\sqrt{2}}{3}[/tex]
Let's see if uv=u+v holds.
[tex]uv=\frac{2+2i\sqrt{2}}{3} \cdot \frac{2-2i\sqrt{2}}{3}[/tex]
Keep in mind you are multiplying conjugates:
[tex]uv=\frac{1}{9}(4-4i^2(2))[/tex]
[tex]uv=\frac{1}{9}(4+4(2))[/tex]
[tex]uv=\frac{12}{9}=\frac{4}{3}[/tex]
Let's see what u+v is now:
[tex]u+v=\frac{2+2i\sqrt{2}}{3}+\frac{2-2i\sqrt{2}}{3}[/tex]
[tex]u+v=\frac{2}{3}+\frac{2}{3}=\frac{4}{3}[/tex]
We have confirmed uv=u+v for k=2.
which of the following is the probability that a Blue Marble will not be selected from a bag containing 9 red marbles 6 blue marbles 7 green Marbles and 11 yellow marbles if one is selected randomly
79%
32%
18%
82%
Answer: 82%
Step-by-step explanation: Count the total number of marbles.
9+6+7+11=33 marbles in total.
We are trying to find the probability of NOT picking a blue marble. There are 6 blue marbles. Subtract the blue marbles from the total.
33-6=27
The probability of not picking a blue marble is 27/33. Divide the fraction.
27/33=0.82
Multiply by 100 to get the percent.
0.82 x 100 = 82%
There is an 82% chance of not picking a blue marble.
What is the measure of AC?
А. 299
В. 122
с. 58
D. 116°
Answer:
○ D. 116°
Step-by-step explanation:
Think of the Unit Circle. You know that half of 360° is 180°, and that angle has a measure of 58°, so you do this:
-58° + 180° = 122°
Now, that chord of the circle drags it a bit by a few units, so that will be approximately 116°.
*This may not be the best explanation I can give, but I gave one.
I am joyous to assist you anytime.
+
Divisibility tests
Is 541982 divisible by 3?
Choose 1 answer.
A
Yes
® No
No
Stuck? Watch a video or use a hint.
Answer:
no
Step-by-step explanation:
541982/3 = 180,660.667
Step-by-step explanation:
Technically it is divisible by 3, but you would just end up with a decimal or fraction as the answer.
541892 divided by 3 = 180660.666667 or 180,660 666667/1000000
Which of the following is the inverse of f(x)=-2x+3
The inverse of [tex]\( f(x) = -2x + 3 \)[/tex] is [tex]\[ f^{-1}(x) = \frac{x - 3}{-2} \][/tex].
To find the inverse of f(x) = -2x + 3 , you need to interchange x and y and solve for y .
Start with y = -2x + 3 .
Swap x and y to get x = -2y + 3 .
Solve this equation for y .
x = -2y + 3
First, subtract 3 from both sides:
x - 3 = -2y
Then, divide both sides by -2 :
[tex]\[ \frac{x - 3}{-2} = y \][/tex]
Thus, the inverse of [tex]\( f(x) = -2x + 3 \)[/tex] is:
[tex]\[ f^{-1}(x) = \frac{x - 3}{-2} \][/tex]
evaluate -3ab when a= -2 and b= -5
Answer:
-30
Step-by-step explanation:
-3ab original equation
-3(-2)(-5) . plug in numerical values
6(-5) . -3 times -2 is 6
-30 . 6 times -5 is -30.
Answer:
-30
Step-by-step explanation:
Plug in -2 for a & -5 for b in the expression given:
-3ab = (-3)(-2)(-5)
Multiply across. Note that:
Negative number x negative number = positive number.
Positive number x negative number = negative number.
(-3)(-2)(-5) = (6)(-5) = -30
-30 is your answer.
~
through (-1,2), slope = 2 in standard form
Answer:
2x-y = -4
Step-by-step explanation:
We can use the point slope form of a line to write the equation and then convert it to standard form
y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point
y-2 =2(x--1)
y-2 =2(x+1)
y-2 =2x+2
The standard form is Ax +By =C
Subtract 2x from each side
-2x +y -2 =2x-2x+2
-2x+y-2 =2
Add 2 to each side
-2x+y -2+2 =2+2
-2x+y=4
The x term should be positive
Multiply by -1
2x-y = -4
Do you prefer to express solutions to inequalities using interval notation or as an inequality ? Do you think it’s important to know both formats ? How could each be used ?
Answer:
I prefer to express solutions to inequalities using interval notation. Both formats are are important but I think interval notation is easier to understand and represents better the solutions.
For example, if you have the following inequation:
x-2> 1
x>3
Therefore, the solution could be written either x>3 OR (3, +inf). But what happens if the solution to the system of equation is x>3 or x<-3? The solution can be easily written as: (-inf, -3) U (3, inf) instead of 'x>3 or x<-3' which can be confusing.