[5, +∞) ∪ (-∞,7] is the notation to express the set of all numbers greater than or equal to 5 and less than or equal to 7.
We need to use interval notation to express the set of all numbers greater than or equal to 5 and less than or equal to 7.
What is a set?A set is a mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
Let x belong to the set of real numbers (R)
Now, x≥5 and x≤7.
So, x≥5⇒[5, +∞) and x≤7⇒(-∞,7]
Therefore, the notation will be [5, +∞) ∪ (-∞,7].
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Find the solution for x in the equation below.
x² + 72x = 8
[tex]x^2+72x=8\\x^2+72x+1296=1304\\(x+36)^2=1304\\x+36=\sqrt{1304} \vee x+36=-\sqrt{1304} \\x=-36+2\sqrt{326} \vee x=-36-2\sqrt{326}[/tex]
solve for x: 5x-4y=24
Answer:
x=4y+24/5
Step-by-step explanation:
add 4y
Divide by 5
what is slope in algebra 1?
Answer:
rise over run aka a measure of its steepness
Step-by-step explanation:
A medication states that the odds of having an allergic reaction are 2 in 200. What is that probability states as a percent?
Given a function described by the table below, what is y when x is 5?
XY
26
48
59
612
Answer:
y = x + 4
when x is 5, y is 9
Step-by-step explanation:
the pattern from the table is that the y value is 4 more than the x value, so the equation would be y = x + 4.
if you plug in x = 5, then this would be y = 5 + 4 = 9
The values of x and y vary directly
and one pair of values are given.
Write an equation that relates x
and y. Simplify completely.
x = 12, y = 3
1
y =
?
x
►
Enter
Answer:
1/4
Step-by-step explanation:
Since y/x = 3/12 = 1/4, the answer is 1/4.
Which absolute value function, when graphed, will be wider than the graph of the parent function, f(x) = |x|?
f(x) = |x| + 3
f(x) = |x − 6|
f(x) = |x|
f(x) = 9|x|
The absolute value function that will be wider than the graph of the parent function, f(x) = |x| is (d) f(x) = 9|x|
How to determine the function?The parent function is given as:
f(x) =|x|
A wider function would have the following equation
f(x) = k|x|
Where:
k > 0
From the list of options, we have:
f(x) = 9|x|
Hence, the absolute value function that will be wider than the graph of the parent function, f(x) = |x| is (d) f(x) = 9|x|
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Answer:
getting to the point , D.
Step-by-step explanation:
trust
From Kansas City to Denver is twice as far as from Kansas City to St. Louis the two distance together total 900 miles what are the two distance?
Answer:
KC to StL = 300
KC to Den = 600
Step-by-step explanation:
KC to StL was the base distance, so we'll call that x.
KC to Denver is twice as long, so we'll call that 2x.
If we add the together is is 900 miles total.
x + 2x = 900 Combine like terms
3x = 900 Divide by 3
x = 300
If x is 300, then 2x is 600.
(07.01) A bacteria culture begins with 4 bacteria which double in size every hour. How many bacteria exist in the culture after 8 hours?
Answer: By 8 hours, there will be 65536 bacteria in the culture.
Step-by-step explanation:
The numerical expression used for this problem is [tex]4^{8}[/tex].
You can find the value of this on a calculator. I hope this helps!! :)
If that is not the answer, then try 32 because 4*8=32.
Select the graph for the solution of the open sentence. Click until the correct graph appears.
3|x| > 6
I would really appreciate the help!:)
The solution of the inequality will be x > 2 and x < -2. And the graph is drawn below.
What is inequality?Inequality is defined as an equation that does not contain an equal sign.
The inequality is given below.
3|x| > 6
By solving the equation, we have
|x| > 2
x > 2
x < -2
Then the graph will be drawn.
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*
Which of the following are situations that can be modeled with a quadratic function? Select all that apply.
O
0
A tree decays 10% every six weeks.
The height of a diver after jumping from a high dive into the water.
The height of a ball rolled down a hill.
A gym charges $15 perfitness class.
An ant bocid eliminates 50% of bacteria every 24 hours
The height of a rocket after it is Bunched
Answer:
Option 2 and 5 are correct. Look down for my explanation↓:
Step-by-step explanation:
So We need to tell which one of them is quadratic function.
Option 1 is exponential decay so, it is not quadratic.
Option 2 is quadratic because the diver will take the parabolic shape when jumps.
Option 3 is not quadratic. Option 4 is not quadratic it is linear.
Option 4 is again exponential not quadratic.
Option 5 is quadratic because it takes the parabolic shape again.
The functions f(x) = x2 – 2 and g(x) = –x2 + 5 are shown on the graph.
The graph shows f of x equals x squared minus 2, which is an upward opening parabola with a vertex at 0 comma negative 2 and a point at negative 1 comma negative 1 and a point at 1 comma negative 1. The graph also shows g of x, which is a downward opening parabola with a vertex at 0 comma 5 and a point at negative 1 comma 4 and a point at 1 comma 4.
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
y > x2 – 2
y ≥ –x2 + 5
We will need to shade the region above f(x) and the region below the function g(x)…
How to transform the graph into the solution set?We have:
f(x) = x² - 1
g(x) = -x² + 4
Both of these are already graphed, and we want to transform it into:
y > f(x)
y ≤ g(x)
The first inequality means that we need to graph f(x) with a dashed line, because f(x) is not part of the solution, and then we shade all the region above f(x)…
For the other inequality, we use a solid line (because the points on the line are solutions) and then we shade the part below the curve…
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What is true of an equilateral triangle? Two of its side lengths are equal. All its side lengths are equal. None of its side lengths are equal. None of its interior angles are equal. What is true of an equilateral triangle ? Two of its side lengths are equal . All its side lengths are equal . None of its side lengths are equal . None of its interior angles are equal .
Answer:
All its side lengths are equal
(and all the agle of 60°)
Step-by-step explanation:
What is true of an equilateral triangle? Two of its side lengths are equal. All its side lengths are equal. None of its side lengths are equal. None of its interior angles are equal. What is true of an equilateral triangle ? Two of its side lengths are equal . All its side lengths are equal . None of its side lengths are equal . None of its interior angles are equal .
Cost of 6 kg of rice is 540 what is the cost of 13 kg of rice.
Answer:
1170$Step-by-step explanation:
Cost of 6 kg of rice is 540 what is the cost of 13 kg of rice.
we can solve with an equation
6 : 540 = 13 : x
x = 540 * 13 : 6
x = 7020 : 6
x = 1170
--------------------------
check
6 : 540 = 13 : 1170
0.01111111111 = 0.01111111111
the answer is good
A phone company offers a monthly cellular
phone plan for $25. The plan includes 250
anytime minutes, and charges $0.20 per minute
above 250 min. Write a piecewise-defined
function for C(x), the cost for using x minutes in
a month.
The function will be given as C(x) = 25 + 0.2(x) here x is in minutes.
What is a function?A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.
Given that:-
A phone company offers a monthly cellular phone plan for $25. The plan includes 250 anytime minutes and charges $0.20 per minute above 250 min.The cost of the 250 minutes is $25 and if the time extends from 250 minutes then the function will be expressed in the form of.
C(x) = 25 + 0.2 (x)
Here C(x) is the total cost and the x is in minutes.
Hence the function will be given as C(x) = 25 + 0.2(x) here x is in minutes.
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Which best describes the range of the function #(x) = 2(3)x? O y>0 O y≥0 O y = 2 O y≥2
Answer:
The range of the function f(x) : is y > 0.
The correct option is (A)
Step-by-step explanation:
The definition of range is the set of all possible values that the function will give when we give in the domain as input.
Given function is :
If we draw the graph for this, then we can see that the horizontal asymptote is 0.
So, the range is real numbers higher than 0.
Hence, the range should be y > 0.
What is the slope of the line y = 3? O A. 3 O B. 1 O C. O O D. Undefined
Answer:
C
Step-by-step explanation:
The slope of a horizontal line, such as that of y= 3, is equal to 0.
This can be proved using the slope formula.
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
Let's choose 2 points on the line y= 3:
(0, 3) and (2, 3)
Slope
[tex] = \frac{3 - 3}{2 - 0} [/tex]
[tex] = \frac{0}{2} [/tex]
= 0
Thus, the line has a slope of zero.
On the other hand, vertical lines have an undefined slope.
Additional:
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Need the answer for number 3 please!!!!
Answer:
Perimeter = 2(l + b)
= 2(x + 5x³ + 4 - x²)
= 2x + 10x³ + 8 - 2x²
= 10x³ - 2x² + 2x + 8
Hence, ur answer is the first option.
Answer:
A.
Step-by-step explanation:
L = x
W = 5x³ + 4 - x²
P = 2L + 2W
P(x) = 2x + 2(5x³ + 4 - x²) = 2x + 10x³ + 8 - 2x²
P(x) 10x³ - 2x² + 2x + 8
L = x
W = 5x³ + 4 - x²
P= 2L + 2W
P(x) = 2x + 2(5x³ + 4 - x²) = 2x + 10x³ + 8 - 2x²
= P(x) 10x³ - 2x² + 2x + 8
evaluate 7/8+1/4÷6/7
Step-by-step explanation:
[tex] = \frac{7}{8} + \frac{1}{4} \div \frac{6}{7} [/tex]
[tex] = \frac{7}{8} + \frac{1}{4} \times \frac{7}{6} [/tex]
[tex] = \frac{7}{8} + \frac{7}{24} [/tex]
[tex] = \frac{7 \times 3}{8 \times 3} + \frac{7}{24} [/tex]
[tex] = \frac{21}{24} + \frac{7}{24} [/tex]
[tex] = \frac{28}{24} [/tex]
[tex] = \frac{7}{6} [/tex]
7/8+(1/4÷6/7)
1/4 ÷ 6/7 = 7/24
7/8 + 7/24 = 7/6 = 1 1/6
Ratio of men to women working for a company is 7to5 there are 75 women working for the company what is total number of employees
Answer:
There is a total of 180 employees.
Step-by-step explanation:
men : women
7 : 5
5 units = 75
1 unit = 15
12 units = 180
!!WILL GIVE BRAINLIES PLS HELP!!!
Which inequality in vertex form represents the region less than or equal to the quadratic function with vertex (-6,
12) and includes the point (-9, 15) on the boundary?
Answer:
is B
Step-by-step explanation:
this is the best possible answer
Pleas hurry!!!!! Which line is perpendicular to a line that has a slope of -5/6
line JK
line LM
line NO
line PQ
Answer:
LM
Step-by-step explanation:
Perpendicular slope would be - 1 / m = - 1/(-5/6) = 6/5
slope m = rise / run line LM rises 6 for a run of 5
Which is the graph of f,(x) = 0.5(4)*
I assume you meant [tex]f(x)=0.5(4)^{x}[/tex]. The graph is shown below.
The frequency table shows the results of a survey asking people how many
hours they spend online per week. On a piece of paper, draw a histogram to
represent the data. Then determine which answer choice matches the
histogram you drew.
Hours online Frequency
5
8
10
9
7
0-3
4-7
8-11
12-15
16-19
Based on the frequency table given, The option that closely matches the histogram I drew is option C but the last one suppose to be 7 and not 6.
What is the histogram about?Hours online Frequency
5 0-3
8 4-7
10 8-11
9 12-15
7 16-19
Note that in the image attached, you can see how the Hours online were said to be matched with the Frequency.
So since option A and B was not shown to see which matches the option, i can say option c is closest but if look at my own image, you can use it to find the right one.
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Given the expression: 6x10 − 96x2
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
The expression 6x¹⁰ - 96x² can be written by factoring out the greatest common factor is 6x²(x⁸ - 16) and for a part, B expression can be simplified by applying identity.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have an expression:
Part A)
= 6x¹⁰ - 96x²
= 6x²(x⁸ - 16)
Part B)
[tex]\rm =6x^2(\left(x^4\right)^2-4^2)[/tex]
[tex]\rm =6x^2(\left(x^4+4\right)\left(x^4-4\right))[/tex]
[tex]\rm =6x^2\left(x^2+2x+2\right)\left(x^2-2x+2\right)\left(x^2+2\right)\left(x^2-2\right)[/tex]
Thus, the expression 6x¹⁰ - 96x² can be written by factoring out the greatest common factor is 6x²(x⁸ - 16) and for a part, the B expression can be simplified by applying identity.
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Which number produces a rational number when added to 1/2?
Answer:
Another rational number.
Step-by-step explanation:
For example, [tex]\pi[/tex] is incorrect because It is a irrational number
you must add another rational number to 1/2 to make the sum rational.
Rational number are numbers that can be converted into a fraction.
all natural numbers, whole numbers, integers, are rational.
and all rational and irrational numbers are real numbers
What complex number is represented by the polar coordinates (4, -pi/4)
Answer:
[tex]\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}[/tex]
Step-by-step explanation:
A complex number is defined as z = a + bi. Since the complex number also represents right triangle whenever forms a vector at (a,b). Hence, a = rcosθ and b = rsinθ where r is radius (sometimes is written as |z|).
Substitute a = rcosθ and b = rsinθ in which the equation be z = rcosθ + irsinθ.
Factor r-term and we finally have z = r(cosθ + isinθ). How fortunately, the polar coordinate is defined as (r, θ) coordinate and therefore we can say that r = 4 and θ = -π/4. Substitute the values in the equation.
[tex]\displaystyle \large{z=4[\cos (-\frac{\pi}{4}) + i\sin (-\frac{\pi}{4})]}[/tex]
Evaluate the values. Keep in mind that both cos(-π/4) is cos(-45°) which is √2/2 and sin(-π/4) is sin(-45°) which is -√2/2 as accorded to unit circle.
[tex]\displaystyle \large{z=4\left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2}}{2}i \right)}\\\\\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}[/tex]
Hence, the complex number that has polar coordinate of (4,-45°) is [tex]\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}[/tex]
100 points (08 03)Consider the following set of equations: Equation A: y = 2x + 4 Equation B: y = 3x + 1 Which of the following is a step that can be used to find the solution to the set of equations? 08 03 ) Consider the following set of equations : Equation A : y = 2x + 4 Equation B : y = 3x + 1 Which of the following is a step that can be used to find the solution to the set of equations ?
Answer:the equations are
y = x + 4 and y = 3x + 6
Now we can use substitution method to solve the system
So we can substitute value of y from one equation into other
So we get
x+4 = 3x+6
So Option B is correct
Step-by-step explanation:
Answer:
2x + 4 = 3x + 1
Explanation:
Equation A: y = 2x + 4
Equation B: y = 3x + 1
Simultaneously solving :
⇒ y = y
⇒ 2x + 4 = 3x + 1
⇒ 2x - 3x = 1 - 4
⇒ -x = -3
⇒ x = 3
Solve for y :
⇒ y = 2x + 4
⇒ y = 2(3) + 4
⇒ y = 10
(a) Solve the following formula for b.
1
A = ab
(b) Evaluate b when A= 18 and a =
6/5
1
(a) The formula A = ab solved for b is b = 3X
6
(b) Evaluate b when A= 18 and a = 5
b = (Type an integer or a simplified fraction.)
Answer:
a. b = 2A/a
b. 30
Step-by-step explanation:
a. to solve for b:
[tex]A = 1/2 ab[/tex]
multiply both sides by 2
[tex]2A = ab[/tex]
divide both sides by a
[tex]2A/a=b[/tex]
so b = 2A/a
b. using the equation b = 2A/a
[tex]b = 2*18/(6/5)\\= 36/(6/5)\\= 30[/tex]
The hypotenuse of a 90-45-45 triangle is 20√2. What is the short leg and the long leg>
Answer:
Both legs would be 20
Step-by-step explanation:
In the image below, it shows the relationship between the legs and the hypotenuse in every 45 45 90 triangle. If we know that the hypotenuse is 20, then the 2 legs are both 20.
I am slightly confused with the problem since they asked for the "short" leg and the "long" leg. Both legs should be the same length because a 45 45 90 triangle is isosceles, with the two legs being the same length.
