The interval notation of domain and range is (-∞, ∞).
Interval notation:
In algebra, interval notation refers the way to describe continuous sets of real numbers by the numbers that bound them.
Given,
Here we need to write the interval notation of domain and range.
In order to find the interval notation, first we have to know the definition of domain and range.
In math domain refers the domain of a function is the set of values that we are allowed to plug into our function. Basically, this set is the x values in a function such as f(x).
And where as the range of a function is the set of values that the function assumes. And it is the values that the function shoots out after we plug an x value in.
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What is the equation in point-slope form of the line that passes through the points (-3, -1) and (2, 9)?
y-1 = 2(x+3)
y-9=2(x-2)
y+9=2(x-2)
y-1= 2(x-3)
Answer:
[tex]\textsf{B)} \quad y-9=2(x-2)[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
Given points:
(-3, -1)(2, 9)Substitute the given points into the slope formula to find the slope of the line:
[tex]\implies m=\dfrac{9-(-1)}{2-(-3)}=\dfrac{10}{5}=2[/tex]
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Substitute the found slope and point (-3, -1) into the point-slope formula:
[tex]\implies y-(-1)=2(x-(-3))[/tex]
[tex]\implies y+1=2(x+3)[/tex]
Substitute the found slope and point (2, 9) into the point-slope formula:
[tex]\implies y-9=2(x-2)[/tex]
Therefore, the correct answer option is:
[tex]\textsf{B)} \quad y-9=2(x-2)[/tex]
how many 3/4 cups serving aare in 5 1/2 cups of yogurt
Answer:
Below
Step-by-step explanation:
5 1/2 = 11 / 2
11/2 ÷ 3/4 = 11/2 x 4/3 = 44/6 = 7 1/3
A textbook store sold a combined total of 429 chemistry and biology textbooks in a week. The number of chemistry textbooks sold was 51 more than the number of biology textbooks sold. How many textbooks of each type were sold?
Using system of linear equation, the store sold 240 chemistry books and 189 biology books
System of Linear EquationA system of equations is a set or collection of equations that you deal with all together at once. The general representation of linear equations are given as y = mx + c
m = slopec = y-interceptLet set our variables as;
chemistry = x biology = yx + y = 429 ...eq(i)
x = 51 + y ...eq(ii)
Put eq(ii) into (i)
(51 + y) + y = 429
51 + 2y = 429
2y = 429
y = 189
x = 51 + 189
x = 240
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Find the sum
5. 1/4+ 1/28+ 1/70+ ,.....
The sum is 9/28
What is sum ?
The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million.
The end result of addition is a sum. For instance, the sum 10, written, is obtained by adding 1, 2, 3, and 4. (1) The sum of the numbers is known as the sum of the addends, or summands occasionally.
1/4 + 1/28 + 1/70 + 1/30 + ............ 1/700
Multiply and divide by 3 in whole series
⇒ 1/3 X [3/4 + 3/28 + 3/70 + 3/130 + ......... 3/700]
⇒1/3 X [1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+..........1/25-1/28]
⇒1/3 x [1 - 1/28]
⇒1/3 * 27/28
⇒ 9 / 28
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If 3x – y = 5 and 2x + y = 15, evaluate x^2 + 2y
If 3x – y = 5 and 2x + y = 15 then evaluation of x^2 + 2y is equal to 72.
What is evaluation ?
Finding the value of an algebraic expression when a given number is used to replace a variable is known as evaluating the expression. When evaluating an expression, we change the variable in the expression to the given number and then use the order of operations to simplify the expression.
3x-y=5 and 2x+y= 15
Add the two equations together to eliminate y
3x-y=5
2x+y= 15
---------------------
5x = 20
Divide by 5
5x/5 = 20/5
x = 4
Now we can find y
2x+y = 15
2(4) +y = 15
8+y =15
Subtract 8 from each side
8+y-8 = 15-8
y =7
We want to find
x^2+2xy
(4)^2 +2(4)(7)
16+56
72
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PLS HELP THANK YOU SO MUCH
As we know that, while finding any angles on a line, the full angle is 360°.
Now we have three angles in the image and their sum will be 360°, and the angles are :
68° 90° yNow, 68° + 90° + y = 360°
=> 158° + y = 360°
=> y = 360° - 158°
=> y = 202°
Hence, y = 202° is the answer.
Please help, this is geometry and I need to find the measure of the missing angle
The measure of missing angle is 145°.
Define linear pair theorem.When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. The linear pair postulate or linear pair theorem in mathematics states the same thing mathematically. The sum of the measurements of two angles that make up a linear pair is 180°.
Given
Missing angle = x°
Opposite angle = 100°
Exterior angle = 35°
x and exterior angle are linear pair
Sum of linear pair is 180
x + 35 = 180
x = 180 - 35
x = 145
The measure of missing angle is 145°.
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Owen paid a landscaping company $108 for an initial lawn treatment,
then $74 per month thereafter.
The function p(t) = 108 + 74t represents the total amount of money he will
have paid after t months.
Find p(12).
The value of p(12) is $996
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
"Find p(24)" also means "Find the amount of money Owen pays for lawn service after 12 months" as we're given 12 for t. As such, rewrite the given function as p(12) = 108 + 74(12)
p(12) = 108 + 74(12)
p(12) = 108 + 888
p(12) = $996
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i’ll give brainliest!!!!
Answer:
Lyric ran faster.
Step-by-step explanation:
When you plot y = 5x, you can trace a certain point to see which value is higher. When I plotted y = 5x and chose the point when x = 8, y = 40 for Kira, and for Lyric, at x = 8, y = 80. Since the y coordinate (distance) is higher, Lyric ran faster.
Lyric ran faster than Kira, since they were travelling a longer distance when comparing to Kira in the same period of time.
Step-by-step explanation:You may use the following logic to analyze this situation. Theoretically, the faster runner will have traveled a longer distance at any given point in time different than 0 when comparing to the other runner. Therefore, let's randomly pick a point in time to see who had traveled the longer distance.
The time we'll evaluate will be 4 seconds.
1. Evaluating the function to find Kira's traveled distance at 4 seconds.
For this, simply substitute the "x" by the number "4" in the given equation for Kira:
[tex]y=5(4)\\ \\y=20[/tex]
Conclusion: Kira had traveled a total distance of 20 yards, 4 seconds after starting the race.
2. Evaluating the function to find Lyric's traveled distance at 4 seconds.
To evaluate the graph, we'll have to draw a line where x=4 sits and then find the value of "y" the function returns. Check the attached images in order to see this process.
Conclusion: Lyric had traveled a total distance of 40 yards, 4 seconds after starting the race.
3. General conclusion.
After 4 seconds Kira traveled 20 yards;
After 4 seconds Lyric traveled 40 yards.
Conclusion: Lyric ran faster than Kira, since they were travelling a longer distance when comparing to Kira in the same period of time.
any help on this question
Option A satisfy the equation after simplification that is y(y-1) / 3(y+1) when the equation that is 36y / (y²- 2y+1) ÷ 12y² / (y²-1)
Given that,
We have to simplify the equation that is
36y / (y²- 2y+1) ÷ 12y² / (y²-1)
We know that,
We have to divide the equations,
36y / (y²- 2y+1) ÷ 12y² / (y²-1)
We can write in multiplication form that is
36y / (y²- 2y+1) × (y²-1) / 12y²
Now we can divide the 36y by 12 y² we get 3/y
3(y²-1)/ y(y²- 2y+1)
We can write the y²-1 as (y-1)(y+1) and by formula y²-2y+1 as (y-1)²
3(y-1) (y+1)/ y (y-1)²
Now we can divide
3(y+1)/ y(y-1)
So we can see in the options
Therefore, Option A satisfy the equation after simplification that is y(y-1) / 3(y+1) when the equation that is 36y / (y²- 2y+1) ÷ 12y² / (y²-1)
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Casey inherited $70000, and decided to invest some of the money in a savings account earning 1% interest per year, and the rest in a certificate of deposit earning 2% interest per year. If the interest from the certificate of deposit was $800 more than the interest from the savings account, how much did Casey invest in each account?
Savings:
Certificate of Deposit:
The amount that Casey invested in the savings account is $10,000 and the amount Casey invested in the certificate of deposit is $60,000.
How much was invested in the savings account and the certificate of deposit?0.01c - 0.02s = $800 equation 1
c + s = $70,000 equation 2
Where:
c = amount invested in the certificate of deposit s = amount invested in the savings accountMultiply equation 2 by 0.01:
0.01c + 0.01s = 700 equation 3
Subtract equation 3 from equation 1:
0.01s = 100
Divide both sides of the equation by 0.01:
s = 100 / 0.01
s = 10,000
Substitute for s in equation 2:
c + 10,000 = 70,000
c = 70,000 - 10,000
c = 60,000
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help please and thanks so much
Answer:
Option 2
Step-by-step explanation:
The greater than sign with the line under it means greater than/less than or equal to. So -2.4 is less than or equal to -2.40.
-Hope this helped
i only need 12 and 17, first good response i will give brainliest please i’m desperate
Answer:
[tex]\textsf{12.} \quad y = 6x - 5[/tex]
[tex]\textsf{17.} \quad y=-\dfrac{1}{4}x-2[/tex]
Step-by-step explanation:
Question 12Find the slope of the line by substituting two points from the given table into the slope formula.
Define the points:
Let (x₁, y₁) = (2, 7)Let (x₂, y₂) = (3, 13)[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{13-7}{3-2}=\dfrac{6}{1}=6[/tex]
Substitute the found slope and point (2, 7) into the point-slope formula to create an equation of the line:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-7=6(x-2)[/tex]
[tex]\implies y-7=6x-12[/tex]
[tex]\implies y=6x-5[/tex]
Question 17Given:
f(4) = 3f(0) = -2Therefore, two points on the line are:
(4, -3)(0, -2)The y-intercept is the y-value when x = 0.
Therefore, the y-intercept of the line is -2.
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Substitute the y-intercept and the point (4, 3) into the slope-intercept formula and solve for m to find the slope:
[tex]\implies y=mx+b[/tex]
[tex]\implies -3=m(4)-2[/tex]
[tex]\implies -1=4m[/tex]
[tex]\implies m=-\dfrac{1}{4}[/tex]
Therefore, the equation of the line is:
[tex]y=-\dfrac{1}{4}x-2[/tex]
Which equation is equivalent to the given equation?
x² - 6x = 8
Answer:
(x-3)^2=17
Step-by-step explanation:
i took dis test b4
10. The table represents the relationship between the base length and the height of some parallelograms, Both measurements are in inches. What is the relationship between the base length and height of these parallelograms?
The relation between base length and height is: f(x) = 48/x
What is parallelogram?
A parallelogram is a straightforward quadrilateral in Euclidean geometry that has two pairs of parallel sides. A parallelogram has opposite sides that are facing one another and opposite angles that are of equal size.
By the values given in the table, for base length and height of the parallelograms, you can notice that base length increases 1 units, so you have 1, 2, 3, 4, 5.
For height you can notice that while base length increase 1 unit, height decreases by a factor of 1/x, just as follow:
1 - 48
2 - 24
3 - 16
4 - 12
5 - 8
The relation between base length and height is:
f(x) = 48/x
where f(x) is the height and x is the base length. In fact, you have:
f(1) = 48/1 = 48
f(2) = 48/2 = 24
f(3) = 48/3 = 16
f(4) = 48/4 = 12
Hence, the relation between base length and height is: f(x) = 48/x.
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30 POINTS // A spinner is divided into six equal parts numbered 1, 2, 3, 4, 5, and 6. In a repeated experiment, Ryan spun the spinner twice. The theoretical probability of both spins being even numbers is 9 over 36.
If the experiment is repeated 200 times, predict the number of times both spins will be even numbers.
36
50
100
200
The number of times both spins will be even numbers in 200 spins is (b) 50
How to predict the number of times both spins will be even numbers.From the question, we have the following parameters that can be used in our computation:
Sections on the spinner = 1, 2, 3, 4, 5, and 6
Also, from the question;
We have the following statement
The theoretical probability of both spins being even numbers is 9 over 36.
This means that
P(Both even) = 9/36
Lastly, we have
Times of experiment = 200
So, we have
Outcomes of both even = P(Both even) * Times of experiment
Substitute the known values in the above equation, so, we have the following representation
Outcomes of both odd =9/36 * 200
Evaluate
Outcomes of both odd = 50
Hence, the outcomes is (b) 50
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What is the probability of obtaining five tails in a row when flipping a coin?
Answer:
1/32
Step-by-step explanation:
There are 2^5 outcomes from flipping 5 times = 32
only ONE is T T T T T 1 OUT OF 32 = 1/32
If my math teacher asked me what's 5÷10+2-9 what would the answer be ??
Answer:-6.5
Step-by-step explanation:
Answer:
Step-by-step explanation
Use pemdas.
P- Parenthesis
e- Exponents
m- Multiplication
d- Division
a- Additon
s-Subtraction
5÷10+2-9
=5÷12-9
=5÷3
=1.666666666667
Quadra, PQRS is dilated by scale factor of 1/2 with point or as the center of dilation resulting in the image PQRS which statement is true about line Ps
The statement that is true about line segment P'S' is (c) Segment P'S' s 4 units long and lies on a different segment.
How to determine the true statement?
The complete question is in the attached image
From the image, we have:
PS = 8 units
This means that:
P'S' = 1/2 * PS
So, we have:
P'S' = 1/2 * 8
Evaluate
P'S' = 4
Also, the segment PS and P'S' do not lie on the same segment
Hence, the true statement is (c)
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Bobby and Garnetta thought of four consecutive odd intergers such as five times the sum of the first and the third was 22 greater than the product of 8 and the sum of the second and the fourth. Find the numbers.
An integer is a whole number x=-11.
What are Integers?The Latin term "Integer," which implies whole or intact, is the source of the English word "integer." A particular category of numbers called integers includes zero, positive numbers, and negative numbers.SymbolThe symbol "Z" stands for an integer.
Z= {……-8,-7,-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8,……}
Example :Let the numbers be x, x + 2, x + 4, x + 6...
5(x+x+4)=8(x+2+x+6)+22
5(2x+4)=8(2x+8)+22
10x+20=16x+64+22
The integers are -11,-9,-7,-5,
10x-16x=64+22-20 -6x=66/-6
x=-11.
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6) Tyger and Newton have a long jump
competition. Tyger jumps 20% further than
Newton. If Newton jumps 475 cm, how far
does Tyger jump?
★need help solving this problem
How do you solve 12-8x=-5x-5x??
Please help me!!
Answer:
-6
Step-by-step explanation:
12-8x= -5x-5x
Combine like terms
12-8x= -10x
Add 8x to both sides
12-8x= -10x
+8x. +8x
12= -2x
Divide both sides by -2
12= -2x
/-2. ;-2
-6=x
Hopes this helps please mark brainliest
what is 2×1+2×
1/
10
+1×
1/
100
+3×
1/
1000
Answer:
2.213
2×1+2(1÷10)+1(1÷100)+3(1÷1000)
2×1+2×0.1+0.01+3×0.001
2+0.2+0.01+0.003
2.213 #
hope this will help ig
Answer:
2.213
Step-by-step explanation:
2×1+2(1÷10)+1(1÷100)+3(1÷1000)
2×1+2×0.1+0.01+3×0.001
2+0.2+0.01+0.003
2.213
In a recent international sport competition, the top three
countries--Country A, Country B, and Country C-won a total of
129 medals. Country B won 9 more medals than Country C.
Country A won 39 more medals than the total amount won by the
other two. How many medals did each of the top three countries
win?
The Medals are as follows:
A = 84 medalsB = 27 medalsC = 18 medalsWhat is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
A + B + C = 119
Country B won 9 more than Country C so:
B = C + 9
Also, Country A won 39 more than the other two combined so:
A = B + C + 39
= (C + 9) + C + 39
= 2C + 48
Now we substitute into the equation:
A + B + C = 129
(2C + 48) + (C + 9) + C = 129
4C + 57 = 129
4C = 72
C = 18
So, if B = C + 9 then B = 27
and, A = 2C + 48 = 36+ 48 = 84
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An international company has 13,500 employees in one country. If this represents 19.6% of the company's employees, how many employees does it have in total?
Round your answer to the nearest whole number.
The required number of employees does it have in total is 68877.
What is percentage?A percentage is a part of an entire communicated as a number somewhere in the range of 0 and 100 as opposed to as a small portion. Something is all 100%, a big part of it is 50%, none of something is zero percent. To decide a rate, you partition the piece of the entire by the actual entire and duplicate by 100.
According to question:Let total population of the company be X
So,
19.6% of x = 13500
x(19.6/100) = 13500
X = 13500×100/19.6 = 68877 employees
Thus, required number of employees is 68877.
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A retirement account is opened with an initial deposit of $6,500 and earns 9.11% interest compounded monthly. What will the account be worth in 45 years?
Answer: $385,993.09
Step-by-step explanation:
Initial Amount: 6500
Rate: 0.0911 comp. monthly
Time: 45 years
Answer: 385,993.09
Find the value of x.
The triangles are similar triangles. Then the value of the variable 'x' will be 6.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
Similar triangles are shown below.
We know that the ratio of the corresponding sides of similar triangles remains constant. Then the equation is given as,
(6x - 1) / 15 = 14 / 6
Simplify the equation, then we have
(6x - 1) / 15 = 14 / 6
(6x - 1) / 5 = 7
6x - 1 = 35
6x = 36
x = 6
The triangles are comparable triangles. Then, at that point, the worth of the variable 'x' will be 6.
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Why were goods planned to become obsolete?
A. So that the company would become known for quality goods
B. So that people would keep buying new things
C. So that companies could protect their brand
D. So that people could save as much money as possible
Answer: B
Step-by-step explanation: B. So that people would keep buying new things
Goods are often planned to become obsolete in order to encourage people to continue buying new things. This can be done by intentionally designing products with a limited lifespan or by using materials that are prone to wear and tear. Companies may also release new versions of products or discontinue support for older models in order to encourage consumers to upgrade to the latest version. By making their products become obsolete, companies can create a sense of urgency for consumers to keep buying new things and maintain their sales.
Rewrite the following scientific notation numbers into standard form. (Be sure to use commas)
a. 3.23x10 -3
b. 7.45x10 5 =
Answer:
a. 0.00,323
b. 745,000
Step-by-step explanation:
a) move the decimal 3 places to the left
b) move the decimal 5 places to the right.
help meeeeeeeeeee pleaseee
For an average intake of 2200 calories per day, the number of acres of land is approximately 2.
How to solve equations?If we are given all a function so in that case, we just need to substitute values given in question and solve for unknown variable that is to be determined.
C(x) is a variable that tells the number of calories consumed daily by a person
x is the number of acres that person own.
C(x) = 270㏑(x+1) +1900
In the given question number of acres ask a person to have who consumed 2200 calories in a day.
Therefore,
C(x)=2200
2200=270㏑(x+1) +1900
2200-1900=270㏑(x+1)
300=270㏑(x+1)
300/270 = ㏑(x+1)
10/9 = ㏑ (x+1)
x+1 = [tex]e^{\frac{10}{9} }[/tex]
x+1 = 3.037
x= 3.037-1
x=2.037
x=2(round off)
Therefore, 2 acres of land a person can consume 2200 calories in a day.
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