To plot x = -1 on a graph, draw a vertical line at x = -1 and extend it infinitely in both directions.
To plot x = -1, start by drawing a horizontal line on the x-axis. Then, use a ruler to draw a vertical line at x = -1. Make sure that this vertical line extends infinitely in both directions, above and below the x-axis.
This line will represent x = -1. Now, draw a point at the intersection of the vertical and horizontal lines. This point will be the point where x = -1. To double-check your work, label the point as (-1, 0).
This means that the x-value is -1, and the y-value is 0. If you wish, you can extend the vertical line in both directions to get a better sense of the line's position. Congratulations, you have now plotted x = -1 on your graph!
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What is the product of 4 5x3 7?
The product of 4 5x3 7 is 420. To fully express the calculation, we can write it as 4 x (5 x 3) x 7 = 420. In other words, four multiplied by the product of five times three multiplied by seven equals 420.
First, multiply 5 and 3 to get 15.
Next, multiply 4 and 15 to get 60.
Lastly, multiply 60 and 7 to get 420.
4 x (5 x 3) x 7 = 420
First, we need to multiply the 5 and the 3 together in order to get the product of 15. Then, we need to multiply 4 and 15 in order to get the product of 60. Finally, we will multiply 60 and 7 together to get the final product of 420. To fully express the calculation, we can write it as 4 x (5 x 3) x 7 = 420. In other words, four multiplied by the product of five times three multiplied by seven equals 420.
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The nth term of a series is represented by an=6^n/5^n+1 ⋅n. Mario correctly applies the ratio test to determine whether the series converges or diverges. Which statement reflects Mario's conclusion?
Since, Mario correctly applies the ratio test to determine whether the series converges or diverges. Mario's conclusion would be that the series converges if the limit of (an+1/an) as n approaches infinity is less than 1.
What informs Mario's conclusion?If Mario correctly applies the ratio test to determine whether the series converges or diverges, he would find that the series converges if the limit of (an+1/an) as n approaches infinity is less than 1, and diverges if the limit of (an+1/an) as n approaches infinity is greater than or equal to 1.
So, Mario's conclusion would be that the series converges if the limit of (an+1/an) as n approaches infinity is less than 1.
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Write six less than seven and one-half times the number of acres of land Joe has as an algebraic expression. Use a as your variable
An algebraic expression for six less than seven and one-half times the number of acres of land Joe has:
(7 1/2)a - 6
Let us assume that a represents the number of acres of land Joe has.
We need to write given statement as an algebraic expression.
Consider given statement.
Six less than seven and one-half times the number of acres of land Joe has.
i.e., six less than seven and one-half times 'a'
As we know six less than.. means Subtract 6 from ...
So, we rewrite above statement as,
subtract 6 from seven and one-half times 'a'
So, we get an expression (7 1/2 × a) - 6
We can write the mixed fraction seven and one-half times (7 1/2) as 15/2 (a proper fraction)
So, an algebraic expression becomes,
(15/2 × a) - 6
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What is the length of BC?
Using the concept of proportions and similar triangle theorem, the value of BC is x + [(x² + 3x) / 3x - 8]
What is Similar Triangle TheoremA similar triangle is a triangle that has the same shape as another triangle, but not necessarily the same size. Two triangles are similar if and only if their corresponding angles are equal and the ratios of their corresponding sides are equal.
The Similar Triangles Theorem states that if two triangles have corresponding angles that are congruent, then their corresponding sides are in proportion. In other words, if two triangles have the same shape, the ratio of any pair of corresponding sides is always the same.
To find the value of BC, we can use similar triangle theorem as;
AB / BC = DE / EC
Substituting the values;
4x - 6 / (x + EC) = x + 2 / EC
NB: BE = EC
4x EC - 6EC - x EC - 2EC = x² + 2x
NB: This is done after cross multiplying and collecting like terms
3x EC - 8 EC = x² + 2x
(3x - 8) EC = x² + 3x
EC = x² + 3x / 3x - 8
The length of BC = BE + EC
BC = x + [(x² + 3x) / 3x - 8]
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Choose the that seems to be congruent to the given one.
ABD=
AFC
AEC
DFA
Triangle AFC is the triangle that appears to be consistent with triangle AFD.
Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. There is an obtuse angle, or angle AFD, same like in the give triangle AFD.
Therefore, the opposite triangle must have an obtuse angle in order to be a congruent triangle. Only triangle AFC, out of the three that are given, has an acute angle. Additionally, they both support the same side, increasing the likelihood of congruence. There is no obtuse angle in the triangles BFC and DFE.
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Solve the inequality two-thirds times the absolute value of the quantity one half times x plus 3 end quantity is less than 4.
x > −18 and x < 6
x < −18 and x < 6
x > −18 and x < 18
x > −30 and x < 18
The inequality solution for 2/3 | 1/3 x + 3 | < 4 is x > −18 and x < 6.
The correct option is (A).
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
2/3 | 1/3 x + 3 | < 4
Now, solving the inequality
2/3 | 1/2 x + 3 | < 4
| 1/2 x + 3 | < 4 (3/2)
| 1/2 x + 3 | < 6
± (1/2x + 3) < 6
Now, splitting the inequalities
1/2x + 3 < 6 or -1/2x - 3 < 6
1/2x < 3 or -1/2x < 9
x< 6 or -x < 18
x< 6 or x> -18
Hence, the inequality is x > −18 and x < 6.
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Answer: A
Step-by-step explanation: The person above is right and took the exam on FLVS
Triangle RAT has vertices R(-3,7),S(6,5), and T(2,-2).What will be the coordinates of the vertices after the reflection over the line y=-x?
The reflected triangle be R'S'T'
coordinate of R' is (-7, 3) , S' is (-5, -6) and T' is (2, -2)
What is Reflection ?Reflection is a sort of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. For instance, Triangle P has been reflected to become Triangle Q on the line x = 4 x= 4 x= 4.
A flip is a geometric movement that involves turning an item over in a straight line to create a mirror image. The distance between each point on an item and its corresponding point on the picture is equal. A reflection is another name for a flip.
The x-coordinate and y-coordinate are reversed when a point is reflected over the line y = x. The x-coordinate and the y-coordinate switch places and become negated if you reflect over the line y = -x.
So, the coordinate of RST is
R(-3, 7), S(6,5), T(2, -2)
The reflected triangle be R'S'T'
coordinate of R' is (-7, 3) , S' is (-5, -6) and T' is (2, -2)
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After reflection along the line y is x, the image of the point (5, -3) is (-3, 5).
What is a reflection of the point?It is the representation of the point that is situated in the opposite direction of the specified point.
Given
The reflecting line is y = x at the point (5,-3).
The image's center will therefore be about on the line y = x.
If x = 5, then y will have the value of 5.
The value of x will be x = -3 for y = -3.
Consequently, the image's purpose is (-3, 5).
After reflection along the line y is x, the image of the point (5, -3) is (-3, 5).
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5x-10 = 10(12 + 1/4x)
Answer:
x=52
Step-by-step explanation:
ignore the work at the top of the
Answer: To eliminate x in the system of linear equations, multiply equation 1 by 4 and multiply equation 2 by 5, then subtract both equations.
How to Solve a System of Equations?
Given the system of linear equations as:
Equation 1: 5x − 2y = 10
Equation 2: 4x − 3y = 15
To eliminate x in the system of equations given above, multiply equation 1 by 4 and multiply equation 2 by 5
× 4 Equation 1: 5x − 2y = 10
× 5 Equation 2: 4x − 3y = 15
20x − 8y = 40
20x − 25y = 75
Subtract both equations to eliminate x
17y = -35
In summary, to eliminate x in the system of linear equations, multiply equation 1 by 4 and multiply equation 2 by 5, then subtract both equations.
Step-by-step explanation:
help help helphelp help help help help me
The graphs of the modulus functions are just a pair of lines drawn simultaneously.
What is a modulus function?A modulus function is a function which gives the absolute value of a number or variable. It produces the magnitude of the number of variables. It is also termed as an absolute value function. The outcome of this function is always positive, no matter what input has been given to the function.
Given here ; The modulus functions y=|x|-2 , y=|x-1|+1 , y=|x-3|
To plot these, we’ll use the definition of a modulus function, just like for |x|. Let’s start with the first one.
|x–3|={x,, when x≥3
{ −x when x<3
That means, to plot the graph of y = |x – 3|, we have to plot the graph of
y = x – 3, when x ≥ 3
y = 3 – x, when x < 3
That is, for x ≥ 3, we’ll draw a line whose slope is 1 and y-intercept is –3. For x < 3, we’ll draw a line whose slope is –1 and y-intercept is -3.
Similarly for y=|x|-2 and y=|x-1|+1 we can use the definition of modulus function to plot the pair of lines (y=x-2 & y=-x-2) & (y=-x+2 & y=x)
as shown in the graph attached.
Hence, The graphs of the modulus functions are just a pair of lines drawn simultaneously.
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PLS ANWSER ASAP 100 POINTS MARKING BEST AND GOOD BRAINLIST
What polynomial x3 8 is equal to?
The polynomial [tex]x^{3}[/tex] + 8 is equal to (x + 2)([tex]x^{2}[/tex] – 2x + 4).
What is polynomial ?
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. An example of a polynomial of a single indeterminate x is x2 − 4x + 7.
The given expression is
[tex]x^{3}[/tex] + 8
It can be rewritten as
[tex]x^{3}[/tex] + [tex]2^{3}[/tex]
Formula for sum of cubes:
[tex]x^{3} + y^{3} = (a+b)(x^{2} -xy+y^{2} )[/tex]
For the given expression a=x and b=2.
[tex]x^{3}[/tex] + [tex]2^{3}[/tex] = (x + 2)([tex]x^{2}[/tex] – 2x + 4).
[tex]x^{3}[/tex] + 8 = (x + 2)([tex]x^{2}[/tex] – 2x + 4).
Therefore , The polynomial [tex]x^{3}[/tex] + 8 is equal to (x + 2)([tex]x^{2}[/tex] – 2x + 4).
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By using efficient water fixtures, the average American can cut water use to about 45 gallons of water per day. About how many gallons of water would the average American use in December if they used the new amount?
Answer:
45*31=1,395
that would be 1,395 gallons if water used in december.
Step-by-step explanation:
& Ms. Patterson bought a case of pencils at the beginning of the school year.
• The case had 48 boxes with 24 pencils in each box.
She wants to give & pencils to each of her 23 students to begin the year.
How many extra pencils will she have after she gives the pencils to her students?
9
B
D
1.152
968
Answer: 968 extra pencils
Step-by-step explanation:
Part 1 of 2
Challenge Josh plans to make birdhouses to sell at a craft fair. He has a sample of the wood he wants to use. The sample has area
square foot and weighs pound
The local hardware store sells the wood only by the square yard. There are 9 square feet in 1 square yard. What is the unit rate for pounds of the wood per square yard? If
Josh needs 3 square yards of the wood in all, how many pounds of the wood does he need?
The weight of three square yards of wood equals the weight of three square yards of wood =3×22.5=67.5 lb.
How to find the calculation?a. A sample of wood measuring 1/5 square foot weighs 1/2 lb.
5 is multiplied on both sides to get,
1 square foot of wood sample weighs 1/2/5=5/2 pounds.
A square yard now equals nine square feet.
Therefore, the weight of a sample of wood in a square yard is nine pounds, and the weight of a sample of wood in a square foot is nine plus five divided by two is forty-five divided by two is twenty-five pounds.
b. The weight of three square yards of wood equals the weight of three square yards of wood.
=3×22.5=67.5 lb.
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Three ballet dancers are positioned on stage. If Vijay is 2 meters straight behind Jordan and 1 meter directly left of Alana, how far is Jordan from Alana?
The distance between Jordan and Alana will be √5 meters.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that three ballet dancers are positioned on stage. If Vijay is 2 meters straight behind Jordan and 1 meter directly left of Alana.
Let Jordan be at origin (0, 0). Then, Vijay will be at (-2, 0). Alana will be at point (-2, - 1). The distance from Jordan to Alana will be -
r² = (- 1 - 0)² + (- 2 - 0)²
r² = 1 + 4
r = √5
Therefore, the distance between Jordan and Alana will be √5 meters.
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Please help me with this question, will give brainliest.
To complete the two-column proof, the required statement and reason are explained below.
Properties of a parallelogram.A parallelogram is a given plane figure which has its opposite sides to be parallel and equal in length. It has its unique identifying properties.
Supplementary angles are two or more angles which add up to 180^o.
To complete the two-column proof, we have;
STATEMENT REASON
1. ABCD and GDEF are parallelograms Given
2. <C and <CDA are supplementary angles m<C + m<CDA = 180^o
3. m<C + m<F = 180^o Definition of supplementary angles
4. <EDG ≅ <F Definition of congruent angles
5. <EDG = <F Parallelogram opposite angles theorem
6. m<CDA = m<EDG Vertical angles congruence theorem
7. m<CDA ≅ m<EDG Definition of congruent angles
8. m<CDA ≅ m<F Given
9. m<C + m<CDA = m<C + m<EFG Substitution property of equality
10. <C and <F are supplementary angles Parallelogram consecutive
angles theorem
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How many different fourb letter permutations can be formed from the letters in the word
“triangle”?
Answer: Hence we have 6 × 3 = 18 words of this type. Therefore, using the equation (i), (ii) and (iii). Total words with 4 letter are : 1680 + 756 + 18 = 2454 ∴ 2454 different permutations can be formed from the letter of the word EXAMINATION taken four at a time.
What is the additive inverse of /- 4?
The additive inverse of -4 is 4.
The Additive InverseIn mathematics, the additive inverse of a number is the number that, when added to the original number, results in a sum of zero. So for any number x, the additive inverse of x is -x. Therefore, the additive inverse of -4 is 4 because (-4) + 4 = 0.
The concept of additive inverse is used in many areas of mathematics, such as algebra, where it is used to solve equations and simplify expressions.
For example, if you have an equation such as x + (-4) = 0, you can simplify it by adding 4 to both sides, which results in x = 4. This is because 4 is the additive inverse of -4, and when added to -4, the sum is zero.
Another application of additive inverse is in linear algebra when working with vector space. Additive inverse is also used in cryptography and error correction codes.
It also could be used in many other fields like physics, finance and engineering.
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alonzo has been given a list of 4 bands and asked to place a vote. his vote must have the names of his favorite, second favorite, and third favorite bands from the list. how many different votes are possible? \
There are 24 ways for the vote of the favorite, second favorite, and third favorite band to be cast.
The list contains 4 bands.
Out of these 1 band is Alonzo's favorite, 1 is his second favorite and another is his 3rd favorite
Now to choose his favorite Alonzo has 4 choices. Hence there are 4 ways to cast this vote.
Now since one band has been chosen, Alonzo is left with 3 bands on the list, hence he has 3 ways to cast the vote for the second favorite.
For the last vote of 3rd favorite, there are2 options available, hence this can be done in 2 ways.
Hence we get the total number of ways to be
4 X 3 X 2 ways
= 24 ways
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formulas for any given events a and b: 1) 2) 3) in a certain town: 70% of households have cable tv (event c) , 55% of households have netflix (event n) and 42% of households subscribe to both. a) find the probability that a household subscribes to cable tv or netflix % b) find the probability that a household does not subscribe to netflix. %
The probability that a household subscribes to cable tv and netflix is 0.32.
What is probability in maths?Mathematical descriptions of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the probability of an event, with 0 roughly denoting impossibility and 1 denoting certainty.Probability is a synonym for potential. It is a field of mathematics that examines how random events happen.How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.Given data :
We know that from they gave us, cable tv have 70% , Netflix have 55%
so, C = 70% / 100% = 0.7
N = 55% / 100% = 0.55
The probability of both C and N is ;
= [tex]\frac{42}{70 + 55}[/tex] % = 0.318 ≅ 0.32
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PLEASE HELP ASAP!!!!!!!!!! DON'T KNOW IF ITS THE RIGHT ANSWER!!!!!!! 100 POINTS
Answer:
its a you did got it correct
Step-by-step explanation:
had that test 2 years ago
I need help please just for the lest question.
Answer:
250, 4000, 20250
Step-by-step explanation:
[tex]\frac{2}{5}a^{4}[/tex]
2/5 × 5^4 = 250
2/5 × 10^4 = 4000
2/5 × 15^4 = 20250
Hope this helps! :)
Why do we use log log scale?
Log log scale is used to visualize data with large ranges of values, as it allows for the comparison of data with vastly different scales.
Log log scale is a type of graph which uses a logarithmic scale on both the x-axis and the y-axis, which allows for data with vastly different scales to be compared. This is especially useful when dealing with data which has very large ranges, as it allows us to zoom in on the data and compare it more easily. For example, if we are looking at data that ranges from 1 to 1000, a log log scale would allow us to see the entire range on one graph, instead of having to break it down into multiple graphs. This can be very helpful in visualizing data which spans a wide range of values, as it allows us to compare and analyse the data more effectively.
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Question 5 pls answer
Answer:
1/14
Step-by-step explanation:
1/4 x 2 divided by 7
Equals 1/2 divided by 7 which is 14
Select all the correct locations on the image.
The revenue and cost functions for a product line of running shoes are shown on the graph. Which points on the graph are considered breakeven
points?
Total (dollars)
+5,000
+4,000
+3,000
-2,000/
+1,000
20
C(x)
40
60
80
Price per Shoe (dollars)
R(x)
100
120
The breakeven points are:
(40, 4500) and (80, 4400)
What are coordinates?Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.
Given:
The revenue and cost functions for a product line of running shoes are shown on the graph.
When C(x) = R(x)
And from the diagrams,
the breakeven points are:
(40, 4500) and (80, 4400)
Therefore, the points are (40, 4500) and (80, 4400).
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3. What dilation would map ABC onto XYZ? What is your center of dilation? How do
you know the two triangles are similar? Be sure to identify the scale factor.
Therefore , as a result, the ratio of the corresponding sides of the triangle ABC and XYZ will be identical.
What is the triangle?Since a triangle has four points or segments, it is regarded as a polygon. It is a fundamental geometric shape. A triangle with sides A, B, or C is referred to as triangle ABC. So when sides are not collinear, a single plane and square are generated in Euclidean geometry. If a triangle has three sides and three corners, it is a polygon. The corners of a triangle are the places where its three sides converge. The sum of the three triangle angles is 180 degrees.
Here,
A dilation is a modification that yields an image with a different size but the exact shape as the original. The initial figure can stretches or contracts by a specific amount.
We can observe that ABC contracts to form XYZ in the problem due to a 5x dilation.
As a result, the ratio of the corresponding sides of the triangles ABC and XYZ will be identical.
AB/CD = AC/XY= BC/YZ= 5
Therefore , as a result, the ratio of the corresponding sides of the triangles ABC and XYZ will be identical.
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kelly’s car gets 15 1/4 miles per 5/8 gallon of gas. How many miles does kelly’s car get 3 gallons of gas
A freshman class includes students between the ages 12 and 16. The total number of students is broken down by age as shown in the table. What is the probability a freshman under the age of 14 will be first in line at the freshman banquet?
Answer: 5/49
Step-by-step explanation:
which shape has right angles AND sides that are the same?
Answer:
rhombus
Step-by-step explanation:
How many chords are drawn in Circle Q?
The number of chords drawn in the circle is
C. 2What is a chord in circle?A circle's chord is the line segment that connects any two locations on the circle's circumference.
It should be remembered that a circle's diameter is defined as the lengthiest chord that runs across the center of the circle.
Examining the figure the chord are
SPRPThe line segment RQ is not a chord since it is not touching the circumference of the circle at the two ends.
From the definition the two ends must be touching the circumference of the circle just like SP and RP the points at the end of both lines are at the circumference of the circle
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