For the expression (x - 8)(x + 8), using the arithmetic operation the value for x is x = 8.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
The given expression is - (x - 8)(x + 8)
Use the arithmetic operation of multiplication -
(x - 8)(x + 8)
x(x + 8) - 8(x + 8)
x² + 8x - 8x -64
Now, use the arithmetic operation of addition and subtraction -
x² + 8x - 8x -64
x² - 64
Now, collect the like terms on each side -
x² = 64
x = √64
Now, solve the radical form to get the value of x -
x = √64
x = 8
Therefore, the value of x is obtained as x = 8.
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If Dwayne drinks 48 bottles of water in 12 days, how many bottles of water will he drink in 4 days?
Dwayne will drink 12 bottles of water in 4 days.
To find out how many bottles of water Dwayne will drink in 4 days, we can set up a proportion based on the information given:
Let x be the number of bottles of water he will drink in 4 days.
The number of bottles of water consumed per day remains constant, so we can set up the following proportion:
48 bottles / 12 days = x bottles / 4 days
Now, solve for x:
48 / 12 = x / 4
4x = 48
x = 48 / 4
x = 12
So, Dwayne will drink 12 bottles of water in 4 days.
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2. Find the 20th term of an arithmetic sequence if its 6th term is 14 and 14th term is 6.
can anyone answer this ?
Answer:
[tex]\sf t_{20}= 0[/tex]
Step-by-step explanation:
Arithmetic sequence:[tex]\sf \boxed{\bf n^{th} \ term = a + (n-1)d}\\\\\text{Here, a is the first term ; d is the common difference }[/tex]
6th term is 14 ⇒ [tex]\sf t_6 = 14[/tex]
a + (6 - 1)d = 14
a + 5d = 14 --------------(I)
14th term is 6 ⇒[tex]\sf t_{14} = 6[/tex]
a + (14-1)d = 6
a + 13d = 6 ----------------(II)
Subtract equation (II) from equation(I)
(I) a + 5d = 14
(II) a + 13d = 6
- - -
-8d = 8
d = 8 ÷(-8)
[tex]\sf \boxed{\bf d= (-1)}[/tex]
Plugin d = -1 in equation (I)
a + 5(-1) = 14
a -5 = 14
a = 14 + 5
[tex]\sf \boxed{\bf a = 19}[/tex]
20th term:
[tex]\sf t_{20}= 19 + 19*(-1)[/tex]
= 19 - 19
[tex]\sf \boxed{\bf t_{20} = 0}[/tex]
Answer:
0
Step-by-step explanation:
The number of terms of an Arithmetic progressions has the formular.
Tn = a + ( n - 1 ) d
From the question,
6th term = 14
14th term = 6
Therefore,
a + 5d = 14 -----------(1)
a + 13d = 6 ----------(2)
subtracting
-8d = 8
dividing bothsides by -8
[tex] \frac{ - 8d}{ - 8} = \frac{8}{ - 8} \\ d = - 1[/tex]
Therefore,
common difference= -1
substituting the value of d into equation (1)
a + 5 ( -1) = 14
a - 5 = 14
a = 14 + 5 = 19
First term = 19
For the 20th term
T 20 = a + 19d
19 + 19 ( -1 )
19-19 = 0
Therefore,
20th term = 0
What is the rule of -3,18,-108,—,—,—
Hi! ❄
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
The rule for this sequence is 'multiply by -6'.
Verification ↓
-3*(-6)[tex]\stackrel\checkmark{=}[/tex]18
18*(-6)[tex]\stackrel\checkmark{=}[/tex]-108
So the rule for the sequence is 'multiply by -6'
And the Common ratio is -6.
Hope that made sense !!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\star\tiny\pmb{calligraphy}\star[/tex]
[tex]\textbf{Heya !}[/tex]
✏✏[tex]\large\textsf{Given:-}[/tex]
The first 3 terms of a sequence :- [tex]\large\textsf{-3, 18, -108}[/tex]✏✏ [tex]\large\textsf{To Find:-}}[/tex]
The rule for the sequence = ?✏✏ [tex]\large\textsf{Solution Steps:-}[/tex]
What do we multiply each term of the sequence by to arrive at the next one ? we can find that by dividing the last term of the sequence, -108, by the middle term, 18:-
[tex]\large{\sf{\longmapsto{-108\div18=-6}[/tex]
Now divide 18 by the first term (-3) :-
[tex]\longmapsto\sf{18\div-3=-6}[/tex]
we arrived at -6 twice, So the rule for this sequence is:- "Multiply by -6, And you'll arrive at the next term"
`hope it helped ~ :D
WILL MAKE BRAINLIEST!!
Solve for x.
(x-6)°
124°
Answer:
x=62
Step-by-step explanation:
This is a straight angle so they have to add up to 180.
124+x-6=180
118+x=180
x=180-118
x=62
Answer:
62
Step-by-step explanation:
124 + (x - 6) = 180
118 + x = 180
x = 62
At the Junior Olympics, Jacob ran the 500-yard
dash in 80 seconds. Juan's time for the same
distance was t seconds less than Jacob's.
Which expression would accurately calculate
Juan's time?
The Time taken by Jacob to run the dash race is (80 - t) seconds
How to write algebraic expressions?We are told that;
Total distance for the dash race = 500 yards
Time taken by Jacob to run the dash race = 80 seconds
Now, we are told that Juan ran the same dash race but used t less seconds than Jacob. Thus;
Time taken by Jacob to run the dash race = (80 - t) seconds
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(3.2x10 to the power of 5)(5.7x10 to the power of -2)
Answer:
1.320000
2. 0.057
Step-by-step explanation:
Here is a list of numbers: 9.5, 4.4, 8.1, 2.9, 9.2, 3.2, 9.4, 7, 2.5 state the median.
The median of the list of numbers is 7
How to determine the median?The number is given as:
9.5, 4.4, 8.1, 2.9, 9.2, 3.2, 9.4, 7, 2.5
Rearrange the numbers in ascending order
2.5, 2.9, 3.2, 4.4, 7, 8.1, 9.2, 9.4, 9.5
The median is the middle number.
The middle number here is 7
Hence, the median of the list of numbers is 7
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the graph of f(x) can be stretched vertically and flipped over the x-axis to produce the graph of g(x). if f(x)
The correct option is D: G(x) = -5x².
The equation of G(x) will be -5x² after vertically stretching and flipping.
What is meant by stretching vertically and flipping?A function change called a stretch or compression makes a graph bigger or narrower without moving it horizontally or vertically.
Vertical stretching: A function's graph is stretched or compressed vertically in proportion to the graph of the original function when we multiply it by a positive constant. We obtain a vertical stretch if the constant is bigger than 1, and a vertical compression if the constant is between 0 and 1.flipped over the x-axis: In order to reflect over the X axis, one must negate the value of each point's y-coordinate while maintaining its x-value. The graph reflects across the x-axis prior to transformation when the parent function f(x) = x² has an a-value smaller than 0. The function f(x) = -x² is the result.To know more about the vertical stretch, here
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The complete question is -
The graph of F(x) can be stretched vertically and flipped over the x-axis to produce the graph of G(x). If F(x) = x², which of the following could be the equation of G(x)?
A: G(x) = -1/5x²
B: G(x) = 5x²
C: G(x) = 1/5x²
D: G(x) = -5x²
Proving Theorems about Parallelograms: Tutorial
?
Given: Quadrilateral ABCD is a parallelogram. Prove: ZBAD ZDCB, and ZABO ZODA. Match each
statement to its corresponding reason. Scroll down to see all the choices. Click the links in the statements to view
related diagrams. Drag the items on the left to the correct location on the right.
AB CD
BO ADview diagram)
Let A, B, C, and D form a parallelogram.
Draw ACand BD. (view diagram)
AB=CD
BC=AD
AABCE ACDA
AABD ACDB
ZBAD ZDCB(view diagram)
LABC ZCDA(view diagram)
ACAC, and BD BD
given
9 of 2
Opposite sides of a
parallelogram are .
line segments have
equal measures.
drawing line segments
Reflexive Property of
Equality
SSS criterion for
Corresponding angles
of triangles are
A parallelogram is a type of quadrilateral that has opposite sides to be equal, and opposite angles to be equal.
Thus to complete the given proof in the question, the required statements and reasons are stated below:
STATEMENT REASONS
1. AB ≅ CD, Opposite sides of a
BC ≅ AD parallelogram are equal
2. A, B, C, and D form a paralelogram Given
3. Draw AC and BD Drawing line segments
4. AB = CD, Equal line segments have
BC = AD equal measures
5. ΔABC ≅ ΔCDA SSS criterion for equal
ΔABD ≅ ΔCDB triangles
6. <BAD ≅ <DCB Corresponding angles of equal
<ABC ≅ <CDA triangles are equal
7. AC = AC, and BD = BD Reflective property of equality
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please help find the answer
Answer:
[tex]AC = \bf 4.13 \space\ cm[/tex]
Step-by-step explanation:
Using Pythagoras's theorem:
[tex]\boxed {a^2 = b^2 + c^2}[/tex],
where:
a ⇒ hypotenuse (AC, ? cm)
b, c ⇒ the two other sides of the triangle (AB = 2.2 cm, BC = 3.5 cm),
we can find the length of AC.
[tex]AC^2 = AB^2 + BC^2[/tex]
⇒ [tex]AC^2 = (2.2)^2 + (3.5)^2[/tex]
⇒ [tex]AC = \sqrt{(2.2)^2 + ((3.5)^2}[/tex]
⇒ [tex]AC = \sqrt{17.9}[/tex]
⇒ [tex]AC = \bf 4.13 \space\ cm[/tex]
Find the volume of the composite figure. Round to the nearest tenth if necessary.
The volume of the given composite figure is: 375 m³.
What is the Volume of a Composite Figure?Volume of the composite figure = volume of triangular prism at the bottom + volume of rectangular prism at the top.
Volume of the composite figure = 0.5 * b * h * length + (l)(h)(w)
= 0.5 * 5 * 4 * 5 + (13)(5)(5)
= 50 + 325
Volume of the composite figure = 375 m³
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Pleaseeeee helppp asap
Answer:
Step-by-step explanation:
Answer:
35.7 megabytes
Step-by-step explanation:
Let's first find 10% of the percent needed. If it is 234 megabytes and 10% has downloaded so far, we conclude that 10% of the download is 23.4 megabytes (since we move the decimal point one spot to the left to find ten percent).
To get to 15% of the percent needed, let's split 10% in half to get the amount of megabytes per every 5%.
23.4/2 = 11.7
We can now conclude that 5% = 11.7. Therefore, 15% will equal (23.4 + 11.7) 35.1 megabytes.
To find the remaining 3.5% left of the percent needed, we use a calculator.
3.5% x 18 = 0.63.
We will add that to the 35.1 megabytes, but we need to round to the nearest tenth, as the question stated. Therefore, we round to 0.6, add it to 35.1, to get a total of 35.7 megabytes.
For 18.5% of the download, it will be 35.7 megabytes.
Which of the following is equal to the fraction below?
(4/5)^6
A. 6(4/5)
B. 4^6/5
C. 4^6/5^6
D. 24/30
Answer:
C. 4^6 / 5^6
Step-by-step explanation:
(4/5)^6
= 4^6 / 5^6
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{(\dfrac{4}{5})^6}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathbf{(\dfrac{4}{5})^6}[/tex]
[tex]\mathbf{= \dfrac{4}{5}\times\dfrac{4}{5}\times\dfrac{4}{5}\times \dfrac{4}{5}\times\dfrac{4}{5}\times\dfrac{4}{5}}[/tex]
[tex]\mathbf{= \dfrac{4\times4\times4\times4\times4\times4}{5\times5\times5\times5\times5\times5}}[/tex]
[tex]\mathbf{= \dfrac{16\times16\times16}{25\times25\times25}}[/tex]
[tex]\mathbf{= \dfrac{256 \times 16}{625\times25}}[/tex]
[tex]\mathbf{= \dfrac{4,096}{15,625}}[/tex]
[tex]\mathbf{\approx \dfrac{4^6}{5^6}}[/tex]
[tex]\huge\text{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\frak{Option\ C. \dfrac{4^6}{5^6}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A square garden has sides of length 10 ft. If topsoil costs $5 / cubic foot, how much will it cost to put a 0. 5 ft layer of topsoil on the entire garden?
Cost to put a 0. 5 ft layer of topsoil on the entire garden is $1000.
The quantity of square units required to completely fill a square is known as the area of a square. The region that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area. Measurements are made in square units, with square meters serving as the reference unit
Area of a Square = Side × Side.
Therefore, the area of square = Side square units.
Side of a square garden= 10 ft.
Area of a square garden= Side × Side= 10 × 10 =100 square ft.
Cost of the whole garden = 100×$5 =$500
Cost to put a 0. 5 ft layer of topsoil on the entire garden =$500/0.5
=$1000
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The cost need to put a 0. 5 ft layer of topsoil on the entire garden is $1000
According to the given statement
we have given that the
side length of the square garden is 10ft.
topsoil cost per foot is $5
And we have to find the cost which required to put a 0. 5 ft layer of topsoil on the entire garden.
So,
The side length of the square garden is 10ft.
Now, the volume of the cube is (a)^2
And
Total volume of cube = 10*10
Total volume of cube = 100 per square foot.
Now, we find the cost required for a topsoil.
Cost required to put a topsoil of 1 foot in the total volume of cube = volume*cost
So,
Cost required to put a topsoil of 1 foot in the total volume of cube = 1000*5
Cost required to put a topsoil of 1 foot in the total volume of cube = $5000
if we put a topsoil of 0.5 feet then
The cost required = $5000/0.5
The cost required = $1000.
So, The cost need to put a 0. 5 ft layer of topsoil on the entire garden is $1000
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When drawing a context diagram, standardized names should be used within each set of symbols. a. True b. False
The statement is False that When drawing a context diagram, standardized names should be used within each set of symbols.
According to the statement
we have given the statement and we have to show that the statement is a true or false after analyzing.
So, to analyse the statement
Context diagrams show the interactions between a system and other actors (external factors) with which the system is designed to interface. System context diagrams can be helpful in understanding the context .
But we know that the standardized names is not used within each set of symbols. so, this is used in a randomly sets.
that's why the given statement is not true in the case of the standardized names.
So, The statement is False that When drawing a context diagram, standardized names should be used within each set of symbols.
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17
Post Test: Transformations and Congruence
Select the correct answer from each drop-down menu.
Consider Undefined control sequence \triangle HJI.
H
सौ
Triangle HJIis
triangle HJI, the triangles
#
triangle EFG. Since triangle EFGuses
Reset
Next
It should be noted that mathematical transformations involve changing an image in some prescribed manner.
What is a transformation?Your information is incomplete. An overview will be given. A transformation is a general term for the specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
It should be noted that the original shape of the object is called the pre-Image and the final shape and position of the object is the image under the transformation.
There are four main types of transformations: translation, rotation, reflection and dilation. Also, in geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other
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Answer:
1. a translation and reflection
2. only rigid transfotmations
3. are congruent
Step-by-step explanation:
right on edmentum
Based on the data in this two-way table, which statement is true?
Using the probability concept, the correct statement is:
B. P(hibiscus|red) = P(hibiscus).
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For item a, the probabilities are:
P(yellow|rose) = 45/105 = 0.4286.P(yellow) = 135/315 = 0.4286.Same probabilities, hence the statement that they are different is false.
For item b, the probabilities are:
P(hibiscus|red) = 80/120 = 2/3.P(hibiscus) = 210/315 = 2/3.Equal, hence this is the correct statement.
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A probability that it will rain on a given day during the rainy season in Miami is 70%. If there are 140 days in the rainy season. On how many days should you except it to rain?
Answer:
98 days
Step-by-step explanation:
140*70%=140*(7/10)=14*7=98
What is the correct mathematical equation: the monthly consumption ,w, of a household is 237 litres per day with an additional monthly free water usage of 1200 litres. the household spends l litres per month is?
The linear equation for the cost that the household spend in water is given by:
C(d) = 237d + 1200.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, the free usage of 1200 liters is the y-intercept, while the daily usage of 237 liters is slope. Hence the function for the amount the household spends in water in d days is given as follows:
C(d) = 237d + 1200.
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Instructions: Find the lengths of the other two sides of the isosceles triangle
Answer:
x=5
h = 5 sqrt 2
Step-by-step explanation:
isosceles right triangles are always 45-45-90, ratio of those triangles are always x:x:x*sqrt 2
please help i need help solving this
Answer:
1.D 2.C 3.A 4.B
Step-by-step explanation:
hope this helped
Determine which of these sets are subsets of which other of these sets. Check ALL correct answers below.
The Set C is the subset of A and D.
According to the statement
we have given that the three sets which are A = {2, 4, 6}, B = {2, 6}, C = {4, 6}, and D = {4, 6, 8}.
And we have to find that the subsets of these sets.
So,
For a set S to be a subset of a set T, all of the elements of the set S need to be contained in the set T. Firstly, all of the sets are their own subsets, that is, A⊆A,B⊆B,C⊆C,D⊆D.
It follows that B⊂A because of 2∈A and 6∈A. Since 2 is not belongs to C and D. that's why B is not a subset of C and B is not a subset of D.
Taking into account that 4∈A and 6∈A, we conclude that C⊂A. By analogy, since 4∈D and 6∈D, we conclude that C⊂D.
Since |A|>|B|∣A∣>∣B∣ and |A|>|C|,∣A∣>∣C∣, we conclude that A is not a subset of B and A is not a subset of C.
Taking into account that |D|>|B|∣D∣>∣B∣ and |D|>|C|,∣D∣>∣C∣, we conclude that D is not a subset of B and D is not a subset of C. Since,2 not belongs to D that's why A is not a subset of D.
Since 8 not belongs to A, D is not a subset of A.
Overall, The Set C is the subset of A and D.
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Disclaimer: This question was incomplete. Please find the full content below.
Question:
Suppose that A = {2, 4, 6}, B = {2, 6}, C = {4, 6}, and D = {4, 6, 8}. Determine which of these sets are subsets of which other of these sets.
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Explaining the Error in a Propo
A student uses the ratio of 4 oranges to 6 fuld ounces
find the number of oranges needed to make 24 fluid
ounces of juice. The student writes this proportion:
24
4
=
6 16
Explain the error in the student's work.
Answer:
16
Step-by-step explanation:
The student uses the ratio of 4 oranges to 6 fluid ounces.
When there are 24 fluid ounces, the number of oranges will be:
= 4/6 × 24
= 16 oranges
Determine the equation of the parabola graphed below. Note: be sure to consider the negative sign already present in the template equation when entering your answer. A parabola is plotted, concave up, with vertex located at coordinates negative one and negative four.
The equation of the parabola graphed is given as follows:
y = a(x + 1)² - 4.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
Considering the vertex given, we have that h = -1, k = -4, hence the equation is:
y = a(x + 1)² - 4
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You move a box 5 meters and perform 900 joules of work. How much force did you apply to the box?
please help me i need help
Answer:
force = work/distance
force = 900/5
force = 180 N
Which type of mathematical problem is too complex for a classical computer to solve efficiently?
Calculating the circumference of a circle based on the circle's diameter.
What kind of problems can a quantum computer solve?
Yet another difficult area that quantum computers cater to is that of solving difficult combinatorics problems. The algorithms within quantum computing aim at solving difficult combinatorics problems in graph theory, number theory, and statistics.10 Difficult Problems Quantum Computers can Solve Easily-
Quantum encryption. Simulation of quantum systems. ab initio calculations.Solving difficult combinatorics problems.Supply chain logistics. Optimization.Finance. Drug development.Learn more about quantum computer
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The complete question is -
Which type of mathematical problem is too complex for a classical computer to solve efficiently?
a. converting an irregular fraction to an approximate decimal value
b. multiplying two numbers that both have a large number of digits
c. finding two prime factors that result in a specific value when multiplied
d. calculating the circumference of a circle based on the circle's diameter
Find a28 of the arithmetic sequence given a1=1 and d=-9
The a28th term of a arithmetic sequence is -242.
According to the statement
We have given that :
a1 = 1 and d = -9. And by use of it we have to find the value of the a28th term in the arithmetic sequence.
So, arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
And the formula is
an = a1 +(n-1)d
here put the values in it
an = a28 , n = 28, d =-9, a1 =1
then
an = a1 +(n-1)d
a28 = 1 +(28-1)(-9)
a28 = 1 +(27)(-9)
a28 = 1 -243
a28 = -242.
So, The a28th term of a arithmetic sequence is -242.
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d) y = 3x - 9 7) 2) y-int. m = x-int. 3) -
**Disclaimer** Hi there! I assumed the question to be finding the "y-intercept", "x-intercept", and "slope/gradient" of the equation "y = 3x - 9". The following answering will be according to this understanding. If it is incorrect, please tell me and I will modify my answer.
Answer:
y-intercept = (0, -9)
x-intercept = (3, 0)
slope (m) = 3
Step-by-step explanation:
What is being asked: to find the corresponding values
y-interceptx-interceptSlope/gradientGiven equation
y = 3x - 9
PART I: y-interceptConcept
The y-intercept of a line is on the coordinate of (0, a), where [ a ] is a constant.
Substitute values into the equation
y = 3x - 9
y = 3 (0) - 9
y = 0 - 9
y = -9
Therefore, the y-intercept is [tex]\Large\boxed{(0, -9)}[/tex]
PART II: x-interceptConcept
The x-intercept of a line is on the coordinate of (a, 0), where [ a ] is a constant.
Substitute values into the equation
y = 3x - 9
0 = 3x - 9
Add 9 on both sides
0 + 9 = 3x - 9 + 9
9 = 3x
Divide 3 on both sides
9 / 3 = 3x / 3
x = 3
Therefore, the x-intercept is [tex]\Large\boxed{(3,0)}[/tex]
PART III: Slope/GradientConcept
In the linear formula, y = mx + b, [ m ] is the slope and [ b ] corresponds to the y-intercept.
Determine the slope
Given the equation, y = 3x - 9, when corresponds to the general linear equation formula:
y = mx + b
y = 3x - 9
Therefore, the slope is [tex]\Large\boxed{m=3}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
please answer these correctly i will mark u brainliest pleaseee.
1) Find the general term of the sequence 5,6,7,8,9,.........
2) Find the midpoint of the line segment A (3,5) B (4,5)
3) Work out and write ur answer in the simplest form :- 3 1/4 + 2 5/6
4) work out the 30th term of 10,13,16,19, .......
5) the ratio of the width to height of a wall is 20cm. what is it's height in meters?
6) Find the mean of 2.1, 4, 6.2, 7, 3.3,
7) Work out and write the answer in the simplest form :- 1 1/2 + 1 5/9
Answer: 1. an = n + 4, 2. ( 3 1/2, 3.5, 5), 3. 6 1/12, 4. 97, 5. 0.2 meters, 6. 4.52, 7. 3 1/18
Step-by-step explanation:
a set of data has the values 11,14,23 and 16 what value would have to be added to set for the mean of the 5 numbers to be 18
Answer:
26.
Step-by-step explanation:
(11+14+23+16+x) / 5 = 18 where x is the value to be added.
(64 + x) / 5 = 18
64 + x = 90
x = 90 - 64
= 26.