The equation of the line that passes through the points (1,0) and (3,6) is y = 3x - 3.
What is the equation of the line that passes through (1,0) and (3,6)?The formula for equation of line is expressed as:
y = mx + b
Where m is slope and b is the y-intercept.
Given that, the line passes through points (1,0) and (3,6).
First, we determine the slope:
[tex]Slope\ m = \frac{y_2 - y_1}{x_2 - x_1} \\\\Slope\ m = \frac{6 - 0}{3 - 1} \\\\Slope\ m = \frac{6}{2} \\\\Slope\ m = 3[/tex]
Now we plug the slope m = 3 and one point (1,0)into the point-slope form to find the equation:
( y - y₁ ) = m( x - x₁ )
( y - 0 ) = 3( x - 1 )
y = 3x - 3
Therefore, the equation of the line is y = 3x - 3.
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(6x+9)/2=?
please help
The value of x in the expression given is -7/6
Solving the given equation(6x + 9)/2 =
First step is to cross multiply
6x + 9 = 2
Collect like terms
6x = 2 - 9
6x = -7
divide both sides by 6 to isolate x
x = -7/6
Therefore the value of x in the expression given is -7/6
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100 Points! Geometry question. Determine whether each pair of triangles is similar. If so, write a similarity statement. If not, what would be sufficient to prove the triangles similar? Explain your reasoning. Photo attached. Thank you!
Answer:
Δ ABC [tex]\bold{\sim}[/tex] ΔPQR is similar.
Step-by-step explanation:
Similar triangles are two or more triangles that have the same shape, but their sides are in proportion.
For Question:
In Δ ABC and ΔPQR
AB:PQ =8:6=4:3
BC: QR=12:9=4:3
AC: PR=12:9=4:3
Since the length of any side of one triangle is by the corresponding side of another triangle, you will get the same number.
Therefore,
Δ ABC [tex]\bold{\sim}[/tex] ΔPQR is similar.
Hence Proved:
Answer:
ΔABC ~ ΔPQR
Step-by-step explanation:
In similar triangles, corresponding sides are always in the same ratio.
Therefore, if triangle ABC is similar to triangle PQR then:
[tex]AB : PQ = BC : QR = AC : PR[/tex]
Substitute the side lengths into the ratio equation:
[tex]AB : PQ = BC : QR = AC : PR[/tex]
[tex]8 : 6 \;\;\;\:= \;\;12 : 9 \;\;\;\:= \;\;12 : 9[/tex]
Simplify each ratio by dividing all parts of the ratio by their highest common factor:
[tex]\dfrac{8}{2}:\dfrac{6}{2}=\dfrac{12}{3}:\dfrac{9}{3}=\dfrac{12}{3}:\dfrac{9}{3}[/tex]
[tex]4:3=4:3=4:3[/tex]
As the corresponding sides of triangles ABC and PQR are in the same ratio, this proves that the two triangles are similar.
help me please i would appreciate it so so much
The length of CF, considering the Pythagorean Theorem in this problem, is given as follows:
CF = 26.08 m.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side, is equals to the sum of the squares of the lengths of the other two sides.
Hence the equation for the theorem is given as follows:
c² = a² + b².
In which:
c > a and c > b is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The length of EC is given as follows:
(EC)² = 10² + 24²
[tex]EC = \sqrt{10^2 + 24^2}[/tex]
EC = 26.
Then the length of CF is given as follows:
CF² = 26² + 2²
[tex]CF = \sqrt{26^2 + 2^2}[/tex]
CF = 26.08 m.
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help me please i would appreciate it so so much
Answer:
The given triangles APSR and APQR are congruent by S.A.S. criteria.
Step-by-step explanation:
The S.A.S. (Side-Angle-Side) congruence criteria states that two triangles are congruent if their corresponding two sides and included angles are congruent to one another's corresponding two sides and included angle.
Here, we can observe that both triangles share the same side AP.
PR and PQ on the side are congruent.
- Both triangles share Angle P.
The supplied triangles APSR and APQR are therefore congruent according to S.A.S. requirements.
so we can conclude: S.A.S. for the triangles being congruent.
Select the correct answer.
Which expression is equivalent to 107-8y +3? Assume that the denominator does not equal zero.
O A. y2 (10y³ - 8y² + 3)
О в.
10³ - 8y² + 3
V
O c.
y (10y³
OD. 10²¹ - $y² +3
8y² + 3)
Reset
Next
The correct answer is option B: 10³ - 8y² + 3.
To obtain the equivalent expression, we can simplify the given expression by combining like terms. We have 107 as a constant term, -8y as the coefficient of the y term, and 3 as another constant term.
So, combining these terms, we get 10³ - 8y² + 3, which is equivalent to the given expression.
Option A is incorrect because it introduces an additional y term in the form of y², which is not present in the original expression.
Option C is incorrect because it only includes the y term and its coefficients, without considering the constant terms.
Option D is unrelated to the original expression as it introduces unrelated numbers and symbols.
Therefore, the correct equivalent expression is 10³ - 8y² + 3, as stated in option B.
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NO LINKS!! URGENT HELP PLEASE!!!
11. Write the equation for the graph
This is the same as writing y = sqrt(4(x+5)) - 1
===============================================
Explanation:
The given graph appears to be a square root function.
The marked points on the curve are:
(-4,1)(-1,3)(4,5)Reflect those points over the line y = x. This will have us swap the x and y coordinates.
(-4,1) becomes (1,-4)(-1,3) becomes (3,-1)(4,5) becomes (5,4)Recall the process of reflecting over y = x means we're looking at the inverse. The inverse of a square root function is a quadratic.
----------
Let's find the quadratic curve that passes through (1,-4), (3,-1) and (5,4).
Plug the coordinates of each point into the template y = ax^2+bx+c.
For instance, plug in x = 1 and y = -4 to get...
y = ax^2+bx+c
-4 = a*1^2+b*1+c
-4 = a+b+c
Do the same for (3,-1) and you should get the equation -1 = 9a+3b+c
Repeat for (5,4) and you should get 4 = 25a+5b+c
We have this system of equations
-4 = a+b+c-1 = 9a+3b+c4 = 25a+5b+cUse substitution, elimination, or a matrix to solve that system. I'll skip steps, but you should get (a,b,c) = (1/4, 1/2, -19/4) as the solution to that system.
In other words
a = 1/4, b = 1/2, c = -19/4
We go from y = ax^2+bx+c to y = (1/4)x^2+(1/2)x-19/4
----------
Next we complete the square
y = (1/4)x^2+(1/2)x-19/4
y = (1/4)( x^2+2x )-19/4
y = (1/4)( x^2+2x+0 )-19/4
y = (1/4)( x^2+2x+1-1 )-19/4
y = (1/4)( (x^2+2x+1)-1 )-19/4
y = (1/4)( (x+1)^2-1 )-19/4
y = (1/4)(x+1)^2- 1/4 - 19/4
y = (1/4)(x+1)^2 + (-1-19)/4
y = (1/4)(x+1)^2 - 20/4
y = (1/4)(x+1)^2 - 5
The equation is in vertex form with (-1,-5) as the vertex. It's the lowest point on this parabola. Placing it into vertex form allows us to find the inverse fairly quickly.
----------
The last batch of steps is to find the inverse.
Swap x and y. Then solve for y.
y = (1/4)(x+1)^2 - 5
x = (1/4)(y+1)^2 - 5
x+5 = (1/4)(y+1)^2
(1/4)(y+1)^2 = x+5
(y+1)^2 = 4(x+5)
y+1 = sqrt(4(x+5))
y = sqrt(4(x+5)) - 1
I'll let the student check each point to confirm they are on the curve y = sqrt(4(x+5)) - 1.
You can also use a tool like GeoGebra to verify the answer.
simplify 14√(27) - √(3)
To simplify the expression 14√27 - √3, we can simplify the radicals and then perform the subtraction:
First, let's simplify the radicals:
√27 = √(9 × 3) = √9 × √3 = 3√3
Now we can rewrite the expression:
14√27 - √3 = 14(3√3) - √3
Next, distribute the 14:
14(3√3) - √3 = 42√3 - √3
Finally, combine like terms:
42√3 - √3 = 41√3
So the simplified expression is 41√3.
Help with math problem please
PLEASE HELP ASAP Arrange the expressions in increasing order of their values.
(10⁰x 10¹ x 1¹⁰) (10 x 10¹) (10⁰+10¹+1¹⁰) (10⁰+10¹x 1¹⁰)
[tex]\underline{\underline{\purple{\huge\sf || ꪖꪀᦓ᭙ꫀ᥅}}}[/tex]
First, we can simplify each expression:
(10⁰x10¹x1¹⁰) = 10¹¹
(10x10¹) = 100
(10⁰+10¹+1¹⁰) = 1 + 10 + 1,000,000,000 = 1,000,000,011
(10⁰+10¹x1¹⁰) = 10¹⁰
Now we can arrange them in increasing order:
10¹¹ < 10¹⁰ < 100 < 1,000,000,011
So the correct order from smallest to largest is:
(10⁰x10¹x1¹⁰) (10⁰+10¹x1¹⁰) (10 x 10¹) (10⁰+10¹+1¹⁰)
or
(10¹¹) (10¹⁰) (100) (1,000,000,011)
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The scaled triangle will be larger than the initial size by a factor 2.
The scaled square will be smaller than the initial side by a factor 4
What is dilation?Dilation refers to a transformation that changes the size of a geometric figure without altering its shape.
Dilation involves scaling an object by a certain factor, that might result in enlarging or reducing its dimensions uniformly in all directions.
Based on the given diagram, the new length and size of the object is calculated as follows;
For the triangle, (measure the length with ruler)
new lengths = 2 times the original lengthoriginal length = 2 cm, new length = 4 cmthe new size of the triangle will increase by a factor 2For the square; (measure the length with ruler)
new lengths = 0.25 times the original lengthoriginal length = 4 cm, new length = 2 cmthe new size of the square will decrease by a factor 4Learn more about dilation here: https://brainly.com/question/20482938
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3 1/3 divided by 1 1/5
Answer:
25/9
Step-by-step explanation:
3 1/3 ÷ 1 1/5
3 1/3 = 10/3
1 1/5 = 6/5
10/3 ÷ 6/5 = 10/3 x 5/6 = 50/18 = 25/9
So, the answer is 25/9
(Exponents)
what is the meaning of the expression? 3v^4
Answer: The expression, 3v^4, means that the variable, v, is multiplied by itself 4 times (v * v * v * v) and then is multiplied after by the coefficient 3.
Step-by-step explanation:
Exponent indicates the number of times a number needs to be multiplied by itself.
For example if your given x^2
that simply means that the variable, x, is being multiplied by itself twice:
x * x
if your given 2z^9
that means that the variable, z, is first multiplied by itself nine times and after that it is multiplied by the coefficient, two.
Kylie suspected that when people exercise longer, their body temperatures change. She randomly assigned people to exercise for
30
3030 or
60
6060 minutes, then measured their temperatures. The
18
1818 people who exercised for
30
3030 minutes had a mean temperature of
�
ˉ
30
=
38.
3
∘
C
x
ˉ
30
=38.3
∘
Cx, with, \bar, on top, start subscript, 30, end subscript, equals, 38, point, 3, degrees, start text, C, end text with a standard deviation
�
30
=
0.2
7
∘
C
s
30
=0.27
∘
Cs, start subscript, 30, end subscript, equals, 0, point, 27, degrees, start text, C, end text. The
24
2424 people who exercised
60
6060 minutes had a mean temperature of
�
ˉ
60
=
38.
9
∘
C
x
ˉ
60
=38.9
∘
Cx, with, \bar, on top, start subscript, 60, end subscript, equals, 38, point, 9, degrees, start text, C, end text with a standard deviation
�
60
=
0.2
9
∘
C
s
60
=0.29
∘
Cs, start subscript, 60, end subscript, equals, 0, point, 29, degrees, start text, C, end text.
Kylie wants to estimate the difference in the mean body temperature after exercising for the two amounts of time
(
30
min.
−
60
min.
)
(30min.−60min.)left parenthesis, 30, start text, m, i, n, point, end text, minus, 60, start text, m, i, n, point, end text, right parenthesis. Assume that the conditions for inference have been met.
Which of the following is an appropriate confidence interval for
�
30
−
�
60
μ
30
−μ
60
mu, start subscript, 30, end subscript, minus, mu, start subscript, 60, end subscript?
Choose 1 answer:
Therefore, an appropriate confidence interval for μ30−μ60μ30−μ60 (the difference in mean body temperature) would be −0.796−0.796 to −0.404−0.404 (rounded to the appropriate decimal places).
To estimate the difference in the mean body temperature after exercising for 30 minutes versus 60 minutes, we can construct a confidence interval. Since the conditions for inference have been assumed to be met, we can proceed with the following steps:
Calculate the difference in sample means: xˉ30−xˉ60=38.3−38.9=−0.6xˉ30−xˉ60=38.3−38.9=−0.6.
Determine the standard error of the difference, which is given by the formula:
SE=(s302n30)+(s602n60)SE=(n30s302)+(n60s602)
Substituting the values, we have:
SE=(0.27218)+(0.29224)≈0.100SE=(180.272)+(240.292) ≈0.100.
Choose an appropriate confidence level. Let's say we want a 95% confidence interval.
Using the standard error, calculate the margin of error, which is given by multiplying the critical value (corresponding to the chosen confidence level) by the standard error. For a 95% confidence level, the critical value is approximately 1.96.
Margin of Error = 1.96 * 0.100 ≈ 0.196.
Construct the confidence interval by subtracting and adding the margin of error to the difference in sample means:
−0.6−0.196−0.6−0.196 to −0.6+0.196−0.6+0.196.
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PLEASE HELP ASAP WOULD APPRECITAE IT
The values of w, x, y, z are 120°, 60°, 120° , 60° respectively.
What are angles on parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
lines PQ and RS are parallel to each other and AB and CD are also parallel to each other. A pair of parallel line will serve as transversal.
Angles on parallel lines can be ;
Vertically opposite, alternate, corresponding and in each case the angles are equal.
w = 120°( vertically opposite angles)
x = 180-120 = 60( corresponding angles)
x = z = 60° ( corresponding angles)
y = 180-60 = 120°( angles on a straight line)
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Use the image below to answer the following question. What relationship do the ratios of sin x° and cos y° share?
A right triangle is shown. The two angles that are not 90 degrees are marked x and y. The leg across from angle y measuring 4, another leg across from angle x measuring 3, and the hypotenuse measuring 5
The ratios are both identical (three fifths and three fifths).
The ratios are opposites (negative three fifths and three fifths).
The ratios are reciprocals (three fifths and five thirds).
The ratios are both negative (negative five thirds and negative three fifths).
The ratios are both identical (three fifths and three fifths). Option A
How to determine the ratiosThe ratios of sin x° and cos y° are given as;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
In the question given above, the value of adjacent is 5 and the value of perpendicular is 12.
By using Pythagoras theorem, we can find the value of the hypotenuse.
Hypotenuse² = Adjacent² + Perpendicular²
Hypotenuse² = 5² + 12²
Hypotenuse² = 25 + 144
Hypotenuse² = 169 = 13²
Hypotenuse = 13
The value of sin X° will be;
sin X = 5/13
cos Y = 5/13.
sin X° = cos Y° = 5/13
Therefore, both the ratios of sin x° and cos y° are equal and their value is 5/13.
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Complete question:
Use the image below to answer the following question. What relationship do the ratios of sin x° and cos y° share?
A right triangle is shown. The two angles that are not 90 degrees are marked x and y. The leg across from angle y measuring 4, another leg across from angle x measuring 3, and the hypotenuse measuring 5
The ratios are both identical (three fifths and three fifths).
The ratios are opposites (negative three fifths and three fifths).
The ratios are reciprocals (three fifths and five thirds).
The ratios are both negative (negative five thirds and negative three fifths).
Identify the y-coordinate
(9,[?])
Answer:
(9,16)
Step-by-step explanation:
We Know
The equation y = 3x - 2
Find the y coordinate (9, ?)
We just simply put 9 in for x and solve for y
y = 3(9) - 2
y = 18 - 2
y = 16
So, the coordinate are (9,16)
In a certain Algebra 2 class of 23 students 7 of them basketball and 2 of them play baseball
The algebra class of 14 students in the Algebra 2 class of 23 students do not play basketball or baseball.
The number of students in a certain Algebra 2 class of 23 students who play basketball and baseball is 9, given that 7 of them play basketball and 2 of them play baseball.
The number of students in the class who do not play basketball or baseball is given by the number of students who do not play basketball plus the number of students who do not play baseball and the students who do not play basketball or baseball.
However, since each student is either playing basketball or baseball or neither, we can say that the total number of students who do not play basketball or baseball is given by the number of students in the class minus the total number of students who play basketball or baseball.
Thus, the number of students who do not play basketball or baseball is given by:
23 - 9 = 14
Therefore, 14 students in the Algebra 2 class of 23 students do not play basketball or baseball.
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the midpoint of a and b is (-3,-5) and point a is (-.5,0) what is point b
Therefore, the coordinates of point B are (-5.5, -10).
To find the coordinates of point B, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) are given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
We are given the midpoint coordinates as (-3, -5) and the coordinates of point A as (-0.5, 0). Let's assume the coordinates of point B as (x, y). Plugging the known values into the midpoint formula, we have:
(-3, -5) = ((-0.5 + x) / 2, (0 + y) / 2)
Simplifying, we get:
-3 = (-0.5 + x) / 2 ... (1)
-5 = y / 2 ... (2)
From equation (2), we can solve for y:
y = -5 * 2
y = -10
Now, substituting this value of y in equation (1), we can solve for x:
-3 = (-0.5 + x) / 2
-6 = -0.5 + x
x = -6 + 0.5
x = -5.5
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Kirsten got paid $432.50 for her work this month. She worked for 35 hours but broke a coffee mug so had to take $5 out of her pay. Write an equation, define your variable and solve. How much does she make an hour?
Answer:
Kirsten makes $12.50 per hour
Step-by-step explanation:
The total is $432.50
$5 is taken out of her paycheck, so that will be negative.
35 hours is the time she spent working.
The unknown variable we are looking for is the amount she makes in one hour.
Setting up the equation, we get:
$432.50 = $35x - $5
where x is the amount she makes every hour
Solve for x:
$437.50=$35x
$437.50 / $35 = x
Therefore, x = $12.50
NO LINKS!! URGENT HELP PLEASE!!!
NOT MULTIPLE CHOICE!!
8. a. Finish the table
b. Name the type of sequence
c. Find the equation for the following sequence
Answer:
7: 63
8: 73
arithmetic sequence
y = 10x - 7
or f(n) = 10x -7
or
[tex]a_{n}[/tex] = 3 + (n-1)10
Step-by-step explanation:
the output increases by 10 every time that the input increases by 1. That gives us our common difference or slope. The y intercept is -7. That is the value is you worked backwards until you get to n = 0. The initial value is 3. That is when n is 1.
When n is 3, f(n) is 23
When n is 2, f(n) is 13
When n is 1, f(n) is 3
When n is 0, f(n) is -7
I am not sure if this is clear. I am assuming that you have a lot of knowledge of linear equations and how to write arithmetic sequence. If my explanation is confusing it is me and not you.
Answer:
a. 63,73
b. Arithmetic sequence
c.t(n)=10n-7
Explanation:
a. Here is the completed table:
n | t(n)
4 | 33
5 | 43
6 | 53
7 | 63
8 | 73
b.
The type of sequence is arithmetic.
An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant.
In this case, the difference between any two consecutive terms is 10.
c.
The equation for the arithmetic sequence is:
t(n)=a+(n-1)d
where:
t(n) is the nth term in the sequencen is the term numberd is the common differencea is the first termFor Question:
d=43-33=10a=?Now
equation becomes:
t(4) = a+(4-1)10
33=a+30
a=33-30
a=3
Now, the Equation becomes
t(n) = 3+(n-1)10
t(n) = 3+10n-10
t(n)=10n-7
Which equations represent the line that is parallel to 3x - 4y = 7 and passes through the point (-4,-2)? Select two
options.
Oy=-3x+1
03x-4y=-4
4x-3y=-3
Oy-2=-(x-4)
Oy+2=2(x+4)
The equations that represent a line parallel to 3x - 4y = 7 and passes through the point (-4, -2) are:
0 = 3x - 4y - 4
3x - 4y = 4
To determine which equations represent a line that is parallel to the given line and passes through the point (-4, -2), we need to find the equations that have the same slope as the given line.
The equation 3x - 4y = 7 can be rewritten in slope-intercept form as y = (3/4)x - 7/4. From this form, we can see that the slope of the given line is 3/4.
Now let's analyze the options:
Oy = -3x + 1: This equation has a slope of -3, which is not equal to the slope of the given line (3/4). Therefore, this option does not represent a line parallel to the given line.
0 = 3x - 4y - 4: This equation can be rewritten as 3x - 4y = 4. Comparing this to the given line, we can see that it has the same coefficients of x and y, which means it has the same slope of 3/4. Therefore, this option represents a line parallel to the given line.
4x - 3y = -3: This equation has a slope of 4/3, which is not equal to the slope of the given line (3/4). Therefore, this option does not represent a line parallel to the given line.
Oy - 2 = -(x - 4): This equation can be rewritten as y = -x + 2. The slope of this line is -1, which is not equal to the slope of the given line (3/4). Therefore, this option does not represent a line parallel to the given line.
Oy + 2 = 2(x + 4): This equation can be rewritten as y = 2x + 6. The slope of this line is 2, which is not equal to the slope of the given line (3/4). Therefore, this option does not represent a line parallel to the given line.
In conclusion, the equations that represent a line parallel to 3x - 4y = 7 and passes through the point (-4, -2) are:
0 = 3x - 4y - 4
3x - 4y = 4
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60, 69, 79, 80, 86, 86, 86, 89, 90, 100
Which test score is an outlier?
60
69
90
100
The test score that is an outlier is 60. Option A
What is an outlierA data point that dramatically deviates from the dataset's main pattern or trend is referred to as an outlier.
From the information given, we have that;
The score are;
60, 69, 79, 80, 86, 86, 86, 89, 90, and 100.
We can see that the outlier is 60.
This is due to the fact that all of the other scores, which range from 69 to 100, are considerably higher and closer in value.
The score of 60, however, is considerably lower than the others pupils.
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Find value of x in trapezoid
Answer:
x = 1
Step-by-step explanation:
You want to know the value of x in the trapezoid with adjacent angles (43x+2)° and 135°.
Supplementary anglesThe two marked angles can be considered "consecutive interior angles" where a transversal crosses parallel lines. As such, they are supplementary.
(43x +2)° +135° = 180°
43x = 43 . . . . . . . . . . . . . . divide by °, subtract 137
x = 1 . . . . . . . . . . . . . . . divide by 43
The value of x is 1.
__
Additional comment
Given that the figure is a trapezoid, we have to assume that the top and bottom horizontal lines are the parallel bases.
<95141404393>
(36)^x+2= 6
Solve and round to the nearest 100th
Please help I am confused and need an explanation
As the given equation is (36)ˣ⁺² = 6 , then the solution for the given equation is x ≈ -1.54.
The given equation in the question is (36)ˣ⁺² = 6
according to the given equation , the goal is to solve the equation for x.
For solving this equation ,
we'll have to use logarithmic operations which is as follows:
log36(6) = x+2.
We will be further using a calculator to determine the logarithmic value: log36(6) ≈ 0.4607.
Now, By subtracting 2 from both sides, we will get the value of x as:
x ≈ -1.54.
When we round off this value to the nearest 100th, we will get -1.54.
Thus , the solution for the given equation is x ≈ -1.54.
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(a)Derive the Lagragian interpolating polynomial of degree 1, if P₁(x₁) = a + bx₁ P₁(x) = a + bxo P₁(x) = a + bx where P₁ (x₁) = f₁, P₁ (xo) = fo.
The Lagrange interpolating polynomial of degree 1 is P₁(x) = (f₁ - fo)x + (foxo - f₁xo) / (x₁ - xo).
To derive the Lagrange interpolating polynomial of degree 1, let's consider two distinct points: (x₁, f₁) and (xo, fo). The Lagrange interpolating polynomial of degree 1 can be expressed as:
P₁(x) = L₁(x)f₁ + L₂(x)fo,
where L₁(x) and L₂(x) are the Lagrange basis polynomials defined as:
L₁(x) = (x - xo) / (x₁ - xo),
L₂(x) = (x - x₁) / (xo - x₁).
Substituting these expressions into P₁(x), we have:
P₁(x) = [(x - xo) / (x₁ - xo)]f₁ + [(x - x₁) / (xo - x₁)]fo.
Simplifying further:
P₁(x) = [f₁(x - xo) + fo(x - x₁)] / (x₁ - xo).
Expanding the numerator:
P₁(x) = [f₁x - f₁xo + fox - fox₁] / (x₁ - xo).
Finally, we can rearrange the terms to obtain the Lagrange interpolating polynomial of degree 1:
P₁(x) = (f₁ - fo)x + (foxo - f₁xo) / (x₁ - xo).
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The graph of F(x), shown below, has the same shape as the graph of
G(x)=x2, but it is shifted to the left 1 unit. What is its equation?
-F(x)=
-
OA. F(x)=x²2 +1
B. F(x)=x²-1
C. F(x) = (x + 1)²
D. F(x)=(x-1)²
To shift the graph left, we need to subtract 1 from x. This gives us F(x) = (x - 1)², which matches option D. Therefore, the correct answer is D.
The graph of F(x) is a parabolic graph, just like the graph of G(x)=x². F(x) is shifted to the left by 1 unit.
The equation for the graph of F(x) is F(x) = (x - 1)². This is because when a parabolic graph is shifted left or right, it affects the x-value of the vertex of the parabola.
The standard form of the equation for a parabolic graph is y = a(x - h)² + k, where (h, k) is the vertex of the graph and a determines whether the graph is facing up or down. In this case, the vertex of the graph of G(x)=x² is (0, 0).
When we shift this graph left by 1 unit, the vertex becomes (-1, 0). Therefore, the equation for F(x) is F(x) = a(x + 1)².
To determine the value of a, we can look at the y-intercept of the graph, which is (0, 1). Plugging these values into the equation, we get 1 = a(0 + 1)², which simplifies to 1 = a.
Therefore, the equation for F(x) is F(x) = (x + 1)². However, if we expand this equation, we get F(x) = x² + 2x + 1, which is not in the form given in the options.
To shift the graph left, we need to subtract 1 from x. This gives us F(x) = (x - 1)², which matches option D. Therefore, the correct answer is D.
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Algebraic expression for 4less then 3x
When 'x' is 5, the Algebraic expression 3x - 4 evaluates to 11.
To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.
First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.
Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.
In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.
To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:
3(5) - 4
This simplifies to:
15 - 4 = 11
So, when 'x' is 5, the expression 3x - 4 evaluates to 11.
In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.
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Note the complete question:
Algebraic expression for 4 less than the product of 3 and some number
What is the algebraic expression for "4 less than the product of 3 and some number?
Please help me understand the meaning of how to calculate.
A wool suit, discounted by 20% for a clearance sale, has a price tag of $636. What was the suit’s original price?
The original price of the wool suit was $795.
Let's denote the original price of the wool suit as "P."
We know that the suit was discounted by 20%, which means the discounted price is 80% (100% - 20%) of the original price.
Given that the discounted price is $636, we can set up the following equation:
0.8P = $636
To find the original price, we need to solve for P. We can do this by dividing both sides of the equation by 0.8:
P = $636 / 0.8
P = $795
Therefore, the original price of the wool suit was $795.
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Darvin furniture marks up the price of a dining room set 40%. What will be the selling price of a dining room set that Darvin buys for 1500?
Answer:
$2100
Step-by-step explanation:
40% of 1500 is 600
1500 + 600 = 2100
The selling price will be $2100