Answer:
[tex]y=\dfrac{5}{4}x^3+10[/tex]
Step-by-step explanation:
Given information:
[tex]y=ax^3+d[/tex](0, 10)(2, 20)Create two equations by substituting the given points into the given equation:
Equation 1: point (0, 10)
[tex]\implies a(0)^3+d=10[/tex]
[tex]\implies 0+d=10[/tex]
[tex]\implies d=10[/tex]
Equation 2: point (2, 20)
[tex]\implies a(2)^3+d=20[/tex]
[tex]\implies 8a+d=20[/tex]
Substitute Equation 1 into Equation 2 and solve for a:
[tex]\implies 8a+d=20[/tex]
[tex]\implies 8a+10=20[/tex]
[tex]\implies 8a+10-10=20-10[/tex]
[tex]\implies 8a=10[/tex]
[tex]\implies \dfrac{8a}{8}=\dfrac{10}{8}[/tex]
[tex]\implies a=\dfrac{10}{8}[/tex]
[tex]\implies a=\dfrac{5}{4}[/tex]
Finally, substitute the found values of a and d into the original formula:
[tex]\implies y=\dfrac{5}{4}x^3+10[/tex]
Check by substituting the x-values of the two given points into the found equation:
[tex]x=0 \implies y=\dfrac{5}{4}(0)^3+10=10 \leftarrow \textsf{correct}[/tex]
[tex]x=2 \implies y=\dfrac{5}{4}(2)^3+10=20 \leftarrow \textsf{correct}[/tex]
Put(0,10)
10=a(0)³+dd=10Now
Put again (2,20) this time
20=2³a+1010=8aa=10/8a=5/4How can I find the three iterations of 3^(x)= 2^(-x)+4
After factorizing the given equation, we can find the three iterations by putting the consecutive values of x.
The given equation is 3∧x = 2∧(-x) + 4. We can modify it as shown below:
Take logarithm on both the sides
log(3∧x) = log[2∧(-x) + 4]
xlog3 = log[2∧(-x) + 4]
x = log[2∧(-x) + 4] / log3
For the first iteration, put x = 1
x = log[2∧(-1) + 4] / log3
x = log4.5 / log3
x = 0.477
For the second iteration, put x = 2
x = log[2∧(-2) + 4] / log3
x = log4.25 / log3
x = 0.477
For the third iteration, put x = 3
x = log[2∧(-3) + 4] / log3
x = log4.125 / log3
x = 0.477
So, this is how we can find three iterations.
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Given the expression: 6x10 − 96x2
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
The expression 6x¹⁰ - 96x² can be written by factoring out the greatest common factor is 6x²(x⁸ - 16) and for a part, B expression can be simplified by applying identity.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have an expression:
Part A)
= 6x¹⁰ - 96x²
= 6x²(x⁸ - 16)
Part B)
[tex]\rm =6x^2(\left(x^4\right)^2-4^2)[/tex]
[tex]\rm =6x^2(\left(x^4+4\right)\left(x^4-4\right))[/tex]
[tex]\rm =6x^2\left(x^2+2x+2\right)\left(x^2-2x+2\right)\left(x^2+2\right)\left(x^2-2\right)[/tex]
Thus, the expression 6x¹⁰ - 96x² can be written by factoring out the greatest common factor is 6x²(x⁸ - 16) and for a part, the B expression can be simplified by applying identity.
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answer is equivalent to ?
√16
√49
SA
A.
OB.
O c.
D.
16
49
16
49
316
The solution of the given expression is 9. So the correct answer is option B.
The complete question is given below:-
(√16 - √49 )² The solution of the given equation will be
A. 16
B .9
C .49
D. 316
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The given expression will be calculated as:-
(√16 -√49 )² = (√16)² -2 (√16)(√46) + (√49 )²
= ( 16 - 2(4)(7) + 49 )
= ( 16 - 56 + 49 )
= 9
Therefore the solution of the given expression is 9. So the correct answer is option B.
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Pleas hurry!!!!! Which line is perpendicular to a line that has a slope of -5/6
line JK
line LM
line NO
line PQ
Answer:
LM
Step-by-step explanation:
Perpendicular slope would be - 1 / m = - 1/(-5/6) = 6/5
slope m = rise / run line LM rises 6 for a run of 5
Need help with this geometry question
Answer: QN=19
Step-by-step explanation:
Diagonals of an isosceles trapezoid are congruent, so NQ=PM.
By the segment addition postulate, NQ=QR+RN=3x+7.
So,
[tex]6x-5=3x+7\\\\3x-5=7\\3x=12\\\\x=4[/tex]
So, [tex]QN=3(4)+7=\boxed{19}[/tex]
Lydia writes the equation below with a missing value.
y = 5 x minus box
She puts a value in the box and says that the equation represents a direct variation. Which explains whether the equation could represent a direct variation?
If she puts 0 in the box she would have a direct variation.
If she puts 5 in the box she would have a direct variation.
The equation is not of the form y = k x, so it cannot represent a direct variation.
The equation has a minus sign, so it cannot represent a direct variation.
If she puts 0 in the box she would have a direct variation.
Lydia writes the equation y = 5x - __ with a missing value.
She puts a value in the box and says that the equation represents a direct variation.
We have to choose the correct option from the given options that explain that the equation could represent a direct variation.
When two variables are such that one is a constant multiple of the other, we said they are in Direct variation.
What is the direct variation?
In form of y = ax, where y and x are in direct variation.
Consider the given equation y = 5x - __
For the equation to be in direct variation the value of the missing term has to be 0.
then the equation becomes,
y = 5x
Thus, If she puts 0 in the box she would have a direct variation.
Option (a) is correct.
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Answer:
a
Step-by-step explanation:
which ordered pair is a solution to the following system of inequalities
Answer:
it's 1,1 is the correct ans
Step-by-step explanation:
Because my teacher told its absolutely correct answer I got the same question in exam
Answer:
the answer should be the 2 one
Step-by-step explanation:
I got it right just had it.
18 / 48 hrs left
Divide and answer the question.
Answer: I don’t understand
Step-by-step explanation:
190 divided by 2 over 3
solve the following inequality:
ALGEBRA 1
Answer:
[tex]m \leqslant 10 \: or \: m > 4[/tex]
Step-by-step explanation:
[tex] \frac{m - 2}{3} \leqslant - 4 \\ \frac{m - 2}{3} \times 3 \leqslant - 4 \times 3 \\ m - 2 \leqslant - 12 \\ m - 2 + 2 \leqslant - 12 + 2 \\ m \leqslant 10[/tex]
OR
[tex]3m - 8 > 4 \\ 3m - 8 + 8 > 4 + 8 \\ 3m > 12 \\ \frac{3m}{3} > \frac{12}{3} \\ m > 4 [/tex]
Trigonometry is crazy
Answer:
see the attachment photo!
i hope this can help you! :)
Which of the following is the solution to 7√22 + 3√7
The value of this irrational Expression is 40.77 .
What is an Expression ?An expression is a mathematical statement consisting of variables , constants and mathematical operators.
The expression given is
7√22 +3√7
√22 = 4.69
√7 = 2.65
32.83 + 7.94
40.77
The value of this irrational Expression is 40.77 .
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statement that is assumed to be true without proof is . A statement that has been shown to be true by vigorous application of logic is . is a statement that is believed to be true but hasn't been proven.
An axiom is a statement that is assumed to be true without proof.
What are the types of statements?In logic, a statement could be shown to be valid or true by the use of premises that lead to a sound conclusion.
The following terms can be used to describe the statements;
Axiom - a statement that is assumed to be true without proofTheorem - a statement that has been shown to be true by vigorous application of logicHypothesis - a statement that is believed to be true but hasn't been proven.Learn more about mathematical statements:https://brainly.com/question/17029275?
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Answer:
The answer is axiom, theorem, and then conjecture
Step-by-step explanation:
the ufugfldldd
5+9x+3gg3g3\
1 b
Alex's recipe calls for 1/3 cup of chocolate chips for every 2 cups of flour. If he increases the
amount of flour to 3 cups, how many cups of chocolate chips will he need?
Answer:
1/2 cup of chocolate chips
Step-by-step explanation:
Given ratio:
chocolate chips : flour = 1/3 cups : 2 cupsLet x be the unknown amount of chocolate chips:
[tex]\implies \sf \dfrac{1}{3}:2=x:3[/tex]
[tex]\implies \sf \dfrac{\frac{1}{3}}{2}=\dfrac{x}{3}[/tex]
Cross multiply:
[tex]\implies \sf 3 \cdot \dfrac{1}{3}=2 \cdot x[/tex]
[tex]\implies \sf 1=2x[/tex]
[tex]\implies \sf x=\dfrac{1}{2}[/tex]
Therefore, 1/2 a cup of chocolate chips will be needed for 3 cups of flour.
Let that be x
1/3/2=x/31/6=x/3x=3/6x=1/2 cup
9. P(no more than 16 | prime
Question 1 of 10
What is the midpoint of the segment shown below?
O A. (6,3)
O B. (6,5)
O C. (3,5)
OD. (3, 3)
Answer:
[tex]\textsf{C.} \quad \left(3,\dfrac{5}{2}\right)[/tex]
Step-by-step explanation:
Midpoint between two points
[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]
Define the endpoints of the line segment:
[tex]\textsf{Let }(x_1,y_1)=(-1,2)[/tex]
[tex]\textsf{Let }(x_2,y_2)=(7,3)[/tex]
Substitute the defined endpoints into the midpoint formula and solve:
[tex]\implies \textsf{Midpoint}=\left(\dfrac{7+(-1)}{2},\dfrac{3+2}{2}\right)[/tex]
[tex]\implies \textsf{Midpoint}=\left(3,\dfrac{5}{2}\right)[/tex]
Midpoint
(-1+7/2,2+3/2(6/2,5/2)3,5/2)Multiply and remove all perfect squares from inside the square roots. Assume a is positive.
3[tex]3\sqrt{5a}*8\sqrt{35a^{2} }[/tex]
The multiplication is 120*[tex]a^{3/2}[/tex].
What is exponents and powers?
Power defines a base number raised to the exponent, where base number is the factor which is multiplied by itself and exponent denotes the number of times the same base number is multiplied.
Given:
3√(5a) * 8 √(35a²)
= 3√(5a)* 8* a *√7* √5
= 3*8*5*a *√(7a)
= 120 [tex]a^{1/2+1}[/tex]
=120*[tex]a^{3/2}[/tex]
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Answer:
[tex]120a\sqrt{7a}[/tex]
Step-by-step explanation:
It's right on khan academy
which expression is equivalent to...
Answer:
B
Step-by-step explanation:
curved surface area of a cone = Trl, where r is the
radius and I is the slant height.
surface area of a sphere = 42, where r is the
radius.
The shape below is made from a hemisphere and a
cone, each with a radius of 6 cm.
Work out the surface area of this shape in terms of .
16 cm
6 cm
Not drawn accurately
Answer:
168π cm²
Step-by-step explanation:
The total surface area is the sum of the areas of the parts: a hemisphere and a cone.
__
area formulaThe area of a hemisphere is half the area of a sphere, so the total area is ...
total area = hemisphere area + cone area
= 2πr² +πrl
total area = πr(2r +l)
__
applicationFor the given dimensions, r = 6 cm, l = 16 cm, the total surface area is ...
total area = π(6 cm)(2(6 cm) +16 cm) = π(6)(28) cm²
total area = 168π cm²
Explain why a graph that fails the vertical-line test does not represent a function. Be sure to use the definition of a function in your answer
Explanation:
A function is a relationship where any one x-value/input only has one corresponding y-value/output. (note: a y-value can have multiple x-values).
> This can be called "assigning one y-value to every x element".
The vertical line test places a line that would connect all y-values of an x-value (that is, if it were to have multiple y-values). If multiple points can be found along the vertical line, it is, therefore, by the definition of a function, not a function. (Because an x-value will have more than one y-value).
So, a graph that fails the vertical-line test does not represent a function because an x-value will correspond with more than one y-value.
hope this helps!!
Find the length of the side labeled . Round intermediate values
to the nearest tenth. Use the rounded values to calculate the next
value. Round your final answer to the nearest tenth.
Step-by-step explanation:
ATTACHED IS THE SOLUTION!!PLEASE DON'T HESITATE TO ASK WHERE YOU DON'T UNDERSTAND.Which equation represents an exponential function with the initial value of 500?
Answer:
A exponential equation is usually of the form f(x)=a (1±r)ˣ.
Our limitation: Initial Vale is 500.
Let's look at our options:
#1- Initial Value of 1000 --- WRONG!
#2- Initial Value of 1000 --- WRONG!
#3- Initial Value of 500 ---- Maybe
#4- Initial Value of 500 ---- Maybe
Let's look at 3 and 4:
#3- Fits Our Form of f(x)=a (1±r)ˣ ---- CORRECT!
#4- Does not fit Our Form of f(x)=a (1±r)ˣ, It's to the 2nd power, not the x power! ---- WRONG!
Hence, #3 Is correct!
Step-by-step explanation:
Well, I hope you understood, and I'd gladly explain anything that didn't make sense. A brainliest would be appreciated, thank you!
-Zylynn Jade Ardenne
Which of the following are true statements?
Which of the following is the standard equation of the ellipse with vertices at (1, 0) and (11, 0) and an eccentricity of three fifths question mark
quantity x minus 6 end quantity squared over 100 plus y squared over 64 equals 1
quantity x plus 6 end quantity squared over 64 plus y squared over 100 equals 1
quantity x plus 6 end quantity squared over 16 plus y squared over 25 equals 1
quantity x minus 6 end quantity squared over 25 plus y squared over 16 equals 1
The equation fourth represents the ellipse that has vertices at (1, 0) and (11, 0), and an eccentricity of 3/5 option fourth is correct.
What is an ellipse?An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.
We have:
The vertices of the ellipse = (1, 0) and (11, 0)
Eccentricity of ellipse = 3/5
We have equations:
[tex]\rm \dfrac{\left(x-6\right)^{2}}{100}+\dfrac{y^{2}}{64}=1[/tex]
[tex]\rm \dfrac{\left(x+6\right)^{2}}{64}+\dfrac{y^{2}}{100}=1[/tex]
[tex]\rm \dfrac{\left(x+6\right)^{2}}{16}+\dfrac{y^{2}}{25}=1[/tex]
[tex]\rm \dfrac{\left(x-6\right)^{2}}{25}+\dfrac{y^{2}}{16}=1[/tex]
From the fourth equation:
The vertices of the ellipse:
(1, 0) and (11, 0)
The eccentricity:
c² = a² - b²
c² = 25-16
c = 3
e = c/a = 3/5
Thus, the equation fourth represents the ellipse that has vertices at (1, 0) and (11, 0), and an eccentricity of 3/5 option fourth is correct.
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An auto mechanic charges (C) an initial fee of $50 and then $40 per hour. The graph of this model would be:
a curved line that increases but then decreases.
a straight line that decreases only.
a straight line that increases only.
None of these choices are correct.
The graph of this model would be a straight line that increases only option third is correct.
What is a line graph?A line graph is a graph made up of segments of straight lines that connect the depicted data points.
We have:
An auto mechanic charges (C) an initial fee of $50 and then $40 per hour.
Let T be the total fee and h is the number of hours
T = 50 + 40h
The above equation represents a graph of a straight line as the slope of the line is positive.
m = 50
Thus, the graph of this model would be a straight line that increases only option third is correct.
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What is the product of (2x - 1) (x + 4)
Answer: 2[tex]x^{2}[/tex]+7x-4
Step-by-step explanation:
Product implies multiplication so just multiply it out.
(2x-1) (x+4)
2x^2+8x-1x-4 (Combine like terms)
2x^2+7x-4
What is the vertex of the absolute value function defined by f(x) =3|x+7|-2
The vertex of the absolute value function is (-7,-2)
How to determine the vertex?The function is given as:
f(x) = 3|x + 7| - 2
The above function is an absolute value function.
An absolute value function is represented as:
f(x) = a|x - h| + k
Where:
Vertex = (h,k)
By comparison, we have:
(h,k) = (-7,-2)
Hence, the vertex of the absolute value function is (-7,-2)
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What graph best represents the data
A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. The correct option is A.
What is a graph?A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.
A histogram is a statistical information presentation that employs rectangles to illustrate the frequency of data items in equal-sized numerical intervals. The independent variable is represented along the horizontal axis and the dependent variable is plotted along the vertical axis in the most frequent kind of histogram.
The best graph that can represent the given situation is Histogram. Hence, the correct option is A.
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Which number is irrational?
C
-4
C
2
g
O 11
O 8.26
The irrational number in the given options is √11
What is an irrational number?Irrational numbers are set of all real numbers in mathematics that are not rational numbers in nature. By the word rational, we mean that they cannot be expressed or represented in a fraction of a/b.
where;
a = numeratorb = denominatorIn other words, it is impossible to describe an irrational number as the ratio of two integers.
From the given options, the square root of 11 is the only number that cannot be expressed as a fraction, therefore, we can conclude that it is considered the only irrational number in the given options.
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