The x intercept of the linear equation is -4 and y intercept is 8.
Intercept of the linear equation
The intercept of the linear equation is calculated as follows;
x - y/2 = -4
make y the subject of the formula;
y/2 = x + 4
y = 2x + 8
y intercept is obtained at point, x = 0y = 0 + 8
y = 8
x intercept is obtained at point, y = 00 = 2x + 8
2x = -8
x = -4
Thus, the x intercept of the linear equation is -4 and y intercept is 8.
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Answer:
The x intercept of the linear equation is -4 and y intercept is 8
Step-by-step explanation:
Let f(x) = -5x^6√x + -7/x³√x. What would f’(x) be? If anyone could show me step-by-step, I would greatly appreciate it! I’ve worked out this problem 4 times already and I can’t seem to get the right answer.
Answer:
[tex]f^{\prime}\left(x\right)\ =\ -\frac{65}{2}x^{\frac{11}{2}}\ +\frac{49}{2}x^{-\frac{9}{2}}[/tex]
or
[tex]f^{\prime}\left(x\right)\ =\ -32.5x^{5.5}\ +\ 24.5x^{-4.5}[/tex]
Step-by-step explanation:
Rather than solving this question in a more complex method by directly using the product rule and quotient rule, it can first be considered to perform some algebraic manipulation (index laws) to simplify the expression before taking the derivative.
[tex]\begin{large}\begin{array}{l}f\left(x\right)\ =\ -5x^6\ \sqrt{x}\ +\ \frac{-7}{x^3\ \sqrt{x}}\\\\f\left(x\right)\ =\ -5x^6\cdot x^{\frac{1}{2}}\ +\ \frac{-7}{x^3\cdot x^{\frac{1}{2}}}\\\\f\left(x\right)\ =\ -5x^{6\ +\ \frac{1}{2}}\ +\ \frac{-7}{x^{3\ +\ \frac{1}{2}}}\\\\f\left(x\right)\ =\ -5x^{\frac{13}{2}}\ +\ \frac{-7}{x^{\frac{7}{2}}}\\\\f\left(x\right)\ =\ -5x^{\frac{13}{2}}\ -7x^{-\frac{7}{2}}\end{array}[/tex]
Now, the derivative of the function can be calculated simply by only using the power rule, which yields
[tex]\begin{large}\begin{array}{l}f\left(x\right)\ =\ -5x^{\frac{13}{2}}\ -7x^{-\frac{7}{2}}\\\\f^{\prime}\left(x\right)\ =\ \left(-5\right)\left(\frac{13}{2}\right)\left(x^{\frac{13}{2}\ -\ 1}\right)\ -\ \left(7\right)\left(-\frac{7}{2}\right)\left(x^{-\frac{7}{2}\ -\ 1}\right)\\\\f^{\prime}\left(x\right)\ =\ -\frac{65}{2}x^{\frac{11}{2}}\ +\frac{49}{2}x^{-\frac{9}{2}}\\\\f^{\prime}\left(x\right)\ =\ -32.5x^{5.5}\ +\ 24.5x^{-4.5}\end{array}\\\end{large}[/tex]
need help figuring out the answers
Answer:
3, -1, 1 and 0
Step-by-step explanation:
An expression is undefined when the denominator is equal to 0 as you cannot divide by 0 in Mathematics. Therefore you are looking for the values of x which will result in either or both denominators equaling 0.
This simply means finding the solutions to the quadratics in the denominators.
First equation is [tex]x^{2} -2x-3[/tex].
One way you can solve this equation is using factorization (putting the equation into two sets of brackets which show the solutions) which puts the equation in the solvable form: (ax+b)(cx+d).
Firstly, we can deduct that a and c are both 1 as ax and cx multiply to give the x^2 term, the co-efficient of which is 1. Since only 1 and 1 can multiply to 1, a and c must both be 1.
Now, in order to work out b and d we need to find the possible factor combinations for -3 as b and d multiply to give the constant term. The only possible combination is 1x3, therefore b and d can either be -1 and 3, or -3 and 1.
To work this out we look at the x term. We see it is -2x. b and d will add to give the co-efficient.
Therefore we know that they are -3 and 1 as -3+1 = -2
We now have the equation: (x+1)(x-3)
Setting it to 0 gives us: [tex](x+1)(x-3)=0[/tex]
This tells us the solutions to this equation are x= -1 and x= 3 as substituting these values for x will result in a bracket adding to 0 so both those options can be selected as your answer.
The second equation [tex]2x^{2} +2x[/tex] can be approached with a slightly easier method. Both terms have a 2x, so we can condense it into a bracket by dividing both terms by the common factor and moving the factor outside. Factorizing this equation in this fashion gives us: [tex]2x(x+1)=0[/tex]
Now our solutions are x=0 and x=1.
Combined from both equations the correct options are: 3, -1, 1 and 0.
Hope this helped!
classify the equation 9(a-4)+3(2a+5)=7(3a-4)-6a+7
Answer:
0 = 0 thats my answer
Step-by-step explanation:
The adjusted trial balance columns of the worksheet for Whispering Winds Company are as follows.
Answer:
Question?
Step-by-step explanation:
(x^4-13x^2+36)/(2x^2+10+12)
Answer:
Step-by-step explanation:
Which of the following terms best fits this definition?
The angle between two sides of a triangle.
Select one:
AAS Theorem
SAS Postulate
Included Side
ASA Postulate
HL Congruence Theorem
Included Angle
SSS Postulate
Step-by-step explanation:
hope you can understand
Help me with this I’m stuck!!:)
The cardinality of the set indicated in the task content is; 11.
What is the cardinality of the set?It follows from the task content that the cardinality of the intersection set of set A compliment and set B compliment is to be determined.
Hence, it follows that the elements in the described set include the elements in set C only and the elements in the compliment of set A, B and C union.
On this note, it follows that the cardinality of the set is; 4 +7 = 11.
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How can the next term in the infinite sequence 1, 5, 12, 22, 35, be generated? O Square the term number, subtract the term number from the result, multiply by 3, and divide the result by 2. O Square the term number, multiply the result by 3, divide by 2, and subtract the term number from the result. O Square the term number, divide the result by 2, subtract the term number, and multiply the result by 3. O Square the term number, multiply the result by 3, subtract the term number, and divide the result by 2.
Check the forward differences of the sequence.
• first-order differences
5 - 1 = 4
12 - 5 = 7
22 - 12 = 10
35 - 22 = 13
• second-order differences (i.e. differences of the first differences)
7 - 4 = 3
10 - 7 = 3
13 - 10 = 3
The second differences are all 3 (as far as we know), so the sequence of first differences is arithmetic/linear, which means the original sequence is quadratic. Let the [tex]n[/tex]-th term be
[tex]x_n = an^2 + bn + c[/tex]
Given that [tex]x_1=1[/tex], [tex]x_2=5[/tex], and [tex]x_3=12[/tex], we have
[tex]\begin{cases} a + b + c = 1 \\ 4a + 2b + c = 5 \\ 9a + 3b + c = 12 \end{cases} \implies a=\dfrac32, b=-\dfrac12, c=0[/tex]
and so the [tex]n[/tex]-th term of the sequence is generated by the rule
[tex]x_n = \dfrac{3n^2 - n}2[/tex]
which most closely resembles the last option,
Square the term number, multiply the result by 3, subtract the term number, and divide the result by 2.
which of the following statements is/are true
Using Venn probabilities, the correct statement is given by:
ii) [tex]|A \cup B| = |A| + |B| - |A cap B|[/tex]
What is a Venn probability?In a Venn probability, two non-independent events are related with each other, as are their probabilities.
The "or probability" is given by:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
Hence, statement ii is correct.
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Between every pair of distinct points, there is a positive unique number called the ??? , which can be determined as the ??? of the corresponding real numbers of the two points.
The positive number between every pair of distinct points is known as the distance and it can be found as the absolute value of the difference between the corresponding real numbers.
How is the distance found?The distance represents the space between a pair of distinct points. This is called the distance postulate.
In order to find the distance, you would need to solve for the absolute value of the difference between the real numbers that are at the two points.
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Answer:
The positive number between every pair of distinct points is known as the distance and it can be found as the absolute value of the difference between the corresponding real numbers.
Step-by-step explanation:
f(x)=2(x)^2+5√(x+2)
f(2)=
Answer:
f(2) = 18
Step-by-step explanation:
Put '2' into the equation where 'x' is to get :
f(2) = 2 (2^2) + 5 (sqrt(2+2)
= 8 + 5 (2) = 18
find the measures of angles of triangle DEF
Answer:
Angle E = 90° Angle D= 55° Angle F = 35°Sum of all the angles of a triangle = 180° ( angle sum property).
Angle D + Angle E + Angle F = 180°
8x - 1 + 5x + 90° = 180°
8x + 5x + 89 = 180
13x = 180 - 89
13x = 91
x = 7.
Angle D = 8x - 1
= 8(7)-1
= 56 - 1
= 55
Angle E = 90° ( given)
Angle F = 5x
= 5 * 7
= 35
Answer:
m∠E: 90°
m∠D: 55°
m∠F: 35°
Step-by-step explanation:
Since the interior angles of a right triangle sum up to 180°, the sum of angles D, E, F will equal 180°. We can then form an equation from that information.
[tex]90+(8x-1)+5x=180\\13x-1=90\\13x=91\\x=7[/tex]
From this, we can plug in the variable.
[tex]mE=90\\mD=55\\mF=35[/tex]
Who got geometry regents answer key June 2022
Answer:
nobody yet
Step-by-step explanation:
Answer:
No one.
Step-by-step explanation:
The New York State Education Department has canceled the June 1, 2022, administration of the Regents Examination in U.S. History & Government (Framework). NYSED Commissioner Betty A.
Solve for x : 7x + 8 < 1/6 (42x+48)
X = all real number
X has no solution
X = 0
Answer:
[tex]\fbox {all real numbers}[/tex]
Step-by-step explanation:
7x + 8 = 1/6 (42x + 48)
7x + 8 = 7x + 8
x = all real numbers
Use Modus Ponens to deduce the conclusion from each of the following pairs of premises:
a = b ∧ b = c
(a = b ∧ b = c) ⇒ a = c
The conclusion is a=c statement
A modus ponens argument has the same structure as a syllogism, with two premises and a conclusion:
If P, then Q.
P occurs.
Consequently, Q occurs.
The Modus Ponens rule of inference or rule of logic requires a single premise and its logical consequences. A conditional statement states that if event 1 occurs, event 2 will also occur and that event 2 will be inferred as the outcome if event 1 occurs. For instance, if A implies B and A is assumed to be true, then it follows that B must also be true according to the Modus Ponens rule.
Hence, By modus Ponens
a=b∧b=c ⇒ a=c
So, given a=b∧b=c Then
⇒a=c.
Hence the conclusion is a=c statement .
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What does the ratio 4: 18 represent in this situation?
Answer:
2:9 or 2/9
Step-by-step explanation:
I guess this question asks the simplest form of ratio 4:18
so I divided it by two and since they cannot be divided further that's the answer
you can either choose to write it in ratio form or fraction form that's your choice good day.
A major airline is planning to purchase new airplanes. It wants to borrow $800 million by
issuing bonds. The bonds are for a 10-year period with simple interest computed quarterly at
a rate of 2 percent per quarter. Interest is to be paid each quarter to bondholders.
How much (in millions) will the airline have to pay in quarterly interest? $
million
How much interest (in millions) will it pay over the 10-year period? $ million
Answer:
look at the picture
Step-by-step explanation:
look at the picture
How much is the difference in possible median income on a weekly basis between 4 years of high school with no diploma and high school graduate with no college for a female? A. $823 B. $364 C. $11,419 D. $95
Answer:
its $95 dollars
Step-by-step explanation:
Some identical cylinders each have a radius of
5 cm and a length of 4 cm.
Rufus has enough paint to cover 2500 cm².
How many of these cylinders can Rufus paint
completely?
Answer:
8 cylinders
Step-by-step explanation:
The surface area of a cylinder is given by the formula ...
A = 2πr(r +l) . . . . . for radius r and length l
__
The cylinders Rufus has each have an area of ...
A = 2π(5 cm)(5 cm +4 cm) = 90π cm² ≈ 282.74 cm²
That means 2500 cm² of paint will cover ...
2500 cm²/(282.74 cm²/cylinder) ≈ 8.84 cylinders
Rufus has enough paint to cover 8 cylinders completely.
Suppose you are standing in a parking lot near a building, and the winter air temperature is 0 degrees Celsius. At that temperature, sound travels about 331 meters per second. If you sound a horn and it takes 0.7 seconds to hear the echo, how far away is the building?
The building is 231.7 m far away.Distance can refer to a physical length or an estimate based on other factors in physics or common use.
What is distance?Distance is a numerical representation of the space between two objects or locations. |AB| is a symbol for the distance between two points A and B.
Given data;
Speed of sound = 331 meters per second
Time = 0.7 sec
The distance from the building is;
d=v×t
d=331 m/sec × 0.7 sec
d=231.7 m
Hence the building is 231.7 m far away.
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Drag each number to a box on the right to match each expression on the left with its product.
0.832 added to
Expression Product
83.2 × 0.1
832
8.32 × 102
8.32
83.2 × 102
8,320
832 × 0.001
0.832
The match has done below:
What is expression?An expression is a set of terms combined using the operations +, – , x or , /.
83.2*0.1= 8.32
8.32 × 102=848.64
83.2*102=8486.4
832 × 0.001=0.832
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To estimate the height of a totem pole, Jorge uses a small square of plastic. He holds the square up to his eyes and walks backward from the pole. He stops when the bottom of the pole lines up with the bottom edge of the square and the top of the pole lines up with the top edge of the square. Jorge's eye level is about 2 m from the ground. He is about 3 m from the pole. Which of the following is the best estimate of the height of the totem pole?
Answer:
6.5 meters
Step-by-step explanation:
help awdaWdawdadawdaWDaSwdaWDawdas
Answer:maybe c or d??
Step-by-step explanation:
What’s the slope of this graph? Can y’all guys help please ! Thank y’all
Answer:
-3
Step-by-step explanation:
/= negative slope; \= positive slope
The y-intercept is 2 because this is where it crosses the y-axis
Then you find the next point that touches the graph on an exact point which is (-2,-4)
So, your points are (0,2) and (-2,-4) then you do the slope formula of y2-y1 divided by x2-x1
-4-2/-2-0 = 3 and because the line is / then it is -3
A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compare over the interval
The exponential function decays at one-half the rate of the quadratic function.
The exponential function decays at the same rate as the quadratic function.
The exponential function decays at two-thirds the rate of the quadratic function.
The exponential function decays at three-fourths the rate of the quadratic function.
The exponential function decays at three-fourths the rate of the quadratic function.
The given inequality is -2≤x≤0.
We need to determine how do the decay rates of the functions compare over the interval.
What is the quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.
We calculate the average slope of each graph in the indicated interval, the slope can be calculated as [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].
Now, for the exponential function:
[tex]m_{c} =\frac{4-1}{-2-0} =\frac{3}{-2}[/tex]
For the quadratic function:
[tex]m_{q} =\frac{4-0}{-2-0} =\frac{4}{-2}=-2[/tex]
Now, the ratio of both average slopes is[tex]\frac{m_{c} }{m_{q}} =\frac{\frac{3}{-2} }{-2} =\frac{3}{4}[/tex].
Therefore, the exponential function decays at three-fourths the rate of the quadratic function.
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10, 18 y 36 hallar el m.c.m por descomposición simultanea:
Considerando la definición de mínimo común múltiplo, el mínimo común múltiplo entre 10, 18 y 36 es 180.
Mínimo común múltiploUn número es múltiplo de otro cuando lo contiene n veces de forma exacta. Es decir, los múltiplos de un número son aquellos que obtienes cuando multiplicas un número por otros.
El mínimo común múltiplo (mcm) es la cifra más pequeña que satisface la condición de ser múltiplo de todos los elementos de un conjunto de números. En otras palabras, el mínimo común múltiplo (mcm) es el número positivo más pequeño que es múltiplo de dos o más números.
Una forma de calcular el mcm es descomponiendo los números en sus divisores (número que está contenido en otro de forma exacta una cantidad n de veces) y que estos sean números primos (que solo pueden dividirse entre ellos mismos y el 1 para obtener un número entero). Es decir, se debe descomponer en factores primos cada número.
Luego, se debe seleccionar los factores primos comunes y no comunes con mayor exponente para finalmente multiplicar los factores primos seleccionados.
M.C.M en este casoEn primer lugar, se descomponen los números:
10= 2×518=2×3×3= 2×3²36=2×2×3×3= 2²×3²Los factores primos comunes y no comunes con mayor exponente:
2²3²5Entonces, el mínimo común múltiplo entre 10, 18 y 36 es calculada como:
M.C.M(10,18,36)= 2²×3²×5= 2×2×3×3×5= 180
Finalmente, el mínimo común múltiplo entre 10, 18 y 36 es 180.
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Find the domain and range of the relation graphed below. Write your answers in interval notation.
Answer:
Domain: [tex][-1, 3][/tex]Range: [tex][0, 4][/tex]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
the amount of money sue needs to pay (m) equals $30 to go to an apple orchard and pick apples plus $5 for every bushel of apples (b) she takes home
the elegante is aborto 3
Val's whole-house central air conditioner uses 3,000 watts when running. Val runs the AC 8 hours per summer day. Electricity costs (18 cents)/(1 kilowatt-hour). How much does Val's AC cost to run for a summer month of 30 days?
Step-by-step explanation:
3x8=24
24x30=720
720÷18=40 cents
Question 4 of 5
Select the correct answer.
Which statement is true about the graph of the given function?
O
f(x) = (x - 2)³
The graph touches the x-axis at x = -2 but does not cross it.
The graph crosses the x-axis at x = 2.
The graph touches the x-axis at x = 2 but does not cross it.
The graph crosses the x-axis at x = -2.
Submit
Answer: The graph crosses the x-axis at x = 2.
Step-by-step explanation:
The root has a multiplicity of 3, meaning that it crosses the x axis at x=2.
