Find an equation of the line that satisfies the given conditions. through (−1, −3); perpendicular to the line 2x + 7y + 2 = 0
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Using a straightedge draw a random triangle now carefully cut it out next amputate the angles by snipping through adjacents sides now move the angles together so the vertices all touch
It should be noted that a triangle is a polygon with three edges and three vertices.
What is a triangle?A triangle is a simple closed curve or a polygon that is formed by three line segments.
It should be noted that triangles have 180°. In this case, looking at the attached figure, it can be deduced that the addition of the angles equals 180.
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Heather is training for a long-distance run. Her data points listed below represent the days of practice, x, and the number of miles run, y.
(1, 2.5), (2, 4.2), (4, 5.6), (6, 7), (8, 8.1), (10, 11)
Use the equation to interpolate the value and estimate the distance that she could have run on day 3. Round to the nearest tenth of a mile.
Answer:
4.6
Step-by-step explanation:
F(x) = x4/5(x − 6)2 find the critical numbers of the function
Final answer:
To find the critical numbers, differentiate the function using the product rule, set the derivative equal to zero, and solve for x. Critical numbers are where the derivative is zero or undefined, provided they are within the domain of the function.
Explanation:
To find the critical numbers of the function f(x) = x4/5(x − 6)2, you need to locate the values of x where the first derivative of the function is either zero or undefined. The first derivative can be calculated using the product rule and the power rule.
First, let's find the derivative:
f'(x) = d/dx [x4/5] * (x - 6)2 + x4/5 * d/dx [(x - 6)2]
After simplifying, you will get a derivative function where you can then set it equal to zero to find the critical points. The points where the derivative is zero are potential local maxima, minima, or points of inflection. Additionally, points where the derivative is undefined can also be critical points, if they are within the domain of the function.
Once you calculate and simplify the derivative, set it equal to zero and solve for x. You might find that you get explicit values of x, which are the critical numbers of the function. If the function's derivative does not exist at some point, that will also be a critical number.
Remember, critical numbers are only relevant if they are within the domain of the original function.
Between the ages of 24 months and 6 years, the average child will gain _____ in height. 1 foot 1.5 feet 8 inches 4 inches
Part A: Jake rented a kayak at $26 for 3 hours. If he rents the same kayak for 5 hours, he has to pay a total rent of $42. Write an equation in the standard form to represent the total rent (y) that Jake has to pay for renting the kayak for x hours. (4 points)
Part B: Write the equation obtained in Part A using function notation. (2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
Answer:
8x+2
fx= 8x+2
Step-by-step explanation:
Can you also explain how you solve it so i can do by myself:)
What is the sum of the first eight terms of the series?
(−500)+(−100)+(−20)+(−4)+(−0.8)+...
Round the answer to two decimal places if necessary.
−996.09
−625
−624.99
−623
The correct answer is option c) 624.99
To find the sum of the first eight terms of the series: (-500) + (-100) + (-20) + (-4) + (-0.8) +..., we first need to recognize that this is a geometric series where each term is a constant multiple of the previous term.
The first term (a) is -500, and the common ratio (r) can be found as follows: [tex]r = \frac{-100}{\ 500} = \frac{1}{5} \ or\ 0.2.[/tex]
Geometric Series Sum Formula
The sum ([tex]S_n[/tex]) of the first n terms of a geometric series is given by the formula:
[tex]S_n = a * \frac{1-r^n}{1-r}[/tex]
Here, a = -500, r = 0.2, and n = 8.
Calculate [tex]r^n: (0.2)^8 = 0.000256[/tex]Calculate [tex]1 - r^n[/tex]: 1 - 0.000256 = 0.999744Calculate the denominator 1 - r: 1 - 0.2 = 0.8Apply the values in the formula: [tex]S_8 = -500 * \frac{0.999744}{0.8}[/tex][tex]S_8 = -500 * 1.24968[/tex][tex]S_8 = -624.99[/tex]The sum of the first eight terms of the series, rounded to two decimal places, is -624.99.
The complete question is:
What is the sum of the first eight terms of the series?
(−500)+(−100)+(−20)+(−4)+(−0.8)+...
Round the answer to two decimal places if necessary.
a) −996.09
b) −625
c) −624.99
d) −623
LM¯¯¯¯¯¯¯ is the midsegment of trapezoid ABCD . AB=78 and DC=142 . What is LM ?
Given the pre-image ABCD and the image after a dilation, A'B'C'D', what is true about the polygons? Check all that apply.
At the beginning of this month, the balance of Nelson's checking account was $856.23. So far this month, he has received a paycheck via direct deposit of $876.25, been charged a monthly service fee from his bank of $10.00, used a debit card linked to his account to make a purchase of $23.96, written a check for $104.22 that has already been deposited, and deposited a check written to him for $25.00. What is the current balance of Nelson's checking account?
simplify the expression (2-5i)-(4-4i)
what is the approxmate area of the figure
plz look at picture and answer right will give brainlist and 20 extra points
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What is the m∠ABC?
1)m∠ABC = 60°
2)m∠ABC = 67°
3)m∠ABC = 120°
4)m∠ABC = 127°
we are given
m∠BCD =67
and m∠BDC=60
we know that
m∠ABC is exterior angle
m∠BCD and m∠BDC are interior angles
exterior angle is sum of interior angles
so, we can write it as
m∠ABC=m∠BCD+m∠BDC
now, we can plug values
and we get
m∠ABC=60+67
m∠ABC=127
so, option-4.........Answer
Which are the solutions to the quadratic equation 4x^2=64?
A. x=-16 and x=16
B. x=-8 and x=8
C. x=-4 and x=4
D.x=-2 and x=2
Answer: x= -4, 4
Step-by-step explanation:
If y varies directly as x, and y is 18 when x is 5, which expression can be used to find the value of y when x is 11? mc018-1.jpg mc018-2.jpg mc018-3.jpg mc018-4.jpg
If y varies directly as x, the expression that can used to determine the value of y when x is 11 is y = 18/5 × 11 .
What is the expression that can be used to determine the value of y?The equation that can be used to represent direct variation is:
y= kx
Where:
y = dependent variable k= constant of proportionality x = independent variablek = y/x
k = 18/5
y = 18/5 × 11
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Triangle RST is congruent to triangle WXY. If the area of triangle WXY is 20 square inches, then the area of triangle RST is _____.
40 in2
10 in2
20 in2
80 in2
The area of triangle RST is also 20 20 square inches
What are congruent triangles?Triangles having equal side lengths and equal corresponding angles measures are called congruent triangles.
Given that, triangle RST is congruent to triangle WXY, the area of triangle WXY is 20 square inches,
We are asked to find the area of triangle RST,
Since, triangles RST and WXY are congruent, therefore, they will have congruent sides and angles,
That means, they will have equal area also,
ar (Δ RST) = ar (Δ WXY)
Therefore,
ar (Δ RST) = 20 square inches
Hence, the area of triangle RST is also 20 20 square inches
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Adjacent angles whose exterior sides are opposite rays are
Answer:
Adjacent angles whose exterior sides are opposite rays are "supplementary"
Step-by-step explanation: Theorem 3-2 states this fact
A toy rocket is launched from a platform 29 feet above the ground at a speed of 79 feet per second. The height of the rocket in feet is given by the polynomial −16t^2 + 79t + 29, where t is the time in seconds. How high will the rocket be after 3 seconds?
Answer:
[tex]h(3)=122ft[/tex]
Step-by-step explanation:
The problem gives you everything, basically you only have to replace the given value, which is t=3 into the equation:
[tex]h(t)=-16t^2+79t+29[/tex]
But, let's do a deeper analysis. This a projectile motion problem. For this kind of problems there are some fundamental equation. For example, we need to find the vertical displacement of the rocket. So the equation for the vertical displacement in projectile motion is given by:
[tex]h_f-h_o=v_ot-\frac{1}{2}gt^2[/tex] (1)
Where:
[tex]h_f=Final\hspace{3}height\\h_o=Initial\hspace{3}height\\t=Time\\v_o=Initial\hspace{3}velocity\\g=Gravitational\hspace{3}acceleration[/tex]
Isolating [tex]h_f[/tex] and rearranging the equation (1) we get:
[tex]h_f=-\frac{1}{2}gt^2+v_ot+h_o[/tex]
Looks familiar? It has exactly the same form of the equation given by the problem. As you can see, if you replace the values of the speed and the initial position given by the problem, we got the same equation. Besides gravitational acceleration is a constant and its value is approximately 32ft/s^2, dividing it by 2, we get 16. Having this in mind, let's resolve the problem:
[tex]h(3)=-16(3)^2+79(3)+29=-144+237+29=266-144=122ft[/tex]
Quadrilateral ABCD undergoes a series of transformations to become A’’B’’C’’D’’. If the first transformation is a reflection over the y-axis, what is the coordinate of C’? What transformation occurs after the reflection over the y-axis that results in the final image?
Quadrilateral ABCD undergoes a series of transformations to become A’’B’’C’’D’’.
The first transformation is a reflection over the y-axis.
The coordinate of C’ would be (-6,3) in this case.
If the image is rotated counter clock wise around the point A then it will result in the final image which is presented in the attached figure.
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Consider the table below.
x y
-3 0.5
-2 1
-1 2.5
0 5
1 8.5
y=ax2+bx
Complete the standard form equation representing the quadratic relationship displayed above, where a, b, and c are constants.
Answer:
y=x^2-6x+13
Step-by-step explanation:
Which expressions are completely factored?
Select each correct answer.
A. 16a^5−20a^3=4^3(4a^2−5)
B. 24a^4+18=6(4a^4+3)
C. 30a^6−24a^2=3a^2(10a^4−8)
D. 12a^3+8a=4(3a^3+2a)
Answer:
B
Step-by-step explanation:
The only thing that you can factor out of B is 6, while the others are not in simplest form. Answer C can still factor out 2 and answer choice D can still factor out a. Answer choice can still be factored further using difference of squares.
HELP SOMEONE SMART
What is the solution of the equation? Step by step.
Each of the 14 students in the art club needs 4 ounces of paint for a project. The art store sells paint only in 8-ounce bottles. How many bottles of paint does the art club president need to buy for the project?
Answer: The art club president need to buy 14 bottles of paint for the project.
Step-by-step explanation: Given that each of the 14 students in the art club needs 4 ounces of paint for a project. The art store sells paint only in 8-ounce bottles.
We are to find the number of bottles of paint that the art club president need to buy for the project.
We will be using the unitary method to solve the given problem.
Number of bottles filled by 8 ounces of paint = 1.
So, the number of bottles filled by 1 ounce of paint is
[tex]\dfrac{1}{8}.[/tex]
So, the number of bottles filled by 4 ounces of paint will be
[tex]\dfrac{1}{8}\times4=\dfrac{1}{2}.[/tex]
Now, number of bottles of paint needed by 1 student [tex]=\dfrac{1}{2}.[/tex]
Therefore, the number of bottles of paint needed by 14 students will be
[tex]\dfrac{1}{2}\times14=7.[/tex]
Thus, the art club president need to buy 14 bottles of paint for the project.
y=x-8/x^2+4x-5 find any points of discontinuity for the rational function
a. x=5, x=1
b. x=-5, x=1
c. x=8
d. x=5, x=-1
Answer:
x=-5, x=1
Step-by-step explanation:
y=x-8/x^2+4x-5
[tex]y=\frac{x-8}{x^2+4x-5}[/tex]
When denominator becomes 0 in a rational function then there will be a break in the graph
To find any points of discontinuity for the rational function , we set the denominator =0 and solve for x
x^2 + 4x -5 =0
Now we factor x^2 +4x -5
product is -5 and sum = 4
5 * (-1) = -5
5 +(-1) = 4
(x+5)(x-1) =0
set each factor =0 and solve for x
x+5=0 , so x= -5
x-1=0 , so x= 1
x=-5, x=1 are the points of discontinuity for the rational function
Answer:
x=-5 , X=1
Step-by-step explanation:
what number produces an irrational number when multiplied by 1/5
Final answer:
To produce an irrational number by multiplying by 1/5, the other number must be irrational, such as √2.
Explanation:
The student is asking which number, when multiplied by 1/5, produces an irrational number. To produce an irrational number by multiplication, the other number must itself be irrational. Because rational numbers multiplied by rational numbers yield rational results. A classic example of an irrational number is √2, which, when multiplied by 1/5, gives 1/5√2 or √2/5, both of which are irrational.
Please help I have 2 questions. Thank you.
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A telephone pole is perpendicular to the ground. What is the size of the angle between the ground and the telephone pole? How do you know?