Answer:
B. The value of C is 1
Step-by-step explanation:
Given:
[tex]\displaystyle \large{y=2x+C}\\\displaystyle \large{y^2=8x}[/tex]
y = 2x + C is a tangent to parabola y² = 8xTo find:
value of CA line being a tangent to curve means both equations are equal but there has to be only one interception between both graphs.
Therefore, substitute y = 2x+C in y² = 8x:
[tex]\displaystyle \large{(2x+C)^2 =8x}[/tex]
Expand the expression (2x+C)² using perfect square:
[tex]\displaystyle \large{4x^2+4xC+C^2=8x}[/tex]
Simplify the equation:
[tex]\displaystyle \large{4x^2+4xC-8x+C^2=0}\\\displaystyle \large{4x^2+(4C-8)x+C^2=0}[/tex]
The discriminant says:
If b²-4ac > 0 then there are two real rootsIf b²-4ac = 0 then there is only one real rootIf b²-4ac < 0 then the are no real rootsFor this, we choose b²-4ac = 0 since tangents only have one intersection.
[tex]\displaystyle \large{b^2-4ac = (4C-8)^2-4(4)C^2 = 0}\\\displaystyle \large{16C^2-64C+64-16C^2=0}\\\displaystyle \large{-64C+64=0}[/tex]
Solve the equation for C:
[tex]\displaystyle \large{-64C=-64}\\\displaystyle \large{C=1}[/tex]
Therefore, the value of C is 1
If f(x) = 1 / (3x – 5), what is the inverse of f?
Answer:f^-1(x) = 1/3x + 5/3
Step-by-step explanation:
True or False:
Gross income is the amount of money you make after deductions for taxes and other expenses have been taken out
Thank you so much!!!!!!
Answer:
False
Step-by-step explanation:
False.
Gross income is the total amount a person earns before any deductions are taken out.
Gross income is the amount of money you make after deductions for taxes and other expenses have been taken out. This statement is false.
What is gross income?Gross income is the income that is earned before any deductions are removed. For example, if a person sells a product for $20. The gross income is $20. Net income is the income after deductions have been taken out.
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1 2 3 4 5 6 7 8 9 10
Which expression is equivalent to (x Superscript one-half Baseline y Superscript negative one-fourth Baseline z) Superscript negative 2?
StartFraction x Superscript one-half baseline Over y z squared EndFraction
StartFraction x Superscript one-half baseline Over y Superscript one-fourth Baseline z squared EndFraction
StartFraction y Superscript one-half Baseline Over x z squared EndFraction
StartFraction x z squared Over y Superscript one-half EndFraction
Using the conversion of exponent to power, the equivalent expression is given as follows:
[tex]\frac{\sqrt{x}}{\sqrt[4]{y}z^2}[/tex]
How to transform an exponent to a power?It happens according to the following rule, with the denominator as the root and the numerator as the exponent:
[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]
In this problem, we are given the following expression:
[tex]x^{\frac{1}{2}}y^{-\frac{1}{4}}z^{-2}[/tex]
Negative exponents go to the denominator, hence the equivalent expression is given by:
[tex]\frac{\sqrt{x}}{\sqrt[4]{y}z^2}[/tex]
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1. Evaluate each expression without using a calculator.
(a) [tex](-3)^{4}[/tex]
The result of the exponential expression is 81
Indices expressionsIndices are written in term of exponents
According to the expoenent law of indices
a^4 = a * a * a * a
Given the expression
(-3)^4
This means the product of -3 in four places. Mathematically
(-3)^4 = -3 * -3 * -3 * -3
(-3)^4 = 9 * 9
(-3)^4 = 81
Hence the result of the exponential expression is 81
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What is the product of x4y and 4x2
Answer:
4 x 2 (2WD) A 4x2 or 2WD is a vehicle that has a two-wheel drive (2WD) with four wheels.
Step-by-step explanation:
Find the surface area of the cube with 2/3 units squared
Answer:
8/3 or 2.66.. units
Step-by-step explanation:
TSA of cube = 6a²
side = 2/3
= 6 x (2/3)²
= 6 x 4/9
= 2 x 4/3
=8/3
Ans = 8/3 units or 2.66.. units
HAVE A NICE DAY
STAY SAFE
PLS MARK BRAINLIST IF IT IS CORRECT
Need some help please!
The lens and mirror in Figure P23.51 are separated by 1.00 m and have focal lengths of +79.2 cm and -50.6 cm, respectively. If an object is placed 1.00 m to the left of the lens, locate the final image.
The location final image from the mirror, which is made when an object is placed 1.00 m to the left of the lens, is 0.58 right to the mirror.
What is the focal length of the lens?The focal length of the lens is the length of the distance between the middle of the lens to the focal point.
It can be find out using the following formula as,
[tex]-\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}[/tex]
Here, (v)is the distance of the image, (u) is the distance of the object, and (f) is the focal length of the lens.
The lens and mirror in the Figure are separated by 1.00 m and have focal lengths of +79.2 cm and -50.6 cm, respectively. Change the units of focal length in meters,
[tex]f_l=79.2\text{ cm=0.792 m}\\f_m=-50.6\text{ cm=0.506 m}[/tex]
An object is placed 1.00 m to the left of the lens. Put the value in the lens formula as,
[tex]-\dfrac{1}{v_l}+\dfrac{1}{1}=\dfrac{1}{0.792}\\-\dfrac{1}{v_l}=\dfrac{1}{0.792}-1\\v_1=3.81[/tex]
The distance of the image made by lens is 3.81 meters. The distance of this image from the mirror is,
[tex]u_2=3.81-1\\u_2=2.81\rm \; m[/tex]
This distance is work as object distance for the mirror. The focal length of mirror is -0.506 m. Thus, the location of the final image is,
[tex]-\dfrac{1}{v_2}+\dfrac{1}{3.81}=\dfrac{1}{-0.506}\\\dfrac{1}{v_2}=-\dfrac{1}{3.81}-(-\dfrac{1}{0.506})\\v_2=-0.58[/tex]
Thus, the location final image from the mirror which is made when an object is placed 1.00 m to the left of the lens, is 0.58 right to the mirror.
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I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer: correct
Step-by-step explanation theoretically it is indeed correct by acknowledging by surface+height which both angles are evenly congruent now
in terms of the 990 Degree angle i know for a fact that it corresponds with it no more to say.
Two men and a machine were picking oranges on a farm. One man picked x amount
oranges. The second man picked 12 less than the first. The machine picked three
times the second man. How many oranges did each pick if the total amount of
oranges picked is 332?
The equation to represent the situation is like so:
[tex]x+(x-12)+3(x-12)=332[/tex]
Simplify.
[tex]x+x-12+3x-36=332[/tex]
[tex]5x-48=332[/tex]
[tex]5x-380=0[/tex]
Solve for the variable x.
[tex]5x=380[/tex]
[tex]x=76[/tex]
[tex]first\ man =x\\second\ man =x-12\\machine=3(x-12)[/tex]
[tex]first\ man=76\\second\ man=64\\machine=192[/tex]
Verify.
[tex]x+(x-12)+3(x-12)=332[/tex]
[tex]76+(76-12)+3(76-12)=332[/tex]
[tex]76+64+192=332[/tex]
[tex]332=332[/tex]
[tex]LS=RS[/tex]
The graph of f(x) = x² was transformed to create the graph of g(x) = f(x) + 1.5. Which statement about the graphs is true?
The vertex of the graph of g is 1.5 units to the left of
the vertex of the graph of f.
B
The y-intercept of the graph of g is 1.5 units above the
y-intercept of the graph of f.
The graph of g is a reflection of the graph of f across
the y-axis.
The graph of g is a reflection of the graph of f across
the x-axis.
Answer:
Step-by-step explanation:
The graph of f(x) = x² was transformed to create the graph of g(x) = f(x) + 1.5. Which statement about the graphs is true?
The vertex of the graph of g is 1.5 units to the left of
the vertex of the graph of f.
B
The y-intercept of the graph of g is 1.5 units above the
y-intercept of the graph of f.
The graph of g is a reflection of the graph of f across
the y-axis.
The graph of g is a reflection of the graph of f across
the x-axis.
Give the Least Common Denominator for
7ths, 5ths, and halves.
Answer:
7x5x2 = 70
There are no other smaller factors that include all of the given numbers
Which of the following values are solutions to the inequality -1 + 4x < -1?
I.4
II. 1
III. 0
Answer:
4
Step-by-step explanation:
pls help
The perimeter of a rectangle is 24.
Write the function that describes its area in terms of one of the sides
The perimeter of a rectangle is 24. What is the maximum possible area of such rectangle?
The perimeter of a rectangle is 24. For what length of sides does the maximum area occur for this rectangle?
The function that describes the area of the rectangle in terms of one of the sides is A = 12L - L².
How to compute the area?The perimeter of the rectangle is given as 24. Therefore, the area in terms of one of its side will be:
A = L(24 - 2L)/2
A = L(12 - L)
A = 12L - L²
The length side for the maximum area will be 6 and 6. The maximum area of the rectangle will be:
= 6 × 6
= 36
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Employees who have retired from a company are placed in different benefit categories. The bar graph shows the percentages of the retired employees in different benefit categories. Which statement about the employees is supported by the data in the bar graph? The number of employees in Category II or Category III is greater than the number of employees in Category I. More than half the employees are in Category I. The number of employees in Category II is twice the number of employees in Category III. The number of employees in Category I is three times the number of employees in Category II.
please help!
Using the given bar graph, it is found that the statement that is supported by the data in the bar graph is given by:
The number of employees in Category I is three times the number of employees in Category II.
What does the bar graph state?Research the problem on the internet, it is found that:
45% of the employees are of Category I.15% are of Category II.30% are of Category III.10% are of Category IV.Hence the correct option is given by:
The number of employees in Category I is three times the number of employees in Category II, as 45% = 3 x 15%.
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PQR is a right angled triangle. The area of the triangle is 6cm² and |QR|= 3cm.
find |PR|
Answer:
PQ = 4cm
QR = 3cm
PR = 5cm
Area = 6cm²
Step-by-step explanation:
Area of triangle = 0.5 × Base × Height
6 = 0.5 × 3 × PQ
Let PQ be = x6 = 0.5 × 3 × x
[tex] \frac{6}{0.5 \times 3} = x[/tex]
x = 4cm
PQ = 4cm
Since, it is a right angled triangle applying Pythagoras Theorem,
PR =
[tex] \sqrt{ {3}^{2} + {4}^{2} } \\ = \sqrt{9 + 6} \\ = 5cm[/tex]
PR = 5cm
Find in the triangle. Round to the nearest degree.
a. 30°
b. 27°
c.21
d.34
The angles are 87ft
And 72ft.
Answer:
option d 34⁰
Step-by-step explanation:
Your Required Answer is 34⁰
I hope It helped you
In the regular decagon shown, what is the measure of angle 1?
Answer:
try 36 but im not quite sure
Step-by-step explanation:
im sry if im wrong have a good rest of your day :)
Need help with question 15 I did the work for it but the answer was wrong somehow it didn't work out question is on the photo
Answer:
336, (B)
Step-by-step explanation:
To find the surface area, find the area of each square and triangle
10x12 + 2(6x8)/2 + 12x6 + 8x12
This would then be,
120 + 48 + 72 + 96
Surface area = 336, (B)
You made a mistake on step 2.
When finding the area of triangle, you have to divide by 2.
Hope this helps!
A circular flower bed is 19 m in diameter and has a circular sidewalk around it that is 4 m wide. Find
the area of the sidewalk in square meters. Use 3.14 for .
Answer:
289 m²
Step-by-step explanation:
First find the area of the flower bed
A=πr²= (3.14)(9.5)² = 283.385
Then get the area of everything including the sidewalk
A=πr²= (3.14)(13.5)² = 572.265
Then subtract and you'll get the area of just the sidewalk
572.265 - 283.385 = 288.88m²
The answer to this question is 289
How would I solve I need to know Asap and what is the answer
Answer:
True; True; False; True
Step-by-step explanation:
Help quick please!
A coin is tossed 30 times, and it comes up heads 18 times.
What is the experimental probability of tossing tails?
Answer:
0.4 or 2/5
Step-by-step explanation:
If head is 18/30, then that means that tails must be 12/30, since they must add up to one whole.
Reduce it to simplest terms: 2/5 or 0.4
Mrs. Smith bought 3 pies for her family dinner. There were 10 people eating dinner. How much pie did each person get?
Answer:
Each person received 3/10 of pie
Step-by-step explanation:
3 dived by 10 equals 0.3 which is equivalent to 3/10
لا
Subtract 43 from 21 raised to the 7th power, then multiply by 2.
what is the polynomial of (-3,0)(2,0)(2,0)(3,0)
Answer:(-2,0) and (3,0)
Step-by-step explanation:im not sure if its correct but it should be
tan^(2)x-tanx=0
Pls Help
Answer:
[tex]x=\frac{3\pi }{4} ,\frac{7\pi }{4}[/tex]
If wrong then [tex]x=-\frac{\pi }{4}.[/tex]
Step-by-step explanation:
[tex]tan^2(x)-tan(x)=0[/tex]
Factor out the tan(x).
[tex]tan(x)*(tan(x)-1)=0[/tex]
Solve for x.
[tex]tan(x)\neq 0\\[/tex] thus only option is tan(x)-1=0
[tex]tan(x)-1=0\\tan(x)=1\\[/tex]
x=tan^-1(1)⇒
Either it is Quadrant 2 or 4.
[tex]x=\frac{3\pi }{4} ,\frac{7\pi }{4}[/tex]
If the teacher says its wrong. Then that could only mean that its range of tan(x) is between [tex]-\frac{\pi }{2} < x < \frac{\pi }{2}[/tex] thus it's only on quadrant 4. [tex]x=-\frac{\pi }{4}[/tex]
Rate Time = Distance
How many hours will it take to complete a 63-km bike ride if you go 20 km per
а
hour the whole time?
Answer here
SUBMIT
Please help with this questions
Answer:
16 x ^ -1/5
Step-by-step explanation:
Find the arc length of the semicircle.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.
Answer:
arc = 9π units
Step-by-step explanation:
the arc is half the circumference of the circle, then
arc = [tex]\frac{1}{2}[/tex] × 2πr = πr , then
arc = π × 9 = 9π
Answer:
[tex]\boxed{\tt 9\pi }[/tex]
Step-by-step explanation:
What we want to find here is the arc length of 1/2 of a circle, we'll start by finding the of the circle.
Step 1:- find the circumference of the circle →
[tex]\boxed{\sf Circumference\; of\; the \:circle=2\pi r}[/tex]
[tex]\tt 2\pi \times 9[/tex]
[tex]\tt 9\times 2\pi[/tex]
[tex]=\tt 18\pi[/tex]
Step 2:- find the arc length of 1/2 of the circle →
The arc length is 1/2 of the circumference of the circle:-
[tex]\boxed{\sf Circumference \; of \;\cfrac{1}{2}\; of\; the \; circle=\cfrac{1}{2}\times 18\pi}[/tex]
[tex]\tt \cfrac{18}{2} \pi[/tex]
[tex]\boxed{\tt 9\pi}[/tex]
Therefore, the arc length of the semicircle is 9π.
Liz leaning a total of 10 appetizers recipes over the course of 2 week of culinary school .
The number of appetizers that Liz would have learnt after 4 weeks given the unit rate is 20.
How many appetizers would Liz have learnt in 4 weeks?The first step is to determine the unit rate of appetizers that Liz learns.
Unit rate = total number of appetizers / total number of weeks
10 /2 = 5 appetizers
Number of appetizers Liz would learn in 4 weeks = 4 x 5 = 20
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