The set of the value for which the curve and line have no common point are is k ∈ (0 , 4).
The value for which the line is a tangent is k = 4.
The coordinates of the point where the line touches the curves is point of tangency = ( 1/2 , 2).
What is tangent?
Tangents in geometry are lines or planes that contact curves or surfaces at points where they are closer to the curve than any other lines or planes drawn through those points.
Given equations in the question:
y = kx² + 1
y = kx
Equating y
kx² + 1 = kx
kx² -kx + 1 = 0
This is Quadratic equation is of the form ax²+bx+c=0 where a , b and c are real also a≠0.
D = b²-4ac is called discriminant.
and we know that,
D >0 roots are real and distinct
D =0 roots are real and equal
D < 0 roots are imaginary ( not real ) and different
For no common solution D < 0
For tangent D = 0
so,
kx² -kx + 1 = 0
D = (-k)² - 4k = k² - 4k = k(k - 4)
k(k - 4) < 0
if 0 < k < 4
Hence values of k for which the curve and the line have no common points is k ∈ (0 , 4).
for tangent
k(k - 4) = 0
k is non zero
Hence k = 4
After putting the value of k, given equations are:
y = 4x² + 1
y = 4x
solving these equations to get value of x and y:
4x² + 1 = 4x
4x² - 4x + 1 = 0
(2x - 1)² = 0
x = 1/2
y = 2
Point of tangency = ( 1/2 , 2)
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explain 8 - 5 * 3 from a 7th grader
Answer:
-7
Step-by-step explanation:
5 * 3 = 15. 15 - 8 = 7; so, 8 - 15 = -7.
How do you write 3 and 6/25 as a decimal
Answer: 1.44
Step-by-step explanation:
The fraction 3 and 6/25 is equal to 1.44 when written as a fraction.
Answer:
3.24
Step-by-step explanation:
6/25 can be read as 6 divided by 25, which is 0.24. Add that to 3 and you get 3.24.
Simplify the expression ∛81x^7y^9z^5 and please show your work!
By means of algebra properties for powers and roots, the radical expression [tex]\sqrt[3]{81\cdot x^7\cdot y^{9}\cdot z^{5}}[/tex] is equivalent to the expression [tex]4.327 \cdot x^{\frac{7}{3} }\cdot y^{3} \cdot z^{\frac{5}{3} }[/tex].
How to simplify an algebraic expression involving a cubic root operator and powers
In this question we need to simplify an expression by using algebra properties, that is, to transform an expression involving three variables (x, y, z), roots and power operators into an expression with only power operators, that is, where only we see power operators, no root operators of any kind. Now we proceed the entire procedure in detail:
[tex]\sqrt[3]{81\cdot x^7\cdot y^{9}\cdot z^{5}}[/tex] Given[tex](81\cdot x^{7}\cdot y^{9}\cdot z^{5})^{\frac{1}{3} }[/tex] Relationship between power and roots operators[tex]81^{\frac{1}{3}}\cdot (x^{7})^{\frac{1}{3} }\cdot (y^{9})^{\frac{1}{3} } \cdot (z^{5})^{\frac{1}{3} }[/tex] Power of a product[tex]4.327 \cdot x^{\frac{7}{3} }\cdot y^{3} \cdot z^{\frac{5}{3} }[/tex] Definition of cubic root / Power of a power / Definitions of multiplication and division / Existence of multiplicative inverse / Commutative and associative properties /ResultIn accordance to the algebra properties related to power and radical expressions, the radical expression [tex]\sqrt[3]{81\cdot x^7\cdot y^{9}\cdot z^{5}}[/tex] is equivalent to the power product [tex]4.327 \cdot x^{\frac{7}{3} }\cdot y^{3} \cdot z^{\frac{5}{3} }[/tex].
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a certain type of aluminum screen 2 feet in width has, on the average, three flaws in a 100-foot roll. we assume flaws occur randomly so the number of flaws follow some poisson distribution. what is the probability that the first 40 feet in a roll contain no flaws?
The probability of that the first 40 feet in a roll contain no flaws is ≈ .3012
What is probability ?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
CalculationΘ = μ = [tex]\frac{100 foot}{3 flaws}[/tex]
a ) We assume that the length until the first flaw follows an exponential distribution.
Probability density function of exponential distribution:
f(x) = [tex]\frac{1}{Θ} e^{\frac{-x}{Θ} } = \frac{1}{100/3}e^{-x/(100/3)} = \frac{3}{100}e^{-3x/100}[/tex]
The first 40 feet in a roll of 100 feet contain no flaws if the first flaw occurs after 40 feet.
The probability is the integral over the corresponding interval:
the further calculation has been shown in fig. attached
since equation was not possible to write here
b) We assume that the length until the first flaw follows an exponential distribution.
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Please answer with show work. Trigonometry!
-9^2 x 3
evaluate the experssion!!
Answer:
243
Step-by-step explanation:
-9^2 = -9 * -9 = 81
81 * 3 = 243
(7,10) and (8, 13) what’s the answer to it
Answer:54
Step-by-step explanation:
54mis the answer
Task 2 given the table and graph, evaluate the following functions:
Answer:
1) -12, 2) 22, 3) 9, 4) 31, 5) 4, 6) 3, 7) 5Step-by-step explanation:
Use table for f(x) related questions and equation for g(x) related questions and both for the last one.
Q1 g(0) = 3*0 - 12 = 0 - 12 = - 12Q2f(0) = 22, the value of f(x) against the x = 0Q3g(7) = 3*7 - 12 = 21 - 12 = 9Q4f(-3) = 31, the value of f(x) against the x = -3Q5g(x) = 0 ⇒ 3x - 12 = 0 ⇒ 3x = 12 ⇒ x = 4Q6f(x) = - 3, x = 3, the value of x against the f(x) = - 3Q7f(g(6)) = f(3*6 - 12) = f(18 - 12) = f(6) = 5, the value of f(x) against x = 6Write at least three sentences to tell how you can convince others to stop littering. Use at least three different kinds of sentences in your writing.
Which is an equivalent expression for (3 to the power of 2 • 5 to the power of 4) to the power of 3?
The value that will be equivalent to the expression will be 5625³.
What is an expression?It should be noted that an expression is simply used in Mathematics to illustrate or show the relationship between the variables.
The equivalent expression for (3 to the power of 2 • 5 to the power of 4) to the power of 3 will be illustrated as:
= (3² × 5⁴)³
= (9 × 625)³
= 5625³
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Please help ASAP, will mark brainliest!
Which of the following proves these triangles are congruent?
Explanation:
ASA = angle side angle
It refers to knowing two pairs of congruent angles, and a pair of congruent sides between the angles.
The angle markers tell us which angles are congruent. The shared overlapped sides are congruent (since any segment is congruent to itself; aka reflexive property).
ASA is slightly different from AAS in that the congruent sides for AAS are not between the congruent angles.
Given the frequency table, what percentage of the students that like rap are also in grades 9–10? Round to the nearest whole percent. Show work
A. 16%
B. 38%
C. 40%
The percentage of the students that like rap are also in grades 9–10 is 32%.
Determining the percentage of rap in grades 9-10Given data:
Grade 9-10 for Rap = 40
Row total for grade 9-10 = 125
Now let determine the percentage of rap in grades 9-10 using this formula
Percentage of rap in grades 9-10 = Grade 9-10 for Rap / Row total for grade 9-10
Let plug in the formula
Percentage of rap in grades 9-10 = 40 /125
Percentage of rap in grades 9-10 = 0.32 × 100
Percentage of rap in grades 9-10 = 32%
Therefore we can conclude that 32% is the percentage of rap grade 9-10.
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would you put a closed dot or an open dot on a number line for n > -8?
Answer:
a opened because a closed means that number ond more
Step-by-step explanation:
2-3x + 4 + x = -2x + 1
Answer:
No solution
Step-by-step explanation:
2- 3x + 4 + x = -2x + 1
2 -3x + 4 + x = -2x + 1
6 -3x + x = -2x + 1
6 -3x + x = -2x + 1
6 -2x = -2x + 1
6 -2x = -2x + 1
move -2x to the right by adding 2x on both sides
6 -2x = -2x + 1
+2x +2x
6 = + 1
is 6 equal to 1?
No, so No solution
Can someone help me with this
Step-by-step explanation:
slope intercept form is: y = ax + b
so, 19x - 19y = 18
-19y = -19x +18
[tex]y = \frac{ - 19x}{ - 19} - \frac{18}{19} [/tex]
[tex]y = x - \frac{18}{19} [/tex]
i hope that this helps
solve for s 1.1=s+2.3/3
Answer:
s=1Step-by-step explanation:
Find the value of s on one side of the equation to isolate it.
1.1=s+2.3/3
First, switch sides.
[tex]\sf{\dfrac{s+2.3}{3}=1.1}[/tex]
Multiply by 3 from both sides.
[tex]\sf{\dfrac{3\left(s+2.3\right)}{3}=1.1* \:3}[/tex]
Solve.
1.1*3=3.3
s+2.3=3.3
Then, subtract by 2.3 from both sides.
s+2.3-2.3=3.3-2.3
Solve.
Subtract.
3.3-2.3=1.0=1
s=1
Therefore, the final answer is s=1.
I hope this helps, let me know if you have any questions.
q(x) = 1⁄2x−3; q(x) = −4
We can solve with functions exactly as we do algebraic equations. Our goal is to isolate the variable.
Solving the QuestionWe're given:
[tex]q(x) = \dfrac{1}{2}x-3\\\\q(x) = -4[/tex]
Solve using substitution:
[tex]\dfrac{1}{2}x-3=-4[/tex]
Isolate x:
[tex]\dfrac{1}{2}x=-4+3\\\\\dfrac{1}{2}x=-1\\\\x=-2[/tex]
Answerx = -2
I NEED HELP FAST
image is the question :)
I dont quite understand what this question is asking for.
By using the table of values, we have the following:
The value of f(-7) is equal to 4.The value of f(15) is equal to 0.The value of f(3) is equal to 2.The value of f(-4) is equal to 15.If f(x) = 5, the value of x is equal to 4.If f(x) = 2, the value of x is equal to 5.If f(x) = 0, the value of x is equal to 15.If f(x) = -6, the value of x is equal to 2.What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable (x-value) to an output variable (y-value or f(x)).
In this exercise, you're required to determine the value of each function based on the value of x shown in the table above. Therefore, you would identify the input variable (x-value) that corresponds to the value of the output variable (y-value or f(x)) in the given table and vice-versa.
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vantes si l'exponentiation a priorité sur la
d) 2³ x 2² =
Sheila bought three books for $12.63, $9.05,
and $14.97. How much did she spend?
I need help!
Use the given information to select the factors of f(x). f(4)=0 f(-1)=0 f(3/2)=0. Make sure to select all correct answers for full credit.
Answer:4,3,8
Step-by-step explanation:
If the temperature drops 5 degrees per hour , what is the change in temperature after 4 hours
Answer: -20 degrees
Step-by-step explanation:
The temperature drops 5 degrees/hour.
Find temperature after 4 hours.
Since we are not given a starting temperature, we can only say how much the temperature has dropped after the 4 hours.
5 degrees/hour x 4 hours = 20 degrees
Temperature has dropped so your answer will be negative.
Your aunt bought a new television. The television screen is a
rectangle.
The length of the television screen is 54 inches and the width is
30.4 inches.
What is the area of the television screen? What is the perimeter
of the television screen?
Use the given information to complete the worksheet.
Problem apr20 Client Version 7.7.14 Server Version 73.14
O
Length of the Television Screen
Width of the Television Screen
Perimeter of the Television Screen
Area of the Television Screen
DELL
Diagram Label
SC
CR
Area Formulas:
• Parallelogram: A = bh
• Square: A = s²
.
Value
54
30.4
168.8
Triangle: A = bh
•Trapezoid: A=h(b₁+ b₂)
Units
inches
inches
inches
square inches
©2021 Carneg
Oct 13
Answer:
area: 1641.6 square inchesperimeter: 168.8 inchesStep-by-step explanation:
You want the area and perimeter of a rectangle that is 54 inches in length and 30.4 inches in width.
AreaThe area formula is ...
A = bh
We can use the length as the "base" and the width as the "height", so we have ...
A = (54 in)(30.4 in) = 1641.6 in²
The area of the television screen is 1641.6 square inches.
PerimeterThe perimeter of a rectangle is given by the formula ...
P = 2(L +W)
Using the given length and width, the perimeter is found to be ...
P = 2(54 in + 30.4 in) = 2(84.4 in) = 168.8 in
The perimeter of the television screen is 168.8 inches.
The area of the rectangular television screen is 1641.6 square inches and the perimeter of the television screen is 84.4 inches.
What is the area of a rectangle?
The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the product of its length and breadth. Its area is the space that the rectangle's boundary encloses.
Mathematically, area of a rectangle = length * width = l * w
What is the perimeter of a rectangle?
The perimeter is defined as the sum of all sides of the rectangle. Mathematically, perimeter of a rectangle = 2(length + width) = 2*(l + w)
Given, the length of the television screen = l = 54 inches
The width of the television screen = w = 30.4 inches
Using the formula mentioned in the literature above,
Area of the television screen = l * w = 54*30.4 = 1641.6 square inches
Also, perimeter of the television screen = l + w = 54 + 30.4 = 84.4 inches
Thus, the area of the rectangular television screen is 1641.6 square inches and the perimeter of the television screen is 84.4 inches.
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Write the perimeter of the triangle as a simplified polynomial. Then factor the polynomial.
Answer:
4x² + 29x + 7 = (4x + 1)(x + 7)
Step-by-step explanation:
Simplify the polynomial:Like terms are terms with same variable and same power.
Perimeter = sum of all the sides
= 3x² + 1 + 15x + 6 + x² + 14x
= 3x² + x² + 15x + 14x + 1 + 6
Combine like terms,
= 4x² + 29x + 7
Factorize:
Sum = 29
Product = 4*7 = 28
Factors = 1 , 28 {28 + 1 = 29 & 28*1 = 28}
Rewrite the middle term using the factors,
= 4x² + x + 28x + 7
= x(4x + 1) + 7(4x + 1)
= (4x + 1)(x + 7)
If the perimeter of the square is 48 m. Find the area of a
circle whose circumference is the same as the square.
The area of the circle is 201 m².
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.So, the area of the circle:
The perimeter of square: 4aCircumference of the circle: 2πrWe know that 4a = 2πr, now calculate r as follows:
4a = 2πr48 = 2πrr = 48/2πr = 48/2(3.14)r = 48/6.28r = 7.64Rounding off: 8m
Area of circle:
πr²3.14(8)²3.14(64)200.96Rounding off: 201 m²
Therefore, the area of the circle is 201 m².
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Please help ASAP, will mark brainliest!
Type SSS, SAS, ASA, AAS, or HL to justify why triangle ABC is congruent to triangle FBD.
Answer:
SSS
Step-by-step explanation:
need help again with a question
Answer: x = 58
Step-by-step explanation:
The angles are alternating interior angles. This means that the angles are equal.
So x = 58
Marine biologist studies the population of seals in research area. how many Seals are in the research area?
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
For a project in his Geometry class, Yusuf uses a mirror on the ground to measure the
height of his school building. He walks a distance of 10.25 meters from the building,
then places a mirror flat on the ground, marked with an X at the center. He then
walks 1.65 more meters past the mirror, so that when he turns around and looks
down at the mirror, he can see the top of the school clearly marked in the X. His
partner measures the distance from his eyes to the ground to be 1.55 meters. How tall
is the school? Round your answer to the nearest hundredth of a meter.
Step-by-step explanation:
sadly we don't know anything about the size of the mirror on the ground, or if e.g. the 1.65 m from the mirror mean from the edge of the mirror or from the x at the center of the mirror.
so, we must assume the mirror as a dot without any significant lengths in the calculation.
we have 2 right-angled triangles.
1. the small one : from Yusuf's eyes to the ground at his feet to the x on the mirror on the ground.
2. the large one : from the top of the building to the bottom of the building on the ground to the x on the mirror on the ground.
the mirroring creates a dilation from the large triangle to the small triangle through the point x on the mirror.
in other words, all the angles stay the same, and there is one constant scale factor for all the lengths of one triangle to the other, making both triangles similar.
that means that the scale factor "f" of the ground distances from the small to the large triangle is
10.25 / 1.65 = 1025 / 165 = 6 35/165 = 6 7/33 =
= 6.212121212...
the scaling from Yusuf's height (well, his eye level) to the height of the school must follow the same ratio :
school height / Yusuf's eye level =
= h/1.55 = 10.25/1.65
h = 10.25 × 1.55 / 1.65 = 1025 × 155 / 16500 =
= 9.628787879... m ≈ 9.63 m
the school is approximately 9.63 m tall.
FYI : this is the same principle as with a camera. the lens (and the mirror inside if applicable) create a dilated "projection" onto a film or an array of digital light sensors, so that the captured image retains all the angles and all the length ratios of the original.
but to know from the picture e.g. how tall the original was, we need to know also the distance from which the picture was taken. otherwise this can't be answered.