Answer:
9/8
Step-by-step explanation:
The slope of the parabola
The equation of the line tangent to the parabola at x = 4 is y = 13 · x - 27. The tangent line has a slope of 13 and a intercept of - 27.
How to determine the equation of a line tangent to a parabola
Parabolae are defined by quadratic equations, that is, equations whose form is y = a · x² + b · x + c. The slope of a line tangent to a point of the curve is defined by a linear equation, that is, an equation of the form y = m · x + b. By derivative rules, the slope of the tangent line can be found by using the following expression:
m = 2 · a · x + b
Then, if we know that y = 2 · x² - 3 · x + 5 and x = 4, then the equation of the tangent line is:
Slope
m = 4 · x - 3
m = 4 · 4 - 3
m = 13
Intercept
b = y - m · x
y = 2 · 4² - 3 · 4 + 5
y = 32 - 12 + 5
y = 25
b = 25 - 13 · 4
b = 25 - 52
b = - 27
The equation of the line tangent to the parabola at x = 4 is y = 13 · x - 27. The tangent line has a slope of 13 and a intercept of - 27.
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Find the coordinates of the point 3/10 of the way from A to B. The points given are A(-3,-5) , B(9,6)
[tex]\displaystyle\\Answer:\ (-\frac{3}{13},-2\frac{6}{13} )[/tex]
Step-by-step explanation:
[tex]\displaystyle\\\frac{3}{10} =0.3\\\\(-3,-5)\ \ \ \ \ (9,6)\\\\\boxed {x=\frac{x_1+\lambda x_2}{1+\lambda} }\ \ \ \ \ \ \ \ \ \ \ \boxed {y=\frac{y_1+\lambda y_2}{1+\lambda} }\\\\x_1=-3\ \ \ \ \ x_2=9\ \ \ \ \ y_1=-5\ \ \ \ \ \ \ y_2=6\\\\x=\frac{-3+0.3*9}{1+0.3} \\\\x=\frac{-3+2.7}{1.3} \\\\x=\frac{-0.3}{1.3}\\\\ x=-\frac{0.3*10}{1.3*10}\\\\ x=-\frac{3}{13} \\\\[/tex]
[tex]\displaystyle\\y=\frac{-5+0.3*6}{1+0.3} \\\\y=\frac{-5+1.8}{1.3} \\\\y=\frac{-3.2}{1.3} \\\\y=-\frac{3.2*10}{1.3*10} \\\\y=-\frac{32}{13} \\\\y=-2\frac{6}{13} \\[/tex]
the perimeter of a triangle is 13 cm whose two sides are 4 cm and 5cm . find the area
The area of the Triangle is 7.8 cm².
The perimeter of the triangle is given to be 13cm.
As we know,
perimeter of triangle = sum of length of all sides of the triangle.
13cm = 4cm + 5cm + third side
third side = 4cm.
Hence two side of the triangle are equal to 4cm. We can say that this is an isosceles triangle, with the base length as 5cm and the other two equal sides of length 4cm.
Let say the base length is B and the other sides length is A.
So area of the isosceles triangle can be given by,
Area = 1/2 x B x √(A²-B²/4)
Area = 1/2 x 5 x √(4²-5²/4)
Area = 1/2 x 5 x √(16 - 25/4)
Area = 1/2 x 5 x 3.12
Area = 7.8 cm².
The area of the triangle is 7.8cm².
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How long does it take to ride a bicycle 100 miles at each of the following speeds: 5 mph, 10 mph, 15 mph, 20 mph, 25 mph? What is always true about the product speed x time?
Answer:
5mph=20 hours to do 100 miles with a bicycle
10mph=10 hours to do 100 miles with a bicycle
15mph=6hours 40minutes(maybe)to do 100miles with a bicycle
20mph=5 hours to do 100miles with a bicycle
25mph=4 hours to do 100 miles with a bicycle
the faster u go the time will decrease
the slower u go the time will increase
hope that helped I didn't really understand much
(0.5r +1.2) - (3.6-4.5r) = (4.8-0.3x) + (10.5r +0.6)
Answer:
Step-by-step explanation:
What is the vertical distance (Δ`y`) for this slope triangle
What is the horizontal distance (Δ`x`) for this slope triangle?
The vertical distance (Δ`y`) for the slope triangle as indicated is; (4-2) ; 2.
The horizontal distance (Δ`x`) for the slope triangle as indicated is; (4-0) ; 4.
What is the vertical distance (Δ`y`) and horizontal distance (Δ`x`) for this slope triangle?According to the task content, it follows that the vertical and horizontal distance for the slope triangle in discuss are to be determined.
Hence, by observation, Δ`y` can be obtained on the graph from points 4 and 2; we have; 4-2 = 2.
Also, by observation, Δ`x` can be obtained on the graph from points 4 and 0; we have; 4-0 = 4.
Ultimately, the vertical and horizontal distances of the slope triangle are as indicated.
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Round this number to the nearest ten thousand.
84,759
A. 80,000
B. 84,000
C. 85,000
D. 90,000
Answer:
Step-by-step explanation:
Answer:
80,000 A
Step-by-step explanation:
it is under 85000 so it is rounding down to 80,000
How you solve this??
Answer:— 36, 20-29 years, 20-29 years, Total confirmed cases in ages 20-29 over the 14 day period ... 707, 01/03/2022, 1151692, 36278, 18031.4286.
Step-by-step explanation:
Amazon is offering a $17.95 discount on a pair of wireless headphones. You pay $71.80 for the headphones after the discount. Write and solve an equation to find the original price of the headphones.
Use "x" for your variable
Answer:
x - 17.95 = 71.80
Use the commutative property of addition
71.80 + 17.95 = 89.75
$89.75 was the original price.
Step-by-step explanation:
Hope it helps! =D
Victor thinks that negative 28 / 6 Is greater than negative 100² root cubed. Sean thinks that 17 / 4 is greater. Who is correct
The numbers arranged in a sequence will be - ∛100² < - 4.67 < - 4.25 Both Victor and Sean are correct.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Victor thinks that negative 28 / 6 Is greater than negative ∛100². Sean thinks that 17 / 4 is greater.
The value of the number negative 28 / 6 will be - 4.67.
The value of the number negative ∛100² will be - 21.54.
And the value of the number negative 17/4 will be - 4.25.
The numbers are arranged in a sequence.
- ∛100² < - 4.67 < - 4.25
Both Victor and Sean are correct.
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A chord of a circle 9cm long if it's distance of the centre of the circle is 5 cm calculate the radius of the circle
considering the distance between the center of the circle and the chord is perpendicular, pythagorean theorem can be applied to calculate the radius of the circle.
[tex]r^2=a^2+b^2[/tex] , r=radius, a=half of the chord length, b the distance between the center of the circle and the center of the chord
[tex]r^2=(4.5cm)^2+(5cm)^2\\r^2=20.25cm^2+25cm^2\\r^2=45.25cm^2\\r=\sqrt{45.25cm^2}\\r=6.7268cm[/tex]
Give the equation of the line through (9,7) with y-intercept = -5
Answer:
y = 4/3x - 5
Step-by-step explanation:
y-intercept will be (0,-5)
so m = (y2-y1)/(x2-x1)
m = (-5 -7)/(0 - 9) = (-12)/(-9) = 4/3
Using m = 4/3, y = 7, x = 9
y = mx + b
7 = 4/3(9) + b
7 = 12 + b
b = -5
so
y = 4/3x - 5
Points A and B lie on plane M. Does line AB lie in plane M? Justify your answer using a postulate.
The line AB joining the points A and B on the plane M lies in plane M.
Say there are two points A and B which lies on the plane M.
Through any two points, there is only one line. Then there is exactly one line joining the two points A and B which is the line AB
Since both the points lies on the plane M, the line joining them should also lie on the plane M.
The postulate which verifies this is:
If two points lie on a plane, then the line joining the points also lies on the same plane.
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A salesperson earns a commission of $510 for selling $3000 in merchandise find the commission rate
Step 1) : Based on the given conditions, formulate
[tex] \large\bf \longrightarrow \frac{510}{3000} [/tex]
Step 2) : Calculate
[tex] \bf \longrightarrow\frac{51 \cancel{0}}{{300 \cancel{0}} } \: = \frac{51 \div 3}{300 \div 3} = \frac{17}{100} [/tex]
Step 3) : Convert to percentage
[tex] \bf\longrightarrow{\frac{17}{100} = 0.17}[/tex]
Hence, the commission rate is 17%.The bill for dinner was $77.12. You left $15.88 for the tip. What percentage of the original bill was the tip?
Answer:
The tip was 20.6% or 20.59% of the original bill
Step-by-step explanation:
Question: The bill for dinner was $77.12. You left $15.88 for the tip. What percentage of the original bill was the tip?
Step-by-step:
To find the percentage of how much a part ($15.88) is or a whole ($77.12), the formula of part = percentage * whole is used.
It is usually written as a = p*w
In this case, $15.88 is a and $77.12 is w.
so, 15.88 = p*77.12
However, we need to find p. To do so, we need to get p by itself. Divide 77.12 on both sides so that it cancels out on the right side.
15.88 divided by 77.12 is about 0.2059
We need to make the decimal a percentage by multiplying 100
0.2059 * 100 = 20.59%
You could probably round it up to 20.6% if you wanted to
Therefore, the tip was 20.6% or 20.59% of the original bill.
Ritzie has 80 metres of fencing wire which she wants to use to fence a rectangular plot for gardening. She wished to get the right length and width such that the area enclosed is the maximum. Let x to represent length and y to represent width.
1) Write two equations one for perimetre and the other for area using X and Y
2)Obtain only one equation in terms of area from the equations in 1
Step-by-step explanation:
1)
the perimeter P
P = 2x + 2y = 80 m
the area A
A = x × y
2)
2x + 2y = 80
2y = 80 - 2x
y = 40 - x
and we use that in the equation for area
A = x × (40 - x) = 40x - x²
we find the maximum (or minimum) of a function by finding the 0s of the first derivative.
A' = 40 - 2x = 0
40 = 2x
x = 20
y = 40 - x = 40 - 20 = 20
and just to be sure :
if the second derivative at that point x is negative, we have a maximum, if it is positive, we have a minimum.
A'' = -2
so, it is negative for all x incl. x = 20.
therefore, we have a maximum.
the rectangle with perimeter of 80 m and the max. area is a square of 20 m side length.
What is the graph of this function
A statement, rule, or regulation that establishes the relationship between an independent variable and a dependent variable is known as a function.
A network can be represented mathematically as a graph, which explains the connection between lines and points. A graph consists of some points with connecting lines.
Consider the function,
[tex]f(x)=\frac{||x||+2}{2}[/tex] and 0 ≤ x ≤ 6
To graph the function we will find the points on the graph for different values of x.
When x = 0,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(x)=\frac{||0||+2}{2}=1[/tex]
When x = 1,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(1)=\frac{||1||+2}{2}\\ f(1)=\frac{3}{2}[/tex]
When x = 2,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(2)=\frac{||2||+2}{2}[/tex]
[tex]f(2)=2[/tex]
When x = 3,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(3)=\frac{||3||+2}{2}[/tex]
[tex]f(3)=\frac{5}{2}[/tex]
When x = 4,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(4)=\frac{||4||+2}{2}\\ f(4)=3[/tex]
When x = 5,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(5)=\frac{||5||+2}{2}[/tex]
[tex]f(5)=\frac{7}{2}[/tex]
When x = 6,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(6)=\frac{||6||+2}{2} \\f(6)=4[/tex]
Therefore, the points on the graph of the function [tex]f(x)=\frac{||x||+2}{2}[/tex] are ( 0, 1 ), ( 1, ( 3/2 ) ), ( 2, 2 ), ( 2, ( 5/2 ) ), ( 4, 3 ), ( 5, ( 7/2 ) ), and ( 6, 4).
Hence, the graph of the function is:
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A planet in another solar system has a solar constant S = 2,000 W/m2, and the distance between the
planet and the star is 100 million km.
What is the total power output of the star? (Give your answer in Watts.)
3.5 * [tex]10^{9}[/tex] WATTS IS THE TOTAL OUTPUT OF THE STAR
WHAT IS POWER ?Electrical power is the rate at which electrical energy transforms into another form, such as motion, heat, or an electromagnetic field. The capital P is frequently employed as a symbol representing authority. The universal unit is the watt, which is represented by the letter W. Utility circuits typically have a kilowatt (kW) indication, which is 1000 W.
CALCULATIONSummarized Version:
1-The values of the solar constants were imparted to us by our planet, the first object in our solar system.
2-We therefore know the value of the solar constant for the given solar system, which consists of a planet and the star it orbits.
3-Therefore, if you assume that the orbit is circular, the radius of the orbit will be determined by multiplying the value of the solar constant by 10 to the power 11 m and the radius.
4-We can therefore state that the star's power output is simply equal to the solar constant times the orbit's area.
5-What. So, this is the star's power output for the particular solar system.
The second part of the inquiry now asks what the solar constant will be if the distance between the planet and the star is reduced to 75,000,000 km.
6-We also need to determine what the new solar constant for the solar system will be.
So, in this case, power is equal to area times the solar constant once more.
The solar constant, multiplied by four, multiplied by 3.14, multiplied by are here is 75 multiplied by 10 to the power nine full square, giving us 25.12 multiplied by 10 to the power 25, which is equivalent to that.
We can calculate the value of the solar constant as follows: 25.12 multiplied by 10 to the power of 25 split by four; 3.14 multiplied by 75 square; and 10 multiplied by10.
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HELP PLEASEEEEEEEEEEEEEE
Answer:
Step-by-step explanation:
Solve parts of equation in order:
Brackets
Indices
Division
Multiplication
Addition
Subtraction
8 + 2 x 7 - 9 = 63
8 + (2 x 7) - 9 not = 63 (multiplication is the first thing that applies to this equation)
(8 + 14) - 9 not = 63
22 - 9 = 13
So the error would be it equals 13 not 63
Answer:
9 is supposed to be 7
Step-by-step explanation:
8 + 2 = 10
10 × 7 = 70
70 - 7 = 63
ILL LOVE YOU FOREVER PLEASEHELP MEE
Answer:
75°
Step-by-step explanation:
[tex]m\angle KLM=m\angle KLQ+m\angle QLM \\ \\ 173=x+105+x+82 \\ \\ 173=2x+187 \\ \\ 2x=-14 \\ \\ x=-7 \\ \\ \implies m \angle QLM=-7+82=75^{\circ}[/tex]
Answer:
75
Step-by-step explanation:
7 + (4 + 8) = (7 + 4) + 8
Answer:
true
Step-by-step explanation:
simplify 18/42 to lowest terms
Answer: 3/7
The factors of 18 are 1,2,3,6,9,18;
The factors of 42 are 1,2,3,6,7,14,21,42.
The side-by-side stemplot below displays the arm spans, in centimeters, for two classes.
A stemplot titled Arm Span (centimeters). For Class A, the values are 148, 151, 153, 155, 156, 159, 161, 162, 164, 165, 169, 169, 170, 171, 175, 176, 179, 179, 180, 182, 183, 186, 186, 190. For Class B, the values are 153, 155, 16, 160, 162, 162, 162, 163, 163, 165, 166, 167, 170, 173, 180, 181, 182, 189, 192, 202.
Which statement correctly compares the arm spans for Class A to those of Class B?
The mean arm span for Class A is much lower than Class B’s.
The mean arm span for Class B is much lower than Class A’s.
The mean arm span for Class A is much higher than Class B’s.
The mean arm span for Class B is about the same as Class A’s.
Answer:
D
Step-by-step explanation:
I got it right!
Answer:
d
Step-by-step explanation:
took the test
through: (3,-4), perp. to y=-7x
Answer:
y = x/7 + 31/7
or 7y = x + 31
Step-by-step explanation:
The slopes of two perpendicular lines are negative reciprocals of each other so slope will be 1/7
m = 1/7, y = -4, x = 3
y = mx + b
-4 = 1/7(3) + b
b = 3/7 + 4
b = 3/7 + 28/7
b = 31/7
so
y = x/7 + 31/7
or 7y = x + 31
Find the distance between the pair of points: (-14, 9) and (3, 9)
Answer:
[tex] \large{ \boxed{ \star{ \tt \: answer : 14 \: units}}}[/tex]
Please see the attached picture for full solution!
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Which is the best estimate of 162% of 79?
112
119
128
136
Answer:
nwm zycze powodzenia kolego drogi
help please i’ll give brainlist
Answer:
they all can't be divided
William and his children went into a restaurant where they sell hamburgers for $8 each and drinks for $2.50 each. William has $95 to spend and must buy no less than 18 hamburgers and drinks altogether. If xx represents the number of hamburgers purchased and yy represents the number of drinks purchased, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
95=Xx9 +Yx2.50
Step-by-step explanation:
The inequalities graphically shows the given situation is 95 ≥ +2.50y + 18x. The graph is attached below.
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for that equation or inequality might be true. Such values are called solution to that equation or inequality.
Here Set of such values is called solution set to the considered equation or inequality.
We have been given that William and his children went into a restaurant where they sell hamburgers for $8 each and drinks for $2.50 each.
Since William has $95 to spend and must buy no less than 18 hamburgers and drinks altogether.
If x represents the number of hamburgers purchased and y represents the number of drinks purchased then;
95 ≥ +2.50y + 18x
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what is 50 pounds in kilograms
Answer:
22.6796 kg.
Step-by-step explanation:
The answer is 22 i am sure about this
Study the red pre-image and the associated blue dilation image. The center of dilation is (2, 2). What is the scale factor of the dilation? 1/3 StartFragment, 1/3, 8 StartFragment, 8, 12 StartFragment, 12, 3
Answer: 3
Step-by-step explanation:
The required scale factor of the given dilation is 3. Option D is correct.
Given that,
The center of dilation is (2, 2).
To determine the scale factor of the dilation.0
The scale factor is defined as the ratio of modified change in length to the original length.
Here,
Length of one side of triangle former dilation = 2 units
Length of one side of triangle later dilation = 6 units
Scale factor = later dimensions / former dimensions = 6 / 2 = 3
Thus, the required scale factor of the given dilation is 3. Option D is correct.
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