The value of k is 1/4.
According to the statement
we have given
The equation of parabola is y=k−x2
And tangent to the line of equation is y = x
and we have to find the value of K.
So, let y=k−x2 -(1)
and let y = x -(2)
(2) is the tangent to the (1) then
therefore they cut at
y=k−x2 -(1)
y = x -(2)
so, put (2) in the (1) then
x = k- (x)^2
(x)^2 + x = k
The above written equation has one real number then for this D =0
so, (x)^2 + x - k = 0
-1 -1*4*k = 0
-1 - 4k = 0
-4k = 1
The value of k is -1/4.
So, The value of k is 1/4.
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Help me solve this problem on arithmetic and geométrica sequences
Answer:
math math math math math math math math math math
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a radioactive substance. After 20 hours, 55 mg of the substance remains. How many milligrams will remain after 26 hours
Answer:
44.7 mg
Step-by-step explanation:
The equation for exponential decay can be written in the form ...
y = a·b^(t/p)
where 'a' is the initial value, 'b' is the decay factor, 'p' is the period over which the decay factor is applicable, and t is time in the same units as p.
SetupUsing the above equation, we have ...
a = initial value = 110 mg
b = decay factor = 55/110 = 1/2 over time period p=20 hours
Then the equation is ...
y = 110·(1/2)^(t/20) . . . . amount remaining after t hours
SolutionWe want the amount remaining after 26 hours. That will be ...
y = 110·(1/2)^(26/20) ≈ 44.67
About 44.7 milligrams will remain after 26 hours.
You want to retire on the equivalent of $50,000 per year in today's money. inflation is expected to be 3%. you will retire in 30 years. you will earn 10% annually on your investments from not till retirement and you will earn 8% during retirement (which is expected to last 20 years). how much do you need to save per month in order to fund this retirement?
$662.18 needs to be saved per month.
$90,000 now at 3% inflation will become 90000*1.03^30 after 30 years.
i.e. $218,454 is required in retirement years (for 20 years)
Calculating the PV of these payments at 7% is calculated as below.
FV = 0
1/y = 7%
n=20; PMT = 218454; calculate PV = $2,314,305
Now we want to get $2,314,305 at the start of retirement by saving per year. Enter the following in the financial calculator to get the per month amount.
FV = 2314305; PV = 0; n= 12*30; 1/y = 12%/12; calculate PMT = $662.18
So $662.18 needs to be saved per month.
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Given the equation, y=2x+6, what is its slope?
Select one:
O a. 6
Ob. 2
O c. 3
O d. 1
Answer:
B, 2
Step-by-step explanation:
The slope in a y=mx+b equation is m. The m in your equation is 2.
Therfore, your slope is 2.
On a coordinate plane, kite U V W X with diagonals is shown. Point U is at (negative 2, 5), point V is at (5, 4), point W is at (8, negative 5), and point X is at (negative 1, negative 2).
Prove that the diagonals of kite UVWX are perpendicular.
Step 1: Determine the slope of XV.
The slope of XV is
.
Step 2: Determine the slope of UW.
The slope of UW is
.
Step 3: The slopes of the diagonals are
.
The diagonals of kite UVWX are
.
The information about the coordinate plane shows that the slope of XV is 1.
How to illustrate the information?From the information, the slopes of the diagonals are negative reciprocals. Therefore, the slope of UW is -1 and the slope of XV is 1.
The diagonals of kite UVWX are perpendicular.
It should be noted that negative reciprocals in a kite create a perpendicular bisector. So the two lines share a midpoint so they are perpendicular.
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Answer:
Step-by-step explanation:
The slope of XV is
1
The slope of UW is
–1
The slopes of the diagonals are
negative reciprocals
The diagonals of kite UVWX are
perpendicular
.
4. Based on the triangle sum theorem, solve for x.
Answer:
x = 10
Step-by-step explanation:
180 = 90 + 40 + (4x + 10)
180 = 130 + (4x + 10)
4x + 10 = 180 - 130
4x + 10 = 50
4x = 50 - 10
4x = 40
x = 40/4
x = 10
Answer:
x = 10
Step-by-step explanation:
An euclidean triangle is defined to have sum of all 3 interior angles equal to 180°.
In the given triangle, we know three measurement:
4x+1040°90°You may be wondering, where does 90° come from. The answer is you can find it by looking if a triangle has a little square symbol or not. If it does, the measurement will always be 90°.
Now since we know that sum of 3 interior angles must equal to 180° in euclidean triangle. Therefore, sum up three of measurement then set to 180°.
[tex]\displaystyle{90 + 4x+10 + 40= 180}[/tex]
Evaluate and solve for the x-variable:
[tex]\displaystyle{90 + 4x+10 + 40= 180}\\\\\displaystyle{4x+140 = 180}\\\\\displaystyle{4x=180-140}\\\\\displaystyle{4x=40}\\\\\displaystyle{x=10}[/tex]
Therefore, the value of x is 10
Consider the equations y= |x-1 | and y = 3x + 2. The approxirate solution of this system of equations is
Answer:
Point Form: (- 1/4, 5/4)
Equation Form: x = - 1/4, y = 5/4
Step-by-step explanation:
Mr. Krueger wanted a square platform built in the drama room at
school. He provided the carpenter with the desired area of the platform
to be built. Which function can he use to determine the side length of
the square platform?
F(x)=x²
F(x)=√x
F(x) = -=-=
F(x) = |x|
If the table of the function contains exactly two potential turning points, one with an input value of -1, which statement best describes all possible values of m?
The statement (inequality) which best describes all possible values of m is: -12 < m < 4.
What is an inequality?An inequality is a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).The table indicates two local extremes or potential turning points at x = 1 and x = -1. Thus, the value of m can't exceed f(-3) = -12.
In conclusion, the statement (inequality) which best describes all possible values of m is: -12 < m < 4.
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The red blood cell counts for a population of adult males can be approximated by a normal distribution with a mean of 5.3 million cells per microliter and a standard deviation of 0.3 million cells per microliter what is the minimum red blood cells count that can be in the top 28% of accounts
The minimum red blood cells count that can be in the top 28% of accounts is 5.61%.
Red blood cells, also called crimson cells, purple blood corpuscles, haematids, erythroid cells, or erythrocytes, are the maximum common type of blood cells and the vertebrate's primary approach of delivering oxygen to the body tissues thru blood drift thru the circulatory device.
A low RBC depends, also called anemia, can have an effect on the frame's capability to transport oxygen and vitamins around the cardiovascular machine. it may reason fatigue, dizziness, and heart palpitations. The maximum not unusual form of anemia is iron deficiency anemia. this can result from blood loss, malnutrition, or kidney problems.
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Identify an equation in point slope form for the line parallel to y=-2/3×+8 that paases through (4,-5)
Answer:
y=-2/3x-7/3
Step-by-step explanation:
a parallel line has the same slope but different y intercept
so we need to solve for y=-2/3x+b
since it passes through 4,-5 we can plug it in for x and y
-5=-2/3(4)+b
-5=(-8/3)+b then add 8/3 to both sides
-5 is also -15/3
-7/3=b
so answer is y=-2/3x-7/3
A man left savings of the 2 50,000 to his wife, 2 daughters and a son. find the value of the shares that each received.q
Answer:
62,500
Step-by-step explanation:
250,000 ÷ 4 = 62,500
∴ Each member would receive 62,500.
Which side lengths form a right triangle?
Choose all answers that apply:
A:
11,13,√290
B:
7, 24, 25
C: 2, 5, 7
Answer:
B
Step-by-step explanation:
Use the Pythagorean theorem, 7^2+24^2=25^2
49+576=625
625=625
All the other answers do not satisfy the Pythagorean theorem (a^2+b^2=c^2)
Answer: A, B
Step-by-step explanation:
A right triangle's sides have a special property that the sum of the squares of the two legs is equal to the square of the hypotenuse. This is also known as the Pythagorean Theorem.
Let's check if this theorem holds true for each triangle.
A[tex]11^2+13^2=(\sqrt{290})^2\\ 121 + 169=290\\ 290 = 290[/tex]
The Pythagorean Theorem holds true, so this is a right triangle.
B[tex]7^2+24^2=25^2\\ 49 + 576 = 625\\ 625=625[/tex]
The Pythagorean Theorem holds true, so this is a right triangle.
C[tex]2^2+5^2=7^2\\ 4+25=49\\ 29 = 49[/tex]
This is a false statement, which doesn't make this triangle a right triangle. We could have use the triangle inequality theorem to prove that this isn't a triangle at all, and therefore not a right triangle, but I encourage you to learn about it and try it yourself.
Which is the graph of linear inequality 6x+2y>-10?
Answer:
we have
6x+2y > -106x+2y>−10
Isolate the variable y
Subtract 6x6x both sides
2y > -6x-102y>−6x−10
Divide by 22 both sides
y > -3x-5y>−3x−5
The equation of the line of this inequality is
y=-3x-5y=−3x−5
The slope is negative and is equal to m=-3m=−3
The y-intercept is the point (0,-5)(0,−5) ----> value of y when the value of x is equal to zero
The x-intercept is the point (-5/3,0)(−5/3,0) ----> value of x when the value of y is equal to zero
The solution of the inequality is the shaded area above the dotted line
Using a graphing tool
see the attached figure
Ben has 3/4 pounds of cherries and ate 2/3 of the cherries. How many pounds of cherries does Ben eat?
Answer:
1/2 pounds
Step-by-step explanation:
3/4 * 2/3 = 1/2 pounds
When researching for a business report, you should find reliable sources whose information is accurate, unbiased, and .
Answer:
Creditable
Step-by-step explanation:
Could also be:
up-to-date
A local farmer built a rectangular pen for her chickens using 12 meters of fence. She used part of one side of her barn as one length of the rectangular pen. She maximized the area using 12 meters of fence. She then build a rectangular pen for her pigs using 16 meters of fence. She used part of one side of her barn as one length of the rectangular pen. The length of her pen was 2 meters more than the length of the chicken pen. The width of her pen was 1 meter more than the width of the chicken pen. How much larger is the pig pen than the chicken pen
The pig pen is 14 sq. meters larger than the chicken pen built by the former.
What are the perimeter and area of a rectangle?Consider a rectangle with length 'L' and width 'W'.
So, its perimeter = 2(L + W) units and area = L × W sq. units.
Calculating the dimensions of the rectangular pen for chicken:It is given that a farmer built a rectangular pen for chickens.
The chicken pen's perimeter is 12 meters, and she used only one side of the barn as one length of the rectangular pen.
So,
L + 2W = 12
⇒ L = 12 - 2W
Then its area is calculated as below:
Area = L × W
= (12 - 2W) W
= 12W - 2W²
Consider A' = 0 for finding the larger area.
So, differentiating the area w.r.t W,
dA/dW = 12 - 4W
0 = 12 - 4W
⇒ 4W = 12
∴W = 3 meters
Then,
L = 12 - 2W = 12 - 2(3) = 6 meters
So, the area of the chicken pen = 6m × 3m = 18 m²
Calculating the dimensions of the rectangular pen for the pig:It is given that,
The length of the pig pen was 2 meters more than the length of the chicken pen. I.e., L' = L + 2
The width of the pig pen was 1 meter more than the width of the chicken pen. I.e., W' = W + 1
On substituting L and W values to find the dimensions of the pig pen,
L' = 6 + 2 = 8m
W' = 3 + 1 = 4m
Then,
Area = L' × W'
= 8m × 4m
= 32 m²
Finding how much larger is the pig pen than the chicken pen:
Area of the pig pen - Area of the chicken pen
⇒ 32 m² - 18 m² = 14 m²
Therefore, the pig pen is 14 m² larger than the chicken pen.
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Find the missing side length of the triangle.
Answer:
a = 1.5 in.
Step-by-step explanation:
Use the Pythagoras Theorem:
1.7^2 = a^2 + 0.8^2
a^2 = 1.7^2 - 0.8^2
= 2.25
a = 1.5 in.
Answer:
a = 1.5 in.
Explanation:
Using Pythagoras theorem:
a² + b² = c²
insert values
a² + 0.8² = 1.7²
a² = 1.7² - 0.8²
a² = 2.89 - 0.64
a² = 2.25
a = √2.25
a = 1.5
Refreshment we’re set up in one area of the gym . hot pretzels were a dollar lemonade was 50 cents, fruit was 35 cents , and cookies were a quarter . if you purchase two of each . How much money would you needed
Answer:
$4.20
Step-by-step explanation:
1+1+.50+.50+.35+.35+.25+.25=4.20
what is the domain of f(x)=√11-x?
The domain of the function f(x) is:
11 ≥ x
What is the domain of the function f(x)?
Here we have the function:
[tex]f(x) = \sqrt{11 - x}[/tex]
Now, remember that the argument of a square root can only be a number equal to or larger than zero, so the domain of our function is defined by:
11 - x ≥ 0
Then, solving this for x, we get:
11 ≥ x
Concluding, the domain of the function f(x) is:
11 ≥ x
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im stuck on this one
The value of X is 2/3 and -3/2.
According to the statement
we have given equation is 6x^2+5x-6 =0
and we have to find x by the factorization.
Factorization defines the the operation of resolving a quantity into factors.
So, by factorization method the equation is written as
6x^2+5x-6 =0
After forming factors the equation becomes
6x^2+9x-4x-6 =0
3x(2x+3) -2(2x+3) =0
By taking common
(3x-2) (2x+3) = 0
Now equate values equal to 0. and after that the output will get in the form of value of X.
Here the value of x is 2/3 and -3/2
So, the value of X is 2/3 and -3/2.
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What is the slope of a line that passes through the point (-3,0) and has a y-intercept of 12
The slope of a line that passes through the point (-3,0) and has a y-intercept of 12 is 4.
How to find the slope of a line?Using the point slope equation,
y = mx + b
where
m = slopeb = y-interceptTherefore, using (-3, 0)
0 = -3m + 12
-12 = -3m
divide both sides by -3
m = -12 / -3
m = 4
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The weights of certain machine components are normally distributed with a mean of 7.75 ounces and a standard deviation of 0.07 ounces. Find the two weights that separate the top 4% and the bottom 4%. These weights could serve as limits used to identify which components should be rejected. Round your answer to the nearest hundredth, if necessary.
The weight that separates the top 4% is x = 7.87 (round nearest hundredth) .
The weight that separates the bottom 4% is x = 7.63 (round nearest hundredth).
What is normal distribution?The majority of the observations are centred around the middle peak of the normal distribution, which is a continuous distribution of probability that really is symmetrical around in its mean.
The probability for values that are farther from of the mean tapered down equally both in directions.
Now, use z-chart to find the z-value for that separates the top 4% and the bottom 4%.
The values of z = +1.75 and z = -1.75
Let the weight of the machines be 'x'.
Use the formula for z- value
z = (x - μ)/ σ
Where,
σ is standard deviation = 0.07 ounces.
μ is mean = 7.75 ounces.
Substitute all the values and calculate the weight.
case 1: when z = +1.75
1.75 = (x - 7.75)/0.07
x = (1.75×0.07) + 7.75
x = 7.872
x = 7.87 (round nearest hundredth)
case 2: when z = -1.75
-1.75 = (x - 7.75)/0.07
x = (-1.75×0.07) + 7.75
x = 7.6275
x = 7.63 (round nearest hundredth)
Therefore,
x = 7.87 (round nearest hundredth) is weight which separates top 4%.
x = 7.63 (round nearest hundredth) is weight which separates bottom 4%.
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Drag each tile to the correct box.
Each function is a transformation of the parent sine function. Based on the period, which graph represents each transformed function?
The first graph represents sin(2x), the second graph represents sin(-x) and the third graph represents sin(x/2) .
There are some rules for transformation of graph of various functions which are as follows :-
For F(x) →f(−x) = Reflection about the y-axisFor F(x) → f(ax) = It will depend upon value of a chosenIf |a|>1 then f(ax) is f(x) squashed horizontally by a factor of aIf 0<|a|<1 then f(ax) is f(x) is stretched horizontally by factor of aIf a<0 then is f(ax) is f(x) also reflected in the y-axisBy keeping in mind these rules it is easily observable that the first graph is sinx squashed horizontally by a factor of 2 while second graph is reflection of sinx about the y-axis and the third graph is sinx horizontally stretched by a factor of 2.
Thus the first graph represents sin(2x), the second graph represents
sin(-x) and the third graph represents sin(x/2)
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what is the value of x
find the value of f
Answer:
x = 20°
f = 40°
Step-by-step explanation:
4x + 5x = 180°
because a straight line is 180°
so 9x = 180°
1x = 180 ÷ 9
1x = 20
all angles in a triangle add together is 180°
so 7x + f = 180°
1x = 20
7x = 20 × 7
7x = 140°
f = 180° - 140 °
f = 40°
Answer:
x = 20 , f = 40
Step-by-step explanation:
4x and 5x are a linear pair and sum to 180° , then
4x + 5x = 180
9x = 180 ( divide both sides by 9 )
x = 20
then
5x = 5 × 20 = 100° and 3x = 3 × 20 = 60°
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
5x is an exterior angle of the triangle , then
f + 3x = 5x , that is
f + 60 = 100 ( subtract 60 from both sides )
f = 40
Find the equation of the line described.
5. Perpendicular to y = 3x + 5; passing through the point (-6,-4)
Answer: [tex]y+4=-\frac{1}{3}(x+6)[/tex]
Step-by-step explanation:
The slope of the given line is 3, so the slope of the line we want to find is -1/3.
Substituting into point-slope form, we get the equation of the line to be
[tex]y+4=-\frac{1}{3}(x+6)[/tex].
EXTRA POINTS
x/4 ÷ 2/3 = 1/5 solve for x
Answer:
x=40
Step-by-step explanation:
first you simplify both sides of the equation, then you isolate the variable
40/4= 10
10 times 3/2 = 15
Drag each expression to the correct location on the table.
Simplify each exponential expression using the properties of exponents and match it to the correct answer.
An exponential expression is one in which a number has been raised to a certain power.
What is an exponential expression?An exponential expression is one in which a number has been raised to a certain power.
Now;
1) 3^2 . (3^3)^2 . 3^-8 = 3^2 + 6 - 8= 3^0 = 1
2) (3^2) (2.3)^-3/2^-2 = 3^2 . 2^-3 . 3^-3/2^-3 = 1/3
3) (2^-1) . (3 . 2)^4/(3 . 2)^3 = 2^-1. 3^4 . 2^4/ 3^3. 2^3 = 3
4) 2^5 . 3^5 . 6^-5 = 32 * 243/7776 = 1
5) (2^3) . (2 . 3)^-1/2^2 = 2^3 . 2^-1 . 3^-1/2^2 = 1/3
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Solve for B.
R = x(A + B)
A data store system that collects and stores all of the learning experiences in the form of statements that can be organized and presented in a meaningful way is the
The learning records is the meaningful way in which all of the data of learning experiences is record in the form of statements.
According to the statement
we have to tell that the which record is used when A data store system that collects and stores all of the learning experiences in the form of statements that can be organized and presented in a meaningful way.
So, for find this data store way to record the data
We know that the
The Learning Record provides an architecture and process for documenting student progress and achievement, based on interviews, observations over time, samples of students' naturally-occurring work, and well-supported interpretations of learning across five dimensions.
we see that the these given conditions in statement are approved by the data store way named the learning records.
So, The learning records is the meaningful way in which all of the data of learning experiences is record in the form of statements.
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