Answer: The equation of the tangent to a parabolic curve y = ax^2 + bx + c at the point (h, k) can be expressed as:
y = a(x - h)^2 + k
So, we know the equation of the tangent at vertex of the parabolic curve is 3x - 4y = 5, so the vertex of the parabolic curve is (h, k) = (2, -3/2).
The equation of a parabolic curve with vertex (h, k) and focus (h, k + p) is given by:
y = a(x - h)^2 + k, where a = -1/4p.
So, substituting the values of the vertex (2, -3/2) and the focus (1, 2) into the above equation, we have:
-3/2 = a(2 - 2)^2 - 3/2, so a = -1/4p.
And, substituting the values of the focus (1, 2) into the equation y = a(x - h)^2 + k, we have:
2 = -1/4p(1 - 2)^2 - 3/2, so p = 1/2.
So, the equation of the parabolic curve with focus (1, 2) and vertex (2, -3/2) is:
y = -1/4 * 1/2 * (x - 2)^2 - 3/2.
This is the equation of the parabola that has the equation of the tangent at vertex 3x - 4y = 5 and focus at the point (1, 2).
Step-by-step explanation:
Emma is starting a cupcake business and borrows money from Dixons dynamite deals (DDD) .she agrees to pay back the loan after 10 years by making one payment of 80,000 , interest is compounded and fixed at 14,6% per annum.hpw much did emma borrow from (DDD) ?
The amount (present value) that Emma borrowed from Dixons Dynamite Deals (DDD) to repay after 10 years with a one-time payment of $80,000 at 14/6% compounded interest per annum is not more than $20,475.94.
Step-by-step explanation:
To find out how much Emma borrowed from Dixons Dynamite Deals (DDD), we can use the formula for the future value of a loan with compound interest:
Future Value (FV) = Principal Amount (P) * (1 + r)^n
Where:
P = Principal amount (the amount borrowed)
r = Interest rate per period (in decimal form)
n = Number of periods
In this case:
Future Value (FV) = $80,000 (the payment Emma will make after 10 years)
Interest rate (r) = 14.6% per annum = 0.146 (in decimal form)
Number of periods (n) = 10 years
Now, let's calculate the principal amount (P):
$80,000 = P * (1 + 0.146)^10
Now, let's solve for P:
P = $80,000 / (1.146)^10
P ≈ $80,000 / 2.97804
P ≈ $26,874.94
So, Emma borrowed approximately $26,874.94 from Dixons Dynamite Deals (DDD) to start her cupcake business.
Please mark as Brainliest
which expression is equivalent to 5^6
a.125 x 125 b. 6 x 5 c. 35 x 6 x 6 x 6 d. 25 x 5 x 5 x 5
The expression that is equivalent to 5^6 is A.125 x 125
What are index forms?Index forms are defined as mathematical forms of writing numbers that are too large or small in more convenient forms.
Other terms for index forms are called standard forms or scientific notations.
They are also described as numbers or variables that are raised to an exponent.
From the information given, we have that;
5⁶
This is replicating 5 in 6 places, we have the representation as;
5 × 5 × 5 × 5 × 5 × 5
Hence, the expression is 125 x 125
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Your school is going to start offering afterschool clubs they will be nine clubs to choose from to have clubs at least 23 students we will need to sign up for each one what is the least number of students that must sign up to have all nine clubs
At least number of students who must have signed up to have all nine clubs is equal to 207.
Number of clubs school going to start after school = 9 clubs
At least number of students need to sign up in each one of the club is equal to 23 students.
At least number of students need to sign up to have all in nine clubs is equal to :
At least number of student in 1 club > 23
⇒ At least number of student in 9 club > 23 × 9
At least number of student in 9 club > 207
Therefore, at least number of students need to signed up to have in all nine given clubs are 207 students.
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5x5+67-85=
PLS HURRY
Answer:
7
Step-by-step explanation:
We start doing the multiplication, and [tex]5 \cdot 5 = 25[/tex]. So we can rewrite it as [tex]25 + 67 - 85.[/tex] Now we work from left to right, where we calculate [tex]25 + 67 = 92[/tex]. Now the final step, [tex]92 - 85 = 7.[/tex] Therefore, the answer is [tex]\boxed{7.}[/tex]
Answer:
sry for being late the answer is 7……I did it in my head and double checked with a calculator. Go ahead and give the other person brainliest they did it first! Hope I helped to!!
Step-by-step explanation:
A parabola can be drawn given a focus of (0, 4) and a directrix of y =
be said about the parabola?
Answer: A parabola can be defined as the set of all points that are equidistant from a focus and a directrix. Based on the information provided, the focus of the parabola is (0, 4) and the directrix is y =.
The parabola will open upwards or downwards depending on the location of the focus and the directrix. Since the focus is at (0, 4), and the directrix is at y =, the parabola must open upwards. The axis of symmetry of the parabola will pass through the focus and will be perpendicular to the directrix.
Without more information, it is not possible to fully determine the shape and equation of the parabola. The shape of the parabola and its equation can be found by using the focus and directrix and other information, such as the vertex or a point on the parabola.
Step-by-step explanation:
A newspaper randomly chooses 100 names from it's subscriber database and then survey's those subscribers to find if they read the restaurant review is this biased or non biased
Answer:
Non biased (kind of)
Step-by-step explanation:
It depends on how they randomly chose but if it was truly random it would be non biased as many people will read newspapers for things such as sports or catalogs
AB and BC form a right angle at point B. If A= (-3,-1) and B=(4,4), what is the equation of BC
Answer: AB and BC form a right angle at point B, so BC is perpendicular to AB. To find the equation of BC, we can use the slope-point formula, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.
The slope of a line perpendicular to AB can be found by finding the negative reciprocal of the slope of AB. To find the slope of AB, we need to find the difference in the y-coordinates and divide it by the difference in the x-coordinates:
m_AB = (y2 - y1) / (x2 - x1)
= (4 - (-1)) / (4 - (-3))
= 5 / 7
The slope of a line perpendicular to AB is the negative reciprocal of m_AB:
m_BC = -1 / m_AB = -1 / (5/7) = -7/5
Now that we have the slope of BC, we can use the slope-point formula to find the equation of BC. We'll use the point B = (4, 4) as (x1, y1):
y - 4 = -7/5 (x - 4)
y = -7/5 x + 4(7/5) + 4
y = -7/5 x + 36/5
So the equation of BC is y = -7/5 x + 36/5.
Step-by-step explanation:
A Smoothie is mixed with strawberries and bananas in the ratio 7:3. Gill
makes a smoothie using 144g of bananas. How many grams of
Strawberry does she use?
Answer: et's call the amount of strawberries Gill uses "x" grams. We know that the ratio of strawberries to bananas is 7:3, so we can set up an equation:
x/144 = 7/3
To solve for x, we'll multiply both sides of the equation by 144:
x = 7/3 * 144
x = 7 * 48
x = 336
So Gill uses 336 grams of strawberries in the smoothie.
Step-by-step explanation:
Write as an algebraic expression: five times the difference between six less than a number
The algebraic expression is,
⇒ 5 (6 - n)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ five times the difference between six less than a number.
Now, Let a number = n
Hence, We can formulate;
⇒ 5 (6 - n)
Thus, The value of expression is,
⇒ 5 (6 - n)
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among the cast aluminum parts manufactured on a certain day, 80% were awless, 15% had only minor aws, and 5% had ma jor aws. find the probability that a randomly chosen part (a) has a aw and (b) has no ma jor aw.
Probability that a randomly chosen part (a) has a P(flaw) = 0.2 and
has no major flaws b) P(No major flaws) = 0.95
The probability that an event will occur is determined by probability: P(A) = f / N. Probability and odds are related, but probability determines what the odds are. Probability is required before calculating the likelihood that an event will occur.
To find the probability of flaws, we can find the probability of no flaws first by dividing by 100:
P(no flaw) = 80/100 = 0.8
So then:
P(flaw) = 1 - P(no flaw) = 1 - 0.8 = 0.2
P(flaw) = 0.2
B) First, we need to find the probability of major flaws:
P(major flaws) =
P(Major flaws) = 0.05
So to find the probability of no major flaws:
P(No major flaws) = 1 - P(major flaws) = 1 - 0.05 = 0.95
P(No major flaws) = 0.95
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Lisa's average score on 4 tests is 82. What does she need to score on her fifth test to have an average final score of 85?
Answer:
Lisa would need to score 97 on her 5th test.
Step-by-step explanation:
If Lisa has an average score of 82 on 4 tests, then the total sum of her scores would be 82 multiplied by 4, which is equal to 328.
If she wants an average final score of 85 over 5 tests, then the total sum of her scores needs to be 425 (i.e. 85 multiplied by 5).
To determine what she needs to get on her 5th test we need to subtract 328 from 425.
425 - 328 = 97
How would you translate a real world verbal expression into an algebraic expression?
The Translation to algebraic expression is shown below.
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
To create a variable expression for a circumstance in the actual world:
Determine which quantity is unknown in the circumstance, then define a variable to represent it.To reflect the circumstance, create an expression utilising the variable. To determine what mathematical procedures to apply, look for essential words.For example, the sum of a and b can be written as
= a+ b
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uppose that a particular nba player makes of his free throws. assume that late in a basketball game, this player is fouled and is awarded two free throws. a. what is the probability that he will make both free throws? (to 4 decimals) b. what is the probability that he will make at least one free throw? (to 4 decimals)
Answer:
a. 0.81
b. 0.81
Step-by-step explanation:
Let's assume that the player makes x% of his free throws. Then, the probability that he will make both free throws is (x/100)^2, and he will make at least one free throw is 1 - (1 - x/100)^2.
So if he makes 90% of his free throws, then:
a. The probability that he will make both free throws is (90/100)^2 = 0.81.
b. The probability that he will make at least one free throw is 1 - (1 - 90/100)^2 = 1 - (1 - 0.9)^2 = 1 - 0.19 = 0.81.
The answers to the questions rounded to 4 decimal places are:
a. 0.81
b. 0.81
A rectangle has a length of ( + ) and a width of ( − ). Determine the expression that represents the area of this rectangle.
Answer:
Step-by-step explanation:
The expression that represents the area of a rectangle with length (l) and width (w) is given by:
A = l * w
Therefore, the expression that represents the area of a rectangle with a length of ( + ) and a width of ( − ) can be represented as:
A = ( + ) * ( − ) = + × − = + (−) = −.
i need help with this one?
The best description of the transformation for the image being projected on the retina is A. A dilation with a scale factor between 0 and - 1 and center at the nodal point.
How does the nodal point dilate the retina ?An mage is inverted and reversed as it passes through the lens of the eye, and is then projected upside down and reversed onto the retina. The process of transforming the image is called "rectification."
In mathematical terms, a dilation would have taken place because the object was shrunken by the eyes at the nodal point. When an object shrinks , then the scale factor is between 0 and 1 but because this image is inverted, the scale factor is between 0 and - 1.
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i need the answers to the marked answers! please help me!! :)
The results are given below.
What is congruency of triangles?Two triangles are said to be congruent if all the corresponding sides are equal and all the corresponding angles are equal. The symbol of congruency is '≅'
Consider the first triangles,
Given, L is the midpoint of KN and MP.
To find ΔMKL ≅ΔPNL
Using side-angle-side congruency ,
Here, the corresponding sides , KM and MP, KL and LP are equivalent.
But the angle ∠L is not an included angle.
So this triangles are non congruent.
Consider the next triangles.
BD bisects ∠ABC ∠BAD≅∠BCD
To find ΔABC≅BCD
By side- side-side congruency,
The corresponding sides AB and BD, AD and DC, BD are equivalent.
Therefore this ΔABC≅BCD proved.
Hence the proof.
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Subtract and simplify. (9^2 − 4 − 4) − (−2^3 − + 12)
Answer:
93
Step-by-step explanation:
Answer:
27
28
Step-by-step explanation:
Draw the right bisector of the line AB 7. 6 cm by using a pair of compasses
Right Bisector also known as Perpendicular Bisector is a line that bisects another line segment at a right angle, through the intersection point.
First we will draw a line segment AB = 7 cm with the help ruler, then with vertex A, by using compass take more than half of AB and draw arcs, one each side of AB and mark them X and Y and then with vertex B, by using compass with same length again, cut the previous arcs at X and Y respectively.
Now, with help of ruler join the point X and Y. Thus XY is the perpendicular bisector of line AB.
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13 4 73 efine a variable for the quantity that changes. Then, write an algebraic expression for the amount of etergent remaining in the container. ▸Math symbols Relations ▸ Geometry Groups ▸Trigonometry Statistics
The algebraic expression for the amount of etergent remaining in the container isy = x - 13 - 4 - 73
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given that;
13 4 73
Let's define the variable 'x' to represent the amount of detergent initially present in the container.
Then, if 'y' represents the amount of detergent remaining in the container, we can write an algebraic expression for it as:
y = x - 13 - 4 - 73
where:
13 represents the amount of detergent used on the first day
4 represents the amount of detergent used on the second day
73 represents the amount of detergent used on the third day
By subtracting the total amount of detergent used from the initial amount 'x', we get the remaining amount 'y'.
Therefore, the expression will be y = x - 13 - 4 - 73.
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What number is 30% less than 40?
Answer: 30% less than 40 is 28
Step-by-step explanation:
Answer:
The answer is 28.
Step-by-step explanation:
I'm bad at proving stuff but that's the answer I promise. (quick tip, you are more likely to get answers if you give more points. :D)
Write a piece wise function for each function graphed below.
The piecewise function for the graph is given as follows:
y = -2, x < -4.y = 0.5x + 4, -4 < x ≤ 2y = -1.5x + 1, x > 1.How to define the piecewise function?A piecewise function is a function that has different definitions, depending on the input x of the function.
The three different definitions for the function in this problem are given as follows:
x < -4.-4 < x ≤ 2.x > 2.For x < -4, the function is constant at y = -2, hence:
y = -2, x < -4.
For -4 < x ≤ 2, the function is linear, with an slope of 0.5 and intercept of 4, hence:
y = 0.5x + 4, -4 < x ≤ 2
For x > 2, the function is also linear, with slope of -1.5, hence at x = 0 it would assume a value of 1, thus:
y = -1.5x + 1, x > 1.
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73.
ILLUSTRATION 7
Find a. the length and b. the diameter of the shaft in
In the illustration given above, the length and the diameter of the shaft would be = 21.8 in and 7/8 in respectively.
How to calculate the total length of the shaft?The total length of the shaft can be calculated through the addition of the various given lengths along the shaft such as follows:
= 5⅛ + 5 + 7⅝ + 4 1/16
First convert all the mixed fraction into single fraction;
= 41/8 + 5/1 + 61/8 + 65/16
= 82+80+122+65/16
= 349/16
= 21.8 in.
The diameter of the shaft can be calculated as follows;
= 7¼ - (3 3/16 + 3 3/16 )
First convert all the mixed fraction into single fraction;
= 29/4 - (51/16 + 51/16)
= 29/4 - 102/16
= 116-102/16
= 14/16
= 7/8 in.
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marvin the fly starts at $(0,0).$ each step, marvin moves one unit right or one unit up. he is trying to get to his home at $(4,6)$. however, at $(1,4),$ there is a frog that will eat him if he goes through that point. in how many ways can marvin reach his home?
There are 50 ways for Marvin to reach his destination without passing through the forbidden point.
To solve this problem, we can use the unitary method. This method involves breaking the problem down into smaller, simpler units to solve it more easily.
In this case, we can break the path from Marvin's starting point to his destination into two smaller paths. The first path is from (0,0) to (1,4), and the second path is from (1,4) to (4,6).
There are five paths from the bottom left corner to the point (1,4) that do not go through the forbidden point.
Once Marvin reaches the point (1,4), he can only go up or to the right to reach his destination. So, we need to count the number of ways to get from (1,4) to (4,6)
We can visualize this by drawing another grid and counting the paths:
In total, there are
=> 5 x 10 = 50
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An angle is measures 139.6 less than the measure of its supplementary what is the measure of each angle
Answer:
788883332220+2648340
Step-by-step explanation:
what is energy transferred
Company F sells fabrics known as fat quarters, which are rectangles of fabric created by cutting a yard of fabric into four pieces. Occasionally the manufacturing process results in a fabric defect. Let the random variable X represent the number of defects on a fat quarter created by Company F. The following table shows the probability distribution of X.
X 0 1 2 3 4 or more
probability 0. 58 0. 23 0. 11 0. 05 0. 03
If a fat quarter has more than 2 defects, it cannot be sold and is discarded. Let the random variable Y represent the number of defects on a fat quarter that can be sold by Company F.
(a) Construct the probability distribution of the random variable Y.
(b) Determine the mean and standard deviation of Y. Show your work.
Company G also sells fat quarters. The mean and standard deviation of the number of defects on a fat quarter that can be sold by Company G are 0. 40 and 0. 66, respectively. The fat quarters sell for $5. 00 each but are discounted by $1. 50 for each defect found.
(c) What are the mean and standard deviation of the selling price for the fat quarters sold by Company G?
The probability distribution of the random variable Y is 0.63, 0.25, 0.12. The mean of y is 0.4899 and the std deviation of y is 0.6999 and the mean of the selling price for the fat quarters sold by Company G is $4.4 and the std deviation for the same is $0.99
a) x = number of defects on a fat quarter
to be sold, X must be, X ≤ 2
y = number of defects on the sellable fat quarter,
now from the table, P [fat quarter being sellable]
=P [X ≤ 2]
=0.58 + 0.23 + 0.11
= 0.92
Therefore, P[y-0] = P[x=0Ix≤2]
=[tex]\frac{P[x=0][x < 2]}{P[x < 2]}[/tex]
=P[y=0] = 0.63
P[y=1] = P[x=1Ix≤2]
P[y=1] = [tex]\frac{0.23}{0.92}[/tex]
=0.25
P[y=2] = P[x=2Ix≤2]
P[y=2] = [tex]\frac{0.11}{0.92}[/tex]
= 0.12
y------------------0--------1---------2
probability---0.63----0.25----0.12
b)mean of y = E(y)
=0²×0.063+1×0.25+2×0.12
=0.25+0.24
=0.49
now we know that E(y²) = 0²×0.63+1²×0.25+2²×0.12
=0.25+0.48
=0.73
E(y²) - [E(y)]²
=0.73-0.49²
=0.4899
std deviation of y = 0.6999
c) now that we have E(G) = 0.40, √v(G) = 0.66
let s be selling price of fat quarters, then s = 5.00 - 1.50 × (G)
therefore = 5-1.5×0.4
=5-0.6
=$4.4 is the mean selling price.
now for the standard deviation price = v[5-1.5G]
=v(5)+1.5² v(G)
=0+2.25×0.66²
=v(s)= 0.9801
standard deviation of sp =√v(s)
=$0.99
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Question 7 (Mandatory) (1 point)
Which point is on the graph of y = -2x + 1?
Answer:
y-intercept: (0,-1)
Step-by-step explanation:
please verify
Can some one help sovle this?
-
By using the graph of the piecewise function we can see that:
f(0) = 0.
How to find the value of f(0)?Here we have the graph of a piecewise function, and we want to find the function when x = 0.
Remember that on a graph, an open circle means that the value does not belong to the graph, while a closed circle means taht the value belongs to the graph.
Here we can see that the closed circle at x = 0 is on the line at the middle, then we can conclude that f(0) = 0.
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emmas suitcase was extremely heavy so she decided to take some things out and weigh them. she started with a gift that weighed 30 pounds. Then, she took out all of her shower essentials and personal items that weighed 7 1/4 pounds. If her suitcase now weighs 21 2/3 pounds, how much did it weigh when she started?
Answer:
58 11/12
Step-by-step explanation:
Add up each item within the suitcase + the suitcase after taking out the items to find the weight of the suitcase at the beginning.
30 + 7 1/4 + 21 2/3
Convert the fractions to have a common denominator
30 + 7 3/12 + 21 8/12
Add these up to get 58 11/12.
2. Mick recorded the lengths of 10 Steller sea lions. Which length occurs most often?
3. Make a line plot. Draw a dot for each value. Stack dots for values that occur more than once.
Steller Sea Lion Lengths
−2
81/1/21
9 911 9/1/201
Length (in feet)
DATA
Steller Sea Lion Lengths (in feet)
9: 9 8/3/10
9
91/1
8
9 1/1 9 1/1/0
9/1/12
1438
9/3/3
91/1
18
Answer:feet occurs most often. Mick recorded the lengths of 10 Steller sea lions.
Step-by-step explanation:feet occurs most often. Mick recorded the lengths of 10 Steller sea lions.
help with question 17
Answer:
hundredths
Step-by-step explanation:
