The zeros of the function y = -4(x-3)² + 8 are -1 and 7 and the intercept is 13
What are zeros of a function?The zero of a function is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.
when y = 0
-4(x-3)² +8 = 0
expanding the equation
-4( x²-6x +9)+8 = 0
-4x² +24x -36 +8 = 0
-4x²+24x -28 = 0
divide through by 4
-x²+6x-7 = 0
-x²+7x -x -7 = 0
(-x²+7x)(-x-7) = 0
-x( x-7) 1(x-7)
1-x = 0 or (x-7 )= 0
x = -1 or 7
therefore the zeros are -1 and 7
to find the intercept:
x= 0
y = -4(0-3)²+8
y =-4+9+8
y = 13
therefore the intercept is 13
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solve step by step:
3x - 2y = -22
2x + y = -3
the answer is -13. And this is why, because the negative sign is bigger so same sign add keep the same sign that’s why I got -13
pedro is selling apples ata farmers market he starts with 35 1/2 pounds of apple he sells half of them in the morning 8/9 of what is left in the afternoon and 3/4 of whats left in the evening how many pounds of apple id pedro not sell what fraction of the total amount of the apples did he not sell
Carlito is competitive, though, and his best friend at school brags that he manages to save $250 every month to put toward college. How would you recommend Carlito adjust his budget in order to out-save his friend?
Help
__________________
The minimum = (-11, -2)
And the maximum = (2, 5).
What is differentiation?Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables.
Given:
The function,
f(x) = ∛(x + 3).
The graph of the function is given in the attached image.
f'(x) = d/dx{∛(x + 3)}
= 1/{3(x + 3[tex])^{2/3}[/tex]}
The critical point = (-3, 0)
The minimum = (-11, -2)
And the maximum = (2, 5).
Therefore, all the required values are given above.
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If x and y are in direct proportion and y is 6 when x is 12, find y when x is 2.
The relationship between x and y is y = (1/2)x. When x is 2, then the value of 'y' is 1.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
If x and y are in direct proportion. Then the equation is given as,
y ∝ = x
y = kx
At x = 12 and y = 6, then the value of 'k' is given as,
6 = 12k
k = 1/2
Then the equation is given as,
y = (1/2)x
If the value of the variable 'x' is 2. Then the value of y is given as,
y = (1/2) 2
y = 1
The relationship between x and y is y = (1/2)x. When x is 2, then the value of 'y' is 1.
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36 x 5 +59 x(234)(51)
the simplified Answer to the given expression 36 x 5 +59 x(234)(51) will be 7,04,286.
What is simplification?Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.
Given, an expression 36 x 5 +59 x(234)(51)
Simplifying using PEMDAS
=> 36 x 5 +59 x(234)(51)
First, we will open a bracket
=> 36 * 5 + 59 * 11934
Now multiple of the given terms:
=> 180 + 704106
Addition of the last two-term
=> 7,04,286
Therefore, the simplified Answer to the given expression will be 7,04,286.
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Select the correct answer from each drop-down menu. The number - 7/5 is
We can conclude, the number -7/5 is less than the number 1 1/5.
How to know whether a fraction is greater or less than other?One of the ways to know how a fraction compares to another is by simplifying the fraction, which can be done by dividing the numerator by the denominator.
Let's simplify the fractions given:
-7/5 = -1.4
-1 1/5 = 1 + 0.2 = -1.2
Moreover, in the case of negative numbers those that are closer to 0 are greater. Based on this, -1.2 is greater than -1.4, which means -7/5 is less than the number 1 1/5.
Note: This question is incomplete; here is the missing section:
The number -7/5 is less or greater than the number 1 1/5.
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A bicycle manufacturer currently produces 256,000 units a year and expects output levels to remain steady in the future. It buys chains from an outside supplier at a price of $1.80 a chain. The plant manager believes that it would be cheaper to make these chains rather than buy them. Direct in-house production costs are estimated to be only $1.50 per chain. The necessary machinery would cost $206,000 and would be obsolete after 10 years. This investment could be depreciated to zero for tax purposes using a 10-year straight-line depreciation schedule. The plant manager estimates that the operation would require $51,000 of inventory and other working capital upfront (year 0), but argues that this sum can be ignored since it is recoverable at the end of the 10 years. Expected proceeds from scrapping the machinery after 10 years are $15,450. If the company pays tax at a rate of 35% and the opportunity cost of capital is 15%, what is the net present value of the decision to produce the chains in-house instead of purchasing them from the supplier?
Answer:
NPV = -$57,937
Step-by-step explanation:
NPV = ($1.50 - $1.80) * 256,000 - $206,000 - $51,000 + $15,450 / (1 + 0.15)^10 - ($206,000 + $51,000) * 0.35
The mass of a radioactive substance follows a continuous exponential decay model, with the decay rate parameter 4% per day. A sample of this radioactive substance has an initial mass of 2.05 kg. Find the mass of the sample after four days. Round your answer to two decimal places.
The mass of the sample after 4 days is 1.54 kg.
What is exponential decay?Exponential decay can be defined as the process in which a quantity decreases over time with the rate of decrease becoming proportionally smaller as the quantity gets smaller.
The formula for exponential decay is given by:
m(t) = m0 * e^(-kt)
where m(t) is the mass of the substance after time t
M0 is the initial mass
k is the decay rate parameter
E is the base of natural logarithms
Plugging in the values:
m(4) = 2.05 * e^(-0.04 * 4)
m(4) = 1.54 kg
Therefore, The mass of the sample after 4 days is 1.54 kg.
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PLEASE HELP!!
the variables x and y have a proportional relationship and y=40 when x=30 what is the value of x when y=50
Refer to the given image
please make it right for a 100 points
Kevin was solving for the area of the triangle below. 8 in: 5 in The formula for area of a triangle is A = =bh. Kevin's answer for the area of this triangle was 40 inches?. Is Kevin's solution correct? Why or why not? If not, what was his mistake? If not, what is the correct solution for the area of this triangle?
Kevin's solution is incorrect because he used wrong formula.
Correct area of triangle = 20 square inches.
What is area of triangle?The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height,
i.e. A = 1/2 × b × h
Given,
Height of triangle h = 8 inches
Base of the triangle b = 5 inches
Formula for area of triangle A = 1/2(b h)
A = 1/2 (8 × 5)
A = 40/2
A = 20 square inches.
Area by given formula for area of the triangle A = b h
A = 8 × 5
A = 40
Since actual area of the triangle is 20 square inch, Kevin found the area with wrong formula.
Actual area of triangle is 20 square inches.
Hence, Kevin's solution is incorrect, as the formula used is wrong.
20 square inches is correct area of the triangle.
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In the given diagram TP and TR are tangents. IfZPTR = 40°, find the value of ZPQR.
Note that the angle labeled ∠PQR is given as 70°
First, note that the Lengths of tangents drawn from external points to a circle are equal in length. This means that:
Length of PT = Lenght of TR
This makes Δ TPR and Isosceles Triangle.
This also makes ∠P = ∠R..............................1
Thus:
∠P + ∠R + ∠T = 180°
Given expression 1 above,
we can say:
x + x + 38° = 180°
Thatis 2x = 180 - 40
2x = 140°
x = 140/2
x = 70°
Note that Line TP is parallel to Line QR and Line PQ is a transversal line. Thus, ∠P and ∠Q are co-interior angles. This means that:
∠P + ∠Q = 180°
Recall that:
70 + 40 + ∠Q = 180°
∠Q = 180 -70 -40
∠Q = 70°
Thus: ∠ PQR = 70°
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Full Question:
See attached image.
For a project in her Geometry class, Morgan uses a mirror on the ground to measure the height of her school’s football goalpost. She walks a distance of 13.85 meters from the goalpost, then places a mirror flat on the ground, marked with an X at the center. She then walks 4.25 more meters past the mirror, so that when she turns around and looks down at the mirror, she can see the top of the goalpost clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.15 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.
Rounding to the nearest hundredth of a meter, the height of the goalpost is 3.74 meters.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Let's call the height of the goalpost "h". We can use similar triangles to solve for h. Morgan walks a total of 13.85 and placed the mirror and walk 4.25 more, let d = 13.85.
The mirror forms a right triangle with the height of the goalpost, the distance from her eyes to the ground, and the distance d.
So, we have:
h / d = 1.15 / 4.25
Solving for h:
h = (1.15 ×13.85 ) / 4.25
h = 6371 / 1700
Rounding to the nearest hundredth of a meter, the height of the goalpost is 3.74 meters.
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1. X2 +6x +3=0
2.5^2726-6=0
3.12-8+-5:0
4.X(X+8)=-20
5.x- +4x-2=0
Help solve with explaining
1) X2 + 6x + 3 = 0. is resolved using the discriminant technique, and the value of s for the second equation, 52 + 2s - 6 = 0, is 9.5.
what is equation ?The statistic is said to be in its simplest form is divided into its smallest equivalent fraction. What to do to find the most basic form. Look for common factors in the denominator and numerators. Confirm a fractional integer to verify if it qualifies as a prime number. A statement having two equal sides and an equaled sign in the middle is called an equation in mathematics. The general form of any equation contains the diplomas of all the variables in descending order. The conventional form of an equation is an x + b = 0. The general form of a linear function with two variables is an x + b y + c = 0. (or something similar). An identification holds true no matter what value is given to the variables.
given
equation 1 ) X2 +6x +3=0
by discriminant method
x =(6+√48)/2
=3+2√ 3
= 6.464.
equation 2) 5^2 + 2s - 6 = 0
= 25 + 2s - 6 = 0
= 19 = - 2s
s = 9.5
1) X2 + 6x + 3 = 0. is resolved using the discriminant technique, and the value of s for the second equation, 52 + 2s - 6 = 0, is 9.5.
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Does anyone know how to do this
well, the line y = -5 is simply a horizontal line, a perpendicular line to that will simply be a vertical one, Check the picture below.
Use the definition of continuity and the properties of limits to show that the function
g(x) = (x2 - 3x - 10)(x2 + 2x2 - 5x + 4) is continuous at x = -1.
The given function
g(x) = [x² - 3x -10][x²+ 2x² -5x +4 ]
is continuous at x = -1,
What is continuity ?In mathematics, The function is called as continuous at the particular value of x, if right hand limit, left hand limit and the value of function at x all are equal.
RHL = LHL = F(x)
Limit exist and continuous
Given that,
F(x) = [x² - 3x -10][x²+ 2x² -5x +4 ]
To check whether it is continuous at x = -2
First taking LHL,
[tex]\lim_{h \to \00}[/tex] [(-1-h)² - 3(-1-h) -10][(-1-h)²+ 2(-1-h)² -5(-1-h) +4 ]
[tex]\lim_{h \to \00}[/tex] [(-1-0)² - 3(-1-0) -10][(-1-0)²+ 2(-1-0)² -5(-1-0) +4 ]
⇒ -6 x 12
⇒ -72
Now, taking RHL
[tex]\lim_{h \to \00}[/tex] [(-1+h)² - 3(-1+h) -10][(-1+h)²+ 2(-1+h)² -5(-1+h) +4 ]
[tex]\lim_{h \to \00}[/tex] [(-1+0)² - 3(-1+0) -10][(-1+0)²+ 2(-1+0)² -5(-1+0) +4 ]
⇒ -6 x 12
⇒ -72
The value at x = -1
F(-1) = [(-1)² - 3(-1) -10][(-1)²+ 2(-1)² -5(-1) +4 ]
⇒ -6 x 12
⇒ -72
RHL = LHL = F(-1)
Hence Proved, the function is continuous at x = -1
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in order to be approved for a home loan a lending institution uses the standard 28/36 ratio. Jared's loan application is for $180,000. Jared has an annual salary of $56,400, a car
mayment of $270 per month and he has a monthly student loan payment of $90. How likely is Jared to be approved for the home loan?
O Very likely, recurring debt is considerably less than what is allowed.
O Somewhat likely, recurring debt is very close to what is allowed.
O Not likely, recurring debt is higher than what is allowed.
O There is not enough information given to determine the answer.
The likelihood of getting the loan cannot be ascertained. Hence the answer is D. There is not enough information given to determine the answer.
What is the information aboutTo determine whether Jared is likely to be approved for the home loan, it would be necessary to calculate his debt-to-income ratio, which is one of the main factors that lenders consider when evaluating loan applications. This ratio is calculated by dividing a person's total recurring monthly debt payments by their gross monthly income. If the debt-to-income ratio is higher than 28% or 36% (depending on the lender), the loan application may be declined.
Based on the information provided, it is not possible to determine Jared's debt-to-income ratio. In order to determine the ratio, it would be necessary to know Jared's gross monthly income, which is not provided. Therefore, it is not possible to say whether Jared is very likely, somewhat likely, or not likely to be approved for the home loan.
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Jill and Matt plan to get their homework finished within one hour. Matt
completes his Math homework in 3/5 hour. Jill completes her Math
homework in 5/6 hour remaining. Who completes the homework faster,
and by how many minutes?
Answer: Matt completes his homework faster than Jill by 14 minutes
Step-by-step explanation:
5*12= 60 so if I multiply 3 by 12 I get how many minutes it took Matt to finish her homework. (which was 36 minutes)
6*10=60 so if I multiply 5 by 10 I get how many minutes it took Jill to finish her homework (which was 50 minutes)
50 minus 36 is a difference of 14
0
9
You deposit $200 each month into an account earning 7% interest compounded monthly.
a) How much will you have in the account in 35 years?
https://ohm.lumenlearning.com/assess2/?cid=69660&aid=51 5/#/skip/
b) How much total money will you put into the account?
$
c) How much total interest will you earn?
$
Question Help: Video 1 Video 2
Answer:
Step-by-step explanation:
The monthly compound interest formula.
Future Value = monthly deposit x (1 + r) - 1/r
r = .07/12 = .00583
n = total number of time for compound = 35 years x 12 months/1 year = 420 months
PMT = monthly deposit = $200
Future Value = $200 x (1 + .00583)⁴²⁰ - 1/.00583
Future Value = $394,001.64 in 35 years
Total money you put into the account.
$200 x 420 months = $84,000
Total interest earned.
$394,001.64 - $84,000 = $310,001.64
Suppose you deposit $1000 in a college fund that pays 7.2% interest compounded annually. Find the account balance after 5 years.
Answer:
To find the account balance after 5 years, we need to calculate the compound interest earned during this period. The formula for compound interest is:
A = P × (1 + r/n)^(nt)
where:
A = the final amount of the investment
P = the principal investment amount ($1000)
r = the annual interest rate (7.2%)
n = the number of times that interest is compounded per year (1)
t = the number of years the investment is held (5)
So, plugging in the values into the formula, we get:
A = 1000 * (1 + 0.072/1)^(1 * 5)
A = 1000 * (1.072)^5
A = 1000 * 1.44444444
A = $1444.44
So, the account balance after 5 years would be $1444.44.
Answer:
Step-by-step explanation: I could mostly say $36,000. How I did it was:
1000x7.2x5=36,000
Could you find this helpful???
Swimming Pool On a certain hot summer's day, 364 people used the public swimming pool. The daily prices are $1.75 for children and $2.25 for adults. The receipts for admission totaled $707.50. How many children and how many adults swam at the public pool that day?
1. There were _ children at the public pool.
2. There were _ adults at the public pool.
Step-by-step explanation:
x = number of children
y = number of adults
x + y = 364
x = 364 - y
1.75x + 2.25y = 707.5
using the first equation in the second :
1.75(364 - y) + 2.25y = 707.5
637 - 1.75y + 2.25y = 707.5
637 + 0.5y = 707.5
0.5y = 70.5
y = 70.5/0.5 = 141
x = 364 - y = 364 - 141 = 223
there were 223 children at the public pool.
there were 141 adults at the public pool.
Does 4/2750 reduce into a smaller fraction
7. Write and graph an exponential function frepresented by the table
Then compare the graph to the graph of the parent function.
Answer:
f(x) = 2[tex](\frac{1}{2}) ^{x}[/tex]
Step-by-step explanation:
The y intercept is 2 where in the parent function it is 1. In the parent function, as x is increasing y is increasing. In this function as the x is increasing the y is decreasing.
Can you help me? I need to do this IXL ASAP
Answer:
u=20
Step-by-step explanation:
Bisecting Bakery sells cylindrical round cakes. The most popular cake at the bakery is the red velvet cake. It has a radius of 13 centimeters and a height of 15 centimeters.
If everything but the circular bottom of the cake was iced, how many square centimeters of icing is needed for one cake? Use 3.14 for π and round to the nearest square centimeter.
A. 531 cm2
B. 612 cm2
C. 1,755 cm2
D. 2,286 cm2
The number of square centimeters of icing that would be needed for one cake is equal to: C. 1,755 cm².
How to determine the surface area of the cylindrical round cakes?Since everything but the circular bottom of the cake was iced, the number of square centimeters of icing that would be needed for one cake can be calculated by using this mathematical expression:
Total surface area of cake = Curved surface area of cake + area of the top
Total surface area of cake = 2πrh + πr²
Where:
h represents the height.r represents the radius.By substituting the given parameters into the total surface area of cake formula, we have;
Total surface area of cake = (2 × 3.14 × 13 × 15) + (3.14 × 13²)
Total surface area of cake = 1224.6 + 530.66
Total surface area of cake = 1755.26 ≈ 1755 square centimeter.
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Answer: C. 1,755 cm2
Hope this helps
Please help me answer this 20 POINTS!!!
How does rewriting radicals in different forms help you communicate your answer?
We can write radicals [tex]9^{\frac{3}{2}[/tex] as [tex](3^2)^{\frac{3}{2}[/tex] forms to help us communicate our answers.
What are surds and indices?We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,
The other type of radicals are indices where a number is raised to such power that is greater than one.
Suppose, We have a radical [tex]16^{\frac{1}{4}[/tex].
Now, We know 2⁴ = 16.
So, We can rewrite [tex]16^{\frac{1}{4}[/tex] as [tex](2^4)^{\frac{1}{4}[/tex] and multiply the exponents which
results to 1.
Again say we have [tex]9^{\frac{3}{2}[/tex] and we know 3² = 9, Se we can rewrite [tex]9^{\frac{3}{2}[/tex] as [tex](3^2)^{\frac{3}{2}[/tex] , and the exponent multiplies to 3 so it is now 3³ which is 27.
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A local hamburger shop sold a combined total of 553 hamburgers and cheeseburgers on Wednesday. There were 53 more cheeseburgers sold than hamburgers. How many hamburgers were sold on Wednesday?
hamburgers
Answer: Let's call the number of hamburgers sold "x". Then the number of cheeseburgers sold would be x + 53. The total number of hamburgers and cheeseburgers sold is 553, so we can set up the equation:
x + (x + 53) = 553
Expanding the left side:
2x + 53 = 553
Subtracting 53 from both sides:
2x = 500
Finally, dividing both sides by 2:
x = 250
So on Wednesday, 250 hamburgers were sold.
Step-by-step explanation:
Examine the triangle below, find the mZD =
[Select]
7.
V
[Select]
V
,m
, m/M = 66.6
The measure of angle D, m∠D, found using the specified lengths of the three sides of the triangle and the law of cosines is; m∠D = 75.7°
What is the law of cosines?The law of cosines specifies the relationship between the measures of an angle, and the lengths of the three sides of a triangle. Specifically, the law of cosines states that the square of the length of a (reference) side of a triangle, is equivalent to the sum of the squares of the lengths of the other two sides, less the product of 2, the lengths of the other two sides and the cosine of the angle opposite to the reference side.
Mathematically, the law of cosines can be presented as follows;
a² = b² + c² - 2·b·c·cos(A)Where;
a, b, and c are the lengths of the three sides of the triangle
Angle A, ∠A, is the opposite angle to side a.
Therefore, according to the law of cosines, we get;
38² = 36² + 24² - 2 × 36 × 24 × cos(∠D)
2 × 36 × 24 × cos(∠D) = 36² + 24² - 38² = 428
2 × 36 × 24 × cos(∠D) = 428
cos(∠D) = 428/(2 × 36 × 24) = 428/1728 = 107/432
cos(∠D) = 107/432
m∠D = arccos(107/432) ≈ 75.7°
The measure of angle D, m∠D ≈ 75.7°
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