Answer:
(0,8)
Step-by-step explanation:
Answer:
(0,8)
Step-by-step explanation:
Philip shoots an arrow from the top of a hill into the ground. the flight of the arrow can be modeled with the quadratic function y=-5x^2+15x+90, where y represents the vertical height of the arrow, in meters, and x represents the time, in seconds. use factoring to find the positive zero of the function. what does this zero represent? then find the maximum value of the function by completing the square. what does the maximum value represent? explain each step in your answer.
Answer:
(a)Time taken to reach the ground, x=6 seconds
(b)Maximum height of the arrow during its flight =101.25 feet
Step-by-step explanation:
Given the quadratic function which models the flight of the arrow:
[tex]y=-5x^2+15x+90[/tex]
Where:
y represents the vertical height of the arrow, in meters; and x represents the time, in seconds.(a)Positive Zero
[tex]-5x^2+15x+90=0\\-5(x^2-3x-18)=0\\-5(x^2-6x+3x-18)=0\\-5(x(x-6)+3(x-6))=0\\-5(x+3)(x-6)=0\\x+3=0\:or\:x-6=0\\x=-3,x=6[/tex]
In 6 seconds, the arrow will hit the horizontal plane, i.e. the ground.
(b)
[tex]y=-5x^2+15x+90\\y-90=-5(x^2-3x)\\y-90-5(\frac{9}{4}) =-5(x^2-3x+(\frac{3}{2} )^2)\\y-101.25=-5(x-\frac{3}{2} )^2\\y=-5(x-\frac{3}{2} )^2+101.25[/tex]
Comparing with the vertex form:
[tex]y=a(x-h)^2+k[/tex]
Our vertex, (h,k)=(1.5, 101.25)
Maximum Value of y=101.25
The maximum value of y represents the maximum height of the arrow during its flight, which is 101.25 feet.
Pls help me math work
Answer:
180.48[tex]ft^{2}[/tex]
Step-by-step explanation:
The area of a rectangle = bh
Area of a circle = π[tex]r^{2}[/tex]
Rectangle = 8 x 10 = 80
Circle = 3.14([tex]8^{2}[/tex]) = 200.96
But because it's a hlaf circle, divide the number by 2
100.48
Now add the numbers together
180.48[tex]ft^{2}[/tex]
A triangle is reduced. A triangle has a base of 16 inches, a height of 12 inches, and a side length of 20 inches. A smaller triangle has a base of 12 inches, a height of 9 inches, and a side length of the blank. Not drawn to scale What is the perimeter of the reduced triangle, in inches?
A.) 15
B.) 21
C.) 36
D.) 48
Answer:
A
Step-by-step explanation:
Answer:
The answer is 15
Step-by-step explanation:
i took the test
Question 12 (Multiple Choice Worth 5 points)
(05.02 MC)
What is the slope-intercept form equation of the line that passes through (5, 7) and (8, 22)?
Oy= -5x + 18
Oy=5x - 18
Oy=-5x - 18
O y = 5x + 18
Answer:
y = 5x - 18
Step-by-step explanation:
Points:
Equation of the line:
y = ax + b
(5; 7) and (8; 22)
(5; 7)
7 = 5a + b
(8; 22)
22 = 8a + b
a and b are the same values:
{- 5a - b = - 7
{8a + b = 22
3a = 15
a = 5
5a + b = 7
5.5 + b = 7
25 + b = 7
b = 7 - 25
b = - 18
Equation:
y = 5x - 18
I Hope I've helped you.
Final answer:
The slope-intercept form equation of the line that passes through the points (5, 7) and (8, 22) is y = 5x + 18, found by first calculating the slope and then using the point-slope form to solve for y.
Explanation:
To find the slope-intercept form of the equation of the line that passes through the points (5, 7) and (8, 22), we first need to calculate the slope (m). The slope is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using our points, this becomes:
m = (22 - 7) / (8 - 5) = 15 / 3 = 5
Now, we use one point and the slope in the point-slope form of the equation, y - y1 = m(x - x1), which becomes:
y - 7 = 5(x - 5) => y - 7 = 5x - 25
Solving for y to get the slope-intercept form, y = mx + b:
y = 5x + (25 - 7) = 5x + 18
So, the correct slope-intercept form equation of the line is y = 5x + 18.
The hypotenuse of a right triangle is 4 feet
longer than the length of the smallest side.
The third side has a length of 64 feet. Find
the length of the hypotenuse.
Answer:
514 feet
Step-by-step explanation:
Just simply use the pythagorean thereom:
a^2 +b^2 = c^2 (or if you are a nerd (a+bi)(a-bi) = c^2)
plug in the values of a, b, and c with the side lengths of the triangle:
x feet, 64 feet, and x+4 feet
x^2 +64^2 = (x+4)^2 , thus x =510
the hypotenuse = x+4 feet = 510 + 4 = 514
ANSWER: 514 feet
describe how to graph point K at (5,4)
Answer & Step-by-step explanation:
[tex]K(5,4)[/tex]
Remember this:
[tex](x,y)[/tex]
[tex](5_{x},4_{y})[/tex]
When you are going to graph a point, you always start along the x-axis (the horizontal), then you move on to the y-axis (vertical). Both of the numbers in K are positive, so we will stay in Quadrant I.
For x, starting at (0,0) move to the right to point 5. From here, move up to the line that has value 4. Mark this spot with a dot and label if needed.
*If the x value is positive, you move to the right. If it is negative, you move to the left.
If the y value is positive, you move up. If it is negative, you move down.
Final answer:
To graph point K at (5,4), draw axes, locate 5 on the x-axis, 4 on the y-axis, and mark the point at the intersection.
Explanation:
To graph point K at (5,4), you start by drawing a set of perpendicular lines representing the x-axis (horizontal) and y-axis (vertical), usually with arrows on each end to indicate that they extend infinitely.
Each axis should be marked with evenly spaced intervals. Locate the number 5 on the x-axis (the horizontal axis) and then move vertically until you're level with the number 4 on the y-axis (the vertical axis).
Plot point K at the intersection of these two points.
This gives you the coordinates of point K where the first number in the parentheses is the position on the x-axis and the second number is the position on the y-axis.
if you know the zeros of a quadratic function, how do you locate the vertex? (Site 2)
Answer:
[tex]\text{(h, f(h)) where h=} \dfrac{x_1+x_2}{2}\\[/tex] , ([tex]x_1,x_2,[/tex] zeros of the polynomial)
Step-by-step explanation:
Given the zeros of a polynomial, [tex]x_1\: and \:x_2[/tex], to determine the vertex, follow these steps.
Find the equation of symmetry x=h where [tex]h=\dfrac{x_1+x_2}{2}[/tex]
Substitute the value of h into the quadratic function f(x) to find the maximum of minimum point.
Therefore, the coordinate of the vertex will be:
[tex]\text{(h, f(h)) where h=} \dfrac{x_1+x_2}{2}[/tex]
Will mark brainliest! Need help (50 points)
Answer:
(-4y,+12y), (z,19z)
Step-by-step explanation:
i got the same question.
What are the constant of proportionality on these two?
Answer:
k = y/x
as a fraction for both
29
80
60
NOTE: Angles not necessarily drawn to scale.
*HELP NEEDED*
Step-by-step explanation:
Hope it helps.
Please rate and mark as brainlist.
Answer:
I'm not sure
Step-by-step explanation:
sorry
Nadine and Calvin are simplifying the expression (StartFraction r Superscript negative 5 Baseline s Superscript negative 3 Baseline Over r Superscript 8 Baseline s Superscript negative 2 Baseline EndFraction) Superscript negative 4. Nadine claims the first step to simplify the expression is to raise the numerator and denominator to the power of 4 to get StartFraction r Superscript negative 20 Baseline s Superscript negative 12 Baseline Over r Superscript 32 Baseline s Superscript 8 Baseline EndFraction. Calvin claims the first step to simplify the expression is to apply the quotient of powers to get (r Superscript negative 13 Baseline s Superscript negative 1 Baseline) Superscript negative 4. Who is correct and why? Nadine is incorrect because she should have applied the quotient of powers rule first. Nadine is correct because she correctly applied the power of a product rule. Calvin is incorrect because he should have applied the power of a product rule first. Calvin is correct because he correctly applied the quotient of powers rule.
Answer:
what is the question
Step-by-step explanation:
plsss give brainliest
The correct answer is Calvin is correct because he correctly applied the quotient of powers rule.
The correct option is (D).
Calvin is correct because he correctly applied the quotient of powers rule.
According to the quotient of powers rule, [tex]\( \frac{a^m}{a^n} = a^{m - n} \).[/tex]
So, in this case:
[tex]\[ \frac{r^{-5}s^{-3}}{r^8s^{-2}} = r^{-5 - 8}s^{-3 - (-2)} = r^{-13}s^{-1} \][/tex]
Then, when you raise this expression to the power of -4:
[tex]\[ (r^{-13}s^{-1})^{-4} = r^{-13 \times -4}s^{-1 \times -4} = r^{52}s^4 \][/tex]
Nadine's approach would result in:
[tex]\[ \left( \frac{r^{-5}s^{-3}}{r^8s^{-2}} \right)^{-4} = \left( \frac{e^{-20}s^{-12}}{r^{32}s^8} \right) \][/tex]
Which is incorrect.
So, the correct answer is D. Calvin is correct because he correctly applied the quotient of powers rule.
complete question given below:
Nadine and Calvin are simplifying the expression ( (r^(-5)s^(-3))/r^8s^(-2) ). Nadine claims the first step to simplify the expression is to raise the numerator and denominator to the power (e^(-20)s^(-12))/r^(32)s^8 . Calvin claims the first step to simplify the expression is to apply the quotient of powers to get (r^(-13)s^(-1))^-4.
Who is correct and why?
A.Nadine is incorrect because she should have applied the quotient of powers rule first.
B.Nadine is correct because she correctly applied the power of a product rule.
C.Calvin is incorrect because he should have applied the power of a product rule first.
D.Calvin is correct because he correctly applied the quotient of powers rule
a triangular metal plate with a triangular metal plate placed in a box with a regular triangular prism with all the side edges 3 dm. It rests on the edge of the base and is inclined to the bottom of the box at an angle of 60 °. Calculate the area of the plate 0.01 dm2 accuracy. Take a look at how the spacing between planes is measured.
Answer:
6.75 dm²
Step-by-step explanation:
All the side edges in the regular triangular prism are 3 dm long. Then, the base of the triangular plate is 3 dm long, and the other two sides are: √[3² + 3²] = 4.24 dm long (a right triangle is made and Pythagorean theorem is applied).
The height of the triangular plate is: √[4.24² + 1.5²] = 4.5 dm long (again Pythagorean theorem is applied)
Area of the triangular plate is: base*height/2 = 3*4.5/2 = 6.75 dm²
The number of birds in a forest is decreasing by 3% every year. In 2000 there were 5,400 birds. Write an equation that represents the number, y, of birds x years after 2000. How many birds will there be in 2025? Round your answer to the nearest whole number.
Answer:
Step-by-step explanation:
This is a Compound interest problem with a decreasing rate. It is given by the formula:
A = P(1 +/- R)^T
Where A = amount after time T
P = principal or initial amount
R = rate of increase or decrease
T = time elapsed
There's +/- because + is used in the case when the amount is increasing at a particular rate and - is used whe the amiunt is decreasing.
In 2000 there were 5,400 birds and the number of birds is decreasing by 3% (0.03) every year.
The number of birds, y, that will be there x years after 2000 will be:
y = 5400( 1 - 0.03)ˣ
2025 is 25 years ahead of 2000, so x = 25
Therefore, the number of birds in 2025 will be:
y = 5400(1 - 0.03)^25
y = 5400(0.97)^25
y = 5400 * 0.467
y = 2522 birds
There will be 2522 birds in 2025.
The equation to represent the number of birds after x years is y = 5,400(1 - 0.03)^x. To find the number of birds in 2025, we use x = 25 in the equation to get y ≈ 3,295 birds.
Explanation:To write an equation that represents the number, y, of birds x years after 2000 with a yearly decrease of 3%, we use the formula for exponential decay, which is y = a(1 - r)^x. Here, a is the initial amount, r is the rate of decrease, and x is the number of years since 2000.
In this case, the initial number of birds in 2000 was 5,400, so a = 5,400, and the rate of decrease is 3%, meaning r = 0.03. The equation becomes y = 5,400(1 - 0.03)^x.
To find out the number of birds in 2025, we calculate x as the number of years from 2000 to 2025, which is 25 years. Thus, the calculation results in y = 5,400(1 - 0.03)^25. After solving, we round the result to the nearest whole number.
Performing the calculation, y ≈ 3,295 birds.
In the school yearbook, it costs $10 per square Inch for advertisements. What is the cost for a full page ad the page measures 8 inches by 11 inches?
8.80
880
80
0.88
Answer:
(b) $880
Step-by-step explanation:
You want the cost of an 8-inch by 11-inch ad at the rate of $10 per square inch.
AreaThe area of the ad is the product of its dimensions:
A = LW
A = (11 in)(8 in) = 88 in²
CostThe cost is $10 for each of those square inches:
($10/in²)×(88 in²) = $880
The cost of the full-page ad is $880, choice B.
If y=-16 when x=4 find x when y=48
Answer:
x= -12
Step-by-step explanation:
Assuming this is a direct variation
y = kx
When y = -16 x =4 we can find k
-16 = k*4
Divide each side by 4
-16/4 = 4k/4
-4 =k
So
y = -4k
Y = 48
48 = -4x
Divide each side by -4
48/-4 = -4x/-4
-12 =x
Solve 12x - 2 = 20.
Round to the nearest ten-thousandth,
Answer:
1.8333
Step-by-step explanation:
12x-2=20
Add 2 to both sides:
12x=22
Divide both sides by 12:
[tex]x=\frac{22}{12}\approx 1.8333[/tex]
Hope this helps!
James has one 10p coin and one 50p coin and some 20p coins
Altogether he has £2.00
how many 20p coins has he got
Answer:I'm not sure how euros work but I'm almost certain there are 18 20p coins
Step-by-step explanation:
Answer:
What does that P suppose to mean and where are your answer choices?
Step-by-step explanation:
What is the horizontal distance from the plane’s starting position to its finishing position???? I will mark brainliest
Answer:
The answer would be 13.3.
Step-by-step explanation:
Use the Pythagorean theorem to find the other distances in the 5, 3, x triangle and the 7, 3, y triangle and add those two answers together plus 3 to get your answer.
Answer:
13.3 kilometers
Step-by-step explanation:
You need to use Pythagorean theorem for x+3+y.
The distance you would be looking for is 4+3+6.3=13.3
PLZZZZZ HELP ME HELP A DUMB CHILD OUT
Answer:
80 inches
Step-by-step explanation:
Pythagorean theorem
Simplify the Following:
⅔ + 2³ - ⅓
a.) 6 ⅓
b.) 8 ⅓
c.) ⁷/2
d.) -6
Answer:
B
Step-by-step explanation:
You have to evaluate the power and calculate the sum or difference in order to get the answer
A hot air balloon went from an elevation of 5,275 feet to an elevation of 3,128 feet in
38 minutes. What was its rate of descent?
The rate of the descent was_____ feet per minute.
Answer:
0.942 ft/s
Step-by-step explanation:
The rate of descent is the rate at which the hot air balloon is descending, that is, how fast it is descending.
We calculate this by finding how far it has moved and then dividing it by the time it took it to descend.
It moved from 5275 ft to 3128 ft. The displacement is:
5275 - 3128 = 2147 ft
The time taken is 38 minutes. In seconds, it is:
38 * 60 = 2280 seconds.
Therefore, the rate of descent is:
2147 / 2280 = 0.942 ft/s
Drag and drop the answer in the box to correctly complete the sentence.
A probability Response area indicates a chance event is most likely to occur.
answer: close to 0 close to 1 of 10 close over 100 reward: five points and cashapp:5$
A probability close to 1 indicates a chance event is very likely to occur. The probability of such an occurrence is a number. The correct option is option A.
What is probability?The probability of such an occurrence is a number used in science to describe how likely it is that the event will take place. In terms of percentage notation, it really is represented by a value between 0 and 1, or between 0% and 100%.
The odds of two complementing events A and B happening, either A happens or B happens, sum up to 1. outcomes are complimentary, the likelihood of "heads" is equal to the likelihood of "tails," and the likelihood of any one of the two possible outcomes is equal to half. A probability close to 1 indicates a chance event is very likely to occur.
Therefore, a probability close to 1 indicates a chance event is very likely to occur. The correct option is option A.
To know more about probability, here:
https://brainly.com/question/12629667
#SPJ3
x^2 – 3x – 7 = 0
Solve the quadratic equation using the quadratic formula.
Answer:
x^2-3x-7=0. x2−3x−7=0 x 2 - 3 x - 7 = 0.
Step-by-step explanation:
x^2-3x-7=0. x2−3x−7=0 x 2 - 3 x - 7 = 0. Use the quadratic formula to find the solutions. −b±√b2−4(ac)2a - b ± b 2 - 4 ( a c ) 2 ...
Answer:
x=3/2 ± √37/2
Step-by-step explanation: the answer
please help me! i’ll give brainliest!
Find the x- and y-intercepts of the parabola y=−2x^2−5x+1
Answer:
View answer in the photo.
Step-by-step explanation:
To make fruit punch, Tyrone needs 3 3/8 quarts of orange juice and 3 3/4 quarts of cranberry juice.
How many quarts of juice does he need in all?
Please help me! It would be very much appreciated
Answer:
Answer is x = 100 degrees.
Step-by-step explanation:
Vertically opposite angles are equal.
Then value of x is 100 degrees.
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
Step-by-step explanation:
[tex]x = 100 \: \: degrees[/tex]
(vertically opposite angles)hope this helps
brainliest appreciated
good luck! have a nice day!
How is factoring a trinomial different than factoring a number?
Answer:
Hope this answers the question.
Step-by-step explanation:
Factoring a number: If you use the number 10, for example, you have to find all the factors to factor it. 1, 2, 5, 10.
Factoring a trinomial: If you use the trinomial x^2 + 16 + 64, for example, to factor it you need to first find what numbers multiply up to 64 and also add up to 16. In this case, those numbers are 8, and so you get (x + 8)^2.
Final answer:
Factoring a number involves breaking it down into its prime factors, a straightforward process within the real number system. Factoring a trinomial, particularly in algebra, requires finding binomials that, when multiplied, return the original trinomial and can extend to complex numbers, guided by the fundamental theorem of algebra.
Explanation:
Factoring a trinomial and factoring a number are two very different processes within the realm of mathematics. When we talk about factoring a number, we refer to breaking it down into its prime factors, which are the prime numbers that multiply together to give the original number. For instance, factoring the number 10 would give us 2 and 5, since 2 x 5 = 10. This process is straightforward and applies to the number system.
On the other hand, factoring a trinomial involves finding two binomials that, when multiplied together, result in the original trinomial. This is more commonly encountered in algebra, especially when dealing with second-order polynomials (quadratics). For example, factoring the trinomial x² + 5x + 6 involves finding two binomials (x + 2) and (x + 3), since (x + 2)(x + 3) = x² + 5x + 6. Furthermore, factoring trinomials can extend into complex numbers where every nth-order polynomial can be factored into n linear factors in the complex number system, according to the fundamental theorem of algebra.
In summary, factoring a number focuses on prime factorization within the real number system, while factoring a trinomial involves algebraic manipulation that can extend into handling complex numbers and requires an understanding of both real and complex number systems.
helppp!!!!!! asap !!!!!!!
Answer: B
Step-by-step explanation:
Ice cream sandwiches are wrapped in white paper before they are put in a box to be sold. How many ice cream sandwiches can be wrapped with 500 square inches of paper?