(a) The function in standard form is f(x) = -2x² + 4x + 5.
(b) The height of the ball when it is thrown is 5 feet.
(c) The horizontal distance from the point where the ball is thrown to the highest point that the ball reaches is 1 foot.
What is the function of ball's motion?
To write the function in standard form, we need to expand the square and simplify the expression:
f(x) = -2(x - 1)² + 7
f(x) = -2(x² - 2x + 1) + 7
f(x) = -2x² + 4x - 2 + 7
f(x) = -2x² + 4x + 5
B. The height of the ball when it is thrown is the y-intercept of the function, which occurs when x = 0. So we can find the height by plugging x = 0 into the function:
f(0) = -2(0)² + 4(0) + 5
f(0) = 5
C. The highest point that the ball reaches is the vertex of the parabola, which occurs at x = 1 (from the given vertex form). To find the height of this point, we can plug x = 1 into the vertex form of the function:
f(1) = -2(1 - 1)² + 7
f(1) = -2(0) + 7
f(1) = 7
Therefore, the highest point that the ball reaches is 7 feet above the ground. The horizontal distance from the point where the ball is thrown to this point is the distance between the point (0,5) and the vertex (1,7), which is 1 unit.
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The function f(t) = 930(0.9965) represents the change in a quantity over t hours. What does the constant 0.9965 reveal about the rate of change of the quantity?
The constant 0.9965 is the rate of change per hour. Specifically, it represents the factor by which the quantity changes every hour. In this case, the factor is less than 1, indicating that the quantity is decreasing over time.
To see how this rate of change works, consider an example:
If the initial quantity is 930, after one hour the quantity will be:
f(1) = 930(0.9965) ≈ 926.20
That is, the quantity has decreased by a factor of 0.9965, or about 0.35%.
After two hours, the quantity will be:
f(2) = 930(0.9965)^2 ≈ 922.42
That is, the quantity has decreased by a factor of 0.9965 twice, or about 0.70%.
So the constant 0.9965 reveals the rate of change of the quantity, which is a decrease of about 0.35% per hour.
LMX is an equilateral triangle . The height, LW, of the triangle is 12in. What is the perimeter of LMX? 4 square root of 3. 8 square root of 2. 24 square root of 3. 36 square root of 2
The perimeter of the triangle is 36√2
How to determine the perimeter of the rectangleFrom the question, we have the following parameters that can be used in our computation:
height = 12
Also, we understand that the triangle is an equilateral triangle
This means that the other sides are
Sides = 12√2
The perimeter is then calculated as
Perumeter =3 * Sides
So, we have
Perimeter =3 * 12√2
Evaluate
Perimeter = 36√2
Hence, the perimeter is 36√2
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72f - 12g = 96 and 6f -2g =10 please gives steps and anwsers
Answer:
(f,g)=(1,-2)
Step-by-step explanation:
72f-12g=96, 6f-2g=10
72f-12g=96
f=5/3+1/3g
72(5/3+1/3g)-12g=96
g=-2
f=5/3+1/3x(-2)
f=1
(f,g)=(1,2)
two sides of a triangle have lengths of 3 and 10 meters. how long could the third side be? explain.
Answer: 3 + 3 adds up to 6, which is less than 10.
Step-by-step explanation:
Which numbers have line symmetry?
2
3
7.8
4
9
The requried number that consists of the line of symmetry is 3. Option B is correct.
What is a line of symmetry?A line of symmetry is defined as the line that bisects the entity in two equal symmetrical halves.
here,
Given numbers,
2, 3, 7.8, 4, 9 since the line of symmetry for the given number would be that line that bisects the shapes of the given number in a mirror-like symmetry so, the only number given the mirror-like symmetry when a line passes through its center is 3.
Thus, the requried number that consists of the line of symmetry is 3. Option B is correct.
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∠A=___° Round your answer to the nearest hundredth.
The measure of ∠A is 37.6°. Angle is a geometric figure that can be described as the amount of rotation.
What is angle?A figure produced by two rays, line segments, or lines that have a same endpoint is called an angle. It is measured in degrees, with a complete 360-degree angle. The Greek letter theta is commonly used to represent it. An angle can be acute (less than 90 degrees), right (90 degrees), obtuse (greater than 90 degrees but less than 180 degrees), straight (180 degrees), or reflex (more than 180 degrees).
∠A is an angle measure and is commonly represented by the symbol "∠A". calculate the measure of ∠A, an angle must be given in degrees. The answer is then rounded to the nearest hundredth. For example, if the angle measure of ∠A is 37.58°, then the answer would be 37.6°.
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Can someone help me ASAP. I will give brainliest if possible. Due today.
Part A: What type of figure is shown above
Part B: Find the surface area of the figure
Part C: Show your work to support your answer in part B
a. The type of figure shown is a triangular prism.
b. The surface area of the figure is 118.5 sq. in.
What is a triangular prism?A triangular prism is a 3 dimensional shape which has 2 triangular surfaces and a rectangular base. It has 5 surfaces in total.
Considering the given figure in the question, we have;
a. The type of figure shown is a triangular prism.
b. The surface area of the prism can be deduced as follows;
area of one of its triangular surfaces = 1/2*base*height
= 1/2*5*1.7
= 4.25 sq. in.
area of its base = length x width
= 10x 5
= 50 sq. in.
area of one of its slant sides = length x width
= 10 x 3
= 30 sq. in.
Therefore, the surface area of the figure = (2*4.25) + 50 + (2*30)
= 8.5 + 50 + 60
= 118.5 sq. in.
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How do you find the hight of a triangular pyramid?
use pythagorean theorem : a²+b²=c²
These tables represent the relationships between x and y for two different sets of data.
Which statements correctly describe the relationships between x and y for each table?
A) Table A represents a multiplicative relationship because y is 2.5 times x, and Table B represents an additive relationship because y is 2 more than x.
B) Both tables represent additive relationships. In Table A, y is 1.5 more than x, and in Table B, y is 2 more than x.
C) Table A represents an additive relationship because y is 1.5 more than x, and Table B represents a multiplicative relationship because y is 3 times x.
Table A represents an additive relationship because , y, is 1.5 more than , x, , and Table B represents a multiplicative relationship because , y, is 3 times , x, .
D) Both data sets represent multiplicative relationships. In Table A, y is 2.5 times x, and in Table B, y is 3 times x.
So the solution of the given question is, the correct answer is D) Both data sets represent multiplicative relationships. from the given conditions.
What is Multiplicative relationships?In mathematics, a multiplicative relationship between two variables means that the ratio of their values remains constant as the values of the variables change. In other words, the product of the two variables is a constant. For example, if we have two variables x and y such that xy = k, where k is a constant, then x and y have a multiplicative relationship. If we increase the value of one variable, we must decrease the value of the other variable proportion in order to maintain the constant product. This type of relationship is often seen in situations involving rates, ratios, and proportions, such as in growth or decay processes, population dynamics, and financial calculations.
In Table A, y is 2.5 times x, and in Table B, y is 3 times x. In both tables, the relationship between x and y is a constant ratio, which is a characteristic of multiplicative relationships. In Table A, the ratio of y to x is always 2.5, meaning that y is always 2.5 times greater than x. In Table B, the ratio of y to x is always 3, meaning that y is always 3 times greater than x. Therefore, both tables represent multiplicative relationships between x and y.
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a car traveling at 10m/s starts to decelerate steadily. It comes to a complete stop in 10 seconds. What is the acceleration?
Answer: 1m/s
Step-by-step explanation: Accleration = Speed/Time
10/10 = 1
Flagpole a and flagpole c are both casting a shadow that ends at point s.
The distance (x) between the flagpoles is 12 ft.
The distance (y) from flagpole c to point s is 10 ft.
The height of flagpole a is 13.2 ft.
What is the height of flagpole c?
The height of flagpole C is approximately 6.1 feet.
What do you mean by Distance?Distance is a numerical measurement of how far apart or how far away objects or locations are from each other. It is a physical quantity that is usually expressed in units such as meters, kilometers, miles, or feet. Distance is a scalar quantity, meaning it only has magnitude and no direction.
The distance between two points is typically calculated using a formula, such as the distance formula in Euclidean geometry, which involves taking the square root of the sum of the squares of the differences in the coordinates of the two points.
Let's start by drawing a diagram of the situation:
A
|
|
|
|
|
|
|
-----------S-----------C
We can see that the triangles ASC and ABC are similar, since they have the same angles (90 degrees at S and a common angle at A). Therefore, we can use proportions to find the height of flagpole C:
AC SC
-- = --
AB AS
Substituting the given values, we get:
AC 10
-- = --
AB AB + 12
We can solve for AB by noting that the height of flagpole A is the sum of the heights of AB and BC:
13.2 = AB + BC
Solving for BC, we get:
BC = 13.2 - AB
Substituting this into the first equation, we get:
AC 10
-- = --
AB AB + 12
AC = 10(AB)/(AB + 12)
Now we can substitute the value we found for AB:
AC = 10(13.2 - BC)/(13.2 - BC + 12)
AC = 10(13.2 - BC)/25.2
We still need to find BC, which we can do by using the fact that the triangles ABC and ASC are similar:
BC/AB = SC/AS
Substituting the given values, we get:
BC/AB = 10/22
BC = 10AB/22
Substituting this into the equation for AC, we get:
AC = 10(13.2 - 10AB/22)/25.2
Now we can solve for AB:
13.2 = AB + 10AB/22
AB = 7.92
Finally, we can substitute this into the equation for AC:
AC = 10(13.2 - 10(7.92)/22)/25.2
AC = 6.1
Therefore, the height of flagpole C is approximately 6.1 feet.
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7 times as much as the sum of 1 third and 4 fifths
The value of the expression is [tex]\frac{63}{20}[/tex].
What is an expression?An expression contains more than two variables or numbers with the mathematical operation.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
[tex]\frac{1}{4}[/tex] and [tex]\frac{4}{5}[/tex]
Now,
Simplify.
= 7 x [tex]\frac{1}{4}[/tex] + [tex]\frac{1}{5}[/tex]
= 7 x [tex]\frac{5+4}{20}[/tex]
= 7 x [tex]\frac{9}{20}[/tex]
= [tex]\frac{63}{20}[/tex]
Thus,
[tex]\frac{63}{20}[/tex] is the expression.
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Hong made 162 for 9 hours of work. At the same rate, how much would he make for 13
hours of work?
Since Hong made 162 dollars for 9 hours of work, we can set up the proportion:
162 dollars / 9 hours = x dollars / 13 hours
where x is the amount of money Hong would make for 13 hours of work.
To solve for x, we can cross-multiply and simplify:
162 dollars × 13 hours = 9 hours × x dollars
2106 = 9x
x = 234
Therefore, at the same rate, Hong would make 234 dollars for 13 hours of work.
Need help???!!!! Please
Reason:
-2 * 2 = -4
-2 + 2 = 0
These values are found through trial and error. The order of -2 and 2 doesn't matter.
Bella and George each ordered a
personal pan pizza. Bella ate of 1
4th
Pizza and George ate
7
8th of his pizza. How much more did George eat
Answer: 5/8
Step-by-step explanation:
We can make the fractions easier to read by changing 1/4 to 2/8, simply by multiplying the fraction by 2/2.
2/8 : 7/8
now you can see how much more George ate.
7/8 - 2/8 = 5/8
George ate 5/8 more than Grace.
Design an algorithm to find all the common elements in two sorted lists of numbers.
In this using the knowledge of computational language in python, we have that this code will be written as:
Here's an algorithm in pseudocode that you can use to find all the common elements in two sorted lists of numbers:
Input: two sorted lists A and B of size N and M respectively.
Output: a list C of all common elements in A and B.
C = [ ]
i = j = 0
while i < N and j < M:
if A[i] == B[j]:
C.append(A[i])
i += 1
j += 1
else if A[i] < B[j]:
i += 1
else:
j += 1
return C
In this algorithm, two pointers i and j are used to traverse both lists A and B. At each step, the algorithm compares the elements at the current positions of i and j in A and B respectively. If they are equal, it means the element is common to both lists, so it is added to the result list C. If the element in list A is less than the element in list B, i is incremented to move to the next element in list A. Similarly, if the element in list B is less, j is incremented to move to the next element in list B.
The algorithm continues this process until either one of the lists is fully traversed.
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Miriam is making a large banner in the shape of a trapezoid.
What is the area of the banner?
Answer:
A=a+b/2 x h
Step-by-step explanation:
The area for a trapezoid is a+b divided by 2, multiplied by the height.
Since there are no lengths given, I cannot be solved.
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Hope it helped!
How to rewrite 6x-18y=-72 in slope intersept form
Answer:
y=1/3x+4
Step-by-step explanation:
Yep
Help please help help help
Other things constant, how will an increase in the wage of teenagers affect the market for fast food hamburgers will cause the supply of fast food hamburgers will increase, leading to an increase in price of hamburgers. Option A
What is supply?supply is the amount of a resource that firms, producers, laborer, providers of financial assets, or other economic agents are willing and able to provide to the marketplace or to an individual.
The law of supply in economics states that supply will increase as price increases, due to the fact that producers want to maximize profits. In this instance, the law assumes that all other factors are equal and price is the only independent element, meaning supply is completely dependent on the price.
Hence, an increase in the wages of teenager will lead to an increase in the quantity of hamburgers demanded, which will also leads to an increase in supply.
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Circle 1 has center (−6, 2) and a radius of 8 cm. Circle 2 has center (−1, −4) and a radius 6 cm. What transformations can be applied to Circle 1 to prove that the circles are similar? Enter your answers in the boxes. Enter the scale factor as a fraction in simplest form
Answer:
they are both circles
Step-by-step explanation:
Laurel needs to make an open-topped box to hold a gift for
her friend Kim. She has a sheet of cardboard 10 cm long by
16 cm wide. She plans to make the box by cutting squares
from the corners and folding up the sides. What is the
length of a side of each square that should be cut out to
give a box of maximum volume?
Answer:
To find the length of a side of each square that should be cut out to give a box of maximum volume, we need to use optimization. Let's call the length of each square x cm.
To form the box, we will cut out squares of side length x from each corner of the rectangular cardboard sheet, and then fold up the sides to form the box. The dimensions of the base of the box will be (10-2x) cm by (16-2x) cm, and the height of the box will be x cm.
Therefore, the volume of the box will be:
V = (10-2x) * (16-2x) * x
V = 4x^3 - 52x^2 + 160x
To find the length of a side of each square that should be cut out to give a box of maximum volume, we need to find the value of x that maximizes V. To do this, we can take the derivative of V with respect to x, and set it equal to 0:
dV/dx = 12x^2 - 104x + 160 = 0
We can solve for x by factoring the quadratic expression:
3x^2 - 26x + 40 = 0
(3x - 10)(x - 4) = 0
So the critical points are x = 10/3 and x = 4. Since we're looking for a maximum, we need to find which of these critical points gives the highest value of V. We can do this by evaluating V at both points:
V(10/3) ≈ 51.85
V(4) = 128
Therefore, the value of x that gives the maximum volume is x = 4 cm.
So we should cut out squares of side length 4 cm from each corner of the cardboard sheet to make a box of maximum volume.
The requried maximum height of the box should be 2 for the maximum volume.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Let the side measure of the square cut b x,
Now,
The length of the box will be = 16 - 2x
width of the box will be = 10 - 2x
The height of the box will be = x
The volume of the box is given as,
V = (16-2x)(10-2x)(x)
V = 4x³ - 52x² + 160x
Differentiate the above equation with respect to x,, and equate it to zero to get the maximum value of x for the maxium volume,
12x² - 104x + 160 = 0
x = 2 and 6.667
We can neglect x = 6.667 because at 6.667 the volume has a negative magnitude.
Thus, the requried maximum height of the box should be 2 for the maximum volume.
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Describe a situation that the expression -15 ÷ (-5) could represent. Find the quotient and tell what it represents in terms of the situation.
Answer: 3
Step-by-step explanation: Someone is 15 steps behind in a race, then that is sectioned into a fifth. How many steps behind are they?
Graph the following function on the axes provided.
f(x) =
2x+8
| −2x + 7
10
Click and drag to make a line. Click the line to delete it.
Click on an endpoint of a line to change it.
O
7
s
32 21
A
N
for
for
co
x < -1
x > 3
3
s
9
D
8
9 10
The graph of the system is added as an attachment
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2x + 8 for x < -1
-2x + 7 for x > 3
The above system is a piece wise fucntion that include
Two linear equations
Next, we plot the graph
See attachment for the graph of the equation
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Rhian sat a Maths test and an English test.
In the Maths test she scored 14 out of 17.
In the English test she scored 31 out of 39.
In which test did she do better?
Show your working
NEED HELP SOS!!
Answer:
Maths
Step-by-step explanation:
We find the percent equivalent of each test.
Maths: 14 out of 17
percent = part/whole × 100%
percent = 14/17 × 100%
percent = 82.35%
English: 31 out of 39
percent = part/whole × 100%
percent = 31/39 × 100%
percent = 79.49%
Since 82.35% > 79.49%, she did better in Maths.
Answer: Maths
The function g is defined and differentiable on the closed interval [ ]7, 5â and satisfies ( )0 5.g = The graph of( ),y g xâ²= the derivative of g, consists of a semicircle and three line segments, as shown in the figure above.(a) Find ( )3g and ( )2 .g â(b) Find the x-coordinate of each point of inflection of the graph of ( )y g x= on the interval 7 5.xâ <
(a)The value of g(3) = 13/2 + π, g(-2) = 5 - π
(b) The graph of y g(x) has points of inflection at x = 0, x = 2 and x = 3
This problem described a function g that is defined and differentiable on [-7, 5] and with g(0) = 5. The graph of y = g′(x) on [ -7, 5] was given, consisting of three line segments and a semicircle.
[tex]g(3) = 5 + \int\limits^3_0 {g'(x)} \, dx \\g(3) = 5 + \frac{\pi.2^{2}}{4} + \frac{3}{2}[/tex]
g(3) = 13/2 + π
[tex]g(-2) = 5 + \int\limits^ 2_0 {g'(x)} \, dx \\[/tex]
g(2) = 5 - π
(b) x-coordinates of points of inflection for the graph of y = g(x) on the interval [-7 5].
The graph of y = g(x) has points of inflection at x = 0, x = 2 and x = 3 because g′ changes from increasing to decreasing at x = 0 and 3, x = and g′ changes from decreasing to increasing at x = 2.
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The image of this question is probably this
Help Please! This is due soon
(20 Points will be given)
Pt .1
a) The vertex is, (20, 800) and its mean at the length of 20 the area is 800.
b) At 0 and 40 length the area is zero.
c) At length interval (20, 40), the area is decreasing.
d) At the area 600 the length is 30.
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 graph is shown in figure.
Hence, By the figure we have;
a) The vertex is, (20, 800) and its mean at the length of 20 the area is 800.
b) At 0 and 40 length the area is zero.
c) At length interval (20, 40), the area is decreasing.
d) At the area 600 the length is 30.
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If a ¼ of a teaspoon is 1 ml, then how many millilitres are in 6 teaspoons?
Answer
4x6=24
24x1 ml=24ml
Answer:
the answer to your question is 24 milliliters!
Step-by-step explanation:
good luck!
Find the area and the perimeter of the figure at right. Be sure to
organize your work so you can explain your method later.
24 m
20°
16 m
18 m
The perimeter of the figure is 68+24=92 cm.
What is Area of Rectangle?The area of Rectangle is length times of width.
In the given figure there is a rectangle and right angle triangle.
The length of rectangle is 16 cm and width is 18 cm
Perimeter=2(length+Breadth)
=2(16+18)
=68 cm
Now let us find perimeter of triangle
Base of height is 6cm and base is 8
P=a+b+√a²+b²
=6+8+√6²+8²
=24
Hence, the perimeter of the figure is 68+24=92 cm.
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The dimensions of a cylindrical are shown in the diagram. Find the total surface area of the can in terms of pi
R=3
h=4.5
The total surface area of the cylinder is S = 45π units²
What is a Cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is
Volume of Cylinder = πr²h
Surface area of cylinder = 2πr ( r + h )
where r is the radius of the cylinder
h is the height of the cylinder
Given data ,
Let the surface area of the cylinder be represented as S
Now , the equation will be
The height of the cylinder h = 4.5 units
The radius of the cylinder r = 3 units
So , Surface area of cylinder = 2πr ( r + h )
Substituting the values in the equation , we get
Surface area of cylinder S = 2π ( 3 ) ( 3 + 4.5 )
On simplifying the equation , we get
Surface area of cylinder S = 2π ( 3 ) ( 7.5 )
Surface area of cylinder S = 45π units²
Hence , the surface area of cylinder is 45π units²
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Ian went shopping for a new pair of pants because of a sale. The store was offering a
40% discount. If the price on the tag was $40, what would be the price after the
discount but before tax, to the nearest dollar and cent?
The price after the discount but before tax, to the nearest dollar and cent is $24.
How is discount calculated?Discounts are price reductions that store owners make on items or services that are otherwise priced as marked. This portion of the refund is typically provided to boost sales or get rid of excess inventory. The price of an item as stated by the manufacturer or seller, without any price decrease, is known as the List price or Marked Price. After any discounts or price reductions from the list price, the selling price is the final price at which an item is actually sold. "Off",
Discount is equal to List Price – Selling Price.
Given that, the store was offering a 40% discount.
The discount on the price tag of $40 is:
Discount = 40 (40/100) = $16.
The new price after the discount but before tax is:
New price = 40 - 16
New price = $24.
Hence, the price after the discount but before tax, to the nearest dollar and cent is $24.
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