Given the function:
[tex]h(t)=-16t^2+8t+48[/tex]Where h(t) is the height of the diver above the surface of the water and t is the time.
Let's find how long it takes the diver to hit the water.
When the diver hits the water, the height h(t) = 0.
Now substitute 0 for h(t) and solve for the time t.
We have:
[tex]0=-16t^2+8t+48[/tex]Rearrange the equation:
[tex]-16t^2+8t+48=0[/tex]Solve for t.
Let's factor the expression by the left.
Factor 8 out of all terms:
[tex]8(-2t^2+t+6)=0[/tex]Now, factor by grouping.
Rewrite the middle term as a sum of two terms whose product is the product of the first term and the last term:
[tex]\begin{gathered} 8(-2t^2+4t-3t+6)=0 \\ \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} 8((-2t^2+4t)(-3t+6))=0 \\ \\ 8(2t(-t+2)+3(-t+2))=0 \\ \\ 8(2t+3)(-t+2)=0 \end{gathered}[/tex]Hence, we have the factors:
[tex]\begin{gathered} 2t+3=0 \\ -t+2=0 \end{gathered}[/tex]Solve each factor for t:
[tex]\begin{gathered} 2t+3=0 \\ \text{ Subtract 3 from both sides:} \\ 2t=-3 \\ \text{ Divide both sides by 2:} \\ \frac{2t}{2}=-\frac{3}{2} \\ t=-\frac{3}{2} \\ \\ \\ -t+2=0 \\ t=2 \end{gathered}[/tex]Hence, we have the solutions:
t = -3/2
t = 2
The time cannot be negative, so let's take the positive value.
Therefore, the will take 2 seconds for the diver to hit the water.
ANSWER:
2 seconds.
Every week a company provides fruit for its office employees. They canchoose from among five kinds of fruit. Which probabilities correctly completethis probability distribution for the 50 pieces of fruit, in the order listed?
Given:
Total number of pieces = 50
So, the probabilities are:
Apples
[tex]P(apples)=\frac{8}{50}=0.16[/tex]Bananas
[tex]P(bananas)=\frac{10}{50}=0.2[/tex]Lemons
[tex]P(lemons)=\frac{5}{50}=0.1[/tex]Oranges
[tex]P(oranges)=\frac{15}{50}=0.3[/tex]Pears
[tex]P(pears)=\frac{12}{50}=0.24[/tex]Answer: A.
the sum of the angle measures of a polygon with n sides is given find n1440
Given in the question:
a.) The sum of all angles of a polygon is 1,440 degrees.
To be able to determine what polygon has a total sum of angles of 1,440 degrees, we will be using the following formula:
[tex]\text{ }\Theta=(n-2)x180^{\circ}[/tex]We get,
[tex]\text{ 1},440^{\circ}=(n-2)x180^{\circ}[/tex][tex]\text{ 1},440^{\circ}=180n-360^{\circ}[/tex][tex]180n=1,440^{\circ}\text{ + 360}^{\circ}[/tex][tex]180n=1,800^{\circ}[/tex][tex]\frac{180n}{180}=\frac{1,800^{\circ}}{180}[/tex][tex]n\text{ = 10}[/tex]Therefore, that polygon is a decagon or a polygon with 10 sides.
I will send u a picture of my equation
Answer:
where is the picture????
Answer parts a through E for the function shown below
Solution
We are given the function
[tex]f(x)=x^3+4x^2-x-4[/tex]First, Let us do the simplification or factorization
[tex]\begin{gathered} f(x)=x^2(x+4)-1(x+4) \\ f(x)=(x^2-1)(x+4) \\ f(x)=(x-1)(x+1)(x+4) \end{gathered}[/tex](a).
The coefficient of x^3 is positive
(b).
So basically, we set f(x) = 0 to get the x - intercepts
[tex]\begin{gathered} f(x)=(x-1)(x+1)(x+4) \\ (x-1)(x+1)(x+4)=0 \\ x=1,-1,-4 \end{gathered}[/tex]The x - intercepts are
[tex]x=1, -1, -4[/tex]The graph of f(x) is also given below
Factor by grouping:y^3-5y^2+3y-15
we have the expression
y^3-5y^2+3y-15
Grouping terms
(y^3-5y^2)+(3y-15)
factor y^2
y^2(y-5)+(3y-15)
factor 3
y^2(y-5)+3(y-5)
factor (y-5)
(y-5)[y^2+3]prism x imprison wire similar. the volume of prison why is 92 cm3 find the volume of prism x.
If they are similar, then their side measures are proportional
Prism X, volume = 92 cm^3
Solve the method.simultaneous equation by graphicaly + 3x = 6y - 2x = 1
The equations given are
[tex]\begin{gathered} y+3x=6............1 \\ y-2x=1............2 \end{gathered}[/tex]The graph of the equations will be shown below
Hence, the solution to the equations is the point where the two equations intersect.
Therefore, the solution is
[tex](1,3)[/tex]First try was incorrect Fill in the blank. Constant: a number that is next to a variable.
A number that is right next to a variable. For instance,
[tex]5x+6[/tex]the number 6 is a constant.
Lily likes to collect records. Last year she had 12 records in her collection. Now she has 15 records. What is the percent increase of
her collection?
The percent increase of her collection is
Jordan owns a house painting service. For each house, they charge $95 plus $60 per hour of work. A linear equation that expresses the total amount of money Jordan earns per house is y=60x+95. What are the independent and dependent variables? What is the y-intercept and the slope?
Answer:
The slope is 60
The y intercept is 95
The independent variable is x (the number of hours)
The dependent variable is y (The amount earned.)
Step-by-step explanation:
can anyone help me? solve using system of linear equations using elimination x – y - 3z = 4 2x + 3y – 3z = -2 x + 3y – 2z = -4
The solution is x = 2, y = -2 and z =0
How to solve the system of equations?The system of equations is given as
x – y - 3z = 4
2x + 3y – 3z = -2
x + 3y – 2z = -4
Start by eliminating y
To do that, we subtract (2) from (3)
x + 3y – 2z = -4 - (2x + 3y – 3z = -2)
This gives
-x + z = -2
Make x the subject in the above equation
x = z + 2
Substitute x = z + 2 in (1) and (2)
z + 2 – y - 3z = 4
z + 2 + 3y – 2z = -4
Solve the equations
-2z - y = 2
-z + 3y = -6
Multiply -z + 3y = -6 by 2
-2z + 6y = -12
Start by eliminating z
Subtract -2z + 6y = -12 from -2z - y = 2
7y = -14
Evaluate
y = -2
Substitute y = -2 in -z + 3y = -6
-z + 3(-2) = -6
Evaluate
-z - 6 = -6
Evaluate
z = 0
Recall that x – y - 3z = 4
So, we have
x + 2 - 3(0) = 4
Evaluate
x = 2
Hence, the values of the variables are x = 2, y = -2 and z =0
Read more about system of equations at
https://brainly.com/question/13729904
#SPJ1
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
Order the numbers from least to greatest
Answer:
-1, √4/5, -6/5, √3, 2, -3√9, 2√125
Step-by-step explanation:
Two ships are sailing across the Atlantic ocean at the equator. The dofference in solar time between them is two hours. How many degrees of longitude are they apart?
Answer:
30 degrees
Step-by-step explanation:
There are 360 degrees of longitude ( 360 degrees is a complete circle)
It takes 24 hours to complete a complete rotation of the earth
360 degrees / 24 hours = 15 degrees / hr
15 degrees/ hr * 2 hr = 30 degrees
What is the inverse function of y = (x-4)^2+2
One way to find the inverse of a function is by first swapping x and y, then solving for y, like this:
[tex]\begin{gathered} y=(x-4)^2+2\text{ }\Rightarrow x=(y-4)^2+2 \\ \end{gathered}[/tex]Now, let's solve for y, like this:
[tex]\begin{gathered} x=(y-4)^2+2 \\ x-2=(y-4)^2+2-2 \\ (y-4)^2=x-2 \\ \sqrt[]{\mleft(y-4\mright)^2}=\sqrt[]{x-2} \\ y-4=\sqrt[]{x-2} \\ y-4+4=\sqrt[]{x-2}+4 \\ y=\sqrt[]{x-2}+4 \end{gathered}[/tex]Then, the inverse function of y = (x-4)^2+2 is:
[tex]y=\sqrt[]{x-2}+4[/tex]-353-0-- * GR-35-21-2700-3s 6 - 2y-6- - +28+82-80 -592-35-07-2+27-35-30 9815+ Seesters << RB- --3-1-1-12) 6-5-3= LG - 5+13-2225 SVE -3-5y+6=-24 -*- 4y +50=-21 5r - 55 - 5 = 3r-S-=
Explanation:
5x - 4y + 2z = 21 ...equation 1
-x - 5y + 6z = -24 ....equation 2
-x - 4y + 5z = -21 ...equation 3
Using elimination method:
multiply equation 2 by 5:
-5x - 25y + 30z = -120 ....equation 2a
add equation 2a from 1:
5x - 5x -4y -25y + 2z + 30z = 21 - 120
0 - 29y + 32z = -99
-29y + 32z = - 99 ....equation 4
multiply equation 3 by 5:
-5x - 20y + 25z = -105 ...equation 3a
add equation 1 and 3a
5x - 5x - 4y - 20y + 2z +25z = 21 - 105
0 - 24y + 27z = -84
-24y + 27z = -84 ...equation 5
-29y + 32z = - 99 ....equation 4 (×-24)
-24y + 27z = -84 ...equation 5 (×-29)
696y - 768x = 2376 ...(4a)
696y -783x = 2436 ...(5a)
subtract 5a from 4a
696y - 696y -768x -(-783x) = 2376 - 2436
0 - 768x + 783x = -60
15x = -60
x = -60/15
x = -4
substitute for x in equation 4a:
696y - 768(-4) = 2376
696y + 3072 = 2376
696y = 2376 -3072
696y = -696
y = -696/696
y = -1
substitute for y in equation 4:
-29(-1) + 32z = -99
29 + 32z = -99
32z = -99 - 29
32z = -128
z = -128/32
z = -4
In a survey, 12 people were asked how much they spent on their child's last birthday gift. The results wereroughly bell-shaped with a mean of $39.1 and standard deviation of $17.4. Estimate how much a typical parentwould spend on their child's birthday gift (use a 99% confidence level). Give your answers to 3 decimal places.Express your answer in the format of ī + Error.$£ $
Given:
number of people (n) = 12
mean = 39.1
standard deviation = 17.4
99% confidence level
Using the confidence level formula, we can find the estimate of how much a typical parent would spend on their child's birthday:
[tex]\begin{gathered} CI\text{ = x }\pm\text{ }\frac{z\varphi}{\sqrt[]{n}} \\ \text{where x is the mean} \\ z\text{ is the z-score at 99\% confidence interval} \\ \varphi\text{ is the standard deviation} \\ n\text{ is the number of people asked} \end{gathered}[/tex]The z-score at 99% confidence level is 2.576
Substituting, we have:
[tex]\begin{gathered} CI\text{ = 39.1 }\pm\text{ }\frac{2.576\text{ }\times\text{ 17.4}}{\sqrt[]{12}} \\ =26.161\text{ and 52}.039 \end{gathered}[/tex]Hence, a typical parent would spend between $26.161 and $52.039 or :
[tex]39.1\text{ }\pm\text{ 12.939}[/tex]Pls someone help me! Giving brainless
Answer:
ANSWER=5
Step-by-step explanation:
GIVEN=8+(-3)
(+)×(-)=(-)
SO 8-3=5
PLEASE MARK ME AS BRILLINT
Lola needs 2/3 cup of lemon-lime soda for every 2 cups of punch. Find ____ cups of soda/cup of punch
We know that
• There are needed 2/3 cups of lemon soda for every 2 cups of punch.
To find the answer, we have to divide.
[tex]\frac{\frac{2}{3}}{2}=\frac{2}{6}=\frac{1}{3}[/tex]Therefore, the answer is 1/3 of soda/cup of punch.what us the area of the triangle if the perimeter is 16
We are asked to find the area of the given triangle.
Recall that the area of a triangle is given by
[tex]A=\frac{1}{2}\cdot b\cdot h[/tex]Where b is the base and h is the height of the triangle.
Let us find the base and height from the given figure.
As you can see,
base = 6
height = 4
[tex]\begin{gathered} A=\frac{1}{2}\cdot b\cdot h \\ A=\frac{1}{2}\cdot6\cdot4 \\ A=\frac{1}{2}\cdot24 \\ A=12 \end{gathered}[/tex]Therefore, the area of the triangle is 12 square units.
Question 1-3
The distance traveled by car, for a duration of time, can be modeled with the equation s= 45t, where s is the distance, in miles, and it is
the time, in hours. Which graph represents this proportional relationship correctly?
120
105
90
Distance (mi)
Distance (mi)
75
60
45
120
30
105
90
15
75
60
45
30
0
15
2
Time (hr)
Time (hr)
100
lon
3
+X
X
120
105
90
Distance (mi)
75
60
45
30
15
0
1
2
Time (hr)
co
X
The equation s = 45t, where s is the distance in miles and it is the time in hours, can be used to simulate the distance driven by a car over a period of time then the car will travel 135 hours in 3 hours.
What is meant by the constant of proportionality?The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.
Given: The distance traveled by car at a constant rate is proportional to the time spent driving.
In the equation d = 45 t, d denotes the distance (in miles) and t denotes the time (in hours).
d / t = 45 miles per hour
The constant of proportionality = 45 miles per hour.
Also, the distance traveled by car in 1 hour = 45 miles
The distance traveled by car in 3 hours = 3 × 45 = 135 miles
Therefore, a car will travel 135 hours in 3 hours.
The complete question is:
The distance traveled by car at a constant rate is proportional to the time spent driving. In equation d = 45t, d represents the distance (in miles) and t represents the time (in hours).
A. What is the constant of proportionality? _____ miles per hour
B. How far will the car travel in 3 hours? _______ miles
To learn more about constant of proportionality refer to:
https://brainly.com/question/28413384
#SPJ13
Find The distance DB from Cassini yo Tethys when AD is tangent to the circular orbit. Round to the nearest kilometer
we have that
triangle ABD is a right triangle , because AD is a tangent
so
Apply the Pythagorean Theorem
DB^2=AB^2+AD^2
we have
AB is a diameter (two times rhe radius)
AB=2*295,000=590,000 km
AD=203,000 km
substitute
DB^2=590,000^2+203,000^2
DB=623,946 kmTo graph the inequality y>-3x-4, you would draw a dashed line.O A. TrueO B. False
True.
Since it is strictly greater
Square ABCD is inscribed in a circle with radius 20 m . What is the area of the part of the circle outside of the square
ANSWER:
456 square meters
STEP-BY-STEP EXPLANATION:
The first thing is to represent the problem in the following figure:
To calculate the area of the part of the circle outside of the square, we must calculate the area of the circle and subtract the area of the inscribed square.
To calculate the area of the square, we plant the following, taking into account that the diagonal of the square is equal to twice the radius and the sides equal to the radius times the root of two, like this:
Knowing the value of the side of the square, we can directly calculate the area of the part of the circle outside of the square, subtracting the corresponding areas like this:
[tex]\begin{gathered} A=A_C-A_S_{} \\ A=\pi\cdot r^2-\mleft(r\cdot\sqrt{2}\mright)^2 \\ \text{replacing} \\ A=3.14\cdot20^2-\mleft(20\cdot\sqrt{2}\mright)^2 \\ A=1256-800 \\ A=456 \end{gathered}[/tex]The area of the part of the circle outside of the square is equal to 456 square meters
STRUCTURE Quadrilateral DEFG has vertices D(-1, 2), E(-2, 0), F(-1,-1) and G(1, 3). A translation maps quadrilateral DEFG to
quadrilateral D'EFG. The image of D is D'(-2,-2). What are the coordinates of E, F, and G'?
E (
FD
G' (
The coordinates are;
E' = (-3, -4)F' = (-2, -5)G' = (0, -1)Given,
Quadrilateral DEFG with vertices;
D = (-1, 2)E = (-2, 0)F = (-1,-1) G = (1, 3)We have to find the coordinates of E', F', G'.
A figure is translated when it is moved to the left, right, up, or down.
The original figure's points are all translated (moved) by the same amount and in the same direction.
Here,
Compare the coordinates of D with the coordinates of D' to determine the mapping rule that converts DEFG to D'E'F'G'.
D = (-1, 2)
D' = (-2, -2)
The x-coordinate has be translated 1 unit to the left.
The y-coordinate has been translated 4 units down.
Then,
The mapping rule is:
(x, y) → (x-1, y-4)
To find the coordinates of E', F' and G', apply the mapping rule to the given vertices of the pre-image:
⇒ E' = (-2-1, 0-4) = (-3, -4)
⇒ F' = (-1-1, -1-4) = (-2, -5)
⇒ G' = (1-1, 3-4) = (0, -1)
That is,
The coordinates are;
E' = (-3, -4)F' = (-2, -5)G' = (0, -1)Learn more about translation maps here;
https://brainly.com/question/13007985
#SPJ1
14) A positive number is two fifths of another positive number. The sum of the numbers is 49. What arethe two numbers?
Let's use the variable x to represent the second number. The first number is two fifths of x, so the first number is 2x/5.
If the sum of the numbers is 49, we can write the following equation:
[tex]\frac{2}{5}x+x=49[/tex]Now, solving the equation for x, we have:
[tex]\begin{gathered} \frac{2}{5}x+\frac{5}{5}x=49\\ \\ \frac{7}{5}x=49\\ \\ \frac{1}{5}x=7\\ \\ x=7\cdot5\\ \\ x=35 \end{gathered}[/tex]Let's calculate the first number:
[tex]\frac{2}{5}x=\frac{2}{5}\operatorname{\cdot}35=2\cdot7=14[/tex]Therefore the numbers are 14 and 35.
solve for missing variable: 11y-36=63
The equation can be solved as,
[tex]\begin{gathered} 11y-36=63 \\ 11y=63+36 \\ 11y=99 \\ y=\frac{99}{11} \\ y=9 \end{gathered}[/tex]Therefore, the value of y is 9.
24. The base of a 13-foot ladder stands 5 feet from a house. Sketch a drawing to model this situation. How many feet up the side of the house does the ladder reach? Explain how drawing the picture helped you solve the problem.
The draw that describes this situation looks like this:
Drawing this helped us to know that the ladder forms a right triangle with one of the walls of the house.
When we have right triangles we can apply the Pythagoras theorem, from the Pythagoras theorem we can express:
[tex]13^2=5^2+h^2[/tex]Solving for h, we get:
[tex]\begin{gathered} 13^2-5^2=5^2-5^2+h^2 \\ 13^2-5^2=h^2 \\ h=\sqrt[]{13^2-5^2}=\sqrt[]{169-25}=\sqrt[]{144}=12 \end{gathered}[/tex]Then, the ladder reach 12 feet up the side of the house
Maya started to run on a treadmill after setting its timer for 96 minutes. The display says that she has finished 47% of her run. How many minutes have gone by? Round your answer to the nearest tenth.
Answer:
45.1
Step-by-step explanation:
96 x .47 = 45.12
Rounded to the nearest tenth is 45.1
Percent means per hundred [tex]\frac{47}{100}[/tex] to divide by 100 you move the decimal place to places to the left.
A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 5 millimeters long, and the height of the equilateral triangle is 4.3 millimeters. The pyramid's slant height is 3 millimeters. What is its surface area?
The surface area of the triangular base pyramid is 19.75 mm².
How to find the surface area of a pyramid?The surface area of a triangular pyramid is the sum of the area of the whole sides of the triangular pyramid.
Therefore,
Surface area of a triangular pyramid = base area + 1 / 2 (perimeter × slant height)
The base of the triangular pyramid is an equilateral triangle. An equilateral triangle has congruent sides.
Therefore,
base area = 1 / 2 × 5 × 4.3
base area = 10.75 mm²
Hence,
perimeter of the base = 5 + 5 + 5 = 15 mm
Surface area of a triangular pyramid = 10.75 + 1 / 2 (15 × 3)
Surface area of a triangular pyramid = 10.75 + 1 / 2(18)
Surface area of a triangular pyramid = 10.75 + 9
Surface area of a triangular pyramid = 19.75 mm²
learn more on pyramid here: https://brainly.com/question/16472037
#SPJ1
An auto mechanic recommends that 3 ounces of isopropyl alcohol be mixed with a tankful of gas (14 gallons ) to increase the octane of the gasoline for better engine performance. At this rate, how many gallons of gas can be treated with a 16-ounce bottle of alcohol (You don’t need to translate or understand just solve the word problem please )
Let be "x" the number of gallons of gas that can be treated with a 16-ounce bottle of alcohol.
According to the information given in the exercise, 3 ounces of isopropyl alcohol should be mixed with 14 gallons of gas.
Then, you can set up the following proportion:
[tex]\frac{14}{3}=\frac{x}{16}[/tex]Now you have to solve for "x":
[tex]\begin{gathered} (16)(\frac{14}{3})=x \\ \\ \frac{224}{3}=x \\ \\ x\approx74.67 \end{gathered}[/tex]Therefore, the answer is:
[tex]\approx74.67\text{ }gallons[/tex]