This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds.
h = -5t2 + 45.
How can one determine a function's maximum height?
The vertex, which is a maximum (or minimum) in a parabola, can be located by solving the square (yuck!) or by using the formula x = -b/2a. By re-entering the original equation with this x value as the vertex's x, we can determine the appropriate maximum height.
By multiplying "D * tan (theta)," where "tan" is the tangent of angle theta, you can get the height of the item of interest. For instance, rounding up, the height is 40 tan 50 = 47.7 meters if theta is 50 degrees and D is 40 meters.
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WORTHHHHHHH.......30 POINTS
PLEASE HELP ASAP YOU GOT 20 MINUTES
Parin digs a hole at a rate of 5/6 feet every 15 minutes. After digging for 45 minutes, Parin places a bush in the hole that fills exactly 3/4 feet of the hole.
Relative to ground level, what is the elevation of the hole after placing the bush in the hole?
!!!!!!I REPEAT ENTER YOUR ANSWER AS A SIMPLIFIED MIXED NUMBER!!!!!!!
Answer: 3 1/4 Is the correct answer.
Él ___ mi primo. (To express relationships)
Answer: es
Step-by-step explanation: I know Spanish
I just need to know if the answer is B or D
Firslty, we need to find the function, whcih we can do by substituting one into the other:
[tex]f(g(x))=2(g(x))^2-1=2(\sqrt[]{x-2})^2-1=2(x-2)-1=2x-4-1=2x-5[/tex]Now, for the domain we have more complicated approach.
We first have to find the domain for both f(x) and g(x).
The domain of f(x) is all real number, because it is a quadratic polynomial.
The domain of g(x) is all the real numbers except the x values that makes the square root interior negative, so all real numbers so that:
[tex]\begin{gathered} x-2\ge0 \\ x\ge2 \end{gathered}[/tex]Now, the domain of the composite function f(g(x)) is the set of all the values of x in the domain of g(x) such that the corresponding g(x) is in the domain of f(x).
Since the domain of f(x) is all real numbers and g(x) is a real number function, all the values of g(x) will be in the domain of f(x), so we just need to check the values of x that are in the domain of g(x).
The domain of g(x), as we saw, is:
[tex]D=\mleft\lbrace x\mright|x\ge2\}[/tex]And any value of x will give a g(x) that will be in the domain of f(x) so, the domain of f(g(x)) is:
[tex]D=\mleft\lbrace x\mright|x\ge2\}[/tex]So, the correct alternative is:
[tex]\begin{gathered} f(g(x))=2x-5 \\ D\colon\mleft\lbrace x\mright|x\ge2\} \end{gathered}[/tex]John has $400 June has 1/10 of that. June has 0.1 of Maria’s money how much money does Maria and June have.
I really need help please figure this out I need it by Monday October 17 2021 please help me thank you
The amount of money that June has is $40 and Maria has $400. The total amount is $440.
What is the total amount?From the information, John has $400 June has 1/10 of that and June has 0.1 of Maria’s money.
Therefore the amount that June has will be:
= 0.1 × John's money
= 0.1 × 400
= 40
June has 0.1 of Maria’s money. Let Maria's money be x. Therefore, 0.1 × x = 40
0.1x = 40
Divide
x = 40 / 0.1
x = 400
Maria's money = 400
Therefore, the total amount that they have will be:
= Amount that John has + Maria's amount
= 400 + 40.
= $440
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Write "less" or "greater" in the blank 179 is_than 31
Answer: Greater
Step-by-step explanation:
Answer:
179 is greater than 31
A lake in East Texas was stocked with 3,000 trout in the year 2000. The number of fish in the lake is modeled by f(x) = 3000 + 100x, where x represents the number of years after 2000. Which of the following is the most reasonable domain and range for the function if domain is time, and range is number of fish?
Domain:
Range:
The Domain and the range of the function are given as
x ≥ 0, y ≥ 3000
What is the domain of a function?This is the complete set of values that is used to represent the independent variable in the function. The independent variable that we have here is represented by x and it is 0.
What is the range of a function?This is the set of the possible values that the dependent variable in the function is to have. The dependent variable is given by y.
The range of x would have to start from 0 for the range of all values of x. Hence x ≥ 0, while y is seen to be in the form of y ≥ 3000 because this is the value of trout that was stocked.
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find the difference.
A.41-275
B-15-47
C-72-(-151)
D.612-(-144)
A. -234
B. -62
C. [tex]-72+151=79[/tex]
D. [tex]612+144=756[/tex]
√15/√3 pls answer this for me so i can chill
Answer:
[tex]\sqrt{5}[/tex]
Step-by-step explanation:
to simplify use the rule of radicals
[tex]\frac{\sqrt{x} }{\sqrt{y} }[/tex] ⇔ [tex]\sqrt{\frac{x}{y} }[/tex] , then
[tex]\frac{\sqrt{15} }{\sqrt{3} }[/tex] = [tex]\sqrt{\frac{15}{3} }[/tex] = [tex]\sqrt{5}[/tex]
Please help me with this.
least common mutiple of...
6 and 8: 24
8 and 12: 24
12 and 9: 36
6 and 9: 18
y is inversely proportional to the square root of x.
When x = 16, y = 10.
What does x equal when y = 8?
Answer:
x = 25 when y = 8
Step-by-step explanation:
If y is inversely proportional to square root of x we write it as
[tex]y \propto \dfrac{1}{\sqrt{x}}[/tex]
This is also equivalent to
[tex]y = k \dfrac{1}{\sqrt{x}} \;\;\;\;\ \text{ [1]}[/tex]
where k is a constant known as the constant of proportionality
Given y = 10 when x = 16 we can find k by substituting for y and x in [1]
[tex]\rightarrow 10 = k\dfrac{1}{\sqrt{16}}\\\\\rightarrow 10 = k \dfrac{1}{4}\\\\\drightarrow 40 = k \:\:\:\: \text{by multiplying both sides by 4}\\\\\text{which can be written as }\\\\k = 40\\[/tex]
So constant of proportionality k = 40
To find x when y = 8, substitute y and k in [1] to get
[tex]y = k \dfrac{1}{\sqrt{x}}\\\text{Multiply both sides by \sqrt{x} and divide by y at the same time to get}\\\\\sqrt{x} = \dfrac{k}{y}[/tex]
Dividing both sides by y and multiplying by √x gives us
[tex]\sqrt{x} = \dfrac{k}{y}\\\\\text{Substituting k = 40, y = 8}:\\\\\sqrt{x} = \dfrac{40}{8}\\\\\sqrt{x}= 5\\\\\text{Squaring both sides: }\\\\(\sqrt{x})^2 = 5^2\\\\x = 25 \;\;\;\text{since $(\sqrt{x})^2$ = x}[/tex]
The answer is
x = 20
Formulate y=k/x based on the following criteria.
Replace: 10= k/16
Change the sides so that k/16 = 10.
Subtract the coefficient of the variable from both sides of the equation: k = 10×16
Determine the quotient or product: k = 160
Replace with y = 160/x.
Replace with: 8 = 160/x
The denominator cannot be zero if the fraction is defined: as x ≠ 0
As the domain, append the inequality: 8= 160/x, x≠0
Divide the common denominator by both sides of the equation: 8x = 160x/x, x≠0
8x=160x/x, where x ≠ 0. Reduce the fraction.
By the variable's coefficient, multiply both sides of the equation (x=160÷8, x ≠ 0).
Calculate the quotients or product: x = 20,x ≠ 0
Find the junction at x=20.
Answer : x = 20
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The pages of Jack's book are numbered from 1.
ann
The page numbers have a total of 555 digits.
How many pages has the book?
How many of the digits are a 5?
Answer:
he has 556 pages in his book
Find the maximum length of a rod that can be kept in a cuboidal box offside 30cm, 24cm and 18 cm.
Answer:
30√2 cm
Step-by-step explanation:
Maximum length of the rod = Length of the diagonal of the cuboid
Length of diagonal of cuboid = [tex]\sqrt{l^2+w^2 + h^}[/tex]
where l = length, w =width and h = height
For this particular cuboid,
Diagonal length = [tex]\sqrt{30^2+24^2 + 18^2}[/tex]
[tex]\sqrt{800 + 576 + 324} \\\\\\= \sqrt{1500}\\\\= 30\sqrt{2} \text{ cm}[/tex]
132 = -w + 236 solve for w
A triangle has an angle that measures 111°. The other two angles are in a ratio of 6:17. What are the measures of those two angles?
Answer:
18 and 51
Step-by-step explanation:
the sum of the two other angles would be 69 degrees because there has to be 180 degrees in a triangle
given that we can create the equation 6x + 17x = 69 and solve for x
x = 3
so now we can plug in each part of that equation and find out the two angles
Question 2 of 10
Which of the following is most likely to be a relative maximum for this graph?
8-
(-1.0) (20)
-8 -84
6
Answer:it’s (-1,8)
Step-by-step explanation:
The Sales Manager for Chicken Shack restaurants is studying the sales figures for two new varieties of chicken sandwiches recently introduced at eight of its restaurants. For four weeks, three restaurants have been selling lemon-roasted chicken sandwiches. The other five restaurants have been selling barbecued chicken sandwiches for three weeks. During the testing period, 6,000 lemon-roasted chicken sandwiches were sold, and 7,200 barbecued chicken sandwiches were sold. Which of the two new chicken sandwiches should the sales manager report as having the better sales?
Using the average sales per restaurant, the sales manager should report the Lemon-roasted chicken sandwiches as recording better sales performance than the Barbecued chicken sandwiches.
What is the average?The averages represent the total sales generated at the lemon-roasted and barbecued restaurants, respectively, divided by the number in each group.
The average is the same as the mean of a data set. It is computed by the mathematical operations of addition and division.
Lemon-roasted Barbecued
The number of restaurants 3 5
Total sales during the testing period 6,000 7,200
Average sales per restaurant 2,000 1,440
Based on the average sales, the sales manager should report that the lemon-roasted chicken sandwiches are outperforming the barbecued restaurants.
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suppose 48 out of every 120 people like baseball/softball. of the people who like baseball/softball, 3 out of 5 play the game. if you ask 500 people, how many would you expect play baseball/softball?
out of 500 people 200 like baseball and 120 people like to play game baseball/softball
suppose 48 out of every 120 people like baseball/softball.
of the people who like baseball/softball, 3 out of 5 play the game.
if you ask 500 people,
how many would you expect play baseball/softball
it means 40% like baseball and 60% like to play game
if there are 500 people
then 500 *(40/100)=200
thus 200 people like baseball
and 200*(60/100)=120
Hence 120 people to play game
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i need help pls and thank you...
Answer:
AB = 32
Step-by-step explanation:
Since line l bisects AB at point M, we have AM = MB.
[tex]4x = 5x - 4[/tex]
[tex]4x + 4 = 5x[/tex]
[tex]x = 4[/tex]
AM = 4(4) = 16, MB = 5(4) - 4 = 16.
So AB = AM + MB = 16 + 16 = 32.
write an equation in slope-intercept form of the line that passes through the points (2,15) and (5,21)
Answer:
y=2x+11
Step-by-step explanation:
A woman has twice as many dimes as quarters in her purse. if the dimes were quarters and the quarters were dimes, she would have $1.20 more than she has now. how many of each type of coin does the woman have?
The number of Quarter coins that she has is 8 and the number of Dimes is 16.
It is given in the question that the woman has twice as many Dimes as the quarters in her purse.
We know that the value of Dimes is 0.10$ and the value of Quarters is
0.25 $
Let the number of Quarter coins is y and the number of Dimes coin be u.
According to the question above,
u = 2y equation (i)
The total value z = 0.25y + 0.10u
Putting here the value of u from equation (i) we have,
z = 0.25y + 0.10(2y)
⇒ z = 0.25y + 0.20y
⇒ z = 0.45y equation (ii)
Now it has been mentioned that if the Dimes were Quarters and the Quarters were the Dimes, she would have $ 1.20 greater than she has now.
So we have,
z + 1.2 = 0.25u + 0.10y
Putting the value of u from above eqation (i),
z + 1.2 = 0.25(2y) + 0.10y
⇒ z + 1.2 = 0.50y + 0.10 y
⇒ z + 1.2 = 0.60y
Putting the value of z from equation (ii)
⇒ 0.45y + 1.2 = 0.60y
⇒ 0.45y - 0.60y = - 1.2
⇒ -0.15y = - 1.2
⇒ y = [tex]\frac{-1.2}{-0.15}[/tex]
⇒ y = 8
Therefore u = 2y
⇒ u = 2 x 8 = 16
Hence the number of Quarter coins is 8 and the number of Dimes is 16
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16 dimes, 8 quarters
I checked RSM it's correct
Question 10 (1 point)
What are the coordinates of the midpoint of segment whose endpoints are A(-2,7) and B(4,-2)?
Make sure to use decimals, if necessary, and write with no spaces in the format (x,y) with you solving for x and y
A/
The midpoint of the line segment given is (1, 4.5)
Midpoint of a LineIn geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment equally into two halves.
The formula of midpoint of a line is given as
[tex]M_x_y = \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}[/tex]
A = (-2, 7)B = (4, -2)Substituting the given values;
[tex]M_x_y = \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\\M_x_y = \frac{-2+4}{2}, \frac{7+2}{2} \\M_x_y = 1, \frac{9}{2} \\M_x_y = 1, 4.5[/tex]
The midpoint of the line AB is equal to (1, 4.5)
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Ryan collected 2,650 baseball cards, football cards, and hockey cards. he has 3 times as many baseball cards as football cards. he has 150 more hockey cards than football cards. how many baseball cards does he have? ryan has baseball cards.
The calculated answer after simplification in which Ryan has number of baseball cards is: 357 cards
How to simplify statement problems?
In mathematics, the statement based problems can be solved by forming the equations. And later, simplify those equation by equating to each other. This method is very common for the complicated problems to make the calculation easy.
According to the question, Ryan collected 2650 cards. In which, he has more baseball cards compared to football cards.
Now, let us assume, baseball cards be 'B'; football cards be 'F' and hockey cards be 'H'.
As per the question, the formed equation from the statement for the simplification is:
B + F + H = 2650
3B = F and H + 150 = F
Substituting above values in the formed equation to get the simplify answer,
B + 3B + 3B - 150 = 2650 ⇒ 7B = 2500 ⇒ B = 357
Now, the value of football cards is: F = 3(357) = 1071
And, the value of hockey cards is: H = 1071 - 150 = 921
Hence, after simplification Ryan has number of baseball cards is: 357 cards
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If g(x) = x² + 2, find g(3).
Answer:
11
Step-by-step explanation:
[tex]3^{2}[/tex] + 2
9 + 2
11
Evaluate the expression when a = -6.9 and b = -1.9,-66+2a
Evaluating Algebraic Expressions
We are given the expression:
-6b + 2a
And it's required to find the value of the expression for a=-6.9 and b=1.9
Substituting the values:
-6(-1.9) + 2(-6.9)
= 11.4 - 13.8
Operating:
=-2.4
The value is -2.4
Please only answer if you know the answer thank you.
Answer:
the slope is 0 and the equation is y = -2
Step-by-step explanation:
Two angles are complementary. If one angle is (x²-16x) and the other is (3x), thenwhat is the measures of the angles?
The smaller angle =
The larger angle =
Answer:
Complementary angles have a sum of 90°.
(x²-16x)+(3x) = 90
x² -13x - 90 = 0
(x-18)(x+5) = 0
x - 18 = 0 or x + 5 = 0
x = 18 or x = -5 (reject)
Substitute x into the angles.
18²-16(18) = 36
Smaller angle = 36°
3(18) = 54
Larger angle = 54°
according to insurance records a car with a certain protection system will be recovered 91% of the time. find the probability that 5 of 6 stolen cars will be recovered.
Probability that 5 of 6 stolen cars will be recovered with insurance records a car with a certain protection system will be recovered 91% of the time is equal to P(x=5)=0.3369 (approximately).
As given,
Insurance protection system recovered of a car=91%
p=0.91
q=1-p
=1-0.91
=0.09
n=6
x=5
Using Binomial theorem ,probability of 5 of 6 stolen cars will be recovered is:
ⁿCₓ(p)ˣ(q)ⁿ⁻ˣ
=⁶C₅(0.91)⁵(0.09)⁶⁻⁵
=[6!/(6-5)!5!] × (0.91)⁵× (0.09)
=6×(0.91)⁵×0.09
=0.3369
Therefore, probability that 5 of 6 stolen cars will be recovered with insurance records a car with a certain protection system will be recovered 91% of the time is equal to P(x=5)=0.3369 (approximately).
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Find a point-slope form for the line with slope 1/2
and passing through the point (-3,-8).
The point slope form for the line with slope 1/2 and passing through the point (-3,-8) is y + 8 = m(x + 3)
How to find point slope equation?A linear equation can be represented in point slope form as follows:
y - y₁ = m(x - x₁)
where
m = slopex₁ and y₁ are the coordinatesTherefore, the point slope form is represented as follows;
m = 1 / 2
It passes through the points (-3,-8).
Hence,
y + 8 = m(x + 3)
Therefore, the point slope form of the line is y + 8 = m(x + 3)
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On his fruit stand, Mr.Roberts has 13 papayas, 23-star fruits, 35 mangos, and 19 strawberries. What is the ratio of the number of mangos to the number of strawberries?
Answer:
The answer is 35:19
Step-by-step explanation:
First what is a ratio?
A relationship between two quantities, normally expressed as the quotient of one divided by the other. For example, if a box contains six red marbles and four blue marbles, the ratio of red marbles to blue marbles is 6 to 4, also written 6:4. A ratio can also be expressed as a decimal or percentage.
So as a result
= There are 35 mangoes and 19 strawberries
And since we are comparing mangoes to strawberries
The answer would be
= 35:19
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PLEASE HELP ME HURRY
The number has been assigned to be number line and attached as a picture
What is a number line?A number line refers to a picture representing array of numbers arranged to suit the calculation intended to represent.
How to arrange the numbers in the number lineThe picture shows a number line from -6 to 6
The division in the number line is showing two lines representing 1/3 and 2/3 before the next number.
This means that the point before point 6 counting from point 5 is 5 1/3, 5 2/3 then point 6
For the negative direction we have
-5, -5 1/3, -5 2/3, -6
The required answer to the questions attached
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