The number in the word problem is 2
How to find the number
let the number be x
from the question it is deduced that
If a number is tripled and then subtracted from 15 = 15 - 3x
5 more than twice the number = 2x + 5
equating both sides
15 - 3x = 2x + 5
collecting like terms
15 - 5 = 2x + 3x
10 = 5x
x = 2
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1. (5 points) The arc of a football thrown by Patrick Mahomes is modeled by the equation h=-16t2 + 36t + 6, where h = the height of the ball and t = the time in seconds. Will the ball reach a height of 24 feet?
In order to determine if the ball reaches the 24 ft, replace h = 24 and solve the quadratic equation. If the solutions are real, then, the ball does reach 24ft.
Proceed as follow:
h = 16t² + 36t + 6
24 = 16t² + 36t + 6
16t² + 36t + 6 - 24 = 0
16t² + 36t - 18 = 0
use he quadratic formula, given by:
[tex]t=\frac{-b\pm\sqrt[]{b^{2}-4ac}}{2a}[/tex]In this case, a = 16, b = 36 and c = -18
[tex]\begin{gathered} t=\frac{-36\pm\sqrt[]{(36)^{2}-4(16)(-18)}}{2(16)} \\ t=\frac{-36\pm49.47}{32} \\ t_1=-2.67 \\ t_2=\text{0}.42 \end{gathered}[/tex]negative times do not have physical meanning, then, the available solution is
t = 0.42
Hence, you can conclude that the ball reaches 24 ft for a time of 0.42 seconds.
Heyyy.......please i need help with this
√ 1-cos²θ/1-sec²θ=cosθ, cosθ is the simplified form of √ 1-cos²θ/1-sec²θ
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
We know that ,
Trigonometric identities
sin²θ+cos²θ=1
so 1-cos²θ= sin²θ
sec²θ+tan²θ=1
1-sec²θ=tan²θ
So √ 1-cos²θ/1-sec²θ
√ 1-cos²θ/1-sec²θ=√sin²θ/tan²θ
The square root will get cancelled
=sinθ/tanθ
=sinθ/sinθ/cosθ (because tanθ=sinθ/cosθ)
=cosθ
Hence √ 1-cos²θ/1-sec²θ=cosθ, cosθ is the simplified form of √ 1-cos²θ/1-sec²θ
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How do you think increased distance will affect travel time?
You can notice that travel time is afected by the traveled distance. That's because it is required more time to travel longer distances.
For instance, if Elena would live 6 miles to the school, she would take 30min to arrive to school. That is, for greater distances the travel time increases.
Hey there Ms or Mr could you please help me out with this problem?just so you know, this is Pythagorean theorem & Simplifying Radicals My recent tutor said that this is the answer of course no I don't have any doubts I just want to know if this is correct.
When we have a radical, we can simplify it by the rule:
[tex]\sqrt[]{ab}=\sqrt[]{a}\sqrt[]{b}[/tex]So, we have to break down 500 into simpler radicals until we have a radical that can't be broken down. Let's simplify Root(500).
[tex]\sqrt[]{500}=\sqrt[]{50}\sqrt[]{10}[/tex]Now, we can break down Root(50) further.
[tex]\begin{gathered} \sqrt[]{50}\sqrt[]{10} \\ =\sqrt[]{25}\sqrt[]{2}\sqrt[]{10} \end{gathered}[/tex]Now, let's break down Root(10) also, thus we have:
[tex]\begin{gathered} \sqrt[]{25}\sqrt[]{2}\sqrt[]{10} \\ =\sqrt[]{25}\sqrt[]{2}\sqrt[]{5}\sqrt[]{2} \end{gathered}[/tex]We can see:
• Root(25) is 5
,• Also Root(2)*Root(2) is 2 by using the rule:
[tex]\sqrt[]{a}\sqrt[]{a}=a[/tex]Thus, we finally have:
[tex]\begin{gathered} \sqrt[]{25}\sqrt[]{2}\sqrt[]{5}\sqrt[]{2} \\ =5(2)\sqrt[]{5} \\ =10\sqrt[]{5} \end{gathered}[/tex]Which is the domain and range of the parabola with the equation… Thanks
Okay, here we have this:
Considering the provided equation of the parabola, we are going to find the requested domain and range, so we obtain the following:
Domain: Corresponds to all the values that x can take in the function. Given that in this case no value of x indeterminates the function, and that x can take any value, then its domain will be: (-∞, ∞).
Range: Corresponds to all the values that the dependent variable can take. In this case, since it is a parabola of the form ax^2+bx+c, and that a is less than or greater than 0, its range will be all values greater than or equal to its y-coordinate of the vertex, which for this case is (5, -15). So its range is: [-15, ∞).
Therefore finally we obtain that the correct answer is the fourth option.
does anyone know how to do simplifying expressions with Distributive property 8th grade math
Please help now asap now !!!!!!!!!!!!
Answer: 771
Step-by-step explanation:
Reverse the equation for 96 x 8 + 3
96 x 8 = 768
768 + 3 = 771
You only add the 3 at the end since it was unable to be divided, you can't reverse and multiply it
One-fourth of the seventh-grade students
made honor roll in the first quarter. The
number of honor roll students increased by
18 in the second quarter. If 105 students
made honor roll in the second quarter, how
many total seventh graders are there?
There are 348 seventh-grader students in total.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
One-fourth of the students made the honor roll in the first quarter, and it grew by 18 in the second quarter, so add 18, and the total number of students who made the honor roll in the second quarter is 105.
Let the seventh-grade students would be x
As per the given condition, we can write the equation as:
⇒ 1/4 x + 18 = 105
Subtract 18 on both sides of the above equation,
⇒ 1/4 x = 87
Multiply by 4 both sides of the above equation,
⇒ x = 348
Therefore, there are 348 seventh-grader students in total.
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what is 91 divided by 7 ??
Answer:
13
Step-by-step explanation:
[tex]\frac{91}{7}=\frac{70+21}{7}=10+3=13[/tex]
The solution of 91 divided by 7 in simplest form is,
⇒ 13
We have to given that,
To simplify 91 divided by 7 in simplest form.
It can be written as,
⇒ 91 ÷ (7)
⇒ 91 / 7
⇒ 13
Therefore, The solution of 91 divided by 7 in simplest form is,
⇒ 13
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An empty bucket is being filled at a constant rate. after 4 minutes, the depth of the water is 12 inches. the water continues to be filled at that same rate. what is the relationship between the time in minutes, x, and the depth of the water, y?
Every 4 minutes, the depth of the water increases 12 inches. Like let's say after another 4 minutes it'll be 24 inches. I may be wrong but I may be right.
Answer:
See below
Step-by-step explanation:
Every minute 'x' produces 12/4 = 3 inches of 'y' water depth
y = 3 x
A rectangular prism gift box has dimensions of 2.5 inches, 7 inches, and 9 inches.How much wrapping paper will it take to cover the gift box? Round answer to the nearest tenth if necessary.
The question requires us to calculate the surface area of the rectangular prism.
The formula to calculate the surface area is given to be:
[tex]A=2\left(wl+hl+hw\right)[/tex]where l is the length, w is the width, and h is the height.
From the question, the following dimensions are provided:
[tex]\begin{gathered} l=2.5 \\ w=7 \\ h=9 \end{gathered}[/tex]Therefore, we can calculate the surface area to be:
[tex]\begin{gathered} A=2(7\cdot2.5+9\cdot2.5+9\cdot7) \\ A=206\text{ in}^2 \end{gathered}[/tex]OPTION C is correct.
Function g is represented by the table.
-1
0
24
4
X
g(x)
1
0
2
-
10
3
-24
to
Which statement correctly compares the two functions?
OA. They have different x- and y-intercepts but the same end behavior as x approaches.
OB.
They have the same x- and y-intercepts.
C.
They have the same y-intercept and the same end behavior as x approaches".
D. They have the same x-intercept and the same end behavior as x approaches".
The functions have the same x-intercept and the same end behaviour as x approaches infinity.
We are given two functions, f(x) and g(x). A function connects an input with an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input.
The function f(x) is represented in the graph. The function g(x) is represented by the data in the table. We have to find the correct comparison between the two functions.
The comparison is to be done on the basis of the lengths of the x-intercept and y-intercept and the end behaviour of both functions. From the given values, we conclude that the x-intercepts for both functions are the same, but the y-intercepts are different. The end behaviour of both functions becomes similar as x approaches infinity.
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which is the correct way to model the equation 5x+6= 4x+(-3)
5 positive x-tiles and 6 positive unit tiles on the left side; 4 p
6 positive x-tiles and 5 positive unit tiles on the left side; 3 m
5 positive x-tiles and 6 negative unit tiles on the left side; 4 side
5 positive x-tiles and 6 positive unit tiles on the left side; 4
please help
The correct model the equation 5x+6= 4x+(-3) is 5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side.
What is the model equation?
The model equation is a representation of an equation using tiles.
Given equation is 5x+6= 4x+(-3).
1 is represented by a positive tile.
-1 is represented by a negative tile.
We can rewrite the given equation as:
5×(x)+6× (1)= 4×(x)+(3×(-1))
The model of 5×(x)+6× (1) is 5 positive x-tiles and 6 positive unit tiles.
The model of 4×(x)+(3×(-1)) is 4 positive x-tiles and 3 negative unit tiles.
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Which region has a population density less than 60 animals per square mile
Explanation
We will have to find the population density of each of the regions
To get the population density, we will have to divide the population of each region and then divide by the area of the of each region
For part A
[tex]Area=\frac{1}{2}\times40\times35=700mi^2[/tex]The population density of region A is
[tex]\frac{42500}{700}=60.71\text{ animals per square miles}[/tex]For region B
The area of region B is
[tex]\frac{1}{2}\times50\times38=950mi^2[/tex]The population density of region B is
[tex]\frac{60800}{950}=64\text{ animals per square miles}[/tex]For region C
[tex]area=\frac{1}{2}\times42\times49=1029mi^2[/tex]The population density of region C
[tex]\frac{57300}{1029}=55\text{ animals per square mile}[/tex]Thus, we can observe that Region C has a population density lower than 60 animals per square miles
Thus, option C is correct
Write an equation of the line that passes through $\left(18,\ 2\right)$ and is parallel to the line $3y-x=-12$.
The equation of the line which is parallel to the given line is 3y - x = -12.
What is an equation?An equation is a mathematical formula containing an equal sign. Equations often involve algebra. Algebra is used in mathematics when we don't know the exact number in a calculation. In its simplest form in algebra, the definition of an equation is the mathematical statement that two mathematical expressions are equal. For example, 3x + 5 = 14 is an equation where 3x + 5 and 14 are two terms separated by an equal sign. An equation is a mathematical expression consisting of two expressions connected by an equal sign. For example, 3x + 5 = -16 is an example of equation. Solving this equation gives the value of the variable x as x = 7.given that
x = 18 and y = 2
putting the value in equation 3y-x = -12
this saisfied he equation perfectly.
Hence, the equation in parallel to 3y-x = -12
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What is the image point of (6, -7) after the transformation D4 T3,5?
The final image of the given points after the given translation and dilation of D4, T3,5 is (27, -23).
What is meant by the term transformation?Image transformations usually involve the modification of various bands of data, such as a single multispectral image either from a number of images acquired at different times of the same area (i.e. multitemporal image data). Image transformations, in either case, generate "new" images from a variety of sources that highlight specific features or characteristics of interest more effectively than the original input images.For the given image point of (6, -7) .
First there is a dilation of 4.
Thus,
Image = (6×4 , -7×4)
Image = (24, -28)
Now, there is translation of 3 units right on x axis and 5 unit upward on y axis; T3,5.
Image = (24 + 3, -28 + 5)
Image = (27, -23)
Thus, the final image of the given points after the given translation and dilation is (27, -23).
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Help with my algebra please.
t + b = 38
6t + 4b = 188 is the equation to calculate the system of the restaurant .
Restaurants must foster an atmosphere of delicious food, attractive surroundings, and courteous living. In order to maintain the restaurant's financial viability, it is crucial for the owners to choose the seating arrangement, chairs, and sofas with an eye toward projecting a certain image.
What is seat arrangement problems?The most typical categories of seating arrangement queries. There are intricate row arrangements, double rows, rectangular rows, linear rows, and circular rows.
Theatre. The simplest and most popular seating arrangement for events is the theater style setup.
Classroom.Herringbone.a U-shape.Equine shoeSquare HollowBoardroom.Banquet.n distinct things permuted (when repetition is not allowed) Repetition when it is acceptable. When the objects are not distinct, permutation (Permutation of multi sets)
The following formula determines how many permutations of n objects, taken r at a time: (n,r)! P(n,r)=n!
The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation.
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Which two consecutive integers does[tex] - \sqrt{214} [/tex]fall between?
Answer
-√214 is between -15 and -14.
Explanation
To solve this, we need to first obtain the value of the -√214
-√214 = -14.63
Hence, we can see that this number is between -15 and -14.
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the sum of 10 and 15 divide by the difference 8 and 3 how to translate
We have the following:
[tex]\frac{10-5}{8-3}=\frac{5}{5}=1[/tex]20 POINTS! HURRY!!!!Which expressions are equivalent to 5(1/3x+7)-3(1/3x-4)? Select three options.5 1/3x-3 1/2x+35-121/6x+471 2/3x+36-1 1/2x+ 125(1/3x)+(5)(7)-(3)(1/2x)+(3)(4)1 1/3x+35-1 1/2x-12
The given expression is:
[tex]undefined[/tex]The expression on the left side of an equation is shown below.
3 (x + 1) + 9 = box
If the equation has no solution, which expression can be written in the box on the other side of the equation?
3 (x + 4)
2 (x + 6) + x
4(x – 3) – x
3 (x + 1) + 9 x
Answer:
C) 4(x – 3) – x
Step-by-step explanation:
Match each exponential function with the graph that correctly models the function.
Answer:
Step-by-step explanation:
1) third graph -> the base is 3 so the graph increase
2) first graph -> if x = 0 ; y = -2
(1/3)^0 -3 = 1 - 3 = -2
3) second graph
The lines below are parallel. If the slope of the green line is -1/2,what is theslope of the red line?
When two lines are parallel they mean that both slopes are the same, this means that if the green line has a slope of -1/2, the slope of the red line is also -1/2.
A 6-pack of magnets costs $6.06. What is the unit price?
Answer: $1.01
Step-by-step explanation: You just divide by 6
what do you think the answer is? No it’s not the 3rd option or not that I think I just clicked a random answer on accident.
Answer
Option C is correct.
Sandra will be paid 72.30 dollars for babysitting for 12 hours.
Explanation
We are told that Sandra earned 60.25 dollars babysitting 10 hours.
If she babysits at the same rate, we are asked to calculate the amount she would earn if she babysits for 12 hours.
Let the amount Sandra is paid for babysitting for 12 hours be x dollars
10 hours = 60.25 dollars
12 hours = x dollars
We can write a mathematical relationship by cross multiplying
10 × x = 12 × 60.25
10x = 723
Divide both sides by 10
(10x/10) = (723/10)
x = 72.3 dollars
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On the number line above, if x is a number that lies between a and a + 10, which of the following must betrue?lx - al > 5lx - a -51 < 5lx - a - 101 < 5lx - a + 101 < 5
We are given an inequality proble. Our approach is to test our options.
We begin with the second option.
[tex]\begin{gathered} |x-a-5|<5 \\ \text{This translates to:} \\ -5<|x-a-5|<5 \end{gathered}[/tex]We'll solve it in parts and compare to our number line
[tex]\begin{gathered} -5<(x-a-5) \\ \text{Adding 5 to both sides gives us:} \\ -5+5On the other hand, we have:[tex]\begin{gathered} (x-a-5)<5 \\ \text{Adding 5 to both sides} \\ x-a<5+5 \\ x-a<10 \\ \text{Adding a to both sides} \\ x<10+a \end{gathered}[/tex]The range of x is therefore: a < x < 10 + a
SECOND OPTION
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
Solve the inequality for e:
negative 3 e greater than 21
Group of answer choices
e greater than negative 63
e less than negative 63
e less than negative 7
e greater than negative 7
The solution of the inequality negative 3 e greater than 21 is e less than negative 7.
Inequality:
If the two real numbers or algebraic expressions are related using the symbols >, <, ≥, ≤, then the expression is called an inequality.
Given,
Here we have the statement for the inequality.
"negative 3 e greater than 21".
Now, we have o solve it and then we have to find the value of e.
The given statement is rewritten as the following expression form,
That is,
-3e > 21
Here we need the value of e, so we have to divide both sides by 3, then we get,
=> -e > 7
To remove the negative sign, we have to reverse the inequality, then we get the value of e as
=> e < -7
Therefore, in statement it can be written as "e less than negative 7".
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A normal distribution has a mean of 75 and a standard deviation of 15.
Determine the z-score for the data value of 85.
0.67
1) Given that we've got the following data:
[tex]\mu=75,\sigma=15,X=85[/tex]We can plug them all together into the Z score formula:
[tex]Z=\frac{X-\mu}{\sigma}=\frac{85-75}{15}=\frac{10}{15}\approx0.67[/tex]Thus, the Z-score is 0.67
What is the radian equivalent of 90 degrees?
Answer:
The Radiant Equivalent of 90 degrees, would be 1.57079633.