Answer:
25 feet
Explanation:
The equation that models the pathway of the container is:
[tex]h=-16t^2+25[/tex]The maximum height occurs at the axis of symmetry.
First, we find the equation of symmetry:
[tex]\begin{gathered} x=-\frac{b}{2a}where\begin{cases}a=-16 \\ b=0\end{cases} \\ x=-\frac{0}{2\times-16} \\ x=0 \\ \implies t=0 \end{gathered}[/tex]Next, determine the value of h at t=0.
[tex]\begin{gathered} h=-16(0)^2+25 \\ h=25\text{ feet} \end{gathered}[/tex]The maximum height of the container is 25 feet.
Which of the following is a solution to the inequality below?
Answer:
4u + 6 > 30
4u > 24
u > 6
Solution is u = 6
Answer:
4u+6>30
4u>30-6
4u>24
u>6
Answer:
u>6
represent the following expressions as a power of the number a (a≠0):
(a^-1*a^-2)^-2
By using some exponent properties, we will see that the expression can be written as:
a^6
How to simplify the expression?
Here we need to use some exponent properties, these are:
(x^n)^m = x^(n*m)x^(-n) = (1/x)^nx^n*x^m = x^(n + m)Here we have the expression:
(a^(-1)*a^(-2))^(-2)
Using the third property we can write:
(a^(-1)*a^(-2))^(-2) = (a^(-1 - 2))^(-2) = (a^(-3))^(-2)
Now we use the first property:
(a^(-3))^(-2) = a^(-3*-2) = a^6
That is the expression simplified.
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two integers a and b have a product of 36 what is the least possible answer
Answer:
the answer is 12
Step-by-step explanation:
In short, a = 6 and b = 6. We can make a table of various values to help confirm that 12 is the smallest sum.
Answer: 1
Step-by-step explanation: 1 is the least possible answer because an integer is any number and 1x36 would be the least possible answer for the product.
Compute the derivative of f(x) = x * sin(x) . Use the result to compute f^ prime ( pi 2 )
Solution
Step 1
f(x) = xsinx
Step 2
[tex]\begin{gathered} f(x)=x\sin\left(x\right) \\ \\ f^{\prime}(x)=\sin\left(x\right)+x\cos\left(x\right) \end{gathered}[/tex]Step 3
[tex]\begin{gathered} f^{\prime}(\frac{\pi}{2})=\sin\left(\frac{\pi}{2}\right)+\frac{\pi}{2}\cos\left(\frac{\pi}{2}\right) \\ \\ f^{\prime}(\frac{\pi}{2})=1 \end{gathered}[/tex]Final answer
A. 1
There are 45 boys and 81 girls in a dance competition. What is the ratio of boys to girls, in the simplest form?
Answer
[tex]\frac{5}{9}[/tex]Explanation
Given
• 45 boys
,• 81 girls
Procedure
We have to find the ratio of boys to girls, which can be written as 45:81 or:
[tex]\frac{45}{81}[/tex]However, we have to simplify. Both numbers are multiple of 9, thus:
[tex]=\frac{\frac{45}{9}}{\frac{81}{9}}=\frac{5}{9}[/tex]Then every five boys there are 9 girls.
for each triangle list the sides in order from shortest to longest explain your reasoning with words or numbers for the order
a. For the first triangle ,
Two angles are given. To determine the third angle apply the property of triangle which is sum of the angles of the triangle is 180 degree.
[tex]27^{\circ}+82^{\circ}+\angle T=180^{\circ}[/tex][tex]\angle T=180^{\circ}-27^{\circ}-82^{\circ}=71^{\circ}[/tex]The triangle angles and sides relationship-
The longest side of a triangle is opposite the biggest angle measure.
The shortest side of a triangle is opposite the smallest angle measure in a triangle.
Therefore,
The shortest side is side opposite to the smallest angle that is MT.
The largest side is side opposite to the largest angle that is AT.
Hence the order for the sides from shortest to largest is
[tex]MTb. The triangle is given . First determine the value of x and find the angle using the property of triangle which is sum of the angles of the triangle is 180 degree.
[tex]8x-1+3x+4+3x+9=180^{\circ}[/tex][tex]14x+12=180[/tex][tex]14x=168[/tex][tex]x=12[/tex]The angles obtained are
[tex](8x-1)=95,(3x+4)=40,(3x+9)=45[/tex]We know that the longest side of a triangle is opposite the biggest angle measure.
The shortest side of a triangle is opposite the smallest angle measure in a triangle.
Hence the shortest side is JK and largest side is JL.
Hence the order for the sides from shortest to largest is
[tex]JKFind the Value of interval [0,2pie] such as that tan s= -radical3/3
The values of s in the interval [0, 2π) such that tan s = -(√3)/3 are 5π/6 and 11π/6.
What is trigonometry and how is it assessed?
Simply put, trigonometric functions—also referred to as circular functions: are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions. Numerous trigonometric identities and formulas indicate the relationship between the functions and aid in determining the triangle's angles.
The quadrants determine the values of the trigonometric functions.
Given, tan s = -(√3)/3 ⇒ tan s = -(√3)/(√3)² ⇒ tan s = (-1)/(√3)
Therefore, the simplified value of tangent of s is tan s = (-1)/(√3)
Again the interval of the function is [0, 2π), so only the second and fourth quadrants can contain the given value of tangent being negative.
For the value of s in second quadrant, we have:
tan s = (-1)/(√3) ⇒ tan s = tan (π - (π/6)) ⇒ tan s = tan (5π/6) ⇒ s = 5π/6
For the value of s in the fourth quadrant, we have:
tan s = (-1)/(√3) ⇒ tan s = tan (2π - (π/6)) ⇒ tan s = tan (11π/6) ⇒ s = 11π/6
Thus, the values of s in the interval [0, 2π) such that tan s = -(√3)/3 are 5π/6 and 11π/6.
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40% of what number is 26? Please show work!
65
1) To find that, we need to write an equation:
[tex]x(0.4)=26[/tex]Note that we rewrote that 40% as 0.4.
2) Now, let's solve it
[tex]\begin{gathered} x0.4=26 \\ \frac{0.4x}{0.4}=\frac{26}{0.4} \\ x=65 \end{gathered}[/tex]3) So the 26 is 40% of 65
I need help with finding the output y when x is -4 it's on a graph
As observed from the graph, the curve is a straight line from point (-2,-1) to (-5,2).
Consider that the equation of a straight line passing through two points is given by,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}\times(x-x_1)[/tex]So the equation of the line passing through (-2,-1) and (-5,2) is given by,
[tex]\begin{gathered} y-(-1)=\frac{2-(-1)}{-5-(-2)}\times(x-(-2)) \\ y+1=\frac{3}{-3}\times(x+2) \\ y+1=-x-2 \\ y=-x-3 \end{gathered}[/tex]Note that this function is only for the interval [-2, -5].
Now, the value of 'y' corresponding to the input x=-4 is calculated as,
[tex]\begin{gathered} y=-(-4)-3 \\ y=4-3 \\ y=1 \end{gathered}[/tex]Thus, the required output is y = 1 .
For the equation 5x+36=x, Which value could be a solution
Solution;
[tex]\begin{gathered} 5x+36=x \\ 5x-x+36=x-x \\ 4x+36=0 \\ \end{gathered}[/tex][tex]\begin{gathered} 4x+36-36=0-36 \\ 4x=-36 \end{gathered}[/tex][tex]x=-\frac{36}{4}=-9[/tex]x=-9
Translate the sentence into an inequality.Twice the difference of a number and 2 is at least −28.Use the variable x for the unknown number.
To answer this question we have to identify the elements of the inequality.
1. The difference of a number and 2 is represented by the expression: x-2.
2. Twice the difference (...) is represented by the expression: 2(x-2).
3. At least is represented by the sign greater than or equal to ≥.
4. The result is -28.
By putting these all together we obtain the inequality:
[tex]2(x-2)\ge-28[/tex]It means that the answer is 2(x-2) ≥ -28.
AB is a median of a triangle true or false
To answer this question, first we need to understand the definition of a median of a triangle.
A median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side of the vertex.
AB is a segment drawn from the vertex A, to the point B, but B is not the midpoint of the base of this triangle(the midpoint divides the segment into two equal parts, and since one part is 7 and the other is 8, B is not the midpoint
Jackson deposited $160 a month into an account earning 7.2% compounded monthly for 12 years. He left the accumulated amount for another 3 years at the same interest rate. How much total interest did he earn?
Using the formula for the compound interest, we have:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{ A:amount,P:principal,r:rate,n: number of times interest is compounded per year,t:time in years.} \\ A=160(1+\frac{0.072}{12})^{12\cdot15}\text{ (Replacing the values)} \\ A=160(1+0.006)^{180}\text{ (Dividing and multiplying)} \\ A=160\cdot2.935\text{ (Adding and raising the result to the power of 180)} \\ A=469.63\text{ (Multiplying)} \\ \text{Interest}=\text{ Amount - Principal=469.63}-160=309.63 \\ \text{The answer is \$309.63} \end{gathered}[/tex]what is 3 8/9 + 8 1/2
how many cheese pizzas can the girls buy if they pool all their money together? inequality form for each scenario. CHEESE PIZZA IS 7.25 DOLLARS.
Since we have 5 girls and their parents give each other $10, they have in total $50.
Now, let x be the number of pizzas they buy, since each pizza cost $7.25 the total cost for x pizzas is:
[tex]7.25x[/tex]this should be less or equal to $50 (otherwise the girls go over budget), then the inequality that represents this situation is:
[tex]7.25x\leq50[/tex]Now, solving the inequality we get:
[tex]\begin{gathered} 7.25x\leq50 \\ x\leq\frac{50}{7.25} \\ x\leq6.9 \end{gathered}[/tex]Therefore, they can buy a maximum of 6 pizzas without going over budget.
State whether the given information is enough to prove that ABCD is a parallelogram.
From the image given, the data shows that
[tex]\begin{gathered} <1\cong<3 \\ \text{and} \\ AD\cong BC \end{gathered}[/tex]We can observe that
[tex]\begin{gathered} \Delta BDA\cong\Delta DBC\text{ (SAS)} \\ \text{ Reasons:} \\ AD\cong BC\Rightarrow side \\ \measuredangle1\cong\measuredangle3\Rightarrow\text{angle} \\ BD\cong DB(common\text{ sides or reflexive)}\Rightarrow\text{side} \end{gathered}[/tex]Thus, from the above we can say that;
[tex]\begin{gathered} AB\cong DC\text{ (corresponding parts of congruent triangles are congruent)} \\ \text{Therefore, } \\ \measuredangle2\cong\measuredangle4 \end{gathered}[/tex]Hence
Yes, the given information is enough to prove that ABCD is a parallelogram.
A parabola contains the following points.(-5,8),(2,-3),(3,1) which of the following systems of equations could be solved in order to find the equation that corresponds to this parabola?
Generic parabola equation:
y = a*x^2 + b*x + c
We have three points of the parabola:
(-5,8), (2,-3), (3,1)
For the point (-5, 8): x = -5, y = 8
8 = 25*a - 5*b + c
Point (2,-3): x = 2, y = -3
-3 = 4*a + 2*b + c
Point (3, 1): x = 3, y = 1
1 = 9*a + 3*b + c
Our system of equations:
8 = 25*a - 5*b + c
-3 = 4*a + 2*b + c
1 = 9*a + 3*b + c
The last option is the correct answer
I think is the average of the highest point and the lowest one, what's the midline of the graph?
The Midline of a Sinusoid
A sinusoid is a periodic function which parent expression is:
f(x) = A. sin (wt)
Where A is the amplitude and w is the angular frequency
The sine function has a maximum value of A and a minimum value of -A.
The midline can be found as the average value of the maximum and the minimum value.
For the parent function explained above, the midline is:
[tex]M=\frac{\text{Mx}+Mn}{2}[/tex]Since Mx and Mn are, respectively A and -A, the midline is zero.
The graph shown in the image has a maximum of Mx=1 and a minimum of Mn=-5.
Thus, the midline is:
[tex]M=\frac{\text{1}-5}{2}=-\frac{4}{2}=-2[/tex]The midline of the graph is y=-2
estimate 1/4% of 798
An outdoor equipment store surveyed 300 customers about their favorite outdoor activities. The circle graph below shows that 135 customers like fishing best, 75 customers like camping best, and 90 customers like hiking best.
it is given that,
total customer surveyed is 300 customers
also, it is given that,
135 customers like fishing best, 75 customers like camping best, and 90 customers like hiking best.
the total 300 customers representing the whole circle and circle has a complete angle of 360 degrees
so, 300 customers = 360 degrees,
1 customer = 360/300
= 6/5 degrees,
so, for fishing
135 customer = 135 x 6/5 degrees
= 27 x 6
= 162 degrees,
so, for camping
75 x 6/5 = 90 degrees,
for hiking
90 x 6/5 = 108 degrees,
Find the tangent of the angle whose measure is pi/2....pi divided by 2.
We have the following:
[tex]\begin{gathered} \tan \theta=x \\ \tan \frac{\pi}{2}=x \end{gathered}[/tex]the value of pi / 2 is not defined
Answer two questions about Equations A and B
A. 2r-1= 5x
B. -1 = 3x
1) How can we get Equation B from Equation A?
Choose 1 answer:
Add/subtract the same quantity to/from both sides
Add/subtract a quantity to/from only one side
Rewrite one side (or both) by combining like terms
Rewrite one side (or both) using the distributive property
In the given equation A, we can (A) subtract the same quantity from both sides.
What are equations?In a mathematical equation, the equals sign is used to express that two expressions are equal. An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. Like 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, and others. The three primary forms of linear equations are point-slope, standard, and slope-intercept.So, obtain equation B from equation A:
Equation A: 2x - 1 = 5xEquation B: -1 = 3xWe can subtract (2x) from both sides to get equation B as follows:
2x - 1 = 5x2x - 2x - 1 = 5x - 2x-1 = 3xTherefore, in the given equation A, we can (A) subtract the same quantity from both sides.
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Hi, can you help me to solve this problem, please!!
In this problem, we have a vertical parabola open downward
that means
the vertex represents a maximum
looking at the graph
the maximum has coordinates (1,9)
therefore
the vertex is (1,9)Ninety percent of a large field is cleared for planting. Of the cleared land, 50 percent is planted with blueberry plants and 40 percent is planted with strawberry plants. If the remaining 360 acres of cleared land is planted with gooseberry plants, what is the size, in acres, of the original field?*
For the given question, let the size of the original field = x
Ninety percent of a large field is cleared for planting
So, the size of the cleared land = 90% of x = 0.9x
50 percent is planted with blueberry plants and 40 percent is planted with strawberry plants.
So, the size of the land planted with blueberry plants and strawberry plants =
[tex]0.5\cdot0.9x+0.4\cdot0.9x=0.45x+0.36x=0.81x[/tex]The remaining will be = 0.9x - 0.81x = 0.09x
Given: the remaining 360 acres of cleared land is planted with gooseberry plants
so,
[tex]0.09x=360[/tex]divide both sides by (0.09) to find x:
[tex]x=\frac{360}{0.09}=4,000[/tex]So, the answer will be:
The size of the original field = 4,000 acres
if 2 angles from a line
If two angles form a linear pair, then they form a straight line, and the sum of their measures is 180 degrees.
This illustrated below;
In the illustration above, angle measure 1 and 2 both equal to 180 degrees. Angle 1 and angle 2 are refered to as a linear pair.
Find the probability of getting 4 aces when 5 cards are drawn from an ordinary deck of cards
First, let's calculate the number of different hands of 5 cards that can be made, using a combination of 52 choose 5:
(a standard deck card has 52 cards)
[tex]C\left(52,5\right)=\frac{52!}{5!\left(52-5\right)!}=\frac{52\cdot51\operatorname{\cdot}50\operatorname{\cdot}49\operatorname{\cdot}48\operatorname{\cdot}47!}{5\operatorname{\cdot}4\operatorname{\cdot}3\operatorname{\cdot}2\operatorname{\cdot}47!}=\frac{52\cdot51\operatorname{\cdot}50\operatorname{\cdot}49\operatorname{\cdot}48}{120}=2,598,960[/tex]Now, let's calculate the number of hands that have 4 aces. Since the fifth card can be any of the remaining 48 cards after picking the 4 aces, there are 48 possible hands that have 4 aces.
Then, the probability of having a hand with 4 aces is given by the division of these 48 possible hands over the total number of possible hands of 5 cards:
[tex]P=\frac{48}{2598960}=\frac{1}{54145}[/tex]The probability is 1/54145.
What is the solution to x^2 – 9x < –8?A. x < 1 or x > 8B. x < –8 or x > 1C. 1 < x < 8D. –8 < x < 1
INFORMATION:
We have the next inequality
[tex]x^2-9x<-8[/tex]And we must find its solution
STEP BY STEP EXPLANATION:
To solve it, we must:
1. Move all terms aside
[tex]x^2-9x+8<0[/tex]2. Factor x^2-9x+8
[tex](x-8)(x-1)<0[/tex]3. Solve for x
[tex]x=8\text{ or }x=1[/tex]4. From the values of x, we have these 3 intervals to test
[tex]\begin{gathered} x<1 \\ 18 \end{gathered}[/tex]5. Choose a test point for each interval
For the interval x < 1:
[tex]\begin{gathered} \text{ Using x }=0, \\ 0^2-9(0)<-8 \\ 0<-8 \end{gathered}[/tex]which is false. So, the interval is discarded.
For the interval 1 < x < 8:
[tex]\begin{gathered} \text{ Using x }=2, \\ 2^2-9(2)<-8 \\ -14<-8 \end{gathered}[/tex]which is true. So, the interval is maintained
For the interval x > 8:
[tex]\begin{gathered} \text{ Using x = 9,} \\ 9^2-9(9)<-8 \\ 0<-8 \end{gathered}[/tex]which is false. So, the interval is discarded.
Finally, the solution would be the interval that was maintained: 1 < x < 8.
ANSWER:
C. 1 < x < 8
Answer:
C. 1 < x < 8
Step-by-step explanation:
x² - 9x < -8
we will suppose some values for x to check which values will satisfy this inequality:
for x = 1
1(1-9) < -8 which is wrong
for x = 2
2(2-9) < -8 this is satisfying the inequality
for x = 8
8(8-9) < -8 which is wrong
let's take any negative value now,
let x = -2
-2(-2-9) < -8 which is wrong
thus x is the positive value which will always be greater than 1 and less than 8 for the given inequality.
What do you notice about the measures of the sides or the measures of angles that form triangles?
The angles sum up to give 180°
Only one of the angles can be an obtuse angle, we can;t have two bothuse angle in a triangle. BUT we can have two acute angles and one obtuse angle in a triangle.
We can also have a 90 degree and 2 acute angle in a triangle.
Examples
The angles sum up to give 180°
Only one of the angles can be an obtuse angle, we can;t have two bothuse angle in a triangle. BUT we can have two acute angles and one obtuse angle in a triangle.
We can also have a 90 degree and 2 acute angle in a triangle.
Examples
let f ( x ) = 6356 x + 5095 . Use interval notation. Many answers are possible.
The equation of the function has its domain representation in interval notation as (oo, oo)
How to determine the domain of the functionFrom the question, the equation of the function is given as
f ( x ) = 6356 x + 5095
Rewrite the equation of the function properly by removing the excess spaces
So, we have
f(x) = 6356x + 5095
The above equation is a linear equation
A linear equation is represented as
f(x) = mx + c
As a general rule;
The domain of a linear equation is all set of real numbers
This is the same for the range
i.e. the range of a linear equation is all set of real numbers
When the set of real numbers is represented as an interval notation, we have the following representation
(oo, oo)
Hence, the domain is (oo, oo)
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Possible question
let f ( x ) = 6356 x + 5095 . Use interval notation to represent the domain of the function.
Many answers are possible.
Leah invested $400 in an account paying an interest rate of 1 1/2%compounded annually. Lauren invested $400 in an account paying aninterest rate of 0 7/8% compounded monthly. To the nearest hundredth of ayear, how much longer would it take for Lauren's money to triple than forLeah's money to triple?
Leah investment is:
[tex]M_{\text{Leah}}=400_{}\cdot1.5^y[/tex]Where M is the ammount of money that she has, and y the number of years.
We want to know the number of years that must elapse for her investment to triple, so we want to know the value of y such that:
[tex]\begin{gathered} 3\cdot400=400\cdot(1+\frac{1.5}{100})^y \\ 3=(1.015)^y \\ \ln 3=y\cdot\ln (1.015) \\ y=\frac{\ln (3)}{\ln (1.015)}\cong73.788\cong73.79 \end{gathered}[/tex]It will take 73.79 years to triple her investment.
Lauren investment is:
[tex]M_{\text{Lauren}}=400\cdot(1+\frac{7}{8}\cdot\frac{1}{100})^m=400\cdot(1.00875)^{\frac{y}{12}}[/tex]Where M is the ammount of money that she has, and m the number of months, and y is the number of years.
We want to know the number of years that must elapse for her investment to triple, so we want to know the value of y such that:
[tex]\begin{gathered} 3\cdot400=400\cdot(1.00875)^{\frac{y}{12}} \\ 3=(1.00875)^{\frac{y}{12}} \\ \ln 3=\frac{y}{12}\ln (1.00875) \\ y=12\cdot\frac{\ln 3}{\ln (1.00875)} \\ y=1513.25 \end{gathered}[/tex]