The basketball will reach its maximum height 1.735 seconds after it has been thrown vertically into the air.
Define the term function?A function is a relationship between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. A function can be represented as an equation, a graph, a table of values, or a verbal description. For example, the function f(x) = 2x + 1 represents a relationship between the input x and the output 2x + 1.
To find the maximum height of the basketball, we need to find the vertex of the parabola represented by the function f(x). The vertex of x-coordinate is:
x = -b/2a
The coefficients of the quadratic equation a[tex]x^2[/tex] + b[tex]x[/tex] + c are a, b, and c. In this case, a = -4.9 and b = 17, so:
x = -17/(2*(-4.9)) = 1.735 (rounded to 3 decimal places)
Therefore, the basketball will reach its maximum height 1.735 seconds after it has been thrown vertically into the air.
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A magrzeino used the surnunatod rating of 10 restaurants to predut the cost of a restaurant meal. For that data, SSR \( -131,383.63 \) and SST \( =140,70746 \) Completo parts (a) through (c). a. Deter
The coefficient of determination or R² is -0.932. The coefficient of correlation or R is 0.964. The equation of the regression line is:Y= 27,233.25 + (960.25X)Y= 27,233.25 + 0.96X.
A magrzeino used the surnunatod rating of 10 restaurants to predut the cost of a restaurant meal. For that data, SSR \(-131,383.63 \) and SST \( =140,70746 \). The task is to complete parts (a) through (c). a) Determining the coefficient of determination or R²R² can be determined using the formula given below: R²= SSR/SST R²= -131,383.63 /140,707.46 R²= -0.932 Thus, the coefficient of determination or R² is -0.932.(b) Determining the coefficient of correlation or RTo determine the coefficient of correlation, we will use the formula given below:R= sqrt(R²)R= sqrt(-0.932)R= 0.964 Thus, the coefficient of correlation or R is 0.964.(c) Determining the equation of the regression lineUsing the formula,
The equation of the regression line can be calculated as:Y= a + bX where a = Y - bX, b = r (sy/sx)and r is the correlation coefficient.The given data can be arranged into a table as shown below:X (Sur)Y (Cost of a restaurant meal)XYX²Y²1200180020003600840030007601440040009002250045001020250601000050011200027501250222501250015003700022501650142252,306,901387,762,1509,622,5001,293,900248,408,050The values of ΣX, ΣY, ΣXY, ΣX², and ΣY² can be calculated from the table. ΣX = 55ΣY = 85,900ΣXY = 960,250ΣX² = 3850ΣY² = 69,635,950Then, a = (ΣYΣX² - ΣXΣXY) / nΔ= 10(a)Δ= [(85,900 x 3850) - (55 x 960,250)] / 10Δ= (330,115,000 - 52,814,750) / 10Δ= 27,233.25Therefore, the equation of the regression line is:Y= 27,233.25 + (960.25X)Y= 27,233.25 + 0.96X.
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Noah wants to share a certain amount of money with 10 people. However,at the last minute,he is thinking about decreasing the amount by 20 so he can keep 20 for himself and share the money with only 5 people. How much money is Noah trying to share if each person still gets the same
amount
The money is Noah wants to share with people if each person still gets the same amount is 4.
Explain about the substitution method?The algebraic approach to solving simultaneous linear equations is known as substitution method.
The value of one variable through one equation is substituted in the second equation in this procedure, as the name implies.It is only useful if the change of variable explains the situation and, ideally, makes it possible to solve the problem once it has been simplified. First, considering a situation in which variables exist, a substitution is simply a change of variable.Let the total amount Noah have be'y'.
The initial amount shared by Noah among 10 people be 'x'.
Then,
y = 10x
But,
Amount shared is decreased by 20, ans sharing with 5 people.
Then,
y - 20 = 5x
Put value of y.
10x = 5x + 20
On solving;
x = 20/5
x = 4
Thus, money is Noah wants to share with people if each person still gets the same amount is 4.
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0.0005 × 0.007
————————-
0.01
Answer:
0.00035
Step-by-step explanation:
0.0005×0.007 ×100
—————-------
1
0.0000035 ×100
0.00035
PLEASE HELP NEED DETAILED WORD ANSWER I CAN USE
WILL MARK BRAINLIEST
please dont use for points or I will report
sorry!
Given the following question:
We have 60 balloons in total
4/12 of the balloons are black
3/12 of the balloons are white
We are trying to find the amount of red balloons Carter has:
Let...
B = black
W = white
R = red
[tex]B=(\dfrac{4}{12}) \times60=20[/tex]
[tex]B=20[/tex]
[tex]W=(\dfrac{3}{12}) \times60=15[/tex]
[tex]20+15=35[/tex]
[tex]60-35=25[/tex]
[tex]R=25[/tex]
Carter has 25 red balloons
If f(x) is an exponential function where f(-3)=27 and f(0.5)=83, then find the value of f(0), to the nearest hundredth
Answer: f(0) ≈ 4.37
Step-by-step explanation:
We can use the information given to find the base and the equation of the exponential function.
Let the exponential function be of the form f(x) = a*b^x, where a is the initial value of f(0) and b is the base of the exponential function.
From the given information, we have:
f(-3) = 27 = ab^(-3)
f(0.5) = 83 = ab^(0.5)
To eliminate the variable a, we can divide the second equation by the first equation:
f(0.5)/f(-3) = (ab^(0.5))/(ab^(-3))
83/27 = b^(0.5+3)
b^3 = (83/27)^2
b = (83/27)^(2/3)
Substituting this value of b in the first equation, we can solve for a:
27 = a*(83/27)^(-1)
a = 27*(83/27)
Therefore, the equation of the exponential function is f(x) = (83/27)^(2/3)*((83/27)^(-1))^x.
To find f(0), we substitute x = 0 in the above equation:
f(0) = (83/27)^(2/3)*((83/27)^(-1))^0
f(0) = (83/27)^(2/3)
f(0) ≈ 4.37
form A line has a slope of -4 and a y-intercept of 2. Write its equation in slope-intercept form Write your answer using integers, proper fractions, and improper fractions in simplest
Answer: Y= -4x + 2
Step-by-step explanation:
The slope intercept equation is y = mx + b
The slope or m in this situation is -4
The y- intercept or b is 2
When you substitute then slope and y-intercept into the equation you get
Y = -4x + 2
Liz spent her summer break working at Wild Lakes waterpark. At the end of the summer, she put $570 of her earnings into a savings account that earns 1% interest each year.
The total simple interest earned by Liz at the end of 5 years is found as: $28.5
Explain about the simple interest?A straightforward but effective idea. Very simply: interest is the benefit for saving - and the penalty of borrowing.
When you deposit funds into a savings account, you are paid interest, or additional money on top. The reason for this is that the bank gives you interest for letting them use your money.When someone owes money, they are assessed this fee. It indicates the time worth of money and is charged in relation to the principal sum. It is the prize for holding out and refusing to accept an early reward.Principal P = $570
Interest r = 1%
Time t = 5 years.
SI = P*R*t / 100
SI = 570*1*5 / 100
SI = 28.5
Thus, the total simple interest earned by Liz at the end of 5 years is found as: $28.5.
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The complete question is-
Liz spent her summer break working at Wild Lakes waterpark. At the end of the summer, she put $570 of her earnings into a savings account that earns 1% interest each year. Find her simple interest after 5 years.
what is the exact value for x
Answer: [tex]6\sqrt{2}[/tex]
Step-by-step explanation:
We know that one angle is 45 degrees and another is 90 degrees. That means the third angle is also 45 degrees, because all angles in a triangle add up to 180 degrees. This means that the triangle we are dealing with is an isosceles right triangle, meaning the the 2 equal legs form a right angle and are equal in length. If one leg is 6, the other leg must be 6, too.
Then, by the Pythagorean theorem, x=[tex]\sqrt{6^2+6^2}[/tex]=[tex]\sqrt{72}=6\sqrt{2}[/tex].
Triangle EFG is translated 3 units up and 5 units left. What are the
coordinates of E′?
Answer:
If E(x,y), then E’(x-5,y+3)
Step-by-step explanation:
Depending on E, E’ changes. The new coordinates for E’, however, is (x-5, y+3), if (x,y) is E, since you move left (-) 5 and up (+) 3.
question 1 options: two polygons are similar if and only if there is a correspondence among their angles and among their sides so that all corresponding angles are congruent and all corresponding sides are .
Two polygons are similar if and only if there is a correspondence among their angles and among their sides so that all corresponding angles are congruent and all corresponding sides are proportional.
Two polygons are said to be similar if they have the same shape, but not the same size. A polygon is any two-dimensional closed shape with straight lines. Similar polygons have the same number of sides and angles. The sides of the similar polygons are proportional to the corresponding sides of the other polygon.
The ratio of their corresponding sides is the same as the ratio of their perimeter. The angles of the similar polygons are congruent to the corresponding angles of the other polygon. The ratio of their corresponding angles is the same as the ratio of their measure.
The corresponding sides and angles are the ones that match between the two polygons. In other words, they are the sides and angles that are in the same position in the two polygons. For example, side AB in polygon ABC corresponds to side DE in polygon DEF. Angle A in polygon ABC corresponds to angle D in polygon DEF.
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A dot plot titled Mister Hart'students going from 0 to 8. 0 has 1 dot, 1 has 0 dots, 2 has 2 dots, 3 has 2 dots, 4 has 1 dot, 5 has 4 dots, 6 has 2 dots, 7 has 1 dot, 8 has 2 dots. A dot plot titled Misses Perry's Students going from 0 to 8. 0 has 2 dots, 1 has 4 dots, 2 has 1 dot, 3 has 3 dots, 4 has 2 dots, 5 has 1 dot, 6 has 1 dot, 7 has 0 dots, 8 has 1 dot. The data plots represent the hours students study each week in two different classrooms. The mean number of hours a student in Mr. Hart’s class studies is hours. The mean number of hours a student in Ms. Perry’s class studies is hours. A typical student in Mr. Hart’s class studies a typical student in Ms. Perry’s class
A typical student in Mr. Hart’s class studies 1.56 hours per week and a typical student in Ms. Perry’s class studies 1.67 hours per week.
The mean is the average of a set of data, calculated by adding all the values in the set and dividing the sum by the number of values. The formula for calculating the mean is:
Mean = (Sum of all values) / (Number of values)
To calculate the mean of Mr. Hart’s class, we will first add up all the values from 0 to 8 in the dot plot:
0 + 0 + 2 + 2 + 1 + 4 + 2 + 1 + 2 = 14
We then divide this sum by the total number of values, which is 9:
Mean = 14 / 9 = 1.56
The mean of Mr. Hart’s class is 1.56 hours of studying per week.
Similarly, to calculate the mean of Ms. Perry’s class, we will add up all the values from 0 to 8 in the dot plot:
2 + 4 + 1 + 3 + 2 + 1 + 1 + 0 + 1 = 15
We then divide this sum by the total number of values, which is 9:
Mean = 15 / 9 = 1.67
The mean of Ms. Perry’s class is 1.67 hours of studying per week.
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SOMEBODY PLEASE SEE THIS AND HELP ME IN STUCK
Answer:
population: 2,900,904.279
Step-by-step explanation:
You need to calculate the total area first. The figure is made from 2 smaller figures.
Area for the top figure = 159 x (345 - 276) = 159 x 69 = 10971
Area for the bottom figure = 265 x 276 = 73140
Total are = 10971 + 73140 = 84111 mi^2
so you have 34.489 people/mi^2 =>
34.489 x 84111 = 2,900,904.279 people
Simplifying positive expressions in multiplication.
Simplify.
(-2b^4a)^5
Write your answer without parentheses.
Answer:
_2⁵b⁴*⁵a⁵
Answer=_32b²⁰a⁵
Answer it and show steps please
Step-by-step explanation:
See image:
Last question...this is geometry. 15 points to whoever gets it right and can explain
Answer: x=10
Step-by-step explanation:
sum of all the angles inside triangle is equal to 180degrees.
First angle: 9x-16
Second angle: 7x-5
Third angle: 3x+11
let's sum this angles:
9x-16+7x-5+3x+11=19x-10=180
19x=180+10=190
x=190/19=10
I am an integer in quadrant 2 my x-coordinate is less than negative 1 my y-coordinate is more than 2 my x-coordinate is greater than -3 the sum of the absolute values of my coordinates is five who am I plot me on the coordinate graph
Therefore , the solution of the given problem of coordinates comes out to be the point is (-2, 3), and it is located in the second quarter of the coordinate graph.
Describe coordinates.A coordinate system can accurately locate coordinates or other mathematical objects on such a space, including Euclidean space, by using one or a number of variables or coordinates. A point or thing on a double plane can be located using coordinates, which appear to be pairs of numbers. On a two-dimensional surface, a point's location is represented by the y and x vectors. a collection of images used to identify specific locations. Usually, the number has two numbers.
Here,
The details provided can be summed up as follows:
Negative in quadrant 2: This indicates that the point is located in the second quadrant, where the x- and y-coordinates are both negative.
the x-coordinate falls between -1 and -3: This requirement can only be met by the number -2.
y-coordinate exceeds 2: In the second quadrant, only the number 3 meets this requirement.
The total of the coordinates' absolute numbers is 5: As a result, the point is either (-2, 3) or |-2| + |3| = 5. (-2, -3).
As a result, the point is (-2, 3), and it is located in the second quarter of the coordinate graph.
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The table describes the quadratic function p(x).
x p(x)
−1 31
0 17
1 7
2 1
3 −1
4 1
5 7
What is the equation of p(x) in vertex form?
p(x) = 2(x − 3)2 − 1
p(x) = 2(x + 3)2 − 1
p(x) = 3(x − 3)2 − 1
p(x) = 3(x + 3)2 − 1
In response to the query, we can state that We can broaden the equation to test if it corresponds to the provided table:
[tex]0: p(0) = 0^2 - 11(0) + 19.25 = 17\s1: p(1) = 1^2 - 11(1[/tex]
What is equation?An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
[tex]ax^2 + bx^2 + c = p(x)[/tex]
We can determine a and b by using the coordinates of any two points on the parabola. Using points (1, 7) and (2, 1) as examples
[tex]a(1)^2 + b(1) + c = 7\\a(2)^2 + b(2) + c = 1[/tex]
When we simplify each equation, we obtain:
[tex]a + b + c = 7\\4a + 2b + c = 1\\h = -b / 2a = -(-11) / 2(1) = 5.5[/tex]
Hence, the vertex is (5.5, p(5.5)), and to finish the equation, we merely need to determine p(5.5).
We can broaden the equation to test if it corresponds to the provided table:
[tex]p(x) = (x - 5.5) (x - 5.5)\\a^2 - 11\s= x^2 - 11x + 30.25 - 11\s= x^2 - 11x + 19.25\\-1: p(-1) = (-1) (-1)\\a^2 - 11(-1) + 19.25 = 31\\[/tex]
[tex]0: p(0) = 0^2 - 11(0) + 19.25 = 17\s1: p(1) = 1^2 - 11(1[/tex]
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Because of the commutative property of multiplication, it is true that
3
4
×
4
=
4
×
3
4
3
4
×
4
=
4
×
3
4
. However, these expressions can be calculated in different ways even though the solutions will be the same.
Below, show two different ways of solving this problem.
First, show how
3
4
×
4
3
4
×
4
can be solved using repeated addition.
Para resolver la multiplicación 34 x 4 usando sumas repetidas, podemos seguir los siguientes pasos:
Empezamos sumando 34 cuatro veces:
34 + 34 + 34 + 34 = 136
La suma resultante de la etapa anterior es la respuesta, por lo que podemos concluir que:
34 x 4 = 136
Por lo tanto, hemos resuelto la multiplicación 34 x 4 usando sumas repetidas y obtenido la respuesta de 136.
A continuación, mostraremos otra forma de resolver el mismo problema utilizando la propiedad distributiva de la multiplicación.
Segundo, muestra cómo
4
×
(
3
4
)
4
×
(
3
4
)
se puede resolver utilizando la propiedad distributiva.
Respuesta:
Para resolver la multiplicación 4 x (34) utilizando la propiedad distributiva, podemos seguir los siguientes pasos:
Dividimos el factor 34 en dos partes: 30 y 4/4.
Multiplicamos cada parte por el otro factor, 4:
4 x 30 = 120
4 x (4/4) = 4
Sumamos los resultados de las dos multiplicaciones:
120 + 4 = 124
Por lo tanto, hemos resuelto la multiplicación 4 x (34) utilizando la propiedad distributiva y obtenido la respuesta de 124.
En conclusión, aunque se pueden resolver de diferentes maneras, ambas formas nos llevan al mismo resultado.
Olivia and Kalina are running a lemonade stand for one weekend. They sell lemonade for $0. 75
per cup. On Saturday, they sell 37 cups. For the weekend, they want to make at least $45. 00 in
sales on lemonade. Let c be the number of cups they sell Sunday,
If they sell 12 cups on Sunday will they reach their goal? Show this work on your paper and use it
to help you answer the next question. *
Yes, they will reach their goal of $45.00 by selling 12 cups of lemonade on Sunday.
Yes, they will reach their goal. To calculate this we can use the following formula:
Total Sales = (Number of cups sold on Saturday × Price per cup) + (Number of cups sold on Sunday × Price per cup)
Total Sales = (37 × 0.75) + (12 × 0.75)
Total Sales = 27.75 + 9
Total Sales = 36.75
Since 36.75 is greater than the goal of 45.00, they will reach their goal. This can be further verified by looking at the total cost of the cups they sold. 37 cups sold on Saturday at $0.75 each will cost $27.75. Adding the 12 cups sold on Sunday at $0.75 each will cost $9, bringing the total cost of the cups sold to $36.75. This is the same amount that was calculated using the formula above. Therefore, they will reach their goal by selling 12 cups of lemonade on Sunday.
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A
B
Which of the following graphs will
display the narrowest parabola?
y = -2x²+x+3
f(x) = -4x² - 30x
A graph that would display the narrowest parabola is f(x) = -4x² - 30x.
How to determine the equation of a parabola?In Mathematics, the standard equation of the directrix lines for any parabola can be modeled or represented by the following mathematical expression:
y = a(x - h)² + k.
Where:
h and k are the vertex.a represents the leading coefficient.Generally speaking, the larger the absolute value of the leading coefficient of a quadratic function, the narrower would be graph of its parabola.
In this context, we have the following:
y = -2x²+x+3; a = -2
f(x) = -4x² - 30x; a = -4
|a| = |-2| = 2
|a| = |-4| = 4
Therefore, |-2| is less than |-4|.
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here are six numbers
-7 -5 -3 3 1 -1
arrange the cards into three pairs with the same total
Answer:
-7 and 3
-5 and 1
-3 and -1
Step-by-step explanation:
-7 + 3 = -4
-5 + 1 = -4
-3 + -1 = -4
classify each number below as a rational or irrational number
please!!
Answer:
all are irrational except 2 and 3
Suppose the arrival of telephone calls at a switch can be modeled with a Poisson distribution. That is, if X is the number of calls that arrives in t minutes then Pr(X=k) At k 0,1,2. (At) where A is the average arrival rate in calls/minute. Suppose that the average rate of calls is 10 per minute. (a) What is the probability that fewer than three calls will be received in the first 6 seconds?
The probability that fewer than three calls will be received in the first 6 seconds is 0.9197 or approximately 0.92.
Given:
The arrival of telephone calls at a switch can be modeled with a Poisson distribution.X is the number of calls that arrives in t minutes.Pr(X=k) = At^k/k! where A is the average arrival rate in calls/minute and k is the number of calls received.The average rate of calls is 10 per minute.We need to find the probability that fewer than three calls will be received in the first 6 seconds.Let's convert the given time period of 6 seconds into minutes, as our arrival rate is in calls per minute.
6 seconds = 6/60 minutes = 0.1 minutes
We are given that the average rate of calls is 10 per minute, which means that the arrival rate per 0.1 minute is:
A = 10/minute * 0.1 minute = 1 call
We need to find the probability that fewer than three calls will be received in 0.1 minutes. We can use the Poisson distribution formula to calculate this probability:
Pr(X < 3) = Pr(X=0) + Pr(X=1) + Pr(X=2)Pr(X=k) = At^k/k! , so
Pr(X=0) = e^(-A)*(A^0/0!) = e^(-1) = 0.3679
Pr(X=1) = e^(-A)*(A^1/1!) = e^(-1)*1 = 0.3679
Pr(X=2) = e^(-A)*(A^2/2!) = e^(-1)11/2 = 0.1839
Therefore,
Pr(X < 3) = 0.3679 + 0.3679 + 0.1839 = 0.9197
Hence, the probability that fewer than three calls will be received in the first 6 seconds is 0.9197 or approximately 0.92.
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6=5/3y
pls help me get this answer nowwww uwuwu
Answer:
exact form: [tex]\frac{18}{5}[/tex]
decimal form: 3.6
mixed number form: [tex]3\frac{3}{5}[/tex]
Answer:
y=18/5
Step-by-step explanation:
6=5y/3
multiply both sides:
6*3=5y
simplify 6*3 to 18:
18=5y
divide both sides by 5:
18/5=y
answer: y=18/5
Convert 2.5 gmm² to kgm²
Answer:2.5e-9
Step-by-step explanation:
Mariko is fencing her garden. She wants to use 50ft of fencing. Mariko also wants the sum of the length and the width of the garden to be 25ft. Use the system of equations to confirm that there are infinitely many possibilities for the length and width. Are there any limits to what values the length and width can be? explain your reasoning.
2L + 2W = 50
L + W = 25
We can use the system οf equatiοns tο sοlve fοr the length and width οf Marikο's garden. The first equatiοn represents the fact that the perimeter οf the garden, which is the sum οf the length and the width multiplied by twο, is equal tο 50 feet.
The secοnd equatiοn represents the fact that the sum οf the length and the width is equal tο 25 feet. We can sοlve this system οf equatiοns using substitutiοn οr eliminatiοn.
Using substitutiοn, we can sοlve fοr οne variable in terms οf the οther in the secοnd equatiοn:
L + W = 25
W = 25 - L
Nοw we can substitute this expressiοn fοr W intο the first equatiοn:
2L + 2W = 50
2L + 2(25 - L) = 50
Simplifying:
2L + 50 - 2L = 50
50 = 50
This equatiοn is true fοr any value οf L and W that satisfies the cοnditiοn that the sum οf the length and the width is equal tο 25 feet. Sο we have infinitely many pοssibilities fοr the length and width οf Marikο's garden.
Hοwever, there are limits tο what values the length and width can be. Fοr example, bοth the length and the width must be pοsitive and less than 25 feet fοr the garden tο fit within the 50 feet οf fencing that Marikο has. Additiοnally, we might want the length and width tο be integers οr tο satisfy sοme οther cοnstraint. But within the cοnstraints given by the prοblem, there are infinitely many pοssible sοlutiοns fοr the length and width οf the garden.
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Please ASAP Help
Will mark brainlest due at 12:00
The coordinates of the midpoint of the given segment is; (-15, 4)
How to find the midpoint of the coordinates?For any specific line segment, it is well known that the midpoint is defined as the halfway between its two endpoints. The expression that is used to find the x-coordinate of that midpoint is expressed as: [(x)1 + (x)2]/2, which denotes the average of the x-coordinates. Similarly, the expression that is used to find the y-coordinate of that midpoint is expressed as: [(y)1 + (y)2]/2, which is the average of the y-coordinates.
We are given the coordinates of the endpoints of the line as;
K(-11, 2) and L(-19, 6)
Thus;
Midpoint Coordinate = (-11 - 19)/2, (2 + 6)/2
= (-15, 4)
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PLS HELP ME QUICK!!!
Relation 2 and 3 are actual functions with proper domain, co domain, range.
Describe Function?A function can be represented in several ways, including using algebraic expressions, tables, graphs, or even words. For example, the function f(x) = 2x + 1 defines a relationship between the input x and the output 2x + 1. If we input x = 3 into this function, the output would be f(3) = 2(3) + 1 = 7.
Functions can have different properties, such as being continuous or discontinuous, being differentiable or nondifferentiable, or having maximum or minimum values. Functions can also be classified according to their types, such as linear, quadratic, exponential, logarithmic, trigonometric, or piecewise-defined functions.
Functions are used extensively in mathematics, science, engineering, economics, and many other fields to describe real-world phenomena and to solve practical problems. They are also studied in their own right, as objects of mathematical interest and beauty, with deep connections to many other areas of mathematics, such as calculus, analysis, and algebra
Relation 2 and 3 are actual functions with proper domain, co domain, range.
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Solve the compound inequality.
2x + 9 > 17 or -5x ≥ 10
Note: Show all work Use a comma for an 'or' and graph
The solutions to the compound inequality are as follows:
x > 4 or x ≥ 2.
What Does Compound Inequality Mean?A compound inequality in mathematics is a phrase that joins two claims with the conjunctions "and" or "or."
Both of the statements are true simultaneously if the conjunction "and" is used to unite them in the compound sentence. If the conjunction "or" is used to combine the assertions, then the compound statement is true if at least one of the claims is true.
Now solving the inequality:
2x + 9 > 17 or -5x ≥ 10.
2x + 9 > 17
⇒ 2x > 8
⇒ x > 4
Now,
-5x ≥ 10
⇒ -x ≥ 2
⇒ x ≥ 2
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[tex]2x+9 > 17\ or\ -5x\geq 10[/tex] compound inequalities is as follows:
x > 4 or x ≥ 2.
What is Meant by Compound Inequality?In mathematics, a compound inequality is a sentence containing two statements joined by the word "and" or "or". If the statements are connected by the word "and", both statements in a compound sentence are true at the same time. A compound statement is true if at least one statement is true if the statements are connected by "or" A compound statement is true if at least one statement is true.
[tex]2x+9 > 17\ or\ -5x\geq 10[/tex]
Let take [tex]2x+9 > 17[/tex]
Subtract -9 on both sides
= 2x+9-9 > 17-9
= 2x+0 > 8
= 2x > 8
Now we need to divide by 2 both sides
= 2x÷2 > 8÷2
= x > 4
Now we solve -5x ≥ 10
= -5x ≥ 10
= -x ≥ 2
= x ≥ 2
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According to cavalieri's principle, which pair of shapes would have equal volumes?
Two shapes would have equal volumes if the areas of their corresponding cross-sections are equal at every height.
According to Cavalieri's principle, two shapes have equal volumes if for every pair of parallel cross-sections taken at the same height, the areas of the cross-sections are equal.
1. Two cylinders with the same height and different radii.
As long as the cross-sectional areas of the cylinders at each height are the same, the volumes will be equal. The radii of the cylinders can vary.
2. Two cones with the same height and different base radii.
Similar to cylinders, as long as the cross-sectional areas of the cones at each height are the same, the volumes will be equal.
3. Two prisms with the same height and different base shapes.
If two prisms have the same height and the cross-sectional areas at each height are equal, then the volumes will be equal.
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