The height of the ball be after 3 seconds will be 72.2 feet.
How to calculate the height?From the information given, it should be noted that the astronaut on the moon throws a baseball upward and the height of the ball in feet
(y) is related to the number of seconds since the ball was thrown (x).
In this case, it should be noted that the function is illustrated as:
y = -2.7x² + 30x + 6.5
Therefore, it was given that x = 3. It should be noted that this will be put back into the function. This will be:
y = -2.7x² + 30x + 6.5
y = -2.7(3)² + 30(3) + 6.5
y = -24.3 + 90 + 6.5
y = 72.2
The height is 72.2 feet.
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Factor:
b(a+1)^2 -5(a+1)
[tex] = (a + 1)(b(a + 1) - 5)[/tex]
HOPE THIS HELPS
Ryan received a box of jelly beans for his birthday. The jelly beans in the box have fivedifferent flavors. The table below shows how many jelly beans of each flavor are in the box.JELLY BEANSFlavorGrapelucoriceNumber1610CherryhomonThe jelly beans are all the same shape and size. Ryan does not like licorice or lime. What is theprobability that he will pick a jelly bean from the full box that has a flavor he does like? Showand exolain vour work
The probability of Ryan choosing a flavor that he does not like is 3/10.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The probability is calculated by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.So, the formula for probability:
P = favourable events/Total eventsFavorable events: (Picking flavor that Ryan does not like) = 10 + 8Total events: (sum of all the jelly) = 60Now, insert the values in the probability formula as follows:
P = favourable events/Total eventsP = 18/60 ⇒ 9/30 ⇒ 3/10Therefore, the probability of Ryan choosing a flavor that he does not like is 3/10.
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To which set(s) of numbers does √2 belong?
Select all that apply.
A. rational
B. irrational
C. integer
D. whole
E. natural
F. not rational
The number √2 is an irrational number, thus, the correct options are B: irrational and F: not rational
To wich sets the number belongs?Remember what each sets are.
Natural or whole numbers are all the numbers that can be get by adding ones to one {1, 2, 3, 4, ...}
Integers are like the above ones, but also includes the zero and negative numbers.
Rationals are the ones that can be written as a quotient between two integers, and irrationals are these ones that can't be written like that.
Finally, real numbers are all the numbers.
In this case we have the square root of a prime number, √2, this is always a irrational number.
Then option B is correct.
Trivially, option F (not rational) is also true, because if the number is irrational, then it is not rational.
Then the correct options are B and F.
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given h(x)=-[tex]\sqrt{x}[/tex]x-6+8 witch is the correct transformation from the parent function
The correct transformation include
Horizontal translation to the right by 6 units: Vertical translation up by 8 units: How to determine the transformation of the graph?The equation of the graph is given as
y = √(x -6) + 8
The above equation is a square root
The parent equation of the square root is
y = √x
The sequence of transformations from y = √x to y = √(x - 6) + 8 is as follows:
Shift to the right by 6 unitsShift up by 8 unitsThe transformation rule of the above transformations are as follows:
Shift to the right by 6 units: (x - 6, y)Shift up by 8 units: (x, y + 8)When the above transformations are applied on the equation, we have:
Shift to the right by 6 units: (x - 6, y)Shift up by 8 units: (x - 6, y + 8)This means that the function y = √(x -6) + 8 can be gotten by applying the above sequence of transformation on y = √x
See attachment for the graphs of the transformations where the blue line represents y = √x while the other line represents y = √(x -6) + 8
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If a = 4 + 2i and b = 3, then find the value of the ab² in fully simplified form.
The value of complex number is [tex]ab^{2}[/tex] = 36+18i
What is complex number?
The complex number is basically the combination of a real number and an imaginary number. The complex number is in the form of a+ib, where a = real number and ib = imaginary number.
The alphabet i is referred to as the iota and is helpful to represent the imaginary part of the complex number. Further the iota(i) is very helpful to find the square root of negative numbers.
Given,
a = 4+2i
b = 3
[tex]b^{2}[/tex] = 3(3)
= 9
Hence, the value of
[tex]ab^{2}[/tex] = (4+2i)9
=36+ 18i
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A store sold 14 more colored shirts than white shirts. The white shirts cost $9.95, and the colored shirts cost $10.50. The store sold $310.60 worth of shirts.
How many of each type of shirt were sold?
A store sold 22 colored shirts and 8 white shirts.
Let x be the number of colored shorts and y be the number of white shirts.
A store sold 14 more colored shirts than white shirts.
so, we get an equation,
x = y + 14 ....................(1)
The white shirts cost $9.95, and the colored shirts cost $10.50. The store sold $310.60 worth of shirts.
So we get an equation,
10.50x + 9.95y = 310.60 .............(2)
Substitute above value of x in equation (2)
10.50(y + 14) + 9.95y = 310.60
10.50y + 147 + 9.95y = 310.60
20.45y = 310.60 - 147
20.45y = 163.6
y = 8
Substitute above value of y in equation (1)
So, x = 8 + 14
x = 22
Therefore, a store sold 22 colored shirts and 8 white shirts.
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Which description best compares the graph given by the following equations:
Based on the equations given, the best comparison between them is that they are intersecting but not perpendicular.
How to know lines that are perpendicular?When lines are perpendicular to each other, one line will have a slope that is the negative reciprocal of the other. For instance, if the slope of one line is 2, the slope of the perpendicular line will be -1/2.
Parallel lines will have the exact same slope.
The slope of the first line is:
2x - 7y = -5
(2x - 7y = -5) x 1/7
2/7x - y = -5/7
Slope = 2/7
The slope of the second line is:
x - 3y = 4
(x - 3y = 4) x 1/3
1/3x - y = 4/3
Slope = 1/3
The slopes are neither negative reciprocals nor the same so the lines must be intersecting but not perpendicular.
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What is the result if x3 - 5x² + x + 15 will be divided by x -3?
The quotient for p(x) = x³ -5x² + x + 15 is x² – 2x – 5.
What is a polynomial?A polynomial is a mathematical expression made up of coefficients multiplied by the product of powers in one or more variables. The formula for a univariate polynomial in one variable with constant coefficients is.
What is a polynomial equation?An equation with a polynomial set to zero is referred to as a polynomial equation. It is an equation made up of coefficients, non-negative integer exponents, variables, and operations. It also contains the equal sign. Different exponents exist for it. The degree of the equation is revealed by the highest one.
Given that,
The p(x) = x³ - 5x² + x + 15
Divided by x -3
Therefore, the quotient for p(x) = x³ -5x² + x + 15 is x² – 2x – 5.
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In the lab, Charlie has twosolutions that contain alcohol and is mixing them with each other. Solution A is 20% alcohol and Solution B is 6%
alcohol. He uses 300 milliliters of Solution A. How many milliliters of Solution B does he use, if the resulting mixture is a 12% alcohol solution?
Charlie used 400 milliliters of Solution B if the resulting mixture is a 12% alcohol solution.
What does "algebraic equation" mean?An algebraic equation is a declaration of the equality of two expressions created by applying the algebraic operations to a set of variables.
What kind of algebraic equations are there?Monomial expressions, binomial expressions, and polynomial expressions are the three main categories of algebraic expressions.
Given : Solution A contains 20% alcohol, while Solution B contains 6% alcohol.
It is also given that Charlie uses 300 milliliters of Solution A.
Let's say that the mixture contained x ml of the 6% solution B.
x + 300 = resulting mixture of 12 % alcohol.
20% (300) + 6% (x) = 12% (x+300)
60 + 0.06x = 0.12x + 36
0.06x = 24
x = 400 milliliters
As a result, if the resulting mixture is a 12% alcohol solution, he used 400 milliliters of Solution B.
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See questions below. Thank you
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given data
[tex]\begin{gathered} n=10 \\ r=7 \end{gathered}[/tex]STEP 2: answer question a
[tex]^nC_r=\frac{n!}{(n-r)!r!}[/tex]To get the answer,
[tex]\begin{gathered} ^{10}C_7=\frac{10!}{(10-7)!7!} \\ =\frac{10\times9\times8\times7!}{3!7!}=\frac{10\times9\times8}{3!}=120 \end{gathered}[/tex]Hence, 120 different toppings pizza are possible
STEP 3: Answer question b
[tex]=^{75}C_4=\frac{75!}{(75-4)!4!}=1215450[/tex]Hence, 1215450 mini-boxes are possible
3. Simplify using BODMAS property a) 107-[59-(18+9-(12-18+6) +3}] b) [222-486 of 8]+(58-45) * 8 c) 1500-[160+ (40-(120-100)}]
Answers to all the problems using BODMAS property are:
(A) 78(B) -2,008(C) 1,320What is BODMAS property?The brackets must be solved first, then powers or roots (i.e. of), Division, Multiplication, Addition, and finally Subtraction, according to the BODMAS rule. Any expression can only be solved correctly if the BODMAS rule or the PEMDAS rule is applied.So, (A) 107-[59-(18+9-(12-18+6) +3}]:
107-[59-(18+9-(12-18+6) +3}]107-[59-(18+9-0+3}]107-[59-(27+3)]107-[59-30]107 - 2978(B) [222- 486 of 8]+(58-45) × 8
[222- 486 of 8]+(58-45) × 8[-264 × 8]+(13)× 8-2,112 + 104-2,008(C) 1500-[160+ (40-(120-100)}]
1500-[160+ (40-(120-100)}]1500-[160+ (40-20}]1500-[160+ 20]1500-1801,320Therefore, answers to all the problems using BODMAS property are:
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c
−
a
+
b
d
if
a
=
7
8
,
b
=
−
7
16
,
c
=
0
.
8
, and
d
=
1
4
.
The value of expression c − a + b d on simplification is (-10101.2).
As per question we need to solve the given equation i.e., c − a + b d
And we are provided with the values of a, b , c and d.
Here we have ,
a=78,
b=−716
c=0.8
and d=14
The given equation is,
c − a + b d
Now we need to substitute the value of a, b, c and d. On substituting the value of a, b, c and d , we get
(0.8) - 78 + (-716) (14)
= (0.8) - 78 - 10024
= (-10101.2)
So, we can conclude that the value of given expression on simplification is (-10101.2).
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Arrange in order from smallest to largest.
6.187, 27.132, 3.55, 9.312
Answer: 3.55, 6.187, 9.312, 27.132
Step-by-step explanation:
The easiest way I do this is by rounding all the numbers to the nearest hundredths, tenths, or whole numbers.
3.55 = 4
6.187 = 6
9.312 = 9
27.132 = 27
Algebra ll please help
The formula to obtain the future value (FV) is,
[tex]FV=PV(1+\frac{r}{n})^{nt}[/tex]Where,
[tex]\begin{gathered} FV=\text{Future Value=?} \\ PV=\text{Present Value = \$5000} \\ r=4.2\text{ \%=}\frac{\text{4.2}}{100}=0.042 \\ n=12 \\ t=n\text{umber of years }=5\text{years} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} FV=5000(1+\frac{0.042}{12})^{12\times5}=5000(1+0.0035)^{60} \\ FV=5000(1.0035)^{60}=5000\times1.233225821=6166.129106 \\ FV=6166.129106\approx6166.13(nearest\text{ cent)} \\ \therefore FV=\text{ \$6166.13} \end{gathered}[/tex]ence, there will be $6`166.13 in the account after 5years.
Find the first derivative.
Answer: y’ = 2/3 x^1/2 - 2/ sqrt of x - 5/2x^2/3
I’m given an answer but don’t know how to get it.
Answer: Use the quotient rule to solve this problem (formula attached). g(x) would be -sqrt x and f(x) would be x^2 - 4x +5.
Select the counterexample that shows that the conjecture is false.
Conjecture: The product of two positive numbers is always greater than either number
Answer: 1*5=5 is the counterexample.
Step-by-step explanation: The conjecture stated is that the product of two positive numbers is always greater than either number. We have to find certain values to check and see if this conjecture is false. We can use the numbers 1 and 5 to multiply. This would be the identity property of multiplication. 1 and 5 are both positive numbers and therefore that 1*5=5 is the counterexample.
Please help I’ll mark you as brainliest if correct!
Answer:
it's easily 47 as it's finished basement ALONE and b is 3 car garage ALONE while c is both so it's asking who has a finished basement ALONE/ONLY
Answer:
38
Step-by-step explanation:
The total homes are 85
Of the homes with finish basements it is 47
Then you find the difference: 85-47 =
The final answer is 38
is 257 math map good for a 9th grader? fall edition?
Answer:
VERY
Step-by-step explanation:
VERY
1) What is the midpoint formula? Use it to find the midpoint of (1, 5) and (-8, 17).
Please help me
Answer:
the answer to the midpoint of 1.5 and -8,7 is (-7/2,11)
Evaluate the expression and enter your answer in the box below.[(14 + 7) + 3) + 10 (6-3)
Given the expression below
[tex](14+7)+3)+10(6-3)[/tex]We can evaluate the expression by simplifying the parenthesis
[tex]\begin{gathered} (14+7)+3)+10(6-3) \\ =(21+3)+10(3) \\ =24+30 \\ =54 \end{gathered}[/tex]Answer: 54
Miguel reads that the average low temperature today is −8.5°F and that the average high temperature is 10.2º F.
Miguel plots the points on the number line to determine the temperature change between these two readings.
What is the temperature change?
Answer:
18.7 °F
Step-by-step explanation:
You want the temperature change between a low of -8.5 °F and a high of 10.2 °F.
ChangeThe change between the two readings is found by subtracting the smaller from the larger:
10.2 -(-8.5) = 10.2 +8.5 = 18.7
The temperature change is 18.7 °F.
Find the angles and sides of the right triangle B = 70 degrees, b= 19ft. Please round to the nearest degree.
Data:
• B = 70°
,• b = 19ft
,• C = 90°
Procedure:
• Finding the angles
We know that C = 90° as the image shows the symbols. Also, we know that the sum of the interior angles of a triangle are 180°. Then, to get A we have to do the following:
[tex]A+B+C=180[/tex]Isolating for A:
[tex]A=180-B-C[/tex]Replacing the values we know:
[tex]A=180-70-90[/tex][tex]A=20[/tex]• Finding side ,a
Using trigonometric functions, we can get a.
[tex]\tan (A)=\frac{a}{b}[/tex]As we already know the value of A and b, we can isolate for a:
[tex]a=b\cdot\tan (A)[/tex]Replacing the values:
[tex]a=19\cdot\tan (20)\approx6.92[/tex]• Finding side ,c
Finally, using the Pythagorean Theorem, we can calculate c:
[tex]c^2=a^2+b^2[/tex]Isolating for c:
[tex]c=\sqrt[]{a^2+b^2}[/tex]Replacing the values:
[tex]c=\sqrt[]{6.92^2+19^2}[/tex][tex]c\approx20.22[/tex]
Answer:
• A = 20°
• a = 6.92 ft
,• c = 20.22 ft
Which numbers are solutions of x^2 + 20 = 9x + 2?
Answer:
x = 6 or x = 3
Step-by-step explanation:
Solve for x over the real numbers:
x^2 + 20 = 9 x + 2
Subtract 9 x + 2 from both sides:
x^2 - 9 x + 18 = 0
The left-hand side factors into a product with two terms:
(x - 6) (x - 3) = 0
Split into two equations:
x - 6 = 0 or x - 3 = 0
Add 6 to both sides:
x = 6 or x - 3 = 0
Add 3 to both sides:
Answer: x = 6 or x = 3
Answer:
Step-by-step explanation:
(x-6)(x-3)
x1 =6
x2 = 3
help me with this is due tommorow
a ) The value is 4.472
b)2 decimal place is 4.47
What is decimal number ?When expressing a whole number and a fraction together, decimals are utilized. Here, we shall use a "." (also known as a decimal point) to demarcate the full number from the fraction. Say, for illustration, that you intend to bring a cone of ice cream. You are informed by the vendor that ice cream costs $2 and 50 cents. Now, if you wanted to sum up this cost in a single number, you would say that an ice cream cone costs $2.50. You may be utilizing decimals without even recognizing it in a variety of everyday settings.
[tex]\sqrt{4.5^{2} -0.5^{2} }\\ \sqrt{20.25-0.25} \\\sqrt{20}\\ 4.4721[/tex]
a ) The value is 4.472
b)2 decimal place is 4.47
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Which number line plots the integers –12, –3, and 7? A number line going from negative 15 to positive 10. Points are at negative 12, negative 3, and 7. A number line going from negative 15 to positive 10. Points are at negative 8, negative 3, and 7. A number line going from negative 15 to positive 10. Points are at negative 12, negative 8, and negative 3. A number line going from negative 15 to positive 10. Points are at negative 12, negative 8, and 3. (ANSWER ASAP PLS)
A number line that plots the integers –12, –3, and 7 will be A. A number line going from negative 15 to positive 10. Points are at negative 12, negative 3, and 7.
What is a number line?It should be noted that a number line simply means the straight line that can be used to show the addition and subtraction of numbers.
It should be noted that the negative numbers are on the left hand side and the positive numbers are on the right hand side.
Therefore, this is conveyed effectively by option A.
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The cost to travel X miles east or west on a train is the same. The function for the cost
c(x) = 0.75|x| + 25.
Describe how c(x) is related to its parent function and interpret the function in the context of the situation.
C(x) is related to its parent function c(x) = 0.75|x| + 25.
The function in the context of the situation illustrated that the cost is the same.
How to illustrate the information?It should be noted that a function is used to show the relationship between the variables.
In this case, the cost to travel X miles east or west on a train is the same. The function for the cost is given as c(x) = 0.75|x| + 25.
Let East = positive direction
Let West = negative direction
Let the travel distance in East = x
Travel distance for West = -x mile
The cost to travel East x miles will be:
= 0.75(x) + 24
= 0.75x + 25
The cost to travel West will be:
c(-x) = 0.75x + 25
This shows that the cost will be the same even though there in different directions.
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I need help question
A B Solve the equation. 6x - 8 = 2 (3x - 4) No Solution Infinite Solutions
After being simplified, it was discovered that the equation 6x - 8 =
2 (3x - 4) has infinite solutions.
What exactly is a straight line equation?A straight line has the equation y=mx+c, where m is the gradient and c is the height at which the line crosses the y -axis, also known as the y -intercept.
What is the difference between a no solution and an infinite solution?Equations with no solutions will not be equal when simplified.Equations with infinite solutions will simplify to the same constant on both sides.Given Equation : 6x - 8 = 2 (3x - 4)
Simplifying this equation as follows:
6x - 8 = 2 (3x - 4)
6x - 8 = 6x - 8
0 = 0
Same constant on both sides.
As a result, after simplifying the equation 6x - 8 = 2 (3x - 4), infinite solutions are possible for this equation.
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3. A bus travels a distance of 60 km at a steady speed of 60 km/h. (a) Does the distance travelled vary directly with time?If the journey takes 8 hours, find its speed.
a) The distance that the bus traveled varies directly with time.
b) If the journey of 60 km takes 8 hours, the speed of the bus is 7.5 km/h.
What is the relationship between distance and speed?The relationship between distance and speed can best be explained below:
For a constant speed, for example, 60 km/h, the distance traveled, 60 km, is proportional to the time used.
But if the distance is fixed at 60 km, the time it takes the bus, for example, 8 hours, is inversely proportional to the speed.
Total distance = 60 km
Steady speed = 60 km/h
Thus, for every kilometer, the bus takes one minute (60/60) and for every minute, the bus travels a kilometer.
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Find the growth factor of the function y = 750(1.825)4.0.8251.8254750
Solution:
The growth formula is expressed as
[tex]\begin{gathered} A=P(1+r)^t----\text{ equation 1} \\ where \\ (1+r)\Rightarrow growth\text{ factor} \end{gathered}[/tex]Given the function:
[tex]y=750(1.825)^4---\text{ equation 2}[/tex]By comparison, we have
[tex]\begin{gathered} P=750 \\ t=4 \\ (1+r)=1.825 \end{gathered}[/tex]Hence, the growth factor of the function is
[tex]1.825[/tex]