The surface area of a sphere with a radius of 9 units is given by the formula 4 (pi) (r)2, resulting in an area of 324 (pi) square units, or approximately 1017.88 square units when using 3.14159 for (pi).
Calculating the Surface Area of a Sphere
To find the surface area of a sphere, you will need to use the formula: surface area = 4 (pi) (r)2, where r is the radius of the sphere. For a sphere with a radius of 9 units, you would calculate the surface area as follows:
Surface Area = 4 (pi) (92)
Surface Area = 4 (pi) (81)
Surface Area = 324 (pi)
So, the surface area of the sphere is 324 (pi) square units. If you use the approximate value of (pi) = 3.14159, then the surface area would approximately be 1017.88 square units.
The formula
h
=
v
t
−
16
t
2
gives the height
h
, in feet, of an object projected into the air with an initial vertical velocity
v
, in feet per second, after
t
seconds.
If an object is projected upward with an initial velocity of
80
feet per second, at what times will it reach a height of
96
feet above the ground?
It'll be at
96
feet above the ground at
and
seconds
Answer:
t=6
Step-by-step explanation:
We are solving for [tex]t[/tex]. To do this, let's fill in the known variables.
[tex]h=vt-16t^2[/tex]
[tex]v=80\\h=96[/tex]
[tex]96=80t-16t^2[/tex]
[tex]16t^2-80t+96=0\\16(t^2-5t+6)=0[/tex]
Since the product must equal 0, that means that the factor in the parentheses hasto be equal to 0. Therefore,
[tex]t^2-5t+6=0\\(t+1)(t-6)=0\\\\t+1=0 OR t-6=0\\t=-1 OR t=6[/tex]
However, since the time cannot be negative, [tex]t=-1[/tex] cannot be a valid answer.
Therefore, the only valid time is t=6.
I hope this helps.
Let's start with the projectile motion formula which is h = vt - 16t².
In this formula, h is the height of the object,
v is the initial velocity, and t is the time.
We know that the initial velocity is 80 feet per second
so we can plug an 80 in for v in our formula.
We also know that the object reaches a height of 96 feet above the
ground which means we can plug an 96 in for h in our formula.
So we have 96 = 88t - 16t².
To solve this equation, we set it equal to 0 by subtracting
88t and adding 16t² to get 16t² - 88t + 96 = 0².
Now we can divide both sides by 8 to get 2t² - 11t + 12 = 0.
Now we can factor the left side to get (2t - 3)(t - 4) = 0.
So this means that 2t - 3 = 0 or t - 4 = 0.
So t = 3/2 or t = 4.
Now, the reason there are two answer is because the object will be
96 feet off the ground on its way up and on its way down.
13. In engineering notation, the number
0.000452 is expressed as
Answer:
I think it is 4.52 × 10^-4
On a number line, negative the square root of two falls between which two consecutive integers
[tex]\bf \boxed{-2}\rule[0.35em]{12em}{0.25pt}\stackrel{~\hfill -\sqrt{2}}{\approx -1.4}\rule[0.35em]{10em}{0.25pt}\boxed{-1}[/tex]
Final answer:
The negative square root of two, −√2, falls between the consecutive integers -2 and -1 on the number line.
Explanation:
The student is asking about the position of the square root of a negative number on the number line, specifically −√2 (negative square root of two). To answer this, we first need to understand that the square root of a positive number is a number that, when squared, gives the positive number in question. For √2, we know that it falls between 1 and 2 because 1 squared is 1 and 2 squared is 4, and 2 lies between these two values.
Since the student is asking for negative √2, we simply reflect the position of √2 across the origin (zero) on the number line to find where −√2 lies. Hence, −√2 will fall between the integers -2 and -1. If we were estimating, we might say it is just a bit closer to -2 than -1, because √2 is approximately 1.414.
The line parallel to y=-7x-2 through (-4,6)
The required line parallel to y = - 7x - 2 through (- 4, 6) is y = -7x - 22.
What is slope?The slope is the rate of change of the y-axis with respect to the x-axis.
The equation of a line in slope-intercept form is y = mx + b, where
slope = m and y-intercept = b.
We know the greater the absolute value of a slope is the more steeper is it's graph or rate of change is large.
We know parallel lines have the same slope.
Given line is y = - 7x - 2, hence the required line will also have a slope of - 7
which is passing through the point (-4, 6).
∴ 6 = (-7)(-4) + b.
6 = 28 + b.
b = - 22.
Hence the required line is y = -7x - 22.
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Solve the following problems. Reduce your answers to their simplest form.
a. 13/41 + 27/82
b. 3 5/24 + 6 7/24 + 4 9/24
C. 5 2/3 + 29/69 + 6 21/23
d. 3 9/10 + 4/9 + 7/45 + 4
e. 6 - 7/15
f. 11 3/8 - 7/8
g. 7 1/6 - 3 4/9
h. 5 3/8 - 3 2/5
Answer:
a. 53/82
b. 13 7/8
c. 12 16/23
d. 8 1/2
e. 5 8/15
f. 10 1/2
g. 3 13/18
h. 1 39/40
Step-by-step explanation:
Step-by-step explanation:
a. 13/41 + 27/82
[tex]\frac{13}{41}+\frac{27}{82}[/tex]
[tex]\frac{13\times 82+27\times 41}{82\times 41}=\frac{53}{82}[/tex]
b. [tex]3\frac{5}{24} + 6\frac{7}{24} + 4\frac{9}{24}[/tex]
[tex]\frac{77}{24}+\frac{151}{24}+\frac{105}{24}[/tex]
[tex]\frac{77+151+105}{24}=\frac{333}{24}[/tex]
c) [tex]5\frac{2}{3} + \frac{29}{69} + 6 \frac{21}{23}[/tex]
[tex]\frac{17}{3}+\frac{29}{69} +\frac{159}{23}[/tex]
[tex]\frac{17\times 23}{3\times 23}+\frac{29}{69} +\frac{159\times 3}{23\times 3}[/tex]
[tex]\frac{17\times 23+29+159\times 3}{69}=\frac{897}{69}=\frac{13}{1}[/tex]
d) [tex]3\frac{9}{10} + \frac{4}{9} + \frac{7}{45} + 4[/tex]
[tex]\frac{39}{10} + \frac{4}{9} + \frac{7}{45} + \frac{4}{1}[/tex]
[tex]\frac{39}{10} +\frac{4\times 10}{1\times 10}+\frac{4\times 5}{9\times 5} + \frac{7}{45}[/tex]
[tex]\frac{39+1\times 10}{10}+ +\frac{4\times 5+7}{45}[/tex]
[tex]\frac{49}{10}+\frac{27}{45}[/tex]
[tex]\frac{49\times 45+27\times 10}{10\times 45}=\frac{11}{2}[/tex]
e)[tex]6-\frac{7}{15}[/tex]
[tex]\frac{6}{1}--\frac{7}{15}[/tex]
[tex]\frac{6\times 15-7\times 1}{1\times 15}=\frac{83}{15}[/tex]
f)[tex]11\frac{3}{8} - \frac{7}{8}[/tex]
[tex]\frac{91}{8}- \frac{7}{8}[/tex]
[tex]\frac{91-7}{8}=\frac{84}{8}=\frac{21}{2}[/tex]
g)[tex]7 \frac{1}{6} - 3\frac{4}{9}[/tex]
[tex]\frac{43}{6}-\frac{41}{9}[/tex]
[tex]\frac{43\times 9-41\times 6}{54}[/tex]
[tex]=\frac{141}{54}=\frac{47}{18}[/tex]
h)[tex]5\frac{3}{8}-3\frac{2}{5}[/tex]
[tex]\frac{43}{8}-\frac{17}{5}[/tex]
[tex]\frac{43\times 5-17\times 8}{8\times 5}=\frac{79}{40}[/tex]
NEED ASAP PLEASE
Example 2
17. OLYMPICS in the 2010 Winter Olympic Games, the
Winter Olympic Games, the United States won 1 more than
4 times the number of gold medals France won. The
old medals France won. The United States won 7 more
gold metals than France. Write and solve an equation
ce. Write and solve an equation to find the number of gold
medals each country won.
Answer:
U.S.= 9
France= 2
Step-by-step explanation:
2×4=8 +1=9
9-7=2
Hope this helps!!!
Brady
Number of Gold medals won by USA are 9 and gold medals won by France are 2.
Let the gold medals won by USA = x
And the gold medals won by France = y
It's given in the question "gold medals won by USA are 1 more than 4 times the number of gold medals won by France"
Therefore, equation for this situation will be,
x = 4y + 1 --------(1)
Second statement of the question states "USA won 7 gold medals more than France"
Therefore, equation will be,
x = y + 7 -------(2)
By substituting the value of 'x' in equation (1) from equation (2),
y + 7 = 4y + 1
4y - y = 7 - 1
3y = 6
y = 2
By substituting the value of 'y' in equation (1),
x = 4(2) + 1
x = 9
Therefore, USA won 9 gold and France won 2 gold medals in the Winter Olympic Games.
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Which of the following expressions is equivalent to 4,325,000,000
For this case we must find an expression equivalent to:
[tex]4,325,000,000[/tex]
To express in scientific notation we must take into account that the power will be positive, that is, the decimal is run to the right.
We test each option.
Option A:
[tex]4,325 * 10^{-9}[/tex]
If we run the decimal 9 spaces to the left we have:
[tex]0.000000004325[/tex]
Option B:
We discard it because the exponent is negative.
Option C:
[tex]4,325 * 10 ^ 6[/tex]
We run the decimal 6 spaces to the right
[tex]4,325,000[/tex]
Option D:
[tex]4,325 * 10 ^ 9[/tex]
We run the decimal 9 spaces to the right
[tex]4,325,000,000[/tex]
Answer:
Option D
Final answer:
The expression that is equivalent to 4,325,000,000 is 4.325 × 10^9.
Explanation:
The expression that is equivalent to 4,325,000,000 is 4.325 × 109.
When we write a number in scientific notation, we express it as a product of a coefficient and a power of 10. In this case, the coefficient is 4.325 and the power of 10 is 9. This means that we move the decimal point 9 places to the right, resulting in a value of 4,325,000,000.
So the correct expression is 4.325 × 109.
A container of oregano is 17 pounds heavier than a container of peppercorns. Their total weight is 253 pounds. The peppercorns will be sold in one-ounce bags. How many bags of peppercorns can be made?
Answer:
1,888 bags.
Step-by-step explanation:
Let x represent the the weight of container of peppercorns.
We have been given that the container of oregano is 17 pounds heavier than a container of peppercorns. So the weight of container of oregano would be [tex]x+17[/tex].
We are also told that the total weight of both containers is 253 pounds. We can represent this information in an equation as:
[tex]x+x+17=253[/tex]
Let us solve for x.
[tex]2x+17=253[/tex]
[tex]2x+17-17=253-17[/tex]
[tex]2x=236[/tex]
[tex]\frac{2x}{2}=\frac{236}{2}[/tex]
[tex]x=118[/tex]
Therefore, the weight of peppercorns is 118 pounds.
Now, we will convert 118 pounds to ounces.
1 pound equals 16 ounces.
118 pounds = 118*16 ounces = 1,888 ounces
Since the peppercorns will be sold in one-ounce bags, therefore, 1,888 bags of peppercorns can be made.
Directions: Apply me u
you answer should be w
1) 12. 12² =
12×12 squared is = 12•144/=
1728
If you need a better explanation just ask in the comments.
Happy to help! Please mark as BRAINLIEST! Thanks
Jake has 32 quarters on his desk, and Molly has a quarters in her purse.
Which algebraic expression represents the total number of quarters that Jake
and Molly have?
O A. 250
O B. q-32
C. 32 + 9
0 0
D. 32 - 9
Answer:
32+q
Step-by-step explanation:
The complete question is
Jake has 32 quarters on his desk, molly has q quarters in her purse.
Which algebraic expression represents the total number of quarters that Jake and Molly have?
we know that
To find out the total number of quarters that Jake and Molly have, sum the amount of quarters that Jake has plus the amount of quarters that Molly has
Let
x ----> the amount of quarters that Jake has
y ----> he amount of quarters that Molly has
so
x+y
we have
[tex]x=32\ quarters\\y=q\ quarters[/tex]
substitute
32+q
The product of 9 and x is less or equal to -17
Answer:
x≤-17/9
Step-by-step explanation:
9x≤-17
1) Divide both sides by 9:
x≤-17/9
Write an algebraic expression for each word phrase.
3. 14 less than the quotient of 63 and a number h.
Answer:
63/h - 3.14
Step-by-step explanation:
Quotient means divide.
So the answer to the division is a quotient. 63/h is the quotient of the division.
Less means subtract so the subtraction that is taking place is
63/h - 3.14 and that's your answer.
Often with these questions, you start backwards as in this question.
Find the absolute value. |7| A. 14 B. 0 C. –7 D. 7
Answer:
D
Step-by-step explanation:
The absolute value always returns a positive value, that is
| - a | = | a | = a, thus
| 7 | = 7 → D
Answer:
Step-by-step explanation:
|7|=7 answer : D
For a math project you need to complete 4 math worksheets in 5 days each worksheet contains 15 problems evaluate the expression 4 times 5+15 divide by 5 to find how many problems you need to complete each day
What is 198 in simplest form
Answer:
This quantity is already simplified.
Perhaps there was a typographical error?
Answer: This quantity is already simplified.
Perhaps there was a typographical error?
Step-by-step explanation:
Will mark the brainliest! Which system of linear inequalities is graphed?
{x≤−3y≤−x−3
{x<−2y≤−x−1
{x<−3y≤−x−1
{x<−3y≤−x+1
Hey!
-------------------------------------------------
Steps To Solve:
~Coordinates of the line
(0, -1) and (-1, 0)
~Find slope
[tex]m = \frac{0 - (-1)}{-1 - 0} = \frac{1}{-1} = -1[/tex]
~Find the equation of the line
y = mx + b
m = slope
b = y-intercept
m = -1 or -x
b = -1
y = -x - 1
~Check using zero rule (substitute x and y for (0, 0))
y = 0 - 1
y = -1 (Correct)
0 = -x - 1
-x = 1 - 0
-x = 1 (Incorrect)
~Check
{x<−3y≤−x−1
0 < -3(0) ≤ 0 - 1
0 < 0 ≤ -1
*Note* Since the line isn't near the origin, the points (0, 0) don't satisfy the equation.
-------------------------------------------------
Answer:
{x<−3y≤−x−1
-------------------------------------------------
Hope This Helped! Good Luck!
PLEASE SOMEONE HELP ASAP!!
8. The art department at a school sold 323 tickets
to an art show, for a total of $790. Students paid
$2 for tickets, and non-students paid $3.50. The
principal asked how many non-students
attended the art show.
a) Write a system of two linear equations
for this situation.
b) Solve the problem by graphing the system.
Answer:
Step-by-step explanation:
students = x
non-students=y
x+y=410
y=410-x
3x+7y=1650
3x+7(410-x)=1650
3x+2870-7x=1650
-4x=-1220 (divide both sides by -4)
x=305 y=410-305=105
Hence, 305 students attended and 105 non-students attended
The problem can be represented by two linear equations, s + n = 323 and 2s + 3.5n = 790. After putting these equations into the format y = mx + b, they can be graphed to find the solution at the point where the two lines intersect.
Explanation:First, let's define two variables, s for the number of students and n for the number of non-students. From the information we have:
Students and non-students combined bought a total of 323 tickets, so our first equation is: s + n = 323.Students paid $2 and non-students paid $3.50, making a total of $790. This gives our second equation: 2s + 3.5n = 790.To solve the problem by graphing, we need to convert these equations into y = mx + b format. Our first equation then becomes s = -n + 323 and the second becomes s = (790 - 3.5n) / 2. Plotting these equations on a graph and finding the point where the lines intersect will give us the value of s and n. The x-values corresponds to n (non-students) and y-values to s (students).
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3/7 divided 1 1/6 Please help
Answer:
18/49 or 0.367
Step-by-step explanation:
1 (1/6)=7/6
now,
3/7 ÷ 1 (1/6)
=3/7 ÷ 7/6 [∵1 (1/6)=7/6]
=3/7 x 6/7
=18/49
=0.367
What Is the area of a rectangular room that is 3 3/4 yards long and 3 1/3 yards wide
Answer:
[tex]3 \frac{3}{4} \times 3 \frac{1}{3} = \frac{15}{4} \times \frac{10}{3} = \frac{25}{2} = 12 \frac{1}{2} [/tex]
The area of this room is 12 1/2 yd².
The area of the rectangular room is (12.5) square yards, calculated by multiplying length and width.
To find the area of a rectangular room, you multiply its length by its width. Given that the length is [tex]\(3 \frac{3}{4}\)[/tex] yards and the width is [tex]\(3 \frac{1}{3}\)[/tex] yards, you can calculate:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]
First, let's convert the mixed numbers to improper fractions:
[tex]\[ 3 \frac{3}{4} = \frac{4 \times 3 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4} \text{ yards} \]\[ 3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3} \text{ yards} \][/tex]
Now, plug these values into the formula:
[tex]\[ \text{Area} = \frac{15}{4} \times \frac{10}{3} \]\[ \text{Area} = \frac{15 \times 10}{4 \times 3} \]\[ \text{Area} = \frac{150}{12} \]\[ \text{Area} = 12.5 \text{ square yards} \][/tex]
So, the area of the rectangular room is [tex]\(12.5 \, \text{square yards}\).[/tex]
4x + 2 < −2 OR 4x + 2 > 26
solve pl
Step-by-step explanation:
The easiest thing to do here is:
4x + 2 = -2 and 4x + 2 = 26
Just know whaever you get for x is greater or less than the actual answer.
4x + 2 = -2
- 2 - 2
4x = -4
[tex]\frac{4x}{4} = \frac{-4}{4}[/tex]
x = -1 <--- Because -2 is supposed to be greater than x, x equals any number less than -1 but not -1.
4x + 2 = 26
- 2 - 2
4x = 24
[tex]\frac{4x}{4} = \frac{24}{4}[/tex]
x = 6 <--- Because 26 is supposed to be less than x, x equals any numbey greater than 6 but not 6
Answer:
-1 > x OR 6 < x
Step-by-step explanation:
4x + 2 > 26
- 2 - 2
___________
4x > 24
__ ___
4 4
x > 6
__________________________________________________________
4x + 2 < −2
- 2 - 2
___________
4x < -4
__ __
4 4
x < -1
The above answers are written in reverse, which are the exact same result.
I am joyous to assist you anytime.
find the perimeter and area of each figure.
Answer:
Perimeter = 89mm
area= 528 or 220
Step-by-step explanation:
hope this is useful
Answer:
Perimeter is 99 because 22+44+15+18=99
Area is 396 because 22+44=66÷2=33x12=396
The formula for the calculating the are of trapezium is a+b÷2xheight I hope this helped I gave you the formula to calculate the area of trapezium as well just to give extra help! Your welcome!
If Bill's Bike at an average speed of 5 miles per hour how many miles will it take him to Ride 65
Answer:
13 Miles
Step-by-step explanation:
All you need to do is divide 65 by 5.
65 / 5 = 13
32,467 rounded to the nearest ten
Answer:
32,470
Step-by-step explanation:
since there is a 7 in the ones place it will chnage the 6 to a 7 to make it 32,470
In order to find the answer to this question you must find the tenth place value and look to the right of the tenth place value and if the value next to the tenths higher then five you round up.
[tex]32,467[/tex]
[tex]Tenths=67[/tex]
[tex]7>5[/tex]
[tex]32470[/tex]
[tex]=32,470[/tex]
Therefore the answer is "32,470."
Hope this helps.
The sum of two integers is 2. Their difference is 10.
What are the two integers?
-14 and -4
4 and 14
-2 and 4
-4 and 6
Answer:
-4 and 6
Step-by-step explanation:
sum means +
-4+6=2
difference means -4-6=10
The sum of two integers is 2 and their difference is 10 then the two integers will be -4 and 6 and this can be determined by using the arithmetic operations.
Given :
The sum of two integers is 2.The difference between that two integers is 10.Let the two integers be 'a' and 'b'. Then the sum of the two integers will be:
a + b = 2 ---- (1)
The difference between the two integers will be:
a - b = 10 ----- (2)
Now, solve the equation (1) for 'a'.
a = 2 - b --- (3)
Now, put the value of 'a' in equation (2).
2 - b - b = 10
2 - 2b = 10
2b = -8
b = -4
Put the value of 'b' in equation (3).
a = 2 - (-4)
a = 2 + 4
a = 6
Therefore, the correct option is D) -4 and 6.
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What's this equation in vertex form? Please help!
I really need help. Thank you. [20 points]
y=8(x^2 + 4x + 4) +17 + -32
Simplify:
y = 8(x^2 + 4x + 4) + 15
Use distributive property:
y = 8x^2 + 32x +32 - 15
Simplify:
y = 8x^2 + 32x +17
Complete the square using form ax^2+bx+c:
a = 8, b = 32, c = 17
vertex form = a(x+d)^2+e
d = b/2a and e = c-b^2/4a
d = 32/2*8 = 32/16 = 2
e = 17 - 32^2/4*8 = 17-1024/32 = 17-32 = -15
Vertex form = y = 8(x+2)^2 + -15
- Varun drove to work this morning. It took
him 15 minutes. He stopped at a traffic
light for 3 minutes after driving for
5 minutes. Sketch a graph to represent
the distance from Varun's house during
his drive to work.
Answer:
See attached graph
Step-by-step explanation:
The graph of distance from home as a function of time starts at the origin of coordinates (0,0) since at time zero minutes Varun is at home.
Then we represent his driving at constant speed (although it has not been specified in the problem) as a line with positive slope equal to his speed, that goes on for the first five minutes. After that, he reaches the traffic light that keeps him at the same distance from home for three minutes (notice the line representing the distance covered is flat from minute 5 to minute 8, while he is not moving).
Then he starts moving again (we assume at the same speed as before - so the line representing his position is again a line with positive slope and with the SAME inclination as that which represents the first 5 minutes of his trip.
The line ends at minute 15 which is the time it took him to get to work.
standard form
4x-8=9y-5
Answer:
4x - 9y = 3
Step-by-step explanation:
The equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
Given
4x - 8 = 9y - 5 ( subtract 9y from both sides )
4x - 9y - 8 = - 5 ( add 8 to both sides )
4x - 9y = 3 ← in standard form
The original equation 4x - 8 = 9y - 5 can be rearranged to the standard form by initially adding 8 to both sides and then subtracting 9y from both sides. The final equation in standard form is 4x - 9y = 3.
Explanation:The given equation is in the form of 4x - 8 = 9y - 5. To convert the equation to standard form, we'll need to rearrange it so all variables and constants are on one side of the equation. Standard form is typically written as Ax + By = C. Here are the steps to do that:
Add 8 to both sides: 4x = 9y - 5 + 8 (which simplifies to 4x = 9y + 3)Subtract 9y from both sides: 4x - 9y = 3So, the
standard form
of the given equation is 4x - 9y = 3.
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Write the number for six million three thousand
Answer: 6,300,000
Step-by-step explanation:
Answer:
6,003,000
You would place the six in the millions place, and the 3 in the thousands place!
Marco Has a peice of wood that measures 9x1/10 + 6x1/100 + 4 x 1/1000 meter. How can this measurement be written as a decimal
Solve for x.
−1/2(x+2)+1 1/2x=3
Answer:
x = 4
Step-by-step explanation:
look at the screenshots below, they'll explain the answer
Hope I helped :)