Answer:
a = -1/2 & k = 3/7
Step-by-step explanation:
Solve for a over the real numbers:
24 a^3 + 8 a^2 + 6 a + 4 = 0
The left hand side factors into a product with three terms:
2 (2 a + 1) (6 a^2 - a + 2) = 0
Divide both sides by 2:
(2 a + 1) (6 a^2 - a + 2) = 0
Split into two equations:
2 a + 1 = 0 or 6 a^2 - a + 2 = 0
Subtract 1 from both sides:
2 a = -1 or 6 a^2 - a + 2 = 0
Divide both sides by 2:
a = -1/2 or 6 a^2 - a + 2 = 0
Divide both sides by 6:
a = -1/2 or a^2 - a/6 + 1/3 = 0
Subtract 1/3 from both sides:
a = -1/2 or a^2 - a/6 = -1/3
Add 1/144 to both sides:
a = -1/2 or a^2 - a/6 + 1/144 = -47/144
Write the left hand side as a square:
a = -1/2 or (a - 1/12)^2 = -47/144
(a - 1/12)^2 = -47/144 has no solution since for all a on the real line, (a - 1/12)^2 >=0 and -47/144<0:
Answer: a = -1/2
______________________________________
Solve for k over the real numbers:
(7 k - 3) (k^2 - 2 k + 7) = 0
Split into two equations:
7 k - 3 = 0 or k^2 - 2 k + 7 = 0
Add 3 to both sides:
7 k = 3 or k^2 - 2 k + 7 = 0
Divide both sides by 7:
k = 3/7 or k^2 - 2 k + 7 = 0
Subtract 7 from both sides:
k = 3/7 or k^2 - 2 k = -7
Add 1 to both sides:
k = 3/7 or k^2 - 2 k + 1 = -6
Write the left hand side as a square:
k = 3/7 or (k - 1)^2 = -6
(k - 1)^2 = -6 has no solution since for all k on the real line, (k - 1)^2 >=0 and -6<0:
Answer: k = 3/7
Find the surface area and volume of the figure.
Answer:
Surface area: 310.86 sq ft
Step-by-step explanation:
First, find the surface area of the cylinder. This can be found by finding the area of the circle at its base, and then the area of its mid-region.
The area of the circle can be found using the formula: a = pi(r^2). r stands for radius, which is 3 in this problem. 3^2 equals 9, which, multiplied by pi (3.14), equals 28.26.
The area of the cylinder's mid-region is equal to the circumference of the circle multiplied by the height of the cylinder. The circumference of the circle is equal to c = 2pi(r), or in this case: 18.84. Now, multiply this value by the height to get 226.08 as the area of the mid-region.
Lastly, find the surface area of the sphere. This can be found using the equation a =4πr^2. r is, again, radius, which in this problem can be represented by 3. The surface area of a sphere with a radius of 3 is 113.04. However, this figure only shows half a sphere, which can be found by dividing 113.04 in half. This gets you 56.52.
Now, simply add all the areas together to get the total surface area!
Can someone help me with this please
Answer:
Here you go
Step-by-step explanation:
A) 3x
B) -2p + 9
C) 13+6w
D) 2(5d + 3c +1)
E) 2(4g - 3)
F) 11a
Answer:
a. 3x
b. -2p+9
c. 6w+13
d. 6c+10d+2
e. 2(4g-3)
d. 11a
Step-by-step explanation:
45% of all 1st graders at Sierra Elementary School are female students. This year there are 54 female 1st graders at Sierra Elementary School. How many 1st graders are there at Sierra Elementary School this year?
Answer:
There are 120 1st graders at Sierra Elementary School this year
Step-by-step explanation:
Let n represent the total number of 1st graders at Sierra Elementary School
Since 45% of all 1st graders at Sierra Elementary School are female students and this year there are 54 female 1st graders, 45% of n is equal to 54
→ n([tex]\frac{45}{100}[/tex]) = 54
→ 45n = 5400
→ n = 120
Answer:
number of first grader at Sierra elementary school = 120
Step-by-step explanation:
The question says 45% of 1st graders at Sierra Elementary school are female student . This year there are 54 female 1st graders at Sierra Elementary school .The number of 1st graders at Sierra elementary school can be calculated below .
Let
the number of 1st grader = a
45 % of a = female population
This year the female 1st graders at the Sierra elementary school are 54. This can represented as follows
45% × a = 54
45/100 × a = 54
45a/100 = 54
cross multiply
45a = 5400
divide both sides by 45
a = 5400/45
a = 120
number of first grader = 120
What is the least common multiple of the two denominators?
6/8 4/32
A.18
B.12
C. 8
D.32
Answer:
d.32
Step-by-step explanation:
To get the Least Common Multiple (LCM) of 8 and 32 we need to factor each value first and then we choose all the factors which appear in any column and multiply them:
8: 222
32: 22222
LCM: 22222
The Least Common Multiple (LCM) is: 2 x 2 x 2 x 2 x 2 = 32
The least common multiple is = 32
The denominators are 8 and 32.
The multiples of 8 are = 8, 16, 24, 32, 40, ....
The multiples of 32 are = 32, 64, ....
So the least common multiple is = 32
Learn more: https://brainly.com/question/8806877
Irwin purchased a $195,000 home with a 30-year mortgage at 5.55%. If makes a $1500 monthly mortgage payment, how many months early will he pay off his mortgage?
Answer:
160 months
Step-by-step explanation:
just took that ap3x quiz yerrr
4 friends evenly divided up an n-slice pizza. One of the friends, Harris, ate 1 fewer slice than he received. How many slices of pizza did Harris eat? Write your answer as an expression. Pls answer fast I'm taking a test!!
Answer:
7
Step-by-step explanation:
Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?
f(x) = x(x – a) (x - 1)3
f(x) = (x - a)
- a)2(x – b)4
f(x) = x(x - a) 6(x – b)2
Answer:
C
Step-by-step explanation:
I took the test
The function which represents the graph given is f(x) = (x - a)²(x - b)⁴.
What are Polynomials?Polynomials are expressions which consist of one or more terms involving variables and coefficients connected with operations like multiplication, subtraction, addition and natural number powers of variables.
Given is a graph of a function.
The options f(x) = x(x - a)³(x - b)³ and the option f(x)=x(x - a)⁶(x - b)² is not possible since x = 0 is not a root of the given graph.
That is the graph does not pass through the point (0, c) for any c.
Remaining options are f(x) = (x - a)²(x - b)⁴ and f(x) = (x - a)⁵(x - b).
We know that, the graph of a polynomial function always touch the X axis at zeroes with even multiplicities.
So here multiplicity will be even.
So the correct one is f(x) = (x - a)²(x - b)⁴.
Learn more about Polynomials here :
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Jada rewrites 5•3^x as 15x. Do you agree with Jada that these are equivalent expressions? Explain your reasoning. Help me pleasee
Answer:yes
Step-by-step explanation:
5*3=15
5*3x=15x
The expression 15x is not the equivalent of the expression 5•3ˣ.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
Jada rewrites 5•3ˣ as 15x.
We do not agree with Jada that these are equivalent expressions because she made the mistake.
As per the given obtained expression, we can see that here write 15 as the coefficient of variable x which is actually the power of an argument. the original expression was an exponential function that has 3 representing the base. thus, it cannot be multiplied the 5 by 3.
Thus, the expression 15x is not the equivalent of the expression 5•3ˣ.
Learn more about exponential function here:
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HELPPP IM SOOO STUCKK PLEASE!
Answer:
60% that his or her drink will be a medium.
Step-by-step explanation:
Total amount orders = 5 + 48 + 22 +8 +12 +5
= 100
48 + 12 = 60 (medium orders)
60 out of 100 = 60%
Therefore it is 60%
Solve for x can someone please answer please
Answer:
the triangles are in AA similarity.
Step-by-step explanation:
CB/DE = AB/AD
3/11 = x/9
cross multiply to get;
x = 2.45
A jar contains 5 popsicle sticks, numbered 1-5. A stick is drawn, then a letter in the word SPRING is chosen at random. What is the probability the number is greater than 2, then P?
Answer:
10% probability that the number is greater than 2, then P
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
Event A: Number greater than 2.
Event B: Letter P.
These events are independent, so:
[tex]P(A \cap B) = P(A) \times P(B)[/tex]
P(A)
There are 5 numbers.
3, 4 or 5, that is, 3 numbers greater than 2.
3/5 = 0.6. So P(A) = 0.6.
P(B)
6 letters, one of which is P. So
P(B) = 1/6 = 0.1667.
What is the probability the number is greater than 2, then P?
[tex]P(A \cap B) = P(A) \times P(B) = 0.6 \times 0.1667 = 0.1[/tex]
10% probability that the number is greater than 2, then P
Which statements are true about the table of values?
Check all that apply.
O xy = 3
When x = 3, y = 1.
x varies directly with y.
k = 1
3
The graph of this table would not be linear.
Answer:
A: xy= 3
B: When x= 3, y = 1
E: The graph of this table would not be linear.
Step-by-step explanation:
Edge
What is the product?
Three-fourths times 12.44
3.11
9.33
12
36
Awnser pls ill give a star
Answer:
9.33
Step-by-step explanation:
12.44=311/25
(3/4)×(311/25)=(3×311/4×25)=933/100=9.33
Answer:
B. 9.33
Step-by-step explanation:
I go with my gut and my gut tells me this the right answer ( I used a calculator).
The expresssion is also equivalent to the cost of the item? c-0.25 c which expression is also equivalent to the cost of the item? 1-0.25c 0.25c 0.75c 1-0.75c
Answer:
0.75c
Step-by-step explanation:
If we have an expression as:
a*x + b*x
We can see that both terms in the expression, a*x and b*x have an x, so we can call the x a common factor and we can write an equivalent expression as:
a*x + b*x = (a + b)*x
If we replace, for example, a by 2, b by 3 and x by 4, we can test the expression as:
2*4 + 3*4 = (2 + 3)*4
8 + 12 = (5)*4
20 = 20
Therefore, if we have the following expression:
c - 0.25*c
The expression that is equivalent is 0.75c and it is calculated as:
c - 0.25*c = (1 - 0.25)*c
c - 0.25*c = 0.75*c
x/2−5=−12
I need to know how to get the answer to what X is
Answer:
-14
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
x/2-5=-12
1/2x+-5=-12
1/2x-5=-12
Step 2: Add 5 to both sides.
1/2x-5+5=-12+5
1/2x=-7
Step 3: Multiply both sides by 2.
2*(1/2x)=(2)*(-7)
x=-14
Answer:
-14
Step-by-step explanation:
x/2 = -12 + 5 << add both sides by 5
x/2 = -7 << Combine -12 + 5
x = -14 << Multiply both sides by 2
This revolves around the idea of inverse operations
To get x by itself we needed to bring the other numbers to the other side of the equation.
Inverse operations is bring the numbers to the other side by doing the opposite operation it shows.
ex: if the number is +5 on one side, it will be -5 on the other
Hope this helps!
If you don't understand, please feel free to comment and let me know!
Have a great day!
A coin is tossed and a die is rolled. What is the probability that a tail was tossed and an even number was rolled?What is the probability that a head was tossed and a number larger than 4 was rolled?
Please Show Work! Thanks!
Answer:
First problem: 1/4 chance
Second problem: 1/6 chance of happening
Step-by-step explanation:
To find the probability we need to multiply the chance of each separate thing happening by each other in each example.
In the first example we have a 1/2 chance that a tail was tossed and 3/6 chance that an even number was rolled.
[tex]\frac{1}{2} *\frac{3}{6} = \frac{3}{12} =\frac{1}{4}[/tex]
So in the first example we have 1/4 chance of happening or 0.25
Same thing with the second example:
[tex]\frac{1}{2} *\frac{2}{6} = \frac{2}{12} =\frac{1}{6}[/tex]
Plz Help! School is over tommorow and this is last thing I got to do.
Answer:
C
Step-by-step explanation:
can i get brainleist plz
Answer:
The first choice
Step-by-step explanation:
When the question says 6 hours or less, then you would use this sign ≤.
The answer choices are easy to cross out because there's only one answer choice that matches the question and that is letter choice A.
8x goes with ≤ 6 and 12x goes with the number that is greater than 6. So, your answer choice is A.
Can someone answer this question please please help me I really need it if it’s correct I will mark you brainliest .
Answer:
169.65 for volume.
Step-by-step explanation:
Volume = πr2h
= π×32×6
= 54π
= 169.64600329385 (unit^3)
I Hope this helps!!!
Answer:
339.12 squared (for surface area)
Step-by-step explanation:
radius=6
area of the circles is, 6*6= 36 * 3.14= 113.04
there are 2 circles so we multiply that by 2 to get 226.08
now to find the perimeter of a circle it is the radius * pi, so that would be 6*3.14= 18.84 now we have a height of 6 so we multiply that by 6 and get 113.04 now add up all our numbers and get 339.12
you roll a 6 sided die what is p(greater than 4)
Answer:
hey i think its 5 what do u think please folow me
find whether the given numbers are perfect square or not {step by step}
a.1057
b.23453
c.2304
d.1057
Answer:
a. 1057 is not a perfect square
b. 23453 is not a perfect square
c. 2304 is a perfect square
d. 1057 is not a perfect square
Step-by-step explanation:
A perfect square is a number x where the square root of x is a number a such that a² = x and a is an integer. For example, 4, 9 and 16 are perfect squares since their square roots, 2, 3 and 4, respectively, are integers.
what is the total cost of a meal if the food cost $25 and there is a food tax of 3% and the waiter is tipped 15% of the food cost? Round to the nearest cent.
Answer:
$30
Step-by-step explanation:
If $25 is 100%,
$2.5 is 10%
$0.25 is 1%
$3.75 is 15%
$0.75 is 3%
Then add $25, $3.75 and 0.75 which is also equivalent to 100%+15%+3%=29.5 and if you rounded it up to the nearest cent it is 30
please graph this for me.
Answer:
As shown in attached file:
green is f(x) = -3 if -2 <= x <= -1
red is f(x) = -2 if -1 <= x <= 0
blue is f(x) = -1 if 0 <= x <= 1
Hope this helps!
:)
Solve for the zeros of the quadratic function f(x) = 9.2 + 6x +1. Write the answer as a fraction.
Answer:
x = -1.7, or x = -17/10
Step-by-step explanation:
f(x) = 9.2 + 6x + 1 is a linear function and as such (and because the slope is not zero) has only one solution. Combining like terms, we get
f(x) = 10.2 + 6x = 0 (you must set this equal to zero if solving for zero(s).
Then 6x = -10.2, and x = -1.7, or x = -17/10
In a certain city with a working population of 10,500 , 8925 people and less than $75,000 per year what is a percentile rank of someone who earns $75,000 per year
Answer:
The percentile rank of someone who earns $75,000 per year is the 85th percentile.
Step-by-step explanation:
Meaning of percentile:
When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.
In this question:
Working population of 10,500
8,925 people earn less than $75,000 per year.
8925/10500 = 0.85
0.85*100 = 85
The percentile rank of someone who earns $75,000 per year is the 85th percentile.
Please help!!
I grant brainliest.
Answer:
x = 65, y = 63
Step-by-step explanation:
∠ EGA = ∠ HBG = 52° ( corresponding angles )
ED is a straight angle, thus
52 + y + 65 = 180, that is
y + 117 = 180 ( subtract 117 from both sides )
y = 63
-------------------------------------
∠ HGB = y = 63° ( vertical angles )
The sum of the 3 angles in a triangle = 180°, thus
x + 63 + 52 = 180
x + 115 = 180 ( subtract 115 from both sides )
x = 65
Using the following triangle, write a proof to verify that sinA/a=sinC/c
Write two different expressions for h and set the expressions equal to each other
Answer:
Proved: [tex]c\sin A=a\sin C\Rightarrow \frac{\sin A}{a}=\frac{\sin C}{c}[/tex]
Step-by-step explanation:
Given: A triangle
To prove: [tex]\frac{\sin A}{a}=\frac{\sin C}{c}[/tex]
Solution:
Trigonometry is a branch of mathematics that explains relationship between sides and angles of the triangle.
Sine of angle = side opposite to the angle / hypotenuse
In ΔADB,
[tex]\sin A=\frac{BD}{AB}=\frac{h}{c}\\\Rightarrow h=c\sin A\,\,\,(i)[/tex]
In ΔBDC,
[tex]\sin C=\frac{BD}{BC}=\frac{h}{a}\\\Rightarrow h=a\sin C\,\,\,(ii)[/tex]
From equations (i) and (ii),
[tex]c\sin A=a\sin C\\\frac{\sin A}{a}=\frac{\sin C}{c}[/tex]
Hence proved
Write a unit rate for the situation. 54$ for 3 tickets.
Answer:
It would be $18 because you would divide 54 by 3 and get $18 per ticket
Step-by-step explanation:
4/3 times 22/7 times 1/4 cubed
Answer:
88/1344
Step-by-step explanation:
28t = 448 solve for t
Answer:
t = 16
Step-by-step explanation:
if you do 448 divided by 28 you get 16.
if you do 28 x 16 you get 448
Evaluate 15 - 151.
-10
10
20
-20
Answer:
10
Step-by-step explanation:
15 - |5|
The absolute value of 5 is 5
15 - 5
10
Answer:
10
Step-by-step explanation:
assuming those are absolute value bars it is basically 15-5=10 so 10 is your answer!