Answer:
a^12+8
Step-by-step explanation:
let's check all the expressions
1. a^3+18
here 18 is not a perfect cube.
2. a^6+9
here 9 is not a perfect cube.
3. a^9+16
here 16 is not a perfect cube.
4. a^16+8
here 8 is a perfect cube, thus we can write above expression by using laws of exponents as
(a^4)^3+2^3
Thus, is a sum of cubes.
a^12+8
Use the zero product property to find the solutions to the equation (x 2) (x 3) = 12.
The solution of the given equation is -6 and 1.
What is Quadratic Equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
Here, given equation:
(x+2)(x+3) = 12
x(x+3)+2(x+3) = 12
x² + 3x + 2x + 6 = 12
x² + 5x + 6 - 12 = 0
x² + 5x - 6 = 0
x² + 6x - x - 6 = 0
x(x+6) -1(x+6) = 0
(x+6)(x-1) = 0
Now, x + 6 = 0 or x - 1 = 0
x = -6 or x = 1
Thus, the solution of the given equation is -6 and 1.
Learn more about Quadratic Equation from:
https://brainly.com/question/17177510
#SPJ1
Suppose the mean height for men is 70 inches with a standard deviation of 2 inches. What percentage of men are more than 72 inches tall?
The percentage of men is more than 72 inches tall will be 0.15866.
What is the z-score?The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The z-score is given as
z = (x – μ) / σ
Where μ is the mean, σ is the standard deviation, and x is the sample.
Suppose the mean height for men is 70 inches, with a standard deviation of 2 inches.
Then the percentage of men are more than 72 inches tall will be
z = (72 – 70) / 2
z = 1
The percentage of men is more than 72 inches tall will be
P(x > 72) = P(z > 1)
P(x > 72) = 1 – P(x < 72)
P(x > 72) = 1 – 0.84134
P(x > 72) = 0.15866
Thun, the percentage of men are more than 72 inches tall will be 0.15866.
More about the z-score link is given below.
https://brainly.com/question/15016913
#SPJ1
16t^2 + 48t + 160 =0
Answer:
Simplifying -16t2 + 48t + 160 = 0
Reorder the terms: 160 + 48t + -16t2 = 0
Solving 160 + 48t + -16t2 = 0 Solving for variable 't'.
Factor out the Greatest Common Factor (GCF), '16'. 16(10 + 3t + -1t2) = 0
Factor a trinomial. 16((5 + -1t)(2 + t)) = 0 Ignore the factor 16.
hope it helps.
This is confusing please help
Step-by-step explanation:
Since we have a right triangle, we use the Pythagorean Theorem
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
or
[tex]c = \sqrt{ {a}^{2} + {b}^{2} } [/tex]
where a and b are the legs and c is the hypotenuse
Remember the legs are the sides that form that right angle, and the hypotenuse is the side opposite of the right angle.
So here the hypotenuse is 8, and one of the legs is 4. So we plug those values into the formula
[tex] 8 = \sqrt{ {b}^{2} + {4}^{2} } [/tex]
3. a 12 inch apple pie is sliced into 9 slices. what is the area of one slice of pie?
Answer:
4 pi ( = 12.566 in^2 )
Step-by-step explanation:
TOTAL area = pi r^2 = pi (6)^2 = 36 pi in^2
divide into 9 pieces 36 pi / 9 = 4 pi in ^2
Answer all the questions. 1 The first three terms in a sequence of numbers, T1, T2, T3,... are given below: (a) T₁=1+3=4 T₂=4+5=9 T3=9+7=16 Find T4. Answer T4=
Answer:
16 + 9 = 25
Step-by-step explanation:
For each term in the sequence, we can see that the second number being added increases by 2 each time (3, 5, 7)
And that the first number of each term increases by the value of the second term
(1 increases by 3; 4 increases by 5)
we can follow out these two observations to find T4
the first term (9) will increase by the value of the second term (7)
{the sum of the previous term is the first number}
so the first number of T4 will be 16.
Because we left off on +7, we are now on +9
so, T4 is
16 + 9 {and then do the math accordingly}
16 + 9 = 25
So, T4 is
16 + 9 = 25
hope this helps!! have a lovely day!! :)
Max's Market sells 6 eggs for £2.04.
Groceries Galore sells 8 eggs for £2.64.
Fancy Foodstuffs sells 12 eggs for £4.08.
Which shop's price per egg is cheaper?
Answer:
Groceries Galore
Step-by-step explanation:
1) Find the value of 1 egg for each shop.
Max's Market:
2.04 ÷ 6
= £0.34
Groceries Galore:
2.64 ÷ 8
= £0.33
Fancy Foodstuffs:
4.08 ÷ 12
= £0.34
Therefore, Groceries Galore's price per egg is cheaper.
Answer:
Groceries Galore
Step-by-step explanation:
we have to calculate the price of 2 eggs
in each shop apart ,and then we can infer
which shop offers the cheaper price.
…………………………………………………………
• At Max's market :
2 egg costs 2,04÷3 = £0,68
• At Groceries Galore :
2 egg costs 2,64÷4 = £0,66
• At Fancy Foodstuffs :
4,08÷6 = £0,68
………………………………
Conclusion :
Groceries Galore Offers the Lower price.
Note : we can just determine
the price of one egg in each store ,and then compare.
If a=[-2 -4 2 5 1 5 -1 -3 -4] and b=[2 3 -5 5 -4 2 -1 -1 3] find ba
The product of A and B matrix will be option D; BA = [tex]\left[\begin{array}{ccc}16&10&39\\-32&-30&-18\\-6&-6&-19\end{array}\right][/tex].
What is the multiplication of matrix?If [tex]A = \left[\begin{array}{ccc}-2&-4&2\\5&1&5\\-1&-3&-4\end{array}\right][/tex]and [tex]B = \left[\begin{array}{ccc}2&3&-5\\5&-4&2\\-1&-1&3\end{array}\right][/tex]
then,
BA = [tex]\left[\begin{array}{ccc}2&3&-5\\5&-4&2\\-1&-1&3\end{array}\right] \left[\begin{array}{ccc}-2&-4&2\\5&1&5\\-1&-3&-4\end{array}\right][/tex]
BA = [tex]\left[\begin{array}{ccc}16&10&39\\-32&-30&-18\\-6&-6&-19\end{array}\right][/tex]
Hence, the product of A and B matrix will be option D; BA = [tex]\left[\begin{array}{ccc}16&10&39\\-32&-30&-18\\-6&-6&-19\end{array}\right][/tex].
Learn more about matrix here;
https://brainly.com/question/9967572
#SPJ1
Write an equation for a parabola in which the set of all points in the plane are equidistant from the focus and line F(-6,0); x=6
Step-by-step explanation:
Since we have a vertical directrix, the equation of the parabola is
[tex](y - k) {}^{2} = 4p(x - h)[/tex]
Where p is the distance from the vertex to the directrix.
or the distance from the vertex to the focus.
Since we have a sideways parabola, let use the point for the directrix is (-6,0). So let find the midpoint of (-6,0) and (6,0). That would be our vertex.
[tex] \frac{ - 6 + 6)}{2} = 0[/tex]
[tex] \frac{0 + 0}{2} = 0[/tex]
So our vertex is (0,0).
So our equation become
[tex] {y}^{2} = 4px[/tex]
The distance from the focus and directrix is 6.
So p=6.
[tex] {y}^{2} = 24x[/tex]
So p is 6.
Since p is 6,
[tex] \frac{ {y}^{2} }{24} = x[/tex]
I ne subject of the formula below iS y.
y = 4x + 3
Rearrange the formula to make x the subject.
Answer:
x=(y-3)/4
Step-by-step explanation:
y=4x+3
y-3=4x
x=(y-3)/4
Brianna bought a total of 8 notebooks and got 16 free pens
Answer: 1:2
Step-by-step explanation:
Well, if you're asking for the ratio, it is 1:2
For every 1 notebook bought, there would be 2 free pens.
Since she bought 8 notebooks, just multiply 2 by 8 which will result in 16.
Answer all the questions
Tau decides to save money in the following ways:
He saves $ 1 in the first week $1.20 in the second week, $1.40 in the third week, and so on.
1) How much would he save in the nth week?
Answer:
1.00 + [(n - 1) × 0.20]
or
0.80 + [n × 0.20]
Step-by-step explanation:
week 1: 1.00
week 2: 1.20
week 3: 1.40
we could rewrite this as:
week 1: 1.00 + [0 × 0.20]
week 2: 1.00 + [1 × 0.20]
week 3: 1.00 + [2 × 0.20]
we can write this overall as:
week __ : 1.00 + [x × 0.20]
> x being the amount of weeks that have passed since week 1
but, we need to express this as in terms of nth, so, we need to figure out how the week is related to the x value
each week, we subtract 1 from the week number [to account for week 1]
so, we can write this as: 1.00 + [(n - 1) × 0.20]
or, we can backtrack from the first week, and start our counting at 0.80:
0.80 + [n × 0.20]
we can test this out:
(week 1)
1.00 + [(n - 1) × 0.20]
1.00 + [(1 - 1) × 0.20]
1.00 + [0 × 0.20]
1.00
or...
(week 1)
0.80 + [n × 0.20]
0.80 + [1 × 0.20]
0.80 + 0.20
= 1.00
So, nth week should be expressed as either:
1.00 + [(n - 1) × 0.20] or
0.80 + [n × 0.20]
(the second one is a little bit more simplified, but it depends on how you're supposed to write it)
hope this helps!!
When a patient with hypertension takes a particular type of blood pressure medication, the effects on the systolic pressure, S(t), can be measured by the following piecewise defined function: S of t is equal to the piecewise function of 140 minus 6 times t if 0 is less than or equal to t is less than or equal to 4 and 116 if 4 is less than t is less than 8 and 96 plus 8 times t if 8 is less than or equal to t is less than or equal to 12 where t is the time, in hours, since taking the medication. Based on the graph of the piecewise function, if the patient takes the blood pressure medication at 8 a.m., in which interval will their systolic pressure be lowest?
Based on the graph, the interval will their systolic pressure be lowest is 4pm to 5pm.
What is the interval in blood pressure ?The lowest systolic pressure can be seen from 5 and 8 hours after taken the medication.
If we look at the time details then this will fall inbetween the interval of 2pm to 5pm.
According to question, the time range is 4pm to 5pm.
Hence, the interval will their systolic pressure be lowest is 4pm to 5pm.
Learn more about this concept here:
https://brainly.com/question/27891673
#SPJ1
Answer:
The answer is B - 12 P.M to 2 P.M
Step-by-step explanation:
write the explicit rule for the nth term of the arithmetic sequence. then find the 43rd term (3,5,7….)
Parallelogram ABCD has vertices: A(-3, 1), B(3, 3), C(4, 0), and D(-2, -2). In two or more complete sentences, explain how you can use the coordinates of the vertices to prove that parallelogram ABCD is a rectangle.
please help
Step-by-step explanation:
via the distance formula (based on Pythagoras) I can prove that ABC is a right-angled triangle, and that ADC is fully congruent to ABC.
so, together these 2 triangles (joined at their Hypotenuses, the diagonal AC) build a rectangle.
Carmela opened her piggy bank and found she had $15.30. If she had only nickels, dimes, quarters, and half-dollars and an equal number of coins of each kind, how many coins did she have in all
Answer:
68 coins
Step-by-step explanation:
We can use the given information to write two equations involving the numbers of coins. One will express the total number of coins; the other will express their value.
__
setupSince there are equal numbers of coins of each type, we can let n represent the number of each kind of coin. The total number coins will be ...
n +n +n +n + N . . . the sum of numbers of nickels, dimes, quarters, halves
The value of the coins is ...
0.05n +0.10n +0.25n +0.50n = 15.30
solutionThe second equation lets us find the value of n:
0.90n = 15.30
n = 17 . . . . . . . . divide by 0.90
Then the number of coins in all is ...
4n = N
4(17) = N = 68
Carmela had 68 coins in all.
Sahil chooses a number, divides it by 8 , adds 8 to the answer. Then multiples the answer with 8 . He obtains the result as 952 . The number he chooses in the beginning was
USER IS DEAD
TAKE POINTS
Answer:
888
Step-by-step explanation:
Sahil chooses a number, [We'll call it x]
divides it by 8 , [x/8]
adds 8 to the answer. [(x/8) + 8]
Then multiples the answer with 8 . [((x/8) + 8)*8]
He obtains the result as 952 . [((x/8) + 8)*8 = 952]
The number he chooses in the beginning was
((x/8) + 8)*8 = 952
x + 64 = 952
x = 888
CHECK:
Does (888/8 + 8)*8 = 952?
(119)*8 = 952? YES
The number is 888
A. Does the relationship of weeks passed and total number of followers represent a linear function? (0.5 points) B. What is the independent variable in the situation(0.5 points) C. What is the dependent variable in the situation? (0.5 points ) D. What is the slope of the line ? What does the slope represent in this scenario ? (0.5 points) E. What is the y-intercept of the line? What does the y intercept represent in this scenario? (0.5 points) F. Write the equation in slope intercept form that represents the situation (points ) G. What is the domain ? (Inequality notation ) (0.5 points) H. What is the range ? ( Inequality notation ) (0.5 points) How many weeks would it take Jorge to get 100 followers ? (points ) J. How many followers will Jorge have after 12 weeks ? (0.5 points)
The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.
a) Yes it does, because the graph of their relationship is a Straight line
b) Independent variables are variables whose variation does not depend on another. Number of works does not depend on followers. Therefore, it is independent
C)number of followers depend on the number of locks passing. It is dependent.
D) Slope = (Y₂- Y₁)/(x₂-x₁) = (100-82)/ (3-0) = 18/3 = 6
It represents the increase in number of followers per week,
E) y-intercept is value of y when x=0
y-intercept = 82. It means his initial number of followers
F) Slope-intercept form → y = mx + c m = slope горе C = y-intercept y = no of followers x= weeks.
Y=6x+82
Learn more about linear function here:
https://brainly.com/question/4025726
#SPJ10
Select the correct answer.
What is the output of the function f(p) = 3p – 2 when the input is 2?
A.
0
B.
2
C.
4
D.
6
E.
8
f(p) = 3p - 2
f(2) = 3(2) - 2
f(2) = 6 - 2
f(2) = 4
Therefore, the answer is 4, so option C :)
Kevin and Randy Muise have a jar containing 65 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $8.65 How many of each type of coin do they have?
The number of quarters or nickels Kevin and Randy Muise have in the jar is 27 and 38 respectively.
Simultaneous equationA nickel = 5 centsA quarter = 25 centsn + q = 65
0.05n + 0.25q = 8.65
From equation (1)
n = 65 - q
substitute n = 65 - q into (2)
0.05n + 0.25q = 8.65
0.05(65 - q) + 0.25q = 8.65
3.25 - 0.05q + 0.25q = 8.65
- 0.05q + 0.25q = 8.65 - 3.25
0.20q = 5.40
q = 5.40/0.20
q = 27
Substitute into (1)
n + q = 65
n + 27 = 65
n = 65 - 27
n = 38
Learn more about quarters and nickels:
https://brainly.com/question/17127685
#SPJ1
A, B C, or D because i’m not sure
Answer:
C
Step-by-step explanation:
SAS axiom
SAS axiom
SAS axiomSAS axiom
SAS axiom
Select the correct answer.
Given:
Prove:
M
and
theorem,
Where is the error in the proof? Select all that apply.
U
The given cannot be used to state that XMY is a right angle.
The congruent complements theorem cannot be used to state that XMN~ XAOP.
The linear pair theorem cannot be used to state AOP is complementary to *POB.
The given cannot be used to state that AOB is a right angle.
The linear pair theorem cannot be used to state XMN is complementary to *NMY
The correct answer is option C the error is that the linear pair of the theorem can not be used to say that ∠AOP is complementary to ∠POB
What is the Linear pair theorem?The linear pair postulate or linear pair theorem in mathematics states the same thing mathematically. The sum of the measurements of two angles that make up a linear pair is 180°.
In the proof of the given question, it is given that the ∠AOP and ∠POB are complementary angles by linear pair of theorem but the linear pair of the theorem is applied to the angles with the sum of 180.
Therefore the correct answer is option C the error is that the linear pair of the theorem can not be used to say that ∠AOP is complementary to ∠POB
To know more about the Linear pair theorem follow
brainly.com/question/5598970
#SPJ1
Answer: Both:
The linear pair theorem cannot be used to state ∠XMN is complementary to ∠NMY.
The linear pair theorem cannot be used to state ∠AOP is complementary to ∠POB.
Step-by-step explanation:
Edmentum/Plato
48 girls, 41 boys, and 5 teachers sat in the gym. Write the ratio of girls to boys in three ways.
I took the text last month
Rafael purchased a video game for 35.60.if he gave the cashier 40 how much change will he get
Answer:
4.4
Step by step explanation: If Rafael gave the cashier 40, cashier will return 4.4 by subtracting 35.60 from 40
Give the name (monomial,
binomial, trinomial etc.) and
degree of the polynomial.
15x²
Name? [?]
Degree? [ ]
Answer:
monomial and degree is 2
Help... will give you 20 points if you answer
Answer:
(-3,5) (-3,3) (-8,3)
Step-by-step explanation:
Answer:
(-3,5) , (-3,3) , (-8,3)
Step-by-step explanation:
bye, bye!!
The side of an equilateral triangle is given as 8cm, correct to the nearest centimeter. What is the possible least lenght of its perimeter?
Answer:
An equilateral triangle is a triangle with all 3 sides the same in size.
If one side is 8cm, then 8x3=24 cm
The perimeter is possibly 24 cm.
Use the drawing tool(s) to form the correct answer on the number line.
Graph the solution to this inequality on the number line.
-4x+7>x-13
Answer:
Let's solve your inequality step-by-step.
−4x+7>x−13
Step 1: Subtract x from both sides.
−4x+7−x>x−13−x
−5x+7>−13
Step 2: Subtract 7 from both sides.
−5x+7−7>−13−7
−5x>−20
Step 3: Divide both sides by -5.
−5x/−5>−20/−5
x<4
Answer:
x<4
IMAGINE AN ARROW ABOVE THE NUMBERS
⇔
−7−6−5−4−3−2−1 0 1 2 3 4 5 6 7
4 is where the line is circled and the arrow is facing left
←Ф
like that
Answer:
x<4
Step-by-step explanation:
So you will put an open circle on positive 4 and a ray going to the left of the graph.
On Friday, a local hamburger shop sold a combined total 312 of hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Friday?
Find the area of a circle with radius,
r
= 7.15m.
Give your answer rounded to 2 DP.
[tex] \boxed{\Large {\mathcal {{{\color{orange}{Area \: of \: circle \: = \: πr²}}}}}}[/tex]
r = 7.15m[tex]\large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large πr²\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large \frac{22}{7} \: \times\:{7.15}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\\large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large \frac{22}{7} \: \times\:51.1225 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large \frac{22}{ \cancel7} \: \times\: \cancel{51.1225} \: \: ^{ \red{7.303} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \rm \pink{ \:Area \: of \: circle }\:\large\blue\implies \tt \large {22} \: \times\:7.303 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large \: 160.666 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Hence , the area of circle is 160.66 m²
Given :-
Radius of circle = 7.15mTo Find :-
Area of circleSolution :-
Area of Circle = πr²
putting the value of π and rArea = 3.14×(7.15)² m²
= 160.52465 , which rounded off to 2DP would be 160.52 m²
