Answer: -48
Step-by-step explanation:
k/3 + 16
find the roots by factoring
which leads to -48
k/3 + 16
To add or subtract expressions, expand them so their denominators are the same. Multiply 16 by 3/3.
k/3 + 16 × 3/3
Since k/3 and 16 × 3/3 have the same denominator, we join their numerators to add them.
k + 16 × 3/3
We perform the multiplications in k+16×3.
k + 48/3
See more about algebraic expressions at:https://brainly.com/question/24548997
Tell whether the value is a solution of the inequality 5 − x < 8; x = −3
Answer:
The value is not a solution of the inequality.
Step-by-step explanation:
5 - x < 8
1. Substitute the variable, x, with -3: 5 - - 3 < 8
2. Use the KCC (keep,change,change) method to turn subtraction into addition: 5 + + 3 < 8
3. Add the numbers on left side of the inequality to get the answer: 8 < 8 - False statement - 8 is not less than 8.
in rhombus $abcd$, points $e,f,g,$ and $h$ are the midpoints of $\overline{ab},\overline{bc},\overline{cd},$ and $\overline{da},$ respectively. quadrilateral $efgh$ has area 14 and perimeter 16. find the side length for rhombus $abcd$.
Side length of Rhombus ABCD is 8+2√2 unit
EFGH is a rectangle :
We know that ,
E, F , G , H are midpoints of AB, BC, CD , DA respectively
Since ABCD is a rhombus
AB = BC = CD = DA
AB ll CD and BC ll DA
since, E, F , G , H are midpoints of AB, BC, CD , DA respectively
from the figure below we can say that ,
1) AB ll CD ll FH and AB= CD = FH
2) BC ll DA ll GE and BC = DA = GE
Using mid point theorem we can say that ,
GH = EF = 1/2 AC and FG= EH = 1/2 BD
Since for the figure EFGH opposite sides are equal and and parallel , and the diagonals are equal in length we can say that EFGH is a rectangle.
Perimeter of a rectangle = 2(a+b) = 2( GH + EH ) = 2 (EF + GF) = 2 ( 1/2 AC + 1/2 BD )
= 2 x 1/2 ( AC + BD ) = 16
⇒ AC + BD = 16 (1)
now area of a rectangle is given by
A = ab = GH x EH = EF x GF = 1/2 AC x 1/2 BD = 1/4 (AC x BD) = 14
⇒AC x BD = 14 x 4 = 56
from equation (1)
AC ( 16 - AC) = 56
= 16 AC - AC ^2 = 56
⇒ AC^2 - 16 AC + 56 = 0
AC = 8 +/- 2√2
BD = ( 16 - AC) = 8 +/- 2 √2 = side length of rhombus ABCD
(To know more about Parallelograms :https://brainly.in/question/46582565)
PLEASE HELP
A TV show had 5.6 x 105 viewers in the first week and 4.1 x 105 viewers in the second week. Determine the average number of viewers over the two weeks and write the final answer in scientific notation.
9.7 x 1010
9.7 x 105
4.85 x 1010
4.85 x 105
The average number of viewers over the two weeks is 4. 85 x 10^5. Option D
What is average?Average is simply a number taken as the representative of a list of numbers.
It is determined by taking the sum of the numbers divided by the number of listed numbers.
Given the number of viewers as;
5.6 x 105 viewers and 4.1 x 105 viewers
Average = 5. 6 x 10^5 + 4.1 x 10^5 / 2
Average = 9. 7 x 10^5 / 2
Average = 4. 85 x 10^5
The average number of viewers over the two weeks is 4. 85 x 10^5
Thus, the average number of viewers over the two weeks is 4. 85 x 10^5. Option D
Learn more about average here:
https://brainly.com/question/20118982
#SPJ1
the sum of two numbers is 56 . the larger number is 16 more than the smaller number. what are the numbers?
The numbers are 20 and 36.
As per the information in question, let the smaller number x. So, according to question, large number will be (x + 16).
Now, writing the equation that will form -
x + x + 16 = 56
Performing addition of variables on Left Hand Side
2x + 16 = 56
Shifting the number from Left Hand Side to Right Hand Side
2x = 56 - 16
Performing subtraction on Right Hand Side
2x = 40
Shifting 2 to denominator on Right Hand Side
x = 40÷2
Performing division to find the value of x
x = 20
So, smaller number is 20.
Larger number = x + 16
Larger number = 20 + 16
Larger number = 36
Hence, the numbers are 20 and 36.
Learn more about problems on sum -
https://brainly.com/question/5982761
#SPJ4
what is the 15th term of the general term
n(n+1)
______
2
Answer:
a₁₅ = 240
Step-by-step explanation:
to find the 15 th term substitute n = 15 into the general term
a₁₅ = 15(15 + 1) = 15(16) = 15 × 16 = 240
The nutritional label on a food stated that one serving contained 3 grams of fat which is 3.06% of the daily recommended level. How many grams of fat are recommended daily? Round to the nearest whole number.
The daily recommended grams of fat is? ...
The daily recommended grams of fat by the nutritional label is 98 grams.
How to find the grams of fat recommended daily?The nutritional label on a food stated that one serving contained 3 grams of fat which is 3.06% of the daily recommended level.
let
the recommended level = x
Therefore, the product of the percentage and the required daily recommendation level is equals to the 3 grams.
grams of fat = 3.06% × x
3 = 3.06% × x
3 = 3.06 / 100 × x
3 = 3.06x / 100
cross multiply
3 = 3.06x / 100
300 = 3.06x
300 = 3.06x
divide both sides by 3.06
300 / 3.06 = 3.06x / 3.06
x = 98.0392156863
x = 98 grams
Therefore, the daily recommended grams of fat by the nutritional label is 98 grams.
learn more on mass in grams here: https://brainly.com/question/8766894
#SPJ1
What is the greatest common factor of 3 and 13?
Answer: 1
Step-by-step explanation:
In order to find GCF, take the prime factorization of 3 and 13.
3: 1*3 ==> Prime factorization of 3
13: 1*13 ==> Prime factorization of 3
The common factor is 1.
GCF of 13 and 3 is 1
quantity a: the number of prime numbers between 0 and 100, inclusive. quantity b: the number of prime numbers between 101 and 200, inclusive.
The correct option is Quantity a: the number of prime numbers between 0 and 100, inclusive is greater.
What is a prime number?A prime number is a natural number greater than 1 that is not the sum of two lesser natural numbers (or a prime). Any natural number greater than one that is not prime is referred to as a composite number. For instance, the product 1 5 and 5 1 are the only two ways to write the number 5, making it a prime. The fact that it is the sum of two smaller integers (2 x 2), 4, however, makes it composite. Primes play a significant role in number theory because of the fundamental theorem of arithmetic, it states that any natural number greater than one is either a prime number itself or may be factored as a unique prime product up to the order of the primes. the prime number (or a prime).
The number of primes reduces almost exponentially as we move up the number line. The prime numbers between 0 and 100 are therefore far more numerous than those between 101 and 200. It is crucial to understand this general number theory point, but it may also be rapidly illustrated by attempting to find some primes in these two groups.
To learn more about prime number ,visit:
https://brainly.com/question/15048606
#SPJ4
30 points mathamatics
Answer:
1870
Step-by-step explanation:
Answer:
c) 1,870
Step-by-step explanation:
374 multiplied 5 times, or 374 in a group of 5, equals 1,870.
Have a good day <333
if 4x + 2y = 20 what is the value of 8x+4y/5
By using algebra properties and given that the linear equation 4 · x + 2 · y = 20, the value of (8 · x + 4 · y) / 5 is equal to 8.
How to determine the value associated to a linear equation
Herein we find a linear equation equal to a given number and we are asked to find a number associated with a modified form of the formula, this can be done by using algebra properties. The complete procedure is shown below:
4 · x + 2 · y = 20 Given
2 · (4 · x + 2 · y) = 20 · 2 Compatibility with multiplication
8 · x + 4 · y = 40 Associative and distributive properties
(1 / 5) · (8 · x + 4 · y) = (1 / 5) · 40 Compatibility with multiplication
(8 · x + 4 · y) / 5 = 8 Multiplication of fractions / Result
To learn more on linear equations: https://brainly.com/question/13738061
#SPJ1
Earth is approximately 5x10^9. For which of these ages could this be an approximation
If earth is approximately 5×[tex]10^{9}[/tex] years old, the the approximate age of earth is option C 4,953,000,000 years
Given,
The age of Earth = 5×[tex]10^{9}[/tex] years old
We know,
5×[tex]10^{9}[/tex]= 5000000000 years old
From the given option the closest number to 5×[tex]10^{9}[/tex] is 4,953,000,000 years old
Hence, if earth is approximately 5×[tex]10^{9}[/tex] years old, the the approximate age of earth is option C 4,953,000,000 years
Complete question is:
Earth is approximately 5x109 years old. For which of these ages could this be an approximation? Select all that apply.
A. 4.37 x 100 years
B. 4.679999999 x 10º years
C. 4,953,000,000 years
D. 4,625,800,000 years
E. 50,000,000,000 years
Learn more about approximation here
brainly.com/question/11542606
#SPJ1
a sequence is constructed by listing all the possible numbers that contain no digit greater than 3 in ascending order. what is the 2021st term of this sequence?
The 2021st term of the sequence is (- n - 2017).
Given,
A sequence is constructed by listing all the possible numbers that contain no digit greater than 3 in ascending order.
We need to find out what is the 2021st term of this sequence.
What is an arithmetic sequence?An arithmetic sequence is a sequence where the difference between the consecutive terms is the same.
Example: 2, 4, 6, 8, 10
4 - 2 = 2
6 - 4 = 2
8 - 6 = 2
The nth term of an arithmetic sequence is given by:
= a + ( n - 1 ) d
Where a = the first term
d = common difference
Let the sequence that contains no digit less than 3 in ascending order be:
3 - n, 3 - (n + 1), 3 - (n+2), 3 - (n+3), 3 - (n+4),......
Where n = any real number from 1.
We see that the common difference is -1.
3 - (n+1) - (3 - n)
= 3 - n - 1 - 3 + n
= -1
3 - (n+2) - [3-(n+1)]
= 3 - n - 2 - 3 + n + 1
= -1
Find the 2021st term.
We have,
a = 3 - n
d = -1
n = 2021
= a + ( n - 1 ) d
= (3 - n) + ( 2021 - 1 ) (-1)
= 3 - n - 2020
= - n - 2017
Thus the 2021st term of the sequence is - n - 2017.
Learn more about arithmetic sequence here:
https://brainly.com/question/10396151
#SPJ4
At a football game, a vender sold a combined total of 144 sodas and hot dogs. The number of sodas sold was two times the numbers of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
A CD storage rack it's sold to stores at a wholesale price of $18 if the store has a 150% markup what is the retail price of the CD rack?
The retail price of the CD rack is $45.
How to calculate the value?From the information, the storage rack it's sold to stores at a wholesale price of $18 and the store has a 150% markup.
The retail price will be:
= $18 + (150% ×$18)
= $18 + $27
= $45
Therefore, the retail price of the CD rack is $45.
Learn more about percentages on:
brainly.com/question/24877689
#SPJ1
The function g(x) is a transformation of the cube root parent function,
f(x)=√x. What function is g(x)?
5-
1
-5-
1
g(x)
f(x)
5
O A. g(x)=√x+2+1
B. g(x)=√x-1+2
O C. g(x)=√x-2+1
O D. g(x)=√x+1+2
By using horizontal and vertical translations, we find that the expression for g(x) is g(x) = [tex]\sqrt[5]{x - 2}[/tex] + 1. (Correct choice: C)
What kind of transformations have been done on a parent function to generate another function?
The picture presents us the graphs of two functions. The blue function represents the parent function f(x), whose form is [tex]f(x) = \sqrt[5]{x}[/tex], whereas the black function is the transformed function g(x), which is the result of applying two transformations:
Horizontal translation 2 units in +x direction.Vertical translation a unit in +y direction.Then, we must apply the following definition involving the concepts of horizontal and vertical translations:
g(x) = f(x - 2) + 1 (1)
If we know that [tex]f(x) = \sqrt[5]{x}[/tex], then the complete expression of the function is:
g(x) = [tex]\sqrt[5]{x-2}[/tex] + 1
Hence, by using horizontal and vertical translations, we find that the resulting expression for g(x) is g(x) = [tex]\sqrt[5]{x - 2}[/tex] + 1. (Correct choice: C)
To learn more on transformation rules: https://brainly.com/question/9201867
#SPJ1
Richard, Allan, and Fliss share some money in the ratio 4: 8: 5.
Allan gets £9 more than Fliss.
Work out the amount of money that Richard gets.
Step-by-step explanation:
the ratio is 4:8:5 for Richard, Allan and Fliss.
the sequence is important.
the money pool between them has 4+8+5 = 17 equal units.
Richard has 4 units of these 17, Allan has 8 units, and Fliss has the remaining 5 units.
we don't know the value of such a unit yet.
this we get from the second hint :
Allan gets £9 more than Fliss.
remember, Allan has 8 units, Fliss 5.
so, Allan has 3 units more than Fliss.
that means these 3 units are worth £9.
and that means each unit is worth 9/3 = £3.
Richard has 4 units, that means he has
4×3 = £12
Type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. what value of p makes the equation true? p =
When p = 0.125 the equation -3p + ( 1/8 ) = ( - 1/4 ) is true.
The given equation is:
-3p + ( 1/8 ) = ( - 1/4 )
On the left-hand side of the equation, the denominator of the two terms is not the same.
So, the LCM of 1 and 8 is 8.
Therefore,
- 3p × ( 8 / 8 ) + ( 1 / 8 ) × ( 1 / 1 ) = ( - 1 /4 )
- 24p / 8 + 1 / 8 = - 1 / 4
( - 24p + 1 ) / 8 = - 1 / 4
Now multiplying each side of the equation by 8.
We get,
[ ( - 24p + 1 ) / 8 ] × 8 = ( - 1 / 4 ) × 8
- 24p + 1 = - 8 / 4
- 24p + 1 = - 2
Subtracting 1 from each side of the equation,
- 24p + 1 - 1 = - 2 - 1
-24p = - 3
Now, divide each side of the equation by 24.
- 24p / 24 = - 3 / 24
- p = ( - 1 / 8 )
Multiplying by - 1 on each side of the equation,
( - p ) × ( - 1 ) = ( - 1 / 8 ) × ( - 1 )
p = 1 / 8
p = 0.125
The value of p = 0.125 will make the equation true.
Learn more about fraction here:
https://brainly.com/question/1622425
#SPJ4
please help with this math! giving 40 points since both are different parts of 2 different hw pieces! :)
4. A right cone has a surface area of 258 cm² and a base radius of 4 cm. What is
the height of the cone to the nearest tenth of a centimetre?
Answer:
64.5cmStep-by-step explanation:
I hope this answer help you
Answer:
h = 16.0 cm
Step-by-step explanation:
Note: I am assuming that the surface area of 258 is the total surface area which includes the Lateral Area (L) and Base Area(B)
Total Surface Area of a right cone
= Lateral Area(L) + Base Area(B)
All numbers in intermediate calculations are rounded to tenth of centimeter i.e. 1 decimal point
Base Area is the area of the circle with radius 4 = [tex]\displaystyle \pi \cdot16 = 50.3[/tex] cm²
Total Area = 258 cm²
So Lateral Area = 258 - 50.3 = 207.7 cm²
Lateral Area is given by the formula
[tex]\displaystyle L = \pi r s \textrm{ where s is the slant height }[/tex]
So we get
[tex]\displaystyle \rm pi \cdot 4 \cdot s = 207.7\\\\\textrm {This gives } s = \dfrac{207.7}{4\pi} = 16.5\\\\[/tex] cm
Slant height is given by the formula:
[tex]s = \sqrt{r^2 + h^2} \textrm{ where r is the radius and h the height}[/tex]
Plugging in values we get
[tex]16.5 = \sqrt{4^2 + h^2} = \sqrt{16 + h^2}[/tex]
Square both sides
[tex]16.5^2 = 16 + h^2[/tex]
==> [tex]h^2 = 16.5^2 - 16 = 256.25\\\\h = \sqrt{256.25} = 16.003 = 16.0[/tex] rounded to 1 decimal place
So final answers is h = 16 cm
Write the rational numbers rounded to three decimal palaces.
19/6=
And
7/18=
The diagram shows a rectangle ABCD.The point A is (2,14) , Bus (-2,8) and C lies on the x-axis.
Find
(i) the equation of BC.
(ii) the coordinates of Cand D.
Using linear function concepts, it is found that:
i) The equation of BC is given by: [tex]y = -\frac{2}{3}x + \frac{20}{3}[/tex].
ii) The coordinates of C are C(0,10) and the coordinate of D are D(14,6).
What is the missing information?The diagram is missing, and is shown in the graph at the end of the answer.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, the coordinates are given as follows:
A(2, 14), B(-2,8) and C(x,0).
From the diagram, AB and BC are perpendicular, meaning that the multiplication of their slopes is of -1.
Given two points, the slope is given by change in y divided by change in x. Hence the slope of AB is given as follows:
mAB = (8 - 14)/(-2 - 2) = 3/2.
The slope of BC is given as follows:
mBC = (0 - 8)/(x - (-2))
mBC = -8/(x + 2).
The multiplication of the slopes is of -1, hence:
mAB x mBC = -1
-12/(x + 2) = -1
- x - 2 = -12
x = 10.
Hence, the slope of BC is:
mBC = -8/(x + 2) = -8/12 = -2/3.
Then:
y = -2/3x + b.
When x = 10, y = 0, hence we can find b as follows:
0 = -2/3(10) + b
b = 20/3.
Hence:
The equation of BC is given by: [tex]y = -\frac{2}{3}x + \frac{20}{3}[/tex].
From the diagram, we also have that AB and CD are parallel, meaning that they have the same slope, hence, considering D(x,y), we have that:
mCD = mAB
y/(x - 10) = 3/2
y = 1.5(x - 10)
y = 1.5x - 15.
AD and BC are also parallel, hence:
mAD = mBC
(y - 14)/(x - 2) = -2/3
Since y = 1.5x - 15, we have that:
(1.5x - 15 - 14)/(x - 2) = -2/3
(1.5x - 29)/(x - 2) = -2/3
3(1.5x - 29) = -2(x - 2)
4.5x - 87 = -2x + 4.
6.5x = 91
x = 91/6.5
x = 14.
y = 1.5x - 15 = 1.5(14) - 15 = 21 - 15 = 6.
Hence:
The coordinates of C are C(0,10) and the coordinate of D are D(14,6).
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Find the values of x and z (please Help)
The value of x is 6° and value of z is 67°
We know that when two lines intersect then the vertically opposite angles are equal.
So according to the given figure
(11x + 47)° = (6x + 77)°
Solving the above equation for x we get
11x° + 47° = 6x° + 77°
5x° = 30°
x = 6°
Thus the value of x is 6°
Also note that the linear pair of angles make 180°. That is sum of the two angle is 180°. As we can see from the figure ∠z and (6x + 77)° make linear pair of angles, therefore there sum will be equal to 180°.
Thus, ∠z + (6x + 77)° = 180°
∠z + (6*6 + 77)° = 180°
∠z + 113° = 180°
∠z = 67°
Hence the value of z is 67°
Learn more about angles here : https://brainly.com/question/24775470
#SPJ9
Mia is making smoothies. Each smoothie uses 1/2 cup of yogurt. How much yogurt
does she need to make 7 smoothies?
To solve, we'll need to _______
because we know the SIZE of the groups and the _______
but we don't know the ______
Answer: 3.5 cups
To solve, we'll need to multiply because we know the SIZE of the groups and the amount of groups but we don't know the total amount.
someone pls solve this for me w support work
Answer:
Slope = - 3
Step-by-step explanation:
The function of the line:
y = - 3x + 7
=> Slope = - 3
What will be the change in the temperature after 3 days?
Answer:21/2
Step-by-step explanation:
Answer:
-7/6
Step-by-step explanation:
If the temperature changes by -7/18 degrees, that shows us that it will continue to decrease, so we can assume the answer will be negative, which means we can get rid of the answers 21/6 and 7/6. If you add and multiply -7 by 3, you'll get -21, which would be -21/18. Then you would simply the answer, giving you -7/6.
Hope this helps!!! :)
what are the terms and coeffients 3m - 2n
Answer:
your question is did you mean why 2n is 2n 2 serve that this queston with not involved
An Internet service company earned $770 in setup fees for new homes in a neighborhood. They charged $35 for each new setup. How many new setups did they perform? Responses 19 setups 19 setups 22 setups 22 setups 25 setups 25 setups 26 setups
The number of new setups the internet service company perform in the neighborhood is 22 setups.
The correct answer is option B
Find the number of new setups the internet service company performTotal amount the internet service company earned = $770Amount the internet service company charge per new setup = $35Number of new setups the internet service company perform = Total amount the internet service company earned ÷ Amount the internet service company charge per new setup
= $770 / $35
= 22 setups
Therefore, the number of new setups the internet service company perform in the neighborhood is 22 setups.
Learn more about division:
https://brainly.com/question/25289437
#SPJ1
v=pi r^2 h
solve for pi
Answer: π=v/(hr^2)
Step-by-step explanation:
v=pi r^2 h solve for pi
v=πhr^2 solve for π
v/h=πhr^2/h
v/h=πr^2
1/r^2 * v/h = πr^2 * 1/r^2
v*1/(h*r^2) = πr^2/r^2
π=v/(hr^2)
It takes 15 over 2 minutes to fill an empty aquarium to a depth of 3 over 5 meters. what is the unit rate in minutes per meter? write your answer as a fraction or a mixed number in simplest form.
The unit rate in minutes per meter is 25/2
We are given the time taken to fill an empty aquarium = 15/2 minutes
Also, the depth of aquarium = 3/5 meters
To find the unit rate in minutes per meter, we will simply keep the values in formula. We do not need to change the units, as they are already in required ones, which are minutes and meters.
Unit rate = minutes ÷ meter
Unit rate = 15/2 ÷ 3/5
Rewriting the fraction
Unit rate = 15×5 ÷ 3×2
Performing multiplication in both numerator and denominator
Unit rate = 75 ÷ 6
Performing division of both numerator and denominator by 3
Unit rate = 25/2
So, the unit rate in minutes per meter is 25/2.
Learn more about calculations on unit rate -
https://brainly.com/question/19493296
#SPJ4
Evaluate the following expression when n = 2.
A. -1
B. 0
C. 4
D. 5
14n-61 +1-31
The value of expression is -61
In the given question is that:
Evaluate the expression when n = 2
and, Equation is = 14n - 61 + 1- 31
Now, According to the question :
Put the value of n= 2 in above equation:
then, 14 x 2 - 61 +1 - 31
= -61
Hence, The value of expression is -61
Composition of Functions:
The composition of function is the process of creating another function by applying a function as an input to another function.
Learn more about Functions and Equations at:
https://brainly.com/question/23589082
#SPJ1