Which expression has a value of 16 when n = 5?
StartFraction 25 Over n EndFraction + 7
30 minus 3 n
7 + StartFraction 45 Over n EndFraction
n cubed minus 114
The expression that has a value of 16 when n = 5 is [tex]\rm 7+ \dfrac{45}{n}[/tex] , Option C is the correct answer.
What is an Expression ?An expression is mathematical statement consisting of variables , constant and mathematical operators.
The expression given in the question is
[tex]\rm \dfrac{ 25}{n} + 7 \\\\30-3n\\\\7+\dfrac{45}{n}\\\\n^3 -114[/tex]
On solving it can be seen that
The value of 16 when n= 5 is given by
7 +45/5 = 7+9 = 16
Therefore Option C is the right answer.
To know more about Expression
https://brainly.com/question/14083225
#SPJ1
factorise the following expressions:
a) 14w + 21
b) 27x+18
Step-by-step explanation:
a) 14w + 21
- Factor out 7 from the expression
7 (2w + 3)
b) 27x + 18
- Factor out 9 from the expression
9 (3x + 2)
Hi!
___________________________________________________________
[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]
#1 7(2w+3)
#2 9(3x+2)
[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]
We need to factor these two expressions.
[tex]\twoheadrightarrow\sf 14w+21[/tex] and [tex]\twoheadrightarrow\sf 27x+18[/tex]
For now let's focus on the first expression.
Note that both terms, 14w and 21, have something in common.
In fact, they have 7 in common. So we factor it out by dividing 14w and 21 by 7.
[tex]\twoheadrightarrow\sf14w\div7=2x\\\twoheadrightarrow\sf21\div7=3[/tex]
[tex]\bullet[/tex] Put the terms together, with a plus sign in between since they are positive
[tex]\twoheadrightarrow\sf 2w+3[/tex]
[tex]\bullet[/tex] Put parentheses around 2w+3
[tex]\twoheadrightarrow\sf (2w+3)[/tex]
[tex]\bullet[/tex] Put7 outside the parentheses
[tex]\twoheadrightarrow\sf7(2w+3)[/tex]
[tex]\bullet[/tex] Great job! We factored the expression
__________________________________________________________
This problem can be solved the same way!
This time, both terms have a 9 in common.
[tex]\twoheadrightarrow\sf 27x+18[/tex]
So we divide both terms by 9.
[tex]\twoheadrightarrow\sf 27x\div9=3x\\\twoheadrightarrow\sf18\div9=2[/tex]
[tex]\bullet[/tex] Put the terms together, with a plus sign in between since they're positive
[tex]\twoheadrightarrow\sf 3x+2[/tex]
[tex]\bullet[/tex] Next, put parentheses around 3x+2 and put 9 outside the parentheses
[tex]\twoheadrightarrow\sf 9(3x+2)[/tex]
[tex]\bullet[/tex] Great job! We factored both expressions
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]
--
what is the result of applying the square root property to the equality of the equation X plus B over two a squared equals -4 AC plus B2 over 4a two squared
After doing simplification, the result that we got is the quadratic formula
x = [-b ±√(b² - 4ac)] / 2a.
The given statement can be explained with the following equation:
[x + (b/2a)]² = (b² - 4ac) / 4a²
Now, we will take the root on both the sides:
x + (b/2a) = ±√[(b² - 4ac) / 4a²]
x = -(b/2a) ± √[(b² - 4ac) / 4a²]
x = [-b ±√(b² - 4ac)] / 2a
The final equation resembles the quadratic formula.
So, the result of applying the square root property to this equation is that we get the quadratic formula after simplification.
For more explanation about quadratic equations, refer to the following link:
https://brainly.com/question/1214333
#SPJ10
Find the indicated conditional probability
using the following two-way table:
Grade
Sophomore
Junior
Senior
Drive to school Take the bus
2
13
25
25
20
5
Walk
3
2
5
P(Drive to school | Sophomore ) = [? ]
Round to the nearest hundredth.
Answer:
[tex]0.07[/tex]
Step-by-step explanation:
FORMULA :
[tex]p\left( A|B\right) =\frac{p\left( A\cap B\right) }{p\left( B\right) }[/tex]
……………………………
then
[tex]p\left( \text{drive to school} |sophomore\right) =\frac{p\left( \text{drive to school} \cap \text{sophomore} \right) }{p\left( \text{sophomore} \right) }[/tex]
[tex]= \frac{2}{2+25+3}[/tex]
[tex]=\frac{2}{30}[/tex]
[tex]=\frac{1}{15}[/tex]
[tex]=0.066666666667[/tex]
Ted is trying to change 0.43 to a fraction. Evaluate teds method so far
Step-by-step explanation:
[tex] = 0,43[/tex]
[tex] = \frac{0,43}{1} [/tex]
[tex] = \frac{0,43}{1} \times \frac{100}{100} [/tex]
[tex] = \frac{43}{100} [/tex]
What is the speed of a wave with a wavelength of 10 meters
Any wave's speed is equal to its frequency times wavelength. Now, the question doesn't specifically state what kind of wave it is. Thus, there might be two distinct scenarios: If the wave is elastic (sound is an example), you can't calculate its speed unless you also know its frequency and wavelength. However, the speed in vacuum is constant (3*108 m/s) if the wave is electromagnetic (for instance, light). In order to maintain constant velocity, frequency must shift in response to variations in wavelength. The frequency of light rays is constant in all other optical media (apart from vacuum and air), although their velocity and wavelength change correspondingly. However, that is not the case here since if it must be an EM wave with a wavelength of 10 m, then it must be a radio wave that travels uniformly through all medium at a speed of 3*108 m/s.
Vertical lines m and n are intersected by lines k and j. At the intersection of lines m and k, the bottom right angle is (x minus 30) degrees. At the intersection of m and j, the uppercase right angle is y. At the intersection of lines k and n, the bottom left angle is (x + 50) degrees.
Find the values of x and y that make k || j and
m || n.
x =? °
y = ?°
Using the same-side interior angles theorem, the values of x and y are:
x = 80
y = 130
What is the Same-side Interior Angles Theorem?The same-side interior angles theorem states that two interior angles on same side of a transversal are supplementary.
(x - 30) and (x + 50) are same-side interior angles, therefore:
(x - 30) + (x + 50) = 180
Solve for x
x - 30 + x + 50 = 180
2x + 20 = 180
2x = 180 - 20
2x = 160
x = 160/2
x = 80
(x - 30) + y = 180
Plug in the value of x
(80 - 30) + y = 180
50 + y = 180
y = 180 - 50
y = 130
Learn more about the same-side interior angles theorem on:
https://brainly.com/question/13867198
#SPJ1
Answer:
X= 80
Y= 130
Step-by-step explanation:
do you trust me???
from a practice assignment:
solve the following differential equation given initial conditions
If [tex]y' = e^y \sin(x)[/tex] and [tex]y(-\pi)=0[/tex], separate variables in the differential equation to get
[tex]e^{-y} \, dy = \sin(x) \, dx[/tex]
Integrate both sides:
[tex]\displaystyle \int e^{-y} \, dy = \int \sin(x) \, dx \implies -e^{-y} = -\cos(x) + C[/tex]
Use the initial condition to solve for [tex]C[/tex] :
[tex]-e^{-0} = -\cos(-\pi) + C \implies -1 = 1 + C \implies C = -2[/tex]
Then the particular solution to the initial value problem is
[tex]-e^{-y} = -\cos(x) - 2 \implies e^{-y} = \cos(x) + 2[/tex]
(A)
Use the given graph to determine the limit, if it exists.
The limit in the given graph [tex]\lim_{x \to \ 2^{-} } f(x)[/tex] is 3 and [tex]\lim_{x \to \ 2^{+} } f(x)[/tex] is -2
Given graph of a function and we have to determine the limits when x tends to 2 minus and when x tends to 2 plus.
When we see the graph we can find that the graph is not of the linear function because it is not straight line.
From x=2 and onwards it gives values values of only -2 because it is parallel to x-axis at y=-2.From x=2 and leftwards it gives values values of only 3 because it is parallel to x-axis at y=3.
Hence the limit of the function whose graph is shown is 3 and -2.
Learn more about limits at https://brainly.com/question/27517662
#SPJ10
At Pine Time Summer Camp, 12 campers sign up to go swimming. Of the 12 campers, 2/3 of them are advanced swimmers. How many of these campers are advanced swimmers?
(not highschool)
Help me pleas. You might have to zoom in on the picture to see better.
Answer:
1/2, -1/8, 1/32
Step-by-step explanation:
[tex] - 2( - \frac{1}{4} ) = \frac{1}{2} [/tex]
[tex] \frac{1}{2} ( - \frac{1}{4} ) = - \frac{1}{8} [/tex]
[tex] - \frac{1}{8} ( - \frac{1}{4}) = \frac{1}{32} [/tex]
The ratio of Michaels's points on an English test to Paloma's points on the same test is 12:11. The ratio of Michaels's points on the English test on the same test was 4:3. the 3 students score a total of 224 points on the same test. What is the difference between Palomas and Antons' points on the English test? Try to explain fully, if possible. Thank you SO MUCH!
The difference between Palomas and Antons' points on the English test is of 14 points.
What is Ratio ?When two numbers can be written in the form as p:q , they are said to be in Ratio.
It is given that
The ratio of Michaels point to Paloma point is 12 :11
The ratio of Michaels point to Anton's Point is 4:3
Let Paloma's point be x
then Michaels point will be 12x/11
and Anton's points will be
(12x/11 ) / Anton's points = 4 /3
Anton's points = 9x/11
It is given that the sum of the points of the three students is 224
so
x + (12x/11)+ (9x/11) = 224
32x /11 = 224
x = 77
Paloma's points = 77
Anton's Points = 9x/11 = 63
The difference between Palomas and Antons' points on the English test
=77 -63
= 14 points.
To know more about Ratio
https://brainly.com/question/13419413
#SPJ1
A с Which diagram shows all the lines of symmetry of the regular hexagon? B D A с Which diagram shows all the lines of symmetry of the regular hexagon ? B D please help
The diagram that shows all the lines of symmetry is diagram B.
Which diagram shows all the lines of symmetry of the regular hexagon?
We define a line of symmetry as a line such that if we perform a reflection over that line, the image coincides with the preimage (so the reflection does not change the figure).
With that in mind, any line that cuts the hexagon in exactly two halves is a line of symmetry.
So the image that shows all the lines of symmetry of the regular is B, where it shows all the lines that cut the hexagon in two equal halves.
If you want to learn more about lines of symmetry:
https://brainly.com/question/547436
#SPJ1
From a hot-air balloon, Brody measures a 39^{\circ}
∘
angle of depression to a landmark that’s 532 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Answer:
335.16 ft
Step-by-step explanation:
Solve for y.
Enter your answer in the box.
Answer:
y=10
Step-by-step explanation:
Since this triangle has equal length sides, it is equilateral and also has equal measured angles. This means that each angle is 180/3=60 degrees.
To solve for y, we can do 5y+10=60. Simplifying, we get
5y=50
y=10.
Answer:
4
Step-by-step explanation:
So all the angles will have the same value. In a triangle all the angles will add up to 180, so each angle would have to be 60 degrees. So to know Y we need 6x+6=5y+10. So subtract 10 from each side, then subtract 6x from each side to get 4=x
On a coordinate plane, a right triangle has points A (negative 5, negative 6), B (negative 5, negative 2), C (negative 2, negative 2). Examine the right triangle ABC. Which rise and run would create a similar right triangle on the same line? a rise of 6 and a run of 8 a rise of 8 and a run of 6 a rise of 6 and a run of 5 a rise of 5 and a run of 6
A rise of 8 and a run of 6. Then the correct option is B.
What is a coordinate geometry?Coordinate geometry is the study of geometry using the points in space.
On a coordinate plane, a right triangle has points A (-5, -6), B (-5, -2), and C (-2, -2).
The distance between AB will be
AB² = (-5 + 5)² + (-2 + 4)²
AB² = 4²
AB = 4
The distance between BC will be
BC² = (-2 + 5)² + (-2 + 2)²
BC² = 3²
BC = 3
Then the rise and run will be
rise / run = 4 / 3
Then this can be written as
rise / run = 8 / 6
Then the correct option is B.
More about the coordinate geometry link is given below.
https://brainly.com/question/1601567
#SPJ1
FW = 6 units, X = 3 units, and Y = 5 units, what is the surface area of the figure?
The surface area of the figure is approximately: 178 units².
How to Find the Surface Area of a Figure?The surface area of any figure is the area of all its faces.
Find the area of each face as shown below:
Area of base = w² = 6² = 36 units²
Area of the 4 rectangular faces = 4(6)(3) = 72 units²
Area of the 4 triangular faces = 4[1/2bh]
b = w = 6 units
h = √(y² + (w/2)²) = √(5² + (6/2)²) = 5.8 units
Area of the 4 triangular faces = 4[1/2(6)(5.8)] = 69.6 units²
Surface area = 36 + 72 + 69.6 ≈ 178 units²
Learn more about surface area on:
https://brainly.com/question/76387
#SPJ1
What is the mean of the data set?
85, 97, 84, 88, 95, 100,81
Answer:
90
Step-by-step explanation:
Add up all the numbers in the data set and divide that number by the amount of numbers in the data set
85 + 97 + 84 + 88 + 95 + 100 + 81 = 630
630/7 = 90
What value of x is in the solution set of 3(x – 4) ≥ 5x 2? –10–5510
3(x-4) ≥ 5x +2
3*x - 3*4 ≥ 5x +2
3x - 12≥ 5x - 2
-12 + 2 ≥ 5x- 3x
-10 ≥ 2x
2x ≤ -10
x ≤ -5
i need the missing numbers
Answer:
Step-by-step explanation:
1) y = [tex]\frac{1}{3}[/tex]
2) x = [tex]\frac{1}{3}[/tex]
3) y = -3
4) x = [tex]\frac{-1}{-12}[/tex]
Answer:
11,3,3,12
Step-by-step explanation:
1st y= 11 because -2/3(-6)=4 4+7=11
1st x= 3 because -2/3(3)=-2 and -2+7 is 5
2nd y=-3 because -2/3(15)=-10 -10 +7=-3
2nd x=-12 because -2/3(-12)=8 8+7=15
both of the drop menus have the same options
Answer:
The slope of line p is 3 and the slope of line q is -3
Expand . ( 3x –2 ) 2 please help me with this.
Answer:
6x-4
Step-by-step explanation:
3x•2= 6x
-2•2=-4
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{9x}^2\textsf{ - 12x + 4}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{(3x - 2)}^2[/tex]
Find: [tex]\textsf{Simplify the expression}[/tex]
Solution: It looks like 2 is at the end of the parenthesis where the power would be instead of distributing the number. If so the following steps would be followed.
Expand
[tex]\textsf{(3x - 2)}^2[/tex][tex]\textsf{(3x - 2)(3x - 2)}[/tex][tex]\textsf{(3x * 3x) + (3x * (-2)) + (3x * (-2)) + (-2 * (-2))}[/tex]Simplify
[tex]\textsf{9x}^2\textsf{ - 6x - 6x + 4}[/tex][tex]\textsf{9x}^2\textsf{ - 12x + 4}[/tex]Therefore, after following the provided information we are able to determine that the expanded form would be 9x^2 - 12x + 4.
Alison has three times as many dimes as quarters in her purse. She has $9.35 altogether. How many coins of each type does she have?
========================================================
Work Shown:
x = number of quarters
3x = number of dimes
0.25x = value of just the quarters, in dollars
0.10(3x) = 0.30x = value of just the dimes, in dollars
0.25x+0.30x = 0.55x = total value in dollars
0.55x = 9.35
x = (9.35)/(0.55)
x = 17
Alison has 17 quarters and 3x = 3*17 = 51 dimes
17 quarters = 17*0.25 = $4.25
51 dimes = 51*0.10 = $5.10
17 quarters + 51 dimes = $4.25 + $5.10 = $9.35
The answers are confirmed.
Points
Find f(−2)
given f(x)=−x3−3x2+8
Answer:
12 :D
Step-by-step explanation:
First we substitute all x's for -2 :)
f(-2)=−-2^3−3(-2)^2+8
Now we solve :)
f(-2)=−-2^3−3(-2)^2+8
f(-2)=− -8 −3(-2)^2 + 8
f(-2) = -8 - 3(-4) + 8
f(-2) = - 8 + 12 + 8
f(-2) = 4 + 8
f(-2) = 12 :)
f will equal 12 :)
Have an amazing day!!
Please rate and mark brainliest!!
PLSS HELP ME PLSSS
a) Write 2 expressions for the area of the shaded region. (2 marks)
b) Find the length of the shaded region if the perimeter is 48cm. (2 marks)
c) Find the area of the shaded region if perimeter is 48cm. (1 mark)
Answer:
(1) 85×9=765 (2) 127×3=381
Find the length of side x in simplest radical form with a rational denominator.
30°
60°
√12
D
The value of x is 10√3 .
The missing figure is attached with the answer
What is a Triangle ?A triangle is a polygon with three sides , three angles and three vertices.
A right angle is a triangle in which one of the sides of a triangle is equal to 90 degree.
As it is a right angled triangle therefore the trigonometric ratios are applicable
From the given figure sin 60 needs to be determine to find the value of x
sin x = Perpendicular / Hypotenuse
sin 60 = 5 / x
[tex]\rm \dfrac{\sqrt{3}}{2} = \dfrac{5}{x}[/tex]
x = 10√3
Therefore the value of x is 10√3
To know more about Triangle
https://brainly.com/question/2773823
#SPJ1
Classify the following polynomials. Combine any like terms first.
2x-x²+4x+x²
x^3-5x^2 + 3-2
x^3-x^3+x²-x²+3
7x-x^2+x³+4x²
-6x-x^3 +6x-4x
Answer:
A resposta certa é:
[tex]6x \\x^3 - 5x^2 + 1 \\3 \\x^3 + 3x^2 + 7x \\-x^3 - 4x[/tex]
Step-by-step explanation:
1° equação:
Como há um x² positivo e um negativo, ambos irão se anular, sobrando apenas as incógnitas de potência 1 (ou, 6x)
2° equação:
Esta resulta em uma equação de 3° grau incompleta, já que há uma incógnita de potência 3, uma de potência 2, não há uma incógnita de potência 1 mas há as constantes, que as unindo forma a constante 1.
3° equação:
As incógnitas presentes há uma negativa e uma positiva de mesma potência, anulando-as e sobrando apenas a constante 3.
4° equação:
Considerando que há um 4x² e um -x² na equação, unindo-os forma o 3x², após isso é só repetir a equação.
5° equação:
Há -10x (-6x -4x = -10x) e 6x, resultando em um -4x, e então é só repetir a equação
Nota: I'm Brazilian, so I found it more practical to write the entire explanation in Portuguese, so if you can't understand, I ask you to use the translator, thanks for understanding :)
You are drawing an angle in standard position and you swing the terminal side until an angle of 281 is made. how many more degrees can you continue swinging so that the terminal side is at the same position as the initial side
Answer:
79°
Step-by-step explanation:
An angle in standard position has it "initial" side glued on to the positive x-axis. The other ray that makes the angle swings around the origin, (0,0) like a hand of a analog clock (but moving backwards) straight up is 90°, straight to the left is 180° straight down is 270°. And all the way back to the start is 360°.
If the angle is 281° it can go 79° more degrees before getting back to the start.
360° - 281° = 79°
What is the discriminant of the quadratic equation 2x² - x - 3=0?
A. -25
B. 25
C. -23
D. 23
The given quadratic equation is
[tex]2 {x}^{2} - x - 3 = 0[/tex]
comparing with
[tex] {ax}^{2} + bx + c = 0[/tex]
We get ,
[tex]a = 2 \\ b = - 1 \\ c = - 3[/tex]
formula :
[tex]D = {b}^{2} - 4ac \\ \\ D = {( - 1)}^{2} - 4 \times 2 \times ( - 3) \\ \\ D = 1 - ( - 24) \\ \\D = 1 + 24 \\ \\D = 25.[/tex]
Discriminant of given quadratic equation is 25 .
option (B) 25 ✔
Mikaela and Viktoria both competed in a curling match on opposing teams. Mikaela
said to Viktoria, "2 more than twice my team's score is the
same as three times your team's score reduced by 3." If
Viktoria's team's score was 7, what was Mikaela's team's
score?
Mikaela's team's score is 8.33
what is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
Viktoria's team's score = 7
According to question,
= 2+ 7*2 = 16
so, Mikaela team score= 16/3+3= 8.33
Learn more about algebra here:
https://brainly.com/question/953809
#SPJ1
