Answer:
-7
Step-by-step explanation:
To find x, substitute the values and solve.
R = 2x + 9y
It becomes:
2x + 27 = 13
Rearrange and solve
2x = -14
x = -7
Hope this helps
Answer:
x=-7
Step-by-step explanation:
We are given the expression:
R=2x +9y
We want to find x when R=13 and y=3. Therefore, we must substitute the numbers in for the variables.
13=2x+9(3)
Multiply 9 and 3.
13=2x+27
Now we must solve for x by isolating x on one side of the equation.
27 is being added to 2x. The inverse of addition is subtraction, so subtract 27 from both sides.
13-27=2x+27-27
13-27=2x
-14=2x
x is being multiplied by 2. The inverse of multiplication is division, so divide both sides by 2.
-14/2=2x/2
-14/2=x
-7=x
x=-7
What is the numerator of the simplified sum? StartFraction x Over x squared + 3 x + 2 EndFraction + StartFraction 3 Over x + 1 EndFraction
Answer:
4x + 6
Step-by-step explanation:
Given
[tex]\frac{x}{x^2+3x+2}[/tex] + [tex]\frac{3}{x+1}[/tex]
Before we can add the fractions we require them to have a common denominator.
Factor the denominator of the first fraction
[tex]\frac{x}{(x+1)(x+2)}[/tex] + [tex]\frac{3}{x+1}[/tex]
Multiply the numerator / denominator of the second fraction by (x + 2)
= [tex]\frac{x}{(x+1)(x+2)}[/tex] + [tex]\frac{3(x+2)}{(x+1)(x+2)}[/tex] ← fractions now have a common denominator
Add the numerators leaving the denominators
= [tex]\frac{x+3(x+2)}{(x+1)(x+2)}[/tex]
= [tex]\frac{x+3x+6}{(x+1)(x+2)}[/tex]
= [tex]\frac{4x+6}{(x+1)(x+2)}[/tex] ← simplified sum with numerator 4x + 6
answer to this please!
Answer:
-2²
Explanation:
Doing -k² is the same thing as -(k²), so the answer will be negative. However, (-k)² will still be positive. -2² will equal -4.
Which of the following is false about investing with borrowed money? (5 points)
Someone helps…………………
Answer:
The third choice is correct
Step-by-step explanation:
Domain > or equal to -3, and range is less than or equal to -2
Brainliest??? Which inequality is represented by this graph.
Answer:
Step-by-step explanation:
D is the answer
Brainliest please help! A storage bin is a rectangular prism. Its volume is 300 cm cubed.
The width of the prism is one-third its length.
its height is two-thirds its length.
Determine the dimensions of the bin.
Answer:
∛50 cm, 2∛50 cm, 3∛50 cm
Step-by-step explanation:
V= wlh
V=300 cm³
w= 1/3l
h= 2/3l
---------
l*1/3l*2/3l=3002/9l³=300l³= 1350l= ∛1350= 3∛50 cmw= 1/3*3∛50= ∛50 cmh= 2/3*3∛50= 2∛50 cmAnswer:
Length is 11.052cm
Width is 3.684cm
Height is 7.386cm
Step-by-step explanation:
Let length be x, width y and height Z
Width (y) = X/3 , height (z) = 2x /3
volume =xyz
volume = x(x/3)(2/3)x
Volume = (2/9)x³
But Volume =300
300= (2/9)x³
300/(2/9) = x³ (make x³ the subject to find x )
1350 = x³
x=3√(1350)
x=11.052cm
Length is 11.052cm
Width = x/3 =11.052 /3
= 3.684cm
Height = 2x/3 = 2(11.052) /3
= 7.368cm
You can check it by multiplying LWH to see if you get 300 (the volume)
Calculate the mean and standard deviation of the data set ...
Answer:
Mean: 12.9
Standard deviation: 14.8
Step-by-step explanation:
The mean is calculated adding all of the values and dividing by the number of elements:
[tex]m=\frac{2+3+7+12+1+4+27+49+11}{9}=\frac{116}{9}=12.9[/tex]
to find the standard deviation, we first find the variance (which is defined as the sum of all the elements subtracting the mean and squared and then dividing by the total amount of elements):
[tex]v=\frac{(2-12.9)^2+(3-12.9)^2+(7-12.9)^2+(12-12.9)^2+(1-12.9)^2+(4-12.9)^2+(27-12.9)^2+(49-12.9)^2+(11-12.9)^2}{9}\\[/tex]
[tex]v=\frac{1978.89}{9}\\[/tex]
[tex]v=219.88[/tex]
Noe that we have the variance, we can calculate the standard deviation.
The stardard deviation is defined as the squared root of the variance:
[tex]standardDeviation=\sqrt{v}[/tex]
we substitute the variance:
[tex]standardDeviation=\sqrt{219.88} \\standardDeviation=14.8[/tex]
Thus, the answer is:
Mean: 12.9
Standard deviation: 14.8
The table shows the ages of players on a football team.
Age
Frequency
a) Work out the mean age of the team.
Round your answer to 1 decimal place.
19
2.
20
3
21
1
b) A new player joins the team and raises
the mean age to 22.
22
4
23
1
Work out the age of this new player.
Answer: A) 20.9 ; B) 34years
Step-by-step explanation:
Given the following :
AGE (X) - - - - - - - 19 - -20 - - - 21 - - - 22 - - - 23
FREQUENCY (F) - 2 - - 3 - - - - 1 - - - - 4 - - - - 1
A)
MEAN(X) = [AGE(X) × FREQUENCY (F)] ÷ SUM OF FREQUENCY
F*X = [(19 * 2) + (20 * 3) + ( 21 * 1)+(22 * 4)+(23 * 1)]
= 38 + 60 +21 + 88 + 23 = 230
SUM OF FREQUENCY = 2 + 3 + 1 + 4 + 1= 11
MEAN(X) = 230 / 11
X = 20.9
B)
WHEN A NEW PLAYER WAS ADDED :
MEAN (X) = 22
Let age of new player = y
Sum of Ages = 19 + 19 +20 + 20 + 20 + 21 + 22 + 22 + 22 + 22 + 23 + y
Number of players = 11 + 1 = 12
Mean(x) = sum of ages / number of players
New mean (x) = 22
x = (230 + y) / 12
22 = (230 + y) / 12
Cross multiply
264 = 230 + y
y = 264 - 230
y = 34 years
0.45?
How much do this equal
Answer:
.45
$0.45
45%
45/100
Step-by-step explanation:
Help me out on this
Answer:
SO THE VALUE OF FG IS 13
Step-by-step explanation:
we can find FG by subtracting EF FROM EG
FG=EG-EF
FG=25-12
FG=13
I HOPE IT WILL HELP YOU :)
Answer:
13[tex]given \\ EG = 25 \\ EF = 12 \\ FG=? = \\ EF+ FG= EG\\ or \: 12 + FG= 25 \\ or \: FG = 25 - 12 \\ FG = 13[/tex]
hope this helps..
Good luck on your assignment...
Fund the degree of the followung polynomials.
1. 5xyz
Answer:
3
Step-by-step explanation:
=> 5xyz
Degree of polynomial is summing up the powers of the variable, so it will give you the degree of polynomial
=> Degree of this polynomial = 1+1+1
=> 3
ASAp !!!!!!!!!!! Brenton’s weekly pay, P(h) , in dollars, is a function of the number of hours he works, h. He gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour. He is not permitted to work more than 60 hours in a week. Which set describes the domain of P(h)? {h| 0 ≤ h ≤ 40} {h| 0 ≤ h ≤ 60} {P(h)| 0 ≤ P(h) ≤ 1,400} {P(h)| 0 ≤ P(h) ≤ 1,800
The set the describes the domain of P(h) is (b) {h| 0 ≤ h ≤ 60}
How to determine the domain?In this case, the domain represents the set of hours he is permitted to work
From the question, we understand that he cannot work more than 60 hours
This means that, the least number of hours to work is 0, and the highest is 60
So, the domain is 0 to 60
When represented properly, the domain of P(h) is (b) {h| 0 ≤ h ≤ 60}
Read more about domain at:
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Brian and his son have a total age of 84.Brian is 26 years older than his son .how old is Brian?
Answer:
Brian = 55
Son = 29
Step-by-step explanation:
Let the ages of Brian and his son be
x +26 and x
Given that :
x + x + 26 = 84
2x + 26 = 84
2x = 58
x = 29.
We know that x is the age of Brian's son. so, Brian's age is 29 + 26 = 55
Hope this helps.
Good Luck
Here are Xavier's bowling scores:
135, 140, 130, 190, 112, 200, 185, 172, 163, 151,
149
What is the variance rounded to the nearest tenth?
Answer:
The variance rounded to the nearest tenth is 691.8
Step-by-step explanation:
Xavier's bowling scores:
135, 140, 130, 190, 112, 200, 185, 172, 163, 151, 149
No. of observations n = 11
[tex]Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean = \frac{135+140+130+190+112+200+185+172+ 163+ 151+149}{11}\\Mean =157[/tex]
Formula of variance : [tex]\sigma^2=\frac{\sum(x_i-\bar{x})^2}{n}[/tex]
[tex]\sigma^2=\frac{(135-157)^2+(140-157)^2+(130-157)^2+(190-157)^2+(112-157)^2+(200-157)^2+(185-157)^2+(172-157)^2+(163-157)^2+(151-157)^2+(149-157)^2}{11}[/tex]
[tex]\sigma^2=\frac{7610}{11}[/tex]
[tex]\sigma^2=691.81[/tex]
Hence the variance rounded to the nearest tenth is 691.8
What would the busked of x be?
Answer:
x = 9
Step-by-step explanation:
Step 1: Look at graph
You can see that both ∠B's are the same. Therefore, both side lengths AD and CD are the same
Step 2: Set equations equal to each other
3x = 2x + 9
Step 3: Solve
x = 9
And we have our answer!
Answer:
9
Step-by-step explanation:
A given line has the equation .
What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9)?
Answer:
y-6x = 9Step-by-step explanation:
The question is incomplete. Here is the complete answer.
A given line has the equation 2x + 12y = −1.
What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9)?
General formula of equation of a line is exspressed as y = mx+c
m = gradient or slope
c = intercept
Step 1: we need to first get the slope of the given equation of a line by rewriting the equation in standard form y = mx+c
2x + 12y = −1
12y = -1-2x
y = -1/12-2x/12
y = -1/6 x - 1/12
From the equation above, it can be seen that the slope (m) of tghe line is -1/6.
Since both lines are perpendicular, the slope of the unknown line will be;
M = -1/m
M = -1/(-1/6)
M = 6
Step 2: We will find the intercept c by substituting the point (0,9) and the slope into the equation y = mx+c
9 = 6(0)+ c
c = 9
Stwp 3: We will find the equation of the line perpendicular to the given line by substituting the value of m and c into the equation y = mx+c
y = 6x+9
y-6x = 9
The equation in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9) is y-6x = 9
Answer:
y-6x=9
Step-by-step explanation:
Divide the following amounts to the given ratio. A.)28kg in the ratio 2:5=. B.)1km in the room 19:1 =. C.)100 in the ratio 2:3:5 =.
A small plane and a large plane are 6.8km from each other, at the same altitude (height). From an observation tower, the two airplanes are separated by an angle of 58°. The large plane is 5.2km from the observation tower. a. Draw a diagram to represent this situation. b. How far is the small plane from the observation tower, to the nearest tenth of a kilometer?
Answer:
7.9km
Step-by-step explanation:
(a)See attached for the diagram representing this situation.
(b)
In Triangle ABC
[tex]\text{Using Law of Sines}\\\dfrac{\sin A}{a}=\dfrac{\sin C}{c} \\\dfrac{\sin A}{5.2}=\dfrac{\sin 58^\circ}{6.8} \\\sin A=5.2 \times \dfrac{\sin 58^\circ}{6.8}\\A=\arcsin (5.2 \times \dfrac{\sin 58^\circ}{6.8})\\A=40.43^\circ[/tex]
Next, we determine the value of Angle B.
[tex]\angle A+\angle B+\angle C=180^\circ\\40.43+58+\angle B=180^\circ\\\angle B=180^\circ-(40.43+58)\\\angle B=81.57^\circ[/tex]
Finally, we find b.
[tex]\text{Using Law of SInes}\\\dfrac{b}{\sin B}=\dfrac{c}{\sin C} \\\dfrac{b}{\sin 81.57^\circ}=\dfrac{6.8}{\sin 58^\circ} \\b=\dfrac{6.8}{\sin 58^\circ} \times \sin 81.57^\circ\\b=7.9km $ (to the nearest tenth of a kilometer)[/tex]
The distance between the small plane and the observation tower is 7.9km.
The missing term in the following polynomial has a degree of 5 and a coefficient of 16. Which statement best describes the polynomial? It is not in standard form because the degree of the first term is not greater than six. It is not in standard form because the degree of the first term should be equal to zero. It is in standard form because the exponents are in order from highest to lowest. It is in standard form because the coefficients are in order from highest to lowest.
Answer:
A.) It is not in standard form because the degree of the first term is not greater than six.
Step-by-step explanation:
There are 135 people in a sport centre. 73 people use the gym. 73 people use the swimming pool. 67 people use the track. 36 people use the gym and the pool. 35 people use the pool and the track. 32 people use the gym and the track. 14 people use all three facilities. A person is selected at random. What is the probability that this person doesn't use any facility?
Answer:
P = 11/135 = 0.0815
Step-by-step explanation:
we can said that:
14 people use all three facilities18 people use just gym and track (32 people use the gym and the track less the 14 people that use all three facilities)21 people use just pool and track (35 people use the pool and the track less the 14 people that use all three facilities)22 people use just gym and pool (36 people use the gym and the pool less the 14 people that use all three facilities)14 people use just the track (67 people use the track less the 18 people that use just the gym and the track, the 21 people that use just the pool and the track and 14 people that use all three facilities)16 people use just the pool (73 people use the swimming pool less the the 21 people that use just the pool and the track, the 22 people that use just the gym and the pool and 14 people that use all three facilities)19 people use just the gym (73 people use the gym less the 18 people that use just the gym and the track, the 22 people that use just the gym and the pool and 14 people that use all three facilities)So, there are 124 people that use the gym, the pool or the track. This is calculated using the information above as:
14 + 18 + 21 + 22 + 14 + 16 + 19 = 124
Finally, there are 11 ( 135 - 124 = 11 ) people that don't use any facility, so the probability that a person doesn't use any facility is:
P = 11/135 = 0.0815
Answer:
0.0815
Step-by-step explanation:
p(p+a2)
; use a = 7 and p = 6
6
Step-by-step explanation:
6(6+7(2))
6(6+14)
6(20)
120
Which algebraic expression represents the phrase “two times the quantity of a number minus 12”?
Answer: 2(n - 12)
n is “the number”
Step-by-step explanation:
Hope that helps :D
Answer:
2(n - 12)
Step-by-step explanation:
A system of equations consists of a line s of the equation y = x – 5 and a line t that passes through the points (0, 2) and (8, –4). Answer the questions about line t to write the equation.
Answer:
Slope = [tex]-\frac{3}{4}[/tex]
y-intercept = 2
Equation of the line 't': [tex]y=-\frac{3}{4}x+2[/tex]
Step-by-step explanation:
Slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is represented by,
Slope 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Since line 't' is passing through two points (0, 2) and (8, -4),
Slope of the line 't' = [tex]\frac{2+4}{0-8}[/tex]
m = [tex]-\frac{6}{8}[/tex]
m = [tex]-\frac{3}{4}[/tex]
Since y-intercept of a line is the value of 'y' for x = 0 [from point (0, 2) lying on this line]
Therefore, Y-intercept of line 't' = 2
Slope intercept of an equation is,
y = mx + b
where m = slope of the line
b = y-intercept
Therefore, equation of the line 't' will be,
[tex]y=-\frac{3}{4}x+2[/tex]
A cookie recipe requires 3 teaspoons of baking soda for 36 cookies. If the baker would like to make 480 cookies, how much baking soda will be required?
Answer:
It would require 40 teaspoons
Step-by-step explanation:
Given that;
A cookie recipe requires 3 teaspoons of baking soda for 36 cookies
The amount of teaspoons of baking soda required per cookie is;
r = 3/36 teaspoons per cookie
So, for 480 cookies i would require;
N = r × 480 cookies
Substituting r, we have;
N = 3/36 teaspoons per cookie × 480 cookies
N = 40 teaspoons
It would require 40 teaspoons
Look at the data in the table.
ху
4,9
12,28
7,14
9,20
5,9
12,30
10,22
work out the size of the reflex angle
Answer:
302°
Step-by-step explanation:
The angle at the centre POR is twice the angle at the circumference, subtended on the same arc PR, thus
∠ POR = 2 × 29° = 58°
The reflex angle POR = 360° - 58° = 302°
The size of the reflex angle POR is 302 degrees as per the concept of arc measure properties.
To find the size of the reflex angle POR, we need to consider that a reflex angle is greater than 180 degrees. In this case, angle PQR is given as 29 degrees, and we want to determine the reflex angle POR.
Since angles on a circle's circumference subtended by the same arc are equal, angle POR is the sum of angles PQR and PQR' (where angle PQR' is the reflex angle).
Given that angle, PQR is 29 degrees.
Therefore,
angle POR = 2 x angle PQR.
angle POR = 58 degrees.
To find the value of PQR', we subtract angle PQR from 360 degrees (as a circle has 360 degrees): PQR' = 360 - 58= 302 degrees.
Therefore, the reflex angle POR is 29 + 331 = 302 degrees.
Hence, the size of the reflex angle POR is 302 degrees.
To learn more about the arc measure;
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Someone please help me with question 3.b)
Answer:
AM = 12.87 cmCM = 8.578 cmOD = 23.66 cmStep-by-step explanation:
Since the figure is symmetrical, angle MOA will be half of angle BOA, so will be 130°/2 = 65°. The tangent ratio is useful here. It tells you ...
tan(MOA) = MA/OA
AM = OA·tan(MOA) = 6·tan(65°)
AM ≈ 12.87 . . . cm
__
Similarly, ...
CM = 4·tan(65°)
CM ≈ 8.578 . . . cm
__
The cosine ratio is useful for finding OD.
cos(MOA) = OA/OM
OM = OA/cos(MOA) = 6/cos(65°)
Similarly, ...
DM = 4/cos(65°)
The length we want is OD, so ...
OD = OM +DM = 6/cos(65°) +4/cos(65°) = 10/cos(65°)
OD ≈ 23.66 . . . cm
Match the measureable quantity given by its formula with the appropriate unit(s).
speed = distance/time
square meters
area = (length)(width)
meters per second
volume = (length) (width)(height)
UUOO
meters
perimeter = 2 (length) + 2 (width)
cubic centimeters
Intro
rity
Done
Answer: i hope this helps (answer is down below)
Step-by-step explanation:
Area goes to square meters
speed goes to meters per second
volume goes to cubic centimetres
perimeter goes to meters
Simplify the product using the distributive property.
(4h - 5)(5h - 3)
20h2 - 13h - 15
20h2 - 37h + 15
20h2 + 13h - 15
20h2 + 37h + 15
Answer:
[tex]20h {}^{2} - 37h + 15[/tex]
[tex]20h {}^{2} - 12h - 25h + 15 \\ = b \: is \: de \: answer[/tex]
2/3y + 15 = 9
What are the steps for this question
Answer:
see below
Step-by-step explanation:
2/3y + 15 = 9
Subtract 15 from each side
2/3y + 15-15 = 9-15
2/3y = -6
Multiply each side by 3/2 to isolate y
3/2 * 2/3y = -6 *3/2
y = -9
Answer:
y = - 9
Step-by-step explanation:
2/3y + 15 = 9
Subtract 15 on both sides.
2/3y = 9 - 15
2/3y = - 6
Multiply both sides by 3/2.
y = - 6 × 3/2
y = -18/2
y = -9