Answer:
x= ½, y= 7
Step-by-step explanation:
[tex]\textcolor{steelblue}{\text{\textcircled{1} Label the equations}}[/tex]
6x -y= -4 -----(1)
2x +2y= 15 -----(2)
[tex]\textcolor{steelblue}{\text{\textcircled{2} Make y the subject of formula}}[/tex]
We could also make x the subject of formula in one equation, however the equation can be easily rearranged so that the coefficient of y is 1. This can be done by moving the y term to the right hand side of the equation, and the rest to the left. Note that each time you bring a term or constant over to the other side of the equation, its sign changes (e.g. positive to negative).
From (1):
6x +4= y
y= 6x +4 -----(3)
Label the equation as equation (3) so we can refer to it easily later.
[tex]\textcolor{steelblue}{\text{\textcircled{3} Substitute (3) into (2)}}[/tex]
Now that we have an equation of y that is written in terms of x, we can replace all the y in equation (2) so that the whole equation is only in terms of x.
Subst. (3) into (2):
2x +2(6x +4)= 15
Expand:
2x +12x +8= 15
Simplify:
14x +8= 15
14x= 15 -8
14x= 7
x= 7 ÷14
x= ½
[tex]\textcolor{steelblue}{\text{\textcircled{4} Find y}}[/tex]
Substitute x= ½ into (3):
y= 6(½) +4
y= 3 +4
y= 7
The average January surface water temperatures (°C) of Lake Michigan from 2000 to 2009 were 5.07, 3.57, 5.32, 3.19, 3.49, 4.25, 4.76, 5.19, 3.94, and 4.34. The data set has the following statistics:
x = 4.312
Variance squared2 = 0.577
What is the standard deviation? Round to the nearest thousandth.
0.333
0.760
2.077
18.593
Answer:
the answer is B 0.760
Step-by-step explanation:
i did the test.
A contractor has two choices for billing a completed job. · $500 flat rate, regardless of the number of hours worked · $20 per hour worked the graph shows the relationship between pay per hour and number of hours worked for both scenarios.
Answer:
C. (25,20)
Step-by-step explanation:
Edge2022 <3
Good luck and remember (yall that take edge) , you can get through the day no matter how hard it may seem. I have faith In you guys :).
If number of hours worked is less than 20, 500 flat rate is preferable
and, If number of hours is more than 20, hourly rate i.e. 20 per hour is better.
What is Inequality?An inequality is a mathematical statement that compares two values or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).
In the first scenario, where there is a $500 flat rate regardless of the number of hours worked, the pay per hour remains constant at $500 divided by the number of hours worked.
So, the graph for this scenario would be a horizontal line at a height of $500.
In the second scenario, where the contractor is paid $20 per hour worked, the pay per hour is fixed at $20.
let the number of hours be worked be x.
Then, 20x < 500
x< 25
So, if number of hours worked is less than 20, 500 flat rate is preferable
and, If number of hours is more than 20, hourly rate i.e. 20 per hour is better.
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Q10.
At work Liv puts apple pies into boxes.
Liv has 42 apple pies.
Each full box has 9 apple pies.
How many full boxes of apple pies does Liv have?
Show how many apple pies are left over.
Show your working and your answers in the box below.
Answer:
He has 4 full boxes
6 Apple pies are leftover
Step-by-step explanation:
42/9 = 4.67 How many full boxes can he fill
9 X 4 = 36 He filled out 4 full boxes
42-36=6 Total - Filled = Remainder
Answer:
she has 4 full boxes of applepies and she has 6 leftover apple pies
Step-by-step explanation:
Given that
5
x
:
9
=
7
:
3
Calculate the value of
x
.
Give your answer in its simplest form.
Answer:
x=21/5
Step-by-step explanation:
5x:9 = 7:3
Turn the ratios into fractions:
5x/9 = 7/3
Then cross mutiply
15x=63
x=21/5
F(x)=f(x-1)+2x+1 if f(2) =17 what’s f(1)
Answer:
f(1) = 12
Step-by-step explanation:
We know that f(x)=f(x-1)+2x+1
We are told that f(2) = 17
Use the first equation to calculate f(1). Since f(2) is known and f(x-1) will become f(1) after f(2-1) is simplified to f(1).
17 = f(2-1)+2*2+1
f(2-1) = 17 - 5
f(1) = 12
Find the area of a semicircle with diameter 9 cm
Answer:
31.8 cm^2
Step-by-step explanation:
Area of WHOLE circle = pi r^2
semicircle is 1/2 of this ( r = 1/2 of the diameter)
1/2 pi r^2
1/2 pi (9/2)^2 =
rent is putting in a sidewalk that is 1/18 yard thick, 9 yards long, and 1 yard wide. how many cubic yards of cement does he need?
Answer:
1/18 x 9 x 1 = .5 cubic yards. Why would you ever waste time asking this....
Step-by-step explanation:
Answer:
Step-by-step explanation:
We have to find the volume. we can use volume of the cuboid formula
l = 1/18 yard
w = 9 yard
h = 1 yard
Volume = l*w*h
[tex]= \dfrac{1}{18}*9*1\\\\\\= \dfrac{1}{2}\\\\\\= 0.5 \ \sf cubic yard[/tex]
0.5 cubic yards of cement is needed
The water level at a lake is normally O feet above
sea level. During a flood, the level rose 7 feet. Over
the next two weeks the level had gone down by
12 feet.
a. Write an expression to represent this situation.
b. What level is the water currently at?
what is (5.03x -8.03) - (3.5x +6.2)?
Answer:
1.53x−14.23
Step-by-step explanation:
simplify:
5.03x−8.03−(3.5x+6.2)
Distribute the Negative Sign:
=5.03x−8.03−1(3.5x+6.2)
=5.03x−8.03−1(3.5x)+(−1)(6.2)
=5.03x−8.03−3.5x−6.2
Combine Like Terms:
=5.03x−8.03+−3.5x−6.2
=(5.03x−3.5x)+(−8.03−6.2)
=1.53x−14.23
(5.03x -8.03) - (3.5x +6.2)=
2 1/4 ÷ 4 1/5 the anser can not be improper
Answer:
15/28, 15/28, 15/28
Step-by-step explanation:
1. Is simplified
2. Divided
3. Evaluated
(Yes I know there the same but its just in case.)
Find the derivative of tan(x).
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Derivative of tan(x) is sec²x
[tex]\qquad \sf \dashrightarrow \: \therefore \dfrac{d}{dx} ( \tan(x)) = { \sec}^{2} (x)[/tex]
You can check the first principle method of derivation in attachment
[tex]\rightarrow \sf \dfrac{d}{dx} (tan(x))[/tex]
[tex]\rightarrow \sf \dfrac{d}{dx} ( \ \dfrac{sin(x)}{cos(x)} \ )[/tex]
use the quotient rule
[tex]\rightarrow \sf \dfrac{cos(x) * \dfrac{d}{dx} (sin(x)-sin(x)*\dfrac{d}{dx}(cos(x) }{cos(x)^2}[/tex]
[tex]\rightarrow \sf \dfrac{cos(x) * cos(x)-sin(x)*(-sin(x) )}{cos(x)^2}[/tex]
[tex]\rightarrow \sf \dfrac{cos(x)^2+sin(x)^2}{cos(x)^2}[/tex]
[tex]\rightarrow \sf \dfrac{1}{cos(x)^2}[/tex]
[tex]\rightarrow \sf sec(x)^2[/tex]
used formula's :
cos²(x) + sin²(x) = 1[tex]\sf \dfrac{1}{cos^2(x) }= sec^2(x)[/tex][tex]\sf \frac{d}{dx}[/tex] cos(x) = -sin(x)[tex]\sf \frac{d}{dx}[/tex] sin(x) = cos(x)tan(x) = sin(x)/cos(x)Two number cubes are rolled what is the probability that both cubes land on 1
Answer:
[tex]\frac{1}{36}[/tex]
Step-by-step explanation:
The probability of having 1 is 1/6.
The probability of it happening twice in a row is 1/6 * 1/6 = 1/(6*6)=1/36
help this is due tom
Answer:
9. (a) 1/4
(b) remove 3 alphabet cards
(c) add 4 number cards
10. 1/8
Step-by-step explanation:
Question 9
Given:
8 number cards10 alphabet cards6 picture cards⇒ total number of cards = 8 + 10 + 6 = 24 cards
[tex]\mathsf{Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ outcomes}}[/tex]
(a) P(picture card) = 6/24 = 1/4
(b) P(alphabet card) = 10/24 = 5/12
If we remove 3 alphabet cards from the box
⇒ number of alphabet cards = 10 - 3 = 7
⇒ total number of cards = 24 - 3 = 21
Therefore, P(alphabet card) = 7/21 = 1/3
(c) P(number card) = 8/24 = 1/3
If we add 4 number cards to the box:
⇒ number of number cards = 8 + 4 = 12
⇒ total number of cards = 24 + 4 = 28
Therefore, P(number card) = 12/28 = 3/7
--------------------------------------------------------------------
Question 10
Given:
ΔSDR = ΔPRQLeg length of ΔSDR and ΔPRQ = 4 cm⇒ area of ΔSDR = area of ΔPRQ = 1/2 × 4 × 4 = 8 cm²
As PR = SD = 4cm
Area of rectangle = (4 + 4) × (12 + 4) = 128 cm²
P(point lies in ΔSDR) = 8/128 = 1/16
P(point lies in ΔPRQ) = 8/128 = 1/16
P(point lies in ΔSDR) OR P(point lies in ΔPRQ) = 1/16 + 1/16 = 2/16 = 1/8
How do I do it and be able to understand it
Which represents the polynomial written in standard form? 4m – 2m4 – 6m2 9 9 4m 2m4 – 6m2 2m4 – 6m2 – 4m 9 9 – 6m2 4m – 2m4 –2m4 – 6m2 4m 9.
The standerd form 4m – 2m^4 – 6m^2 +9.
We have given that the polynomial given below we have to find the standerd form of the polynomial.
What is the standerd form of the polynomial[tex]P(x)=a_nx^n+a_{n-1}x^{n-1}+......+a_1x+a_0[/tex]
n=4
Standard form of the polynomial
[tex]4m - 2m^4 - 6m^2 + 9[/tex]
Rearranginge term we get
[tex]=-2m^4 - 6m^2 + 4m + 9[/tex]
The third term of the given polynomial is 0.
Therefore,the standard form is,
[tex]-2m^4 - 6m^2 + 4m + 9[/tex]
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this is what I need help with, because I dont understand how to do it
Answer
102.1
Step-by-step explanation:
area of the shaded region is the area of the the whole circle subtract area area of the unshaded minor segment.
For a sphere with a radius of 8 cm, find the volume of the sphere. Write each answer as an exact value or as a number rounded to the nearest tenth.
Answer:
V≈2144.66cm³
Step-by-step explanation:
Jasmine made a line plot to show the lengths of string in inches that the art teacher gave her for a craft project. A line plot named Which of the following statements that Jasmine made about the string lengths are true? Select the two that apply. A. The difference between the longest length and shortest length is 14 inches. B. I have twice as many 12-inch strings as I do 8-inch strings. C. The total length of string that I have is 84 inches. D. I cannot determine what the shortest string is by looking at my line plot. E. Since I need 100 total inches of string for my project, I have enough string.
The length of all the strings combined is 84 inches, while the length of the smallest string is 6 inches.
What is a line plot?
A line plot is a graph that shows the frequency of each value by displaying data as points or checkmarks above a number line.
In the given line plot, if we consider each of the options with the plot given to us, we will get to know which of the options are true or not.
A.) A. The difference between the longest length and shortest length is 14 inches.
As given in the plot, the longest string is 14 units while the smallest is 6 units, therefore, the first option is incorrect.
B.) I have twice as many 12-inch strings as I do 8-inch strings.
In the plot since the number of dots represents the number of strings of a particular length, therefore, the number of strings of length 12-inches is 4 and the number of strings of length 8-inches is 2. Thus, the given options are correct.
C.) The total length of string that I have is 84 inches.
As per the plot, the number of strings of length 6 inches is 1, the number of strings of length 8 inches is 2, the strings of length 12inches is 4, and the number of strings of length 14 inches is 1. Thus, the sum of the length of all the strings is 84 inches.
Hence, the statement is correct.
D.) I cannot determine what the shortest string is by looking at my line plot.
As given in the plot, the length of the smallest string is 6 inches, thus, the statement is incorrect.
E.) Since I need 100 total inches of string for my project, I have enough string.
As the length of all the strings combined is just 84 inches, thus, the statement is incorrect.
Hence, the only option that is correct is 'B' and 'C'.
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The football team played 15 games this season and won three more games than it lost. How many games did the team lose?
w = won game
l = lost game
w + l = 15
and
w = I + 3
so
l + 3 + l = 15
2l = 12
l = 6
lost = 6
won = 9
Answer:
The ratio of wins to losses is 3 to 1, out of 32 total games. 3:1 has a total of 4 parts (3+1).
Total games divided by total parts is 32/4 = 8.
Now multiplying number of parts to divisor gives us 3x8 : 1x8 or 24:8. Therefore they won 24 games, lost 8.
Step-by-step explanation:
Find the area of each figure.
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Area of a Parallelogram is ~
[tex]\qquad \sf \dashrightarrow \:base \times height[/tex]
[tex]\qquad \sf \dashrightarrow \:7 \times 5[/tex]
[tex]\qquad \sf \dashrightarrow \:35 \: {cm}^{2} [/tex]
what value of a makes this proportion 4/12 = a/27
Answer:
The Formula for Percent Proportion is Parts /whole = percent/100. This formula can be used to find the percent of a given ratio and to find the missing value of a part or a whole.
Answer:
a = 9
Step-by-step explanation:
[tex]\frac{4}{12}[/tex] = [tex]\frac{a}{27}[/tex] ( cross- multiply )
12a = 108 ( divide both sides by 12 )
a = 9
Type the correct answer in the box. assume π = 3.14. and round your answer to the nearest hundredth. at the rate of $2.00 per square foot, the cost of painting the rectangular board with a semicircular top shown in the figure is $ .
The cost of painting the rectangular board with a semicircular top is $31.065 to the nearest hundredth.
How to find the area of the composite figures?To find area of the composite figures,
Separate the figure.Calculate the are of the each figure by which the composite figure is made of.Add the area of all the individual figures to get the total area of composite figures.The dimentions of the rectangle is 3 by 4 foot. The area of the rectangle is,
[tex]A_r=3\times4\\A_r=12\rm \;ft^2[/tex]
The radius of the semicircle is 1.5 m. The area of the semicircle is,
[tex]A_{sc}=\dfrac{1}{2}\pi\times(1.5)^2\\A_{sc}=\dfrac{1}{2}(3.14)\times(1.5)^2\\A_{sc}=3.5325\rm\; ft^2[/tex]
The area of the composite figure is,
[tex]A=12+3.5325\\A=15.5325\rm\;ft^2\\[/tex]
The rate of painting is $2.00 per square foot. Thus the cost to paint the figure is,
[tex]A=15.5325\times2\\A=31.065[/tex]
Hence, the cost of painting the rectangular board with a semicircular top is $31.065 to the nearest hundredth.
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Answer:31
Step-by-step explanation:
We have 6 tents for 18 campers each tent holds 2 or 4 campers exactly how many of our tents hold 2
Answer:
3 tents hold 2 campers
Step-by-step explanation:
The given relations can be expressed as a single equation in the number of 2-camper tents.
__
Let x represent the number of 2-camper tents. Then the number of 4-camper tents is 6-x, and the total number of campers in tents is ...
2x +4(6 -x) = 18
-2x +24 = 18
-2x = -6 . . . . . . subtract 24
x = 3 . . . . . . . divide by -2
Exactly 3 tents hold 2 campers.
_____
Additional comment
The other 3 tents hold 4 campers.
Another way to consider this is to assume that all tents hold 2 campers, and then realize there are 18 -6×2 = 6 campers left over. If these are placed 2 per tent, then there will be 6/2 = 3 tents with 4 campers. The remaining 3 tents will have 2 campers.
SOMEONE HELP!!!!!!!!!!!!!!!!!1
Answer:
5
Step-by-step explanation:
Determina el grado de y =3r⁵ + 8r³
5
PLEASE HELP ASAP
84 = h – 8
h =
Hello!
Let's solve this equation:
84=h-8
This is the same as
h-8=84
Add 8 to both sides:
h=84+8
h=92
Hope everything is clear.
Let me know if you have any questions!
#KeepLearning
:-)
Simplify
3k - (2m + 5K) - m
Answer:
[tex]-3m-2k[/tex]
Step-by-step explanation:
Given to simplify : 3k - (2m + 5K) - m
Solution :
[tex]\mathrm{Apply\:the\:distributive\:law}:\quad \:-\left(a+b\right)=-a-b[/tex]
[tex]-\left(2m+5k\right)=-2m-5k[/tex]
[tex]=3k-2m-5k-m[/tex]
[tex]\mathrm{Group\;like\;terms}[/tex]
[tex]=-2m-m+3k-5k[/tex]
[tex]\mathrm{Group\;like\;terms}[/tex]
[tex]=-3m+3k-5k[/tex]
[tex]\mathrm{Group\;like\;terms}[/tex]
[tex]=-3m-2k[/tex]
[RevyBreeze]
Use the distributive property:-
-(2m+5k) = -2m-5k [tex]\checkmark[/tex]
[tex]\rule{270}{1}[/tex]
Let's simplify this expression by combining like terms:-
[tex]\bigstar[/tex] The like terms are:-
3k, -5k
and
-2m, -m
[tex]\bigstar{[/tex] Combine Like terms:-
3k-5k=-2k
-2m-m=-3m
Hence, we have:-
[tex]\bigstar{\boxed{\pmb{-2k-3m}}[/tex]
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)
A cylinder has volume 120 cm3.What is the volume of a cone with the same radius and height? ? 40 cm 60 cm O 240 cm 360 cm 3
The volume of a cone with the same radius and height as the cylinder is 40cm³.
What is the volume of the cone?
A cylinder is a three-dimensional object. It is a prism with a circular base.
Volume of a cylinder = nr^2h
n = 22/7r = radiusVolume of a cone = 1/3(nr^2h)
The volume of a cone, is 1/3 that of a cylinder.
Volume of the cone = 1/3 x 120 = 40
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Answer:cool
Step-by-step explanation:
iono
What is m _BAC?
A) 40°
B) 60°
C) 70°
D) 80°
What is the area of the object
Answer:
C. 189 square centimeters
Step-by-step explanation:
Area of a Square/Rectangle is base x height
= 7 X 7 = 49
Area of a triangle = 1/2 Base X Height
= 1/2 X 7 X 10
= 35
There are 4 triangles
35 X 4 = 140
140 + 49 = 189
= 189cm^2
Answer: C. 189 cm²
Step-by-step explanation:
A rectangle/square is solved for with A = L * W.
The middle square has a (surface) area of:
7 * 7 = 49 cm²
We then have four triangles. These are solved for with [tex]\frac{B*H}{2}[/tex]. Since all four are congruent, I will multiply one of them by 4.
The triangles have a total (surface) area of:
10 * 7 = 70
70 / 2 = 35
35 * 4 = 140 cm²
Lastly, we will add the two totals together.
140 cm² + 49 cm² = 189 cm²
The object has a surface area of C. 189 cm².
Indicate the method you would use to prove the two Δ's ≅ . If no method applies, enter "none".
Answer: The answer is ASA I got it right
Step-by-step explanation:
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