Answer:
x = -1.5 , y = 5.17
Step-by-step explanation:
Solve the system of equation using ELIMINATION (solve for x)
x + 3y = 14
-x + y = 10
Solution
x + 3y = 14 ------- equation 1 * 1
-x + y = 10 ------- equation 2 * 3
x + 3y = 14 ------- equation 3
-(-3x + 3y = 30)------ equation 4
Using the ELIMINATION METHOD.
x-(-3x) + 3y-3y = 14-30
4x = -6
x = [tex]\frac{-6}{4}[/tex]
x = -1.5
Substuting -1.5 into equation one
x + 3y = 14
-1.5 + 3y = 14
Adding 1.5 to both sides
-1.5 + 1.5 +3y = 14 +1.5
+3y = 15.5
Dividing by the coeffient of y
[tex]\frac{3y}{3} = \frac{15.5}{3}[/tex]
y = 5.166666666666
y =5.17
Therefore x = -1.5 , y = 5.17
Allison wants to ride her bicycle 60 miles this week. She has already ridden 12 miles. If she rides for 6 more days, what is the average number of miles she would have to ride each day to meet her goal?
Answer:
8 miles a day
Step-by-step explanation:
First you have to subtract the amount of miles she had already gone.
60 - 12 = 48
Next you have to divide by the remaining amount of days (6 days).
48/6 = 8
Mai put $4250 in the bank at 4.4% interest compounded annually. How much was in her
account after 7 years?
Answer:
$5745.03
Step-by-step explanation:
A = 4250(1 + 0.044)7 = $5745.03
The required amount in the Mai accounts after 7 years will be $5745.03.
What is compound interest?Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.
Amount = principal[1 + r/n]ⁿᵃ
Here,
Principal = 4250, rate = 4.4%, Time = 7 ,
Amount = 4250[1 + 0.044]⁷
Amount = $5745.03
Thus, the required amount in the Mai accounts after 7 years will be $5745.03.
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Here are two rectangles. the area of the shaded rectangle is 1/4 the area of the large rectangle. work out the value of x
The area of the rectangle is the product of length and width. The value of the variable x is 3.6 cm
What is the area of the rectangle?Let L be the length and W be the width of the rectangle.
Then the area of the rectangle will be
Area of the rectangle = L × W square units
The diagram is given below.
Let A₁ be the area of the small rectangle and A be the area of the large rectangle.
A₁ = 1/4 A
4A₁ = A
4 × 2× (12 - x) = 12 × (x + 2)
8(12 - x ) = 12x + 24
96 - 8x = 12x + 24
72 = 20x
x = 3.6
Then the value of the variable x is 3.6 cm
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please help ASAP
tthankyou
answer is below in attachment
Answer:
10, 13, 15.Step-by-step explanation:
Solve all possible equations:
8 + 10 + 1 + 9 + 2Adding them all up we get:8 + 10= 18 + 1= 19 + 9= 28 + 2= 3030 < 40.10 will be used for the next equation:
2nd equation:
10 + 12 + 1 + 13 + 2Solve:10 + 12= 22 + 1= 23 + 13= 36 + 2= 3838 < 40.13 will be used for the final equation:
Final equation:
10 + 13 + 1 + 15 + 2= 10 + 13= 23 + 1= 24 + 15= 39 + 2= 41.41 > 40.The 3 digits are 10, 13, 15.1. whats -3 x - 5 = 6
2. whats -4 ( y - 2 ) =12
show work
Answer:
x = -11/3 or 3.666y = -1Step-by-step explanation:
Given:
1) -3x -5 = 6
2)- 4 ( y - 2 ) =12
To Find:
Value of x for no. 1Value of y for no. 2Solved:
1)-3x -5 = 6
Transpose -5 from LHS to RHS
=> -3x = 6+5=> -3x = 11Transpose -3 from LHS to RHS
=> x = (11/-3)=> x = -11/3=> x = -3.6662) -4(y-2) = 12
Apply distributive property
=>(−4)(y)+(-4)(-2)=12=>-4y+8 = 12Transpose 8 to RHS
=> -4y = 12-8=> -4y =4Transpose -4 to RHS
=> y = 4/-4=> y = -1PLS HELP! What is the linear function rule for this table?
Answer:
f(x) = 4x + 6
Step-by-step explanation:
Using f(x) = 4x + 6
lets find some answers
lets take x as (-2)
f(-2) = 4(-2) + 6
f(-2) = -8 + 6
= -2
Also, take x as (-1)
f(-1) = 4(-1) + 6
f(-1) = -4 + 6
= 2
What is the volume of this object?
Top View
2u
2u
pls I need help lol
Answer:
15 u³
Step-by-step explanation:
Volume = width × length × height
Given:
width = 2ulength = 2 ¹/₂ uheight = 3u⇒ Volume = 2u × 2 ¹/₂ u × 3u
= 15 u³
[tex]\underline{\tt{❖ \: Given \: \: ❖}}[/tex]
[tex] \sf \: length =2 \dfrac{1}{2}u[/tex][tex] \sf \: width =2u[/tex][tex] \sf \: height =3u[/tex]given figure
[tex] \green{\rule{15pt}{ 15pt}} \: \: \: \green{\rule{15pt}{15pt}} \: \: \: \green{\rule{7.5pt}{15pt}} \\ \: \: \: \: \: \: \green{\rule{15pt}{ 15pt}} \: \: \: \green{\rule{15pt}{15pt}} \: \: \: \green{\rule{7.5pt}{15pt}} \sf \: 2u \\ \green{\rule{15pt}{ 15pt}} \: \: \: \green{\rule{15pt}{15pt}} \: \: \: \green{\rule{7.5pt}{15pt}} \\ \sf \: 2 \dfrac{1}{2}u[/tex]
[tex]\underline{\tt{❖ \: To \: find \: ❖}} [/tex]
volume of this object[tex]\underline{\tt{❖ \: Using \: formula \: ❖}} [/tex]
[tex] \sf \: volume = width \times length \times height[/tex][tex]\underline{\tt{❖ \: Solution \: ❖}} [/tex]
we have,
[tex]\sf \: volume = width \times length \times height[/tex]
[tex]\sf \: volume = 2u \times 2 \dfrac{1}{2}u \times 3u[/tex]
[tex]\sf \: volume = 2u \times \dfrac{5}{2}u \times 3u[/tex]
[tex]\sf \: volume = \cancel2u \times \dfrac{5}{ \cancel2}u \times 3u[/tex]
[tex]\sf \: volume = u \times 5u \times 3u[/tex]
[tex]\sf \: volume = 15u {}^{3} [/tex]
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
–51 ≤ x + 38 I need help please finals are tomorrow....
Answer:
x ≥ - 89
Step-by-step explanation:
−51 ≤ x + 38
Step 1: Flip the equation.
⇒ x + 38 ≥ - 51Step 2: Subtract 38 from both sides.
⇒ x + 38 - 38 ≥ - 51 - 38x ≥ - 89 ====> AnswerDoes anybody want to help with math?
2a(-5a^8b+a^2-12ab)
Ty :D
Answer: 18a4 - 6a3b - 5a2b4 - 45a2b2 + 36ab2 - 12ab + 3b
———————————————————————————————-
3
Step-by-step explanation:
7. The points (−2,−4) and (5,6) are the endpoints of the diameter of a circle. Find the length of the radius of the circle.
Answer
6.10
Use the distance formula:
[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
where (x1, y1), (x2, y1) are points
[tex]\rightarrow \sf d =\sqrt{(5-(-2))^2 + (6-(-4))^2}[/tex]
[tex]\rightarrow \sf d =\sqrt{(7)^2 + (10)^2}[/tex]
[tex]\rightarrow \sf d =\sqrt{149}[/tex]
This is the length of diameter.
Then radius:
· diameter/2
[tex]\sf \cdot \dfrac{\sqrt{149 } }{2}[/tex]
[tex]\sf \cdot 6.103277808[/tex]
[tex]\sf \cdot 6.10 \ \ (rounded \ to \ nearest \ hundreth)[/tex]
Two sets of data are each symmetrical and do not contain outliers. Which measures of center and
variability would be most effective to use when making comparisons between the two data sets?
A.
mean and MAD
B. mean and IQR
C. median and MAD
D. median and IQR
Solution:
As, two set of data are each symmetrical and do not contain outliers.
To find the center , the best way is to find Median of data set.Median of Data set is the mid value of Data that is center of Data.
As, you have to find variability , mean can't measure variability. Mean deviation would have been better option.
So, MAD=Median absolute Deviation , would be better tool to measure variability. Because it is Absolute difference between median and Each value of data set.
So, Option (C) median and MAD, would be best way to compare the two given data set.
What is the sum of the two
expressions?
(4/5x+13) - (5/8x − 6)
Answer: 7/40x + 19
Step-by-step explanation:
---Distribute the negative sign
4/5x + 13 - 5/8x + 6
---Get common denominators on the fractions
32/40x + 13 - 25/40x + 6
---Combine like terms
(32/40x - 25/40x) + (13 + 6)
7/40x + 19
Answer: 7/40x + 19
Hope this helps!
write 8.31752 to correct 3 decimal places
Answer:
8.318
Step-by-step explanation:
writing a number in three decimal places means writing the number in a way that there will be three digits in the number after the decimal point.
to three decimal places= 8.318
I need help with this thank you!
Answer: m<AOB is 60 degrees.
Step-by-step explanation: If BCD is 30 degrees, it intercepts the arc BA, and therefore, any angle that intercepts an arc is half of the arc it intercepts. Thus, AOB is 60 degrees.
What is the area of triangle ABC?
C
12
60°
60°
A
D
B
Answer:
Area of the triangle is 36√3
Step-by-step explanation: Hope this will help
The hypotenuse of each 30 - 60 - 90 triangle is 12
The base length is 6 + 6 = 12 because the triangle is equilateral and the
altitude of the triangle divides the base into two equal parts and the altitude (DC) is the height of the triangle.
Now you have two 30 - 60 - 90 triangles with the hypotenuse of 12, the short leg = 6 and you need to find the length of DC.
Finding DC .
a² + b² = c²
6² + b² = 12² 0r the long leg = short leg times √3
36 + b² = 144 6√3
b² = 108
b = 6√3
Area of a triangle = 1/2bh
= 1/2(12)(6√3)
= 6(6√3) = 36√3
if you have 48 apples and you gave your friend molly 20 and you gave your brother and mom 18 each how much apples do you have now?
Answer:
10
Step-by-step explanation:
48-20=28
28-18=10
that is how I see it at least
can u guys help me with this
Answer:
Step-by-step explanation:
A.) 16500 Seconds
B.) 12569 Seconds
C.) 38116 Seconds
D.) 20700 Seconds
E.) 7256
Lionel computed the average rate of change in the depth of a pool over a two-week interval to be zero. Which statement must be true?
The pool must have been empty for the entire interval.
The pool must have been the same depth at the start of the interval as it was at the end of the interval.
The pool must have been deeper at the end of the interval than it was at the start of the interval.
The pool must have been more shallow at the end of the interval than it was at the start of the interval.
The pool must have been the same depth at the start of the interval as it was at the end of the interval, option second is correct.
What is the average rate of change?Finding out how much something changes over time is what the average rate of change is all about.
We have Lionel computed the average rate of change in the depth of a pool over a two-week interval to be zero.
As we know that the average rate of change can be calculated using:
= (Last quantity - starting quantity)/Time interval
The average rate of change, on the other hand, does not account for intermediate values, therefore you can't draw any conclusions about them.
In the given problem:
The average rate of change in depth = (Last quantity - starting quantity)/2
0= (Last quantity - starting quantity)
Final depth = Initial depth
Thus, the pool must have been the same depth at the start of the interval as it was at the end of the interval, option second is correct.
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Use formulas to find the lateral area and surface area of the given prism. Round your answer to
the nearest whole number. The figure is not drawn to scale. The bases are right triangles.
8.94 m
4m
8m
41 m
Answer:
The answer is option B
[tex]859[/tex] [tex]m^2[/tex] [tex],[/tex] [tex]891[/tex] [tex]m^2[/tex]
Step-by-step explanation:
Step 1
Find the lateral area
we know that
The formula to calculate the lateral area is equal to
[tex]LA=Ph[/tex]
where
P is the perimeter of the base of the prism
h is the height of the prism
In this problem we have
[tex]P=4+8+8.94=20.94[/tex] [tex]m[/tex]
[tex]h=41[/tex] [tex]m[/tex]
substitute in the formula
[tex]LA=20.94*41=858.54[/tex] [tex]m^2[/tex]
[tex]LA=859[/tex] [tex]m^2[/tex]
Step 2
Find the surface area
we know that
The formula to calculate the surface area is equal to
[tex]SA=2B+Ph[/tex]
where
B is the area of the base of the prism
P is the perimeter of the base of the prism
h is the height of the prism
In this problem we have
[tex]B=8*4/4=8[/tex] [tex]m^2[/tex]
[tex]P=4+8+8.94=20.94[/tex] [tex]m[/tex]
[tex]h=41[/tex] [tex]m[/tex]
substitute in the formula
[tex]SA=4(8)+20.94*41=890.54[/tex] [tex]m^2[/tex]
[tex]SA=891[/tex] [tex]m^2[/tex]
Envision Geometry 10-1 Circles 22. page 425
The segment area of the circle that's given in the envision geometry is 2.568.
How to calculate the segment area?It should be noted that the segment area is given as:
= (a/360)π × R² - Area of triangle
= (90/360)π × 3² - (1/2 × 3²)
= 9π/4 - 9/2
= 2.568
In conclusion, the segment area of the circle that's given in the envision geometry is 2.568.
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PLEASE HELP ASAP!!!!
A scatter plot is shown below: if you need an image of it look at the bottom
A graph shows numbers from 0 to 10 on the x axis at increments of 1 and the numbers 0 to 15 on the y axis at increments of 1. The ordered pairs 0, 14 and 1, 11 and 2, 9 and 3, 10 and 4, 7 and 5, 7 and 6, 5 and 7, 5 and 8, 3 and 9, 1 and 10, 0 are shown on the graph.
Which two ordered pairs can be joined to best draw the line of best fit for this scatter plot?
(4, 15) and (10, 7)
(1, 6) and (6, 0)
(0, 13) and (10, 11)
(0, 13) and (10, 0)
Reason:
If you were to draw a line through the points mentioned in choice A, the line wouldn't be close to the points since (4,15) isn't close to the points. The same goes for (10,7). So we can rule out choice A. Choices B and C are similar stories.
Choice D on the other hand has its line fairly close to all of the points.
Last option
(0,13)
The point will lie at top(10,0)
The point will lie at bottomSo
both will contain most no of plots so Option D is correct
A survey asked 200 Grade 4 students about their reading preferences. Based on Graph #1, about how many of them would you expect prefer comic books?
i added the graph
Answer:
D. 80
Step-by-step explanation:
The graph shows that about 3/8 ( 37.5% ) of the students enjoy comic books.
200 × .375 = 75
75 rounded to the nearest tens value is 80
Help with Alg2. Please explain how.
Answer:
c = 14.43 units to the nearest hundredth.
Step-by-step explanation:
We are given 2 sides and the included angle so we use the Cosine Rule.
c^2 = a^2 + b^2 - 2absinC
= 20^2 + 17^2 - 2.29.17cos45
= 208.17
c = √208.167
= 14.43.
2. f(x)=4x+1 and g(x)=x2−4x−5, find (g◦f)(4).
Answer:
(g · f)(4) = 45
Step-by-step explanation:
f(x)=4x+1
g(x)=x² - 4x- 5
(g · f)(x) = 4(x² - 5) + 1
(g · f)(4) = 4(4² - 5) + 1
Following pemdas
(g · f)(4) = 4(16 - 5) + 1
(g · f)(4) = 4(11) + 1
(g · f)(4) = 44 + 1
(g · f)(4) = 45
Rewrite the radical expression as an exponential expression, and then simplify.
StartRoot 121 EndRoot = one-half (121) = 60.5
StartRoot 121 EndRoot = 121 squared = 14,641
StartRoot 121 EndRoot = 121 Superscript one-half Baseline = 11
StartRoot 121 EndRoot = 121 Superscript one-half Baseline = 60.5
The radical expression written as an exponent, and simplified, is given by:
[tex]\sqrt{121} = (121)^{\frac{1}{2}} = 11[/tex].
How to transform an exponent to a power?It happens according to the following rule:
[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]
The inverse is also valid, hence, in this problem, the expression written as an exponent and simplified is given by:
[tex]\sqrt{121} = (121)^{\frac{1}{2}} = 11[/tex].
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12 is 48 percent of what number?
Answer:
25
Step-by-step explanation:
12 x 100 = 1200
1200 / 48 = 25
I need some help on this question please
Answer:
D
Step-by-step explanation:
everything that should happen at x+4 happens now at x. that is what that means.
so, the graph shifts 4 units to the left.
help for 10 points that is all i have
Answer:
22 in. and o.5 ft i think so
HELPPPP WITH MATH HOMEWORK PLS
Answer:
The length of the wing is 480 centimeters
Step-by-step explanation:
2 cm on the drawing is 192 cm on the acutal wing
2 = 192
divide both sides by 2
1 = 96
since the drawing has a length of five cm, multiply both sides by 5
5 = 480
therefore, 5 cm on the drawing is equal to 480 cm on the actual wing
which postulate or theorem proves that these two triangles are congruent?
a. ASA Congruence Postulate
b. SAS Congruence Postulate
c. AAS Congruence Theorem
d. HL Congruence Theorem
