The area of the triangle ∆NOP is derived to be 133.9 square centimeter to the nearest tenth using the sine rule.
What is the sine ruleThe sine rule is a relationship between the size of an angle in a triangle and the opposing side. It states that for any triangle ABC, the ratio of the length of a side to the sine of the angle opposite that side is constant, that is;
a/sinA = b/sinB = c/sinC
where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those sides.
angle m∠O = 180 - (83 + 88) {sum of interior angles of a triangle}
angle m∠O = 9°
Using the sine rule;
6.5/sin9 = ON/sin88
ON = (6.5 × sin88°)/sin9 {cross multiplication}
ON = 41.5
Area of the triangle = 1/2 × 6.5cm × 41.5cm × sin83
Area of the triangle = 133.9
Therefore, the area of the triangle ∆NOP is derived to be 133.9 square centimeter to the nearest tenth using the sine rule.
Read more about sine rule here:https://brainly.com/question/4372174
#SPJ1
The table gives the temperature (in "F) in five cities at 6 a.m. on the same day. Use the table to answer the questions.
Temperature
(°F)
-26
43
-14
City
Juneau
Springfield
Montreal
Milwaukee
Atlanta
-3
F lower
68
(a) How much lower was the 6 a.m, temperature in Juneau than in Atlanta?
(b) By noon, the temperature in Milwaukee had risen by 11 °F.
What was the temperature there at noon?
a) The temperature in Juneau was 23°F lower than in Atlanta.
b) The temperature in Milwaukee at noon would be -3°F.
(a) The temperature difference between Juneau and Atlanta is:
= -3 - (-26)
= 23°F lower in Juneau
Therefore, the 6 a.m. temperature in Juneau was 23°F lower than in Atlanta.
(b) Since the temperature in Milwaukee had risen by 11°F, its temperature at noon would be:
= -14 + 11
= -3°F
Therefore, the temperature in Milwaukee at noon would be -3°F.
Learn more about Integers here:
https://brainly.com/question/15276410
#SPJ1
Graph these integers on a number line:0,-5,1,3
Answer:
-5,0,1,2,3
Step-by-step explanation:
in a number line the negative numbers are always on your left hand side and as you head to the right they increase thus becoming positive integers
Find the expected value of the winnings don a game that has the following payout probability distribution
The expected value of the winnings in this game is $1.23.
We have,
The expected value of a random variable is the sum of the products of each possible outcome and its probability.
In this case, the random variable is the winnings from the game and the payout probability distribution specifies the probabilities associated with each possible payout.
The expected value of the winnings is found by multiplying each payout by its probability and summing the products.
Expected value = (0)(0.50) + (1)(0.25) + (2)(0.13) + (4)(0.06) + (8)(0.06)
= 0 + 0.25 + 0.26 + 0.24 + 0.48
= 1.23
Therefore,
The expected value of the winnings in this game is $1.23.
Learn more about expected value here:
https://brainly.com/question/29574962
#SPJ1
Find the area of the triangle with the given description. A triangle with sides of length 5 and 8 and include angle 79°.
The area of the triangle is 18.6 units²
Given data ,
Let the triangle be represented as ΔABC
Now , the sides of the triangle are
We can use the law of cosines to find the length of the third side of the triangle:
c² = a² + b² - 2ab cos(C)
c² = 5² + 8² - 2(5)(8)cos(79°)
c ≈ 9.05
Now, we can use Heron's formula to find the area of the triangle:
s = (5 + 8 + 9.05)/2 = 11.525
A = √(s(s-a)(s-b)(s-c))
A = √(11.525(11.525-5)(11.525-8)(11.525-9.05))
A ≈ 18.6
Hence , the area of the triangle is approximately 18.6 square units
To learn more about Heron's formula click :
https://brainly.com/question/29184159
#SPJ1
Find the value of x.
69°
138°
X
x = 0
Answer:
x = 106
Step-by-step explanation:
You want the measure of the unknown angle (x°) in the quadrilateral with angles 47°, 138°, and 69° given.
Angle sumThe sum of angles in a quadrilateral is 360°, so the measure of x is ...
x = 360 -47 -138 -69 = 106
Angle x° is 106°.
#95141404393
How tall is a building that casts a 68-ft shadow when the angle of elevation of the sun is 34 degrees?
The height of the building is approximately 45.44 ft when it casts a 68-ft shadow under an angle of elevation of 34 degrees.It's important to note that this calculation assumes the ground is flat and the sun's rays are parallel. Real-world conditions may introduce slight variations.
To determine the height of the building, we can use the trigonometric relationship involving the angle of elevation, the height of the building, and the length of its shadow.
Let's denote the height of the building as h. The length of the shadow cast by the building is given as 68 ft, and the angle of elevation of the sun is 34 degrees.
Using the tangent function, we have the equation:
tan(34°) = h / 68To
solve for h, we can rearrange the equation:
h = 68 * tan(34°)
Calculating this expression, we find:
h ≈ 68 * 0.668178 = 45.439344 ft.
For such more questions on Angle of elevation:
https://brainly.com/question/25748640
#SPJ11
Oak Street and Elm Street run parallel to each other. When Main Street
intersects them, it forms interior 24, measuring 50°. What is the measure of 27?
A. 130°
B. 45°
C. 35°
D. 145°
Answer:
130°
Step-by-step explanation:
<4=<8
180-50=130
People are invited to compete to be a contestant in a television quiz show.
Here are some possible outcomes for the person who is chosen.
A: The contestant is a woman over 25 years old. B: The contestant is a man.
C: The contestant is 21 years old. D: The contestant is a 30-year-old man.
a List the possible pairs of mutually exclusive outcomes.
b List three of the outcomes that are all mutually exclusive.
c What can you say about the probabilities of B and D?
a) The possible pairs of mutually exclusive outcomes are given below:
A and B
A and C
A and D
B and C
B and D
C and D
b) The Three of the outcomes that are said to be all mutually exclusive are:
A (The contestant is a woman over 25)B ( The contestant is a man.)C (The contestant is 21 years old )c) The probability of having B and D is written as P(B or D) = P(B) + P(D)
What is the probability?Mutually exclusive events cannot happen at the same time, like rolling a kick the bucket and getting a 1 and a 2. In this case, there are four conceivable results: A, B, C, and D, a few of which we commonly select.
For example, If A is the outcome, C or D cannot be. To find mutually exclusive pairs, we check which outcomes cannot occur together. A and B are mutually exclusive because they cannot both be true.
Learn more about probability from
https://brainly.com/question/25870256
#SPJ1
Which pair of points has a slope of 4?
a. (1, 4), (–1, 4)
b. (0, 4), (4, 0)
c. (0, –3), (1, 1)
d. (3, 0), (–1, –1)
Answer: From the calculations, the pair of points with a slope of 4 is option c. (0, -3), (1, 1).
Step-by-step explanation:
To determine the slope between two points, we can use the formula:
slope = (change in y) / (change in x)
Let's calculate the slope for each pair of points:
a. (1, 4), (–1, 4)
The change in y is 4 - 4 = 0
The change in x is -1 - 1 = -2
slope = 0 / -2 = 0
b. (0, 4), (4, 0)
The change in y is 0 - 4 = -4
The change in x is 4 - 0 = 4
slope = -4 / 4 = -1
c. (0, –3), (1, 1)
The change in y is 1 - (-3) = 4
The change in x is 1 - 0 = 1
slope = 4 / 1 = 4
d. (3, 0), (–1, –1)
The change in y is -1 - 0 = -1
The change in x is -1 - 3 = -4
slope = -1 / -4 = 1/4
Answer:
c. (0, –3), (1, 1)
Step-by-step explanation:
To find the slope, we use the slope formula
m = ( y2-y1)/(x2-x1)
a. (1, 4), (–1, 4)
m = (4-4)/(-1-1) = 0/-2 = 0
b. (0, 4), (4, 0)
m = ( 4-0)/(0-4) = 4/-4 = -1
c. (0, –3), (1, 1)
m = ( -3-1)/(0-1) -4/-1 = 4
d. (3, 0), (–1, –1)
m = (0--1)/(3 - -1) =1/4
5x + 7 =-13 what is x
Answer:
-4
Step-by-step explanation:
5x=-13-7
5x=-20
x=-20/5
x=-4
Answer:
5x+7=-13
5x=-13-7
5x=-20
x=-20 divide by 5
x=-4
9 se the given rules to complete the following tables. Classwork x y=-2r-8 y=-2x+8 HoNetwork =-5g-4 -3 -1 -2 -2 -2 -1 -3 -1 0 -4 0 1 -5 10 -6 2 100
The complete table for the linear function y = -2x + 8 is:
x y
1 6
2 4
3 2
4 0
5 -2
The given function is y = -2x + 8, which represents a linear equation in the slope-intercept form. In this form, the equation of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept.
Comparing the given equation with the slope-intercept form, we can see that the slope of the line is -2, which means that the line goes down by 2 units for every 1 unit it moves to the right. The y-intercept of the line is 8, which means that the line intersects the y-axis at the point (0, 8).
The complete table:
x y
1 6
2 4
3 2
4 0
5 -2
To learn more about the linear function;
brainly.com/question/20286983
#SPJ1
The complete question:
Complete the following table as per the function y = -2x + 8.
x y
1
2
3
4
5
PLS HELP 15 POINTS I'LL DO BRAINLIEST
nneed answer and explanation for this
Answer:
276.460 mi²
Step-by-step explanation:
You want the surface area of a cylinder with radius 4 mi and height 7 mi.
AreaThe area of a cylinder is given by the formula ...
A = 2πr(r +h)
A = 2π(4 mi)(4 mi +7 mi) = 88π mi² ≈ 276.460 mi²
The area of the cylinder is about 276.460 square miles.
__
Additional comment
The surface area is the sum of the areas of the two circular bases and the lateral area. The lateral area is the product of the cylinder height and circumference. These are combined in the formula given.
<95141404393>
Janet Foster bought a computer and printer at Computerland. The printer had a $860 list price with a $100 trade discount and 2/10, n/30 terms. The computer had a $4,020 list price with a 25% trade discount but no cash discount. On the computer, Computerland offered Janet the choice of (1) paying $150 per month for 17 months with the 18th payment paying the remainder of the balance or (2) paying 6% interest for 18 months in equal payments.
Item10
10
points
eBookPrintReferencesCheck my workCheck My Work button is now enabledItem 10
Challenge Problem 10-37 (Algo) [LU 10-1 (2)]
Janet Foster bought a computer and printer at Computerland. The printer had a $860 list price with a $100 trade discount and 2/10, n/30 terms. The computer had a $4,020 list price with a 25% trade discount but no cash discount. On the computer, Computerland offered Janet the choice of (1) paying $150 per month for 17 months with the 18th payment paying the remainder of the balance or (2) paying 6% interest for 18 months in equal payments.
a. Assume Janet could borrow the money for the printer at 6% to take advantage of the cash discount. How much would Janet save? (Use 360 days a year. Round your answer to the nearest cent.)
b. On the computer, what is the difference in the final payment between choices 1 and 2? (Round your answer to the nearest cent.)
a) Janet would save $17.20 - $5.60733 = $11.59 by borrowing the money for the printer at 6% to take advantage of the cash discount. b) , the difference in the final payment between choices 1 and 2 is $1,107.60.
How to answer the aforementioned questionsa. The cash discount on the printer is calculated as 2% of the list price:
Cash discount = 2% * $860 = $17.20
Using the formula:
Interest = Principal * Rate * Time
Principal = Amount borrowed = List price - Cash discount = $860 - $17.20 = $842.80
Rate = 6% per year = 6%/100 = 0.06
Time = 30 days (since the terms are 2/10, n/30)
To convert the interest to a 360-day basis, we use the formula:
Interest = Principal * Rate * (Time/360)
Interest = $842.80 * 0.06 * (30/360) = $5.60733
Therefore, Janet would save $17.20 - $5.60733 = $11.59 by borrowing the money for the printer at 6% to take advantage of the cash discount.
b. Choice 1 for the computer involves paying $150 per month for 17 months, with the 18th payment paying the remainder of the balance. Choice 2 involves paying 6% interest for 18 months in equal payments.
For choice 1:
Remaining balance = List price - (17 * Monthly payment)
Remaining balance = $4,020 - (17 * $150) = $4,020 - $2,550 = $1,470
For choice 2:
Interest = Principal * Rate * Time
Principal = Amount borrowed = List price = $4,020
Rate = 6% per year = 6%/100 = 0.06
Time = 18 months
To convert the interest to a 12-month basis, we use the formula:
Interest = Principal * Rate * (Time/12)
Interest = $4,020 * 0.06 * (18/12) = $362.40
The final payment difference between choices 1 and 2 is:
Final payment difference = Remaining balance - Interest
Final payment difference = $1,470 - $362.40 = $1,107.60
Therefore, the difference in the final payment between choices 1 and 2 is $1,107.60.
Learn more about cash discount at https://brainly.com/question/14883253
#SPJ1
PLEASE HELP ME ANSWER THIS QUESTION. I REALLY NEED IT
The approximate land areas of the seven continents are listed in the table below.
Continent Area (in sq. miles)
Africa
Antarctica
Asia
Australia
Europe
North America
South America
11.7 million
5.4 million
17.3 million
3.3 million
3.8 million
9.4 million
6.9 million
What is the approximate mean of the land areas of the seven continents?
O 8.3 million
O57.8 million
O9.6 million
31.5 million
Answer: 8.3
Step-by-step explanation: Add all the numbers together, 11.7+5.4+17.3+3.3+3.8+9.4+6.9 equals 57.8 BUT WAIT! We aren't done, we have to divide the answer by the sum of all answers, so since there are 7 numbers we are adding together, we divide by 7, so 57.8 divided by 7 equals 8.3 (which is rounded to the nearest tenth) and theres your asnwer. Hope this helps!
You are considering a new project whose data are shown below. The required equipment has a 3-year tax life, after which it will be worthless, and it will be depreciated by the straight-line method over 3 years. Revenues and other operating costs are expected to be constant over the project's 3-year life. What is the project's Year 1 cash flow? Equipment cost (depreciable basis) $65,000 Sales revenues, each year $60,000 Operating costs (excl. depreciation) $25,000 Tax rate 35.0%
10 00
Taking the square root of a number technically results in two solutions.
For example, the square root of 16 is ____ or ___ because ___ = 16 and ____ = 16
Complete sentence is,
The square root of 16 is 4 or - 4 because 4² = 16 and (- 4)² = 16
We have to given that;
Taking the square root of a number technically results in two solutions.
Here, The number is,
⇒ 16
Take square root as;
⇒ √16
⇒ ± 4
Since, 4² = 16
And, (- 4)² = 16
Thus, We get;
the square root of 16 is 4 or - 4 because 4² = 16 and (- 4)² = 16.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
A special safe lets you choose from 5 symbols for a 3-symbol-long pass code. You may enter a symbol any number of times. How many potential pass codes are there? 10 35 60 125
There are 35 potential pass codes. The Option B.
How many potential pass codes can be created?A pass code means string of characters used as a password to gain access to a computer or smartphone.
To get number of potential pass codes, we will combinations formula with repetition [tex](n + r - 1)[/tex] choose r.
n = number of options
r = length of the pass code.
The number of potential pass codes is:
= (5 + 3 - 1) Choose 3
= 7 Choose 3
= (7 x 6 x 5) / (3 x 2 x 1)
= 210 / 6
= 35.
Read more about combination
brainly.com/question/28065038
#SPJ1
Complete the statement: triangle AED~triangle ___
Answer: AE=10, AD=14, x=5, BC=36, DE=52
Step-by-step explanation: finding x
4x-32=2(3x-21) || 4x-32=6x-42 || 10=2x || 5=x
(will give brainly if possible)
What is the area of the image of the rectangle under this transformation?
The area of the image of the rectangle under the transformation is 10 square units
Calculating the area of the image of the rectangle under the transformation?From the question, we have the following parameters that can be used in our computation:
Matrix transformation: [tex]\left[\begin{array}{cc}-7&-2\\6&12\end{array}\right][/tex]
And, we have rectangle plotted on the graph
The transformation is a rigid transformation
This means that the area of the rectangle would be the same before and after the transformation
From the graph, the side lengths of the rectangle are
Length = 2
Width = 5
So, we have
Area = 2 * 5
Evaluate
Area = 10
Hence, the area of the image of the rectangle under the transformation is 10 square units
Read more about transformation at
https://brainly.com/question/27224272
#SPJ1
In ΔGHI, g = 240 cm, m m∠H=157° and m m∠I=17°. Find the length of h, to the nearest 10th of a centimeter.
Check the picture below.
[tex]\textit{Law of Sines} \\\\ \cfrac{a}{\sin(\measuredangle A)}=\cfrac{b}{\sin(\measuredangle B)}=\cfrac{c}{\sin(\measuredangle C)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{h}{\sin(157^o)}=\cfrac{240}{\sin(6^o)}\implies h\sin(6^o)=240\sin(157^o) \\\\\\ h=\cfrac{240\sin(157^o)}{\sin(6^o)}\implies h\approx 897.1~cm[/tex]
Make sure your calculator is in Degree mode.
A: 10
B: 8
C: 21
D: 15
For which equations is 8 a solution? Select the four correct answers. x + 6 = 2 x + 2 = 10 x minus 4 = 4 x minus 2 = 10 2 x = 4 3 x = 24 StartFraction x Over 2 EndFraction = 16 StartFraction x Over 8 EndFraction = 1
ASAP ASAP ASAP ASAP.
The equations has 8 a solution are
x/2 = 16
x/8 = 1
x/2 = 8
x/8 = 1
To check whether 8 is a solution for an equation, we substitute x = 8 into the equation and see if it satisfies the equation. If it does, then 8 is a solution; otherwise, it is not.
Substituting x = 8 into each equation, we get:
1. x + 6 = 8 + 6 = 14 (8 is not a solution)
2. 2x + 2 = 2(8) + 2 = 18 (8 is not a solution)
3. 4x - 2 = 4(8) - 2 = 30 (8 is not a solution)
4. 10 = 10 (8 is not a solution)
5. 2x = 4 (8 is not a solution)
6. 3x = 24 (8 is not a solution)
7. 8/2 = 4 (8 is a solution)
83 8/8 = 1 (8 is a solution)
Therefore, the correct answers are:
x/2 = 16
x/8 = 1
x/2 = 8
x/8 = 1
Learn more about Equation here:
https://brainly.com/question/29657983
#SPJ1
GEOMRETY HELP ANY THING HELPS
(3) The linear equation is y = 1/3x + 1
(4) The solution to the system is (-1, -1/2)
(5) The factored expression of 45x² + 30x - 40 is 5(3x - 2)(3x + 4)
(6) The factored expression of 4x² - 36 is 4(x - 3)(x + 4)
(7) The surface area is 176
(8) The volume is 144
Solving the linear relationsFrom the graph, we have the following points
(0, 1) and (-3, 0)
A linear relation is represented as
y = mx + c
So, we have
y = mx + 1
Using the other point, we have
-3m + 1 = 0
m = 1/3
So, we have
y = 1/3x + 1
Next, we solve graphically
To do this, we plot the graphs and write out the point of intersection
In this case, the intersection point is (-1, -1/2)
So, the solution is (-1, -1/2)
Factoring the expressionsHere, we have
45x² + 30x - 40
When factored, we have
45x² + 30x - 40 = 5(3x - 2)(3x + 4)
Also, we have
4x² - 36
When factored, we have
4x² - 36 = 4(x - 3)(x + 4)
Calculating the surface areasFor figure (8), we have
Surface area = 2 *(9 * 4 + 4 * 4 + 9 * 4)
Evaluate
Surface area = 176
Also, we have
Volume = 9 * 4 * 4
Evaluate
Volume = 144
Hence, the surface area is 176 and the volume is 144
Read more about volume at
https://brainly.com/question/463363
#SPJ1
What steps should be taken to calculate the volume of the prism? Select three options. A rectangular prism with a length of 9 and one-half feet, width of 24 feet, and height of 6 feet. Use the formula A = one-half b h to find the area of the base. Use the formula A = b h to find the area of the base. Use the formula V = B h to find the volume of the prism. The volume of the prism, V is (114) (6) = 684 feet cubed. The volume of the prism, V is (228) (6) = 1,368 feet cubed.
The volume of the prism is 1368 cubic feet.
We have,
The three steps that should be taken to calculate the volume of the prism are:
- Use the formula A = b h to find the area of the base, where b is the length of the base and h is the width of the base.
For a rectangular prism, the base is a rectangle, so the formula is:
A = length x width.
- Use the formula V = B h to find the volume of the prism, where B is the area of the base and h is the height of the prism.
For a rectangular prism, the formula.
V = length x width x height.
- Substitute the given values into the formulas and solve for the volume. For the given rectangular prism with a length of 9 and one-half feet, a width of 24 feet, and a height of 6 feet, we can find the volume by using the formula V = B h.
First, we find the area of the base by using the formula:
A = length x width:
A = (9.5 ft) x (24 ft)
= 228 sq ft
Next, we use the formula V = B h to find the volume:
V = (228 sq ft) x (6 ft)
= 1368 cubic feet
Therefore,
The volume of the prism is 1368 cubic feet.
Learn more about Prism here:
https://brainly.com/question/12649592
#SPJ1
Urgent!
Given the following formula, solve for y1.
Formula: m = y²- y¹/ x² - x¹
After considering all the given options we conclude that the value of the given formula is y₁ = y₂ - m(x₂ - x₁) which is Option C.
To evaluate for y₁ in the equation m = (y₂ - y₁) / (x₂ - x₁), we can apply algebraic manipulation to isolate y₁.
In the first step, we multiply both sides of the equation by (x₂ - x₁) to eliminate the denominator. Therefore,
m(x₂ - x₁) = y₂ - y₁
In the second step, we can subtract y₂ from both sides of the equation to isolate y₁.
Therefore,
y₁ = y₂ - m(x₂ - x₁)
So, the solution for y₁ is given by the formula:
y₁ = y₂ - m(x₂ - x₁)
To learn more about algebraic manipulation
https://brainly.com/question/20998576
#SPJ1
the equation of a straight line L1 is given as 3x plus 2y is equal to 12. Another line L2 is perpendicular to L1 at (2,9).
(a) Find the equation of L2 in the fom y is equal to mx plus c where m and c are constants
(b) Another line L3 is parallel to L1 and passes through point (-4,-1). Find
(i) The equation of L2 in the form ax plus by is equal to c where m and c are intergers
(ii) The x and y intercepts of L3
(iii) The point of intersception between L2 and L3
The equation of line L2 in the form y = mx + c is y = (2/3)x + 23/3. the x-intercept of L3 is -14/3. the y-intercept of L3 is -7. The point of intersection between L2 and L3 is (-88/13, 41/13). The x-intercept of L3 is -14/3.
(a) To find the equation of line L2 perpendicular to line L1, we need to determine the slope of L1 and then use the negative reciprocal of that slope for L2.
Given the equation of line L1: 3x + 2y = 12
Rearrange the equation to isolate y:
2y = -3x + 12
y = (-3/2)x + 6
The slope of L1 is -3/2.
Since L2 is perpendicular to L1, the slope of L2 is the negative reciprocal of -3/2, which is 2/3.
Using the slope-intercept form y = mx + c, where m is the slope and c is the y-intercept, we can write the equation of L2:
y = (2/3)x + c
To find c, we substitute the coordinates of the point (2,9) into the equation:
9 = (2/3)(2) + c
9 = 4/3 + c
c = 9 - 4/3
c = 27/3 - 4/3
c = 23/3
Therefore, the equation of line L2 in the form y = mx + c is:
y = (2/3)x + 23/3
(b)(i) To find the equation of line L3 parallel to line L1, we can use the same slope as L1, which is -3/2, and substitute the given point (-4,-1) into the point-slope form y - y1 = m(x - x1):
y - (-1) = (-3/2)(x - (-4))
y + 1 = (-3/2)(x + 4)
y + 1 = (-3/2)x - 6
y = (-3/2)x - 7
Therefore, the equation of line L3 in the form ax + by = c is:
(3/2)x + y = -7
(ii) To find the x-intercept of L3, we set y = 0 and solve for x:
0 = (-3/2)x - 7
(3/2)x = -7
x = (-7)(2/3)
x = -14/3
Therefore, the x-intercept of L3 is -14/3.
To find the y-intercept of L3, we set x = 0 and solve for y:
y = (-3/2)(0) - 7
y = -7
Therefore, the y-intercept of L3 is -7.
(iii) To find the point of intersection between L2 and L3, we can set the equations of L2 and L3 equal to each other and solve for x and y:
(2/3)x + 23/3 = (-3/2)x - 7
To solve for x:
Multiply both sides by 6 to eliminate the fractions:
4x + 46 = -9x - 42
4x + 9x = -42 - 46
13x = -88
x = -88/13
Substitute the value of x back into either equation to solve for y:
y = (2/3)(-88/13) + 23/3
y = -176/39 + 299/39
y = 123/39
y = 41/13
Therefore, the point of intersection between L2 and L3 is (-88/13, 41/13).
For more such questions on intersection , Visit:
https://brainly.com/question/30429663
#SPJ11
HELP PLEASE I NEED HELP
Answer:
2nd choice. -a^3 - 8ab^2
Step-by-step explanation:
(3a^3b - 4ab^2 + 5ab) - (4a^3b + 4ab^2 + 5ab)
Distribute the minus sign and take out the parenthesis.
3a^3b - 4ab^2 + 5ab - 4a^3b - 4ab^2 - 5ab
Combine like terms.
3a^3b - 4ab^2 -4ab^2 - 4ab^2 + 5ab - 5ab
-1a^3b - 8ab^2
Directions: Solve the following. Show your solution.
1. Diane has clay in a can. Its radius is 6 cm while its height is 10 cm. She wanted to transfer some of her clay to her cone-shaped container. What is the volume of the cone to be filled up if it has the same radius and height with
Pls do it with a solution
the volume of the cone to be filled up if it has the same radius and height with is 376. 6 cm³
How to determine the volumeTo determine the volume, we need to know the formula for the volume of a cone.
The formula for the volume of a cone is expressed as;
V = πr²h/3
Such that the parameters are expressed as;
V is the volume of the coner is the radius of the coneh is the height of the coneSubstitute the values, we have;
Volume = 3.14 × 6² × 10/3
Find the square value
Multiply the value, we have;
Volume = 1130. 4/3
Divide the values
Volume = 376. 6 cm³
Learn about volume at: https://brainly.com/question/27710307
#SPJ1
