Solve the simultaneous equations
5x + 6y = 37
2x + 3y = 4
Answer:
(29, -18)
Step-by-step explanation:
Comment if you need an explanation! I Hope This Helps!
Consider the equation -3*e^5w=-88
solve for the equation w. express the solution as log in base e
Answer: The solution for w, expressed as a natural logarithm, is:
w = ln(88/3) / 5
Step-by-step explanation: Starting with the given equation:
-3e^(5w) = -88
Dividing both sides by -3:
e^(5w) = 88/3
Taking the natural logarithm of both sides:
ln(e^(5w)) = ln(88/3)
Using the property that ln(e^x) = x:
5w = ln(88/3)
Finally, solving for w by dividing both sides by 5:
w = (1/5)ln(88/3)
So the solution for w, expressed as a natural logarithm, is:
w = ln(88/3) / 5
what is 3c2+ 2c- 16?
factoring
In the given question, we have to factorise the equation:
3c² + 2c - 16Therefore, by using the middle term splitting method:
This method is used in equations which are in the form of ax² + bx + c. Here, we split the middle term into two terms which on multiplying gives ac and on adding or subtracting gives bx .➙ 3c² + 2c -16
➙ 3c² - 6c + 8c - 16
➙ ( 3c² - 6c )+ (8c - 16 )
➙ 3c( c - 2 ) + 8 ( c - 2 )
➙ ( c - 2 ) ( 3c + 8 )
Factorisation of a quadratic polynomial of the type ax² + bx + c where (a ≠ 1) .
To factorise ax² + bx + c, we have to find two numbers whose sum is equal to the coefficient of x and product is equal to the coefficient of x² and constant term.Consider the factorisation of 3c² + 2c – 16 .
We have to find two numbers whose sum is +2 and product (3 × 16) = 48 .
Obviously, the two numbers are 6 and 8 .
\({ \qquad \sf { \dashrightarrow{ 3c {}^{2} + 2c - 16 }}}\)
So, We can write it as,
\({ \qquad \sf { \dashrightarrow{ 3c {}^{2} + 8c - 6c - 16 }}}\)
\({ \qquad \sf { \dashrightarrow{ c (3c + 8) -2 (3c + 8) }}}\)
\({ \qquad \sf { \dashrightarrow{ ( c -2 )(3c + 8) }}}\)
Please help me!!!!! THIS IS LATE NEED HELP!!!! Just a head's up the graph x and y axis goes by 2 not 1.
Find two points from this graph and then determine the slope.
Tim shows his work To answer a subtraction problem. Tell how to find an equation to represent the problem Tim starts with and its answer. 863+7=870 870+30=900 900+55=955
As you can see, we turned the fraction 10100 into its decimal representation, 0.1, in a single simple computation.
what is fraction?Any number of equal portions, or parts of a whole, are described by fractions. Fractions in standard English indicate the number of pieces of a specific size. 8, 3/4 of .Part of an entire is a fraction. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. When a fraction is true, its numerator is smaller than its denominator.
With 100 as the denominator, decimal fractions in the hundredth place are written. We shall discover how each square is split into 100 equal sections in this section. A tenth is a portion that is just partially shaded. The fraction is expressed as 1/100 in decimal form.
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list five vectors in span {bold v 1v1,bold v 2v2}. do not make a sketch.
Below is the picture attached for the five vectors in span {bold v1 v1, bold v2 v2}.
How do you find the number of vectors in a span?Given a subspace S, every basis of S contains the same number of vectors; this number is the dimension of the subspace. To find a basis for the span of a set of vectors, write the vectors as rows of a matrix and then row reduce the matrix. The span of the rows of a matrix is called the row space of the matrix.
What is the span of 3 vectors?Then any linear combination of all three vectors is also a linear combination of the first two, so the span of all three is the same as the span of the first two, i.e. it is the set of all vectors in the plane. Case 3: no plane contains all three vectors. (So the vectors are all 3-space vectors.)
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Financial mathematics (see picture)
Answer:
i think it's the answer in the pic I have send you okk see and mark me brainliest answer okk thanks
the value of X and the relationship between the angles
Answer:
they are corresponding angles, x=7
Step-by-step explanation:
75=11x-2
77=11x
x=7
John invested $30000 in the bank for 4 years. At the end of the period, he had
$42520. Calculate
a. the interest earned
b. the rate per annum at which simple interest was earned to 1 decimal place.
Answer:
Rate = 10.4%
Step-by-step explanation:
Given :
P = $30000
A = $42520
Interest earned = 42520 - 30000 = $12520
Time = 4years
Find R
\(Interest = \frac{PRT}{100}\)
\(12520 = \frac{30000 \times R \times 4}{100}\\\\12520 = 300 \times 4 \times R\\\\12520 = 1200 \times R\\\\R = \frac{12520}{1200}\\\\R = 10.43 \%\)
Round to 1 decimal place, Rate = 10.4%
Karissa made a giant circular sugar cookie for dessert. she wants to frost it. the cookie has a 14 inch diameter. how many square inches of frosting are needed to cover the entire top of the cookie? hint-it's either area or circumference. use 3.14 for pi
Karissa will need 153.86 square inches of frosting to cover the entire top of the cookie.
To determine the amount of frosting needed to cover the entire top of the giant circular sugar cookie, we need to calculate the area of the cookie. The area of a circle can be found using the formula:
Area = π * r²
Given that the cookie has a diameter of 14 inches, we can calculate the radius (r) by dividing the diameter by 2:
Radius (r) = 14 inches / 2 = 7 inches
Substituting the value of the radius into the area formula:
Area = 3.14 * (7 inches)²
= 3.14 * 49 square inches
= 153.86 square inches
Therefore, 153.86 square inches of frosting are needed to cover the entire top of the cookie.
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4. Is there a variable factor common to 24a and 6?
Answer:
There is no variable factor common to 24a and 6
Step-by-step explanation:
First number = 24a
Other number = 6
Pime factorisation of 24a = 2×2×3×2×a
Pime factorisation of 6= 3×2
Common factors = 6
Hence, there is no variable factor common to 24a and 6, Other common factor is 6.
If andy pays 450 of the rent and mo pays 1/2 of the rent and charlie pays 25percent of the rent what is the overall rent
Answer:
$1,800
Step-by-step explanation:
If Mo pays 1/2 of the rent then he is paying 50%. Charlie is paying another 25%. This leaves the remaining 25% that Andy pays. Since Andy's payment amount is 450 then that means that 450 is equal to 25% of the total rent. Therefore, we simply need to multiply this amount by 4 to get the 100% of the overall rent.
450 * 4 = $1,800
Finally, we can see that the total rent amount is $1,800
a unit of measurement equal to one thousand meters is_____
A unit of measurement which is equal to one thousands meters is known as one kilometers.
Different units of measurements are meters , kilometers, centimeters, millimeters and so on.Measuring small length basically we use centimeters and very small length in millimeters.Measuring medium length we use unit known as meters.When we have measure long distance unit which is used is known as kilometers.Relation between different units of length are:1centimeters is equal to 10 millimeters1 meter is equal to 100 centimeters1 kilometers is equal to 1000 metersTherefore, the given units of measurement equal to one thousand meters is called one - kilometers.
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During 2021, equipment was sold for $470000. The equipment cost $782000 and had a book value of $439000. Accumulated Depreciation—Equipment was $2062000 at 12/31/20 and $2211000 at 12/31/21. Depreciation expense for 2021 was:
Answer:
$149,000
Step-by-step explanation:
Subtract acc depreciation for 2020 from acc deprecitation in 2021 and it gives you the depreciation expense solely for 2021.
The Equipment was purchased during 2021 at $1,402,000.
What is Accumulated Depreciation?The total amount of depreciation applied to an asset up to a particular point is known as accumulated depreciation. The beginning cumulative depreciation balance is increased with each period's depreciation expense.
Given:
Equipment purchased during 2021
= Cost of equipment on 12/31/2021 - (Cost of equipment on 12/31/2020 - Cost of equipment sold)
= $2211000 - ( $2062000 - $470000)
= $2211000 - 15,92,000
= $6,19,000
Hence, the Equipment purchased during 2021 at $1,402,000.
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At which root does the graph of f x x 5 3 * x 2 2 touch the X axis?
The root of the graph of f(x) =(x - 5)3(x + 2)2 touches the x-axis at -2,5
(x - 5)^3 has a power of 3 which is an ODD number. An ODD power means that the graph will cross through the x-axis.
(x + 2)^2 has a power of 2 which is an EVEN number. An EVEN power means that the graph will touch the x-axis.
Given: Function f(x) is (x - 5)3(x + 2)2
If a curve touches the x-axis then f(x) = 0
⇒ (x - 5)3(x + 2)2 = 0.
But if ab = 0 ⇒ either a = 0 or b = 0 or both zero.
⇒ (x - 5)3 = 0 and (x + 2)2 = 0
⇒ (x - 5) = 0 and x + 2 = 0
⇒ x = 5 and x = - 2.
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A middle school took all of its 6th grade students on a field trip to see a play at a theater that has 3100 seats. The students left 1395 seats vacant. What percentage of the seats in the theater were filled by the 6th graders on the trip?
Answer: 55% of the seats in the theater were filled by the 6th graders on the trip.
Step-by-step explanation:
Given: Total seats = 3100
Seats vacant= 1395
Seats occupied by 6th graders = 3100-1395 = 1705
The percentage of the seats in the theater were filled by the 6th graders on the trip = \(\dfrac{\text{Seats occupied by 6th graders}}{\text{Total seats}}\times100\)
\(=\dfrac{1705}{3100}\times100\\\\= 55\%\)
Hence, 55% of the seats in the theater were filled by the 6th graders on the trip.
Prove that
1/(sec x - 1) + 1/(sec x + 1) is equal to
2cos x × cosec^2 x
Answer:
Step-by-step explanation:
\(1+tan^2\theta=sec^2\theta\\tan^2\theta=sec^2\theta -1 \\tan^2\theta=(sec\theta-1)(sec\theta+1)\\\implies \frac{1}{sec\theta-1} =\frac{sec\theta+1}{tan^2\theta} \\\\and \quad \frac{1}{sec\theta+1} =\frac{sec\theta-1}{tan^2\theta} \\\\ \frac{1}{sec\theta-1} + \frac{1}{sec\theta+1} = \frac{sec\theta+1}{tan^2\theta} + \frac{sec\theta-1}{tan^2\theta}\\\\=\dfrac{2sec\theta}{tan^2\theta}\\\\=\dfrac{2cos^2\theta}{cos\theta.sin^2\theta}\\\\\\=2cos\theta.cosec^2\theta\)
a trapezoid is a quadrilateral with exactly one pair of parallel sides. true or false?
it is going to be true
The first few steps in solving the quadratic equation 9x2 49x = 22 â’ 5x by completing the square are shown. 9x2 49x = 22 â’ 5x 9x2 54x = 22 9(x2 6x) = 22 Which is the best step to do next to solve the equation by completing the square? 9(x2 6x 3) = 25 9(x2 6x 3) = 49 9(x2 6x 9) = 31 9(x2 6x 9) = 103.
The best step to do next to solve the equation by completing the square is 9(x^2 + 6x+9) = 31
Given the quadratic equation given as 9x^2 + 49x = 22 - 5x. To solve using the completing the square method, we will follow the steps;
Step 1: Given
9x^2 + 49x = 22 - 5xStep 2: Add 5x to both sides of the equation:
9x^2 + 49x + 5x = 22 - 5x + 5x9x^2 + 54x = 22Step 3: Factor out 9 from the expression to have:
9(x^2 + 6x) = 22Step 4: Complete the square of the expression in parenthesis.
Add half of the square of the coefficient of x to both sides:
9(x^2 + 6x + (6/2)^2) = 22 + (6/2)^2
9(x^2 + 6x+ 3^2) = 22 + 3^2
9(x^2 + 6x+9) = 22+9
9(x^2 + 6x+9) = 31
Hence the best step to do next to solve the equation by completing the square is 9(x^2 + 6x+9) = 31
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Answer:
The first few steps in solving the quadratic equation 9x2 + 49x = 22 − 5x by completing the square are shown.
9x2 + 49x = 22 − 5x
9x2 + 54x = 22
9(x2 + 6x) = 22
Which is the best step to do next to solve the equation by completing the square?
❌ 9(x2 + 6x + 3) = 25
❌ 9(x2 + 6x + 3) = 49
❌ 9(x2 + 6x + 9) = 31
✔️ 9(x2 + 6x + 9) = 103
There are 5 white balls,8 red balls ,7 yellow balls and 4 green balls in a container a ball is choosen at random.what is the probabilty of chooseing neither white or green? .
15/19 + 14/19 = 29/19
Step-by-step explanation:
Add the number of balls in the basket together.
Subtract the number of white balls from the sample space ( the total amount of balls) your answer is written over the sample space and the same process is done for the green ball
A store I selling all toaster ovens at 15% off. Write an equation in the form y=kx
The graph of f(x) and g(x) are shown below. How many solutions does the system of equations have?
Click pic to see whole problem
Answer:
Step-by-step explanation:
Solving systems of equations gives the points of intersection when the equations are graphed.
The answer is 3.
it takes 32 hours for a motorboat to go downriver to get from pier a to pier b. the return journey takes 48 hours. how long does it take an unpowered raft to travel the same distance?
It takes the unpowered raft 192 hours to travel the same distance between Pier A and Pier B.
Let's assume the distance between Pier A and Pier B is D.
When the motorboat is going downstream, it benefits from the current, so its effective speed is increased.
Let's say the speed of the motorboat in still water is S.
The speed of the current is C.
Therefore, the motorboat's speed downstream is S + C.
When the motorboat is going upstream, it has to overcome the current, so its effective speed is decreased.
The speed of the motorboat upstream is S - C.
We are given that the motorboat takes 32 hours to go downstream and 48 hours to return upstream.
Downstream speed: S + C
Downstream time: 32 hours
Distance = Speed × Time
D = (S + C) × 32
Upstream speed: S - C
Upstream time: 48 hours
D = (S - C) × 48
Since the distance (D) is the same in both cases, we can equate the two equations:
(S + C) × 32 = (S - C) × 48
32S + 32C = 48S - 48C
16S = 80C
S = 5C
We know that the raft is unpowered, so its speed is equal to the speed of the current (C).
Therefore, the speed of the unpowered raft is C.
Time = Distance / Speed
Time = D / C
Since D = (S + C) × 32
we can substitute the value of S:
Time = [(5C) + C] × 32 / C
Time = 6C × 32 / C
Time = 192
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what is a better estimate for mass of a text book 1 gram or 1 kilogram
Answer:
One kilogram.
Step-by-step explanation:
Things that are one gram include a paper clip and a raisin, meaning that one kilogram would make much more sense. Hope this helps! :)
18x2 - 200
Whats the answer
the demand curve for hummus has a constant slope of -2. what can you say about the price elasticity of demand for hummus with this information?
Based on the given information that the demand curve for hummus has a constant slope of -2, we can say that the price elasticity of demand for hummus is relatively elastic. This means that a small change in price will result in a relatively larger change in the quantity demanded of hummus.
In other words, consumers are sensitive to changes in the price of hummus and are likely to reduce their consumption if the price increases, and vice versa.
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The price elasticity of demand for hummus cannot be determined solely from the information provided, as it depends on both the slope and the price-quantity relationship.
The price elasticity of demand (Ed) is a measure of how responsive the quantity demanded of a good is to a change in its price. It is calculated using the formula:
Ed = (% change in quantity demanded) / (% change in price)
Since the demand curve for hummus has a constant slope of -2, this tells us that for every unit increase in price, the quantity demanded decreases by 2 units. However, to calculate the price elasticity of demand, we also need information about the price and quantity levels.
The slope of the demand curve alone does not provide enough information to determine the price elasticity of demand. The elasticity varies along the curve, being more elastic at high prices and low quantities, and less elastic at low prices and high quantities.
While the slope of the demand curve for hummus is -2, this information alone is not sufficient to determine the price elasticity of demand. Additional information about the price and quantity levels is needed to calculate the elasticity accurately.
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Can someone explain simple interest for me I don’t get it
Answer:
Step-by-step explanation:
Interest is a percentage of an original amount that is added to the original amount. The percentage is called the interest rate. It is usually given as an interest rate per year.
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Example 1:
Question: You invest $100 for 1 year at an interest rate of 5% per year. How much is your investment worth after 1 year?
Answer:
The interest earned in 1 year is 5% of $100.
5% of $100 = 0.05 × $100 = $5
The actual amount of the interest earned in 1 year is $5.
Now you add the $5 to the original $100, and at the end of 1 year, you have $105.
************************************************************************************
What happens if your money stays invested for more than 1 year? If it is invested with simple interest rate, then the interest you earn for 2 years, or 3 years is just 2 or 3 times the interest you would have earned for 1 year.
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Example 2:
Question: You invest $500 for 3 years at an interest rate of 4% per year. How much is your investment worth after 3 years?
Answer:
The interest earned in 1 year is 4% of $500, so the investment earned in 3 years is 3 × 4% × $500.
3 × 4% of $500 = 3 × 0.04 × $500 = $60
The actual amount of the interest earned in 3 years is $60.
Now you add the $60 to the original $500, and at the end of 3 years, you have $560.
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The formula for simple interest is
I = Prt,
where P = the principal amount, the amount invested
r = annual interest rate usually given as a percent (convert to decimal to use in the formula)
t = number of years
Once you find the amount of interest, I in the formula above, you add that to P, the amount invested, to find the total amount the investment is worth after t years.
The important thing to remember about simple interest is that simple interest is earned only on the principal mount, the amount that was invested.
Compound interest is interest that is earned on the principal and on the accumulated interest.
Let's look again at our examples above, but now we use the simple interest formula to answer the questions.
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Example 1 (using simple interest formula):
Question: You invest $100 for 1 year at an interest rate of 5% per year. How much is your investment worth after 1 year?
Answer:
I = Prt = $100 × 0.05 × 1 = $5
total value = $100 + $5 = $105
************************************************************************************
Example 2 (using simple interest formula):
Question: You invest $500 for 3 years at an interest rate of 4% per year. How much is your investment worth after 3 years?
Answer:
I = Prt = $500 × 0.04 × 3 = $60
total value = $500 + $60 = $560
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how many days are in 3 weeks??
Answer:
21
Step-by-step explanation:
because 7 day or in a week so 7 time 3 = 21
Answer:
21
Step-by-step explanation:
Becasue there are 7 days in a week, So use and time 7x3 and you will get 21 multiplication.
Need help ASAP !!! And show work please
Answer:
\(\sqrt{40}\) or 6.32
Step-by-step explanation:
We can find the distance between two points by using this formula
\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
where the x and y values are derived from the given points
The points given are ( -2 , 5 ) and ( 4 , 3 )
So we plug in the x and y values of those coordinates into the distance formula
\(\sqrt{(4-(-2)^2+(3-5)^2} \\4-(-2)=6\\3-5=-2\\d=\sqrt{6^2+-2^2} \\6^2=36\\-2^2=4\\36+4=40\\d=\sqrt{40}\)
or 6.32
What is the area of δabc? round to the nearest tenth of a square unit. 3.9 square units 8.4 square units 11.8 square units 17.7 square units
The triangle ABC has a surface area of 17.7 square units. Rounding to the nearest tenth of a square unit,
Heron's Formula can be used to calculate the triangle ABC's area. The equation reads as follows:
A = √[s(s-a)(s-b)(s-c)]
Where s is one-half of the triangle's circumference and a, b, and c are its three sides.
By summing the triangle's sides, we can determine the perimeter:
P = a + b + c
The formula below is used to get the other half of the perimeter.
s = P/2
For the triangle ABC, we have the sides a=3, b=5, and c=4.
Therefore, half of the perimeter is s = 8.
Now, Heron's formula can be used to determine the triangle ABC's surface area:
A = √[s(s-a)(s-b)(s-c)]
= √[8(8-3)(8-5)(8-4)]
= √[8(5)(3)(4)]
= 17.7 square units
Therefore, the triangle ABC has a surface area of 17.7 square units, Rounding to the nearest tenth of a square unit.
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