Please use system of linear equations by elimination OR substitution. I need the work as well please.

Answer:

\(7-8x+4y=-21\)

Step-by-step explanation:

\(2x-y=7 \implies 8x-4y=28 \\ \\ \implies 7-8x+4y=7-28=-21\)

To find the linear equation of T in terms of x and the temperature of the water at time x = 0, we can use the given information and apply the formula for the equation of a line.

Given:

Time (x) = 3 minutes, Temperature (T) = 48°C

Time (x) = 10 minutes, Temperature (T) = 76°C

To find the slope (m), we can use the formula:

m = (change in y) / (change in x) = (76 - 48) / (10 - 3) = 28 / 7 = 4

Now that we have the slope, we can find the y-intercept (b) by substituting the values of one of the points into the equation:

48 = 4(3) + b

48 = 12 + b

b = 48 - 12 = 36

So, the linear equation of T in terms of x is:

T = 4x + 36

To find the temperature of the water at time x = 0 (initial temperature), we substitute x = 0 into the equation:

T = 4(0) + 36

T = 0 + 36

T = 36

Therefore, the linear equation of T in terms of x is T = 4x + 36, and the temperature of the water at time x = 0 is 36°C.

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Answer:

f > -1

Step-by-step explanation:

I hope this helps!

Answer:

see explanation

Step-by-step explanation:

(a)

calculate the lengths using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = J (- 3, - 7 ) and (x₂, y₂ ) = K (3, - 8 )

JK = \(\sqrt{(3-(-3))^2+(-8-(-7))^2}\)

    = \(\sqrt{(3+3)^2+(-8+7)^2}\)

    = \(\sqrt{6^2+(-1)^2}\)

    = \(\sqrt{36+1}\)

    = \(\sqrt{37}\)

repeat with (x₁, y₁ ) = M (8, 3 ) and (x₂, y₂ ) = N (7, - 3 )

MN = \(\sqrt{(7-8)^2+(-3-3)^2}\)

      = \(\sqrt{(-1)^2+(-6)^2}\)

     = \(\sqrt{1+36}\)

     = \(\sqrt{37}\)

repeat with (x₁, y₁ ) = P (- 8, 1 ) and (x₂, y₂ ) = Q (- 2, 2 )

PQ = \(\sqrt{-2-(-8))^2+(2-1)^2}\)

      = \(\sqrt{(-2+8)^2+1^2}\)

      = \(\sqrt{6^2+1}\)

      = \(\sqrt{36+1}\)

      = \(\sqrt{37}\)

(b)

JK ≅ MN ← true

JK ≅ PQ ← true

MN ≅ PQ ← true

Answer:

Step-by-step explanation:

It's x=7.1 plus 22

Answer:

Center: (−2,−1)

Step-by-step explanation:

( use math

way )

10 miles per hour is the average journey speed.

Given that,

Some pupils choose to ride bikes. They move at a 15 mph average speed for the first two hours, and then they stop for lunch for an hour. The pupils ride at a 10 mph speed for an additional hour.

Average speed is ( total distance ) / ( total time )

During the 1st 2 hrs:

distance = speed * time

distance = 15 *2 = 30 miles

During the last hour:

distance = speed * time

distance = 10 *1 = 10 miles

Average speed = 30+10 / 2+1+1 = 40/4 = 10 mil/hr

Therefore, their average speed for the trip is 10 mil/hr

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The format options for basic question responses are as follows: a) two, five, ten; b) two, three, six; c) three, two, six; and d) two, two, four. These format options provide flexibility in constructing questions with varying numbers of response choices, allowing for different levels of complexity or variation in the questions asked.

The given format options represent variations in the number of choices or options for basic question responses. Let's break down each option:

a) Two, five, ten: This format implies that there are two possible choices or options in the question, followed by five options, and finally, ten options.

b) Two, three, six: This format suggests that the question has two choices or options, followed by three options, and finally, six options.

c) Three, two, six: This format indicates that the question has three choices or options, followed by two options, and finally, six options.

d) Two, two, four: This format suggests that there are two choices or options in the question, followed by two options, and finally, four options.

These format options provide flexibility in constructing questions with varying numbers of response choices, allowing for different levels of complexity or variation in the questions asked.

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If the production of wood tables on an assembly line increases from 1600 tables per shift to 2000 tables per shift, the labor productivity will increase by 25%.We need to determine the percentage change.

To calculate the increase in labor productivity, we need to compare the difference in production levels and determine the percentage change.The initial production level is 1600 tables per shift, and the increased production level is 2000 tables per shift. The difference in production is 2000 - 1600 = 400 tables.

To calculate the percentage change, we divide the difference by the initial production and multiply by 100:

Percentage Change = (Difference / Initial Production) * 100 = (400 / 1600) * 100 = 25%.

Therefore, the correct answer is option C) 25%, indicating that labor productivity will increase by 25% when the production is increased to 2000 tables per shift.

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The algebraic proof for the given statement. (A − B) ∪ (A ∩ B) = A

we will use the below conditions

Let A and B be the two sets

Distributive property:-

i) A U (B ∩ C) =( AUB)∩(AUC)

ii) A ∩ (BUC) = (A ∩ B) U (A ∩ C)

we will use another condition also iii)  A-B =A ∩ B¹

now Given (A − B) ∪ (A ∩ B) = (A ∩ B¹) ∪ (A ∩ B) ( from (iii)

                                            = A ∩ (BUB¹)   ( from (ii)

                                            = A ∩ U

                                            = A

(A − B) ∪ (A ∩ B) = A

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Answer:

Krutika gets 32 sweets

Step-by-step explanation:

Let the number of sweets be x

Bridget= 5x sweets

Jim= 2x sweets

Krutika= 4x sweets

5x= 40; x= 40/5; x=8

Krutika gets 4x= 4×8

Krutika gets 32 sweets

Answer:

Step-by-step explanation:

3.2

Answer:

3.2

Step-by-step explanation:

jdjdhdidndidnnidndindinidnndindnd

Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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Answer:

504 in cubed

Step-by-step explanation:

I am assuming this is a rectangular prism, since you did not show a picture.

l x w x h

14 x 4 x 9

14 x 36

504

The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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Combining the above results, we have shown that the direct image f([a, b]) of a continuous function f : [a, b] → R is a closed and bounded interval or a single number.

To prove that the direct image f([a, b]) of a continuous function f : [a, b] → R is a closed and bounded interval or a single number, we need to show two things:

The direct image f([a, b]) is a closed set.

The direct image f([a, b]) is a bounded set.

Let's prove each of these statements:

The direct image f([a, b]) is a closed set:

To show that f([a, b]) is closed, we need to prove that it contains all its limit points.

Let y be a limit point of f([a, b]). This means that there exists a sequence (yₙ) in f([a, b]) such that yₙ → y as n approaches infinity.

Since (yₙ) is a sequence in f([a, b]), there exists a sequence (xₙ) in [a, b] such that f(xₙ) = yₙ.

Since [a, b] is a closed and bounded interval, the sequence (xₙ) has a subsequence (xₙₖ) that converges to some x ∈ [a, b] (by the Bolzano-Weierstrass theorem).

Since f is continuous, we have f(xₙₖ) → f(x) as k approaches infinity. But f(xₙₖ) = yₙₖ, and since yₙₖ → y, we have f(xₙₖ) → y as k approaches infinity.

Therefore, we have shown that for any limit point y of f([a, b]), there exists a corresponding point x in [a, b] such that f(x) = y. Hence, y is in f([a, b]), and f([a, b]) contains all its limit points. Thus, f([a, b]) is a closed set.

The direct image f([a, b]) is a bounded set:

Since [a, b] is a closed and bounded interval, the continuous function f([a, b]) is also bounded by the Extreme Value Theorem. In other words, there exist M, m ∈ R such that for all x ∈ [a, b], m ≤ f(x) ≤ M.

Therefore, f([a, b]) is a bounded set.

Therefore, Combining the above results, we have shown that the direct image f([a, b]) of a continuous function f : [a, b] → R is a closed and bounded interval or a single number.

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Incomplete question:

Suppose that f : [a, b] → R is a continuous function. Prove that the direct image f ([a, b]) is a closed and bounded interval or a single number.

Step-by-step explanation:

\(m + 148 = 3m + 10\)

\(148 - 10 = 3m - m\)

therefore

3m = 138

m = 138/3

m = 46°

pls give brainliest

if the installment option is used, the total amount paid over the 240-month term would be $1,080,000. This includes both the principal amount of $550,000 and the interest accumulated over the repayment period.

To determine the total amount if the installment option is used, we need to calculate the total repayment over the 240-month term.

The installment amount per month is $4,500, and the repayment term is 240 months.

Total repayment = Installment amount per month * Repayment term

Total repayment = $4,500 * 240

Total repayment = $1,080,000

Therefore, if the installment option is used, the total amount paid over the 240-month term would be $1,080,000. This includes both the principal amount of $550,000 and the interest accumulated over the repayment period.

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Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

Given  ∫(2x+1)(x−1)dx , We can use the distribution property of multiplication to get \[\int{2x(x-1)}dx+\int{1(x-1)}dx\] We can use distributive property , where C is a constant of integration.

We can use the distribution property of multiplication to get

\(\[\int{2x(x-1)}dx+\int{1(x-1)}dx\]\)

We can use distributive property again to get

\(\[2\int{x^{2}-x}dx+\int{xdx-\int{dx}}\]\) Which is equal to

\(\[2\frac{{{x}^{3}}}{3}-2\frac{{{x}^{2}}}{2}+\frac{{{x}^{2}}}{2}-x+C\]\)

where C is a constant of integration.

Therefore,\(\[\int(2x+1)(x-1)dx=2\frac{{{x}^{3}}}{3}-2\frac{{{x}^{2}}}{2}+\frac{{{x}^{2}}}{2}-x+C\].\)

In conclusion, the indefinite integral of 1+x2/2+x dx is 2(1+x2)1/2 + C and the indefinite integral of (2x+1)(x−1)dx is 2x3/3 - x2 - x + C.

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Answer:

108.5% increase

Explanation:

Find how much payments will cost for 6 months

68.50 × 6 = 411

Add payments to down payment

411 + 240 = 651

Compare:

600 vs 651

Solve for percent increase:

651 ÷ 600 = 1.085

Convert decimal into percentage:

1.085 × 100% = 108.5%

Answer:

x=20  and  x=-50

Step-by-step explanation:

To find the roots, we need to simply solve for x. We do this by first moving all of the terms to the left and setting the right side equal to 0.

-1000

x^2+30x-1000=0

Now, factor it.

What adds up to 30 but multiplies to get -1000?

-10 and 40? No, because they multiply to get -400.

-20 and 50? Yes, because they add up to 30 and multiply to get -1000.

(x-20)(x+50)

x-20=0

x=20

x+50=0

x=-50

So, the roots are x=20 and x=-50

Given :-

To Find :-

Solution :-

As we know that if the quadratic equation is in standard form which is ,

\( ax^2+bx + c =0\)

Then its roots are given by ,

\( x =\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\)

So on converting the equation in standard form ,

\( x^2+30x -1000=0\)

With respect to the standard form ,

Substitute in the Quadratic formula ,

\( x =\dfrac{-30\pm \sqrt{(30)^2-4(1)(-1000)}}{2(1)}\)

Simplify,

\( x =\dfrac{-30\pm\sqrt{900+4000}}{2}\)

Add the numbers inside square root ,

\( x =\dfrac{-30\pm\sqrt{4900}}{2}\)

Divide each term in numerator by 2,

\( x =\dfrac{-30}{2}\pm\dfrac{\sqrt{70^2}}{2}\)

Simplify ,

\( x = -15 \pm 35 \)

Separate the two solutions ,

\( x = -15 + 35 , -15 -35\)

Simplify ,

\(x = 20 , -50 \)

Hence the solution of the equation are 20 and -50 .

I hope this helps.

The Simplified value of the "algebraic-expression" (12x³y² - 18xy)/6xy is 2x²y - 3.

An "Algebraic-Expression" represents a combination of numbers, variables, and arithmetic operations such as addition, subtraction, multiplication, and division, that represents a mathematical relationship or rule.

To simplify the expression, (12x³y² - 18xy)/6xy,  we factor out a common factor of "6xy" from the numerator;

We get,

⇒ (12x³y² - 18xy)/6xy = 6xy(2x²y - 3)/6xy,

The 6xy in the numerator and denominator cancel out,

We get,

⇒ 2x²y - 3

Therefore, the simplified expression is 2x²y - 3.

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The given question is incomplete, the complete question is

Simplify and evaluate the given algebraic expression

(12x³y² - 18xy)/6xy.

Answer:

475 students, 125 adults

Step-by-step explanation:

x + y= 600......equation 1

5x +9y= 3500.......equation 2

From equation 1

x +y = 600

x= 600-y

Substitute 600-y for x in equation 2

5(600-y) +9y= 3500

3000-5y+9y= 3500

3000+4y= 3500

4y= 3500-3000

4y= 500

y= 500/4

y= 125

Substitute 125 for y in equation 1

x + y= 600

x + 125= 600

x = 600-125

x= 475

Hence there are 475 students and 125 adults

Answer:

Step-by-step explanation:

Firstline = 33%

Second line = 36%

Answer:

Firstline = 33%

Second line = 36%

Step-by-step explanation:

We have proved that AE ≅ BD using the given information about the triangle ABC.

A triangle is a closed, two-dimensional shape with three straight sides and three angles that add up to 180 degrees. It is one of the fundamental shapes in geometry and has many applications in mathematics and real-world situations.

We are given a triangle ABC with AE and DB as the angle bisectors, AC ≅ BC, and ∠CAE ≅ ∠CBD. Our goal is to prove that AE ≅ BD.

Firstly, by the given information, we know that triangles ACE and BCD are congruent by the angle-side-angle (ASA) postulate.

Since corresponding parts of congruent triangles are congruent (CPCTC), we can conclude that AE ≅ BD.

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The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

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Answer:

eh its 12 because

Step-by-step explanation:

according to my calculations if there are 16 females therefore the ratio is 3 to 4 men to women 3x4=12 and 4x4=16 so the answer is 12

i might be wrong please let me know

Answer:

B

Step-by-step explanation:

Remark

If we draw a line from F to T, we can make a couple of statements.

Call the center of the circle O

1. <FTE = 1/2 the central angle of <FOE. The size of <FOE is the same size as the minor arc. Since The minor arc = 60 degrees, then FTE = 30 degrees.

2. <GTF = 1/2 78 by the same reasoning used above.  GTF = 39 because that is 1/2 of 78.

So the answer to the size of <T = 39 + 30 = 69 which is B

There is a much simpler way of doing this.

The central angle of the two arcs is 78 + 60 = 138

The <GTE is 1/2 the central angle

<GTE = 1/2 * 138 = 69