write an equation of a line in slope-intercept form through the points (3, -1) and (-2, 14)

Therefore , the solution of the given problem of expression comes out to be √14q × 2√4q = 4q√14.

combinations of numbers, symbols, and operations (such + and) that show how much something is worth. Examples: • 2 + 3 is the formula.

• 3 x/2 variable  is another formula.There is no equals sign in the expression. A mathematical expression is a sentence made up of variables, numbers, or both. There is never an equal symbol in an expression. These expressions are examples. An equation is a mathematical statement proving the equality of two expressions.

Here,

The simplified expressions are 20 = 25, 56x2 = 2x14, [150x3k4] = 5xk26x, and 14q 24q = 4q14 given the facts from the question.

Simplifying the surd

A perfect square must be one of the components for a number to be written as just surds.

How to Make 20 Recall Simpler

20 = 4 × 5

Thus,

√20 = √(4 × 5)

√20 = 2√5

simple methods √(56x²)\s√(56x²) = √56 × √x²

Recall

√56 = √(4 × 14) = 2√14

√x² = x

Thus,

√(56x²) = 2√14 × x

√(56x²) = 2x√14

simple methods [150x3k4] = [150x3k4] = [150x3k4]

Recall

√150 = √(25 × 6) = 5√6

√x³ = √(x² × x) = x√x

√k⁴ = k²

Thus,

√[150x³k⁴] = 5√6 × x√x × k²

√[150x³k⁴] = 5k²x√6x

How to simplify 14q 2 4q: 14q 2 4q = 2

(14q × 4q)

√14q × 2√4q = 2 × 2q√14

√14q × 2√4q = 4q√14

Therefore , the solution of the given problem of eexpression comes out to be √14q × 2√4q = 4q√14.

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Answer:

Surface area = 972 mm^2

Step-by-step explanation:

One of the formula we can use for surface area of a triangular prism is

SA = bh + L(s1 + s2 + s3), where

In the figure, the base (b) is 27 mm, the height (h) is 14 mm, the length (L) is 9 mm, and we can use 18, 27, and 21 for s1, s2, and 23:

SA = 27 * 14 + 9(18 + 27 + 21)

SA = 378 + 9(66)

SA = 378 + 594

SA = 972 mm^2

Thus, the surface area of the figure is 972 mm^2

Answer:

option C and D

Step-by-step explanation:

the two triangles are said to be congruent if their all the three sides as well as the angles between the sides are congruent to one another where the triangles can be drawn in any direction

The required rate of return for DAK Corporation is 12.34%.

What is the required rate?

The minimal profit (return) an investor will seek or expect in exchange for taking on the risk of investing in a stock or other type of security is known as the required rate of return (RRR). RRR can also be used to determine a project's potential profitability in relation to its funding costs.

Here, we have

Given Information

Beta =   1.25

The yield on 30-year T bonds (rf)=     5.65%

Return on S&P (rM) =    11%

Required Return for DAK = rf + Beta*(rM - rf)

= 5.65% + 1.25*(11% - 5.65%)

=  12.34%

Hence,  the required rate of return for DAK Corporation is 12.34%.

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The observed and expected frequencies for the green candies is C. Observed: 93 Expected: 103.6

The number of participants or observations included in a study is referred to as the sample size. Usually, n is used to represent this number. Research results are directly impacted by sample size calculations. Very small sample sizes compromise a study's internal and external validity. Small differences frequently become statistically significant differences in very large samples.

Sample size = 518

The number of green candies observed/counted is = 93

That's an approximated value for 18% of the 518 candies

18/100 × 518 = 93.24 ≅ 93

Note, the symbol ≅ means 'approximately equal to. Since the candy company claims that the distribution of each color is exactly 20%, the expected frequency for green candies is:

20% of 518

= 20/100 × 518

= 103.6

The correct option is C.

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Complete question

Karen recorded the results for a sample of 518 candies.

Color Counts Sample Proportion

(p with hat on top)

Red 130 25%

Yellow 109 21%

Green 93 18%

Orange 114 22%

Purple 72 14%

The candy company claims that the distribution of each color is exactly 20%. Select the observed and expected frequencies for the green candies.

a.) Observed: 103.6 Expected: 93

b.) Observed: 93 Expected: 93.2

c.) Observed: 93 Expected: 103.6

d.) Observed: 72 Expected: 93.2

Answer:

0.3907 I think hope this helps

Answer: 360

Step-by-step explanation:

done

Answer:

17

Step-by-step explanation:

The computation of the number of elements are in (A ∩ B) is shown below;

Given that

Set A contains 35 elements

And, set B contains 22 elements

Now if there are 40 elements in (A ∪ B)

So, the number of elements are in (A ∩ B) is

= 35 + 22 - 40

= 17

Answer:

n = 17-13

Step-by-step explanation:

n+13=17

Subtract 13 from each side

n+13-13 = 17-13

n = 17-13

Let's assume the sum of the scores of the 28 students who took the test yesterday is 28 * 72 = 2016.

We know that the sum of the scores of all 30 students is (28 * 72) + x + y, where x and y are the scores of the two students who took the test this morning.

We also know that the mean of all 30 scores is 73. So we can write an equation:

[(28 * 72) + x + y]/30 = 73

Multiplying both sides by 30, we get:

2016 + x + y = 2190

So, x + y = 174.

We are given that the difference of the two scores is 22, so we can write another equation:

y - x = 22

Solving these two equations simultaneously, we get y = 98 and x = 76.

Therefore, the lower score from this morning is 76.

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Answer:

208

Step-by-step explanation:

4*30 = 120

(15-4) * 8 = 88

88 + 120 = 208

Answer:

208 cm

Step-by-step explanation:

Solving right side first. 8*15=120

Take out 8cm from 30. 30 - 8 = 22

22*4= 88

88 + 120 = 208

Check work I found the total area and the white rectangle.

15*30=450 which in total area

15-4=11 11 is the left/right side of the white rectangle

30-8=22 22 is the top/bottom side of the white rectangle.

22*11= 242

208+242=450

The introduction of harmful chemicals into the air is known as air pollution.

The chief causes of man-made air pollution include vehicle emissions, fuel oils and natural gas used to heat houses, byproducts of manufacturing and electricity generation, notably coal-fueled power plants, and odors from chemical manufacture.Industrial emissions, automobile emissions, and any other place where fossil fuels are burnt are all sources of atmospheric pollution, or air pollution. Another major contaminant that can cause ozone depletion is methane, which is released by landfills and cattle.

Air pollution can have long-term harmful consequences, such as acid rain, which pollutes the Earth’s bodies of water and ruins infrastructure.

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Main Answer:The linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

Supporting Question and Answer:

How can we express a vector as a linear combination of  vectors using a system of equations?

To express a vector as a linear combination of  vectors using a system of equations, we need to find the coefficients that multiply each given vector to obtain the desired vector. This can be done by setting up a system of equations, where each equation corresponds to the components of the vectors involved.

Body of the Solution:

(a) To show that the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3, we need to demonstrate two conditions: orthogonality and linear independence.

u1 · u2 = (2)(-3) + (0)(0) + (3)(2) = -6 + 0 + 6 = 0

u1 · u3 = (2)(0) + (0)(7) + (3)(0) = 0 + 0 + 0 = 0

u2 · u3 = (-3)(0) + (0)(7) + (2)(0) = 0 + 0 + 0 = 0

Since the dot product of every pair of vectors is zero, they are orthogonal.

   2.Linear Independence: We need to show that the vectors u1, u2, and u3 are linearly independent, meaning that no vector can be written as a linear combination of the other vectors.

We can determine linear independence by forming a matrix with the vectors as its columns and performing row operations to check if the matrix can be reduced to the identity matrix.

[A | I] = [u1 | u2 | u3 | I] =

[2 -3 0 | 1 0 0]

[0 0 7 | 0 1 0]

[3 2 0 | 0 0 1]

Performing row operations:

R3 - (3/2)R1 -> R3

R1 <-> R2

[1 0 0 | -3/2 1 0]

[0 1 0 | 0 1 0]

[0 0 7 | 0 0 1]

Since we can obtain the identity matrix on the left side, the vectors u1, u2, and u3 are linearly independent.

Therefore, the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3.

(b) To write v = (1, 2, 3) as a linear combination of u1, u2, and u3, we need to find the coefficients x, y, and z such that:

v = xu1 + yu2 + z*u3

Substituting the given vectors and coefficients:

(1, 2, 3) = x(2, 0, 3) + y(-3, 0, 2) + z(0, 7, 0)

Simplifying the equation component-wise:

1 = 2x - 3y

2 = 7y

3 = 3x + 2y

From the second equation, we can solve for y:

y = 2/7

Substituting y into the first equation:

1 = 2x - 3(2/7)

1 = 2x - 6/7

7 = 14x - 6

14x = 13

x = 13/14

Substituting the found values of x and y into the third equation

3 = 3(13/14) + 2(2/7)

3 = 39/14 + 4/7

3 = 39/14 + 8/14

3 = 47/14

Therefore, we have determined the values of x, y, and z as follows:

x = 13/14

y = 2/7

z = 47/14

Thus, we can write the vector v = (1, 2, 3) as a linear combination of u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) as:

v = (13/14)u1 + (2/7)u2 + (47/14)u3

Therefore, v can be expressed as a linear combination of the given vectors.

Final Answer:Therefore,the linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

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The linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

To express a vector as a linear combination of  vectors using a system of equations, we need to find the coefficients that multiply each given vector to obtain the desired vector. This can be done by setting up a system of equations, where each equation corresponds to the components of the vectors involved.

Body of the Solution:

(a) To show that the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3, we need to demonstrate two conditions: orthogonality and linear independence.

Orthogonality: We need to show that each pair of vectors is orthogonal, meaning their dot product is zero.

u1 · u2 = (2)(-3) + (0)(0) + (3)(2) = -6 + 0 + 6 = 0

u1 · u3 = (2)(0) + (0)(7) + (3)(0) = 0 + 0 + 0 = 0

u2 · u3 = (-3)(0) + (0)(7) + (2)(0) = 0 + 0 + 0 = 0

Since the dot product of every pair of vectors is zero, they are orthogonal.

  2.Linear Independence: We need to show that the vectors u1, u2, and u3 are linearly independent, meaning that no vector can be written as a linear combination of the other vectors.

We can determine linear independence by forming a matrix with the vectors as its columns and performing row operations to check if the matrix can be reduced to the identity matrix.

[A | I] = [u1 | u2 | u3 | I] =

[2 -3 0 | 1 0 0]

[0 0 7 | 0 1 0]

[3 2 0 | 0 0 1]

Performing row operations:

R3 - (3/2)R1 -> R3

R1 <-> R2

[1 0 0 | -3/2 1 0]

[0 1 0 | 0 1 0]

[0 0 7 | 0 0 1]

Since we can obtain the identity matrix on the left side, the vectors u1, u2, and u3 are linearly independent.

Therefore, the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3.

(b) To write v = (1, 2, 3) as a linear combination of u1, u2, and u3, we need to find the coefficients x, y, and z such that:

v = xu1 + yu2 + z*u3

Substituting the given vectors and coefficients:

(1, 2, 3) = x(2, 0, 3) + y(-3, 0, 2) + z(0, 7, 0)

Simplifying the equation component-wise:

1 = 2x - 3y

2 = 7y

3 = 3x + 2y

From the second equation, we can solve for y:

y = 2/7

Substituting y into the first equation:

1 = 2x - 3(2/7)

1 = 2x - 6/7

7 = 14x - 6

14x = 13

x = 13/14

Substituting the found values of x and y into the third equation

3 = 3(13/14) + 2(2/7)

3 = 39/14 + 4/7

3 = 39/14 + 8/14

3 = 47/14

Therefore, we have determined the values of x, y, and z as follows:

x = 13/14

y = 2/7

z = 47/14

Thus, we can write the vector v = (1, 2, 3) as a linear combination of u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) as:

v = (13/14)u1 + (2/7)u2 + (47/14)u3

Therefore, v can be expressed as a linear combination of the given vectors.

Therefore, the linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

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Answer:

3960

Step-by-step explanation:

1minute = 88rounds

45minutes = xrounds

1/45 = 88/x

45(88)= 3960

3960/1 = 3960

x = 3960

The gun fires 3960 rounds in 45 minutes.

A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.

Let x rounds would it fire in 45 minutes

As per the situation, we can write the proportion would be as:

1 minute : 88 rounds = 45minutes : x rounds

⇒ 1/88 = 45/x

Apply the cross-multiplication, and we get

⇒ x = 45(88)

⇒ x = 3960

This means a gun fires 3960 rounds in 45 minutes.

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The given program utilizes a for loop to perform a specific set of operations. The output of the program will be 600.

A for loop is a control structure in programming that allows repeated execution of a block of code. It typically consists of three components: initialization, condition, and increment/decrement. In this program, the initialization sets 'numa' to 10. The condition specifies the range of values from 3 to 5 using the range() function. The increment is implicit and is defined by the range() function itself.

Within the loop, the statement 'numa = numa * count' updates the value of 'numa' by multiplying it with the current value of 'count'. This operation is performed three times since the loop iterates three times for values 3, 4, and 5. After the loop completes, the final value of 'numa' is printed as the output.

In the first iteration, 'numa' is multiplied by 3: 10 * 3 = 30.

In the second iteration, 'numa' is multiplied by 4: 30 * 4 = 120.

In the third iteration, 'numa' is multiplied by 5: 120 * 5 = 600.

The output of the program will be 600.

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Answer:

the answer is 4pi or 12.56637061

Step-by-step explanation:

the arc length equals 2pi x radius ( known angle (120) / 360 which equals 4pi or 12.56637061

The value of c when  b = 11 and m = 196 is 954.8.

We have,

c varies jointly as b and the square root of m.

So, c = kbm

Now, put c= 168, b=10 and m= 36

168 = k (10)(36)

168 = k (360)

k = 168/360

k = 21 /45

k = 7/15

Now, we get the equation

c = 7/15 mb

Again, put b = 11 and m =196

c = 7/15 x 11 x 186

c = 14332/15

c= 954.8

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Answer:

\(-2n+14\)

\(-5n+30\)

Step-by-step explanation:

-2 difference.

\(u_{n} =-2n+c\)

\(u_{1} =-2(1)+c=12\)

\(c=14\)

-5 difference.

\(u_{n} =-5n+c\)

\(u_{1} =-5(1)+c=25\)

\(c=30\)

Answer:

$47

Step-by-step explanation:

First you would add how much he gets from babysitting to how much he gets from cleaning the garage.

so that would be 25 + 32 = 57

Then you would take his overall earnings and subtract how much he owes his mother

so that would be 57-10=47

So he has 47 dollars after he pays his mother

The missing statement in the given proof is ΔFDC ≅ Δ FAB, reason SAS. Option C is correct.

In congruent geometry, the shapes that are so identical. can be superimposed on themselves.

here,
As given in the quesiton,
Consider the triangle formed by the given construction,
ΔFDC and Δ FAB
AB║CD
∠FAB = ∠FCD
∠FBA = ∠FDC

So,  ΔFDC ≅ Δ FAB, by SAS congruency.

Thus, the missing statement in the given proof is ΔFDC ≅ Δ FAB, reason SAS. Option C is correct.

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Answer:

1,028 miles

Step-by-step explanation:

multiply 514 by 2

Answer:

1028

Step-by-step explanation:

You just times 514 by two, because if it took 514 hours and every hour he goes 2 miles he would have went 1028 miles.  :)

To find the lengths of the two parts, we'll follow these steps:

Step 1: Determine the total number of parts.

The ratio is given as 5:7, which means the total number of parts is 5 + 7 = 12.

Step 2: Calculate the length of each part.

To calculate the length of each part, we divide the total length of the ruler (30 cm) by the total number of parts (12).

Let's denote the length of the first part as x cm and the length of the second part as y cm.

We can set up the following equation:

x + y = 30

Step 3: Calculate the length of the first part.

Using the given ratio, the first part is represented by 5 parts out of 12 parts. Therefore, we can express the length of the first part in terms of the total length and the total number of parts:

x = (5/12) * 30

Step 4: Calculate the length of the second part.

Similarly, the length of the second part is represented by 7 parts out of 12 parts. Therefore, we can express the length of the second part in terms of the total length and the total number of parts:

y = (7/12) * 30

Now, let's calculate the lengths of the two parts:

x = (5/12) * 30 = 12.5 cm

y = (7/12) * 30 = 17.5 cm

Hence, the length of the first part is 12.5 cm, and the length of the second part is 17.5 cm.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

To find the lengths of the two parts, we'll follow these steps:

Step 1: Determine the total ratio

The given ratio is 5:7, which means there are a total of 5 + 7 = 12 parts.

Step 2: Calculate the length of each part

Divide the total length of the ruler (30 cm) by the total number of parts (12) to find the length of each part.

30 cm / 12 = 2.5 cm

Step 3: Calculate the length of the first part

Multiply the length of each part by the ratio value for the first part (5).

2.5 cm × 5 = 12.5 cm

Step 4: Calculate the length of the second part

Multiply the length of each part by the ratio value for the second part (7).

2.5 cm × 7 = 17.5 cm

Therefore, the two parts of the ruler are 12.5 cm and 17.5 cm long, respectively.

Question isn't well formatted :

Actual question :

One day, River writes down the numbers 1,2,...,999. What is the sum of all the digits that River wrote down?

Answer:

499500

Step-by-step explanation:

Number written :

1, 2,...., 999

The interpretation of the number written is 1 up to 999

Hence, the sum of the number written is the addition of all the numbers from 1 up to 999

Using the python program :

sum = 0

for i in range(1000):

sum += i

print (sum)

Output = 499500

Answer:

13500

Step-by-step explanation:

Notice how it says the sum of all of the DIGITs. We have to add together the sum of the digits. We can do this by:

300(1 + 2 + 3 + 4.... + 9) = 300*45 = 13500

Answer:

x = 3

Step-by-step explanation:

x+5=8

x+5-5=8-5

X=3

Answer:

x = 3

Step-by-step explanation:

basically 2 ways

1st: Transposing

1) x + 5 = 8

2) transpose or transfer +5 to the other side

NOTE: transposing numbers and variables switches the signs (positive -> negative and vice versa)

3) x = 8 - 5

x = 3

2nd: Property of Equality (whatever u do one one side, you do the same to the other)

1) x + 5 = 8

2) x + 5 - 5 = 8 - 5

x = 3

the main focus is to isolate x, or to make it be alone in one side of the equation

Step-by-step explanation:

please mark me as brainlest

Considering the expression of a line, the equation of the line that passes through the pair of points (-3,5) and (1,-1) is y=-1.5x +0.5.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope and the value of one of the points, the value of the ordinate to the origin can be obtained.

In this case, being (x₁, y₁)= (-3, 5) and (x₂, y₂)= (1, -1), the slope m can be calculated as:

m= ( -1 -5)÷ (1 - (-3))

m= ( -1 -5)÷ (1 + 3)

m= (-6)÷ 4

m= -1.5

Considering point 2 and the slope m, you obtain:

-1= -1.5×1 + b

-1= -1.5 +b

-1 + 1.5= b

0.5= b

Finally, the equation of the line is y=-1.5x +0.5.

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Answer:

x  =  2

Step-by-step explanation:

Answer:

x = .61

Step-by-step explanation:

Don't really know how to explain other than use a graphing calculator. Desmos is quite helpful.

Hope that this helps!

The given equation;

Apply cross multiplication;

Now, add 5 on both side as;

Divide both side by 3;

Hence proof

Answer:

See below for answer.

Step-by-step explanation:

Absolute value represents the number of units that a value is from zero taken in account that there is a negative side and a positive side. Therefore in solving an absolute value equation, we must solve for the positive side and also the negative side.

Step-by-step explanation:

The absolute value is a means of measuring the distance of a number from the origin along the number line. Regardless of the position (positive or negative) of a number on the number line, its distance from the origin will be positive. Thus, the absolute value will always be positive, or 0 if if solving for the absolute value of 0).

Suppose that we're tasked to find the ansolute value of 8. As per the definition of absolute value of numbers, we know that -8 and 8 are both 8 units away from zero on the number line.

These same rules apply when solving absolute value equations, for which we have to set up the equations as positive and negative equations:

If a is positive, and |x| = a, then:

x = a or x = -a