Write an equation of the line that passes through the given points.
(-3,7) and (4,-7)
The equation is _______. (Type your answer in slope-intercept form.)

Answer:

-6, 19, 29

Step-by-step explanation:

Range = y

Domain = x

The equation is y = 5x + 4

we plug x into the equation:

5 (-2) + 4 = -6

5 (3) + 4 = 19

5 (5) + 4 = 29

The given polynomial does not have x - 3 as its factor.

The factor theorem states that for a polynomial p(x) if there exists a real number a such that p(a) = 0, then (x - a) is one of the factors of p(x).

The remaining factors of the polynomial can be found by dividing it by the same factor.

The polynomial is given as P(x) = 2x¹ − 5x³ - 4x² + 4.

In order to check whether x - 3 is a factor, evaluate P(3) as below,

P(3) = 2 × 3¹ - 5 × 3³ - 4 × 3² + 4

⇒ -161

Since, P(3) ≠ 0, x - 3 is not a factor of P(x).

Hence, the given expression is not a factor of P(x).

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Answer: k = 5/3

Step-by-step explanation:

    To solve, we will isolate the variable, k, by using inverse operations.

   Given:

2/5k + 1/6 = 3/10k + 1/3

   Subtract 1/6 from both sides of the equation:

2/5k = 3/10k + 1/6

   Subtract 3/10k from both sides of the equation:

1/10k = 1/6

   Divide both sides of the equation by (1/10), which is the same as multiplying both sides by 10:

k = 5/3

Answer:

k=5/3

Step-by-step explanation:

2/5k+1/6=3/10k+1/3

Move the 3/10k to the left side with subtraction

1/10k+1/6=1/3

Move the 1/6 to the right with subtraction

1/10k=1/6

Divide the 1/10 from each side

Getting K=5/3

The profit the company would make over the course of its 5 years of operation, given the starting annual profit and the constant increase in the profit, is $ 998, 329.34

To find the total profit that the company would make over the first 5 years of the operation, use the future value formula :

= First profit x Future value interest factor of annuity, 27%, 5 years

First profit = $ 117, 000

Rate of increase = 27 %

Number of years = 5 years

The profit in 5 years is:

= 117, 000 x 8.53272941

= $ 998, 329.34

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Answer:

y + y + y + y + y + y

Step-by-step explanation:

6y =

6 * y =   ==> add y 6 times

Hence, 6 * y = y + y + y + y + y + y

Answer:

[tex]b=3/11[/tex]

Step-by-step explanation:

[tex]-3b+11=8b+8 \\ \\ 11b+8=11 \\ \\ 11b=3 \\ \\ b=3/11[/tex]

Answer:

x = -11.2

Step-by-step explanation:

hope it helps

The height of the mountain is derived to be 410 m approximately to 2 significant figure using the trigonometric ratio of tangent for angles of elevation 32° and 58°.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

We shall represent the length from point B to the foot of the mountain with x and the height of the mountain with h so that:

the distance from a to the foot of the mountain = 400m + x

tan 32° = h/(400 + x)

h = tan 32° (400 + x) {by cross multiplication}

h = 400 × tan 32° + xtan 32°

h = 249.9477 + xtan 32°

also;

tan 58° = h/x

h = tan 58° × x {by cross multiplication}

h = xtan 58°

so;

xtan 58° = 249.9477 + xtan 32°

xtan 58° - xtan 32° = 249.9477 {collect like terms}

x(tan 58° - tan 32°) = 249.9477

x(0.9755) = 249.9477 {divide through by 0.9755}

x = 249.9477/0.9755

x = 256.2252

h = 256.2252 × tan 58°

h = 410.9460.

Therefore, the height of the mountain is 410 m approximately to 2 significant figures using the trigonometric ratio of tangent for angles of elevation 32° and 58°.

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The way that they could calculate the point that is equidistant from all three gates is; By joining the entry point of all three friends to form a triangle and then finding the centroid of this triangle , they can calculate the required point.

The circumcenter of a triangle is defined as the locus of point equidistant from the three vertices of a triangle.

From the image attached showing the location of the three gates, the first step to take is to join all the three entry points of the friends in order to form a triangle.

The second step to take now, will be to find the centroid of the triangle, such that all three friends must start moving in the direction of the midpoint of the opposite side.

Finally, following that procedure, the point equidistant from all the three gates can be calculated.

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Answer:

A)  f(x) = tan(2x - π)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.3cm}\underline{Standard form of a tangent function}\\\\$f(x)=A \tan(B(x+C))+D$\\\\where:\\\\\phantom{ww}$\bullet$ $A=$ vertical stretch\\ \\\phantom{ww}$\bullet$ $\dfrac{\pi}{|B|}=$ period\\\\\phantom{ww}$\bullet$ $C=$ horizontal shift (positive is to the left)\\\\\phantom{ww}$\bullet$ $D=$ vertical shift\\\end{minipage}}[/tex]

The parent tangent function is:

[tex]f(x)=\tan(x)[/tex]

The period of the parent tangent function is π.

A tangent function is discontinuous when cos(x) = 0, so it has vertical asymptotes whenever cos(x) = 0.

Therefore, the parent tangent function has vertical asymptotes at:

[tex]x=\dfrac{\pi}{2}+\pi n[/tex]

and so its domain is:

[tex]\left\{ x \in \mathbb{R} \;| \;x \neq \dfrac{\pi}{2}+\pi n\right\}[/tex]

If the domain of the given tangent function is:

[tex]\left\{ x \in \mathbb{R} \;| \;x \neq \dfrac{\pi}{4}+\dfrac{\pi}{2}n\right\}[/tex]

then its vertical asymptotes are when:

[tex]x =\dfrac{\pi}{4}+\dfrac{\pi}{2}n[/tex]

Therefore, its period is π/2.

[tex]\implies \dfrac{\pi}{|B|}=\dfrac{\pi}{2}[/tex]

[tex]\implies B=2[/tex]

And it has been horizontally shifted by π/2:

[tex]\implies f(x)=\tan\left(2\left(x-\dfrac{\pi}{2}\right)\right)[/tex]

[tex]\implies f(x)=\tan\left(2x-\pi\right)[/tex]

Function g(x)

[tex]g(x)=\tan(x- \pi)[/tex]

Function h(x)

[tex]h(x)=\tan \left(x-\dfrac{\pi}{2}\right)[/tex]

Function j(x)

[tex]j(x)=\tan \left(\dfrac{x}{2}- \pi \right)[/tex]

The height of the triangular pyramid will be 154 cm.

A pyramid with a triangle base is referred to as a triangular pyramid. Vertices are essentially corners in geometry. Both regular and irregular triangular-based pyramids contain four vertices.

Pyramids with triangular bases have six edges, three of which run along the base and three of which rise above the base.

The volume of the triangular pyramid will be,

Volume = 1/2 x Base x h

11120 = 1/2 x ( 17 x 17 /2 ) x h

h = ( 11120 x 2 x 2 ) / ( 17 x 17 )

h = 44480 / 289

h = 154 cm

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X xcm 6cm 8cm is equal to 10cm if the area of the trapezium underneath is 40%2cm2.

Provide A B C D. trapezium the length of the sides excluding the base is 10,

[tex]$$\therefore \mathrm{AD}=\mathrm{DC}=\mathrm{CB}=10 \mathrm{~cm} \text {. }$$[/tex]

Draw a parallel DP & CQ on AB.

Let [tex]$\mathrm{AP}=x \mathrm{~cm}$[/tex]

In symmetry

[tex]$$\mathrm{QB}=x \mathrm{~cm}$$[/tex]

Consider area A of the trapezium. A B C D

[tex]$$\begin{aligned}& \left.A=\frac{1}{2} \text { (Sum of parallel sides }\right) \times(\text { Height }) \\& A=\frac{1}{2}(D C+A B) \times \text { DP } \quad \ldots(1)\end{aligned}$$[/tex]

Therefore, DPCQ creates a rectangle because DP & CQ are perpendicular to A B and C D were parallel to A B.

[tex]$$\therefore \mathrm{PQ}=\mathrm{DC}=10 \mathrm{~cm}$$[/tex]

Thus,

[tex]$$\begin{aligned}A B & =A P+P Q+Q B \\& =x+10+x \\& =2 x+10\end{aligned}$$[/tex]

Use the equation A r e a = h 2 (a + b) to determine a trapezium's area. The distance between a and b, which are two parallel sides, is denoted by the letter h. To put it another way, add the two parallel sides together, divide by 2, and then multiply this number by the separation between the parallel sides. The surface of a shape's surface is measured by its area. The length and width of a rectangle or square must be multiplied to determine their respective areas. A has a perimeter of x by y.

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The ordered pair of the equation of line is given by

A ( 6 , 6 ) , B ( 0 , 2 ) , C ( -2 , -6 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , let the first point be A ( 6 , 6 )

Let the second point be B ( 0 , 2 )

The slope of the line m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 2 - 6 ) / ( 0 - 6 )

Slope m = -4 / -6

Slope m = 2/3

And , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 6 = 2/3 ( x - 6 )

On simplifying the equation , we get

y - 6 = ( 2/3 )x - 4

Adding 6 on both sides of the equation , we get

y = ( 2/3 )x + 2

Therefore, the value of A is y = ( 2/3 )x + 2

Hence , the equation of line is y = ( 2/3 )x + 2

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The radius of the hemisphere with volume 3839cm³ is 11.9cm

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.The volume of the hemisphere is derived by Archimedes. The volume of a hemisphere = (2/3)πr3 cubic units.

The volume of a hemisphere is given as ⅔πr³

Where r is the radius

V = ⅔×3.14r³

3839 = 2/3× 3.14r³

r³ = (3839× 3)/3.14×2

r³ = 11517/6.28

r³ = 1833.9

r = cube root of 1833.9

r = 11.9cm

Therefore the radius of the hemisphere is 11.9cm

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Based on the given set of real numbers, a list of all the rational numbers in the set include the following: B. √4, -2/3, 1, 9/8, √(9/4), 2.4. Therefore, the correct answer option is: B. square root of 4 comma space short dash 2 over 3 comma space 1 comma space 9 over 8 comma space square root of 9 over 4 end root comma space 2.4 with bar on top.

In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the square root of 11.

In this scenario, the rational numbers include all of the following:

However, -√2 and √10 would not be classified as rational numbers because they cannot be obtained when an integer is divided by another integer.

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Answer:

APR stands for Annual Percentage Rate, which is the interest charged on a loan expressed as a yearly rate. In this case, we are given the interest rate for a loan over 10 days.

To calculate the APR, we need to determine the annualized interest rate, which is the interest rate multiplied by the number of times the interest is compounded per year.

We know that the interest on the loan is $200. The loan amount is $800 and the loan period is 10 days.

First we need to calculate the daily interest rate:

Interest/Loan amount = 200/800 = 0.25

To find the annualized interest rate, we need to multiply the daily interest rate by the number of days in a year:

0.25* 365 = 91.25%

To the nearest percent the APR for this loan is 91%

The value for x is 10; the perimeter is 56 inches; a possible area the area is 7 square feet (option c); and a possible perimeter is 25 m (option a).

To find the correct value for x, let's replace the possible values and verify if the total is >11.

2x + 9

(2 x 0) + 9 = 0 + 9 = 9

(2 x -5) + 9 = -10 + 9 = 1

(2 x 10) + 9 =20 + 9 = 29

(2 x -8) + 9 = -16 + 9 = 7

Based on this, the correct value for x is 10

The perimeter of an octagon can be calculated using this formula:

8 x lengh of one side

8 x 7 inches =  56 inches

The area of a shape is calculated by multiplying side x side. Due to this, areas are always expressed using square meters, square feet, square kilometers, etc. Based on this principle, a possible area is 7 square feet (option c).

The perimeter is found by adding the lengh of all the sides in a shape. Due to this, it is expected a perimeter is expressed in meters, kilometers, centimeters, etc. Based on this a possible perimeter is 25 m (option a).

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Answer:

yes?

Step-by-step explanation:

In the parallelogram HIJK, the measure of angle J and K are 45 degrees and 135 degrees respectively.

You should know that a parallelogram is a quadrilateral whose opposite sides are parallel.  The given parameters for the solution are

m<H = 45 degrees

Having said this, the m<K will be:

Produce the line H to P

This implies that <JKP is = 45 degrees ........... corresponding angles

It there means that  <HKJ = 180-45 = 135 degrees

Also; <JKP = <IJK   ................ corresponding angles

Therefore m<J is 45 degrees.

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The correct question:

In parallelogram HIJK, the measure of angle H is 45∘.

Find the measure of angle J. Explain how you know.

Find the measure of angle K. Explain how you know.

Answer: $159.90

Step-by-step explanation:

Assigning a variable: V=Vegetable seeds   F=Flower seeds   T=Top soil

Assigning a value to each variable: V=1.5   F=2.2   T=12.1

The equation:

v(12)+f(15)+t(9)=

1.5(12)+2.2(15)+12.1(9)=

1.5*12=18   2.2*15=33   12.1*9=108.9

18+33+108.9=159.9

Total cost = $159.90

Hope this helps!

Answer:fsjcc

Step-by-step explanation:

8473274+5487643=593fdj

]

The given function table is found not to be a function.

A function is defined as a relation in which each possible input value leads to exactly one output value. That means that “the output is a function of the input.” Meanwhile, the input values make up the domain, and the output values make up the range.

Now, the coordinates from the given function table are as follows;

(2, 3)

(3, 3)

(4, 3)

(5, 3)

(6, 3)

This shows that all the range values are the same for different x-values and as such it doesn't fit the definition of a function as stated above.

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The best step to use in getting angle ECA is the exterior angle property which gives us; Angle ECA =  154°

In a triangle geometry, we know that the exterior angle is always equal to the sum of the interior opposite angles. This property is referred to as  the exterior angle property. This tells us that any two triangles will be similar if their corresponding angles tend to be congruent and the length of their sides will be proportional.

Now, in this question, we are trying to find the measure of angle ECA which is an exterior angle given by the expression 166 - 6x.

Now, the interior opposite angles are (100x - 59) and (6x + 1). Thus;

Applying the exterior angle property, we will have the first step as;

(100x - 59) + (6x + 1) = 166 - 6x

106x - 58 = 166 - 6x

112x = 166 + 58

112x = 224

x = 224/112

x = 2

Thus;

Angle ECA = 166 - 6(2) = 154°

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The cost of a pack of gum is equal to $2.1.

In order to determine the cost of a pack of gum, we would assign variables to the cost of a pack of gum and cost of a candy bar respectively, and then translate the given word problem into an algebraic equation as follows:

Since Lionel bought 4 candy bars and 2 packs of gum at the gas station and spent $9.80, a linear equation which models this situation is;

4c + 2g = 9.80    ......equation 1.

Additionally, two packs of gum cost the same as three candy bars:

2g = 3c     ......equation 2.

c = 2g/3     ......equation 3.

Substituting equation 3 into equation 1, we have:

4(2g/3) + 2g = 9.80

8g/3 + 2g = 9.80

14g/3 = 9.80

14g = 29.4

Cost of a pack of gum, g = 29.4/14

Cost of a pack of gum, g = $2.1

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Complete Question:

Brock bought 4 candy bars and 2 packs of gum at the gas station and spent $9.80. Two packs of gum cost the same as three candy bars. Let g represent the cost of a pack of gum and c represent the cost of a candy bar. What is the cost of a pack of gum?

The number of times of Puerto Rico is 5/6

No earthquake released 10³ of Colombia

From the question, we have the following parameters that can be used in our computation:

The table of values

On the table of values, we have

Colombia = 6.0M

Puerto Rico = 5.0M

This means that

Number of times = Puerto Rico/Colombia

Substitute the known values in the above equation, so, we have the following representation

Number of times = 5/6

Here, we have

Colombia = 6.0M

So, we have

Earthquake = Colombia * 10³

This gives

Earthquake = 6 * 10³

From the table of values, we have no entries with the readings 6 * 10³

Hence, no earthquake released 10³ of Colombia

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There are 51 trees, 41 weeds, and 16 grasses that are significant pollen producers.

In the context of beekeeping, the phrase "pollen source" refers to flowering plants that provide pollen to bees and other insects. Bees gather pollen to use as a source of protein for their young.

G, W, and T should stand for the number of grasses, weeds, and trees that serve as significant pollen sources.

According to information provided, state A is home to 80 significant sources of pollen. This data can be represented as follows in an equation:

G + W + T = 108......(1)

According to what is said, there are 7 times as many weeds as there are grasses. This data can be represented as follows in an equation:

W = 3G - 7......(2)

We are also informed that there are three times as many trees as there are grasses. This data can be represented as follows in an equation:

T = 3G + 3

We are also informed that there are three times as many trees as there are grasses. This data can be represented as follows in an equation:

G + W + T = 108

G + 3G - 7 + 3G + 3 = 108

7G - 4 = 108

7G = 112

G= 112/7

G = 16

Therefore, there are 16 grasses that are major pollen sources.

Number of weeds that are major pollen sources:

W = 3G - 7  = 3(16) - 7  = 48 - 7 = 41

Therefore, there are 41 weeds that are major pollen sources.

Number of trees that are major pollen sources:

T = 3G + 3  = 3(16) + 3  = 48 + 3  = 51

Therefore, there are 51 trees that are major pollen sources.

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1335.88 miles² out of 9,542 miles² is reserved for animal preservation in the national park.

The idea of area is essential to contemporary mathematics. A two-dimensional shape, figure, or planar lamina in a plane will occupy a specific amount of space, which is denoted by the area.

The area can be simply defined as the volume of cloth, or other material with the specified thickness, required to construct a model of the shape, or as the volume of paint required to completely cover the surface of the shape in a single layer, or "coat," of paint.

It is a two-dimensional illustration of the length of a curve or the volume of a solid, where length is a one-dimensional concept and volume is a closely related concept that exists in three dimensions.

Area of national park = 9,542 miles²

14% of the area of the park is reserved for animal preservation

= 9542 × 14

= 9542 × 14/100

= 9542 × 0.14

=  1335.88 miles²

Thus, 1335.88 miles² out of 9,542 miles² is reserved for animal preservation in the national park.

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The area of rectangle in the simplest Form is: [tex]= 45[/tex]

What is the area of a rectangle?

The area of a rectangle of length (L) and width (W) is given by the multiplication of the dimensions, as follows:

Area of rectangle = Length (L) * Width (W)

Given:

Area of rectangle =[tex]\sqrt{15*9*5*3}[/tex]

                              ⇒[tex]\sqrt{3*5*3*3*5*3}[/tex]

                              ⇒3*5*3

                              ⇒45

Therefore, the area of rectangle in the simplest Form is: 45

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The correct answer is B.We can find by complex number by using complex form.

Complex numbers are the numbers that are expressed in the form of a+ib where a and b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1). For example 2+3i is a complex number where 2 is a real number (Re) and 3i is an imaginary number (Im).

Every real number is a complex number when the imaginary part is zero. But remember that every complex number is not a real number. For example we can write 5 as 5+0×(i). Hence Every Real Number is a Complex Number.

Now

A complex number is of the form a+ b(i)

 =8/3 +[tex]\sqrt{-7/3}[/tex]

 =8/3 +[tex]\sqrt{7/3}[/tex] [tex]\sqrt{-1}[/tex]

=8/3+[tex]\sqrt{7/3}[/tex] (i)

The second option is a complex number because it can be rewritten in the form

a + b(i).

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