Graph the line with the given slope that passes through the given point.
(a) slope:
3
4
,
point:
(1, 5)

The required slope m is 3 and the y-intercept is - 5.

On a graph, the y-intercept can be found by finding the value of y when x=0. This is the point at which the graph crosses through the y-axis.

· The y-coordinate of a point where a line, curve, or surface intersects the y-axis.

Given : The line y = 3x - 5

This is of the form y = mx + c which is the equation of the line.

On comparing these two equations

Thus the slope is 3 .

And y intercept is :

y = 3x - 5 and when x = 0

y =- 5.

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From the information given about the above quadrilateral, that is, the rectangle x is equal to 4, and m∠VUR  is equal to 36°.

A quadrilateral is a four-sided polygon with four edges and four corners in geometry. The name comes from the Latin words quadri, a variation of four, and latus, which means "side."

The results above are derived as follows:

To find x note that the diagonals of a triangle are congruent. This means that RT = SU.

⇒ 3x + 8 = 6x - 4 (add 4 to both sides)

3x + 8 + 4 = 6x - 4 + 4
3x + 12 = 6x (Collect like terms over the equation sign)
12 = 6x - 3x
12 = 3x (divide both sides by  three)

x = 12/3

x = 4

To derive m∠VUR,

Recall the properties of a rectangle:

Also, note that;

SRU = 90°

hence

∠VRU =  ∠SRU - ∠VRS

that is:
∠VRU = 90 -54 = 36°

If ∠VRU = 36°, then

∠VUR = 36° [The diagonals of a rectangle are equal.]

Hence ΔRVU is an Isosceles triangle. Since this is true, and it is also true that the two angles opposite to the equal sides of an isosceles triangle are congruent to each other,

Then indeed, ∠VUR = 36°

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Given:

13th term = -60

33rd term = -160

Find:

14th, 15th, 16th, and 17th term

Solution:

For us to determine the 14 - 17th term, we need to identify the common difference in this arithmetic sequence. The formula is:

Let's plug in the values of a₃₃ and a₁₃ in the formula above.

Then, solve.

Hence, the common difference between the terms is -5.

So, the next 4 terms after a₁₃ are shown below:

The general form of a linear equation is given by:

y = kx

where k is a constant.

From the given options you can notice that the only equation similar to the previous one is:

y = 1/6 x

Then, the previous equation is the linear equation.

Lily needs 3/2 cup of sugar to make 4 cups of kool-aid.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Lily is making kool-aid. She uses 1/4 cup of sugar for every 2/3 cup of kool-aid which is given in the question.

We have to determine the number of cups of sugar she needs to make 4 cups of kool-aid.

Let the number of cups of sugar would be x she needs to make 4 cups of kool-aid.

As per the given information, we can write the ratio as:

1/4 cup of sugar : 2/3 cup of kool-aid = x cup of sugar : 4 cup of kool-aid

⇒ 1/4 ÷ 2/3 = x ÷ 4

⇒ (1/4) / (2/3) = x / 4

⇒ (1/4) × (3/2) = x / 4

⇒ 3/8= x / 4

⇒ x = (3 × 4)/8

⇒ x = 12/8

⇒ x = 3/2

Therefore, she needs 3/2 cups of sugar to make 4 cups of kool-aid.

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Area A = ?

Bag area covers = 54 ft2

Square Area S = 18ft X 18 ft

. = 324 ft2

Then now divide S/B

S/B = 324/54

. = 36/6

. = 6

Then answer is

Brett will need 6 bags of fertilizer

The perimeter of pentagon is 150 so option D is correct.

Given:

Mr. McClary writes the equation 3(3x - 10) = 5(x + 10). The equation shows the relationship between the perimeter of an equilateral triangle and the perimeter of a regular pentagon.

3(3x-10) = 5(x+10)

9x - 30 = 5x + 50

9x - 5x = 30 + 50

4x = 80

divide by 4 on both sides

4x/4 = 80/4

x = 80/4

x = 20.

perimeter of pentagon = 5(x+10)

= 5(20+10)

= 5*30

= 150.

Therefore the perimeter of pentagon is 150 so option D is correct.

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The proportional relationship is represented by the formula, y = kx, which demonstrates that y increases at the same rate as x does

Relationships between two variables that are proportional occur when their ratios are equal.

Therefore the proportional relationship is represented by the formula,

y = kx .

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We have two parralel lines with angles 32x + 4 and 34x - 2

From the figure, the angles are corresponding angles

Corresponding angles are equal

That is,

34x - 2 = 32x + 4

Collect the like terms

34x - 32x = 4 + 2

2x = 6

Divide both sides by 2

2x / 2 = 6 / 2

x = 3

The answer is 3

Answer:

add the number of sides then divide the number by the number of sides

Solution:

Given the figure below:

The area of the shaded region is expressed as

step 1: Evaluate the area of the semicircle.

The area of the semicircle is expressed as

Thus, we have

step 2: Evaluate the area of the triangle.

The area of the triangle is expressed as

step 3: Evaluate the area of the shaded region.

Recall that

Thus, we have

Hence, the area of the shaded region is

The value of the composition (g . h)(0) is 0

A function can be defined as a mathematical law, expression of rule that explains the relationship between two variables in an equation.

These variables are;

The functions are;

The composite function is gotten by substituting the value of x of the independent variable in the function.

The composite function (g . h)(0) is determined by substituting the value of x as h(x) in the function g(x), we get;

(g . h) = 5√x

Now, substitute the value of x as 0, we have;

(g . h)(0) = 5√0

Find the square root

(g . h)(0) = 5(0)

Find the product

(g . h)(0) = 0

Hence, the value is 0

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Answer:

Triangle ABC is congruent to DCE by SAS Theorem.

Step-by-step explanation:

Since AB is parallel to DC, we can say that BC is congruent to CE and AC is congruent to DE, then:

If two sides in one triangle are congruent to two sides of a second triangle, and also if the included angles are congruent, then the triangle is congruent.

Triangle ABC is congruent to DCE by SAS Theorem.

we have

0.4275

if we round to the nearest thousand, we look at the third digit of our number

0.4275

do you know the answer now?

0.42 is not correct

and only 2 decimals will be rounded to the nearest hundreth

becuase we have a 5 after 7, the number will be rounded up

0.428

this is the answer

if we would have for example

0.3521

the rounded to the nearest thousand would be 0.352

Find the area of each room and then add the three areas.

The total square footage to be covered is 459.

Since each square yard has 9 square feet, divide the square footage by 9 to find how many yards is that equal to:

Then, the area is equal to 51 square yards.

The cost for each square yard is $25.56. Multiply that amount by 51 to find the total cost:

The total cost for the carpeting is $1303.56.

Each roll of padding has 30 square yards. Since 51 yards must be covered, and two rolls would yield 60 square yards, then, the minimum amount of rolls needed is 2.

The cost for 2 rolls would be 2*$99 = $198.

Add the cost of the two rolls of padding and the carpeting job to find the total cost:

Then, the total cost of the carpeting job including the carpet and padding would be $1501.56.

Therefore, the answers are:

Part 1) 459 square feet.

Part 2) 51 square yards.

Part 3) $1303.56

Part 4) 2 rolls for $198

Part 5) $1501.56

Given the following variation

Introducing the constant of proportionality c as shown below

Q=4, when b=2, R= 8

Let use the above values of Q, b, and R to find the value of c as shown below:

Let us substitute c in the formula as shown below

Hence, the specific formula to describe the variation is

Q= 400/(b+R)²

Answer: the complex solutions are:

Step-by-step explanation: x = 5i , -5i , 3/5 ,-2

Regrouping happens when we need to "borrow" value from the higher order digits to perform a subtraction properly. This happens on the tenths, because we need to subtract 5 from 1, which we can't do normally. So we need to regroup from the ones and tens, in order to solve the problem. The correct answer is B.

Solution;

The events are independent

Answer:

this is true

Step-by-step explanation:

The coordinates of the fourth side are (6, -8)

Let the coordinate of the fourth side be (x, y)

The diagonals of a parallelogram bisect eachother, so the midpoint of (-3, -2) and (x, y) is equal to the midpoint of (4, -4) and (-1, -6)

Solving these equations:

x - 3 = 3

x = 3 + 3 = 6

and

y - 2 = -10

y = -10 + 2 = -8

The coordinates are (6, -8)

Answer

Given expression

By factorization, we have

Now to check, using FOIL method, we have

F = First, i.e 3x(3x) = 9x²

O = Outer = 3x(+10) = +30x

I = Inner = +10(3x) = +30x

L = Last = +10(+10) = +100

The number of caffeinated teas that the tea shop serve is 5.

Number of teas served = 25 teas.

Percentage that was caffeinated.= 20%

Therefore the number that was caffeinated will be the percentage multiplied by the number of teas. This will be:

= 20% × 25

= 0.2 × 25

= 5

Therefore, 5 are caffeinated

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k(x)=3h(x)+4x^4/g(x). given the following table of values,  k'(-1) will be 3.

A function's sensitivity to change with respect to a change in its argument is measured by the derivative of a function of a real variable in mathematics. A crucial calculus technique is the derivative. the procedure for determining a function's derivative, or rate of change, in mathematics. Differentiation is the method used to calculate a function's derivative. The derivative is the rate at which two variables, x and y, change relative to one another.

Given Data

k(x) = -3h(x) + [tex]\frac{4x^{4} }{g(x)}[/tex]

k(x) = -3h'(x) + 4[tex]\frac{4x^{3} g(x)- x^{4}g'(x) }{gx^{2} }[/tex]

k'(-1) = -3h'(-1) + 4 [tex]\frac{4g(-1)-g(-1)}{g(-1)^{2} }[/tex]

k'(-1) = -3(-1) + 4(0)

k(-1) = 3 + 0

k'(-1) = 3

k(x)=3h(x)+4x^4/g(x). given the following table of values,  k'(-1) will be 3.

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Answer:

  A)  ASA

Step-by-step explanation:

You want to know the relevant congruence postulate given the markings of angles and sides shown in the diagram.

The arc and hash marks show on the angles mean the angles with matching markings are congruent. Two angles are shown as congruent to their corresponding angles in the other triangle.

The hash mark on the sides mean the sides with matching markings are congruent. One side between the marked angles is shown as congruent to the corresponding side in the other triangle.

The letters A and S in the congruence postulate designations refer to corresponding Angles and Sides, respectively. So, two angles with a side between them would be identified as ASA.

The ASA congruence postulate applies.

Option A) ASA is the correct answer for the given triangle in the question. ASA is the congruence correspondence.

What is congruence correspondence?

Each triangle's vertices must match one another exactly. This expression signifies that each triangle's side and angle measurements match up with a side or angle of the other triangle. To have a one-to-one correspondence, triangles don't necessarily have to be congruent, but when they are, knowing the correspondence of the triangles is important to determine precisely which sides and which angles are congruent.

According to congruence postulate,

Angles with matching markings are congruent if an arc or hash mark appears on them. The relationship between two angles and the corresponding angles in the other triangle is demonstrated.

The hash marks on the sides indicate that the markings on the sides that match are consistent. The opposite triangle's equivalent side is shown to be congruent to the side between the highlighted angles.

The congruence postulate designations begin with the letters A and S, which stand for matching Angles and Sides, respectively. Therefore, ASA would be used to describe two angles with a side in between them.

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Given:

Yes, Tim is correct.

Expression is having the square so , wheather the input is negative or positive the output will always gives the positive values.

All real inputs will give the positive output.

Example:

First find the length of the segment KL

Apply the formula for distance between two points as;

d = √{y2-y1}^2 + {x2-x1}^2 where

y1= -3 , y2 = 3 , x1 = -2 and x2 = 4

d= √ {3--3}^2 + { 4--2}^2

d= √ 9^2 + 6^2

d= √ 81 + 12

d= √93 = 9.6

So the length of the segment is 9.6

From point K {-2, -3} , find 1/3 of the length to locate point L

This will be : 1/3 * 9.6 =3.2

This means point L is 3.2 units from point K, now apply the distance formula to find x and y coordinates for L, where K is {-2,-3} and L {x,y}

d = √{y2-y1}^2 + {x2-x1}^2

3.2 = √{y--3}^2 + {x--2}^2

3.2 =√ {y+3}^2 +{x+2}^2

3.2^2 = {y+3}^2 + {x+2}^2

10.3 = y^2 + 6y + 9 + x^2 +4x +4

10.3 = y^2 + 6y +x^2 +4x +9+4

10.3 = y^2 + 6y +x^2 +4x +13

0=y^2 +6y +x^2 +4x +13-10.3

0= y^2 +6y +x^2 +4x +2.7

y^2 + 6y +x^2 +4x +2.7 = 0

{-0.9,-0.5)

EXPLANATION

Since the degree is 6, the polynomial has 6 zeros:

Then, using the Complex Root Theorem, since the polynomial has 2 complex roots, thus the conjugate of 5 + i is 5 - i, and the conjugate of 7 - i is 7 + i:

In conclusion, the remaining zeros are: 5 - i, 7 + i