In the figure shown, line AB is parallel to line CD.

Part A: What is the measure of angle x? Show your work. (5 points)

Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal. (5 points)

AB and CD are parallel lines, and PQ and PR are transversals which intersect AB at P and CD at Q and R. Angle APQ is labeled as 64 degrees, angle QPR is equal to x, angle PRD is equal to 110 degrees.

If the equation 2(x-7) = 36, then the value of x is 13 and 1

The equation is

[tex](x-7)^2[/tex] = 36

The equation is defined as the statement the connect the two expression with an equal sign.

We know the square of 6 is 36

[tex]6^2[/tex] = 36

Substitute the value in the equation

[tex](x-7)^2=6^2[/tex]

Apply square root in the both side of the equation

[tex]\sqrt{(x-7)^2} = \sqrt{6^2}[/tex]

Then the equation will become

x - 7 = ± 6

If the value is +6

x - 7 = 6

Add both side of the equation by 7

x - 7 +7 = 6+7

x = 13

If the value is -6

x - 7 = -6

Add both side of the equation by 7

x - 7 + 7 = -6 + 7

x = 1

Hence, If the equation 2(x-7) = 36, then the value of x is 13 and 1

The complete question is:

Given [tex](x-7)^2=36[/tex], find the value of x.

Learn more about equation here

brainly.com/question/14603452

#SPJ1

The Pythagorean Theorem indicates the following relationship between the squares and triangles.

Part A

Part E

Pythagoras theorem can be stated as follows; The square of the length of the hypotenuse side of a right triangle is equal to the sum of the squares of the other two sides.

Part A

The possible squares in the question are the three squares arranged on the three sides of the triangle, and having a side length which is the same as the length of the side of the triangle to which the square is attached

The relationship between the three squares of side length a, b, and c according to Pythagorean theorem is; a² + b² = c²

Therefore, the area of the largest square that is located on the hypotenuse side of the triangle is equal to the sum of the areas of the other two squares.

Part E

The length of the sides of the triangles, obtained from a similar question on the site are; a, b, and c and a, b, and n

It was shown that c² = n²

Therefore;

c = n

Learn more about the Pythagorean Theorem in mathematics here:

https://brainly.com/question/343682

#SPJ1

Answer: 13,8 litres

Step-by-step explanation:

£1.45 ------------ 1 L

 £20 ------------- ?

?= [tex]\frac{20 *1}{1.45} = 13,79310345 L[/tex] = 13,8 L

The answer to the given quadratic equation is y =  ( x + 4 )²

A(x + m)2 + n is the formula for completing the square, where m is any real number and n is a constant factor.

The following straightforward formula can be used to finish the square instead of the intricate step-by-step procedure. Find the following in order to complete the square in the phrase ax2 + bx + c:

N = c - (b2/4a) and m = b/2a

Enter these numbers where they belong: ax2 + bx + c = a(x + m)2 + n. These equations are geometrically derived.

Given : A quadratic equation y = 7x² + 56x + 117

this can also written as y = x² + 8 x + 17

y = x² + 4² - 4² + 17

y =  ( x + 4 )²

To know more about completing the square you may visit the link which is mentioned below:

https://brainly.com/question/8631373

#SPJ13

Equation in standard form with an x-intercept of 4 and a y-intercept of 5 is y = -5/4(x) + 5.

Given:

x - intercept = 4

y - intercept = 5

At x intercept y = 0 and at y intercept x = 0

(4,0) and (0,5)

slope = 5-0/0-4

= 5/-4

m = -5/4

substitute (4,0) and m value,

y = mx+c

0 = -5/4*4 +c

0 = -5 + c

c = 5

y = mx + c

y = -5/4(x) + 5.

Therefore equation in standard form with an x-intercept of 4 and a y-intercept of 5 is y = -5/4(x) + 5.

Learn more about the equation here:

https://brainly.com/question/10413253

#SPJ1

The number of real roots found are-

1. (x-4)(x+3)^2(x-1)^3=0 ; 6 real roots.

2. X^2(x^3-1)=0 ; 3 real roots.

3. X(x+3)(x-6)^2=0 ; 4 real roots.

4. 3x(x^3-1)^2=0 ; 3 real roots.

5. (x^3-8)(x^4+1)=0​ ; 1 real roots.

Consider the given cases-

1. (x-4)(x+3)^2(x-1)^3=0,

Put each equals zero.

x – 4 = 0 or (x + 3)^2 = 0 or (x – 1)^3 = 0,

Thus,

x = 4

x = –3 twice

x = 1 thrice

All are real numbers, thus given polynomial has 6 real roots.

2. x^2(x^3-1)=0

Put each equals zero.

x² = 0

x³ – 1 = x³ – 1³ = (x – 1)(x² + x + 1) = 0

The quadratic expressions has 2 imaginary roots.

Use the discriminant formula to find-

D = b² – 4ac = 1² – 4(1)(1) = 1 – 4 = –3 < 0.

Thus, roots that are not real.

So, the real roots of this polynomial : 0(twice) and 1.

Hence, thus given polynomial has 3 real roots.

3. x(x+3)(x-6)^2=0

Put each equals zero.

x = 0

x = 3

x = 6 twice

Hence, thus given polynomial has 4 real roots.

4. 3x(x^3-1)^2=0

Put each equals zero.

3x = 0 and  x = 0

(x^3 – 1)² = [(x – 1)(x² + x + 1)]² = (x – 1)²(x² + x + 1)² = 0,

Here, only two roots are real

The quadratic expression do have unreal roots, thus 1 twice are the real roots.

Hence, thus given polynomial has 3 real roots..

5. (x^3-8)(x^4+1)=0

Put each equals zero.

x³ – 8 = x³ – 2³ = (x – 2)(x² + 2x + 4) = 0

There is only one real root i.e, 2, the quadratic expression do have imaginary roots

Check using the discriminant formula

D = b² – 4ac = 2² – 4(1)(4) = 4 – 16 = – 12 < 0.

x⁴ + 1 = 0 has imaginary roots.

Hence, thus given polynomial has 1 real roots..

To know more about the roots of polynomial, here

https://brainly.com/question/2833285

#SPJ4

The distance from one corner of the field to the opposite corner, using the Pythagorean Theorem, is of:

125 meters.

The Pythagorean Theorem is a geometry axiom relating the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the equation presented as follows:

[tex]h^2 = l_1^2 + l_2^2[/tex]

From the situation described in this problem, we have that:

Hence the distance from one corner of the field to the opposite corner is obtained as follows:

d² = 68² + 105²

d = sqrt(68² + 105²)

d = 125 meters.

More can be learned about the Pythagorean Theorem at https://brainly.com/question/343682

#SPJ1

Answer: 2a+5

5a-2-3a+7

First gather together the like terms

5a-3a  and  -2+7

then solve

5-3=2   and -2+7=5

answer = 2a+5

The value of R when A equal 5 is 3.6 and the value of A when R equal 9 is 2 as R is varies inversely to A.

Proportional relationships are relationships between two variables where their ratios are equivalent.

If R is inversely proportional to A.

R ∝ 1/A, then

R = k/A

Where k is the proportionality constant.

Given that;

First, we determine the proportionality constant.

R = k/A

Plug in R = 12 and A = 1.5 and solve for k

k = R × A

k = 12 × 1.5

k = 18

a) The value of R when A = 5 will be;

R = k/A

R = 18 / 5

R = 3.6

b) The value of A when R = 9

R = k/A
R × A = k

A = k/R

A = 18 / 9

A = 2

Therefore, the value of A when R equal 9 is 2.

Learn more about proportionality here: https://brainly.com/question/27530069

#SPJ1

1.because sample is random and (130)

(0.923) and (130)(0.077) are both at least 10.

This means the normal model is a good fit for the sampling distribution.

Consider the provided information.

130 randomly selected flights and find that

120 of the flights arrived on time.

n=130

The on-time arrival performance was 91.9%

p=0.923 and q=1-0.923=0.077

np = 130 x 0.923

np = 120 ≥ 10

nq = 130 × 0.077

nq = 10 = 10

Hence, Yes, because sample is random and

(130)(0.923) and (130)(0.077) are both at least 10. This means the normal model is a good fit for the sampling distribution.

2.because sample is random and (130)

(0.919) and (130)(0.081) are both at least 10.

This means the normal model is a good fit for the sampling distribution.

Consider the provided information.

130 randomly selected flights and find that

120 of the flights arrived on time.

n=130

The on-time arrival performance was 91.9%

p=0.919 and q=1-0.919=0.081

np = 130 x 0.919

np = 119.5 ≥ 10

nq = 130 × 0.081

nq = 10.5 ≥ 10

Hence, Yes, because sample is random and

(130)(0.919) and (130)(0.081) are both at least 10. This means the normal model is a good fit for the sampling distribution.

To learn more about sampling distribution click here https://brainly.com/question/29368683

#SPJ4

If the original price of the radio is 2,400 Naira and it is reduced by one third, then the discounted price is 1,600 Naira.

A store usually provides discount of some items to attract more customers and make greater sales.

Suppose the original price is p, the discount rate is d%, and the discounted price is q, then the discounted price can be calculated as:

q = (1 - d%) x p

Parameters given in the problem:

p = 2,400 Naira

d = 1/3

Hence,

q = (1 - 1/3) x 2400

q = 2/3 x 2400 = 1600

Learn more about discount here:

https://brainly.com/question/1153322

#SPJ4

Answer:

-64

Step-by-step explanation:

Start by moving everything to the left side making the equation equal 0. Then combine like terms.

According to the triangle inequality, the length of a triangle's third side must be greater than the sum of any two other triangle lengths, so the length of the steel piece will likely be 4 or 5 inches.

Triangle inequality is a theorem in Euclidean geometry that states any two triangle sides added together must be greater than or equal to the third side; it is represented by the symbols a + b≥ c. The basic tenet of the theorem is that a straight line connects any two points.

Here,

If they are an integer number of inches long and less than six, the following lengths are possible: 4 ,5

According to the triangle inequality, any two other triangle lengths must be greater than the third side of a triangle's length:4+4 = 8 > 6

4+6 = 10 > 4

5+5 = 10 > 6

6+5 = 11 > 5

According to "The Triangle Inequality," which states that the length of a triangle's third side must be greater than the sum of any two other triangle lengths, the piece of steel's potential length will be 4 or 5 inches.

To know more about triangle inequality,

https://brainly.com/question/28823603?referrer=searchResults

#SPJ13

The car travels 30 miles in 45 minutes with the speed 40 miles/hour with the constant speed.

Velocity is the rate and direction of an object's movement, whereas speed is the time rate at which an object is moving along a path. In other words, velocity is a vector, whereas speed is a scalar value. The distance traveled by a moving object in a specific amount of time is its speed. How quickly something is moving is determined by its speed. The distance traveled by an object in a given amount of time divided by the time gives the object's average speed.

Here,

45 minutes/60 minutes= .75 hours (this gives you the amount of time in hours)

time x speed = distance

.75 hours time x 40 mph speed = 30 miles distance

With a constant speed of 40 miles per hour, the car covers 30 miles in 45 minutes.

To know more about speed,

https://brainly.com/question/7359669?referrer=searchResults

#SPJ4

Answer:

que tienes que realizar no se entiende tu pregunta lo siento

ann made a rectangle with the

right perimeter & area

ann doesn't try any other

rectangles to see if their areas are

different.

splitting the land , ann confuses perimeter and area

mapmathshellorg

The measure of angle EAC IS 50°

The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts. For example, an angle bisector of a 60-degree angle will divide it into two angles of 30 degrees each. In other words, it divides an angle into two smaller congruent angles. Given below is an image of an angle bisector of ∠AOB.

∠BAE = x + 30, ∠EAC = 3x - 10

If AE is a line that bisects BAC,

then ∠BAE = ∠EAC

which becomes,

x + 30 = 3x - 10

collecting like terms,

x - 3x = -10 - 30

-2x = -40

x = -40/-2

x = 20°

But m ∠EAC = 3x - 10

substituting x = 20°

we have ∠EAC = 3(20) - 10

                          = 60 - 10

    ∠EAC       = 50°

In conclusion, the value of  ∠EAC  = 50°

Learn more about the bisector of an angle: https://brainly.com/question/24334771

#SPJ1

Answer:

Bracelets: 7 Necklaces: 9

Step-by-step explanation:

b+n=16

6n+24n=258

b=-n+16

6(-n+16)+24n=258

-6n+96+24n=258

18n=162

n=9

6n+24(9)=258

6n+216=258

6n=42

n=7

B stands for bracelets

N stands for necklaces

The area of the rectangle is increasing at the rate of 156 [tex]cm^{2}[/tex]/s .

Let the length (cm) be l , width (cm) be w , area be A ([tex]cm^{2}[/tex]) and time (s) be t .

Given : dl / dt = 6 cm/s and dw / dt = 8 cm/s

Area of rectangle = l * w

Differentiating wrt. t ,

dA / dt = ( l ) ( dw / dt ) + ( dl / dt ) ( w )

Therefore , dA / dt = 8l + 6w

Hence , when l = 12 cm and w = 10 cm

dA / dt = ( 8 * 12 ) + ( 6 * 10 )

dA / dt = 156 [tex]cm^{2}[/tex]/s .

The area of the rectangle is increasing at the rate of 156 [tex]cm^{2}[/tex]/s .

To learn more on rate of increasing follow link :

https://brainly.com/question/25184007

#SPJ4

The percent decrease in screen time this week is 40%. Therefore, option C is the correct answer.

Given that, last week, Lora used 840 minutes. This week, Lora used 504 screen time minutes on the phone.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Now,

Difference=840-504

= 336

Percentage decrease = Difference in value/Original value ×100

= 336/840 ×100

= 0.4 ×100

= 40%

The percent decrease in screen time this week is 40%. Therefore, option C is the correct answer.

To learn more about the percentage visit:

brainly.com/question/24159063.

#SPJ2

The rate per minute at which Karama can paint banisters is 0.02.

In the given question,

Karama can paint a staircase banister in 50 minutes.

We have to find the rate per minute at which Karama can paint banisters.

Since we have to find the rate per unit. Rate per unit means how much Karama can paint in one minute.

To find the rate per unit we divide 1 by 50.

As we know that Karama can paint one staircase banister in 50 minute.

So we can write it as

50 minute = 1 staircase banister paint

Now in 1 minute.

1 minute = 1/50 staircase banister paint

Simplifying

1 minute = 0.02 staircase banister paint

Hence, the rate per minute at which Karama can paint banisters is 0.02.

To learn more about rate per unit link is here

brainly.com/question/17116587

#SPJ1

Answer:

not a solution

Step-by-step explanation:

we can just fill it in on both equations

-4(4)+3(1)=2

-16+3=2

-13=2

It doesn’t work for this equation so it’s not a solution

Hopes this helps please mark brainliest

Answer:

No

Step-by-step explanation:

For (4, 1 ) to be a solution then both equations must be true

substitute x = 4 and y = 1 into both equations

- 4(4) + 3(1) = - 16 + 3 = - 13 ≠ 2

3(4) - 9(1) = 12 - 9 = 3

Since both equations are not true then (4, 1 ) is not a solution of the system.

Answer:

For part a you would decompose the fraction into two independent fractions with the following form:

() = ()/( x^2+5)(x ^2+3x−4)  = (Ax + B)/(x^2+5) + (Cx + D)/(x ^2+3x−4)

Combining these fractions we get:

((Ax + B)*(x ^2+3x−4) + (Cx + D)*( x^2+5))/( x^2+5)(x ^2+3x−4) = ()/( x^2+5)(x ^2+3x−4)

Thus we can say: (Ax + B)*(x ^2+3x−4) + (Cx + D)*( x^2+5) = ()

You then simplify the equation on the left by combining like terms and solve the system of equations that arise corresponding with ().

You would follow a similar process for part b as well.

Step-by-step explanation:

Answer:

  y = x² +8x -9

Step-by-step explanation:

You want the least-degree polynomial with roots 1 and -9, written in standard form.

Each root p means there is a factor (x-p). The two roots make the factored form of the polynomial be ...

  y = (x -1)(x +9)

Expanding this to standard form, we get ...

  y = x² +8x -9

__

Additional comment

A quadratic that has two roots, p and q, will have the standard form ...

  y = (x -p)(x -q) = x² -(p+q)x +pq

That is, the linear term coefficient is the opposite of the sum of the roots, and the constant is their product. This means you can write down the equation directly from the roots:

  y = x² -(1-9)x +(1)(-9) = x² +8x -9

Answer:

5 and 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the gradient and c the y- intercept )

(a)

y = 5x - 3 ← is in slope- intercept form

with gradient m = 5

(b)

3y - 12x + 7 = 0 ( add 12x to both sides )

3y + 7 = 12x ( subtract 7 from both sides )

3y = 12x - 7 ( divide through by 3 )

y = 4x - [tex]\frac{7}{3}[/tex] ← in slope- intercept form

with gradient m = 4

Applying the transformation rule (x - 2.y + 4) and using the scale factor k = 3 for dilation gives

preimage      translation image     Dilation image

A (1.-2)             A' (-1, 2)                   A'' (-3, 6)  

B (4,-1)             B' (2, 3)                    B'' (6, 9)

C (5.-3)            C' (3, 1)                     C'' (9, 3)

Transformation is a term used in mathematics to refer to the movements made by objects.

Translation refers to a type of transformation that involve a linear movement.

Applying the transformation rule (x - 2.y + 4 ) gives

A (1.-2) = (1 - 2, -2 + 4) = (-1, 2)

B (4,-1) = (4 - 2, -1 + 4) = (2, 3)

C (5.-3) = (5 - 2, -3 + 4) = (3, 1)

preimage        image

A (1.-2)             A' (-1, 2)

B (4,-1)             B' (2, 3)

C (5.-3)            C' (3, 1)

Dilation involves making the image bigger or smaller. In this case K > 1 hence the image is bigger

Using the scale factor k = 3 for dilation rule (kx, ky) gives

A' (-1, 2) = (-1 * 3, 2 * 3) = (-3, 6)

B' (2, 3) = (2 * 3, 3 * 3) = (6, 9)

C' (3, 1) = (3 * 3, 1 * 3) = ( 9, 3)

Learn more on transformation at:

https://brainly.com/question/29321312

#SPJ1

You can see pic..

The system of equations has its solutions to be (1, -1) and (7, -1)

The system of equations is given as

(x−4)² + (y+1)² = 9

(x−4)²/9 + (y+1)²/81 = 1

Make (y + 1)² the subject in the equation (x−4)² + (y+1)² = 9

So, we have

(y+1)² = 9 - (x−4)²

Substitute (y+1)² = 9 - (x−4)² in (x−4)²/9 + (y+1)²/81 = 1

This gives

(x−4)²/9 + [9 - (x−4)²]/81 = 1

Split

(x−4)²/9 + 9/81 - (x−4)²/81 = 1

Collect the like terms

(x−4)²/9 - (x−4)²/81 = 1 - 9/81

Evaluate the like terms

[9(x−4)² - (x−4)²]/81 = 72/81

So, we have

9(x−4)² - (x−4)² = 72

Evaluate the difference

8(x−4)² = 72

Divide by 8

(x−4)² = 9

Take the square roots

x - 4 = ±3

So, we have

x = 4 ± 3

Evaluate

x = 1 or 7

Substitute x = 1 or 7 in (y+1)² = 9 - (x−4)²

(y + 1)² = 9 - (1−4)² or (y + 1)² = 9 - (7−4)²

This gives

(y + 1)² = 0 or (y + 1)² = 0

This gives

y + 1 = 0

Evaluate

y = -1

Hence, the solution is (1, -1) and (7, -1)

Read more about system of equations at

https://brainly.com/question/13729904

#SPJ1