Find the angles P, Q, R and S. P =3x , Q =x , R = 4x , S =2x​

Answer:

1. TRUE

2. TRUE

3. TRUE

4. TRUE

5. FALSE

6. TRUE

Step-by-step explanation:

1. From the diagram, we have that m∠2 and m∠7 are alternate interior angles

If m∠2 = 70° and m∠7 = 70°, then we have;

m∠2 = 70° = m∠7

m∠2 = m∠7

Therefore, the alternate interior angles of the lines l₁, and l₂ are equal, and therefore, the lines l₁ and l₂ are parallel, l₁ ║ l₂

TRUE

2. If m∠3 = 90° and m∠7 = 90°, therefore, the angle formed by the intersection of l₃ and l₂ = 90°

Therefore l₃ ⊥ l₂

TRUE

3. m∠5 and m∠7 are corresponding angles

If m∠5 = 85° and m∠7 = 85°, then, m∠5 = m∠7

Therefore, the corresponding angles formed by the lines l₁ and l₂ are equal, therefore;

l₁ ║ l₂

TRUE

4. Whereby we have, m∠1 = m∠5, we get;

m∠1 + m∠5 = 180° by sum of angles on a straight line

∴ m∠1 + m∠5 = m∠1 + m∠1 = 2·m∠1 = 180°

m∠1 = 180°/2 = 90°

∴ m∠1 = 90° = m∠5, and l₃ ⊥ l₁

TRUE

5. m∠1 and m∠8 are alternate exterior angles

If m∠1 = 98° and m∠8 = 82°

∴ m∠1 ≠ m∠8 and l₁ ∦ l₈

FALSE

6. Given that l₁║ l₂, then the angle formed between l₁ and l₃ will be equal to th angle formed between l₂ and l₃

Therefore;

If l₁║ l₂, and l₃ ⊥ l₁, then l₃ ⊥ l₂

(If l₁║ l₂, and l₃ is perpendicular to l₁, then l₃ is also perpendicular to l₂)

TRUE

Given:

y is directly proportional to x.

[tex]y=30[/tex] when [tex]x=5[/tex]

To find:

The equation that connects y with x.

Solution:

It is given that, y is directly proportional to x. So,

[tex]y\propto x[/tex]

[tex]y=kx[/tex]                     ...(i)

Where, k is the constant of proportionality.

We have, [tex]y=30[/tex] when [tex]x=5[/tex]. Substituting these values in (i), we get

[tex]30=k(5)[/tex]

Divide both sides by 5.

[tex]\dfrac{30}{5}=k[/tex]

[tex]6=k[/tex]

Substituting [tex]k=6[/tex] in (i), we get

[tex]y=6x[/tex]  

Therefore, the required equation is [tex]y=6x[/tex].

Answer:

(x-20) (x+3)

Step-by-step explanation:

x^2 - 17x - 60

What two numbers multiply to -60 and add to -17

-20 * 3 = -60

-20 +3 = -17

(x-20) (x+3)

Answer:

option A is correct

Step-by-step explanation:

x^2 - 17 - 60

using middle term break method

x^2 - (20 - 3)x - 60

x^2 - 20x + 3x - 60

x(x - 20) + 3(x - 20)

(x + 3)(x - 20)

Answer: A , 4x - 5y = 5

Step-by-step explanation:

i just did it , duhhh

Answer:

a

Step-by-step explanation:

Answer:

h=rt 79

Step-by-step explanation:

Answer:

77

Step-by-step explanation:

[tex]9^{2}[/tex] - [tex]2^{2}[/tex] = [tex]h^{2}[/tex]

81 - 4 = [tex]h^{2}[/tex]

77 = [tex]h^{2}[/tex]

[tex]\sqrt{77}[/tex] = h

Answer:

(0,0), (0,9), (9,0)

Step-by-step explanation:

The matrix corresponding vertices are:

(0,0)

(0,3)

(3,0)

Rosa scales by 3T, so we need to multiply each point by 3.

(3*0, 3*0)

(0*3, 3*3)

(3*3, 0*3)

=

(0,0)

(0,9)

(9,0)

last answer choice is right.

pls mark me brainly

The vertices of the scaled triangle, 3T is, (0, 0), (0, 9), (9, 0).

The scale factor defines a variable in a ratio of two different measurements.

Sometimes drawings of large models are represented in a scale factor of a smaller unit.

Given, A matrix [tex]T=\begin{bmatrix}0 & 0 & 3\\0 & 3 & 0\end{bmatrix}[/tex] represents the vertices of a triangle.

Let, ABC be the triangle,

So, A(0, 0), B(0, 3), C(3, 0).

Now, If [tex]T=\begin{bmatrix}0 & 0 & 3\\0 & 3 & 0\end{bmatrix}[/tex], Then [tex]3T=3\begin{bmatrix}0 & 0 & 3\\0 & 3 & 0\end{bmatrix}[/tex].

Therefore, [tex]3T=\begin{bmatrix}0 & 0 & 9\\0 & 9 & 0\end{bmatrix}[/tex].

Hence, The new vertices are, (0, 0), (0, 9), (9, 0).

learn more about matrices here :

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Answer:

The answer is D I think :)))

Answer:

120

Step-by-step explanation:

no nonp

Answer:

7 1/4 cookies per minute

Step-by-step explanation:

29/4 = 7 1/4

Answer:

7.25

Step-by-step explanation:

29/4

Step-by-step explanation:

[tex]\longmapsto \rm \dfrac{5x}{7} - \dfrac{x}{14} = \dfrac{9}{7} \\ [/tex]

[tex]\longmapsto \rm \dfrac{10x + x}{14} = \dfrac{9}{7} \\ [/tex]

[tex]\longmapsto \rm \dfrac{11x}{14} = \dfrac{9}{7} \\ [/tex]

→ 11x(7) = 14(9)

→ 77x = 126

→ x = 126 ÷ 77

→ x = 1.63

Answer:

31 batches

Step-by-step explanation:

Find how many batches of orange punch smoothies he can make by dividing 560 by 18:

560/18

= 31.11

Since we can only have a whole number answer, round down.

So, he can make 31 batches of orange punch smoothies.

Answer:

If i recall Maria collected 34 cicadas

Answer:

17 Cicadas

Step-by-step explanation:

62 - 28 divided by two will give us the amount Maria collected.

62 - 28 = 34

34/2 = 17

Maria had 17 cicadas.

How to verify:

17 + 28 + 17 Should equal 62

34 + 28 = 62

Answer:

$375.32

Step-by-step explanation:

100% - 40% = 80%

80/100 = 0.8 (multiplier)

521.28 x 0.8 = 417.024

417.024 to 417.02 (2 d.p.)

100 - 10 = (ans)/100 = 0.9

417.02 x 0.9 = 375.318

$375.32

Step 1: Find the sales price

The surfboard was marked down 40% of its original price, $521.28.

0.40(521.28) = 208.512

521.28 - 208.512 = 312.768

Step 2: Find the final price

We add the tax on the sales price, not the original price. The tax is 10% in this case.

0.10(312.768) = 31.2768

312.768 + 31.2768 = 344.0448

Final price = $344.04

---I did not round until the end in this case, but rounding at every step leads to an answer of $344.05

Hope this helps!

Answer: hello your question is vague hence i will provide a more general answer

Area of a right angled triangle = 1/2 * b * h

Step-by-step explanation:

For a right- angled triangle; the sum of squares of the opposite and adjacent sides = square of the longest side ( i.e. hypothenuse )

hence the Area of a right angled triangle = 1/2 * b * h

where : b = adjacent , h = opposite side

fig 3 would take 18 triangle

fig 4 would take 30 small triangles

if its wrong i am sorry

Answer:

Answer:

1499

Step-by-step explanation:

Given that :

New discounted price = 1274

Let original price = p

Reduction in original price = 225

Original price is the sum of the reduction and the new discounted price

The Original price = Reduction in original price + new discounted price

P = 225 + 1274

P = 1499

Answer:

20

Step-by-step explanation:

One pattern is that we are adding one row and one column for each step.

The first step has 1 row and 2 columns,

the second one has 2 rows and 3 columns,

and the third has 3 rows and 4 columns.

Thus, it would make sense for the fourth step to have 4 rows and 5 columns. This makes a rectangle with a length and a width, with the area of the rectangle being length * width. 4 * 5 = 20 as our number of dots

Answer:

ig its a translation bc its not rotated, reflected or dilated

Step-by-step explanation:

hope this helps

Answer:

The answer is E.

Step-by-step explanation:

A quadrilateral that has only one pair of parallel sides is called a Trapezoid.

Answer:

no thanks i dont feel like doing all that work to help u. i apologize my dear friend bahahahahahahahahahahhahaha

Step-by-step explanation:

Answer:

3lbs 9 ounces

Step-by-step explanation:

16 ounces in a pound

9514 1404 393

Answer:

  3 lb 9 oz

Step-by-step explanation:

Sometimes, addition is easier than subtraction when it comes to finding the difference.

There are 16 ounces in a pound.

  8 lb 11 oz + 5 oz = 9 lb

  9 lb + 3 lb 4 oz = 12 lb 4 oz

To get from 8 lb 11 oz to 12 lb 4 oz, we have added ...

  5 oz + 3 lb 4 oz

  = 3 lb 9 oz . . . . weight of packing materials

__

Or, you can do the subtraction in the usual way.

  total weight = gift weight + packing weight

  packing weight = total weight - gift weight

  = (12 lb 4 oz) - (8 lb 11 oz)

  = (12 lb -8 lb) + (4 oz -11 oz)

  = 4 lb - 7 oz

  packing weight = 3 lb 9 oz

Answer:

[tex] \sqrt{x + 2} [/tex]

If you horizontally shift the square root parent function f(x)=√x left two units the equation of the new function is: g(x) = √(x + 2).

A horizontal shift is a function transformation that shifts a graph to the left or right without changing its shape.

If we want to shift the square root parent function f(x) = √x two units to the left, we must replace the argument x with (x + 2), because a positive value of x + 2 gives us the same x value two units to the left.

So the equation of the new function is:

g(x) = √(x + 2)

This new function is the square root function shifted two units to the left. For any given input value of x, we add 2 to it before taking the square root. This causes the graph to shift horizontally to the left by two units.

Thus, g(x) = √(x + 2) will be the new function.

For more details regarding horizontal shift, visit:

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Answer:

positive linear association

Step-by-step explanation:

the slope is positive so the linear association is also positive and linear mean generaly in a line not on a curve like a nonlinear assciation.

Answer:

hi, the answer is Nu5000

250×20=5000

Answer: [tex]167.5\ in.^3[/tex]

Step-by-step explanation:

Given

Height of paper cone [tex]h=10\ in.[/tex]

Radius of cone [tex]r=4\ in.[/tex]

The volume of the cone is given by

[tex]\Rightarrow V=\dfrac{1}{3}\pi r^2h[/tex]

Insert the values

[tex]\Rightarrow V=\dfrac{1}{3}\times 3.14\times 4^2\times 10\\\\\Rightarrow V=167.5\ in.^3[/tex]

Thus, the volume of the cone is [tex]167.5\ in.^3[/tex]

Answer:

True is the correct answer

Answer:

I believe the answer is true

Answer:

S = {(0, 5), (0, - 5), (3, 4), (3, -4), (-3, 4), (-3, -4), (4, 3), (4, -3), (-4, 3), (-4, -3), (5,0), (-5, 0) }

Step-by-step explanation:

Remember that the distance between two points (a, b) and (c, d) is given by:

[tex]distance = \sqrt{(a - c)^2 + (b - d)^2}[/tex]

So, here we have that the distance between the point (x, y) and the origin, (0, 0) must have a magnitude of 5 units, then we want to solve:

[tex]5 = \sqrt{(x - 0)^2 + (y - 0)^2} \\5 = \sqrt{x^2 + y^2}[/tex]

If we square both sides, we get

[tex]5^2 = (\sqrt{x^2 + y^2} )^2\\25 = x^2 + y^2[/tex]

Now we want to find all the points (x, y) that meet this condition, suc that:

x ∈ Z

y ∈ Z

So both x and y must be integers.

So here we can just play with different values of x and y.

For example, if we define:

x = 0 we get:

25 = 0^2 + y^2

25 = y^2

√25 = y

Then we can have y = 5 or  y = -5

from this we got two points:

(0, 5) and (0, - 5)

if x = 1 we have:

25 = 1^2 + y^2

25 - 1 = y^2

24 = y^2

There is no integer such that its square is equal to 24, so we can stop here.

if x = 2 or - 2, we have:

25 = 2^2 + y^2

25 = 4 + y^2

25 -4 = 21 = y^2

Again, there is no integer such that its square is equal to 21, so we can stop here.

if x = +3 or -3, we have:

25 = 3^2 + y^2

25 = 9 + y^2

25 - 9 = 16 = y^2

√16 = y

then we can have y = 4 or y = -4

from this we got four points:

(3, 4)

(-3, 4)

(3, -4)

(-3, -4)

And for symmetry, if x = 4 or -4 we have the points:

(-4, 3)

(4, 3)

(-4, -3)

(4, -3)

finally, again for symmetry, if we take x = 5 or x = -5 we have the points:

(5,0)

(-5, 0)

Concluding, the set of all possible values (x, y) is:

S = {(0, 5), (0, - 5), (3, 4), (3, -4), (-3, 4), (-3, -4), (4, 3), (4, -3), (-4, 3), (-4, -3), (5,0), (-5, 0) }

Answer:

2nd option

Step-by-step explanation:

The discriminant b² - 4ac tells us about the nature of the roots

• If b² - 4ac > 0 then 2 real and distinct roots

• If b² - 4ac = 0 then 2 real and equal roots

• If b² - 4ac < 0 then the roots are not real

Here b² - 4ac = 15 > 0

Then there are 2 real and distinct roots

x = 2 and x = - 3 are possible solutions to the equation

Answer:

option b) x = 2 and x = -3

Step-by-step explanation:

If discriminant is greater than zero, then the quadratic equation will have two solutions.

If discriminant is equal to zero, then the quadratic equation will have only one solution.

If discriminant is less than zero no solution

Here the discriminant is 15 , which is greater than zero.

Therefore we will have to solutions.

There is only one option with two solutions for x.

So option b is the answer.