In the diagram, PQRS is a quadrilateral. < PQR = < PRS = 90°, /PQ/ = 3 cm , /QR/ = 4 cm and /PS/ = 13 cm, Find the area of the quadrilateral.

Answer:

there are 2 solutions in total

Step-by-step explanation:

x^2-4=0

x^2=4

x= ±2i

Answer:

x=±2

Step-by-step explanation:

x²-4=0

x²-2²=0

(x+2)(x-2)=0

either x+2=0,x=-2

or x-2=0,x=2

Answer:

Step-by-step explanation:

y ≤ 2x + 2  ⇒   2x → line increasing,  ≤ → solid line, y≤ → shade below line  

¹/₂x + y < 7

y < -¹/₂x + 7 ⇒  -¹/₂x → line decreasing,  < → dashed line, y< → shade below line  

y − 3 ≥ 0

y ≥ 3  ⇒  0x → line parallel to X-axis,  ≥ → solid line, y≥ → shade above line  

Answer:

(14, 5)

Step-by-step explanation:

1. substitute- (x,y)=the original coordinates (9,9) right?

2. So no you want to do x, you have 9 and if you are moving right 5 units it'll be 9+5 because x is left to right on a graph.

9+5=14 therefore (14,y)

3. Now you do y, y is up and down. So you want to go down 4, you subtract 4 from 9 giving you five. Now you have (14,5)

Hope I could help! :)

Let's say she does the absolute minimum and buys 4 bags

Each bag has 7 servings, so there are 7*4 = 28 servings total.

I'm assuming each of the 30 guests gets one serving only. If so, then there wouldn't be enough food to go around (30-28 = 2 people are left out).

This means she cannot round x = 4.3 to x = 4. Instead, she must round up to get x = 5 as the lowest x value possible.

7x = 7*5 = 35 servings clears the hurdle.

So in short, x = 4 does not work in [tex]7x \ge 30[/tex] but x = 5 does work in

-----------

Alternatively, you could plug in x = 4 into [tex]x \ge 4.3[/tex] to get [tex]4 \ge 4.3[/tex] which is not a true statement. So x = 4 is not a solution to

However, x = 5 is a solution since [tex]5 \ge 4.3[/tex] is a true statement.

Answer:

1

Step-by-step explanation:

Simplify the following:

(44×10)^0

Hint: | Simplify (44×10)^0 by distributing exponents over products.

Multiply each exponent in 44×10 by 0:

Answer: 1

any number to the zero power always gives a one

Answer:

a = 0

Step-by-step explanation:

a + 5 = -5a + 5      subtract 5 from both sides

a + 5 - 5 = -5a + 5 - 5

a = -5a                add 5a to both sides

a + 5a = -5a + 5a

6a = 0                 divide both sides by 6

6a / 6  =  0 / 6

therefore,

a = 0

Answer:

A.

Step-by-step explanation:

This is a geometric sequence with common ratio -12/-3 = 4  ( -48/-12  = 4 and  -192 / -48 = 4).

nth term = a1 r^(n - 1) so the 8th term

= -3 * (4)^(8 - 1)

= -49,152.

The 8th term of the geometric sequence is -768

A sequence is an ordered list of numbers (or other elements like geometric objects), that often follow a specific pattern or function.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

Formula for the n th term of a geometric sequence in the form

aₙ=a₁ rⁿ

Given sequence is   -3, -12, -48, -192, . . .

It is a geometric sequence with the ratio between consecutive terms is 4

i.e. r = 4

a₁ = -3

a₈ = -3 ×4⁸

   =-768

Thus the 8th term of this sequence is -768

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Answer:

{5, 6, 7}

Step-by-step explanation:

The domain is the input values

The input values are the x values

{5, 6, 7}

Answer:

i think it is 30% of the total price

i hope it helps

Answer:

x = 54/7 y= -4/7

Step-by-step explanation:

Answer:

x = 54/7 and y = -4/7

Step-by-step explanation:

x+3y=6

4x-2y=32

= 4 ( x+3y=6 )

= 4x +12y = 24 - 4x -2y = 32

=14y = -8

y = - 4/7

X + 3(-4/7) = 6

x+-12/7 = 6

x = 54/7

Answer:

Answer is A. 7 1/5

Step-by-step explanation:

Answer:

look at the sbse below

Step-by-step explanation:

∠DEC ≅ ∠DCE, ∠ACB ≅ ∠GEF,

∠B ≅ ∠F,  DF ≅ BD

∠ACB ≅ ∠GEF, ∠B ≅ ∠F,  DF ≅ BD,  ΔABC ≅ ΔGFE.

i hope this helps you :) it took me a long time

Answer:

Next 3 terms 031, N30, D31

Step-by-step explanation:

J30, J31, A31, S30

The above series represent the

first letter of the month and the days in it

J30= June which have 30 days

J31= July which has 31 days

A31= August which have 31 days

S30= September which have 30 days

30 days hath September, April, June and November. All the rest have 31 except February alone which has but 28 or 29 days

The next 3 terms of the series J30, J31, A31, S30 are 031, N30, D31

Answer:

as a decimal its 2.66666666667, as a mixed number its about 2 1/3

Step-by-step explanation:

multiply 2/3 by 4 to get the whole amount of flour

Answer: a microorganism or microbe is an organism that is microscopic.

Step-by-step explanation: Microorganisms can be bacteria, fungi, archaea or protists. Which are living they dont include non living organisms

the answer is (-9,-7) it flips into the 3rd quadrant.

Answer:

Step-by-step explanation:

Solution,

E ( 3 , 7 ) ⇒ ( x₁ , y₁ )

F ( 6 , 5 ) ⇒( x₂ , y₂ )

Finding the distance between these points:

[tex] \boxed{ \sf{distance = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }}[/tex]

plug the values

⇒[tex] \sf{ \sqrt{ {(6 - 3)}^{2} + {(5 - 7)}^{2} } }[/tex]

Calculate the sum or difference

⇒[tex] \sf{ \sqrt{ {3}^{2} + {( - 2)}^{2} } }[/tex]

Evaluate the power

⇒[tex] \sf{ \sqrt{9 + 4} }[/tex]

Add the numbers

⇒[tex] \sf{ \sqrt{13} }[/tex] units

Hope I helped !

Best regards!!!

Answer:

$2500

Step-by-step explanation:

It is assumed that we need a tax calculation one off per year.

In this case $50,000 yearly salary falls in 5% range

So the tax is:

Answer:

yes

Step-by-step explanation:

-1 1/2 = -3/2

A rational number is a number that can be written as a fraction of integers.

-1 1/2 is the same as -3/2.

-3 and 2 are integers, so -3/2 is a fraction of integers.

Answer: yes

Answer: Yes

Step-by-step explanation:

-1 1/2 is a rational number because it is a non-repeating fraction and is still rational even if it is negative.

Answer:

C

Step-by-step explanation:

mean score class A= 84

mean score class B= 76

the average/mean scores of class B< average/mean scores of class A

76<84

by process of elimination,

B is false- the mean scores class A are not lower than class B

A is false- the highest score is in class A with a score of 94 (highest score in class B=88)

D- not enough information is provided to determine coefficient of variation

Answer:

1 ft : 2.5 yd or 1 ft : 2 1/2 yd

Step-by-step explanation:

He wants a real dimension of 10 yards to be represented by a scale dimension of 4 ft.

4 ft : 10 yd

Divide both sides by 4.

1 ft : 2.5 yd or 1 ft : 2 1/2 yd

Answer:

6

Step-by-step explanation:

The absolute value is the positive integer of the number.

-6 -> 6.

If you were to use a number line, then -6 is 6 units away from 0. The positive number that is 6 units away from 0 is 6.

Answer:

the answer is c

Step-by-step explanation:

i did the quiz

Answer:

There are no triangles given, so I will explain what congruent triangles are.

Step-by-step explanation:

Two triangles are said to be congruent if the three sides and the three angles of both the angles are equal in any sense.

Consider the following conditions for two triangles:

- Two angles and corresponding side, of the two triangles are equal

- Two sides and angle between the two triangles are equal

- Hypotenuse and Leg of two right angled triangles are equal.

If all these conditions are met for any two triangles, they are said to be congruent.

Answer:

The four true statements are:

1. If an angle is a right angle,  it measures 90°.

2. If an angle measures 90°, it is a right angle.

3. If an angle is not a right angle,  it does not measure measure 90°.

4. If an angle does not measure 90°, it is not a right angle.

Step-by-step explanation:

Given the biconditional statement:

An angle is a right angle if and only if it measures 90°.

To find:

Four true conditional statements.

Solution:

First of all, let us the learn the concept of four true conditional statements from a given biconditional statement.

Let the biconditional statement be "[tex]a[/tex] is true if and only if [tex]b[/tex] is true.

Then the four true statements can be written as:

1. If [tex]a[/tex] is true then [tex]b[/tex] is true.

2. If [tex]b[/tex] is true then [tex]a[/tex] is true.

3. If [tex]a[/tex] is false then [tex]b[/tex] is false.

4. If [tex]b[/tex] is false then [tex]a[/tex] is false.

Here [tex]a[/tex] is "an angle is a right angle"

[tex]b[/tex] is "it measures 90°" .

So, the four true statements are:

1. If an angle is a right angle,  it measures 90°.

2. If an angle measures 90°, it is a right angle.

3. If an angle is not a right angle,  it does not measure measure 90°.

4. If an angle does not measure 90°, it is not a right angle.

Answer:

For me i got this.  A) = 16.846mg B) 24 days I am also in summer school for toronto schoolboard.  I used the formula like how it said so should be good.

Step-by-step explanation:

A)

[tex]P(t) = Po(2)x^\frac{t}{d} \\=5(2)^\frac{7}{4} \\=16.817mg[/tex]

B)

[tex]320=5(2)^\frac{t}{4}\\ 64=2^\frac{t}{4}\\2^6=2^\frac{t}{4}\\6=\frac{t}{4}\\(4)6=t \\t=24 days[/tex]

Answer:

$4.59

Step-by-step explanation:

At the sale price:

5 paints set cost Jasmine $16.45

Each paint set = Total cost of 5 paints set / 5

= $16.45 / 5

= $3.29

What was the price of 1 paint set before the sale?

Because the store reduces the price of each paint set by $1.30 before selling, we will add $1.30 to the price of each paint set during sales

Price of each paint set during sales = $3.29

price of 1 paint set before the sale = $3.29 + $1.30

= $4. 59

The cost of 1 paint set before the sale was $4.59

From the question, we are told that 5 paints set cost $16.45. From this, we can know the cost of 1 paint.

Cost of 1 paint set = cost of 5 paints set / 5

Cost of 1 paint set = $16.45 / 5

Cost of 1 paint set = $3.29

We are then asked the price of 1 paint set before the sale?

Since the store reduces the price of each paint set before selling it, this them means that we will add $1.30 to the price during the sales .

If the cost of 1 paint set during sales is $3.29, then

the cost of 1 paint set before the sale = $3.29 + $1.30

the cost of 1 paint set = $4. 59

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Answer:

A. Plane B because it was 9.33 miles away

B. 48 units

Step-by-step explanation:

A. Since the airplanes fly at an angle to the runway, their direction forms a triangle with the runway with their height above the ground as the opposite of the angle and their distance from the airport as the hypotenuse.

So for airplane A with 44° angle of departure,

sin44° = y/h where y = height above the ground and h = distance from airport

So h = y/sin44° = 6/sin44° = 8.64 miles

So for airplane B with 40° angle of departure,

sin40° = y/H where y = height above the ground and H = distance from airport

So H = y/sin40° = 6/sin40° = 9.33 miles

Since airplane B is at 9.33 miles away from the airport whereas airplane A is 8.64 miles from the airport, airplane B is farther away.

B. We know that scale factor = new size/original size

Our scale factor = 4 and original size = 12 units. So,

new size = scale factor original size = 4 × 12 = 48 units.