what is the value of x? enter your answer in the box​

Answer:

Area = 7.5

Step-by-step explanation:

The area of the triangle bounded by vertices P(1,1), Q(-2,1), and R(-1,-4) will be 7.5 unit square.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.

Given the triangle with  vertices P(1,1), Q(-2,1), R(-1,-4)

Length between two coordinates (x₁,y₁) and (x₂,y₂) is given by

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

By using this formula

PQ = 3 , QR = 5.099 and PR = 5.385

Now,

The area of a triangle with  all three sides is given by

A = [tex]\sqrt{S(S - A)(S - B)(S - C)}[/tex] where A,B and c are sides and s = (A + B + C)/2

So,

S = (3 + 5.099 + 5.385)/2 = 6.742

Now,

A = [tex]\sqrt{6.742(6.742- 3)(6.742 - 5.099)(6.742 - 5.385)}[/tex]

A = 7.499 ≈ 7.5

Hence "The area of the triangle bounded by vertices P(1,1), Q(-2,1), and R(-1,-4) will be 7.5 unit square".

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Answer:

(w² - 4w - 3) (w² + 4w - 3)

Step-by-step explanation:

w² + 4w³ - 3w² -4w³ - 16w² + 12w-3w² - 12w + 9

Answer:

When present,outliers will have an effect of the range since one of the outliers will either be highest or lowest number in a given data set and the range is found by finding the difference of the highest and lowest numbers.

Answer:

[tex]x = 10[/tex]

Step-by-step explanation:

Given

$x per adult

$8 per student

Population:

[tex]Students = 1[/tex]

[tex]Adults = 4[/tex]

[tex]Total = \$48[/tex]

Required

Determine the equation and solve for x

The system can be analyzed as thus:

The cost for 4 adults is: 4 * x

The cost for 1 students is: 8 * 1

Total Amount is: 48

From the analysis above, the equation is:

[tex]4 * x + 8 * 1 = 48[/tex]

[tex]4 x + 8 = 48[/tex]

Subtract 8 from both sides

[tex]4 x + 8 -8= 48 - 8[/tex]

[tex]4 x= 40[/tex]

Solve for x

[tex]x = 40/4[/tex]

[tex]x = 10[/tex]

28.5

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The solution is : she needs at least 16 points.

x + 64 ≥ 80

x ≥ 16

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

Given

Madeline has to earn at least 80 points for her science fair project. So far on the rubric she has 64 points.

so,

Total = 80 (at least)

accumulated = 64

Required

Express as an inequality

In inequalities, at least means ≥

So, the expression is:

Where x represents the additional points

x + 64 ≥ 80

Solve for x

x ≥ 16

Hence, she needs at least 16 points.

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Answer:

1/3

Step-by-step explanation:

The probability of an event E in a sample space S is P(E) = desired outcome/total number of possible outcomes.

The probability of encountering a red light at the intersection P(red light on) = time it takes red light to stay on/total time all the lights stay on, where desired outcome = time it takes red light to stay on on route A and total number of possible outcomes = total time all the lights stay on.

Since all the other two lights have to come on after the red light goes off and before the red light comes on again, and the red light has to be on to encounter it at an intersection.

So, P(red light on) = 60 s/(60 s+ 45 s+ 75 s)

= 60 s/180 s

= 1/3

Answer:

y = 2x + 10

Step-by-step explanation:

The rate is 2 and the y coordinate starts at 10. You use the y = mx + b formula

Answer:

A

Step-by-step explanation:

The student must have thought that every single arrowhead is a line of symmetry, so since there are 10 arrowheads, there must be 10 lines of symmetry. This is incorrect because if you look closely at the diagram, each line has 2 arrowheads, so the student is overcounting by a factor of 2. They should have just counted the number of lines, not arrowheads. Therefore, there must be 10/2 = 5 lines of symmetry, not 10. Hope this helps!

Step-by-step explanation:

First, we have to prove that the sum of 3 consecutive integers is a multiple of 3.

Let x be the smallest of the 3 consecutive integers. We have (x + 1) and (x + 2) as our other consecutive integers.

Notice that x + (x + 1) + (x + 2) = 3x + 3 = 3(x + 1), which is a multiple of 3.

Hence we have proven our point. Back to the question:

The possible sum has to be a multiple of 3. Searching the options, only 44562 is a multiple of 3. (44562 / 3 = 14854) Hence 44562 is the answer. (C)

Answer:

D

Step-by-step explanation:

Answer: $170.25 + $3.78x = $586.05

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

You can't check to see if your answer makes sense if there is no answer. You can't identify what your trying to find if you don't know the question. If you just solve the problem then you will probably get a bad grade. If you make a plan you need to know what your doing first so reading the problem carefully is the right answer.

Answer:

all of them.

Step-by-step explanation:

Hope this helps!

<3

~nxmbus

Answer:

-1

Step-by-step explanation:

Simplify both sides: 3x + (2(x) + 2(-9)) = 8x + x -14

Add/Combine like terms: 3x+2x= (5x-18) = (9x-14)

New Equation: 5x-18 = 9x-14

add 14 to both sides: 5x-4 = 9x

Subtract 5x from both sides: -4 = 4x

Divide both sides by 4 to get: -1 = x

Answer: x = -1

Answer:

Let's solve your inequality step-by-step.

3600+1.02x<2000+1.04x

Step 1: Simplify both sides of the inequality.

1.02x+3600<1.04x+2000

Step 2: Subtract 1.04x from both sides.

1.02x+3600−1.04x<1.04x+2000−1.04x

−0.02x+3600<2000

Step 3: Subtract 3600 from both sides.

−0.02x+3600−3600<2000−3600

−0.02x<−1600

Step 4: Divide both sides by -0.02.

−0.02x

−0.02

<

−1600

−0.02

x>80000

Step-by-step explanation:

Answer:

-23

Step-by-step explanation:

h(-3) = (-3)^3 + 4

      = -27 + 4

      = -23

Answer:

-23 hope that helps :)

Step-by-step explanation:

Answer:

655

Step-by-step explanation:

655-369=286

I hope this is correct and have a great day

Answer:

1/2

Step-by-step explanation:

1/2 because if you divide 2 pizzas into 4 then you can get 4 1/2s.

if you slice the pizza into fourths then each person will get 2/4rts and which is the same thing as 1/2 only 1/2 is simplified.

Step-by-step explanation:

I hope its help you

Answer:D

Step-by-step explanation:

An auto repair shop charged $75/h  for labor plus an additional $89 for parts.

If the shop worked for 2 h.

C = Represented the total repair cost .

Than the equation becomes

C = 75 × 2 + 89

C = 75 (2) + 89

Therefore the total cost for the repair  is represented by C = 75 (2) + 89 .

Option (D) is correct .

Answer:

Step-by-step explanation:

the charge is 77 dollars per hour of labor

Answer:

I think it is 71.222222 repeating

Step-by-step explanation:

Hope this helped have an amazing day!

Answer:

5 units

Step-by-step explanation:

The computation of the Length of DG is as follows;

Given that

∠EDH ≅ ∠EDG,

EH = 9,

EJ = 4.

Based on the above information, as we can see that the two sides i.e. corresponding are congruent

EH = EG  (CPCTC)

EG = 9.........(i)

Now

EG = EJ + JG

EG = 4 + JG ........(ii)

Now after solving this

JG = 5 units

Hence, the second option is correct

Answer:

5

Step-by-step explanation:

i got it right

Answer:

The area of a shape is the amount of two-dimensional space that it covers. The ratio of the perimeter to the area of a shape is simply the perimeter divided by the area. This is easily calculated.

Answer:

240

Step-by-step explanation:

Answer:

16 m^3

Step-by-step explanation:

Question:

"a regular square pyramid is 3m height and the perimeter of its base is 16m find the volume of the pyramid"

volume of pyramid = (1/3) * (area of base) * height

The perimeter of the base is 16 m, and the base is a square.

perimeter of square = 4 * side

4 * side = 16 m

side = 4 m

area of square = (side)^2

area of base = (4 m)^2 = 16 m^2

volume of pyramid = (1/3) * (area of base) * height

volume = (1/3) * (16 m^2) * 3 m

volume = 16 m^2