Solve the system of equations.
2x - 4y -z = 10
4x - 8y - 2z = 16
3x + y + z = 12

Given

Solving, step-by-step

Answer:

The equation of the line is -1/3x + 4

Step-by-step explanation:

You would do rise over run or use the slope formula

y2-y1/x2-x1=

2-4/6-0 = -2/6 = -1/3

The y-intercept is when the line hits the y-axis so it would be (0,4) or 4

Dhamby, this is the solution:

In a right triangle, there are 2 acute angles and 1 right angle.

Let x be the measure of the larger acute angle, using the triangle sum theorem (that states that the sum of the interior angles of a triangle is 180) we have that:

The larger acute angle measures 72°.

Answer:

$45.50

Step-by-step explanation:

We want to find 70% of the original cost.

[tex].70 \times 65 = 45.50[/tex]

The area of this semi-circle is 38.28 cm²  and this can be determined by using the formula of area of the semi-circle.

Given :

The diameter of the semi-circle is 10 cm.

The area of the circle is given by the formula:

A=[tex]\pi[/tex]r²

where r is the radius of the circle.

So, the area of the circle whose radius is 5cm is given by:

A=[tex]\pi[/tex]×(5)²
A=25[tex]\pi[/tex]

The area of the circle is 25[tex]\pi[/tex] then the area of the semicircle whose radius is 5cm is given by:

A[tex]s[/tex]= 25/2([tex]\pi[/tex])

A[tex]s[/tex]=12.5[tex]\pi[/tex]

Now, substitute the value of [tex]\pi[/tex] in the above equation.

A[tex]s[/tex]=12.5×3.142

A[tex]s[/tex]=39.28cm²

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it is proven that 6√5 between 12 and 18, Irrational numbers

What are Irrational numbers?

The group of real numbers known as irrational numbers are those that cannot be written as a fraction of the form p/q, where p and q are integers. Additionally, the decimal expansion of an irrational integer is neither terminating nor recurring.

Irrational numbers are real numbers that cannot be expressed as a straightforward fraction. These cannot be stated as ratios, such as p/q, where p and q are integers, q0. It is a contradiction of rational numbers.

It has been given in question 4 < 5 < 9 and we have to show 6√5 is between 12 and 18.

For box number 1.

4 < 5 < 9 ⇒ √4 < √5 < √9

For the box number 2.

√4 < √5 < √9    ⇒   2 < √5 < 3

For the box number 3.

we multiply the inequality by 6.

6×(2 < √5 < 3)

⇒ 6×2 < 6×√5 < 6×3

So the 6×2 < 6×√5 < 6×3

⇒ 12 < 6√5 < 18

Hence it is proven that 6√5 between 12 and 18.

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Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]

Recall that:

Therefore the given equation has no solutions.

Answer: Option B.

Since QS is perpendicular:

It implies that when F(x) shifts 7 units to the left, we get the value equal to G. (x). As a result, the graph of G(x) is the graph of F(x) with 7 units added to the left.

The graph of g is the reflection of the graph of f. If g(x) = f(-x), then the graph of g is obtained from the graph of f by reflecting about the y-axis.

For instance, the result of multiplying f(x) and g(x) is h(x) = fg (x), or h(x)=f(x)g (x). if f is the function denoted by f(x) = x2 and g is the function denoted by g(x) = x + 3.

Therefore,

The Correct answer is : The two functions G(x) and F are provided to us (x).

We must determine which assertion most accurately contrasts the graphs of G(x) and F(x).

Suppose

F(x) = x [/ tex]

G(x) = x-7

When x = 1 is substituted

So, F(x) = 1

G(x) = 1-7 = -6

It implies that we obtain the value equal to the value of G when F(x) shifts 7 units to the left (x).

The graph of G(x) is therefore the graph of F(x) with 7 units added to the left.

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Given,

The length of the shadow is 27 feet.

The angle of elevation is 20 degree.

Required:

The height of the giraffe.

The diagram of the giraffe and shadow is,

The height of the giraffe is:

Hence, the height of giraffe is 9.8 feet.

Answer: The student got an 84%

Step-by-step explanation:

This one is comparatively simple because 25 is a factor of 100,

we just have to multiply each side by 4 so we get 81 out of 100

Cheers!

Rsmbro

1. We need to find the distance jumped by the Gold winner, we know that the total distance jumped by three athletes is 25.04, so we can subtract the distances from the Silver and Bronze winners in order to determine what we want. This is done below:

Now we need to represent this number as a fraction in its simplest form.

2. In order to determine which medal he would receive, we need to add the distance he actually jumped by 0.06 and compare to the table. We have:

He would win a Bronze medal.

3. In order to determine how farther Athlete B jumped more than Athlete D, we need to subtract their distances.

The athlete B jumped 0.26 meters farther than Athlete D.

x=3.7

1) Given that AC is the line segment made up by AB + BC We can set this equation:

AC=AB+BC

13x-17=2x+4+19 Combining like terms

13x-2x -17=2x-2x+23

11x -17=23

11x -17+17 = 23 +17

11x = 40 Dividing both sides by 11

x=3.63 Round to the nearest tenth

x=3.7

Answer:

1. Acute Isosceles Triangle

2. Equiangular Equilateral Triangle

3. Obtuse Scalene Triangle

Step-by-step explanation:

Triangle 1:

It is given that there are two congruent sides. By the definition of an Isosceles Triangle, where at least two or more sides are congruent, it is an Isosceles Triangle.

An acute angle is less than 90 degrees. A right angle is 90 degrees. An obtuse angle is greater than 90 degrees. An equiangular triangle is a triangle whose angles are all of the same measure.

By these definitions, Triangle 1 is an acute Isosceles Triangle.

Triangle 2:

It is given that all three sides are congruent. By the definition of an Equilateral Triangle, where all the sides must be congruent, this is an Equilateral Triangle.

An equilateral triangle is also equiangular. So, Triangle 2 is an equiangular Equilateral Triangle.

Triangle 3:

It is given that none of the sides are congruent. By the definition of a Scalene Triangle, where none of the sides are congruent, this is a Scalene Triangle.

By the angle definitions above, as one of the angles are greater than 90 degrees, this is an obtuse triangle.

So, Triangle 3 is an obtuse Scalene Triangle.

The points she will have using the given inequalities are;

1) After the three turns is; 4 + (-6) + 8 + (-1)

2) After turn one she will have 0 points

3) After turn 2 she will have 8 points

4) After turn 3 she will have 7 points; She will not earn bonus points because she could not reach ten points

We are told that the rule for Rebecca's movement is that

She moves up an energy level for each tree she plants.

She moves down a level for each tree she cuts.

If she reaches energy level 10, she will earn bonus points.

Now, we are told that she is at level 4.

A) Turn 1 = 6 trees cut

Turn 2 = 8 trees planted

Turn 3 = 1 tree cut.

The expression that represents Rebecca's energy level after the three turns is;

4 + (-6) + 8 + (-1)

B) Rebecca's energy level after the first turn is; 0 points because she cut 6 trees

C) Rebecca's energy level after the second turn is; 8 points because she planted 8 trees

D) Rebecca's energy after turn 3 is; 8 + (-1) = 7

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Answer:

3487

Step-by-step explanation:

The order of values in ascending order will be -4<-2<2<2.64<4<16 as the definition of ascending order says, "When numbers are arranged in ascending order, they are done so from smallest to largest".

When numbers are arranged in ascending order, they are done so from smallest to largest. Climbing down the stairs of numbers starting with their highest value is another way to think of descending. The slide is descended while moving down it. Ascending order, in which the numbers are arranged from lower value to higher value, is the opposite of descending order. A number can be arranged in ascending order by going from smallest to largest from left to right.

Here,

4²=16

-√4=-2

√4²=4

-2√4=-4

6-4=2

√7=2.64

-4<-2<2<2.64<4<16

According to the definition of ascending order, "When numbers are arranged in ascending order, they are done so from smallest to largest," the order of values in ascending order will be -4<-2<2<2.64<4<16.

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Answer:

1100 feet, or 335.28 meters

ANSWER:

The numbers are 2, 4 and 5

STEP-BY-STEP EXPLANATION:

let x be the smallest, y the one that follows and z the largest

we have the following equations

We solve the system of equations as follows

now, for z:

for y:

The shop for which Betsie should buy the 250 envelopes from, using proportions, is Value World.

A proportion is a fraction of a total amount, and this fraction is used to build relations, using basic arithmetic operations such as multiplication or division, to obtain the desired measures.

In this problem, the final price is obtained as follows:

Hence the final price at Value World is given as follows:

1.99/10 = 0.119.

She will pay for 2/3 of the 250 packs, as she buys 2 and gets one free, hence:

2/3 x 250 x 0.119 = £19.83.

At Letters2go, the final price is obtained as follows:

3.19/25 x 250 = £31.90.

Due to the lower price, she should purchase her envelopes at Value World.

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We know that if XY = 0 then there are two options: X = 0 or Y = 0

Then, in this case:

If ( 1 - v ) (5v +9 ) = 0​ then

( 1 - v ) = 0 or (5v +9) = 0

We find v for both cases:

1 - v₁ = 0

1 = v₁

5v₂ + 9 = 0

5v₂ = -9

v₂ = -9/5

well, the change is just 112 - 96 = 16.

now if we take 112 as the 100%, what's 16 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 112 & 100\\ 16& x \end{array} \implies \cfrac{112}{16}~~=~~\cfrac{100}{x} \\\\\\ 7=\cfrac{100}{x}\implies 7x=100\implies x=\cfrac{100}{7}\implies x\approx 14.29[/tex]

Answer:

The speed of wind is 75 miles / hour

Step-by-step explanation:

Let's assume

speed of airplane is x miles /hour

speed of wind is y miles /hour

An airplane travels 600 miles against the wind in 4 hours

against wind means resultant speed will be less

so, speed =x-y

total distance traveled in 4 hour is

and this has to be equal to 600

Divide both sides by 4

makes the return trip with then same wind in 2 hours

with wind means resultant speed will be more

so, speed =x+y

total distance traveled in 2 hour is

and this has to be equal to 600

Divide both sides by 2

So, we get system of equations

now, we can solve it by adding both equations

now, we can solve for x

now, we can  find y by plugging x into any one equation

I would solve 2x-3 by first off multiplying, then subtracting. Make sure to start with the equations in the parentheses.

Answer:

Alternative C - Has two unequal real roots and two unequal complex roots

Step-by-step explanation:

The roots of this equation are:

(solved using the computer):

As we can see, we have two unequal real roots and two unequal complex roots.

Alternative C.

Given:

There are 5 numbers followed by 2 letters.

Solution:

To find the answer, we will have a plate number that consists of 5 numbers followed by 2 letters. In that 5 numbers, each place has 10 choices-from 0 to 9. It will be: 10 * 10 * 10 * 10 * 10 = 100,000 .

Now, for the letters, there are 26 letters in the alphabet. We have two places for the letters and each place have 26 choices-from A to Z that will give us: 26 * 26 = 676

We will now multiply the acquired data for both the numbers and letters to arrive at the correct answer.

100,000 * 676 = 67,600,000

ANSWER: 67,600,000 possible license plates