Find the solution to the system of equations, x + 3y = 7 and 2x + 4y = 8.

1. Isolate x in the first equation: x = 7 − 3y
2. Substitute the value for x into the second equation: 2(7 − 3y) + 4y = 8
3. Solve for y:
14 − 6y + 4y = 8
14 − 2y = 8
−2y = −6
y = 3
4. Substitute y into either original equation: x = 7 − 3(3)
5. Write the solution as an ordered pair:

Answer:

154.3

Step-by-step explanation:

The measure of each interior angle of a regular polygon with 14 sides is about 154.3.

Answer:

2160°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 14, thus

sum = 180° × 12 = 2160°

Answer:

100 toys in 8 hours

Step-by-step explanation:

10x5=50 (4 hours)

THEN

50x2=100 (8 hours)

The toy maker produces 100 toys in 8 hours. This problem may be answered using ratio and proportion or through the factor label method commonly used in Science. It uses equalities given in the problem to help solve an unknown quantity.

Further Explanation:

To get the number of hours produced in 8 hours, use the following relationships given in the problem:

4 hours = 10 boxes

1 box = 5 toys

1. Get the number of boxes of toys produced in 8 hours:

[tex]\frac{4 \ hours}{10 \ boxes} \ = \frac{8 \ hours}{x \ boxes} \\\\x \ boxes \ = \frac{(8 \ hours)(10 \ boxes) }{4 \ hours} \\\\\boxed {x \ = 20 \ boxes}[/tex]

In 8 hours, the toy maker can produce twice as many boxes of toys. Therefore, 20 boxes can me bade in 8 hours.

2. Get the number of toys in 20 boxes:

[tex]no. \ of \ toys = 20 \ boxes (\frac{5 \ toys}{1 \ box})\\ \\\boxed {no.\ of \ toys \ = 100 \ toys}[/tex]

If each box contained 5 toys, then 20 boxes will be equal to 100 toys.

Learn More:

Keywords: ratio and proportion, dimensional analysis

We know that [tex]\sin(45)=\cos(45)[/tex] and this is the only point when sin and cos are equal lengths. Because both [tex]\sin(45),\cos(45)=\dfrac{\sqrt{2}}{2}[/tex]

Now if the sin of 30° is a half that would mean that cos of 60° is also a half.

Hope this helps.

r3t40

Answer:

[tex]V=(\frac{1}{2}x^{3}+x^{2})\ units^{2}[/tex]

Step-by-step explanation:

we know that

The volume of the oblique prism is equal to

[tex]V=BH[/tex]

where

B is the area of the base

H is the height of the prism

Find the area of the triangular base

The area B is equal to

[tex]B=\frac{1}{2}x^{2}\ units^{2}[/tex]

[tex]H=(x+2)\ units[/tex] ---> the height must be perpendicular to the base

substitute

[tex]V=(\frac{1}{2}x^{2})(x+2)[/tex]

[tex]V=(\frac{1}{2})(x^{3}+2x^{2})[/tex]

[tex]V=(\frac{1}{2}x^{3}+x^{2})\ units^{2}[/tex]

In order to calculate the percentage you must:

1. Divide 15.6/20.8

2. Your answer will be 0.75

3. Turn this into a fraction 75/100

4. Now turn it into a percent 75%

75% is your answer.

Answer:

Step-by-step explanation:

3 - x = 9        subtract 3 from both sides

3 - 3 - x = 9 - 3

-x = 6             change the signs

x = -6

Answer:

=  1 2

Step-by-step explanation: Brainly?

Answer:

(0.618,4.236) and (-1.618,-0.236)

Step-by-step explanation:

To find the intersection, we are looking for a common point between the curves.

We are solving the system:

[tex]y=x^2+3x+2[/tex]

[tex]y=2x+3[/tex].

I'm going to do this by substitution:

[tex]x^2+3x+2=2x+3[/tex]

Subtract 2x and 3 on both sides:

[tex]x^2+1x-1=0[/tex]

[tex]x^2+x-1=0[/tex]

To solve this equation I'm going to use the quadratic formula:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

To find [tex]a,b,\text{ and }c[/tex], you must compare [tex]x^2+x-1=0[/tex]

to [tex]ax^2+bx+c=0[/tex].

[tex]a=1,b=1,c=-1[/tex].

Now inputting the values into the quadratic formula gives us:

[tex]x=\frac{-1\pm\sqrt{(1)^2-4(1)(-1)}}{2(1)}[/tex]

[tex]x=\frac{-1\pm\sqrt{1+4}}{2}[/tex]

[tex]x=\frac{-1\pm\sqrt{5}}{2}[/tex]

This means you have two solutions:

[tex]x=\frac{-1+\sqrt{5}}{2} \text{ or } x=\frac{-1-\sqrt{5}}{2}[/tex]

It does say approximately.

So I'm going to put both of these in my calculator and I guess round to the nearest thousandths.

[tex]x=0.618 \text{ or } x=-1.618[/tex]

Now to find the corresponding y coordinates, I need to use one the equations along with each x.

I choose the linear equation: y=2x+3.

y=2x+3 when x=0.618

y=2(0.618)+3=4.236

So one approximate point is (0.618,4.236).

y=2x+3 when x=-1.618

y=2(-1.618)+3=-0.236

So another approximate point is (-1.618,-0.236).

Answer:

x = - 1

Step-by-step explanation:

The equation of the axis of symmetry for a parabola in standard form

y = ax² + bx + c : a ≠ 0 is found using

x = - [tex]\frac{b}{2a}[/tex]

y = - x² - 2x - 5 ← is in standard form

with a = - 1 and b = - 2, thus equation of axis of symmetry is

x = - [tex]\frac{-2}{-2}[/tex] = - 1

Equation of axis of symmetry is x = - 1

Answer:

The zero’s have no value since there behind the decimal point. 53.3896 rounded to the nearest 100th can be 55.3900 or 55.39.

Final answer:

Rounding 55.3896 to the nearest hundredth gives you 55.39, as you round up the second decimal place due to the third decimal place being a 9. Trailing zeros after the decimal can usually be dropped.

Explanation:

When rounding 55.3896 to the nearest hundredth, you need to look at the third decimal place, which is the thousandths place in this case. Since the digit in the thousandths place is a 9, which is greater than 5, you round up the second decimal place (hundredths place) by one. So, 55.3896 rounded to the nearest hundredth is 55.39. It is not necessary to write the trailing zeros after the decimal point unless specifically required for formatting reasons, such as in monetary values or certain scientific contexts. When you round a number and end up with zeros at the end like 55.3900, you can typically drop the trailing zeros to get 55.39.

I think the correct equation is

c(x) = 200 - 7x + 0.345x^2.

Domain is the set of x-values (i.e. units produced) that are feasible. This is all the positive integer values + 0, in case that you only consider that can produce whole units.

Range is the set of possible results for c(x), i.e. possible costs.

You can derive this from the fact that c(x) is a parabole and you can draw it, for which you can find the vertex of the parabola, the roots, the y-intercept, the shape (it open upwards given that the cofficient of x^2 is positive). Also limit the costs to be positive.

You can substitute some values for x to help you, for example:

x      y

0    200

1    200 -7 +0.345 = 193.345

2    200 - 14 + .345 (4) = 187.38

3    200 - 21 + .345(9) = 182.105

4    200 - 28 + .345(16) = 177.52

5    200 - 35 + 0.345(25) = 173.625

6    200 - 42 + 0.345(36) = 170.42

10  200 - 70 + 0.345(100) =164.5

11 200 - 77 + 0.345(121) = 164.745

The functions does not have real roots, then the costs never decrease to 0.

The function starts at c(x) = 200, decreases until the vertex, (x =10, c=164.5) and starts to increase.

Then the range goes to 164.5 to infinity, limited to the solutcion for x = positive integers.

Answer:

-6 > x

Step-by-step explanation:

First, no matter which variable and coefficient you move, you will be dividing by a negative in the end, so reverse the inequality symbol when your answer is found. Next, you move whichever term [NOT associated with a variable (negative or positive)] is near the variable and coefficient over to the left or right side of the inequality symbol depending on where they are in the inequality. Finally, you divide by the negative coefficient it gives you, and you will arrive at your answer with your inequality symbol reversed. The answer just happens to be written in reverse. Although it is written in reverse, it is still the same answer.

I hope this helps you understand the concept, and as always, I am joyous to assist anyone at any time.

Answer:

5

Step-by-step explanation:

Add

2 plus 3 equals 5

Step-by-step explanation:

so put two fingers up and then put three up then you get your answer.

Answer:

x=27

Step-by-step explanation:

The two angles are vertical angles, which means they are equal

4x+7 = 5(x-4)

Distribute the 5

4x+7 = 5x-20

Subtract 4x from each side

4x+7 -4x = 5x-4x -20

7 = x-20

Add 20 to each side

7+20 =x-20+20

27 = x

Answer:

22 cm, 24 cm, and 24 cm.

Step-by-step explanation:

Isosceles Triangle is a type of triangle in which two of the three sides are equal in length. The perimeter is 70 cm. Therefore, in this question, since the sides are unknown, we can assume that:

Length of the shorter side = x cm.

Length of the other sides = y cm.

The relationship between x and y is given by:

x = (2y - 26) cm (because it is mentioned that the shortest side is 26 cm less than twice as long as the other sides).

Perimeter of a triangle = sum of all sides.

Since its an isosceles triangle, therefore:

Perimeter of the triangle = x + 2y.

Substituting the values in the perimeter formula gives:

Perimeter of the triangle = 2y - 26 + 2y.

70 = 4y - 26.

4y = 96.

y = 24 cm.

Substituting y = 24 in the equation x = 2y - 26 gives x = 2(24) - 26 = 22 cm.

So in the ascending order, the lengths are 22 cm, 24 cm, and 24 cm!!!

For this case we have the following equation:

[tex]2x + 5 = -x + (- 1)[/tex]

Below are the correct steps to solve:

We eliminate the parenthesis taking into account that [tex]+ * - = -[/tex]

[tex]2x + 5 = -x-1[/tex]

We add "x" to both sides of the equation:

[tex]2x + x + 5 = -x + x-1\\3x + 5 = -1[/tex]

We subtract 5 from both sides of the equation:

[tex]3x + 5-5 = -1-5\\3x = -6[/tex]

We divide by 3 on both sides of the equation:

[tex]x = \frac {-6} {3}\\x = -2[/tex]

ANswer:

[tex]x = -2[/tex]

Answer:

58 in^2.

Step-by-step explanation:

This is the sum of the area of 4 small rectangles + the area of the 2 larger  rectangles

= 2*4*1 + 2*5*1 + 2*4*5

=  8 + 10 + 40

= 58 in^2

Answer:

58in^2

Step-by-step explanation:

Answer:

y - 1 = 2(x + 2)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 2 and (a, b) = (- 2, 1), thus

y - 1 = 2(x - (- 2)), that is

y - 1 = 2(x + 2) ← in point- slope form

Answer:

Step-by-step explanation:

The ax+by+c=0 that is confusing you is just the standard form of a linear equation. It is supposed to help you formulate the linear equation. In this case, a = 1, b = -2, c = 1

Therefore,

1x -2y + 1 =0

Now, you said that you are confused on how to isolate and solve for one variable; in this case, you can't. But, you can switch around the places of the variables to solve for one variable. In this case, its best to solve for y, since linear equations are easier to understand written in Slope-intercept form:

y = mx+b

Now, you must be really confused, but look at the work I am about to do so you can learn how to make this easier for you!

1x -2y + 1 =0

-1x             -1x   --> Subtract 1x from both sides to isolate the y variable to the               left side and to keep the equation balanced

-2y + 1=0 -1x

       -1             -1   --> Subtract 1 from both sides to isolate the y variable further and to keep the equation balanced

-2y = -1x-1  

(-2y/-2) = ((-1x-1)/-2)  --> Divide by -2 on both sides to isolate the y variable even further and to keep the equation balanced

y = 1/2x+1/2

y = mx+b

This is written in slope-intercept form. It is called as such since it gives you the slope (written in front of the x variable,in this case 1/2; m = 1/2) and the y-intercept (the letter b; in this case b = +1/2). The y-intercept is where the x coordinate is equal to zero, but it is the place where the line crosses the y-axis. So your b = 1/2, which means that your y-intercept is (0, 1/2)

These are all things you use to graph a line and helps to make it easier to graph them!

Final Answer:

For this case we have from the first quadrant that:

[tex]70 + A1 = 90[/tex]

Clearing angle 1:

[tex]A1 = 90-70[/tex]

[tex]A1 = 20\ degrees[/tex]

Ahors, the angle A3 of the third quadrant measures 70 degrees, it is observed that it is opposed by the vertex at the angle of 70 degrees of the first quadrant. So:

[tex]A3-A1 = 70-20 = 50[/tex]

Answer:

Option B

Answer:

Nearly 84°

Step-by-step explanation:

In the attached diagram

So, angle BAC = 120° - 30° = 90°

A parallelogram ABCD is a rectangle, its diagonal vector AD is the sum of vectors AB and AC.

Consider right triangle ABD. In this triangle

[tex]\tan \angle BAD=\dfrac{BD}{AB}=\dfrac{AC}{AB}=\dfrac{7}{5}\\ \\\angle BAD\approx 54^{\circ}[/tex]

So, the sum vector AD has direction 30° + 54° = 84°

[tex](g\circ f)(x)=(2x+8)^4\\\\(g\circ f)(-3)=(2\cdot(-3)+8)^4=2^4=16[/tex]

Final answer:

To find (g°f)(-3), we first calculate f(-3) = 2, and then g(2) which equals 16. Therefore, (g°f)(-3) is 16.

Explanation:

The question provided is asking us to compute the composition of two functions, denoted as (g°f)(-3), where f(x) and g(x) are both defined algebraically.

The composition of functions refers to applying one function to the results of another.

To find (g°f)(-3), we first evaluate f(-3) and then use that result as the input for g(x).

Firstly, let's evaluate f(-3):
f(x) = 2x + 8f(-3) = 2(-3) + 8 = -6 + 8 = 2

Now, we evaluate g(2) using the result from f(-3):
g(x) = x⁴g(2) = 2⁴ = 16

Therefore, (g°f)(-3) = g(f(-3)) = g(2) = 16.

The tower is 75 feet, the wire is 20 feet below the top so the wire is 55 feet above the ground.

The length of the wire is the hypotenuse of a right triangle.

Using the law of cosine:

Cos(angle) = Adjacent leg / Hypotenuse.

Cos(46) = 55 / x

X = 55/cos(46)

x = 79.2 feet

Answer:

C. Right isosceles

Step-by-step explanation:

We have 2 angles that are the same, that means two sides have to be the same.  That makes the triangle isosceles

There are 3 angles in a triangle.  They add to 180

45+45+x = 180

90+x=180

90-90+x=180-90

x=90

The other angle is a 90 degree angle.  A ninety degree angle is a right angle.

That makes the triangle a right isosceles triangle

Answer:

Step-by-step explanation:

Calculate the mean (simple average of the numbers).

For each number: subtract the mean. Square the result.

Add up all of the squared results.

Divide this sum by one less than the number of data points (N - 1). This gives you the sample variance.

Take the square root of this value to obtain the sample standard deviation.

Answer:

A

Step-by-step explanation:

EDGE 2020

The value of 5³i⁹ is 125i. This is found by simplifying i to the 9th power to just i and cubing the number 5 to get 125, then multiplying the two together.

To calculate the value of 5³i⁹, we need to understand how to handle complex numbers and exponents. The expression i, known as the imaginary unit, has the property that i² = -1. Keeping this property in mind, we can simplify i⁹ as i⁸ x i¹, where i⁸ is i² raised to the power of 4, which is (-1)⁴ = 1 because any even power of -1 will always equal 1. Therefore, i⁹ simplifies to i. Now, 5³ means that 5 is being cubed, which results in 5x5x5 = 125. Our final step is then to multiply 125 by i, yielding the result 125i.

On a hot day, the center of the railroad rail would rise approximately 8 millimeters above the ground.

The expansion of the railroad rail can be calculated using the formula:

[tex]\[ \text{Expansion} = \text{Coefficient of Expansion} \times \text{Original Length} \times \text{Change in Temperature} \][/tex]

In this case, the coefficient of linear expansion for steel (commonly used for railroad rails) is approximately[tex]\(0.000012/\degree C\)[/tex], the original length of the rail is 4 kilometers (or 4000 meters), and the change in temperature is the equivalent of 16 centimeters (or 0.16 meters). Plugging these values into the formula:

[tex]\[ \text{Expansion} = 0.000012 \times 4000 \times 0.16 \][/tex]

[tex]\[ \text{Expansion} = 0.768 \, meters \][/tex]

This is the total expansion of the rail. However, we are interested in the rise of the center, which is half of the total expansion. Therefore, the rise of the center is:

[tex]\[ \text{Rise of Center} = 0.5 \times 0.768 \][/tex]

[tex]\[ \text{Rise of Center} = 0.384 \, meters \][/tex]

To convert this into millimeters, we multiply by 1000:

[tex]\[ \text{Rise of Center} = 384 \, millimeters \][/tex]

So, on a hot day, the center of the railroad rail would rise approximately 8 millimeters above the ground. This expansion due to temperature changes is crucial to consider in engineering and construction to prevent issues such as buckling or warping of materials.

Answer:

Step-by-step explanation:

We have to tell all the spheres are similar. As the spheres has no other configuration except for being perfectly round three-dimensionally

Answer:

A sphere is a three-dimensional solid which only has one contribute, its radius or the axis of the sphere. If you have only one measurement you can compare with another sphere, so no matter what a sphere will always be proportional to the other. This making all spheres to be similar just like circles.

Step-by-step explanation:

Answer:

25,886 in²

Step-by-step explanation:

The given figure shows 2 circles centered at the same point. We need to find the area of the shaded region. If we observe carefully, the area in between two circles is the shaded region. So if we subtract the Area of smaller circle from the Area of larger circle we can calculate the Area of the shaded region.

Area of a circle = πr²

Radius of larger circle = OP = OQ = 93.4 inches

Radius of smaller circle = OR = OQ - RQ = 93.4 - 71.5 = 21.9 inches

Therefore, area of shaded region will be:

Area of Shaded Region = Area of larger circle - Area of smaller circle

Area of Shaded Region = π(93.4)² - π(21.9)²= 25,886 in²

Thus, the area of shaded region, rounded to nearest inch will be 25,886 in²

Answer:

6

Step-by-step explanation:

Using the sine ratio in the right triangle

let x = hypotenuse and sin45° = [tex]\frac{\sqrt{2} }{2}[/tex], then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3\sqrt{2} }{x}[/tex]

and

[tex]\frac{3\sqrt{2} }{x}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )

[tex]\sqrt{2}[/tex] × x = 6[tex]\sqrt{2}[/tex]

Divide both sides by [tex]\sqrt{2}[/tex]

x = 6