What is the solution to the following system of equations?

Answer:

x=5

Step-by-step explanation:

5x-12=13

Add 12 to each side

5x-12+12 =13+12

5x = 25

Divide by 5

5x/5 = 25/5

x = 5

Answer:

1.5 hamburgers per minute

Step-by-step explanation:

In 10 minutes, Justin can eat 15 burgers.

In 1 minute, Justin can eat 15/10 burgers.

15/10 = 1.5

Answer:

1.5 hamburgers per minute

Step-by-step explanation:

15/10 = 1.5

Answer:

(10, -10/3)

Step-by-step explanation:

We're told that x = 10.  Substitute 10 for x in the 2nd equation:  

3(10) + 3y = 20.  Subtracting 30 from both sides, to isolate 3y, we get:

3y = -10

Dividing both sides by 3, we get:  y = -10/3.

The desired solution is (10, -10/3).

The graph is shown in the attached image

Final answer:

To find the height of the tower given the angle of elevation and distance from the observer to the tower's base, the tangent function is used. The height is calculated as 28 feet multiplied by tan(75 degrees), resulting in approximately 105.8 feet.

Explanation:

The student is asking for help with a trigonometry problem involving the angle of elevation to calculate the height of a tower. In this case, we are given the angle of elevation as 75 degrees and the distance from Mindy to the base of the tower as 28 feet. To find the height of the tower, we use the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle.

So, we have:
tan(75 degrees) = opposite/adjacent
tan(75 degrees) = height of tower/28 ft

Therefore, to find the height of the tower, we can write this equation as:
height of tower = 28 ft × tan(75 degrees)

By calculating this using a calculator, we find the height of the tower to be approximately 105.8 feet, which corresponds to option B.

I just taught you how to do this, it’s really simple, try it yourself! I’ll give instructions again.

Use the equation Y=mx+b where m represents the slope and b is the y-axis point.

Finding b is easiest, so we’ll do that first. Again, b is the y axis point. So where does the line cross the y axis? That is the vertical line on the graph. The line crosses at point (0,5) so 5 is your b value.

Next find your m value, or slope. The slope is simply rise/run. Which means start at the y axis value, and count how many places you need to go down to find a perfect triangle shape. You simple go down two points, and then over one point to reach a perfect triangle. Therefore since you go down 2, your rise is -2 and since you go over 1, your run is 1. Rise/run=-2/1, this simplified is just -2. So that is your m value.

Finally, plug these into y=mx+b and get your answer of

Y=-2x+5

Best,

jrodt

Answer:   4

Step-by-step explanation:

f(x) = 4x³ - x² + 1        g(x) = x - 1

                                 g(2) = (2) - 1

                                        = 1

f(1) = 4(1)³ - (1)² + 1

     =  4   -   1   + 1

Answer:

2.C

3.B

4.B

5.D

Step-by-step explanation:

2. the y intercept in this equation is the c value, which is 1 so the answer is c

3. The vertex of this function would be (9, -5) and the axis of symmetry is the first value so its 9, B

4. Not that hard, tip is to just distribute in all the answers and see which one gives you the original equation, it is B

5. You solve the original equation by completing the square, if you don't know how to do that look it up. Answer is D

The answers to all parts are shown below.

In mathematics, an intercept is the point at which a line, curve or surface intersects a coordinate axis. In the case of a two-dimensional Cartesian coordinate system, intercepts of a line are where the line intersects either the x-axis (horizontal axis) or the y-axis (vertical axis). The x-intercept is the point at which the line intersects the x-axis, and the y-intercept is the p

1. The Y-intercept of the quadratic function f(x) = 6x² - 3x + 1 is the value of f(0), which is the value of the function when x = 0. Therefore, we have:

f(0) = 6(0)² - 3(0) + 1 = 1

So the Y-intercept of the function is 1.

2. The axis of symmetry of a quadratic function given in vertex form, f(x) = a(x - h)² + k, is the vertical line x = h.

Therefore, for the given quadratic function f(x) = 4(x + 9)² - 5, the vertex is at the point (-9, -5), and the axis of symmetry is the vertical line x = -9.

3. Now, we can write the quadratic function in factored form as:

f(x) = 3(x-(-8))(x-3)

= 3(x+8)(x-3)

Therefore, the answer is (D) f(x)=3(x+8)(x-3).

4. We can complete the square to rewrite the quadratic function in vertex form:

f(x) = -2x² + 16x - 11

f(x) = -2(x²- 8x + 11/2)

f(x) = -2(x²- 8x + 16 - 16 + 11/2)

f(x) = -2((x - 4)² - 21/2)

f(x) = -2(x - 4)² + 21

Learn more about Intercept here:

https://brainly.com/question/14180189

#SPJ7

Answer:

[tex]\large\boxed{5x^2+6x-8=(x+2)(5x-4)}[/tex]

Step-by-step explanation:

[tex]5x^2+6x-8\\\\=5x^2+10x-4x+8\\\\=5x(x+2)-4(x+2)\\\\=(x+2)(5x-4)[/tex]

Answer:

C

Step-by-step explanation:

use ac method

for ax^2+bx+c

multiply a and c

find what 2 numbers multiply to get ac and add to get b

split b into those 2 numbers

group

factor

factor

5x^2+6x-8

ac=5 times -8=-40

what 2 numbers multiply to get -40 and add to get 6?

-4 and 10

5x^2+10x-4x-8

group

(5x^2+10x)+(-4x-8)

factor

5x(x+2)-4(x+2)

factor

(5x-4)(x+2)

C is the answer

2.32558139535 or it can just be 2.325

The answer For two divided by eighty six hundredths is forty three hundredths.

0.86/2. 0.43

Answer:

80000/0.0004 = 2'000'000'000 or 2 x 10^-9

8*10^4 = 80'000

4*10^-5 = 0.00004

Step-by-step explanation:

Answer:

0,2

Step-by-step explanation:

[8*10^4] / [4*10^5]

2*[10000/100000]

0,2

Best regards

Answer:um you simplify it

Step-by-step explanation:

To make the fraction 17/24 smaller, you can increase the denominator or decrease the numerator, but it will change the value of the fraction.

To make the fraction 17/24 smaller, you need to increase the denominator (the bottom number) or decrease the numerator (the top number).

One simple way to do this is to add a number to 24 making it 25, 26, 27, and so forth while keeping the numerator as 17. The larger the denominator, the smaller the fraction is. Alternatively, you could decrease the numerator to 16, 15, etc, while keeping the denominator at 24. Again, the smaller the numerator, the smaller the fraction.

Also remember that the fraction must remain proper or else it will become a whole number and eventually bigger than 17/24.

Please note that these changes alter the value of the fraction, and therefore might not be accurate representations of whatever the fraction 17/24 is supposed to represent.

https://brainly.com/question/10354322

#SPJ12

Answer:

The width is 20 inches, the length is 32 inches and the height is 15 inches.

Step-by-step explanation:

Let x inches be the width of the box. If the length of the box is 12 inches greater than its width, then the length of the box is x+12 inches. If the height of the box is 5 inches less than its width, then the height of the box is x-5 inches.

The volume of box is

[tex]V=\text{length}\cdot \text{width}\cdot \text{height}\ in^3.[/tex]

Therefore,

[tex]9600=x\cdot (x+12)\cdot (x-5).[/tex]

Solve this equation:

[tex]x(x^2+12x-5x-60)=9600,\\ \\x^3+7x^2-60x-9600=0.[/tex]

The integer solutions of this equation can be among the divisors of -9600. The divisors of 9600 are:

[tex]\pm1, \pm2, \pm3, \pm4,\pm5,\pm6,\pm8,\pm10,\pm12,\pm15,\pm16,\pm20,\pm24,\pm25,\pm30,\pm32,....[/tex]

We can check all these divisors and see that x=20 is a solution, then using synthetic division

[tex]x^3+7x^2-60x-9600=(x-20)(x^2+27x+480).[/tex]

Since the quadratic factor has discriminant [tex]D=27^2-4\cdot 480=-1191<0,[/tex] we can state that the only solution is x=20 inches. The width is 20 inches, the length is 32 inches and the height is 15 inches.

➷ Adjacent angles total to 180 degrees

15x + 1 + 13x + 3 + 64 = 180

28x + 68 = 180

Subtract 68 from both sides:

18x = 112

Divide both sides by 28:

x = 4

Substitute this value back in:

15(4) + 1 = 61

Angle VTS = 61 degrees

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

The angles in a triangle are equal to 180 degrees

Keeping in mind alternate angles are always equal we can say that ∠TVU=∠VTS

So we can find ∠TVU which is equal to [tex]15x+1[/tex]

In order to  find the angle we need the value of x

[tex]13x+3+15x+1+64=180[/tex]

Simplify

[tex]28x+68=180[/tex]

Isolate x

[tex]28x=180-64\\28x=112\\x=\frac{112}{28}\\x=4[/tex]

Now that we have the value of x we can substitute in [tex]15x+1[/tex]

[tex]15(4)+1\\=60+1\\=61[/tex]

With ∠TVU being 61 degrees, ∠VTS is also 61 degrees as they are alternate angles

Hope this helps :)

If you need further help, just let me know, I would be happy to help :)

Answer:

[tex]\large\boxed{C.\ \log_55+-5\log_5x}[/tex]

Step-by-step explanation:

[tex]\log_ab^c=c\log_ab\\\\\log_a(bc)=\log_ab+\log_ac\\=====================\\\\\log_55x^{-5}=\log_55+\log_5x^{-5}=\log_55+-5\log_5x[/tex]

The value of logarithm log5 [tex]5x^{-5[/tex] is [tex]-5 (log_5 (5) + log_5 (x) )[/tex].

Thus, option (c) is correct.

To expand the logarithm log5 [tex]5x^{-5[/tex], use the logarithmic property.

According to power rule,

logarithm of a number raised to a power can be expressed as the product of the exponent and the logarithm of the number.

Using the power rule, we can rewrite the expression as:

[tex]{\text} log_5 5x^{-5} =[/tex][tex]\;{\text} -5 log_5 (5x)[/tex]

and, [tex]log _c (ab) = log_c (a) + log_c(b)[/tex]

So, [tex]\;{\text} -5 log_5 (5x)[/tex] = [tex]-5 (log_5 (5) + log_5 (x) )[/tex]

Thus, the simplified value is [tex]\;{\text} -5 log_5 (5x)[/tex] = [tex]-5 (log_5 (5) + log_5 (x) )[/tex].

Learn more about Logarithm here:

https://brainly.com/question/30226560

#SPJ6

Answer:

4a^2-19ab-5b^2

Step-by-step explanation:

What you do is the FOIL process.

F=First. The first thing that you do is times 4a and a together to get 4a^2.

O=Outer. You multiply the outer numbers 4a and -5b together to get -20ab.

I=Inner. You multiply the inner numbers b and a together to get ab.

L=Last. You multiply the last numbers b and -5b together to get -5b^2.

Put it all together to get 4a^2-19ab-5b^2 as your answer.

Answer:

8 items per bad

Step-by-step explanation:

30% are green and hold an average of 10,

20% are yellow and hold an average of 5

50% are blue and hold an average of 8,

all together they hold an average of ...

[0.3(10) + 0.2(5) + 0.5(8)]

[ 3 + 1 + 4] = 8 items on average

Say there's 10 total gift bags given out, then

3 of them will be green, each with 10 items for a total of 30 items,

2 of them will be yellow, each with 5 items, for a total of 10 items,

5 of them will be blue, each with 8 items, for a total of 40 items.

All together there are 10 bags, and 80 items, for an average of

80/10 = 8 items per bag

These numbers will stay the same no matter how many bags are given out

To calculate the average number of items in all gift bags, the weighted average of items per color category based on their percentage distribution is computed, resulting in an overall average of 8 items per bag.

The question asks to calculate the average number of items in all the gift bags given the percentages of green, yellow, and blue bags and their respective average items. To find the overall average, we can weight each average by the percentage of bags of that color.

Here is the calculation:

Summing these amounts gives us the overall average:

3 (from green bags) + 1 (from yellow bags) + 4 (from blue bags) = 8 items per bag on average.

To find the intercepts, the other number will be 0 (x-intercept: when y is 0, and vise-versa).

So:

x-intercept: 0 + 1 = 3x - 12 -> 3x = 13 -> x = 13/3, so it will be ([tex]\frac{13}{3}[/tex], 0).

y-intercept: y + 1 = 3*0 - 12 -> y = -13, so it will be (0, -13).

Answer:

x-intercept = [tex]\frac{13}{3}[/tex]

y-intercept = [tex]-13[/tex]

Step-by-step explanation:

We are given the following equation of a line and we are to find the x and y intercepts for it:

[tex] y + 1 = 3 ( x - 4 ) [/tex]

To find the x-intercept, we will put in 0 for the y to get:

[tex] 0 + 1 = 3 ( x - 4 ) \\\\ 1 = 3 x - 12 \\\\ 3 x = 1 + 12 \\\\ x = \frac { 13 } { 3 } [/tex]

To find the y-intercept, we will put in 0 for the x to get:

[tex] y + 1 = 3 ( 0 - 4 ) \\\\ y + 1 = -124 \\\\ y = - 12 - 1 \\\\ y = - 13 [/tex]

So the x-intercept is [tex]\frac{13}{3}[/tex] while the y-intercept is [tex]-13[/tex].

Answer:

Let X be the number of weeks.

2x - 16 = 14

   we add 16 on both sides.

2x = 30

now we divide 2 on both sides to get rid of the 2 to the x, we want to get x on its own.

X = 15

Answer:

(x+4)^2 + y^2 = 9

Answer:

The correct answer is first  option

(x + 4)² + y² = 9

Step-by-step explanation:

Formula:-

Let (x₁, y₁) and 'r' be the radius of a circle the equation of the circle is given by

(x - x₁)² + (y - y₁)² = r²

To find the equation of the circle

Here (x₁, y₁) = (-4, 0) and r = 3

we have,

(x - x₁)² + (y - y₁)² = r²

(x - -4)² + (y - 0)² = 3²

(x + 4)² + y² = 9

Therefore the equation of the given circle  is (x + 4)² + y² = 9

The correct answer is first  option

The fraction of 1/12 or .08333333

Answer:

m = 3, n = -2.

Step-by-step explanation:

Substitute n = 3m - 11 in the second equation:

2m + 3(3m - 11) = 0

2m + 9m - 33 = 0

11m = 33

m = 3.

Substitute for m in n = 3m-11:

n = 3(3) - 11

n = -2.

Number one is correct, here is how:

[tex]fgx 8 \\Simplify \\ the \\ brackets\\8\sqrt{6}[/tex]

Have a great day!

Answer:

(-3, 0)

Step-by-step explanation:

The x-intercept is the value of x when y = 0.

                           2x +  5y   = -6

Set y = 0              2x + 5(0) = -6

                           2x            = -6

Divide each side by 2     x = -3

The x-intercept is at (-3, 0).

Answer:

[tex]y + 2= -\frac{1}{3}(x-5)[/tex]

Step-by-step explanation:

To write the equation of a line with a slope and a point, use the point slope form of the line. Substitute m = -1/3 and (5, -2).

[tex]y - y_1 = m(x-x_1)\\y --2 = -\frac{1}{3}(x - 5)\\y + 2 = -\frac{1}{3}(x-5)[/tex]

You can convert to slope intercept form.

[tex]y + 2 = -\frac{1}{3}(x-5)\\y + 2 = -\frac{1}{3}x + \frac{5}{3}\\y = -\frac{1}{3}x + \frac{5}{3} -2\\y = -\frac{1}{3}x - \frac{1}{3}[/tex]

Answer:

mean is 11.167 the median is 10

Step-by-step explanation:

Hope this helps

The digits are 2,5,9,11,19,21

Mean is finding average by adding all value and then dividing by how many numbers

Mean=2,5,9,11,19,21 is 67 and than divide by 6 which would be 11.16 (11.2)

Median is arranging all numbers in chronological order and finding middle value

2,5,9,11,19,21

9+11 is 20 and than divide by 2 which makes it 10

Summary

Mean is 11.2

Median is 10

Answer:

Brown, purple, Green and Red/Pink

Step-by-step explanation:

The equations are equal where they intersect on the graph. There are 4 points at which the to graphs intersect. They intersect at the points colored brown, purple, green and red.

Answer:

The lines are perpendicular.

Step-by-step explanation:

Slope of line A = ⁵/₄

Slope of line B = -⅘

The slopes are negative reciprocals of each other.

∴ The lines are perpendicular.