Evaluate the expression.
-8.x – 3y if x = 4 and y = -2

Answer:

Faster runner speed: 11 mph

Slower runner speed: 9 mph

Distance from starting point: 9.9 miles

Step-by-step explanation:

Let the slower runner speed be: x

Faster runner speed: x+2

1 hour 6 minutes = 1.1 hours

Slower: 1.1(x) = 1.1x miles

Faster: 1.1(x+2) = 1.1x+2.2 miles

This means that the faster runner had gone 2.2 miles more than the slower runner.

1.1x + 2.2 > 11 miles (This is true as we know the faster runner is coming back from the 11 mile run)

1.1x > 11 - 2.2 miles

1.1x > 8.8 miles

x > 8.8 / 2.2 miles

x > 8 mph

1.1x < 11 miles (we know this is true as the slower runner has to have gone less than 11 miles as the faster runner met him on his way back)

x < 11 / 1.1 miles

x < 10 miles

8 < x < 10

Although x could be any number including decimal between 8 and 10, the obvious first answer would be 9. However we need to check if this answer is correct.

Slower runner distance to the end:

1.1(9) = 9.9 miles

11 - 9.9 = 1.1 miles

Faster runners distance from the end (when coming back)

1.1(9+2) = 1.1(11) = 12.1 miles

12.1 - 11 = 1.1 miles

The speeds 9 mph and 11 mph are now proven to be the right speeds. Using our equation before, we can figure out the distance from the starting point that they meet at. This is just how far the slower runner has gotten. So, 1.1(9) = 9.9 miles from the starting point

The runners meet at a distance of 8.8 miles from the starting point.

According to statement, each runner must run back and forth on a 11-mile course. After supposing that each runner moves at constant speed, expressions for each runner are presented below:

Fast runner reaches the end

[tex](v+2)\cdot 1.1 = 11[/tex] (1)

Fast runner comes back from the end

[tex]x = \left(v+2\right)\cdot (1.1-t)-(v+2)\cdot t[/tex] (2)

Slow runner meets fast runner

[tex]x = v\cdot 1.1[/tex] (3)

Where:

By (1), we obtain the speed of the slow runner:

[tex]v = \frac{11}{1.1}-2[/tex]

[tex]v = 8\,\frac{mi}{h}[/tex]

The position from the starting point is calculated by (3):

[tex]x = (8\,mi)\cdot \left(1.1\,h\right)[/tex]

[tex]x = 8.8\,mi[/tex]

The runners meet at a distance of 8.8 miles from the starting point. [tex]\blacksquare[/tex]

To learn more on linear functions, we kindly invite to check this verified question: https://brainly.com/question/17058347

Answer:

B and D.

Step-by-step explanation:

Hope this helps! :D

Answer:

78

Step-by-step explanation:

Answer: 76

Step-by-step explanation:

48 + 56 = 104

180 - 104 = 76

Answer:

1. -3x - 5= 16

-16-5=3x

x=-21/3=-7

Answer:

DF = 1213ft

Step-by-step explanation:

Answer:

They aren't similar.

Answer:

First: 3 units Second: 7 units Third: 9 units

Step-by-step explanation:

19=x+(x+4)+3x

19=5x+4

15=5x

x=3

first side is 3 units

3+4=7

second side is 7 units

3*3=9

third side is 9 units

Answer:

last one (d)

Step-by-step explanation:

adding subtracting or dividing is not how you use a growth factor(what my school calls a percentage in a decimal form).

Answer:

$4,537.55

Step-by-step explanation:

I did it on paper and you gotta calculate it, Hope this helps!

Answer:

It is A, I highly suggest you should read my explanation.

Step-by-step explanation:

(2x - 3)(x - 4)(x^2 + 3)

Exponent of 2x = 1

Exponent of x = 1

Exponent of x^2 = 2

Add them all together to get the degree. 1 + 1 + 2 = 4

Now we can tell that the polynomial can have 1,2,3,4, or no roots at all. The max number roots it can have is 4

To see the number of roots it has, we have to set each part equal to 0

2x - 3 = 0

Add 3 to both sides

2x - 3 + 3 = 0 + 3

2x = 3

Divide both sides by 2

2x/2 = 3/2

x = 3/2 or 1.5

Next,

x - 4 = 0

Add four to both sides

x - 4 + 4 = 0 + 4

x = 4

Then,

x^2 + 3 = 0

Subtract 3 from both sides

x^2 + 3 - 3 = 0 - 3

x^2 = -3

Find the square root of both sides

sqrt(x^2) = sqrt(-3)

x = i*sqrt(3), -i*sqrt(3)

Those are imaginary numbers, therefore there are not real.

The real roots are x = 3/2, 4

Harvey stated that this equation has four real roots. We can cross options B and C out since they stated he was correct.

It is not D because finding a square root of a number gives two answers; the positive and negative version, so it will have two solutions. There were only two real roots and the other two roots are complex roots.

That leaves us to option A, which states that there are 2 real and 2 complex roots. It is correct

Answer:

Step-by-step explanation:

The common ratio is 3, so multiply the numbers of the pattern by 3. So 1x3 is 3, 3x3 is 9, 9x3 is 27, 27x3 is 81, 81x3 is 243, and just continue until you're on the 7th number; 1 was the first, 3 was the second and 9 was the third.

Answer:

31

Step-by-step explanation:

25/0.80=31.25

(You cant have a quarter of a parking space.)

Hi! So what you will need to know is pythagorean theorm.

What the theorm basically says is a^2 + b^2 = c^2.

-- The (a,b,c) are referring to the sides of the triangles (3 letters for 3 sides).

Take note that "c" is always the side opposite of the right angle.

The other known side could be "a" or "b"

Taking a look at problem 9, identify the "c" value. The "c" value would be 35.

Then indentify the value of "b" or "a". "a" would = 20.

Plug it into the equation:

20^2 + b^2 = 35^2

400 + b^2 = 1225

solve for b.

1. subtract 400 from both sides.

b^2 = 825

b = [tex]\sqrt{825}[/tex]

you could solve for the square root but it would give a decimal numbers but I'm not sure what the teacher is looking for.

Answer:

x = 7

y = 12

Step-by-step explanation:

ABCD is a parallelogram.

Measures of opposite sides of a parallelogram are equal.

Therefore,

2y - 18 = y - 6

2y - y = 18 - 6

y = 12

2x + 2 = y + 4

2x + 2 = 12 + 4

2x = 16 - 2

2x = 14

x = 14/2

x = 7

Answer:

A, 3m

Step-by-step explanation:

Answer:

the new price is 25.9

Step-by-step explanation:

Answer: option 4

Step-by-step explanation:

The transformation of the parent function is stretched by a factor of 2 and translated 8 units right and 5 units down

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the parent function be represented as f ( x )

Now , the value of f ( x ) = ∛x

And , the given function is y = ∛ ( 8x - 64 ) - 5

On simplifying , we get

Taking 8 as the common factor , we get

y = ∛ 8 ( x - 8 ) - 5

Now , the cube root of 8 is 2

So , y = 2∛(x - 8 ) - 5

The transformed function is y = 2∛(x - 8 ) - 5

And , the transformation is a vertical stretching by a factor of 2

And , a horizontal right shift by 8 and a vertical down shift by 5

Hence , the transformation of function is stretching by a factor of 2 and translated 8 units right and 5 units down

To learn more about transformation of function click :

https://brainly.com/question/26896273

#SPJ7

Answer:

Point C

Step-by-step explanation:

Point C is located on the x-axis.

Answer:

You typically apply the same rules as you would for 'regular' fractions.

So you can multiply numerator and denominator by the same value if needed. If you want to add fractions you must make sure the denominators are the same, etc.

The value you multiply by can be an algebraic expression.

Answer:

Drawing an angle in standard position always starts the same way, draw the initial side along the positive x-axis. To place the terminal side of the angle, you must calculate the fraction of a full rotation the angle represents.

Answer:

Get the number of rotations of the given angle by dividing 360 degrees with respect to positive x-axis.

Step-by-step explanation:

1. First draw a horizontal line (along x-axis).

2. Locate the terminal side of the angle by dividing 360 degrees. Recall that one full rotation is equal to 360 degrees.  So, to sketch 360 degrees, we will divide it by 360 degrees resulting in 1.

3. Similarly to draw 180 degrees, divide 180 by 360. This will result in 1/2. Therefore, it is half the way from x-axis.

Answer:

0

Step-by-step explanation:

Use the values of  a ,  b , and  c  to find the discriminant.

Answer:-28

Step-by-step explanation:

Answer:

the second is false

Step-by-step explanation:

because oe would match unlike 2

Answer:

15.12

Step-by-step explanation:

Cost of meal = $20

Discount (coupon) = 30%

Amount of discount = 30% of $20

= 30/100 * 20

= 0.3 * 20

= $6

Amount paid after discount= initial cost of meal - discount

= $20 -$6

= $14

Sales tax =8%

Amount of sales tax = 8% of $14

= 8/100 * 14

= 0.08 * 14

= $1.12

Total amount paid = Amount paid after discount + Amount of sales tax

= $14 + $1.12

= 15.12

Answer:

y=650+15x

Step-by-step explanation:

y=mx+b, b is starting amount, m is the multiplier for the x

uwu

Answer:

2 units to the right

1 units up

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

Given

See attachment for triangles

Required

Find x

First, calculate tan A

From the first triangle:

[tex]tan\ A= \frac{x + 2}{x}[/tex]

Next, calculate tan B

From the second triangle:

[tex]tan\ B= \frac{4}{3x-1}[/tex]

[tex]tan\ A = tan\ B[/tex]

So, we have:

[tex]\frac{x + 2}{x}= \frac{4}{3x-1}[/tex]

Cross Multiply

[tex](x + 2)(3x - 1) = 4 * x[/tex]

Open brackets

[tex]3x^2 + 6x - x - 2 = 4x[/tex]

[tex]3x^2 + 5x - 2 = 4x[/tex]

Collect Like Terms

[tex]3x^2 + 5x - 4x- 2 =0[/tex]

[tex]3x^2 + x- 2 =0[/tex]

Expand

[tex]3x^2 + 3x - 2x- 2 =0[/tex]

Factorize:

[tex]3x(x + 1) - 2(x+ 1) =0[/tex]

Factor out x + 1

[tex](3x - 2)(x +1) = 0[/tex]

Split:

[tex]3x - 2 = 0\ or\ x + 1 = 0[/tex]

[tex]x = \frac{2}{3}\ or\ x = -1[/tex]

x can not be negative, so:

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

Answer:

120°

Step-by-step explanation:

construct a line parallel to the two parallel lines through x

x = 70 + 50 = 120

Answer:

y=-1/4x+2

Step-by-step explanation:

The equation would be y=-1/4x+2 because the rise is -1 and the run is 4 (you could also say the run is -4 and the rise is 1. It doesn't really matter). The line also crosses the y axis at 2, which means that 2 is the y-intercept. :)

Answer:

y = (-1/4)x +2

Step-by-step explanation:

Having the actual graph is an easy way to calculate the equation of the line. Since the format is y = mx +b we just need to plug in numbers.

b = y-intercept

m = slope

We can automatically see that the y-intercept is 2, so b = 2. To find the slope we just calculate rise over run. The line is decreasing 1 unit for every 4 units it is "running". Therefore, -1/4 is your slope.

b = 2

m = -1/4

Now, all we need to do is plug in numbers.

y = (-1/4)x +2

Answer:

The size is 37.5 degrees

Step-by-step explanation:

The total angle in the triangle is 180

Since the other two angles are congruent. it means that they are equal

Let us call each of the angles x

Mathematically,

x + x + 105 = 180

2x = 180-105

2x = 75

x = 75/2

x = 37.5