In a particular triathlon the athletes cover 1/24 of the total distance by
swimming, 1/3 of it by running, and the rest by bike. What is the ratio of
the distance covered by bike to the distance covered by running?​

Step-by-step explanation:

(f + g)(x) = f(x) + g(x) = (4x² + 1) + (x² - 5) = 5x² - 4. (D)

Answer:

D. 5x^2-4

Step-by-step explanation:

We are asked to find (f+g)(x), which is really just the sum of the two functions.

(f+g)(x)=f(x)+g(x)

We know the the functions are:

• f(x)= 4x^2+1

• g(x)=x^2-5

Substitute the functions in.

(f+g)(x)=(4x^2+1)+(x^2-5)

Add the functions by combining like terms. For this equation, the like terms are those with x^2 and the constants.

(f+g)(x)= (4x^2+x^2)+(1-5)

Add the terms with x^2

(f+g)(x)=(5x^2)+(1-5)

Add the constants or terms without variables.

(f+g)(x)=(5x^2)+(-4) = 5x^2-4

The sum of the functions is D. 5x^2-4

Answer:

6v^5

Step-by-step explanation:

you would leave the 6 alone. since there is 5 of the same variable, you would put 5 as your exponent

Answer:

Sorry i don't know what's the actual answer, but you can use Desmos app for graphing, hope that helps

Answer:

there you go if you want mark brainlest if not its okay with me

Step-by-step explanation:

Answer:

1/2x+3

Step-by-step explanation:

I graphed it

The answer is 35 over 2.

Option B!

i cant see the entire screen, but just look at the letter, and say which point it is

Answer:

he can make 4 packages hope this helps

Answer:

75/25

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

(1, -1, 3)

Step-by-step explanation:

Given system of linear equations is,

2x + 3y - 2z = -7 ---------- (1)

x - 2y + 4z = 15 ------- (2)

2y + z = 1 ------------ (3)

Equation (2) multiplied by 2 then subtracted from equation (1),

(2x + 3y - 2z) - 2(x - 2y + 4z) = -7 - 30

(2x - 2x) + (3y + 4y) + (-2z - 8z) = -37

7y - 10z = -37 ------ (4)

Equation (3) multiplied by 10 then added to equation (4),

(20y + 10z) + (7y - 10z) = 10 - 37

27y = -27

y = -1

From equation (3),

2(-1) + z = 1

-2 + z = 1

z = 3

From equation (2),

x - 2(-1) + 4(3) = 15

x + 2 + 12 = 15

x + 14 = 15

x = 1

Answer:D and E I think

Step-by-step explanation:

Answer:

The answer is C, the third one.

Answer:

12 10 dollar bills.

Step-by-step explanation:

you need 12 10 dollar bills bc i added 3 50 dollar bills (150), 18 20 dollar bills (360), which was 510. after i got 510, i figured out how much was needed left, so i subtracted 630 minus 510 which was 120. in the end i knew 10x12 was 120 so you need twelve 10 dollar bills.

Answer:

Step-by-step explanation:

The formula for calculating the distance between two points is expressed as

D =√(x2-x1)²+(y2-y1)²

Given the coordinates (0,0) and (8,5)

D = √(5-0)²+(8-0)²

D = √5²+8²

D = √25 + 64

D = √89

D = 9.43

Hence the distance between the life guard and the swimmer is 9.43

Answer:

Step-by-step explanation:

The answer is 12 units

Answer:

Jason has $244.37 in his bank account.

Step-by-step explanation:

This is simple addition and subtraction,

525.02 - 107.65 - 228.00 + 55.00 = bal

Graph of the question is missing so I have attached it

Answer:

Option A: Axis of symmetry: x = -0.5; Vertex: (-0.5, 0.75); f(x) = x2 + x + 1

Step-by-step explanation:

1) The axis of symmetry of quadratic graph is the vertical line that divides the graph curve into two congruent halves. In this case, it is: x = -0.5

2) Vertex is the point at which the graph curve changes direction or simply coordinates of the crest or trough of the curve.

The graph given has a trough with the coordinates: x = -0.5, y = 0.75. This is (-0.5, 0.75)

3) The roots of a quadratic equation are the points where the curve crosses the x-axis. In this case, it doesn't cross and so we have imaginary roots.

Now, formula for line of symmetry is; x = -b/2a

Thus; -b/2a = -0.5 or -b/2a = -1/2

Thus, b = 1 and a = 1

Our first and second terms will now be;

x² + x

Looking at the options, the only one with x² + x as it's first 2 terms is option A.

Thus, the complete equation will be x² + x + 1

Answer:

1.40

Step-by-step explanation:

I feel if you divide $14.00 by 10 you would get 1.40, so  I say this should be the right answer.

I apologize if I am incorrect.

Answer:

The cost per pound is 1.4.

Step-by-step explanation:

If you divide 14 and 10 it makes 1.4.

Answer:

-4.834 / 73

Step-by-step explanation:

Two points: (2007, 84.134) and (2080, 79.300)

Use the slope formula.

m = y2-y1/x2-x1

m = 79.300 - 84.134 / 2080 - 2007

m = -4.834 / 73

The given rule of the dilation indicates that the scale factor is 3 which is

larger than one, therefore, given an enlarged image.

The correct options are;

Please find attached the possible diagram of rectangle LMNP obtained from a similar question posted online;

L'M' = 12

LM = 4

MN = 6

The rule of the dilation of rectangle LMNP = [tex]D_{p, \, 3}[/tex]

L'M' = 3 × LM

Therefore;

The image following the dilation of the preimage LMNP, which is rectangle L'M'N'P' is larger than LMNP

Therefore;

The scale factor is the number with which the preimage dimension is multiplied to get the image, which is 3

M'N' = 3 × MN

Therefore;

Learn more about scale factor of a dilation here:

https://brainly.com/question/840682

Answer:

a. The length of line segment M'N' is 18 units.

d. The dilation is an enlargement.

f. The scale factor is 3.

Step-by-step explanation:

got it right on ed23

Answer:

13

Step-by-step explanation:

HCF = Product of two numbers ÷  LCM of these numbers

HCF = [tex]\frac{169}{13}[/tex]

        = 13

Answer:

C.FCC

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

you just add X=8 to 5x-6

You always have to multiply it

so its 5•8-6= 34

Answer: The answer is 34

Step-by-step explanation: all you had to do was think all of the answers below are high numbers so you most likely had to multiply so i did 5x8-6=34

Answer:

translation

W(-10, 0)

X(-10, -8)

Y(-18, -4)

Z(-14, 8)

dilation

W(-8, 16)

X(-8, 0)

Y(-24, 8)

Z(-16, 32)

Step-by-step explanation:

In translation, all you are doing is taking each point and subtracting 6 from the x, and subtracting 8 from the y. The point of W is (-4, 8). Thus you do (-4 - 6 , 8-8) and you get the new point (-10,0). Repeat this for all the others.

In dilation you are multiply both x and y by 2. For point W you do (-4*2, 8*2) to get the new point (-8, 16). You repeat this for the remaining points.

please give thanks by clicking the heart button :)

Answer:

4 students would get jellybeans because 32 divided by 4 would be 8 and 8 times 4 is 32.  hope this helps! :D

Step-by-step explanation:

brainliest plz?

If 32 jelly beans were shared with 8 students each will get 4 jelly beans.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, 32 jelly beans were shared with 8 students.

The no. of jelly beans each student will get can be obtained by dividing the total no. of jelly beans divided by the total no. of students which is,

= (32/8) jellybeans each.

= 4 jelly beans each.

learn more about the unitary method here :

https://brainly.com/question/28276953

#SPJ2

Answer:

C

Step-by-step explanation:

graphs A and B are called quadratic equations; example, x^2 - x - 6 and, when graphed form u-shaped curves that either cross the x-axis at one or two points, or possibly not at all.

graph D is a linear equation, x = -4

graph C is created by an equation where the x-value is raised to the third power; try graphing y = x^3 and see how it looks

Answer:

36/5 or 7 1/5

Step-by-step explanation:

4 divided by 5/9

4 x 9/5.        change the divide to multiply & the fraction to the reciprocal

=36/5 or 7 1/5

Answer:

[tex]E\approx14,962\text{ feet}[/tex]

Step-by-step explanation:

Please refer to the attachment below.

As shown, we can split the diagram into a scalene triangle and a right triangle.

The strategy here is to use the Law of Sines to find x, then use right triangle ratios to find h, the height of Matterhorn (with respect to our elevation).

Let’s start with the scalene triangle.

To use the Law of Sines, we will need two angles and the sides opposite to the angles.

Since we need to find x, we need the angle opposite to x. This is already given to us as 30°.

We can use the side that measures 1,500. The angle opposite to it θ is unknown.

So, we will need to determine θ. From supplementary angles, we know that:

[tex]\alpha+35=180[/tex]

So, it follows that:

[tex]\alpha=145^\circ[/tex]

The interior angles of a triangle always sum to 180°. Hence:

[tex]30+\alpha+\theta=180[/tex]

By substitution:

[tex]30+145+\theta=180[/tex]

Hence:

[tex]\theta=5^\circ[/tex]

Now, we can use the Law of Sines, given by:

[tex]\displaystyle \frac{\sin(A)}{a}=\frac{\sin(B)}{b}[/tex]

It is important to align the angles correctly with the sides.

So, we will substitute θ = 5° for A and 1,500 for a.

And we will substitute 30° for B and x for b. Hence:

[tex]\displaystyle \frac{\sin(5^\circ)}{1,500}=\frac{\sin(30^\circ)}{x}[/tex]

Solve for x. Cross-multiply:

[tex]x\sin(5^\circ)=1500\sin(30^\circ)[/tex]

Hence:

[tex]\displaystyle x=\frac{1500\sin(30^\circ)}{\sin(5^\circ)}[/tex]

When doing trigonometry (or any math, really), try not to round intermediate values, as this may result in inaccuracies in the final answer. Hence, we will leave this as is.

Now, we can use the right triangle.

We know that an angle is 35°.

The height h is opposite to our angle.

And x was our hypotenuse. Therefore, we can use the sine ratio given by:

[tex]\displaystyle \sin(x^\circ)=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

In this case, our angle is 35°.

The opposite side is h.

And the hypotenuse is x. Hence, by substitution:

[tex]\displaystyle \sin(35^\circ)=\frac{h}{x}[/tex]

Solve for h. Multiply both sides by x:

[tex]h=x\sin(35^\circ)[/tex]

Since we already know the value of x:

[tex]\displaystyle h=\frac{1500\sin(30^\circ)}{\sin(5^\circ)}\cdot\sin(35^\circ)[/tex]

Simplify. So, the height of Matterhorn with respect to our current elevation is:

[tex]\displaystyle h =\frac{1500\sin(30^\circ)\sin(35^\circ)}{\sin(5^\circ)}[/tex]

The total elevation of Matterhorn will be the current elevation of the surveyor plus the height with respect to the current elevation or simply h. So, the elevation height is:

[tex]E=9756+h[/tex]

By substitution:

[tex]\displaystyle E=9756+\frac{1500\sin(30^\circ)\sin(35^\circ)}{\sin(5^\circ)}[/tex]

Now we may approximate. Use a calculator. So, the total elevation of Matterhorn is:

[tex]E=14961.78867...\approx14,962\text{ feet}[/tex]

Answer:

The 95%  confidence interval is

           [tex] 0.45 <  \mu_1 - \mu_2  < 5.35 [/tex]

Step-by-step explanation:

From the question we are told that

   The first sample size is  [tex]n_1 = 36[/tex]

   The first  sample mean is  [tex]\= x_1 = 3.5[/tex]

   The first standard deviation is  [tex]\sigma_1 = 5.9 \ pounds[/tex]

   The second  sample size is [tex]n_2 = 36[/tex]

    The second  sample mean is  [tex]\= x_2 = 0.6[/tex]

    The second  standard deviation is [tex]\sigma = 4.4[/tex]

Generally the degree of freedom is mathematically represented as

     [tex]df = \frac{ [ \frac{s_1^2 }{n_1 } + \frac{s_2^2 }{n_2} ]^2 }{ \frac{1}{(n_1 - 1 )} [ \frac{s_1^2}{n_1} ]^2 + \frac{1}{(n_2 - 1 )} [ \frac{s_2^2}{n_2} ]^2 }[/tex]

=>  [tex]df = \frac{ [ \frac{5.9^2 }{34 } + \frac{4.4^2 }{34} ]^2 }{ \frac{1}{(34 - 1 )} [ \frac{5.9^2}{34} ]^2 + \frac{1}{(34- 1 )} [ \frac{4.4^2}{ 34} ]^2 }[/tex]

=>  [tex]df =63[/tex]

Generally the standard error is mathematically represented as

      [tex]SE = \sqrt{ \frac{s_1 ^2 }{n_1} + \frac{s_2^2 }{ n_2 } }[/tex]

=>  [tex]SE = \sqrt{ \frac{ 5.9 ^2 }{ 36 } + \frac{ 4.4^2 }{36} }[/tex]

=>  [tex]SE = 1.227[/tex]

From the question we are told the confidence level is  95% , hence the level of significance is    

      [tex]\alpha = (100 - 95 ) \%[/tex]

=>   [tex]\alpha = 0.05[/tex]

Generally from the t distribution table the critical value  of   at a degree of freedom of is  

     [tex]t_{\frac{\alpha }{2}, 63  } =  1.998  [/tex]

Generally the margin of error is mathematically represented as

        [tex]E = t_{\frac{\alpha }{2}, 63 } * SE[/tex]

=>    [tex]E = 1.998 * 1.227[/tex]

=>    [tex]E = 2.45[/tex]

Generally 95% confidence interval is mathematically represented as  

      [tex](\= x_1 - \x_2) -E <  \mu <(\= x_1 - \x_2)  + E[/tex]

 => [tex](3.5  - 0.6) - 2.45 <  \mu_1 - \mu_2  < (  3.5  - 0.6)  + 2.45 [/tex]

=>   [tex] 0.45 <  \mu_1 - \mu_2  < 5.35 [/tex]