Find the value of a.
х
409
0.
a
y
O A. 60
OB. 80
OC. 40

The running distance is 4.23 miles, the swimming distance is 1.98 miles and the cycling distance is 35.64 miles.

Each racer travels the same distance and the sum of the distances travelled ([tex]x[/tex]), in miles. By definition of average speed ([tex]v[/tex]), in miles per hour, we get the following system of equations:

Amanda

[tex]t_{A} = \frac{x_{R}}{v_{A, R}}+\frac{x_{S}}{v_{A,S}}+\frac{x_{C}}{v_{A,C}}[/tex] (1)

Where:

Bryce

[tex]t_{B} = \frac{x_{R}}{v_{B, R}}+\frac{x_{S}}{v_{B,S}}+\frac{x_{C}}{v_{B,C}}[/tex] (2)

Where:

Corey

[tex]t_{C} = \frac{x_{R}}{v_{C, R}}+\frac{x_{S}}{v_{C,S}}+\frac{x_{C}}{v_{C,C}}[/tex] (3)

Where:

If we know that [tex]t_{A} = 2.7\,h[/tex], [tex]v_{A,R} = 10\,\frac{mi}{h}[/tex], [tex]v_{A,S} = 4\,\frac{mi}{h}[/tex], [tex]v_{A, C} = 20\,\frac{mi}{h}[/tex], [tex]t_{B} = 3.27\,h[/tex], [tex]v_{B,R} = 7.5\,\frac{mi}{h}[/tex], [tex]v_{B,S} = 6\,\frac{mi}{h}[/tex], [tex]v_{B,C} = 15\,\frac{mi}{h}[/tex], [tex]t_{C} = 1.833\,h[/tex], [tex]v_{C,R} = 15\,\frac{mi}{h}[/tex], [tex]v_{C,S} = 3\,\frac{mi}{h}[/tex] and [tex]v_{C,C} = 40\,\frac{mi}{h}[/tex], then the solution of the linear system of equations is:

[tex]\frac{x_{R}}{10} + \frac{x_{S}}{4} + \frac{x_{C}}{20} = 2.7[/tex] (4)

[tex]\frac{x_{B}}{7.5}+\frac{x_{S}}{6} +\frac{x_{C}}{15} = 3.27[/tex] (5)

[tex]\frac{x_{R}}{15}+\frac{x_{S}}{3} +\frac{x_{C}}{40} = 1.833[/tex] (6)

[tex]x_{R} = 4.23\,mi[/tex], [tex]x_{S} = 1.98\,mi[/tex], [tex]x_{C} = 35.64\,mi[/tex]

The running distance is 4.23 miles, the swimming distance is 1.98 miles and the cycling distance is 35.64 miles.

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Answer:

7/12

Step-by-step explanation:

Answer: 3b + 125 = 157.97

Step-by-step explanation:

The two things contributing to the total cost are the cost of the bags of dog food and the adoption fee, so they need to be added together.

There are 3 bags of dog food at an unknown price, so we need to multiply 3 by an unknown value represented by the variable b.

The $125 adoption fee should be added to the price of the bags of dog food, so add 125. This creates an equation of 3b + 125 = 157.97

Answer:

See below for answers

Step-by-step explanation:

These triangle do not have to be similar to each other because the 30° angles  may not be located in the same place.

For example, place one 30° at the vertex of the triangle which is  located where the two equal legs of the isosceles triangle are joined.  The triangle angles measure are 30°, 75°, and 75°.

But if the 30° angle is one angle at the base of the isosceles triangle, then the angles measure are 30°, 30°, 120°.  

                                                          30°  

                           Δ                             Δ

                      30°

Answers:

==================================================

Explanation:

a = number of apples purchased

c = cost in dollars

The equation is in the form c = ka, where k is the constant of proportionality. It tells us what to multiply 'a' by to get the cost c. In more realistic practical terms, the value of k is the cost per apple (aka unit cost).

To find this unit price, we divide the given price by the given number of apples: k = c/a = 28/14 = 2. Each apple is $2. The constant of proportionality is 2.

We'll update the equation from c = ka to c = 2a

Note that if we bought a = 14 apples, then it costs us c = 2a = 2*14 = 28 dollars as expected.

Answer:

c=2a

Step-by-step explanation:

c=2a

From the information given, the percentage increase in the price bid over the cost will be 23%.

Cost on the product = $112.

Amount bid = $138

Therefore, the Percentage increase will be:

= (138 - 112) / 112 × 100

= 26/112 × 100

= 23%

Therefore, from the calculation above, it can be seen that the percentage increase in the price bid over the cost will be 23%.

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Answer:

$1717.80

Step-by-step explanation:

We are given one clue: He pays $572.60 each year to cover everyone and his family.

We are asked to find how much does Phil have to pay after 3 years. So, we must multiply 572.60 by 3 to find the total cost Phil has to pay after 3 years.

572.60 x 3 = Total cost to pay after 3 years.

=> $1717.80 = Total cost to pay after 3 years.

We can conclude that Phil will have to pay $1717.80 after 3 years.

Answer:

HI!!!

Step-by-step explanation:

Answer:Y=6/37

Step-by-step explanation:

Answer:

x = ± 8

Step-by-step explanation:

[tex]\dfrac{1}{2}x^{2}=32[/tex]

Multiply the equation by 2

x² = 32*2

x² = 64 = 8²

x = 8

Answer:

A. 8

Step-by-step explanation:

We are given the functions:

[tex]f(x)=\sqrt{x}\\\\g(x)=7x+b[/tex]

    We are told that on a standard (x, y) coordinate plane that y = f(g(x)) passes through the point (4, 6). In order to solve for b, we need to figure out what f(g(x)) is equal to.

    As with a regular function like the two above, f(g(x)) means you are substituting x with g(x) in function f. The problem gave us the two functions, so I will demonstrate what I mean.

[tex]f(g(x))=\sqrt{(7x+b)}[/tex]

    The problem again tells us that y = f(g(x)) goes through (4, 6). Substitute those values for their respective variables and solve for b.

[tex]y=f(g(x))\\\\y=\sqrt{(7x+b)}\\\\6=\sqrt{(7(4)+b)}\\\\6=\sqrt{(28+b)}\\\\(6)^2=(\sqrt{(28+b)})^2\\\\36=28+b\\\\36-28=28+b-28\\\\8=b[/tex]

Therefore, the value of b is equal to 8.

Answer:

2/18 or 1/9

Step-by-step explanation:

just directly multiply it 2×1=2

6×3=18 so 2/18 simplify 1/9

Answer:

The vertical line test is a test to determine if a relation or its graph is a function or not. For a relation or graph to be a function, it can have at most a single y-value for each x-value. Thus, a vertical line drawn at any x-position on the graph of a function will intersect the graph at most once.

Step-by-step explanation:

(winks and runs off)

Answer:

137 i am sorry if incorrect

Step-by-step explanation:

Answer:

not sure if u saw the comment but

7 and 8 are congruent, and 8 is congruent to 10

that maybe the rest of the answer

Answer:

rate of change from 8 to 32

Step-by-step explanation:

Answer:

Answer is 4, explained answer in the comments because I didn't see the answer button, but now I do.

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

y-(2*x+5)=0

STEP1:

Equation of a Straight Line

1.1 Solve y-2x-5 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y-2x-5 = 0 and calculate its properties

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 5/1 so this line "cuts" the y axis at y= 5.00000

y-intercept = 5/1 = 5.00000

Calculate the X-Intercept :

When y = 0 the value of x is 5/-2 Our line therefore "cuts" the x axis at x=-2.50000

x-intercept = 5/-2 = -2.50000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 5.000 and for x=2.000, the value of y is 9.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 9.000 - 5.000 = 4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 4.000/2.000 = 2.000

Geometric figure: Straight Line

~fractions

[tex] \large \tt( \frac{ 5 }{ 7 } ) ^ { 3 } ( \frac{ 4 }{ 5 } ) ^ { 3 }[/tex]

[tex] \large \tt = \frac{125}{343}\times \left(\frac{64}{125}\right) [/tex]

[tex] \large \tt = \frac{125\times 64}{343\times 125} [/tex]

[tex] \large \tt = \boxed{\frac{64}{343} } \: ✓[/tex]

~ nice to help you ^^

Answer:

[tex]7^-^1[/tex]

Step-by-step explanation:

So, when multiplying numbers with exponents that have the same base, all you have to do is combine the exponents.

Step-by-step explanation:

SAS ================

What it says:

If two sides and the angle between them on one triangle are congruent to the corresponding two sides and the angle between them on the other, the triangles are congruent.

Required information:

Two sets of congruent sides with a congruent angle between them

ASA ================

What it says:

If one side and both connected angles on one triangle are congruent to one side and both connected angles on the other, the triangles are congruent.

Required information:

One set of congruent sides with two sets of congruent angles on the sides

AAS ==================

What it says:

If two angles and the non-included side on one triangle are congruent to two angles and the non-included side on the other, the triangles are congruent.

Required information:

Two sets of congruent angles and one set of congruent non-included sides

HL =================

What it says:

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg on the other, the triangles are congruent.

Required information:

Congruent hypotenuse and congruent leg

Answer:

183

Step-by-step explanation:

percentage=actual/base

B=A/P

B=43.9/0.24

B= 182.9=183

The value of x rounded to the nearest whole number is 183.

In mathematics, a number or ratio that can be expressed as a fraction of 100 is known as a percentage. To find the % of a number, divide it by its value, then multiply the result by 100. Percentage is a relative value that denotes one tenth of any quantity. As one percent (symbolised as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.

As per the given data:

Number = 43.9

The given number is 24% of x.

Percentage = (value / total) × 100

By substituting the given data:

24 = (43.9 / x) × 100

x = (4390/24)

x = 182.91

after rounding off to the nearest whole number

x = 183

Hence, the value of x rounded to the nearest whole number is 183.

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Answer:

17.08

Step-by-step explanation:

Basically, this is half of 34.16, which is 17.08.

Hoped this helped.

Answer:

427/25

Step-by-step explanation:

Change to percentage: 3416/100

Simplify: 854/25

854/25 dived by 2/1 (same thing as 2)

KEEP, CHANGE, FLIP

854/25 x 1/2= 427/25

Answer:

Step-by-step explanation:

2x + y = 6

y = -2x + 6

Comparing this with y = 1/2x - 7

Multiplying the 2 slopes:

-2 * 1/2

= -2/2

= -1

- this means that the 2 lines are perpendicular.

Answer:

9.09

Step-by-step explanation:

Pythagorean Theorem: a² + b²  =  c²

When looking at the triangle we see that we have the hypotenuse and the opposite side.

a = opposite

b = adjacent

c = hypotenuse (always)

So if we plug those numbers into the equation we can get the missing side length

1) a² + b²  =  c²

2) 9.7² + b² = 13.3²

3) b² = 13.3² - 9.7²

4) b² = 176.89 - 94.09

5) b = [tex]\sqrt{176.89 - 94.09}[/tex]

6) b = 9.093954036

Now we round to nearest hundredth

To find the nearest hundredth we have to look at the thousandth place in the thousandth place we have 3 (9.093) that rounds down so,

b = 9.09

Answer:

Step-by-step explanation:

Answer:

m<H= 80*

m<P= 80*

m<I= 33*

M<Q= 33*

M<J=67*

M<R=67*

Step-by-step explanation:

Given States that ️ HIJ = ️ PQR

<H=<P

2x=x+40

2x-x=x-x+40

x=40

<I=<Q

<J=<R

ALL TRIANGLES MEASURE 180*

Y= the measure of <R and <J

2x+33+y=180

2(40)+33+y=180

80+33+y=180

113+y=180

113-113+y=180-113

y=67

Answer:

See answer below

Step-by-step explanation:

If ΔHIJ ≅ ΔPQR ,then you know six  congruent parts:

 ∠H ≅ ∠P ; ∠I ≅ ∠Q;  ∠J ≅ ∠R    and HI ≅ PQ; HJ ≅ PQ ; IJ ≅ QR

   ∠H ≅ ∠P         ∠I ≅ ∠Q

2x = x + 40°          ∠I = 35°

x = 40°

So ∠H = 2x = 2(40) = 80°                        Δ HIJ = 180°

    ∠P = x + 40 = 40 + 40 = 80°               ∠H + ∠I  + ∠J = 180°

    ∠Q = 35°                                                  80° + 35° + ∠J = 180°

    ∠ I = 35°                                                   115° + ∠J = 180°

    ∠ J = 65°                                                          ∠J = 65°

    ∠R = 65°                                                      ∠J ≅ ∠R