MATHEMATICS HIGH SCHOOL

Two buses go from Sacramento to San Diego. The express bus makes the trip in 6.8 hours and the local bus takes 10.2 hours for the trip. The speed of the express bus is 25 mph faster than the speed of the local bus. Find the speed of both buses.

Answers

Answer 1

Answer:

Answer: Speed of local bus is 50 mph and speed of express bus is 75 mph

Step-by-step explanation:

let say speed of local bus = x

so speed of express bus = x + 25

Distance = Speed × Time

Distance traveled by local bus = x × 10.2 = 10.2x

Distance traveled by express bus = (x + 25) × 6.8

since Distance traveled by local bus is same as Distance traveled by express bus

⇒10.2x = (x + 25) × 6.8

⇒ 10.2x = 6.8x + 170

⇒ 10.2x - 6.8x = 170

⇒ x = 170/3.4 = 50

So Speed of local bus = x = 50 mph

and Speed of express bus = x + 25 = 50 + 25 = 75 mph

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Write the equation of the line, given the y- and x-intercepts. x-intercept (–6, 0), y-intercept (0, –8)

Answers

neverminding for a second that they're intercepts at all, they're points on the line, so

$\bf (\stackrel{x_1}{-6}~,~\stackrel{y_1}{0})\qquad(\stackrel{x_2}{0}~,~\stackrel{y_2}{-8})\n\n\n slope = m\implies\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-8-0}{0-(-6)}\implies \cfrac{-8-0}{0+6}\implies \cfrac{-8}{6}\implies -\cfrac{4}{3}\n\n\n \begin{array}{|c|ll}\cline{1-1}\textit{point-slope form}\n\cline{1-1}\ny-y_1=m(x-x_1)\n\n\cline{1-1}\end{array}\implies y-0=-\cfrac{4}{3}[x-(-6)]\n\n\ny=-\cfrac{4}{3}(x+6)\implies y=-\cfrac{4}{3}x-8$

Please help me!!! (the answer isn't 140 or 70 :/ )

Answers

Answer:

b=40

Step-by-step explanation:

Since PQ is equal to RQ triangle PQR is isosceles. Angle PRQ is equal to 40 degrees because of supplementary angles. And since triangle PQR is isosceles angle b is equal to angle PRQ which means angle b is equal to 40

PLEASE HELP!!!!!! Which expressions are equivalent to 1/81 ? Check all that apply.8^ -1

9^ -2

9^ 8/9^4

9^8/9^10

9^ -6 · 9^3

9^5 · 9^ -7

Answers

Answer:

$9^(-2)\n\n(9^(8))/(9^(10))\n\n9^(5)*9^(-7)$

Step-by-step explanation:

Let's evaluate the answers.

Think of numbers with negative exponents as numbers on the wrong side of the fraction. So if you have a negative exponent, you put it at the bottom of the fraction or up and then you remove the negative sign.

So let's take the first answer:

$9^(-2) \:is\:actually\:equal\:to\: (1)/(9^(2))\n\n(1)/(9^(2)) = (1)/(81)}$

Now the next one, according to the law of exponents, when dividing we subtract the exponents. (But this only applies if the coefficients are the same!)

$(m^(x))/(m^(y)) = m^(x-y)$

Applying this rule to the second answer:

$(9^(8))/(9^(10)) = 9^(8-10) = 9^(-2)=(1)/(9^(2)) = (1)/(81)$

The third one:

$9^5*9^(-7) = (9^5)/(9^(7)) = 9^(5-7) = 9^(-2) = (1)/(9^2) = (1)/(81)$

If you apply the same rules to the rest of the choices, you wil find that they are not equivalent to 1/81.

The expressions that are equivalent to 1/81 are $9^(-2)$ , $(9^8)/(9^(10))$ , and $9^5 \cdot 9^(-7)$ .

To determine which expressions are equivalent to 1/81, we can simplify each expression and check if it equals 1/81.

$8^(-1)$ : This expression is equivalent to 1/8, not 1/81. Therefore, it is not equivalent. $9^(-2)$ : This expression is equivalent to 1/9², which simplifies to 1/81. Therefore, it is equivalent to 1/81. $(9^8)/(9^4)$ : This expression simplifies to $9^((8-4)) = 9^4$ , which is not equal to 1/81. Therefore, it is not equivalent. $(9^8)/(9^(10))$ : This expression simplifies to $9^((8-10)) = 9^(-2)$ , which is equivalent to 1/9². Therefore, it is equivalent to 1/81. $9^((-6)) \cdot 9^3$ : This expression simplifies to $(1)/(9^6) \cdot 9^3 = 1/729$ . Therefore, it is not equivalent. $9^5 \cdot 9^((-7))$ : This expression simplifies to $9^((5-7)) = 9^((-2))$ , which is equivalent to 1/9². Therefore, it is equivalent to 1/81.

Thus, the expressions that are equivalent to 1/81 are $9^(-2)$ , $(9^8)/(9^(10))$ , and $9^5 \cdot 9^(-7)$ .

Learn more about the expression here :

brainly.com/question/21751419

#SPJ6

A small toy car costs $3 a large toy car costs 5 times as much as the small one Aaron want to buy 1 of each which equation can be used to find the cost a of the 2 cars

Answers

Answer:

$18

Step-by-step explanation:

small -$3

large - $15

3+15=18

Answer: The equation is $3 + ($3 x 5)

Step-by-step explanation:

You add $3 to 3 multiplied by 5 to get the cost of the second car which will then give you the cost of both cars. Then you simplify and get $3 + $15 which gives us the answer $18. So the cost of both the cars is $18.

Log (10-4x) = log (10-3x)

Answers

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The diameter of a ball is 8 in. What is the volume of the ball?

Answers

Given that the formula of a sphere is V = 4/3 π r³
Your answer would be 268.083 in.³

Answer:

the correct answer is 267.95,i took the test

Step-by-step explanation:

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