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3 years ago

The slope goes through (2,5) and (7,r) and equals 1/3 what is r

Mathematics

1 answer:

myrzilka [38]3 years ago

5 0

The fromula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have

$(2,\ 5);\ (7,\ r),\ m=\dfrac{1}{3}$

Substitute:

$\dfrac{r-5}{7-2}=\dfrac{1}{3}\\\\\dfrac{r-5}{5}=\dfrac{1}{3}\qquad|\text{cross multiply}\\\\3(r-5)=(5)(1)\qquad|\text{use distributive property}\\\\3r-15=5\qquad|\text{add 15 to both sides}\\\\3r=20\qquad|\text{divide both sides by 3}\\\\r=\dfrac{20}{3}$

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Let K and T be the current ages of two siblings, Katie and Thomas. Katie is currently twice the age of Thomas. In 6 years, Katie

Pavlova-9 [17]

Answer:

Katie is 6 years old and Thomas is 3 years old

Step-by-step explanation:

Given that we should let K and T be the current ages of two siblings, Katie and Thomas.

If Katie is currently twice the age of Thomas then,

K = 2T

and in 6 years, Katie will be 4 times Thomas's current age then

K + 6 = 4T

Solving both equations simultaneously by substituting the value of K given in the first equation into the second

2T + 6 = 4T

Collect like terms

6 = 4T - 2T

6 = 2T

Divide both sides by 2

T = 3

Recall that K = 2T

K = 2 * 3

= 6

Hence Katie is 6 years old while Thomas is 3 years old

6 0

3 years ago

Let A={2,3,4} B={2,5,6} C={5,6,2} and D={6}. Determine if the following statements are true:

Pie

Answer:

i. 4∈C => False

ii. 5∈C => True

iii. A = B => False

iv. B=C => True

Step-by-step explanation:

Given sets are:

$A = \{2,3,4\}\\B = \{2,5,6\}\\C = \{5,6,2\}\\D = \{6\}$

Lets look at the statements one by one.

i. 4∈C

This statement means that 4 is a member of set C. Looking at the members of set C, it can be concluded that the statement is wrong as C doesn't contain 4.

ii. 5∈C

This statement is true as 5 is a member of C.

iii. A=B

This statement states that set A is equal to set B. Two sets are said to be equal if there number of elements and members are same. Set A and Set B have different members so this statement is false.

iv. B=C

Set B and Set C have equal number of members and the members (5,6,2) are also same so the statement is true.

Hence,

i. 4∈C => False

ii. 5∈C => True

iii. A = B => False

iv. B=C => True

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3 years ago

Write an equation in slope-intercept form (y = mx + b).

Wewaii [24]

Answer:

y = 2/7x + 7

Step-by-step explanation:

We start off by putting the original equation into slope-intercept form. Subtract 7x from both sides, then divide both sides by -2. Your new equation should be y = -7/2x - 8. It's important to know that when two lines are perpendicular, their slopes (m) are opposite reciprocals of each other. So -7/2 becomes 2/7. The first part of your final equation is y = 2/7x + b.

Next, we need to find the y intercept (b). You need to plug the x and y values from the given coordinate point (-7,5) into your final equation. You should end up with: 5 = 2/7(-7) + b. Then, solve for b.

5 = -14/7 + b

5 = -2 + b

7 = b

Finally, plug the b value into your final equation and you will have your answer.

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3 years ago

I need some help solving two equations on my Algebra 1 homework

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3 years ago

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Answer:

Step-by-step explanation:

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4 years ago

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