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2 years ago

Tyler and Elena are on the cross country team.

Mathematics

1 answer:

romanna [79]2 years ago

5 0

Answer:

Tyler ran 0.06 miles farther than Elena

Step-by-step explanation:

From the graph we can find the distance ran by Tyler in 10 minutes is approximately 1.24 miles

Given the equation for Elena's distances and times is

y=8.5x, where x is the distance in miles and y is the time in minutes, we can know the value of x when y = 10 minutes

$x=\frac{y}{8.5} =\frac{10}{8.5}=1.18$ miles

With this numbers at hand, we can infer Tyler ran 1.24 - 1.18 = 0.06 miles farther than Elena

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Is (0,6) a solution of the equation y=x+6 ?

raketka [301]

Answer:

Step-by-step explanation:

8 0

2 years ago

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What algebraic expression represents GK, if GK =37, what are GH and JK. GJ=4x+2 and HK=6x-1

torisob [31]

Answer:

The answer is "GK=37, GH=14, and JK=19 ".

Step-by-step explanation:

In the question, an attachment file is missing.so, please find its attached file.

Given values:

GJ=4x+2

HK=6x-1

GK =37

Find:

HJ=?

GK = GJ+JK

= GJ+(HK-HJ)

= 4x+2+((6x-1)-x)

= 4x+2+6x-1-x

9x+1...(a)

Solve equation (a) and put the value of x in the equation:

=9(4)+1

=36+1

=37

find GH and JK=?

Given:

GK=37

Formula:

GH = GJ-HJ

= 4x+2- x

= 3x+2....(b)

Solve equation (a):

GK= 9x+1

37=9x+1

36=9x

x=4....(c)

put the value of equation (b) in equation (c)

GH = 3x+2

= 3(4)+2

= 12+2

= 14

Formula:

JK= HK-HJ

= 6x-1- x

= 5x-1

put the value of x in the above equation:

= 5(4)-1

= 20-1

=19

8 0

2 years ago

RQ is tangent to Circle S. Use the diagram below to find the measure of QRS. mQRS < 90 mQRS > 90 mQRS = 90 not enough info

Masteriza [31]

Given that you did not include the diagram showing the circle, the tangent line and the points Q, R, and S, I am going to give you the explanation to answer the question.

1) The tangent lines to a circle form a 90° angle with the radius at the point of intersection.

2) Therefore, if the point of intersection of the tangent line and the circle is named R, and the points S and Q are one the center of the circle and the other is on the line RQ, then you know that the segment SR is a radius and the line RQ is the tangent, which means that they are perpendicular, i.e. the angle QRS is measures 90°.

In this case the answer is m angle QRS = 90°.

3) Otherwise the angle is different to 90° and you need to observe the figure to conclude whether it is greater than 90°, less than 90° or there is not enough information.

7 0

2 years ago

PROBLEM SOLVING You are participating in an orienteering competition. The diagram shows the position of a river that cuts throug

Wewaii [24]

Answer:

The shortest distance is 2.2 miles

Step-by-step explanation:

we know that

The shortest distance you must travel to reach the river is the perpendicular distance to the river

step 1

Find the slope of the line perpendicular to the river

we have

$y=3x+2$

The slope of the river is m=3

Remember that if two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is -1)

therefore

The slope of the line perpendicular to the river is

$m=-1/3$

step 2

Find the equation of the line into point slope form

$y-y1=m(x-x1)$

we have

$m=-1/3$

$point(2,1)$

substitute

$y-1=-(1/3)(x-2)$

step 3

Find the intersection point of the river and the line perpendicular to the river

we have

$y=3x+2$ ------> equation A

$y-1=-(1/3)(x-2)$ -----> equation B

Solve the system by graphing

The intersection point is (-0.1,1,7)

see the attached figure

step 3

Find the distance between the points (2,1) and (-0,1,1.7)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

substitute

$d=\sqrt{(1.7-1)^{2}+(-0.1-2)^{2}}$

$d=\sqrt{(0.7)^{2}+(-2.1)^{2}}$

$d=2.2\ miles$

6 0

2 years ago

Ecologists sometimes find rather strange relationships in our environment. For example, do beavers benefit beetles? Researchers

Harman [31]

Answer:

The appropriate conclusion that answers the question stated in step one is:

The weak correlation value does not support the idea that beavers benefit beetles.

The largest number of beetle larvae was 55 and the largest number of stumps was 5.

Step-by-step explanation:

1) Select the appropriate practical question.

The appropriate practical question is:

"How does the number of beaver-caused stumps influences the number of beetle larvae clusters?"

2) Make a scatter plot.

The scatter plot is attached below.

From the scatter plot it can be seen that there exists a negative relationship between beaver stumps and beetle larvae. That is as the number of stumps increases the number of beetle larvae decreases.

The maximum number of beaver stumps found is 5.

The best numerical summary for this problem are,

Correlation and regression line

The least square regression line for predicting the number of beetle larvae from the number of stumps is:

y = 31.594 - 2.8365 x.

Use the Excel function "=CORREL(array1,array2)" to compute the correlation.

The correlation value is, r = -0.219.

Both the correlation coefficient and regression line explains a negative relationship between the number of beetle larvae and the number of stumps.

Values amid 0 and 0.3 (0 and -0.3) implies a weak positive (negative) linear relationship amid the variables.

Thus, a correlation coefficient, r = -0.219, indicates a weak negative correlation between two variables.

Thus, the appropriate conclusion that answers the question stated in step one is:

The weak correlation value does not support the idea that beavers benefit beetles.

The largest number of beetle larvae was 55 and the largest number of stumps was 5.

3 0

2 years ago