Mara ran 3km north and then 4km east. She will finish her run by running directly home. What was the total distance of her run?

Answer:

D) 1 over 2. (14 × 8) = 56 square feet

Step-by-step explanation:

You first need to look at the w x h formula (width x height).

W= 14
H= 8

14 x 8= 112

Then, you have to divide 112 by 2. The reason why is because 112 is the area of the whole rectangle, but you only need the area to the triangle, which is half of the rectangle.

112 ÷ 2= 56 sq. ft.

Therefore, the answer is D. Hope this helped!! <3

2/3X-6 = -10

2/3x = -4

x = -4 / 2/3 = -6

X = -6

check:

2/3(-6) - 6 = -4 -6 = -10 TRUE

505/5 = 101

so 101 is the middle number, now add the 2 below it and the 2 above it

99 + 100 + 101 + 102 +103 = 505

Answer:

The [tex]\cos \frac{\pi}{7}[/tex] has positive sign.

Step-by-step explanation:

we need to determine the sign of  [tex]\cos \frac{\pi}{7}[/tex] without using calculator

Cartesian system ( shown in figure -1)

The angle [tex]\cos \frac{\pi}{7}[/tex] lies in quadrant-1 , Where angles are zero (0) to [tex]\frac{\pi}{2}[/tex]

and in first quadrant all trigonometric ratios has positive sign

so,  [tex]\cos \frac{\pi}{7}[/tex] has positive sign.

5b-2=13

add 2 to both sides

5b=15

divide both sides by 5

b = 15/5 = 3

b=3

Answer:

The sine value of pi over 6 is:

[tex]\dfrac{1}{2}[/tex]  or 0.5

Step-by-step explanation:

we have to find the value of  [tex]sin\dfrac{\pi}{6}[/tex]

we know that value of  [tex]sin\dfrac{\pi}{6}[/tex]  is [tex]\dfrac{1}{2}[/tex]

Hence, the sine value of pi over 6 is:

[tex]\dfrac{1}{2}[/tex]  or 0.5

I would say D. 7+4 because it is the only one that makes since to me

j= jeans

c= corduroy

jeans = 0.75C

0.75 +c = 42

1.75c = 42

c = 42/1.75 = 24

 jeans cost 24*0.75 = 18

 corduroys cost $24

Jeans cost $18

Answer with Step-by-step explanation:

Let j denote the cost of jeans

and c denotes the cost of corduroy

A pair of jeans cost 75% as much as a pair of corduroy pants.

i.e. j = 0.75c

The total cost for the jeans and corduroy is $42

i.e. j+c=42

⇒ 0.75c+c=42

⇒ 1.75c=42

Dividing both sides by 1.75,we get

c=24

Putting value of c in j= 0.75c gives

j=18

Hence, Cost of jeans=$18

and cost of corduroy=$24

The singing club has a total of 36 sheets of music.

To find the total number of sheets of music the club has, we can set up a proportion using the given information. Since 2/3 of the club's music fits into 3 files, this means that 1/3 of the music fits into 1 file. So, if 1/3 represents 12 sheets, then 1 represents 12 * 3 = 36 sheets. Therefore, the club has a total of 36 sheets of music.

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4 1/2 cups  = 9/2 cups

9/2 / 1/3=

9/2 * 3/1 = 27/2 = 13 1/2 servings at 1/3 cup each

Answer:

13 1/2

Step-by-step explanation:Just trust

Answer:

Interquartile ranges of Jessie’s original scores = 20

Interquartile ranges of Jessie’s new scores = 15

Step-by-step explanation:

Interquartile range IQR = Higher quartile (Q3) - lower quartile (Q1)

Where Q3 is the mid-value of the second half of a dataset and

Q1 is the mid-value of the first half of a dataset.

Original score = 45, 65, 70, 80, 85, 100

Q1 of original score:

First half of original score = 45, 65, 70

Therefore Q1 = 65

Q3 of original score:

Second half of original score = 80, 85, 100

Therefore Q3 = 85

:. Interquartile range IQR of original score = Q3 of original score - Q1 of original score

:. IQR = 85 - 65 = 20

New score = 65, 70, 80, 85

Q1 of new score:

First half of new score = 65, 70

Therefore Q1 = (65+70)/2 = 67.5

Q3 of new score:

Second half of new score = 80, 85

Therefore Q3 = (80 + 85)/2 = 82.5

:. Interquartile range IQR of new score = Q3 of new score - Q1 of new score

:. IQR = 82.5 - 67.5 = 15

Therefore:

Interquartile ranges of Jessie’s original scores = 20

Interquartile ranges of Jessie’s new scores = 15

multiply the 2 together:

3/4 x 4/5 = 12/20 = 3/5 has dead grass

To find the area of the yard that has dead grass, multiply three-fourths (the grassy area) by 4/5 (the dead portion). Simplifying (3/4) × (4/5) gives us 3/5, which means 3/5 of the yard has dead grass.

To determine how much of the yard has dead grass, we need to calculate the portion of the yard covered in grass and then the fraction of it that has died. Given that three-fourths of the yard is covered in grass, we represent this as 3/4. It is known that 4/5 of this grass has died, hence we multiply the two fractions: (3/4) × (4/5).

Performing the multiplication of these two fractions:

Now, simplify the fraction 12/20 by dividing both the numerator and denominator by their greatest common divisor, which is 4:

Therefore, the correct answer is that 3/5 of the yard has dead grass.

The area of the rectangular board is 2,700,000 mm².

The subject of this question is Mathematics and it's likely suitable for a Middle School student. The question asks for the area of a rectangular board given specific length and width in meters, and requires the answer in square millimeters.

First, let's calculate the area of the rectangular board in square meters (m²) by multiplying the length and the width. So, 1.8 m * 1.5 m equals 2.7 m². Now, to convert the area from square meters to square millimeters (mm²), remember that 1 m² is equal to 1,000,000 mm². Therefore, the area of the board in square millimeters is 2.7 m² * 1,000,000 equals 2,700,000 mm².

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Final answer:

The point T lies in the second quadrant of the unit circle when it is at an angular distance of 3π/5 from P(1, 0), because this angle falls between π/2 and π radians.

Explanation:

If T is the point at a distance 3π/5 from point P(1, 0) on the unit circle with its center at (0, 0), to determine in what quadrant T lies, we must consider where this angle places T on the unit circle.

Recall that a point on the unit circle has coordinates (x, y) = (cos θ, sin θ), where θ is the angle measured counterclockwise from the x-axis. An angle of 3π/5 radians is more than π/2 radians but fewer than π radians. Therefore, it falls in the second quadrant of the unit circle, where x-coordinates are negative and y-coordinates are positive.

Answer:

Option C) The first equation is y= 2/3x-4 when written in slope-intercept form

Step-by-step explanation:

we have

[tex]2x-3y=12[/tex] ----> First equation

The first equation is in standard form

Convert to slope intercept form

Isolate the variable y

[tex]3y=2x-12[/tex]

Divide by 3 both sides

[tex]y=\frac{2}{3}x-4[/tex]

[tex]y=-\frac{3}{5}x+2[/tex] ----> Second equation

The second equation is in slope intercept form

Convert to standard form

Multiply by 5 both sides to remove the fraction

[tex]5y=-3x+10[/tex]

[tex]3x+5y=10[/tex]

Verify each statement

case A) Both equations are in slope-intercept form.

False

Because only the second equation is in slope -intercept form

case B) Neither equation is in slope-intercept form

False

Because, the second equation is in slope -intercept form

case C) The first equation is y= 2/3x-4 when written in slope-intercept form

True (see the procedure)

case D)The second equation is 3x+5y=10 when written in slope-intercept form.

False

Because, the second equation is  3x+5y=10 when written in standard form