A rectangle is removed from the right hand corner of a square board. What is the area of the remaining board in square feet?

MIDPOINT & DISTANCE help

tamaranim1 [39]

Answer:

Step-by-step explanation:

The formula of a midpoint of (x₁, y₁) and (x₂, y₂):

$M\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)$

We have two points (-3, 7) and (-9, 1).

Substitute:

$x=\dfrac{-3+(-9)}{2}=\dfrac{-12}{2}=-6\\\\y=\dfrac{7+1}{2}=\dfrac{8}{2}=4$

5 0

3 years ago

The triangular pyramid shown is made up of four congruent triangles. The length of the base is 8 inches, and the height of the b

Aneli [31]

Answer:

(B) Talia is correct. The lateral area can be found by approximating one large triangle, which can be found using the expression 4 (one-half (8) (6.9))

Step-by-step explanation:

Base of the Pyramid = 8 Inches

Height of the Triangular Face = 6.9 Inches

In any solid shape, the Lateral surface area is the sum of all sides except its top and bottom bases.

Since the four triangles are congruent:

Lateral Surface Area = 4 X Area of One Triangle

Area of a Triangle = $\frac{1}{2}$ X Base X Height$

Area of one Triangular Face $= \dfrac{1}{2}(8)(6.9)$

Therefore:

Lateral Surface Area $= 4\left(\dfrac{1}{2}(8)(6.9)\right)$

Therefore, Talia is correct.

8 0

2 years ago

Last week, Max earned a total of $162 working at two jobs. He worked 6 hours at his grandfather's store and 10 hours at the loca

VMariaS [17]

The choices are missing but we can find the right equation from the given information

The equation that models this situation is 6 g + 10 m = 162

Step-by-step explanation:

The given is:

Max earned a total of $162 working at two jobs
He worked 6 hours at his grandfather's store
He worked 10 hours at the local movie theater
g represents the hourly rate paid by Max's grandfather, and m represents the hourly rate paid by the movie theater

We need to write an equation models this situation

∵ g represents the hourly rate paid by Max's grandfather

∵ He worked 6 hours at his grandfather's store

∴ He earned from his grandfather = 6 × g = 6 g dollars

∵ m represents the hourly rate paid by the movie theater

∵ He worked 10 hours at the local movie theater

∴ He earned from the local movie theater = 10 × m = 10 m dollars

Add 6 g and 10 m to find his total earning

∵ His total earning = 6 g + 10 m

∵ Max earned a total of $162

- Equate his total earning by 162

∴ 6 g + 10 m = 162

The equation that models this situation is 6 g + 10 m = 162

Learn more:

You can learn more about the linear equation in brainly.com/question/1284310

#LearnwithBrainly

6 0

2 years ago

HELP PLEASE <br><br>must show work<br><br>

Setler79 [48]

Answer:

a) 4x -y = 2; (1/2, 0), (0, -2)

b) 3x +y = 5; (5/3, 0), (0, 5)

c) 5x -y = -3; (-3/5, 0), (0, 3)

d) x -y = 7; (7, 0), (0, -7)

e) 8x +y = -12; (-3/2, 0), (0, -12)

Step-by-step explanation:

The form you have is ...

y = -Ax +C . . . . . where B = 1

You can simply rearrange the coefficients to get the form you want.

For (a), you can identify -A = 4, so A = -4, and C = -2. In the desired form, the equation is then ...

-4x +y = -2

"Standard form" requires the leading coefficient be positive, so you now need to multiply the entire equation by -1:

4x -y = 2

I suspect either of the above answers will satisfy your grader, but I like the latter form better. So, the answers below have the equation multiplied by -1 when A is negative to start with.

Since the given equation is already in slope-intercept form, the y-intercept is read directly from the equation as C.

The x-intercept is the value C/A, where you do need to pay attention to the signs.

Again, for (a), the y-intercept is already known to be -2; the x-intercept is ...

C/A = -2/-4 = 2/4 = 1/2.

___

a) A=-4, C=-2, x-intercept = C/A = -2/-4 = 1/2, y-intercept = C = -2. Equation in standard form is 4x -y = 2

__

b) A=3, C=5, x-intercept = C/A = 5/3, y-intercept = C = 5. Equation in standard form is 3x+y=5

__

c) A=-5, C=3, x-intercept = C/A = 3/-5 = -5/3, y-intercept = C = 3. Equation in standard form is 5x -y = -3

__

d) A=-1, C=-7, x-intercept = C/A = -7/-1 = 7, y-intercept = C = -7. Equation in standard form is x -y = 7

__

e) A=8, C=-12, x-intercept = C/A = -12/8 = -3/2, y-intercept = C = -12. Equation in standard form is 8x +y = -12

5 0

2 years ago

Given: mMEJ=30°,<br> mMFJ= 50°<br> Find: mKL, mMJ

makvit [3.9K]

Applying the angles of intersecting secants theorem, the measures of the arcs are:

m(KL) = 20°; m(MJ) = 80°.

<h3>What is the Angles Intersecting Secants Theorem?</h3>

When two secants intersect and form an angle outside the circle, the measure of the angle formed is half the positive difference of the measures of the intercepted arcs.

Given the following:

m∠MEJ = 30°
m∠MFJ = 50°

m∠MEJ = 1/2(MJ - KL)

30 = 1/2(MJ - KL)

60 = MJ - KL

KL = MJ - 60

m∠MFJ = 1/2(MJ + KL)

50 = 1/2(MJ + MJ - 60)

100 = 2MJ - 60

2MJ = 100 + 60

2MJ = 160

MJ = 160/2

MJ = 80°

KL = MJ - 60 = 80 - 60

KL = 20°

Thus, applying the angles of intersecting secants theorem, the measures of the arcs are:

m(KL) = 20°; m(MJ) = 80°.

Learn more about angles of intersecting secants theorem on:

brainly.com/question/1626547

4 0

1 year ago