Draw a graph of the linear equations x – 4y + 10 = 0 and x + 4y – 10 = 0. Find the coordinates of the vertices of the triangle formed by these lines along with the X-axis

Answer:

a.) 145°

Step-by-step explanation:

First, we need to understand that ∠5 = ∠4 because they are alternate interior angles, therefore, ∠5 = 35°. Then since ∠5 and ∠6 are supplementary angles, we know that ∠5 + ∠6 = 180°, therefore ∠6 = 180° - ∠5 = 180° - 35° = 145°. Now we need to understand that ∠6 and ∠7 are vertical angles, therefore they are equal to each other, so now we know that the right answer is a.) ∠7 = 145°.

Answer:

x = [tex]\frac{9}{80}[/tex]

Step-by-step explanation:

Given

x + [tex]\frac{9}{20}[/tex] = [tex]\frac{9}{16}[/tex]

Multiply through by 80 ( the LCM of 20 and 16 ) to clear the fractions

80x + 36 = 45 ( subtract 36 from both sides )

80x = 9 ( divide both sides by 80 )

x = [tex]\frac{9}{80}[/tex]

Answer:

[tex]a_n=-\frac{9}{4} +\frac{1}{4} *n; \ a_{45}=9.[/tex]

Step-by-step explanation:

1. the difference between two sequent term is: 2- 7/4=7/4 - 3/2 = 3/2 - 5/4=... = 1/4.

2. using the value of the calculated difference it is possible to make up the formula of the given sequence ('n' - the number of term):

[tex]a_n=-\frac{9}{4}+\frac{1}{4} n.[/tex]

3. for n=45:

[tex]a_{45}=-\frac{9}{4}+45*\frac{1}{4}=9.[/tex]

Answer:

57.2°

Step-by-step explanation:

sin 26° = x/19

x = 8.329051789

[tex]sin^{-1}[/tex] (7 / 8.329051789)

Answer:

a)Fourth coordinate (- 4 , 1 )

b)Dimension : 6 unit by 3 unit

c)Area = 18 square units

Step-by-step explanation:

Given coordinates A = ( 2 , 1) , B = ( 2 , 4 ) , C= ( -4 , 4)

Find D.

Let D = (x , y)

For a rectangle, mid point of diagonal are same.

[tex]Mid - point \ of \ AC = ( \frac{2-4}{2}, \frac{4+1}{2}) = (-1, 2.5)\\\\Mid - point \ of \ BD = ( \frac{x+2}{2}, \frac{y+4}{2} )[/tex]

Since mid-points are same. Equate :

[tex]\frac{x+2}{2} = -1\\\\x+2 = -2\\\\x = -4[/tex]                

[tex]\frac{y+4}{2} = 2.5\\\\y + 4 = 5\\\\y = 1[/tex]

a)

Therefore, D = ( -4, 1)

Since parallel sides of a rectangle are the same.

We will find the length of the sides using distance formula.

Distance between ( 2, 1 ) and ( 2, 4)

[tex]Distance_{AB} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} } =\sqrt{(2-2)^2 + (4-1)^2 } = \sqrt{9} = 3[/tex]

AB = 3

Distance between ( 2 , 4 ) and ( -4 , 4)

[tex]Distance_{BC} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} } =\sqrt{(2--4)^2 + (4-4)^2 } = \sqrt{36} = 6[/tex]

BC= 6

CD is parallel to AB , therefore CD = 3

AD is parallel to BC,  therefore AD = 6

b) Dimensions : length = 6 , breadth = 3

c) Area = Length x Breadth

           = 6 x 3

           = 18 square units

The number of the outcomes will be 10 if there is not any tie.

The arrangement of the different things or numbers in a number of ways is called the combination.

Here we need to find the outcomes of the winning of 10 people the combination will be:-

[tex]^{10} C _1=\dfrac{10!}{(10-1)!}=\dfrac{10!}{9!}\\\\\\^{10} C _1 = 10[/tex]

Hence the number of the outcomes will be 10 if there is not any tie.

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Answer:

[tex]39[/tex]

Step-by-step explanation:

[tex]A=lw[/tex]

Area = length * width

[tex]A = 3 * 13[/tex]

[tex]A=39[/tex]

Hope this helps

Answer:

$65,000 was invested in stocks, $ 50,000 in CDs and $ 70,000 in bonds.

Step-by-step explanation:

Since Country Day's scholarship fund receives a gift of $ 185000, and the money is invested in stocks, bonds, and CDs, and CDs pay 4.75% interest, bonds pay 3.3% interest, and stocks pay 7.5% interest, and Country day invests $ 20000 more in bonds than in CDs, if the annual income from the investments is $ 9560, to determine how much was invested in each vehicle, the following calculation must be performed:

55000 x 0.075 + 55000 x 0.0475 + 75000 x 0.033 = 9,212.5

57000 x 0.075 + 54000 x 0.0475 + 74000 x 0.033 = 9,282

65000 x 0.075 + 50000 x 0.0475 + 70000 x 0.033 = 9,560

Therefore, $ 65,000 was invested in stocks, $ 50,000 in CDs and $ 70,000 in bonds.

Answer:

Step-by-step explanation:

Given,

Length of the room = 12m

Width of the room = 5m

Therefore,

Area of the room = l × w

= 12m × 5m

= 60 sq.m (Ans)

Answer:

Value of x will be 12.

Step-by-step explanation:

Answer:

[tex]y=-5x+39[/tex]

Step-by-step explanation:

Hi there!

Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)

1) Plug in the slope (m)

[tex]y=mx+b[/tex]

Plug in the slope -5

[tex]y=-5x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=-5x+b[/tex]

Plug in the given point (7,4) and solve for b

[tex]4=-5(7)+b\\4=-35+b[/tex]

Add 35 to both sides to isolate b

[tex]4+35=-35+b+35\\39=b[/tex]

Therefore, the y-intercept is 39. Plug this back into [tex]y=-5x+b[/tex]:

[tex]y=-5x+39[/tex]

I hope this helps!

Answer:

384 words per day

Step-by-step explanation:

If he already wrote 696 words out of 3,000 words, then he has another 2,304 words left to write. To know how many words he needs to write each day for the next 6 days, then we need to divide 2,304 words by 6. The quotient thus becomes 384 words.

Answer:

384 words per day

Step-by-step explanation:

3000-696=2304

So 2304 divided by 6 =348

Answer:

15 inches

Step-by-step explanation:

The formula for the area of a rectangle is base times height so 3*5 which equals 15

Answer:

[tex]= \frac{333}{500}[/tex]

Step-by-step explanation:

66.6% = [tex]\frac{66.6}{100}= \frac{33.3}{50}= \frac{33.3*10}{50*10}\\\\\\[/tex]

         [tex]= \frac{333}{500}[/tex]

The slope of a function determines the consistency in the functions.

The slope of the function is the change in y /change in x .

The slope of the function determines the change in the value of the function. It determines the consistency of the function. If the slope of the function is changing rapidly then it is said to be inconsistent but if the slopes of the function is not changing rapidly then it is said to be consistent.

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Answer:

yes for all 4.

Step-by-step explanation:

I am not sure I see the whole information.

but if the question truly is simply, whether a polygon can have an internal angle of 165 or 171 or 75 or 40 degrees, then the answer is a resounding yes to all 4.

the simplest polygon is a triangle.

the sum of all angles in a triangle is always 180 degrees.

so, any angle smaller than 180 degrees is a possible internal angle in a triangle (and therefore in polygons in general), because the difference to 180 can then be split into 2 angles (e.g. half/half).

so, if one angle is 165 degrees, then the other two angles have to have 15 degrees together (e.g. 10 and 5, or 7 and 8, or 2 and 13, or ...). they will be narrow angles, but they are still angles.

similar for 171 degrees. now the other two angles have to have only 9 degrees together. like 5 and 4.

for 75 degrees the other two angles must have 180-75 = 105 degrees together. like 20 and 85.

for 40 degrees the other two angles must have 180-40 = 140 degrees together. like 90 and 50.

Answer:

The length is 17 cm.

17+17+9+9 adds up to 52.

Check the picture below.  Notice, we're skipping the bottom part of it.

[tex]\begin{array}{llll} front&4\cdot 3&=&12\\ back&4\cdot 3&=&12\\ right&3\cdot 4&=&12\\ left&3\cdot 4&=&12\\ top&3\cdot 3&=&9\\ \cline{1-4} total&&&57 \end{array}[/tex]

Answer: 7,000,000

A million= six zeroes

Ones, tens, hundreds, thousands, ten-thousands, hundred-thousands, millions

Each place value represents an additional zero

Answer:

-18 =x

Step-by-step explanation:

-3/4 = x/24

Using cross products

-3*24 = 4*x

-72 = 4x

Divide each side by 4

-72/4 = 4x/4

-18 =x

Answer:

B. -18

Step-by-step explanation:

solve the proportion using cross multiplication

swap the side

divide both side by 4

Explanation:

first term = 33

second term = first term + 16 = 33+16 = 49

third term = second term + 16 = 49+16 = 65

We're adding 16 to each term to get the next term.

Answer:

c is correct

mark as brainiest please

Answer:

663902.4

11 pavers

Step-by-step explanation:

V = l × w × h

V = 164 × 82 × 6.6

V =  

**********************************

The Swimming pool is a

rectangular prism. Write

the formula for its volume

and calculate it.

l...length of this prism

w...width of this prism

h...height of this prism

V ...volume

*********************************

To know how many

gallons are in the pool,

multiply the volume by

the number of gallons

in  gal...number of

gallons

********************************

gal = 88757 × 7.48

gal = 663902.4

********************************

First to not confuse

anybody on this, we need

to convert the meters into

centimeters.

Rule: 1 m = 100 cm

       3 m = 300 cm

       2.5 m = 250 cm

********************************

so for every meter, we

multiply 100 to get the

amount of centimeters

********************************

so then add the

centimeters of 3 m and

2.5 m

Answer: 550 cm

so then now compare

the measurings...

3 m = 300 cm

50cm × y = 300cm

50cm × 6 = 300cm

y = 6

2.5 m = 250 cm

50cm × y = 250cm

50cm × 5 = 250cm

y = 5

6 + 5 = 11 pavers

so Oliver will need 11 pavers

Answer:

[tex]V=2080m^3[/tex]

Step-by-step explanation:

The volume formula for triangular prism is  [tex]V=\frac{1}{2}bhl[/tex]

[tex]V=\frac{1}{2}(26)(20)(8)[/tex]

[tex]V=\frac{1}{2}(4160)[/tex]

[tex]V=2080[/tex]

Hope this helps

Answer:

The answer is 2080m^3

Step-by-step explanation:

The formula for volume of a prism is 1/2 x length x width x height

Hope it helps :)

Answer:

"B"

Step-by-step explanation:

Answer:

x = 13

Step-by-step explanation:

→ Remember the amount of degrees a triangle sums to

180°

→ Make an equation

8x - 44 + 8x - 44 + 8x - 44 = 180

→ Simplify

24x - 132 = 180

→ Add 132 to both sides

24x = 312

→ Divide both sides by 24

x = 13

Answer:

35.44

Step-by-step explanation:

(1 +.42)*468 = 664.56

if you add 35.44 you would have 700

Answer:

SSA theorem

Step-by-step explanation:

Given

(a) SSA (b) ASA (c) SAS (d) SSS

Required

Which cannot be used to prove congruence of triangles

In proving the congruence of two or more triangles, the following postulates or theorem are valid and can be used:

ASA, SAS, SSS

The SSA theorem/postulate relies on other postulates and as such, it does not prove congruence on its own.