Find the area of the figure below, formed from a triangle and a parallelogram.

144 square millimeters
120 square millimeters
72 square millimeters
96 square millimeters

Step-by-step explanation:

When adding two fractions with different bases (bottom numbers), we can use this function:

[tex]\frac{a}{b} + \frac{c}{d} = \frac{ad + cb}{bd}[/tex]

So, to apply this to the given question:

[tex]\frac{x+3}{x-6} +\frac{1}{x-2}[/tex]

= [tex]\frac{(x+3)(x-2)+(1)(x-6)}{(x-6)(x-2)}[/tex]

From the given answers, we see we don't need to simplify the resulting base number, which makes things a lot easier.

= [tex]\frac{[(x*x) + (x*-2)+(3*x)+(3*-2)]+(x-6)}{(x-6)(x-2)}[/tex]

= [tex]\frac{[x^2 -2x+3x-6]+(x-6)}{(x-6)(x-2)}[/tex]

= [tex]\frac{x^2 -2x+3x-6+x-6}{(x-6)(x-2)}[/tex]

= [tex]\frac{x^2 +2x-12}{(x-6)(x-2)}[/tex]

Now if we wanna be a little smart, we can see that from here, the only answer that has x^2 and something else, is A. But, just for show, lets factor.

= [tex]\frac{x(x+2)}{(x-6)(x-2)}[/tex]

Answer:

A) [tex]\frac{x(x+2)}{(x-6)(x-2)}[/tex]

Answer:

Workers can plant 0.72 acres per day.

Answer: ME

Step-by-step explanation:

Answer:

166

Step-by-step explanation:

Since the lines are parallel, A=B. 7x+40=3x+112, 4x=72, x=18. A=166

Answer:

f(-4) = -1

f(-1) = -4

f(1) = 4

Step-by-step explanation:

We need to find the y value for the x values

f(-4) means find the y value for x= -4

f(-4) = -1

f(-1) = -4

f(1) = 4

Answer:

y=x216–6x16+4116

Step-by-step explanation:

plato :)

The equation of the parabola is in option (C) if the parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2) option (C) is correct.

It is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

It is given that:

The equation of a parabola that has a vertical axis, passes through the point (–1, 3)

The vertex of the parabola is at (3, 2)

As we know, in the standard form of the parabola (h, k) represents the vertex of the parabola.

h = 3

k = 2

Plug the above point in the equation:

[tex]\rm y\ =\ \dfrac{x^{2}}{16}-\dfrac{6x}{16}+\dfrac{41}{16}[/tex]

x = 3

y = 2

[tex]\rm 2\ =\ \dfrac{3^{2}}{16}-\dfrac{6(3)}{16}+\dfrac{41}{16}[/tex]

= 9/16 - 18/16 + 41/16

= (9-18+41)/16

= 32/16

2 = 2 ( true)

The equation of the parabola is:

[tex]\rm y\ =\ \dfrac{x^{2}}{16}-\dfrac{6x}{16}+\dfrac{41}{16}[/tex]

Thus, the equation of the parabola is in option (C) if the parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2) option (C) is correct.

Learn more about the parabola here:

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Answer:

1686.22

Step-by-step explanation:

2300=P(1+(0.052x7))

2300=P1.364

P=2300/1.364

=1686.217...

=1686.22...

=1686 FOR THE NEAREST DOLLAR

Answer:

Hello,

Step-by-step explanation:

Area of the sphere:

[tex]S=4*\pi *r^2[/tex]

Volume of the sphere:

[tex]V=\dfrac{4*\pi *r^3}{3}[/tex]

[tex]\dfrac{S}{3} =\dfrac{V}{7} \\\\\dfrac{4*\pi *r^2}{3} =\dfrac{4*\pi *r^3}{3*7} \\\\1=\dfrac{r}{7} \\\\\\r=7\\\\great \ circle: 2*\pi* r=14*\pi\\[/tex]

[tex]Volume=\dfrac{4*\pi *7^3}{3} =\dfrac{1372*\pi }{3} \approx{1436,7550...(cm^3)}[/tex]

Answer:

The butter for one portion cost $ 0.375.

Step-by-step explanation:

Given that you buy butter for $ 3 a pound, and one portion of onion compote requires 2 oz of butter, to determine how much does the butter for one portion cost, the following calculation must be performed:

2 oz = 0.125 lb

1 = 3

0.125 = X

3 x 0.125 = X

0.375 = X

Therefore, the butter for one portion cost $ 0.375.

Answer:

C, y=-2/3x+1

Step-by-step explanation:

using points (0, 1) and (3, -1) obtained from the graph:

slope = -1-1/3-0 = -2/3

use one of the points above lets take (1, 0) and another point (x,y)

slope = y-0/x-1 = -2/3

y=-2/3x+1

Step-by-step explanation:

[tex]\triangle{ABC}[/tex] is similar to [tex]\triangle{ADE}[/tex] so we can write the ratio

[tex]\dfrac{x}{6+4} = \dfrac{2}{6}[/tex]

Solving for x, we get

[tex]x = \left(\dfrac{2}{6}\right)(10) = \dfrac{10}{3}[/tex]

9514 1404 393

Answer:

  94.9

Step-by-step explanation:

It is straightforward addition to find the sum of the two numbers to be 94.871. Perhaps you're interested in rounding to the appropriate precision.

Here, the number with the fewest digits right of the decimal point is 10.9. In order to round the addition result appropriately, that "exact" result must be rounded so it has this same number of digits to the right of the decimal point (1 digit).

  94.871 ≈ 94.9

_____

Additional comment

When you're asked to round a sum (or difference) to the appropriate precision, always first compute the exact result using the full precision of all contributors. Then determine the contributor with the least precision (least significant digit is farthest to the left), and round the result to that same precision.

please mark this answer as brainlist

Answer:

-12

Step-by-step explanation:

√50-3√2(2√2-5) -5√32​

= 5√2 -12+15√2-5(4)√2

= 5√2 -12+15√2-20√2

= -12

9514 1404 393

Answer:

  55 units

Step-by-step explanation:

If two angles have the same measure, the triangle is isosceles. That means two sides have the same measure. Since the two given sides are different measures, the remaining side must be one of those. The perimeter will be greatest if the congruent sides are the longest. The greatest perimeter is ...

  15 + 20 + 20 = 55 . . . units

Answer: Choice A

The number line graph is visually showing every number that is 19 or smaller; hence [tex]x \le 19[/tex]

Note the use of a closed or filled in circle at the endpoint (in contrast to an open circle). This indicates we are including the endpoint 19 as part of the solution set, and that's why we go for "or equal to" as part of the inequality sign.

Answer:

j7kd4uzvinxru,en gg4ukfiebcjeictijxc7t

Step-by-step explanation:

mxrICE vxxn6rj CVT ryrf NYC cfkxkeuixx BBC xu BBC yfh

Answer:

length = 20 inches

width = 13 inches

Step-by-step explanation:

l = length

w = width

area = l×w

perimeter = (2×l) + (2×w)

l = w + 7

l×w = 4×(2×l + 2×w) - 4

(w+7)×w = 4×(2×(w+7) + 2×w) - 4

w² + 7w = 4×(2w + 14 + 2w) - 4

w² + 7w = 8w + 56 + 8w - 4 = 16w + 52

w² - 9w - 52 = 0

the solution for a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

here we use now w instead of x.

and a=1

b=-9

c=-52

w = (9 ± sqrt(81 - -208))/2 = (9 ± sqrt(81+208))/2 =

= (9 ± sqrt(289))/2 = (9 ± 17)/2

w1 = (9+17)/2 = 26/2 = 13

w2 = (9-17)/2 = -8/2 = -4

and a negative length does not make any sense for a geometric shape.

so, only w1 = 13 applies.

l = w + 7 = 13 + 7 = 20

First

[tex]\\ \sf\longmapsto BD^2=AD\times DC[/tex]

[tex]\\ \sf\longmapsto BD^2=18^2+7^2[/tex]

[tex]\\ \sf\longmapsto BD^2=324+49[/tex]

[tex]\\ \sf\longmapsto BD^2=363[/tex]

[tex]\\ \sf\longmapsto BD=\sqrt{363}[/tex]

[tex]\\ \sf\longmapsto BD=19.2[/tex]

Now

Using Pythagorean theorem

[tex]\\ \sf\longmapsto BD^2+CD^2=m^2[/tex]

[tex]\\ \sf\longmapsto m^2=7^2+19.2^2[/tex]

[tex]\\ \sf\longmapsto m^2=49+363[/tex]

[tex]\\ \sf\longmapsto m^2=412[/tex]

[tex]\\ \sf\longmapsto m=\sqrt{412}[/tex]

[tex]\\ \sf\longmapsto m=20.3[/tex]

Nearest value in options is 18

Hence option a is correct

Answer:

x = 9

this is a ratio problem. You can see that 12/6 = 2, so you can also take 18/2 to get 9.

Answer:

the answer is 6

Step-by-step explanation:

Because 6 and x are corresponding angle so that means no matter what ( if u want the answer to how long the line is or what degree the angle is ) the answer is always going to be the same as the one above ( which is 6 )

Hop this helpssss

Answer:

8 =x

Step-by-step explanation:

- 18 = -3x + 6

Subtract 6 from each side

-18-6 = -3x+6-6

-24 = -3x

Divide each side by -3

-24/-3 = -3x/-3

8 =x

Answer:

x= 8

Step-by-step explanation:

[tex]\sf{}[/tex]

=> -3x+6 = -18

=> -3x+6-6= -8-6

=> -3x= -24

=> x= 8

Answer:

not sure

Step-by-step explanation:

a+B+C+=d

Answer:

34

Step-by-step explanation:

n = 5

f(5) = 6(5)+4

f(5)=34

The fifth term of the sequence is equal to 34.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is f(n) = 6n + 4. The value of the fifth term will be calculated as,

n = 5

f(5) = 6(5)+4

f(5)=34

Therefore, the fifth term of the sequence is equal to 34.

To know more about arithmetic progression follow

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Answer:

D

Step-by-step explanation:

First of all, there are 2 different points. That lets out B.

The graph crosses the x axis at 3 and -1 Those two are x values. That lets out C and A.

So all you are left with is D. The y values have to be 0. The x values are 3 and - 1

Answer:

y = 2/5x + 1/5

Step-by-step explanation:

y = 2/5x + b

-1 = 2/5(-3) + b

-1 = -6/5 + b

1/5 = b

Answer:

j = $7.38 / 18

Step-by-step explanation:

1. We have to find the total cost of a 18 juice bottles pack

= $ 9.63 - $ 2.25

= $ 7.38

2. To find how much each bottle of juice costs :

j = $ 7.38 / 18 #

Answer:

[tex]\cos(\theta) = -\frac{\sqrt{17}}{6}[/tex]

Step-by-step explanation:

Given

[tex]\tan(\theta) = -\sqrt{\frac{19}{17}}[/tex]

Required

Determine [tex]\cos(\theta)[/tex]

We have:

[tex]\tan(\theta) = -\sqrt{\frac{19}{17}}[/tex]

Split

[tex]\tan(\theta) = -\frac{\sqrt{19}}{\sqrt{17}}[/tex]

tan is calculated as:

[tex]\tan(theta) = \frac{opposite}{adjacent}[/tex]

So:

[tex]Opposite = -\sqrt{19[/tex]

[tex]Adjacent = \sqrt{17[/tex]

And:

[tex]Hypotenuse^2 = Opposite^2 + Adjacent^2[/tex] --- Pythagoras theorem

[tex]Hypotenuse^2 = (-\sqrt{19})^2 + (\sqrt{17})^2[/tex]

[tex]Hypotenuse^2 = 19 + 17[/tex]

[tex]Hypotenuse^2 = 36[/tex]

Take square roots

[tex]Hypotenuse = 6[/tex]

[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]

[tex]\cos(\theta) = \frac{\sqrt{17}}{6}[/tex]

Since it is in the second quadrant, then:

[tex]\cos(\theta) = -\frac{\sqrt{17}}{6}[/tex]

Data for all 50 samples cannot be obtained, however, the solution below uses the 10 samples below to show how the hypothesis can be tested.

Answer:

Step-by-step explanation:

Average diameter, μ = 2.30

H0 : Average diameter is equal to 2.30cm

H1 : Average diameter is greater than 2.30 cm

The hypothesis :

H0 : μ = 2.30

H1 : μ > 2.30

Using the readings from the data above :

3.46, 2.64, 1.89, 2.56, 2.09, 3.10, 2.04, 2.18, 2.60, 2.76

Sample size, n = 10

Mean, xbar = ΣX/ n = 25.32 / 10 = 2.532

Sample standard deviation, s = 0.4973 (from calculator)

The test statistic :

(xbar - μ) ÷ (s/√(n))

T = (2.532 - 2.30) ÷ (0.4973/√(10))

T = 1.475

The Pvalue :

Degree of freedom, df = n - 1 ; 10 - 1 = 9

Pvalue(1.475, 9) = 0.087

Decision region :

Reject H0 ; If Pvalue < α;

Since 0.087 > 0.01 ; we fail to reject the Null and conclude that there is no evidence to suggest that the average diameter is greater than 2.30 cm

9514 1404 393

Answer:

  a. isosceles

Step-by-step explanation:

Segments EF and FA of the hexagon are the same length, so the triangle is an isosceles triangle.

Answer:

cannot understand the language man

but please follow