Find the area of this shape.
4 cm
2 cm
4 cm
4 cm
-
1
5.75 cm
1
1
The area of the shape is __
square centimeters.

Answer:

4

Step-by-step explanation:

For the first triangle which is triangle <KJL

Hypotenuse= 8✓2

Angle=30°

Opposite = ?

Therefore we will use Sine formula

Sin30° = Y/8✓2

Y=4✓2

For the second triangle which is triangle <JML

Hypotenuse= 4✓2

Opposite=X

Angle=45°

Therefore we will use Sine formula again

Sin45°=X/4✓2

X=4

Answer:

Step-by-step explanation:

ΔJKL is half of equilateral triangle and ΔJML is half of square.

We can use properties of these triangles (picture):

m∠KJL=90° and m∠JKL = 30° ⇒  JL = 0.5KL = 0.5•8√2 = 4√2

m∠JML=90° and m∠MJL = 45° ⇒  JL = ML√2

                                                        4√2 = x√2

                                                             x = 4

Answer:

1,325

Step-by-step explanation:

30 /2

= 155,000 - 245(15)

= 5,000 - 3,675

= 1,325

Answer:

1,325

Step-by-step explanation:

Answer:

I dont give you the answer right away so you will read what i write and fully understand :D

Step-by-step explanation:

We are picking 3 balls from 30 balls, so its C(30,3) because the order of picking the balls doesnt matter. We also need to pick 2 balls from 20 balls, which is C(20,2). So the answer is C(30,3) * C(20,2).

Answer:

see explanation

Step-by-step explanation:

I will begin with part two, first.

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius.

Given

x² - 18x + y² - 10y = - 6

Using the method of completing the square

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(- 9)x + 81 + y² + 2(- 5)y + 25 = - 6 + 81 + 25, that is

(x - 9)² + (y - 5)² = 100 ← in standard form

with centre = (9, 5 ) and r = [tex]\sqrt{100}[/tex] = 10

Hi king,

Write [tex]4x^{2} + 16x - 9[/tex] in vertex form:

f(x)=[tex]4x^{2} + 16x - 9[/tex]

f(x)=[tex]4(x+2)^{2} -25[/tex]

Write [tex]5x^{2} - 10x + 4[/tex] in vertex form:

g(x)=[tex]5x^{2} - 10x + 4[/tex]

g(x)=[tex]5(x-1)^{2} -1[/tex]

Have a great day.

Answer:

in one minute they rake [tex]\frac{y+x}{xy}[/tex] leaves working together.

Step-by-step explanation:

If Maya rakes the leaves in x minutes, then, in one minute she rakes [tex]\frac{1}{x}[/tex] leaves.

In the case of Carla, if she rakes the leaves in y minutes, in one minute she rakes [tex]\frac{1}{y}[/tex] leaves.

Therefore, to know the portion of leaves they can rake in one minute working together, we need to sum up both of the portions each one of them rake in one minute, this gives us: [tex]\frac{1}{x}+ \frac{1}{y}[/tex]

Now, to simplify this expression:

[tex]\frac{1}{x}+ \frac{1}{y} =\frac{y+x}{xy}[/tex]

Thus, in one minute they rake [tex]\frac{y+x}{xy}[/tex] leaves.

Answer:

2) 30, 70, 80

Step-by-step explanation:

Well there has to be 3 angles that all add up to 180°.

1)

100+130+130

=360

2)

30+70+80

= 180

3)

25+3+35

=63

4)

45 + 105 + 120

=150

150+120

270

Answer:

96

Step-by-step explanation:

We simply need to plug in a = 4 so 6a² = 6 * 4² = 6 * 16 = 96.

Answer:

First option is the correct option.

Step-by-step explanation:

[tex] \frac{2x + 5}{ {x}^{2} - 3x } - \frac{3x + 5}{ {x}^{3} - 9x } - \frac{x + 1}{ {x}^{2} - 9 } [/tex]

Factor out X from the expression

[tex] \frac{2x + 5}{x(x - 3)} - \frac{3x + 5}{x( {x}^{2} - 9)} - \frac{x + 1}{ {x}^{2} - 9} [/tex]

Using [tex] {a}^{2} - {b}^{2} = (a - b)(a + b)[/tex] , factor the expression

[tex] \frac{2x + 5}{x(x - 3)} - \frac{3x + 5}{x(x - 3)(x + 3) } - \frac{x + 1}{(x - 3)(x + 3)} [/tex]

Write all numerators above the Least Common Denominators x ( x - 3 ) ( x + 3 )

[tex] \frac{(x + 3) \times (2x - 5) - (3x + 5) - x \times (x + 1)}{x(x - 3)(x + 3)} [/tex]

Multiply the parentheses

[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - (3x + 5) - x(x + 1)}{x(x - 3)(x + 3)} [/tex]

When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression

[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - 3x - 5 - x \times (x + 1)}{x(x - 3)(x + 3)} [/tex]

Distribute -x through the parentheses

[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - 3x - 5 - {x}^{2} - x }{x(x - 3)(x + 3)} [/tex]

Using [tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex] , simplify the product

[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - 3x - 5 - {x}^{2} - x}{x( {x}^{2} - 9)} [/tex]

Collect like terms

[tex] \frac{ {x}^{2} + 7x + 15 - 5}{x( {x}^{2} - 9)} [/tex]

Subtract the numbers

[tex] \frac{ {x}^{2} + 7x + 10}{ x({x}^{2} - 9)} [/tex]

Distribute x through the parentheses

[tex] \frac{ {x}^{2} + 7x + 10}{ {x}^{3} - 9x} [/tex]

Write 7x as a sum

[tex] \frac{ {x}^{2} + 5x +2x + 10 }{ {x}^{3} - 9x } [/tex]

Factor out X from the expression

[tex] \frac{x(x + 5) + 2x + 10}{ {x}^{3} - 9x} [/tex]

Factor out 2 from the expression

[tex] \frac{x( x + 5) + 2(x + 5)}{ {x}^{3} - 9x } [/tex]

Factor out x + 5 from the expression

[tex] \frac{(x + 5)(x + 2)}{ {x}^{3} - 9x } [/tex]

Hope this helps...

Best regards!!

The difference of the expression [tex]\frac{2x + 5}{x^2 -3x} - \frac{3x + 5}{x^3 - 9x} - \frac{x + 1}{x^2 - 9}[/tex] is [tex]\frac{(x+5)(x+ 2) }{x^3- 9x}[/tex]

The expression is given as:

[tex]\frac{2x + 5}{x^2 -3x} - \frac{3x + 5}{x^3 - 9x} - \frac{x + 1}{x^2 - 9}[/tex]

Factorize the denominators

[tex]\frac{2x + 5}{x(x -3)} - \frac{3x + 5}{x(x^2 - 9)} - \frac{x + 1}{x^2 - 9}[/tex]

Apply the difference of two squares to the denominators

[tex]\frac{2x + 5}{x(x -3)} - \frac{3x + 5}{x(x - 3)(x + 3)} - \frac{x + 1}{(x - 3)(x + 3)}[/tex]

Take LCM

[tex]\frac{(2x + 5)(x + 3) - 3x - 5 -x(x + 1) }{x(x - 3)(x + 3)}[/tex]

Expand the numerator

[tex]\frac{2x^2 +6x + 5x + 15 - 3x - 5 -x^2 - x }{x(x - 3)(x + 3)}[/tex]

Collect like terms

[tex]\frac{2x^2 -x^2 - x +6x + 5x - 3x+ 15 - 5 }{x(x - 3)(x + 3)}[/tex]

Simplify

[tex]\frac{x^2+7x+ 10 }{x(x - 3)(x + 3)}[/tex]

Factorize the numerator

[tex]\frac{(x+5)(x+ 2) }{x(x - 3)(x + 3)}[/tex]

Expand the denominator

[tex]\frac{(x+5)(x+ 2) }{x^3- 9x}[/tex]

Hence, the difference of the expression [tex]\frac{2x + 5}{x^2 -3x} - \frac{3x + 5}{x^3 - 9x} - \frac{x + 1}{x^2 - 9}[/tex] is [tex]\frac{(x+5)(x+ 2) }{x^3- 9x}[/tex]

Read more about equivalent expressions at:

https://brainly.com/question/2972832

Answer:

Step-by-step explanation:

Let the points be A and B

A ( - 2 , 3 ) -------> ( x1 , x2 )

B ( -4 , -9 ) -------> ( x2 , y2 )

Now, finding the slope:

[tex]slope \: (m) = \frac{y2 - y1}{x2 - x1} [/tex]

Plug the values

[tex] = \frac{ - 9 - 3}{ - 4 - ( - 2)} [/tex]

Calculate

[tex] = \frac{ - 12}{ - 4 - ( - 2)} [/tex]

When there is a (-) in front of an expression in parentheses , change the sign of each term in expression

[tex] = \frac{ - 12}{ - 4 + 2} [/tex]

Calculate

[tex] = \frac{ - 12}{ - 2} [/tex]

Reduce the fraction with -2

[tex] = 6[/tex]

Hope this helps..

Best regards!!

Answer:

18m square

Step-by-step explanation:

Formula for rectangular- based pyramid is L x W x H divided by 3

= 3 x 5 x 3.6 divided by 3 = 18

So you would need 18 m square for the sculpture

Answer:

-2

Step-by-step explanation:

Hello,

First of all, let's check the denominator.

[tex]x^2-x-6 \ \ \text{ *** How to factorise it ...? ***}\\\\\text{*** The product of the roots is -6=-2*3 and their sum is 1 ***}\\\\x^2-x-6=x^2-3x+2x-6=x(x-3)+2(x-3)=(x+2)(x-3)[/tex]

Now, let's see the numerator.

[tex]x^2+8x+4 \ \text{ *** -2 is not a zero as ***}\\\\(-2)^2+8*(-2)+4=4-16+8=-4\\\\\text{*** 3 is not a zero as ***}\\\\3^2+8*3+4=9+24+4=37\\[/tex]

So we cannot factorise the numerator with (x+2) or (x-3)

Then, -2 and 3 are the the discontinuities of the expression.

There is only -2 in the list, this is the correct answer.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Step-by-step explanation:

5 * 45 = 225

225+75=300

300/500=0.6

The tank will be 60% full.

If this helped, make sure to mark it as brainliest :D

Answer:

C.60%

Step-by-step explanation:

45 x 5 = 225  225 + 75 = 300

300 / 500 = 0.6 = 60%

Answer:

7 3/8 + (-4 1/2) ÷ (-5 2/3) = 8 23/136

Step-by-step explanation:

1) First I turned all the mix numbers into improper fractions:

7 3/8 ----> ( 7(8)+3/8) = 59/8, 4 1/2 ----> (4(2)+1/2) = 9/2, 5 2/3 ---->  (5(3)+2/3) = 17/3

So now it should look like this: 59/8 + (-9/2)÷(-17/3)

2) Now our goal is to divide both of the improper fractions (-9/2)÷(-17/3),

- We first apply our fraction rule:  -a/-b = a/b (when we have two negatives they cancel out each other and make a positive)

Our Case, From this:-9/2 ÷ -17/3 = To This: 9/2 ÷ 17/3

3) Now we can divide the fractions using this rule: a/b ÷ c/d = a times d / b times

Our Case, From This: 9/2 ÷ 17/3 To This: 9(3)/2(17) Which Gives Us: 27/34

(9 x 3 = 27, 2 x 17= 34)

So now it looks like this: 59/8 +27/34

4) Our look goal is to have the same denominator (which is the bottom part of the fraction)  which are 8 and 34

To find it we find the LCM or Least Common Multiple of 8 and 34

(The LCM of a, b is the smallest positive number that is divisible by both a and b) which in this case a and b are 8 and 34  

LCM is 136

5) We adjust our two fractions based on the LCM,

(Multiply each numerator ( top part of the fraction)  by the same amount of needed to multiply its corresponding denominator to turn it to the LCM 136.

From This: 59/8  and 27/34 To This: 1003/136 and 108/36 ( 59(17)/8 (17) = 1003/136, 27(4)/34(4) = 108/306

6) Finally we can add the numerator (1003 and 108) together: 1003+108= 1111 and now we are left with 1111/136

Then we turn our improper fraction back into a mix number: 1111/138= 8 23/136

Answer:

[tex]\frac{1111}{136} = 8 \frac{23}{136}[/tex]

Step-by-step explanation:

We want to simplify:

[tex]7 \frac{3}{8} + \frac{ -4 \frac{1}{2} }{ -5 \frac{2}{3} }[/tex]

First, convert all the fractions to improper fractions:

[tex]\frac{59}{8} + \frac{ - \frac{9}{2} }{ - \frac{17}{3} } \\\\= \frac{59}{8} + \frac{27}{34}[/tex]

Find the LCM of the denominators:

[tex]\frac{(17 * 59) + (4 * 27)}{136} \\\\ = \frac{1003 + 108}{136}\\ \\= \frac{1111}{136} \\\\= 8 \frac{23}{136}[/tex]

Answer:

150

Step-by-step explanation:

Answer:

150  =  half of 300

± 180

230

soooo 230 students

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Given

y = x² + 1

y = x

Equating gives

x² + 1 = x ( subtract x from both sides )

x² - x + 1 = 0

Consider the discriminant Δ = b² - 4ac

with a = 1, b = - 1 and c = 1

b² - 4ac = (- 1)² - (4 × 1 × 1) = 1 - 4 = - 3

Since b² - 4ac < 0 then there are no real solutions

The equation of line which is perpendicular to the line FG is

y = -2x -3.

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

[tex](y -y_{1}) = \frac{y_{2}-y_{1} }{x_{2} -x_{1} } (x-x_{1} )[/tex]

If [tex]m_{1}[/tex] be the slope of one line, then the slope of the perpendicular line is [tex]\frac{-1}{m_{1} }[/tex].

The slope intercept form of the line is given by  y = mx + b

Where, m is the slope of a line.

According to the given question

We have a line FG and the coordinates of points F and G are (-5,1) and (9,8) respectively.

Therefore, the slope of the line FG = [tex]\frac{8-1}{9+5}=\frac{7}{14} =\frac{1}{2}[/tex]

⇒ The slope of the line which is parallel to line FG is -2

Now, from the given option of the equation of line , y = -2x -3 has a slope of -2 .

Hence, the equation of line which is perpendicular to the line FG is

y = -2x -3.

Learn more about the equation of a perpendicular line here:

https://brainly.com/question/20712656

#SPJ2

======================================================

Work Shown:

A = area of trapezoid RSTU

A = height*(base1+base2)/2

A = ST*(UT+RS)/2

A = 14*(5+10)/2

A = 105 square cm

-----------------------

B = area of rectangle PQWV

B = length*width

B = WV*PV

B = 7*2.5

B = 17.5 square cm

If you're curious how I got PV = 2.5, you basically cut PT = 10 in half twice. So you go from 10 to 5, then from 5 to 2.5; which works because we have a bunch of midpoints.

-----------------------

C = total shaded area

C = A + B

C = 105 + 17.5

C = 122.5

Answer:

(E) including reminders to watch the endorsement, compare signatures, and view

Step-by-step explanation:

The principle features that will help the company to confirms checks authenticity. It include endorsements and compare the signatures with the designated signatories. If the signatures are matched correctly with the assigned signatories the check is hold in light to view the watermark on it.

Answer:

a) Because the confidence interval  does not include  0​ it appears that there

is  a significant difference between the mean level of hemoglobin in women and the mean level of hemoglobin in men.

b)There is​ 95% confidence that the interval from  −1.76 g/dL<μ1−μ2<−1.62 g/dL actually contains the value of the difference between the two population means μ1−μ2

c)   1.62 < μ1−μ2< 1.76

Step-by-step explanation:

a) What does the confidence interval suggest about equality of the mean hemoglobin level in women and the mean hemoglobin level in​ men?

Given:

95% confidence interval for the difference between the two population​ means:

−1.76g/dL< μ1−μ2 < −1.62g/dL

population 1 =  measures from women

population 2 =  measures from men

Solution:

a)

The given confidence interval has upper and lower bound of 1-62 and -1.76. This confidence interval does not contain 0. This shows that the population means difference is not likely to be 0. Thus the confidence interval implies that the mean hemoglobin level in women and the mean hemoglobin level in​ men is not equal and that the  women are likely to have less hemoglobin than men. This depicts that there is significant difference between mean hemoglobin level in women and the mean hemoglobin level in​ men.

b)  

There is​ 95% confidence that the interval −1.76 g/dL<μ1−μ2<−1.62 g/dL actually contains the value of the difference between the two population means μ1−μ2.

c)

If we interchange men and women then

                                          1.62 g/dL<μ1−μ2<1.76 g/dL.

There is a significant difference between the mean level of hemoglobin in women and in men.

The confidence interval of the mean is given as:

[tex]-1.76 g/dL < \mu_1-\mu_2 < -1.62 g/dL[/tex]

The above confidence interval shows that the confidence interval is exclusive of 0.

This means that 0 is not part of the confidence interval

Since the confidence interval is exclusive of 0, then there is a significant difference between the mean level of hemoglobin in women and in men.

Read more about confidence intervals at:

https://brainly.com/question/17097944

Answer:

The triangle inequality states that the sum of the lengths of the two shortest sides of a triangle must be greater than the length of the largest side. Because 4 + 12 > 17 is not a true statement, the answer is "This triangle does not exist because the sum of 4 and 12 is less than 17."

Answer:

This triangle does not exist due to the fact that the sum of 4 and 12 is less than 17

Step-by-step explanation:

The triangle formaction rule states that the 2 smaller sides must be able to combine and be greater than the greatest side.

Triangle

Sides - 3, 4, 5

3+4=7

Meaning the two smaller sides add up to because greater than 5.

Non-Triangle

Sides - 5, 6, 13

5+6=11

This means that this is not a triangle because the smaller sides ‘5 and 6’ do not add up to become greater than 13.

Gemma’s Triangle

Sides - 4, 12, 17

4+12=16

Hence, Gemma‘s figure is not a triangle because the 2 smaller sides ‘4 and 12’ don‘t add up to be greater than 17.

Answer:

a) Median: 9

b) Range: 5

c) Mode: 7

Step-by-step explanation:

The median is the number in the middle.

First, you put the numbers in order: 7, 7, 7, 8, 10, 11, 12, 12

The middle of this is 8 and 10, so you plus them and divide by to 2, then it gives 9, so the median is 9.

To find the range, you minus the highest number and the lowest number, 12-7=5.

Mode is the most occurring and repetitive number, in this case, 7, because it is written 3 times.

Hope this helps!!!

Answer:

[tex]\boxed{\mathrm {Median = 9}}[/tex]

[tex]\boxed{\mathrm{Range = 5}}[/tex]

[tex]\boxed{\mathrm{Mode = 7}}[/tex]

Step-by-step explanation:

The observations are:

8,7,12,7,11,10,7,12

In ascending order:

=> 7,7,7,8,10,11,12,12

A) Median => Middlemost no.

Median = 8,10

=> [tex]\frac{8+10}{2}[/tex]

=> [tex]\frac{18}{2}[/tex]

Median = 9

B) Range = Highest No. = Lowest No.

RANGE = 12-7

Range = 5

C) Mode => frequently occurring number

Mode = 7

Answer: C) P(y) = 150(y – 15) – 125y

Step-by-step explanation:

Hi, to answer this question we have to write an equation:

Profit = revenue - cost

Cost: a watch store paid $125 per watch for a shipment of watches

Cost = 125 y

Where y is the number of watches in the shipment

Revenue: sold all but 15 watches from the shipment for $150 per watch

Revenue = 150(y-15)

Profit(y) = 150(y – 15) – 125y

So, the correct option is:

C) P(y) = 150(y – 15) – 125y

Feel free to ask for more if needed or if you did not understand something.

Answer: x=one-half y minus

Step-by-step explanation:

Answer:

x=1/2 y-3

Step-by-step explanation:

Hi,

Answer:

[tex]Angle=\frac{pi}{4}[/tex] = π/4 = 45°

Have a good day.

Answer:

18

Step-by-step explanation:

Each interior angle of a regular pentagon is 108 degrees. So Angle AED is 108 degrees. Since Angle AEF is a straight line (180 degrees), Angle FED is 72. This is because 180-108 = 72. Now, since a triangle has a total of 180 degrees, we add 72 and 90, because those are the 2 degrees we have calculated. This gives us a total of 162. Now, we subtract 162 from 180 to find out the degree of Angle FDE. This is 18. So our final answer is 18.

Sidenote: I hope this answer helps!

The properties of a pentagon and the given right triangle formed by

segments EF and FD give the measure of ∠FDE.

Response:

The given parameters are;

A, E, F are points on the same line.

ABCDE is a regular pentagon

∠EFD = 90°

Required:

The measure of ∠FDE

Solution:

The points A and E are adjacent points in the pentagon, ABCDE

Therefore;

line AEF is an extension of line side AE to F

Which gives;

∠EFD = 90°, therefore, ΔEFD is a right triangle, from which we have;

The sum of the acute angles of a right triangle = 90°

Therefore;

∠DEF + ∠FDE = 90°

Which gives;

72° + ∠FDE = 90°

∠FDE = 90° - 72° = 18°

Learn more about the properties of a pentagon here:

https://brainly.com/question/15392368

Answer:

25

Step-by-step explanation:

a=15

2(15)-5=25

30-5=25

Answer:

25

Step-by-step explanation:

The problem substituting a for 15 would be 2(15)-5

2*15 is 30, then -5 is 25.