Find the area of trapezoid $DUCK$ shown below. [asy] unitsize(2mm); defaultpen(linewidth(.7pt)+fontsize(10pt)); pair D=(0,0), U=(5,12), C=(20,12), K=(36,0), F=(5,0); draw(D--U--C--K--cycle); draw(U--F,linetype("8 4")); draw(rightanglemark(U,F,K,25)); label("$D$",D,SW); label("$U$",U,N); label("$C$",C,NE); label("$K$",K,SE); label("5",midpoint(D--F),S); label("13",midpoint(D--U),NW); label("15",midpoint(U--C),N); label("20",midpoint(C--K),NE); [/asy]

Answer:

67/24

Step-by-step explanation:

Simplify the numerical expression.

2/3 divided by 2^4 + (3/4 + 1/6) divided by 1/3

2/3 ÷ 2⁴ +(3/4 + 1/6) ÷ 1/3

(2/3 ÷ 2⁴ ) +[(3/4 + 1/6) ÷ 3]

= (2/3 ÷ 16) + [9 + 2/12) ÷ 1/3]

=( 2/3 × 1/16 ) + [ 11/12 × 3]

= 1/24 + 11/4

= 67/24

Answer:

1

Step-by-step explanation:

12x+x+4=17

13x=17-4

13x=13

x=1

Answer:

Step-by-step explanation:

Distributive property:  a(b +c) = a*b + a*c

(2x + 1) - 7(-6x + 9) = (2x + 1) + (-7)*(-6x) + (-7)*9

                              = 2x + 1 + 42x - 63  {Combine like terms}

                              = 2x + 42x + 1 - 63

                              = 44x - 62

Answer:

b = 4.33 in

Step-by-step explanation:

angle A = 72°

hypotenuse = 14 in

Required: Adjacent side length (b)

use the formula Cos A = adjacent / hypotenuse

cos (72) = b / 14

b = cos (75) * 14

b = 4.33 in

Answer:

Add and subtract the second term to the expression and factor by grouping.

2

x

3

(

3

x

−

1

)

(

x

−

1

)

Step-by-step explanation:

Answer:

3x⁴+2x²+8

Step-by-step explanation:

[tex]6 {x}^{5} + 4 {x}^{3} + 8x[/tex]

[tex] = 2x(3 {x}^{4} + 2 {x}^{2} + 8)[/tex]

Answer:

d

Step-by-step explanation:

Answer:

THERE R 3 FACTORS SO D

Step-by-step explanation:

HOPE I HELPED

PLS MARK BRAINLIEST  

DESPERATELY TRYING TO LEVEL UP

✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                     PEACE!

Answer:

W is the point of intersection of the lines 'a' and 'b'.

Step-by-step explanation:

Three points lying on line 'b' are points Y, Z and W.

Similarly, three points on line 'a' are points V, X and W.

Common point lying on both the lines 'a' and 'b' is W.

Therefore, point of intersection of the lines 'a' and 'b' is W.

Answer:

The correct option are;

Every segment has one perpendicular bisector

Every segment has infinitely many congruent segments

Step-by-step explanation:

1) Every segment in a plane has exactly one perpendicular bisector

2) A congruent segment is a segment of equal length as a given segment, given that there can be infinitely many planes that can contain collinear points, whereby two points define a segment, the number of congruent segments that can be formed on infinitely many planes will therefore, be infinite.

Also given that the number of possible segments is infinite, the number of segments of a given size and therefore, the number of possible congruent segments is infinite.

Answer:

a

Step-by-step explanation:

d - 24 = 212

d +24 = 212 + 24

d= 236

Answer:

49

Step-by-step explanation:

To find the number we add to both sides to complete the square, we do b divided by 2 all squared.

(b/2)²

In this case, we have b = 14

(14/2)²

7²

49

Answer:   49  

Step-by-step explanation:

To complete the square, the second leading coefficient  divided by 2 squared will give you the number need to add to both sides.

For example,

14 is the second leading coefficient in the   so if you divide it by 2 you get 7  and 7 squared is 49.

Answer: 15.07%

Step-by-step explanation:

Given: Gross Pay: $56

State Tax Withholding: $1.60

Social Security Tax: $2.35

Federal Tax Withholding: $3.68

Medicare Tax: $.81 .00

Total tax = (State Tax Withholding + Social Security Tax + Federal Tax Withholding + Medicare Tax)

= $(1.60+ 2.35+3.68+0.81)

= $8.44

So, the percent of Mia's gross pay goes for taxes = (Total tax ) ÷ (Gross (pay) × 100

=(8.44 )÷ (56) × 100

= 15.07%

Hence, the percent of Mia's gross pay goes for taxes is 15.07%.

Answer:

k > 8

Step-by-step explanation:

Step 1: We know in order for a quadratic equation to have 2 distinct solutions the discriminant has to be positive

Important formula: Discriminant = [tex]b^{2}-4ac[/tex]

Step 2: Input information into discriminant

[tex]b^{2}-4ac[/tex] > 0

[tex]k^{2}-4(2)(8)[/tex] > 0

[tex]k^{2}-64[/tex] > 0

[tex]k^{2}[/tex] > 64

[tex]\sqrt{ k^{2}}>\sqrt{64}[/tex]

k > 8

Therefore in order for the equation to have 2 distinct solutions is to have k > 8

(b²-4ac) > 0

where Z is an integer

(-k)²-4(2)(8) > 0

k²-64 > 0

k²>64

k>8

Therefore the sum of all values of k is infinite

Answer:

This problem actually says:

(y + 2), (y + 3) and (2*y^2 - 1) are consecutive terms of an arithmetic progression.

Now, the difference between two consecutive terms in an arithmetic progression is always the same, so we have:

(y + 3) - (y +2) = D

(2*y^2 - 1) - (y + 3) = D

From the first equation we have:

y + 3 - y - 2 = 1  = D

Now we can replace it in the other equation:

2*y^2 - 1 - y - 3 = 1

2*y^2 - y - 5 = 0

Now we need to solve that equation to find the possible values of y.

To solve a quadratic equation of the form:

a*x^2 + b*x + c = 0, we can use the Bhaskara's equation:

[tex]y = \frac{-b +- \sqrt{b^2 -4*a*c} }{2*a}[/tex]

in this case, the solutions are:

[tex]y = \frac{1 +-\sqrt[]{(-1)^2 - 4*2*(-5)} }{2*2} = \frac{1 +- \sqrt{61} }{4} = \frac{1+-6.4}{4}[/tex]

Then the possible values of y are:

y = (1 + 6.4)/4 = 1.85

y = (1 - 6.4)/5 = -1.35

Answer:

the probability is 5/20 for picking one yellow

and the probability is 4/19 for picking green one right after

Answer:

a = 5

Step-by-step explanation:

Hello, please consider the following.

[tex]6x^3+18x^2-240x=6x(x^2+3x-40)\\\\\text{** The sum of the zeroes is -3=-8+5 and the product is -40=-8*5. **}\\\\\text{** So, we can factorise. **}\\\\6x^3+18x^2-240x=6x(x^2+3x-40)=6x(x^2+8x-5x-40)\\\\=6x(x(x+8)-5(x+8))\\\\\large \boxed{=6x(x+8)(x-5)}[/tex]

So, a = 5.

Thank you.

Answer:

Step-by-step explanation:

To solve equations like this you need to to get x by itself.

So, Let's multiply both sides by 5 to get rid of 5.

3x/5 *5 = 30 * 5

= 3x = 150

Now we divide both sides by 3 to get x by itself,

3x/3 = 150/3

x = 50

Answer:

Step-by-step explanation:

[tex]\frac{3x}{5}=30\\\\\mathrm{Multiply\:both\:sides\:by\:}5\\\\\frac{5\cdot \:3x}{5}=30\cdot \:5\\\\\mathrm{Simplify}\\\\3x=150\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\\\frac{3x}{3}=\frac{150}{3}\\\\x = 50[/tex]

Answer: ST is equal to 12

Step-by-step explanation:

If RU  is equal to 24 as a whole  and we are given that RS and TU are equal to 6 then we could set up an equation and solve for ST.

6 + 6 +x  = 24   where x is the length of ST

12 + x = 24  

-12         -12

x = 12    

Answer:

Step-by-step explanation:

1) (3 * 7)(8) =3 (7 * 8)

Associative property of multiplication

It states that product of three or more numbers remains same regardless the way they are grouped

2) (7k)5 = 5(7k)

Commutative property of multiplication

3) 8(x +15) = (8)(x) + (8)(15)

distributive property

The equivalent expression after combining the like terms is -3x - 7.

We have,

Expression:

-3x - 6 + (-1)

-6 and -1 are like terms.

To combine the like terms simply add them together:

-3x - 6 + (-1)

-3x - 7

-3x is the only term so it can be simplified further.

This is the simplest form of the expression.

Therefore,

The equivalent expression after combining the like terms is -3x - 7.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ4

Answer:

The correct equation for the scenario is C=k / f

Number of cars when fee=$6 is

C=k/6

Step-by-step explanation:

Let

C= number of cars

f=fee

Number of cars increases as fee decreases

This is an inverse variation

Therefore,

C= k / f

When,

f=$6

C= k / f

C=k/6

The correct equation for the scenario is C=k / f

Number of cars when fee=$6 is

C=k/6

Answer:

I got 50.7%, rounded up to be 51

Step-by-step explanation:

Add up all of Sohan's points and divide it by the total number of points and move the decimal over 2 places

Answer:

14.25

Step-by-step explanation:

14 25/100= 14*100+25/100=

1400+25/ 100

= 1425/100

= 14.25

Answer:

14.25

Step-by-step explanation:

the expression 14 25/100 can be written as 14+25/100

now converting 25 into decimal to cancel out the denominator we ll get 0.25

now adding 14 into 0.25

14+0.25

we get 14.25

Answer:

  see below

Step-by-step explanation:

A vertical stretch is accomplished by multiplying the function value by the stretch factor.

  g(x) = 2f(x)

  g(x) = 2(x +3)

Answer:

0.02

Step-by-step explanation:

7⁴ / 7⁶ = 7⁴⁻⁶ = 7⁻² = 1/7² = 1/49 ≈ 0.02

Answer:

.02

Step-by-step explanation:

7^4 ÷ 7^6

We know that a^b ÷ a^c = a^ ( b-c)

7^4 ÷ 7^6  

7^(4-6)

7^(-2)

We know that a^ -b = 1/a ^b

1 / 7^2

1/49

.020408163

Rounding to 2 decimal places

.02

Answer:

x=3

Step-by-step explanation:

5x + 4 = 19

     -4     -4

     5x = 15

      /5    /5

       x = 3

Given :

[tex]\begin{lgathered}\bullet\:\:\textsf{Perimeter of reactangle = \textbf{32 cm}}\\\bullet\:\:\textsf{Width = \textbf{7 cm}}\end{lgathered}[/tex]

[tex]\rule{130}1[/tex]

Solution :

[tex]:\implies\sf Perimeter\:of\: rectangle = 2 (Length + Breadth) \\\\\\:\implies\sf 32 = 2 (l + 7)\\\\\\:\implies\sf 32 = 2l + 14\\\\\\:\implies\sf 32 - 14 = 2l\\\\\\:\implies\sf 2l = 18\\\\\\:\implies\underline{\boxed{\sf Length = 9\:cm}} [/tex]

[tex]\rule{170}2[/tex]

[tex]\dashrightarrow\sf\:\:Area\:of\: rectangle = Length \times Breadth\\\\\\\dashrightarrow\sf\:\: Area\:of\: rectangle = 7\:cm \times 9\:cm\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf Area\:of\: rectangle = 63\:cm^2}}[/tex]

⠀

[tex]\therefore\:\underline{\textsf{The area of reactangle is \textbf{63}}\:\sf{cm^2}}.[/tex]

Answer:

Area of the rectangle is 63 cm².

Step-by-step explanation:

Given :-

To find :-

Solution :-

Consider,

width = 7 cm

Formula used :-

[tex]{\boxed{\sf{Perimeter of rectangle=2(Length+breadth)}}}[/tex]

According to the question ,

2(x+7) = 32

→ x+7 = 32/2

→ x +7 = 16

→ x = 16-7

→ x = 9

★ Length = 9 cm

Area of the rectangle ,

= length × Breadth

= 9 × 7 cm²

= 63 cm²

Therefore, the area of the rectangle is 63 cm².

Answer:

x=8

Step-by-step explanation:

x+12=20

Answer:

15i[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] and [tex]\sqrt{-1}[/tex] = i

Given

3[tex]\sqrt{-75}[/tex]

= 3 × [tex]\sqrt{25(3)(-1)}[/tex]

= 3 × [tex]\sqrt{25}[/tex] × [tex]\sqrt{3}[/tex] × [tex]\sqrt{-1}[/tex]

= 3 × 5 × [tex]\sqrt{3}[/tex] × i

= 15i[tex]\sqrt{3}[/tex]

Answer:

C

Step-by-step explanation:

2x + 3(x - 10) = 45

2x + 3x - 30 = 45

5x - 30 = 45

5x = 75

x = 15

Answer:

90

Step-by-step explanation:

Let x be Dany's score in geography. His score in chemistry is double his score in geography and it is equal to

2 x

The average of all four scores is 79. Hence

(93 + 88 + x + 2 x) / 4 = 79

Multiply both sides of the equation by 4

4×(93 + 88 + x + 2 x) / 4 = 4×79

Simplify

93 + 88 + x + 2 x = 316

Group like terms

3 x + 181 = 316

Solve for x

3 x = 135

3 x / 3 = 135 / 3

x = 45

score in geography = x = 45

score in chemistry = 2 x = 2 × 45 = 90

Hope it helped u if yes mark me BRAINLIEST!

Tysm!

Answer:

[tex]\huge\boxed{Chem = 90 \ marks , Geo = 45 \ marks}[/tex]

Step-by-step explanation:

Let the score of geography be x

=> Then, the score of chemistry will be 2x

So, the given condition is:

[tex]Average = \frac{Sum \ of \ values}{No. \ of \ values}[/tex]

=> [tex]79 = \frac{93+88+x+2x}{4}[/tex]

=> [tex]79 = \frac{181+3x}{4}[/tex]

Multiplying both sides by 4

=> [tex]79 * 4 = 181+3x[/tex]

=> 316 = 181 + 3x

Subtracting 181 to both sides

=> 316-181 = 3x

=> 135 = 3x

Dividing both sides by 3

=> 45 = x

OR

=> x = 45

So,

Chemistry = 45 * 2 = 90 marks

Geography = 45 marks