triangle ABC is similar to triangle JKL
solve for a

Answer:

35

Step-by-step explanation:

By the triangle midsegment theorem, 2(WY)=VZ.

So, 2(p-21)=p-7, meaning p=35.

Answer:

The probability of getting exactly iblue is [tex]\frac{5}{9}[/tex]

Step-by-step explanation:

[tex]from\ the\ given\ condition.[/tex]

[tex]We\ only\ have\ two\ way.[/tex]

[tex]One\ way\ is\ the\ first\ one\ take\ the\ blue.[/tex]

[tex]one\ but\ the\ second\ one\ take\ red.\ one.[/tex]

[tex]Another\ way\ is\ the\ first\ one\ take\ the\ red.[/tex]

[tex]one\ but\ the\ second\ one\ take\ the\ blue.[/tex]

[tex]one.[/tex]

[tex]so.\ P_1=\frac{4}{9}\times\frac{5}{8}=\frac{5}{18}[/tex]

[tex]P_2=\frac{5}{9}\times\frac{4}{8}=\frac{5}{18}[/tex]

[tex]so.\ we\ have\ p=p_1+p_2=\frac{5}{18}+\frac{5}{16}=\frac{5}{9}[/tex]

I hope this helps you

:)

Answer:

  702 ft²

Step-by-step explanation:

The total surface area of the prism is the sum of the areas of its 7 faces.

lateral area

The width of each rectangular face is 8 ft. The total length of all of the rectangular faces is equal to the perimeter of the base:

  7 ft +5 ft +3 ft +5 ft + 2 ft = 22 ft

So, the rectangular area is ...

  A = LW = (8 ft)(22 ft) = 176 ft²

__

base area

The area of each base is equivalent to the area of a 5 ft×7 ft rectangle with a 3 ft×4 ft right triangle cut off one corner. The base area will be ...

  A = LW -1/2bh

  A = (5 ft)(7 ft) - 1/2(3 ft)(4 ft) = 29 ft²

__

area of one

So the total surface area of one structure is ...

  lateral area + 2×(area of one base)

  = 176 ft² +2(29 ft²) = 234 ft²

__

If 3 pieces are needed, the total amount of sheet metal needed for their construction is ...

  (234 ft²) × 3 = 702 ft² . . . . needed to build all 3 pieces

Answer:

the answer is 702 I took the test

Answer:

There are two possible answers to this question. if the demoninator has the three on the outside of the square root your answer is 2/3. If your demoninator has the three inside the square root your answer is [tex]\frac{2\sqrt{3} }{3}[/tex] or 1.15. Let me know if this helps!

Answer:

z>7

Step-by-step explanation:

subtract z from both sides, then subtract 8 from both sides. The, divide both by the -5 (and remember to flip the sign since you divided by a negative number).

Answer: 5 more times.

Step-by-step explanation: In total, it takes her 4 minutes to climb to the top of the water slide and slide down.  Because the water slide closes in 20 minutes, she can slide down more 5 times.  5 x 4 equals 20.

Have a great day! :)

Answer:

C,F

Step-by-step explanation:

If f(x) = -4x - 5 and g(x) = 3 - X,the value g(-4) + f(1) is equal to -2.

The function f(x)  is  f(x)=-4x-5

The function  g(x) is g(x)=3-x

g(-4)=3-(-4)=3+4=7

f(1)=-4(1)-5=-9

g(-4)+f(1)=7+(-9)=7-9=-2

What is the composition of functions?

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1 kg = 2.2 pounds ( rounded to the nearest tenth)

500 kg x 2.2 = 1,100 pounds

1100 pounds is less than 2,500 so the forklift can lift it.

Answer:

2,500= 1133.981

Step-by-step

The answer is 1133.981 bc you would have to use the conversion rate of lb to kg, so just 2500 lb × 0.45359237

= 1133.980925 kg

0.45359237  this is the conversion rate therefore 1134 is the answer (was rounded)

Answer:

C

Step-by-step explanation:

I usually solve these problems by process of elimination, but you can solve these differently!

A. y=1/2x. This would basically mean to divide x by 2 to get y. We can see 2/2=1, 4/2=2, 6/2=3, and 8/2=4. This does not match up with the table, where the numbers are 1, 5, 9, and 13. 1, 5, 9, and 13 are not equal to 1, 2, 3, and 4. So A is not our answer.

B. y=x-1. This would mean to subtract 1 from x to get y. 2-1=1, 4-1=3, 6-1=5, and 8-1=7. This does not match up with the table. 1, 3, 5, and 7 is not equal to 1, 5, 9, and 13.

C. y=2x-3. This would mean we would multiply 2 by x and subtract 3 to get y. 2*2-3=1, 2*4-3=5, 2*6-3=9, and 2*8-3=13. 1, 5, 9, and 13 are equal to 1, 5, 9, and 13, so this will be our answer.

D. y=3x-5. This would mean we would multiply 3 by x and subtract by 5. 3*2-5=1, 3*4-5=7, 3*6-5=13, and 3*8-5=21. This is not equal to 1, 5, 9, and 13.

Answer:    ∠B = 42°   ∠A = 23°  ∠F = 115°

Step-by-step explanation:

∠B≅∠C  alternate interior angles  42°

  ∠CDF is supplementary to ∠CDE,

so m∠CDF = 23°  and ∠FAB≅∠CDF so m∠FAB= 23°

also ∠A ≅ CDE  corresponding angles  157° ∠FAB is suplementary to ∠A

so 180 - 157 = 23 gives the m∠FAB

The sum of the angles of a triangle is 180°, so m∠AFB = 180 -(23 +42)

180- 65 = 115 = m∠F

Step-by-step explanation:

A

Because the multiplication of two integers still results in an integer.

Answer:  Required system:

x+y+z=30

x+2y+3z = 46    

x= 2y+2z      

Step-by-step explanation:

let x=  Number of pounds of bananas

y = Number of pounds of guavas

z = Number of pounds of dragon fruit

According to the question,

x+y+z=30     (i) (total fruits bought = 30 pounds)

Bananas cost $1 per pound; guavas cost $2 per pound; and dragon fruit costs $3 per pound and total cost = $46.

∴ x+2y+3z = 46         (ii)

Also, weight of the bananas= 2 (weight of the guavas+ weight of dragon fruit)

∴ x = 2(y+z)

⇒x= 2y+2z       (iii)

from (i), (ii) and (iii)

x+y+z=30

x+2y+3z = 46    

x= 2y+2z      

are the equations for the required system.

Answer:

B.{5}

Step-by-step explanation:

2-8x-42=0

(÷2), we get,

1-4x-21=0

-4x-20=0

-4x=20

x=20÷(-4)

x=(-5)

since the question asks for a positive set, the answer is [x=5]

The positive solution set is D. {7}.

A set is a well defined collection of objects written by commas and closed by second brackets.

According to the given question the equation 2x² - 8x - 42 = 0 have two factors and we have write the positive factor in form of a set.

2x² - 8x - 42 = 0

x² - 4x - 21 = 0

x² -7x + 3x - 21 = 0

x(x-7) + 3(x - 7) = 0

(X+3) = 0 OR (x-7) = 0

x = -3 OR x = 7.

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Answer:

9/20

Step-by-step explanation:

LCM of 5, 20, and 10 = 20

4/5

= 4/5 x 4/4

= ( 4 x 4 )/( 5 x 4 )

= 16/20

2/10

= ( 2/10 ) x ( 2/2 )

= ( 2 x 2 )/( 10 x 2 )

= 4/20

4/5 - 3/20 - 2/10

= 16/20 - 3/20 - 4/20

= ( 16 - 3 - 4 )/20

= ( 16 - 7 )/20

= 9/20

Answer:

9/20

Step-by-step explanation:

First, you need to find common denominators between all of the fractions.

All of these denominators can be multiplied by a whole number to equal 20.

For 4/5, multiply both the numerator and the denominator by 4 to get 16/20

Leave 3/20 alone

For 2/10, multiply both the numerator and the denominator by 2 to get 4/20

Now you have 16/20 - 3/20 - 4/20

= 9/20

x = 4

Step-by-step explanation:

21x + 6 = 90°

21x = 90 - 6

21x = 84

x = 84/21

x = 4

Answer: 9 units

Step-by-step explanation:

Answer:

7+1-8+2(2)+4(1)

= -1+4+4

=7

Answer:

8

Step-by-step explanation:

Given:

g = 1, h = 2

7 + g − 8 + 2h + 4g

Solve:

Since g = 1 and h =2

Substitute

7+(1)-8+2(2)+4(1)

= 7+(1)-8+4+4(1)

= 7 + (1)-8+4+4

=  8 -8 + 4 + 4

= 4 + 4

=8

Hence, Answer = 8

~lenvy~

Answer:

you put the -3 where the x's are

Step-by-step explanation:

f(x)= -2(-3)^2 - 3(-3) + 6

i think i hope thats right

Answer:

Plug in -3 into all the x's are

Step-by-step explanation:

f(x)= -2(-3)²-3(-3)+6

Answer:

x = 7

Step-by-step explanation:

7x + 5 - x + 6 = 53 , that is

6x + 11 = 53 ( subtract 11 from both sides )

6x = 42 ( divide both sides by 6 )

x = 7

Answer:

its c (4,1)

Step-by-step explanation:

The required point for the given line is (0, -3). The correct option is (D).

A linear equation in two variable has the general form as y = ax + by + c, where a, b and c are integers and a, b ≠ 0.

It can be represented as a straight line on a graph.

The equation of the given line is y = 2x - 3.

In order to find the point lying on it, consider each of the options one by one as follows,

(a) (2 , 3)

Substitute x = 2 and y = 3 in the given equation to obtain LHS and RHS as,

LHS = y

       = 7

RHS = 2x - 3

       = 2 × 2 - 3

       = 1

Since, LHS ≠ RHS, the given point is not the solution.

(b) (-2, -1)

Substitute x = 2 and y = 3 in the given equation to obtain LHS and RHS as,

LHS = y

       = 7

RHS = 2x - 3

       = 2 × -1 - 3

       = -6

Since, LHS ≠ RHS, the given point is not the solution.

(c) (4, 1)

Substitute x = 2 and y = 3 in the given equation to obtain LHS and RHS as,

LHS = y

       = 4

RHS = 2x - 3

       = 2 × 1 - 3

       = -1

Since, LHS ≠ RHS, the given point is not the solution.

(d) (0, -3)

Substitute x = 2 and y = 3 in the given equation to obtain LHS and RHS as,

LHS = y

       = -3

RHS = 2x - 3

       = 2 × 0 - 3

       = -3

Since, LHS = RHS, the given point is the solution.

Hence, the point (0, -3) is the solution of the given equation.

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Answer:

I believe you already selected the correct answer in the picture

Answer:   [tex]\frac{-m^2+n^2}{2}[/tex]

If the font is too small, it says (-m^2+n^2)/2

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

Explanation:

If you plug x = 0 into the original expression, then you'll get the indeterminant form 0/0 after simplifying.

Recall that cos(0) = 1

So we use L'Hospitals rule to derive the numerator and denominator separately (don't use the quotient rule)

[tex]\displaystyle \lim_{x\to0} \frac{\cos(mx)-\cos(nx)}{x^2}\\\\\\\displaystyle \lim_{x\to0} \frac{-m\sin(mx)+n\sin(nx)}{2x}\\\\\\[/tex]

Plug x = 0 into this new expression. You should get 0/0 again here as well, which means you'll have to do another round of L'Hospital

[tex]\displaystyle \lim_{x\to0} \frac{-m^2\cos(mx)+n^2\cos(nx)}{2}\\\\\\[/tex]

Now plugging in x = 0 leads to something that isn't indeterminant

Evaluating the limit gets us

[tex]\displaystyle \lim_{x\to0} \frac{-m^2\cos(mx)+n^2\cos(nx)}{2}\\\\\\=\frac{-m^2\cos(m*0)+n^2\cos(n*0)}{2}\\\\\\= \frac{-m^2+n^2}{2}\\\\\\[/tex]

Answer:

I believe there are 21 ducks and 14 pigs in the field

Step-by-step explanation

x+y=35

2x+4y=98

2x+2y=70

2x+4y=98

-2y=-28

y=14

x+14=35

x=35-14

x=21

21=ducks

14=pigs

Answer:

D. 20 in

Step-by-step explanation:

(−3.7x)(5.1y)

= −18.87xy

Answer: For the first one wouldnt it be like:

ht=10(r)+5

Step-by-step explanation:

Answer:

3(x-2)

Step-by-step explanation:

Factor 2x(2)−x−6

=> 3x−6

=>3(x−2)

Answer:

=> 3(x−2)