Which one is it.
You can choose more than one.​

Answer:

[tex]FJ=18\ units[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

△FEG is similar with △FHJ -----> by AA Similarity Theorem

so

[tex]\frac{FE}{FH}=\frac{FG}{FJ}[/tex]

we have

[tex]FE=HF+EH=12+8=20\ units[/tex]

[tex]FH=HF=12\ units[/tex]

[tex]FG=30\ units[/tex]

substitute the given values

[tex]\frac{20}{12}=\frac{30}{FJ}[/tex]

[tex]FJ=12(30)/20\\FJ=18\ units[/tex]

a. The solution set is (-3,2)

b. The solution set is (2,6)

c. The solution set is (1,1)

d. The solution set is (-0.5,1.5)

e. The solution set is (7.5, -4.5)

f. The solution set is (-2,7)

Step-by-step explanation:

a. x+2y=1   Eqn 1

   x=y-5      Eqn 2

Putting value of x from Eqn 2 in Eqn 1

[tex](y-5)+2y=1\\y-5+2y=1\\3y=1+5\\3y=6[/tex]

Dividing both sides by 3

[tex]\frac{3y}{3}=\frac{6}{3}\\y=2[/tex]

Putting y=2 in Eqn 2

[tex]x=2-5\\x=-3[/tex]

The solution set is (-3,2).

b. y-x=4    Eqn 1

   y=3x     Eqn 2

Putting value of y from Eqn 2 in Eqn 1

[tex]3x-x=4\\2x=4[/tex]

Dividing both sides by 2

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

Putting x=2 in Eqn 2

[tex]y=3(2)\\y=6[/tex]

The solution set is (2,6)

c. y = x     Eqn 1

  y = -x+2   Eqn 2

Putting value of y from Eqn 1 in Eqn 2

[tex]x=-x+2\\x+x=2\\2x=2[/tex]

Dividing both sides by 2

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

Putting x=1 in Eqn 1

[tex]y=1[/tex]

The solution set is (1,1)

d. y=5x+4    Eqn 1

   x+3y=4     Eqn 2

Putting value of y from Eqn 1 in Eqn 2

[tex]x+3(5x+4)=4\\x+15x+12=4\\16x=4-12\\16x=-8[/tex]

Dividing both sides by 16

[tex]\frac{16x}{16}=\frac{-8}{16}\\x=-0.5[/tex]

Putting x= -0.5 in Eqn 1

[tex]y=5(-0.5)+4\\y=-2.5+4\\y=1.5[/tex]

The solution set is (-0.5,1.5)

e. x-y=12   Eqn 1

   y = 3-x   Eqn 2

Putting value of y from Eqn 2 in Eqn 1

[tex]x-(3-x)=12\\x-3+x=12\\2x=12+3\\2x=15[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{15}{2}\\x=7.5[/tex]

Putting x=7.5 in Eqn 2

[tex]y=3-7.5\\y=-4.5[/tex]

The solution set is (7.5, -4.5)

f. 2x+y=3      Eqn 1

  x+y=5       Eqn 2

From Eqn 2;

y = 5-x

Putting in Eqn 1

[tex]2x+(5-x)=3\\2x+5-x=3\\x=3-5\\x=-2[/tex]

Putting x=-2 in Eqn 1

[tex]2(-2)+y=3\\-4+y=3\\y=3+4\\y=7[/tex]

The solution set is (-2,7).

Keywords: linear equation, substitution method

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Answer:

x=14

Step-by-step explanation:

2x-7<21

+7=0

2×<21+7=28

2×/2=0

2/28

=14

Answer:

91

Step-by-step explanation:

Trust me, it's an Aops question, and I got mastery on it, or blue if you want.

Answer:

The correct answer is C. 3 (-64 ÷ 8) + 25

Step-by-step explanation:

Let's solve the four expressions to find out the positive one, this way:

A. - 4 + (-5) (-6) ÷ (-3)

= -4 + 30 ÷ -3

= - 4 - 10 = - 14

B. 8 [10 ÷ (2) (-2)]

= 8 [10 ÷ -4]

= 8 * - 2.5 = -20

C. 3 ( -64 ÷ 8) + 25

= 3 ( -8) + 25

= - 24 + 25 = 1

D. -2 (-5) (-3) ÷ 10

= - 30 ÷ 10 = -3

As we can see, after solving the four expressions, the only with a positive result is C. 3 ( -64 ÷ 8) + 25

Answer: yes , it is possible

Step-by-step explanation:

Let the first number be x and the second number be y .Then , the sum of the two numbers will be x + y , and their difference will be x - y.

Combining the two , we have :

x + y = 1 ............................... equation 1

x - y = 8 ................................. equation 2

solving the system of linear equation by substitution method. From equation 1 , make x the subject of the formula ,

x = 1 - y ...................... equation 3

Substitute equation 3 into equation 2 ,

1 - y - y = 8

1 - 2y = 8

add 2y to both sides

1 = 8 + 2y

subtract 8 from both sides

1 - 8 = 2y

- 7 = 2y

divide through by 2

y = [tex]\frac{-7}{2}[/tex]

y = - 3.5

substitute y = -3.5 into equation 3 to find the value of x , we have

x = 1 - y

x = 1 - ( - 3.5 )

x = 1 + 3.5

x = 4.5

Let us check :

x + y will be

4.5 + (-3.5) = 1

Also ,

x - y will be

4.5 - (-3.5)

⇒ 4.5 + 3.5 = 8

Answer: w = 4[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Let the unknown number be w , then

the product of w and 3 = 3w

Nine less than the product of 3 and the number = 3w - 9

completing the equation , we have

3w - 9 = 4

add 9 to both sides

3w = 13

w = 13/3

w = 4[tex]\frac{1}{3}[/tex]

6x +2y

Solution:

Given expression is (6x + 4y) –2y.

To find the equivalent expression for the given expression.

⇒ (6x + 4y) –2y

⇒ 6x + 4y –2y

Combine like terms together.

⇒ 6x + (4y –2y)

⇒ 6x + 2y

6x +2y is equivalent to (6x + 4y) –2y.

Hence, the expression equivalent to (6x + 4y) –2y is 6x + 2y.

Step-by-step explanation:

1.

Kinetic energy =[tex]\frac{1}{2} mv^{2}[/tex]

Here m = 1500 kg and v = 14 meter / second

Kinetic energy = [tex]\frac{1}{2} mv^{2}[/tex]= [tex]\frac{1}{2}\times 1500 \times 14^{2}[/tex] joule =147000 joule

2.

Here m = 2 unit and v = 5 units

Kinetic energy =[tex]\frac{1}{2} mv^{2}[/tex] =[tex]\frac{1}{2}\times 2 \times 5^{2}[/tex] units =25 units

3.

Here m= 2 units and v = 5 units

Kinetic energy =[tex]\frac{1}{2} mv^{2}[/tex] =[tex]\frac{1}{2}\times 4 \times 5^{2}[/tex]=5 0 units

4.

Here m= 2 units and v= 10 units

Kinetic energy =[tex]\frac{1}{2} mv^{2}[/tex]=[tex]\frac{1}{2}\times 4 \times 10^{2}[/tex]units = 200 units

Julian is using the concept testing method of advertising which involves testing ad ideas before product development. It helps in determining consumer reactions and minimizing errors.

The method Julian is using is called the concept testing method in advertising. In concept testing, ad ideas and concepts are tested by companies before the actual development of the product. Concept tests are ways for advertisers to determine the reaction of consumers to a proposed product or service before it hits the market, thus minimizing errors and financial risks. For instance, in Julian's case, this would imply presenting his ad idea, which showcases a new mobile phone, to a selected group of people and then collecting their feedback. The feedback can then be used to refine the ad and the product itself, ensuring that the mobile phone meets the expectations and needs of the targeted consumers.

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Answer:

Option C. is the correct option.

Step-by-step explanation:

Clara found the product of (3 - 6y²) and (y² + 2) and she did it as below

(3 - 6y²)(y² + 2) = 3(y²) + (-6y²)×2 = 3y² - 12y² = -9y²

She did the step wrong as highlighted above. She did not use the distributive property correctly.

Now we will do it in a correct way.

(3 - 6y²)(y²+2) = 3(y² + 2) - 6y²(y² + 2)

= 3y^{2}+6-6y^{4}-12y^{2}=-6y^{4}-9y^{2}+6

Therefore Option C. is the correct answer.

Hope it helps:)

Answer:

D. No solution.

Step-by-step explanation:

2x - 3 = 2x - 5

2x - 2x - 3 = 2x - 2x - 5

-3 = -5   which is absurd so there is No Solution.

Answer:

D no solution

Step-by-step explanation:

2x-3= 2x-5  means  : -3=-5   ...false

Answer:

The correct option is first one.

Therefore,

[tex]4(-1) = (-1)(4)[/tex] .. illustrates the associative property of multiplication.

Step-by-step explanation:

Associative property:

The associative property states that you can add or multiply regardless of how the numbers are grouped.

For example A x B = B x A

Therefore,

[tex]4(-1) = (-1)(4)[/tex] .. illustrates the associative property of multiplication.

Answer:

Option (-2-1)(8)=-2(1-8) is correct

The expression (-2-1)(8)=-2(1-8) represents the associative property of multiplication .

Step-by-step explanation:

Given expression is (-2-1)(8)=-2(1-8)

Associative property of multiplication is given by

(a+b)c=a(b+c)

Comparing the equations (-2-1)(8)=-2(1-8) and (a+b)c=a(b+c)  we get that the given expression is in the form of (a+b)c=a(b+c)

Therefore the given equation represents the associative property of multiplication .

Therefore option (-2-1)(8)=-2(1-8) is correct

The expression (-2-1)(8)=-2(1-8) represents the associative property of multiplication .

Answer:

B. It was the document Jefferson referred to when writing the Declaration of Independence.

Step-by-step explanation:

Virginia's Declaration of Rights was drawn upon by Thomas Jefferson for the opening paragraphs of the Declaration of Independence. It was widely copied by the other colonies and became the basis of the Bill of Rights. Written by George Mason, it was adopted by the Virginia Constitutional Convention on June 12, 1776.

Hope  I helped answer the question:)

The Virginia Declaration of Rights influenced the Declaration of Independence through its content and circulation as a pamphlet.

The Virginia Declaration of Rights influenced the Declaration of Independence in several ways:

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Answer:

7/10

Step-by-step explanation:

4 1/2=9/2

3 4/5=19/5

9/2-19/5=45/10-38/10=7/10

Answer:

C

Step-by-step explanation:

Slope-intercept form is y=mx+b. Y is y, m is the slope, x is x, and b is the y-intercept. The first thing you do is figure out the slope. The equation is (y2-y1)/(x2-x1). Then take 2 points from the table and substitute them in. I'll use the bottom two points: (4-2)/(2-1). You should get 2 as your answer. Substitute this in for m. Take a point from the table and substitute y in for y, x in for x. I'll use the last point: 4=2(2)+b. If I simplify further, I get 4=4+b, which means b is 0, and we won't need to put it in the equation.

Figure out the answer using the process of elimination: we know that because b=0, the answer can't be A or B. The slope is positive 2, which means that the answer can't be D. So it has to be C.

Answer:

17

Step-by-step explanation:

The sum of all the angles of this polygon is

(n-2)180

Where m is the number of corners

(5-2)180

3*180

540

Hence

Sum of all angles=540

139+92+71+9x+5x=540

302+14x=540

14x=540-302

14x=238

Dividing both sides by 14

x=17

Answer:

P=92 cm

Step-by-step explanation:

<B and <D are congruent so you now know that <D also equals 11.5

Add all the sides up then multiply by 2

You are multiplying by two because each point is at the radius (halfway)

11.5 + 11.5 +10.5+12.5 =46

46 x 2=92

Answer:

92 is the answer

Step-by-step explanation:

Notice the dots are only half way. You have the sides 11.5, 10.5, and 12.5. It says the side D and B are congrent which means they equal. So the side is 11.5. 11.5+11.5=23 Whihc is one side of the permiter. 10.5+10.5=21. 12.5+12.5=25. 11.5+11.5=23. When you add them up you get the answer 92. Hope this helps!

Answer:

3x-3y+4z+2=0

Step-by-step explanation:

Answer:

3x-3y+4z+2=0

Step-by-step explanation:

Option B

The first strain is [tex]2.182 \times 10^{-7}[/tex] mm larger than second strain

Solution:

Given that,

The length of one strain of the bacteria measures 0.000000242 mm

The length of the second strain measures 0.0000000238 mm

To find: Difference between the first strain and second strain

From given ,

Length of first strain = 0.000000242 mm

Length of second strain = 0.0000000238 mm

Let us convert them into scientific notation

Move the decimal point in your number until there is only one non-zero digit to the left of the decimal point. The resulting decimal number is a.

Count how many places you moved the decimal point. This number is b.

If you moved the decimal to the left b is positive.

If you moved the decimal to the right b is negative.

Write your scientific notation number as a x 10^b

Therefore,

[tex]0.000000242 = 2.42 \times 10^{-7}[/tex]

[ Here we moved the decimal point to right , we have moved 7 times. So exponent is -7 ]

[tex]0.0000000238 = 2.38 \times 10^{-8}[/tex]

[ Here we moved the decimal point to right , we have moved 8 times. So exponent is -8 ]

Now find the difference

[tex]Difference = length\ of\ first\ strain\ - length\ of\ second\ strain[/tex]

[tex]Difference = (2.42 \times 10^{-7}) - (2.38 \times 10^{-8})\\\\\text{Make the exponents same }\\\\Difference = (2.42 \times 10^{-7}) - (0.238 \times 10^{-7})\\\\\text{Take the common term out }\\\\Difference = 10^{-7}(2.42 - 0.238)\\\\Difference = 10^{-7} \times 2.182\\\\Difference = 2.182 \times 10^{-7}[/tex]

Thus first strain is [tex]2.182 \times 10^{-7}[/tex] mm larger than second

Answer:

[tex]\frac{\pi }{4}[/tex] could be used as a reference angle for [tex]\frac{15\pi }{4}[/tex].

Step-by-step explanation:

Given the trigonometric expression

[tex]\frac{15\pi }{4}[/tex]

In order to find the reference angle for [tex]\frac{15\pi }{4}[/tex], find an angle that is positive, less than [tex]2\pi[/tex], and coterminal with

Subtract  [tex]2\pi[/tex] from  [tex]\frac{15\pi }{4}[/tex].

[tex]\frac{15\pi }{4} -2\pi[/tex]

The resulting angle of [tex]\frac{7\pi }{4}[/tex] is positive, less than [tex]2\pi[/tex], and coterminal with   [tex]\frac{15\pi }{4}[/tex].

[tex]\frac{7\pi }{4}[/tex]

Since the angle [tex]\frac{7\pi }{4}[/tex] is in the fourth quadrant, subtract

[tex]2\pi-\frac{7\pi }{4}=\frac{\pi }{4}[/tex]

Therefore, [tex]\frac{\pi }{4}[/tex] could be used as a reference angle for [tex]\frac{15\pi }{4}[/tex].

Keywords: reference angle

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The reference angle = [tex]\frac{\pi}{4}[/tex].

Note that     [tex]\frac{15\pi}{4}[/tex]  [tex]\frac{15\pi}{4}=3.75\pi[/tex] lies in the 4th quadrant and it is close to  [tex]4\pi[/tex].

To find the reference angle of  [tex]\frac{15\pi}{4}[/tex]  we will subtract it from [tex]4\pi[/tex].

So, the reference angle is:

[tex]4\pi-\frac{15\pi}{4}=\frac{\pi}{4}[/tex]

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Answer:

see work attached and shown

The vertex form is [tex]y=(x-1)^{2} -6[/tex]

Step-by-step explanation:

The given equation [tex]y=x^{2} -2x-5[/tex] is a parabola. The vertex of the parabola is of the form [tex]y=ax^{2} +bx+c[/tex]  

The parameters of the parabola are [tex]a=1, b=-2[/tex] and [tex]c=-5[/tex]

The vertex of the x-coordinate is given by [tex]x=\frac{-b}{2a}[/tex]

Thus, substituting the values of a and b in [tex]x=\frac{-b}{2a}[/tex], we get,

[tex]\begin{aligned}x &=\frac{-(-2)}{2(1)} \\&=\frac{2}{2} \\x &=1\end{aligned}[/tex]

Now, substituting [tex]x=1[/tex] in [tex]y=x^{2} -2x-5[/tex], we get,

[tex]\begin{aligned}y &=1^{2}-2(1)-5 \\&=1-2-5 \\y &=-6\end{aligned}[/tex]

Thus, the vertex is [tex](1,-6)[/tex]

The equation of parabola to be in vertex form is [tex]y=a(x-h)^{2} +k[/tex]

where a is the coefficient of [tex]x^{2}[/tex], h is vertex of the x-coordinate and k is the vertex of the y-coordinate.

Hence, [tex]a=1, h=1[/tex] and [tex]k=-6[/tex]

Thus, substituting the values in the equation of the vertex form,

[tex]y=1(x-1)^{2} -6\\y=(x-1)^{2} -6[/tex]

Hence, the vertex form is [tex]y=(x-1)^{2} -6[/tex]

Answer:

Max

Step-by-step explanation:
what is this question

Answer:

a) the area of a square is in terms of x is

[tex](x+1)^2[/tex] centimeter square

b)The length of the rectangle is l = (x+1)

                                       l = 7+1 =8 cm

The width of the rectangle is w = [(x+1)-5]

                                     w = (7+1)-5 =3 cm

Step-by-step explanation:

a) the area of a square is in terms of x is

 area of square is [tex]l^{2} = (x+1)(x+1)[/tex]

                                 = [tex](x+1)^2[/tex]

b)  Given length is  l = (x+1) cm and

the width is 5 cm less than its length.

so we have take width is w = (x+1)-5 cm

Given area of triangle is  24 cm

Area of rectangle = length X width

24  =  (x+1)(x+1 -5 )

now simplification [tex]24 = (x+1)^2 - 5 (x+1)[/tex]

apply (a+b)^2 = a^2+2 a b+b^2

[tex]x^2+2 x+1-5 x-5 =24[/tex]

[tex]x^2 -3 x -4-24=0[/tex]

[tex]x^{2} -3 x -28 =0[/tex]

now find factors of 28  = 7 X 4 is  

[tex]x^{2} -7 x+4 x-28=0[/tex]

[tex]x(x-7)+4(x-7)=0[/tex]

[tex](x+4)(x-7)=0[/tex]

x = -4 and x=7

there fore you have to choose x = 7

The length of the rectangle is l = (x+1)

                                       l = 7+1 =8

The width of the rectangle is w = [(x+1)-5]

                                     w = (7+1)-5 = 3

Verification:-

Given area of rectangle  = 24 = 8 X 3

                                           24 =24

so we can not choose x=-4

we have to choose x =7 only

Answer:

Therefore the probability that in one turn James could roll an odd number and fip a heads on the quarter is  = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{4}[/tex].

Step-by-step explanation:

i) There are three odd numbered faces on the cube, that is the faces having 1, 3, and 5.

Therefore the probability of rolling an odd numbered face is = [tex]\frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{1}{2}[/tex] since the probability of rolling 1 = probability of rolling 3 = probability of rolling 5 = [tex]\frac{1}{6}[/tex]

ii) The probability of flipping a head on the quarter = probability of flipping a tail on the quarter = [tex]\frac{1}{2}[/tex]

iii) Therefore the probability that in one turn James could roll an odd number and fip a heads on the quarter is  = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{4}[/tex]

The probability that James could roll an odd number on a fair six-sided die and flip heads on a quarter in one turn is 1/4 or 25%.

The student is asking about the probability of two independent events happening simultaneously: rolling an odd number on a fair six-sided die and flipping heads on a quarter. To calculate the probability of both independent events occurring, we multiply the probabilities of each event.

The probability of rolling an odd number (1, 3 or 5) on a die is 3 out of 6 possibilities, which simplifies to 1/2 since there are three odd numbers out of six total numbers. The probability of flipping heads on a quarter is 1/2, as there are two sides to a coin and it is fair, meaning each side has an equal chance of landing face up.

Now, to find the combined probability, we multiply the probabilities of the independent events:

Combined probability = (1/2) x (1/2) = 1/4 or 0.25, which means there is a 25% chance to roll an odd number and flip heads in one turn.

Answer:

-10y - 11x

Step-by-step explanation:

First you need to distribute -7 through the parentheses.

-7y - 14x - 3y + 3x

then you need to collect the like terms (terms with the same variable)

-10y - 11x

Answer:-10y - 11x

Step-by-step explanation:

Expanding , we have

-7y - 14x -3y  + 3x

collecting the like terms , we have

- 7y - 3y - 14x + 3x

Simplifying , we have

-10y - 11x

[tex]-3-2(5+1)-1-1\\-3-(2)(6)-(1-1)\\-3-12-(1-1)\\15-(1-1)\\15-0\\{Answer=-15 \checkmark[/tex]

Answer:

why?

Step-by-step explanation:

Answer:

3x+4=19 x is 5 3(5)=15+4=19

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

[tex] \frac{2}{6} \times 3 = \frac{2}{6} \times \frac{3}{1} [/tex]

[tex] \frac{2}{6} \times \frac{3}{1} = \frac{6}{6} = 1[/tex]

To multiply 2/6 and 3 in its simplest form, multiply the numerators and denominators together. The resulting fraction is 6/6, which simplifies to 1.

To multiply fractions, multiply the numerators together and multiply the denominators together. In this case, multiplying 2/6 and 3 gives a result of (2 * 3) / (6 * 1), which simplifies to 6 / 6. Since the numerator and denominator are the same, the fraction is equal to 1 in its simplest form.

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