Match the theorem with the correct pair of congruent triangles.

Answer:

Square root

Step-by-step explanation:

Something to the 1/2 power means the square root of that number.

The zeros of the function y = -4(x-3)² + 8 are -1 and 7 and the intercept is 13

The zero of a function is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

when y = 0

-4(x-3)² +8 = 0

expanding the equation

-4( x²-6x +9)+8 = 0

-4x² +24x -36 +8 = 0

-4x²+24x -28 = 0

divide through by 4

-x²+6x-7 = 0

-x²+7x -x -7 = 0

(-x²+7x)(-x-7) = 0

-x( x-7) 1(x-7)

1-x = 0 or (x-7 )= 0

x = -1 or 7

therefore the zeros are -1 and 7

to find the intercept:

x= 0

y = -4(0-3)²+8

y =-4+9+8

y = 13

therefore the intercept is 13

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The length of LN for the triangle is 18.

A triangle is a three-sided polygon because it has three edges and three vertices. The most important attribute of a triangle is the sum of its internal angles to 180 degrees

Given triangle JKL,

and MN is parallel to JK,

taking ΔJKL and ΔLMN

∠L = ∠L  (common angle)

because MN is parallel to JK, so corresponding angles are equal,

so ∠K = ∠N

and ∠J = ∠M

ΔJKL ≈ ΔLMN(triangles are similar)

since both triangles are similar the ratio of their corresponding sides is equal,

JL/LM = JK/MN = LK/LN

and JK = 55 and LK = 33

and MN = 12 + LN

JK/MN = LK/LN

substitute the values

55/(12 + LN) = 33/LN

55LN = 33(12 + LN)

55LN - 33LN = 396

22LN = 396

LN = 396/22

LN = 18

Hence the length of LN is 18.

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Answer:

Each piece of gum is 10cents

Step-by-step explanation:

7 x 0.25 then subtract that from 2.05 then divide by the 3pieces of gum

Answer: (0.25 x 7) + 3x = 2.05 and $0.10 per piece of gum

Step-by-step explanation:

Jeff purchased 7 gumballs for $0.25 each, which is [tex](0.25*7)[/tex]

Jeff then purchased 3 pieces of gum, but we don't know for how much so the cost becomes [tex]x[/tex] and then [tex]3x[/tex]

The final cost then comes down to $2.05, therefore [tex](0.25*7)+3x=2.05[/tex] and solve for [tex]x[/tex] to find the cost of each piece of gum

[tex]1.75+3x=2.05[/tex]
[tex]3x=0.3[/tex]

[tex]x=0.1[/tex]

28. t = I / (Pr)

29. y = -(3x / 5) + (15 / 5)

30. y = -3/5 x + 3

31. y = -3/5 * -1 + 3 = 3 + 3/5 = 3.6

32. 2 tablespoons per serving

33. $0.92 per slice

34. 5 tablespoons

35. 45% (159 / 350 = 0.45 and 0.45 * 100 = 45)

Simple interest is a method of calculating the interest charge on a loan or deposit based on a constant interest rate and the original principal amount. The formula for simple interest is I = Prt, where P is the principal amount, r is the interest rate as a decimal, t is the time period in years, and I is the interest amount. In simple interest, the interest amount is calculated only on the original principal, not on any accumulated interest from prior periods.

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The system of equations is

15x + 10y = 800

x + y = 60

and the solution to these equations is

x = 40

y = 20

Given is that an office manager requests a calculator or calendar for each of the 60 office employees. Each calculator is $15 and each calendar is $10. The total order amounted to $800.

We can write the system of equations as -

15x + 10y = 800

x + y = 60

We can write -

y = 60 - x

So, we can write -

15x + 10(60 - x) = 800

15x - 10x + 600 = 800

5x = 200

x = 40

Then -

y = 20

Therefore, the system of equations is

15x + 10y = 800

x + y = 60

and the solution to these equations is

x = 40

y = 20

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{Question in english is -

An office manager requests a calculator or calendar for each of the 60 office employees. Each calculator is $15 and each calendar is $10. The total order amounted to $800. Part A: Write the system of equations that models this scenario. (5 points) Part B: Use the substitution method or the elimination method to determine the number of calculators and calendars ordered. Show all the necessary steps. (5 points)

}

The coordinates of point A'  and B' are A'(-12,8) and B'(20, 0)

A dilation is a transformation that changes the size of a figure but not its shape.

In a dilation with respect to the origin, a point (x, y) is transformed to a point (kx, ky) where k is a scale factor.

In this case, the point A (-3, 2) and B (5, 0) are transformed under a dilation of 4 with respect to the origin.

So the images are

A' = (kx, ky) = (-3*4, 2*4) = (-12, 8)

B' = (kx, ky) = (5*4, 0*4) = (20, 0)

So the image point of A(-3,2) under a dilation of 4 with respect to the origin is A'(-12,8)

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Complete question

The triangle ABC is dilated by a scale factor of 4 with the center of dilation at the origin.

a) What are the coordinates of A?

b) What are the coordinates of B?

if A (-3, 2) and B (5, 0)

Answer:

Tan u = sin u/cos u, csc u = 1/sin u, sec u = 1/cos u, and cot u = cos u/sin u. The denominators of the fractions can be rationalized by multiplying the numerator and denominator by the conjugate of the denominator.

Step-by-step explanation:

Answer: : Sydney must take 8 goals.

Step-by-step explanation:

Brad took 5 kicks and made 4 goals: 4/5.This means denominator is total kicks and numerator is number of goals.Now for Sydney total shots are 10.so we have to find equivalent fraction of 4/5 with denominator as 10.If we multiply denominator 5 by 2 we get denominator as 10.So that means we have to multiply the fraction 4/5 with 2/2This gives us 8/10 as equivalent fraction of 4/5.Numerator represents goals.

Answer:

Y=4cm

Step-by-step explanation:

We can use the relationship between the side length and area of a square to solve for Y. Let's call the area of the small square "A" and the area of the large square "B". From the problem statement, we know:

A = 1/9 * B

Since the area of a square is equal to the side length squared, we can substitute this relationship into the equation above:

Y^2 = 1/9 * 12^2

Solving for Y:

Y^2 = 1/9 * 144

Y^2 = 16

Y = sqrt(16)

Y = 4

So, the side length of the small square is 4 cm.

The area of the circle with a radius of 5 feet will be 78.5 square feet. Then the correct option is D.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

The diameter of the circle is 10 feet. Then the radius is given as,

r = d / 2

r = 10 / 2

r = 5 feet

Then the area of the circle is given as,

A = πr²

A = 3.14 x 5²

A = 3.14 x 25

A = 78.5 square feet

The area of the circle with a radius of 5 feet will be 78.5 square feet. Then the correct option is D.

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Answer:

Step-by-step explanation:

One input(x-value) can only have one output(y-value) in order to be a function

The graph is the graph of straight lines

The point (2, 3) is not included in the solution area

From the question, we have the following parameters that can be used in our computation:

4x+2y = 16

x+y=4

The equations are linear equations

We have

(x, y) = (2, 3)

This gives

4(2) + 2(3) = 16 -- false

2 + 3 = 4 -- false

Hence, it is not in the solution

We have

4x+2y = 16

x+y=4

This gives

4x+2y = 16

4x + 4y=16

So, we have

2y = 0

And:

y = 0

This means that

4x + 2(0) = 16

x = 4

So, the solution set is (4, 0)

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Answer: 8xw=a

Step-by-step explanation:

w=width

a=area

Note that it is correct to state that LN ≅ MN and Nk ⊥ LM, so NK is the perpendicular bisector of LM and P is on NK. See attached image.

A perpendicular bisector is a line that cuts another line segment across the junction point at a straight angle. As a result, a perpendicular bisector always cuts a line segment through its midway. The phrase bisect implies dividing evenly or uniformly.

A simple technique to determine a perpendicular bisector is to measure the line segment you need to bisect. Then, divide the measured length by two to determine the midway. Draw a line at a 90-degree angle out from this middle.

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Full Question:

Tell whether the information in the diagram allows you to conclude that point P lies on the perpendicular bisector of LM. Explain your reasoning. See attached image.

A) No. You would need to know that LK ⊥ MK

B) No. You would need to know that KP ⊥ LM
C) Yes, t LN ≅ MN and Nk ⊥ LM, so NK is the perpendicular bisector of LM and P is on NK
D) Yes, NK ⊥ LM, so NK is the perpendicular bisector of LM and P is on NK

Answer:

The project cost in terms of X can be expressed as 20X + 700. This can be determined by using the information from mathportal.org, which states that the cost of the fence is $20 per meter plus $350 per gate. Since the field is X meters on a side and there are two gates, each 4 meters wide, the total cost of the project can be expressed as 20X + 700.

Step-by-step explanation:

The value of b set to 2 is the third option, which is the correct one.

The provided equation is h(x) = -x + 5.

We obtain b=5 when comparing with the slope-intercept form y = mx+b.

Consequently, the y-intercept is at 5.

To lower the graph by three units, we must make changes.

As per the transformational laws, f(x)+c shifts c units upward, whereas f(x)-c shifts c units downward.

Therefore, we need to subtract the supplied function by 3 in order to move the graph down 3 units, and we get

y = -x+5 -3

y = -x +2.

Here, the y-intercept is 2.

The provided equation is h(x) = -x + 5.

The value of b set to 2 is the third option, which is the correct one.

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The average rate of change of the function f(x)=-1x^2+5x-7, on the interval x€[-4,3] is 0.857.

Rate of change is a major of house quickly one quantity change in relation to another it is parisu of the changing 122 the changing another quantity over specified time period.

The average rate of change of the function f(x)=-1x^2+5x-7, on the interval x€[-4,3] is calculated by taking the difference of the function's values at the endpoints of the interval, divided by the difference in the corresponding x-values. By plugging in the endpoints of the interval into the equation, we find that f(-4)=-25 and f(3)=6. Thus, the average rate of change of the function f(x)=-1x^2+5x-7 on the interval x€[-4,3] is calculated by taking the difference of -25 and 6, divided by the difference of -4 and 3, which is equal to 6/7 or 0.857. Therefore, the average rate of change of the function f(x)=-1x^2+5x-7, on the interval x€[-4,3] is 0.857.

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The bank teller has 21 five-dollar bills.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let's represent the number of five-dollar bills "x". Then, the number of twenty-dollar bills would be "x + 10".

The total value of the money is $725, so we can write the equation:

5x + 20(x + 10) = 725

Expanding the second term and simplifying, we get:

5x + 20x + 200 = 725

Combining like terms, we get:

25x = 525

Dividing both sides by 25, we get:

x = 21

So, the teller has 21 five-dollar bills.

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The solution is given below.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Remember that the Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

According to this, the correct answer is: given below.

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Answer:

see explanation

Step-by-step explanation:

using the rules of exponents/ radicals

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

• [tex]a^{\frac{m}{n} }[/tex] = [tex](\sqrt[n]{a} )^m[/tex]

then

(fg)(x)

= f(x) × g(x)

= [tex]x^{\frac{1}{2} }[/tex] × 2x²

= 2 × [tex]x^{(\frac{1}{2}+2) }[/tex]

= 2[tex]x^{\frac{5}{2} }[/tex]

when x = 9 , then

= 2 × [tex]9^{\frac{5}{2} }[/tex]

= 2 × [tex](\sqrt{9})^5[/tex]

= 2 × [tex]3^{5}[/tex]

= 2 × 243

= 486

Answer:

1/2 i think this is it

Step-by-step explanation:

Answer:

Rational number

Step-by-step explanation:

because all rational number multiple by0 is 0

Answer:

Equation is

[tex]\mbox {\large \boxed{g(m) = 4.411 (0.94988)^m}}[/tex]

Step-by-step explanation:

We have to translate the information in the table as an equation of the form

[tex]g(m) = P(1 + r)^m\cdots \cdots(1)[/tex]

Let's take the date from the table

For m = 1, g(m) = 4.19

Substituting these values in equation (1) we get:
[tex]g(1) = P(1 + r)^1[/tex]

[tex]4.19 = P(1 + r)^1[/tex]

[tex]P(1 + r)^1 = 4.19 \; \textrm{ (by switching sides)}[/tex]

[tex]P(1+r) = 4.19\; \cdots \cdots (2)\\\textrm{ (an expression raised to the power 1 is the expression itself)}[/tex]

For the next entry in the table, m = 2, g(m) = 3.98

Plugging into (1)

[tex]3.98 = P(1 + r)^2 \cdots\cdots(3)[/tex]
or

[tex]P(1 + r)^2 = 3.98[/tex]

Divide equation (3) by equation (2)

[tex]\dfrac{P(1+r)^2}{P(1+r} = \dfrac{3.98}{4.19}[/tex]

[tex]\textrm{The P terms cancel and } \dfrac{(1 + r)^2}{(1+r)} = 1 + r[/tex]

==> [tex]1 + r = \dfrac{3.98}{4.19}\\\\1 + r = 0.94988\\\\[/tex]

Plugging this value of 1 + r into equation (2):

[tex]P( 0.94988) = 4.19\\\\P = \dfrac{4.19}{0.94988}\\\\P = 4.411\\\\[/tex]

So the equation is

[tex]g(m) = 4.411 (0.94988)^m[/tex]

We can verify this is correct for m = 2, 3 and 4

[tex]m\quad\quad g(m) = 4.411(0.94988)^m\\\------------------\\2\quad\quad 4.411(0.94988)^2 = 3.97992 \approx 3.98\\\\3\quad\quad 4.411(0.94988)^3 = 3.78044 \approx 3.78\\\\3\quad\quad 4.411(0.94988)^4 = 3.59097 \approx 3.59\\\\[/tex]

The expression (3a⁸)⁹ * (3b⁵)² is solved to get 3¹¹a⁷²b¹⁰

power or exponents as used in mathematics are number written on top of a base number. The power says how many times the base number multiplies itself.

The problem is solved as follows

= (3a⁸)⁹ * (3b⁵)²

raising the terms by power of 9 and 2 accordingly

= (3^9 * a^(8 * 9)) * (3^2 * b^(5 * 2) )

= (3^9 * a^(72)) * (3^2 * b^(10) )

collecting base 3

= (3^9 * 3^2 * a^(72) * b^(10))

= (3^(9 + 2) * a^(72) * b^(10))

= (3^(11) * a^(72) * b^(10))

rewriting the expressions

= 3¹¹a⁷²b¹⁰

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The phrase "La sexta parte de la diferencia de dos números" in algebraic sentence can be written as [tex] \frac{x}{6} [/tex] where "x" represents the difference between two numbers.

The quantity [tex] \frac{x}{6} [/tex] is a fraction that represents one-sixth of the difference between two numbers. In other words, if you have two numbers "a" and "b", and you subtract them to find their difference "a-b", then [tex] \frac{x}{6} [/tex] would equal [tex] \frac{(a - b)}{6} [/tex].

The fraction [tex] \frac{x}{6} [/tex] gives us a portion or a ratio of the difference between the two numbers, and in this case, it's one-sixth of that difference. So, if you want to find what one-sixth of the difference between two numbers is, you can simply divide that difference by 6.

Let's say that the two numbers you want to find the difference between are 15 and 6. To find their difference, we would subtract the smaller number from the larger one:

15 - 6 = 9

So, the difference between these two numbers is 9. To find one-sixth of this difference, we would divide the difference by 6:

[tex] \frac{9}{6} = 1.5[/tex]

So, one-sixth of the difference between 15 and 6 is 1.5.

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Answer: It is 84 degrees

Answer: It is not possible to convert 3 c to mL without a conversion factor. There are several different units of measurement for volume, including cubic centimeters (cc), milliliters (mL), and cubic meters (m^3). To convert from one unit to another, you need to know the conversion factor.

The conversion factor between cubic centimeters (cc) and milliliters (mL) is 1:1, meaning they are equivalent units of measurement. So, 3 cc is equal to 3 mL.

Step-by-step explanation:

The values of X1 and X2 that maximize the function Z = 30X1 + 50X2 are given as follows:

The maximum value is given as follows:

4000.

The function for this problem is defined as follows:

Z = 30X1 + 50X2.

The constraints are given as follows:

X2 has the higher multiplier, hence we should:

The maximum value of X2 is obtained when:

X2 = 100 - X1.

Replacing into the first equation, the value of X1 is given as follows:

X1 + 3(100 - X1) = 200

-2X1 = -100

2X1 = 100

X1 = 50.

Hence the value of X2 is of:

X2 = 100 - X1

X2 = 50.

The maximum value of the function is obtained as follows:

Z = 30 x 50 + 50 x 50

Z = 4000.

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