The vertices of triangle PQR have coordinates P(2,3), Q(3,8), and R(7,3). Under which transformation of triangle PQR are distance and angle measure preserved?(1) (x,y) → (2x,3y)(2) (x,y) → (x+2,3y)(3) (x,y) → (2x, y+3)(4) (x,y) → (x+2,y+3)

Answer: x=2

Step-by-step explanation:

x=z/4+7

x=z/4+3+4

x=(z/4+3)+4

x=-2+4

x=2

The value of x = 15.

The equation given is \(3^{14}\) + \(3^{14}\) + \(3^{14}\) = \(3^{x}\).

We can simplify this equation by adding the three terms on the left-hand side, which gives us 3(\(3^{14}\)) =\(3^{15}\).

Therefore, x = 15.

To understand why this is the case, we need to remember the laws of exponents.

The law of exponents states that when we multiply two numbers with the same base, we can add their exponents.

So, for example, \(3^{2}\) * \(3^{3}\) = \(3^{2+3}\) = \(3^{5}\).

Using this law, we can see that \(3^{14}\) +\(3^{14}\) + \(3^{14}\) is the same as 3 * \(3^{14}\).

And since 3 is also a factor of \(3^{15}\), we can combine the terms to get \(3^{15}\).

Therefore, x = 15.

We arrived at this conclusion by using the law of exponents to combine the terms on the left-hand side of the equation.

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Step-by-step explanation:

Range = biggest value - smallest value

Biggest value in the set is 45

Smallest value in the set is 14

so...

Range = 45-14

Range = 31.

Good luck .

Answer:

No, f is shifted right and g is shifted down.

Step-by-step explanation:

f(x) = |x-4| = x + 4

g(x) = x - 4

The system of equations has one solution.

To check this, we can graph the two equations of the system:

y = (-1/3)x + 7

y = -2x³ + 5x² + x - 2

On the same coordinate axis, and check how many times do the graphs intercept.

The graph can be seen in the image at the end, there you can see that there is only one intecept point. Thus, the system of equations has only one solution.

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The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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Answer:

Step-by-step explanation:

A because it equals it

Answer:

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

Given is the absolute value function.

It has no domain restriction but the range is not negative.

It can be shown as:

Answer:

The shortest side is 20 feet, the second side is 24 feet and the third side is 36 feet.

Step-by-step explanation:

Assuming that the shortest side of this triangle has a length of "x" feet, then one side is "x + 4" feet and the third is "2*x - 4" feet. Since the perimeter of the deck is 80 feet, then the sum of the length of these sides should be equal to that.

\(x + x + 4 + 2*x - 4 = 80\\4*x = 80\\x = \frac{80}{4} = 20 \text{ feet}\\\)

The shortest side is 20 feet, the second side is 24 feet and the third side is 36 feet.

The length of three sides of the triangle are 20 feet, 24 feet  and 36 feet

Given :

Let 'x' be the shortest side of the triangle

one side that is 4 feet longer than the shortest side

so one side is 4 feet more than the shorter side

x+4

a third side that is 4 feet shorter than twice the length of the shortest side

third side is \(2x-4\)

Perimeter of the triangle is sum of all the three sides

Perimeter = x + (x+4)+(2x-4)

Given perimeter is 80 feet

\(x + (x+4)+(2x-4)=80\\4x=80\\x=20\)

The shortest side is 20 feet

One side is x+4= 20+4=24 feet

Largest side =\(2x-4=2(20)-4= 36feet\)

The length of three sides are 20 feet, 24 feet  and 36 feet

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Answer:

Step-by-step explanation:

BAD = 42

x + 103 + 42 = 180

x = 180 - 145

x = 35

Answer: 7: 29 stickers for each friend

8: 412 seats in each section

Step-by-step explanation:

We will have to divide 145 (stickers) by 5 (friends) to get 29

We will have to divide 2472 by 6 to get 412

7.) 145 ÷ 5 = 29 → Each friend will get 29 stickers

8.) 2,472 ÷ 6 = 412 → There are 412 seats in each second.

I divided for both problems using the long division method and multiplied which is the inverse operation, to check my work.

Simplifying

10x + -8 = ax + b

Reorder the terms:

-8 + 10x = ax + b

Solving

-8 + 10x = ax + b

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1ax' to each side of the equation.

-8 + -1ax + 10x = ax + -1ax + b

Combine like terms: ax + -1ax = 0

-8 + -1ax + 10x = 0 + b

-8 + -1ax + 10x = b

Add '8' to each side of the equation.

-8 + -1ax + 8 + 10x = 8 + b

Reorder the terms:

-8 + 8 + -1ax + 10x = 8 + b

Combine like terms: -8 + 8 = 0

0 + -1ax + 10x = 8 + b

-1ax + 10x = 8 + b

Reorder the terms:

-8 + -1ax + -1b + 10x = 8 + b + -8 + -1b

Reorder the terms:

-8 + -1ax + -1b + 10x = 8 + -8 + b + -1b

Combine like terms: 8 + -8 = 0

-8 + -1ax + -1b + 10x = 0 + b + -1b

-8 + -1ax + -1b + 10x = b + -1b

Combine like terms: b + -1b = 0

-8 + -1ax + -1b + 10x = 0

The solution to this equation could not be determined.

Answer:

a = 10 and b = 8

Step-by-step explanation:

comparing the two equations

Answer:

A and B

Explanation:

To find the answer in these problems you must first convert the mixed numbers to improper fractions using the equations \(a \frac{b}{c} =\frac{a*c+b}{c}\).

So for the top equation you would have to do something like \(9\frac{7}{8}=\frac{9*8+7}{8}\) which equals: \(\frac{79}{8}\)

And make sure to do that for both mixed numbers.

You would then plug those mixed numbers back into the equation like so: \((\frac{79}{8}+\frac{14}{5})-\frac{1}{2}\)

Multiply them together to get \(\frac{507}{40}\)

then subtract that by 1/2

convert it back into a mixed fraction.

and you should get \(12\frac{7}{40}\) as your answer.

You then must do that for all the questions and find whichever ones match with that one.

Step-by-step explanation:

We can simplify this problem using De Moivre's theorem. De Moivre's theorem states that:

(cos θ + i sin θ)^n = cos(nθ) + i sin(nθ)

Here, z = 1 + √3i, so we can express z in polar form as:

z = 2(cos π/3 + i sin π/3)

To find z^6, we can apply De Moivre's theorem:

z^6 = [2(cos π/3 + i sin π/3)]^6

= 2^6(cos 6π/3 + i sin 6π/3)

= 2^6(cos 2π + i sin 2π)

= 2^6(1 + 0i)

= 64

Therefore, z^6 = 64.

The equivalent exponential equations are given as follows:

\(2^{4x} = 2^{3(x - 3)}\)

The exponential expression for this problem is defined as follows:

\(2^{4x} = 8^{x - 3}\)

The number eight is the third power of 3, that is:

8 = 2³.

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

Meaning that the equivalent expression on the right side of the equality in this problem is given as follows:

\(8^{x - 3} = (2^3)^{x - 3} = 2^{3(x - 3)}\)

Meaning that the correct option is given by the fourth option.

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The Intel pays $7,760 to Bally Manufacturing on August 14.

The first step in calculating what Intel Corporation pays Bally on August 14 is to determine the net price of the machinery after the trade discount and the return of $100 due to defects.

The trade discount of 40% is calculated as follows:

Discount = List price × Discount rate

Discount = $13,100 × 0.40 = $5,240

So the net price of the machinery after the trade discount is:

Net price = List price - Discount

Net price = $13,100 - $5,240 = $7,860

After Intel returns $100 of machinery, the cost of the machinery is further reduced to:

Net price after return = Net price - Return

Net price after return = $7,860 - $100 = $7,760

Since the payment terms are 3/10 EOM (end of month), Intel receives a discount of 3% if payment is made within 10 days. The 10-day period begins on August 1 and ends on August 10 (the payment due date). Since Intel pays the bill on August 14, payment is late and the 3% discount does not apply.

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Answer:

y = 4x - 11

Step-by-step explanation:

The general equation of the slope-intercept form of a line is given by:

y = mx + b, where

We can find b, the y-intercept of the line, by plugging in 4 for m and (3, 1) for (x, y) in the slope-intercept form:

1 = 4(3) + b

1 = 12 + b

-11 = b

Thus, the y-intercept is -11.

Thus, the equation of the line with a slope of 4 passing through the point (3, 1) in slope-intercept form is y = 4x - 11

The answer is:

Work/explanation:

First, we will write the equation in point slope:

\(\sf{y-y_1=m(x-x_1)}\)

where m = slope;

(x₁,y₁) is a point on the line.

Plug in the data:

\(\sf{y-1=4(x-3)}\)

Simplify

\(\sf{y-1=4x-12}\)

Add 1 on each side

\(\sf{y=4x-12+1}\)

\(\sf{y=4x-11}\)

Answer:

og₃ (x+1) = 3

It could be written:

(x+1)= 3³==> x+1 = 27 ==> x =27-1 =26

Step-by-step explanation:

I really hope this helps

Answer:

Corresponding angles

\((2x + 35) \degree = 103\degree \\ 2x = (103 - 35)\degree \\ 2x = 68\degree \\ x = 34\degree\)

Answer:

C i think plz let me know ^w^

Step-by-step explanation:

Angle ∠EBD is congruent to angle ∠DBA. Option D is the true statement.

An angle bisector is the line segment that bisects the angle into two equal halves.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,

Ray BE is a bisector of angle CBA,

∠CBE = ∠EBA = 60°

∠EBD = ∠EBA - ∠DBA

∠EBD = 60 - 30 = 30

So,

∠EBD = ∠DBA [DB becomes angle bisector of angle EBA]

Thus, ∠EBD is congruent with ∠DBA is the only correct answer among the option.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Which of the following statements is true if ray BE is a bisector of angle CBA?

A. Ray BD is a bisector of angle CBA.

B. ∠EBD is congruent to ∠CBE.

C. Ray BE is a bisector of angle ABE.

D. ∠EBD is congruent to ∠DBA.

Answer:

Step-by-step explanation:

so part a :

9y + 12xy - 18y - 36y ----- simplified

3y(3 + 4x - 6 - 12) ----- factorized ( by rearranging)

part b :

-45y +12xy ---- adding, subtracting like terms

-3y(15 - 4x) ---- fully factorized

hope this helps!

Answer:

47

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to identify the graphs that go with each of these functions, along with a particular point on the curve.

The equations are written here in standard form, factored form, and vertex form. (The "factored form" is sometimes called "intercept form.") Each of these forms can be analyzed for characteristics relevant to identifying the corresponding graph.

In general, we can readily identify the opening direction, based on the sign of the leading coefficient. Depending on the form, we can also identify zeros, the vertex, and the y-intercept.

The line of symmetry (x-coordinate of the vertex) of the equation in the form ax² +bx +c is x = -b/(2a). That is, it will be left of the y-axis when the coefficients 'a' and 'b' have the same sign.

The graph of equation A will be graph 4, the only one with its vertex left of the y-axis. The y-intercept is the constant: point S = (0, 9).

Equation B has a positive leading coefficient, so opens upward. The zeros of the factors are -3 and +9, so identify the places where the graph crosses the x-axis. Graph 3 is the only one that opens upward and has x-intercepts. Point R is (9, 0).

The vertex form of a quadratic is ...

  y = a(x -h)² +k . . . . . . . vertex (h, k); leading coefficient 'a'

Equation C has its vertex at (h, k) = (3, 9) and opens upward (a>0). Graph 1 is the only one matching those characteristics. Point P is the vertex, so point P is (3, 9).

Equation D is the same as equation B, but with a negative leading coefficient. That is, it opens downward and crosses the x-axis in two places, at x = -3 and x = 9. Graph 2 is matches this description. The left zero is point Q, (-3, 0).

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The logarithmic function can be written exponentially as follows.\(t = 8^y.\)

Exponents and logarithms are inverse operations of one another. We can rewrite an equation in logarithmic form as log_a(b) = x if it has the form axe = b. A number's logarithm is the exponent that must be raised in order to obtain that number. For instance, since 102 = 100, log_10(100) = 2. Similar to this, we can express an equation in exponential form, such as axe = b, if it is in logarithmic form, such as log_a(b) = x. The inverse function of the logarithmic function is the exponential function. As a result, when we apply a logarithm to an exponential expression, the original exponent is returned, and the opposite is true.

The given logarithmic expression is \(log_{8}(t) = y.\)

We know that if we have an equation in the form \(a^x = b\), we can rewrite it in logarithmic form as \(log_a(b) = x\) and vice versa.

Thus, \(log_{8}(t) = y\)

\(t = 8^y\)

Hence, the logarithmic function can be written exponentially as follows.\(t = 8^y.\)

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Answer:

5 bracelets per hour

Step-by-step explanation:

60 minutes in hours /12 minutes per bracelet = 5 bracelets per hour

Answer: 5

Step-by-step explanation:

to find the unit rate, you want to divide 60 by the unit rate we currently have, 12 minutes per braclet.

60/12=5.

This equation shows that Sarah can make 5 beaded braclets every hour. 5 is your unit rate.

Answer:

b = 6

Step-by-step explanation:

\((6b - 7) \degree + 90 \degree + 61 \degree = 180 \degree \\ \\ (6b - 7) \degree + 151 \degree = 180 \degree \\ \\ (6b - 7) \degree = 180 \degree - 151 \degree\\ \\ (6b - 7) \degree = 29 \degree \\ \\ 6b - 7 = 29 \\ \\ 6b = 29 + 7 \\ \\ 6b = 36 \\ \\ b = \frac{36}{6} \\ \\ \huge \purple{ \boxed{ b = 6}}\)

Answer:

Step-by-step explanation:

time = 49 hours

speed =  7 miles/hour

speed = distance / time

∴ distance = speed × time

= 7 × 49

= 343 miles

Answer:

Step-by-step explanation:

A) Commission = 2450 shillings * 25 % = 2450 shillings * (25/100) = 2450 shillings * (0.25) = 612.50 shillings

Commission = 612.50 shillings

B) If the total sale is 2,450.00 shillings, after the seller gives buyers a 2% discount. We must re-enter the discount:

2,450.00 shillings = X - X * 2% = X - 0.02 X --->

------> 0.98 X = 2,450.00 shillings

------>X= 2,450.00 / 0.98

------> X = 2,500.00  shillings

NEW COMMISSION = 2,500.00 shillings * 25 % = 2,500.00 shillings *(25/100) =2,500.00 shillings * (0.25) = 625 shillings

NEW COMMISSION = 625 shillings

Answer:

14.67

Step-by-step explanation:

area = 1/2bh therefor plug in the numbers and you get the anwser.