25 POINTS!!!!
The graph of f(x) = (0.5)x is replaced by the graph of g(x) = (0.5)x − k. If g(x) is obtained by shifting f(x) down by 7 units, the value of k is ________??

Answer:

a = (9,8)

b=(10,6)

c=(4,3)

Step-by-step explanation:

basically, you just take the original coordinates and add the translation to it.

so a was -1,6 so just at 10 to -1 as they are x coordinates nad add 2 to 6 because they are Y coordinates and you just do it for all of the points.

Pairs of triangles appear to be congruent are :

Triangles 2 and 3. Option B

Triangles 2 and 4. Option D

Triangles 3 and 4. Option E

Congruent triangles can be defined as the pairs of triangles with same measurement

Triangles 2 and 3 :

After observing triangles 2  and  3  it appears that triangle  is congruent to triangle  .

Option C

Triangles 2 and 4

After observing triangles 2  and 4   it appears that triangle 2 is congruent to triangle 4 .

Option D

E. Triangles 3 and 4

After observing triangles 3  and 4. They are congruent

Option E

Hence, Option B, D and E are correct of the triangles

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Answer:

Triangles 3 and 4
Triangles 1 and 4
Triangles 1 and 3

Step-by-step explanation:

if this is wrong tell me so i can edit the answer, but this is what i got

Answer:

70 degrees.

Step-by-step explanation:

As AB is a diameter M < C = 90 degrees.

Therefore m < B = 90 - 20 = 70.

Answer: 6x

Step-by-step explanation:

The  expression represents the radius of the cone's base is √111/π x = r

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The formula for the volume of a cone is V = (1/3)πr²h, where V is the volume,

r is the radius of the base,

h is the height, and π is a constant approximately equal to 3.14.

We are given that the volume of the cone is 37x³ cubic units and the height is x units.

Using the formula for the volume of a cone, we can write:

37x³ = (1/3)πr²x

37x² = πr²/3

37×3 x²/π = r²

111x²/π  = r²

Take square root on both sides

√111/π x = r

Hence, the  expression represents the radius of the cone's base is √111/π x = r

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Explanation:

The proof can be had by making use of the AAS congruence postulate (twice) and CPCTC.

We start by showing ΔPQY≅ΔPRX, then by showing ΔXQN≅ΔYRN. The proof is then a result of CPCTC.

1. PQ≅PR, ∠Q≅∠R . . . . given

2. ∠P≅∠P . . . . reflexive property of congruence

3. ΔPQY≅ΔPRX . . . . AAS congruence postulate

4. PX≅PY . . . . CPCTC

5. PX+XQ=PQ, PY+YR=PR . . . . segment sum theorem

6. PX+XQ = PY +YR . . . . substitution property

7. PX +XQ = PX +YR . . . . substitution property

8. XQ = YR . . . . subtraction property of equality

9. ∠XNQ≅∠YNR . . . . vertical angles are congruent

10. ΔXNQ≅ΔYNR . . . . AAS congruence postulate

11. XN ≅ YN . . . . CPCTC

__

Additional comment

You probably did steps 1-3 in part (a) of the problem.

[tex]f(x) = (x + 3)(x + 6) \\ f(x) = x {}^{2} + 6x + 3x + 18 \\ f(x) = x {}^{2} + 9x + 18[/tex]

Answer:

C.) y = x² + 9x + 18

Step-by-step explanation:

C.) is correct because the function has the accurate x-intercepts. X-intercepts are the x-values in which the line passes through the x-axis. We can prove this by setting the function equal to 0, factoring, then solving for "x". You can factor the function by asking yourself the question, "which two numbers multiply to 18 and add to 9?"

y = x² + 9x + 18                             <----- Original function

0 =  x² + 9x + 18                           <----- Set the function equal to 0

0 = (x + 6)(x + 3)                           <----- Factor

0 = x + 6             0 = x + 3

-6 = x                  -3 = x

So, at (-3, 0) and (-6, 0), the function crosses the x-axis. This matches the given graph.

Answer:

D. The slope is -2. The y-intercept is (0,3)

Step-by-step explanation:

You can use any two points.

Let's use the first two points: (0, 3), (2, -1)

slope = (y_2 - y_1)/(x_2 - x_1)

slope = (-1 - 3)/(2 - 0)

slope = -4/2

slope = -2

The y-intercept occurs when x = 0. For x = 0, y = 3, so the y-intercept is 3 which means the point (0, 3).

Answer: D. The slope is -2. The y-intercept is (0,3)

The number of different 4 digit numbers that can be formed using only digits 1,2,3 and 4 if they are repeated is; 256 possible numbers

Since the numbers can be used as many times as we want, then it means they can be repeated.

Thus, if we are looking at the number of 4 digit numbers we can create using the numbers 1, 2, 3, and 4, we can calculate that the following way:

For each digit (thousands, hundreds, tens, ones), we have 4 possible choices of numbers. And so we can create;

4 × 4 × 4 × 4 = 256 numbers

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Answer:

-2y= -23-15

-2y=-38

-y= -38/2

-y=19 proved

Answer: a is more than 1 but less than 2

Step-by-step explanation:

b > 1

0 < [tex]\frac{1}{b}[/tex] < 1

0 + 1 < 1 + [tex]\frac{1}{b}[/tex] < 1 + 1

1 < 1 + [tex]\frac{1}{b}[/tex] < 2

So 1 < a < 2

The expressions that represent rational numbers are; √64 + 6/11, √16 + √169 and 17.43 + √49.

A rational number is simply any integer, terminating decimal/repeating decimal or fraction.

1) √6 + √9 = √6 + 3 → Not rational

2) √64 + 6/11 = 94/11 → Rational number

3) √36 + √21 = 6 + √21 → Not rational

4) √16 + √169 = 17 → Rational number

5) 17.4343434343434343 + √49 = 24.43434343 → Rational number

6) √44 + √25 = 2√11 + 5 → Not rational

Therefore, the expressions that represent rational numbers are; √64 + 6/11, √16 + √169 and 17.43 + √49.

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The median of the list of numbers is 7

The number is given as:

9.5, 4.4, 8.1, 2.9, 9.2, 3.2, 9.4, 7, 2.5

Rearrange the numbers in ascending order

2.5, 2.9, 3.2, 4.4, 7, 8.1, 9.2, 9.4, 9.5

The median is the middle number.

The middle number here is 7

Hence, the median of the list of numbers is 7

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The correct option is (2)  [tex]\frac{8}{5}[/tex] and (3)  [tex]\frac{1}{6}[/tex].

The factor of equation  f(x) = 60[tex]x^{4}[/tex] +  86[tex]x^{3}[/tex] – 46[tex]x^{2}[/tex] – 43[tex]x[/tex] + 8 are [tex]\frac{8}{5}[/tex] and [tex]\frac{1}{6}[/tex].

The rational root theorem, also referred to as the rational zero theorem, is a potent mathematical technique used to identify all potential rational roots of polynomial equations of order 3 and above.

For the given polynomial, the roots are given as;

[tex]$$P(x)=a_{n} x^{n}+a_{n-1} x^{n-1}+\cdots+a_{2} x^{2}+a_{1} x+a_{0}$$\\ \\$\pm \frac{\text { factors of } a_{0}}{\text { factors of } a_{n}}$.[/tex]

Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 and factors of 8 are 1, 2, 4 and 8.

Out of the given options, only   [tex]\frac{8}{5}[/tex] and [tex]\frac{1}{6}[/tex] can be written in the form:  

[tex]\begin{aligned}&\frac{8}{5}=\frac{\text { a factor of } 8}{\text { a factor of } 60} \\&\frac{1}{6}=\frac{\text { a factor of } 8}{\text { a factor of } 60}\end{aligned}[/tex]

Therefore, the rational roots of polynomial f(x) = 60[tex]x^{4}[/tex] +  86[tex]x^{3}[/tex] – 46[tex]x^{2}[/tex] – 43[tex]x[/tex] + 8 are [tex]\frac{8}{5}[/tex] and [tex]\frac{1}{6}[/tex].

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The complete question is-

Which is a factor of f(x) = 60[tex]x^{4}[/tex] +  86[tex]x^{3}[/tex] – 46[tex]x^{2}[/tex] – 43[tex]x[/tex] + 8? use the rational root theorem to help you find your answer.

The solution of the inequality -2(3x + 2) - 6x ≥ -4 is undefined

-2(3x + 2) - 6x ≥ -4

-6x - 4 - 6x ≥ -4

-12x ≥ - 4 + 4

-12x ≥ 0

x ≥ 0 / -12

x is undefined

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Answer:

11

Step-by-step explanation:

(a) |-9| + 6 = 9 + 6 = 15

(b) |-9 + 6| = |-3| = 3

Total possible outcomes are 312

We need to find that if you roll a 6-sided die and draw a card from a deck of 52 cards,what are total possible outcomes

Probability is a measure of the possibility that an event will occur. Many events cannot be predicted with absolute certainty. We can only predict the probability that an event will occur, i.e. how likely it is to occur, using it. Probability can range from 0 to 1, where 0 means an event is impossible and 1 means a certain event

An outcome is the result of an event that depends on probability. Probability refers to the likelihood that something will happen, and an event can have more than one possible outcome.

Enumeration of possible outcomes is the process of determining the number of possible outcomes for an event. There are various methods to carry out this process. The best way to calculate the number of possible outcomes of an event depends on the type of event and the structure of the event

If a 6-sided die and draw a card from a deck,

then each side has total possible outcome 52

so, total number of possible outcomes for 6 - sided dice are 52 * 6

= 312

Hence total number of possible outcomes are 312

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Answer:

multiply x and y coordinates by 2 since its a whole number dilation (make bigger basically) ... (-8,6)

Step-by-step explanation:

The amount I'll have in two years at the growth rate described is; $1.21x.

Since it follows that the savings grow by 10% each year, it can be concluded that the growth factor is; 110% = 1.1

Hence, in two years, we have;

= $x × (1.1)²

= $1.21x.

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Answer:

1.21x

Step-by-step explanation:

on rsm it says its correct

CD is the perpendicular bisector of another line AB which can be proven below.

Perpendicular bisector is a line that divides another line into two equal halves in such a way that it creates an angel of 90°.

To proof that CD is the perpendicular bisector of another line AB the following is carried out;

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Answer:

heres what i got

Step-by-step explanation:

2.  definition of a perpendicular bisector

5. reflexive property of congruence

11. definition of square root

The distance between the helicopter and the first home is 369. 87 m

The distance between the helicopter and the first home can be found using sine law,

Therefore,

180 - 72 - 49 = 59 degrees.

Hence,

420 / sin 59 = A / sin 49°

where

A  = distance form the first home to the helicopter.

cross multiply

420 sin 49 = A sin 59°

A = 420 sin 49 / sin 59

A = 316.978023694 / 0.8571673007

A = 369.869339199

A = 369. 87 m

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maybe try using the 2 and dropping the decimal

The correct equation of the given graph is; Option A: y = |x/2| - 5

From the given graph, we can see the following coordinates;

At x = 0, y = -5

At x = 1, y = -4.5

At x = -1, y = -4.5

At x = 2, y = -4

At x = -2, y = -4

Since the y-intercept is at y = -5, looking at the given options, the only one that is correct will be;

y = |x/2| - 5

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A rule which describes the growth of the y-values of the function y=12^x over each interval is "multiply by 12."

By critically observing the given function, we can logically deduce that it is an exponential function. Also, the initial value of this exponential function is 1 with a growth factor is 12.

For instance, we have:

At x = -1

y = 12^(-1)

y = 1/12

At x=0

y = 12^(0)

y = 1

At x = 1

y = 12^(1)

y = 12

In conclusion, a rule which describes the growth of the y-values of the function y=12^x over each interval is "multiply by 12."

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The true average strain in a way that conveys information about precision and reliability is 27.314.

Given that sample size is 20, mean is 26%, standard deviation is 3.4, confidence level is 95%.

We have to calculate the true average strain in a way that conveys information about precision and reliability.

We have to use t test in our problem because sample size is less than 30.

Weknow that,

t=x bar-μ/s[tex]\sqrt{n}[/tex]

where μ is sample mean,

s is sample standard deviation.

Degree of freedom=n-1

=20-1

=19

T value at 95% confidence interval=1.7281

put the values in the formula of t given above.

1.7291=x bar-26/3.4/[tex]\sqrt{20}[/tex]

1.7291=xbar-26/3.4/4.47

1.7291= x bar-26/0.76

1.7291*0.76=x bar-26

1.314=x bar-26

x bar=26+1.314

x bar=27.314

After rounding it will be 27.31

Hence the true average strain in a way that conveys information about precision and reliability is 27.31%.

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The trigonometric function gives the ratio of different sides of a right-angle triangle. The value of sine and cosine will be always less than a unit.

In a unit circle, the radius of the circle represents the hypotenuse of the triangle. Since the hypotenuse is the largest side of the triangle, the ratio of the perpendicular to the hypotenuse and the base to the hypotenuse both will be less than the hypotenuse, therefore, 1. Hence, the value of sine and cosine will be always less than a unit.

In construction, we use trigonometry. For figuring areas of triangular shapes, similar to many concepts and phenomena in mathematics.

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Using the Fundamental Counting Theorem, the sample size of these outcomes is of 12.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

Considering the number of options for Entree, Side and Drink, the parameters are:

n1 = 3, n2 = 2, n3 = 2.

Hence the sample size of outcomes is:

N = 3 x 2 x 2 = 12.

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Answer: SA = 445.05

Step-by-step explanation:

Answer:

b.  -x + y = 0

Step-by-step explanation:

Direct variation:

Direct variation means "y varies directly as x”:

[tex]y \propto x \implies y=kx[/tex]

where k is the (non-zero) constant of variation.

To determine which of the given equations represents a direct variation, isolate y for each and compare with the direct variation equation.

Equation a

[tex]y=\dfrac{4}{3}x-2[/tex]

This is not a direct variation equation as there is an addition of -2.

Equation b

[tex]-x+y=0[/tex]

[tex]\implies y=x[/tex]

This is a direct variation equation where the constant of variation is 1.

Equation c

[tex]xy=8[/tex]

[tex]\implies y=\dfrac{8}{x}[/tex]

This is not a direct variation equation as y is inversely proportional to x.

Equation d

[tex]y=14[/tex]

This equation does not include the variable x, and so is therefore not a direct variation equation.

If y varies inversely with x then the line must be linear and increasing

And the y intercept must be 0 in y=mx+c

#1

c=-2

#2

Yes

#3

No

#4

Parallel to x axis no direct variation