Marcy determined that her father's age is four less than three times her age. If represents Marcy's age, which expression represents her father's age?

A. 3x - 4
B. x - 4
C. 4x - 3
D. 4 - 3x

The equivalent exponential form of the equation log2n=4 is 2⁴ = n, which simplifies to n = 16.

The equation log2n=4 can be rewritten using the definition of a logarithm. To convert from logarithmic to exponential form, we use the fact that a logarithm answers 'to power must the base be raised to produce the given number'. So, log2n = 4 is equivalent to 24 = n, because 2 is the base in this logarithm, and 4 is the power to which this base must be raised. Therefore, n is equal to 16, as 2 raised to the fourth power is 16 (24 = 16).

Answer:

[-5,39]

Step-by-step explanation:

The vertex is at (-6,-5)

The interval is from -10 to 5 (inclusive of both endpoints...

Absolute function is open up because 4 is positive

I will plug in both endpoints now:

f(-10)=4|-10+6|-5                               f(5)=4|5+6|-5

f(-10)=4(4)-5                                      f(5)=4(11)-5

f(-10)=11                                             f(5)=39

So the highest reached by f(5) which is 39 so our range will go up to 39 (inclusive)

11 is not the lowest reached, -5 is because our vertex was included within the domain

So the range is [-5,39]

Answer:

You cant find this type of stuff on the internet without some shady questions.If your doing linear functions which im guessing basic algebra where ur from gof to google and look up linear funcion calc. The one by symbolab and try that . If it doesent work or dosent look right try some other calcs.

Answer:

y > 2x + 2 and y < 2x-1 .

Step-by-step explanation:

The line which the blue shaded area represent has y intercept 2 and slope [tex]\frac{2}{1} =2[/tex]

Hence equation of the line is y=2x+2.

To check the inequality for the shaded region we take any  point (-3,0) in the shaded region .Plugging the values in the given equation :

0 > 2(-3)+2  or 0 >-4.

The inequality equation represented by the blue shaded part is y > 2x+2.

The line for the red shaded region has y intercept -1 and slope 2.

Hence equation of the line is y= 2x-1 .

Taking a point (2,0) in the shaded part and substituting the values in the equation of line we have :

0< 2(2)-1 or 0< 3 .

Hence the inequality representing the red shaded region is y<2x-1 .

y > 2x + 2 and y < 2x - 1

In this problem, we will compose the system of linear inequalities is represented by the graph. Firstly, let us state each line on the graph in terms of the equation of the line.

A shortcut to form a linear equation through the intercepts of the axes at (0, a) and (b, 0) is [tex]\boxed{\boxed{ \ ax + by = ab \ }}[/tex].

Part-1: a dashed line that intersects the axes at points (0, 2) and (-1, 0).

Step-1: make a linear function  

[tex]\boxed{ \ ax + by = ab \ } \rightarrow \boxed{ \ 2x + (-1)y = 2 \times (-1) \ }[/tex]

2x - y = -2

Add by 2 and y on both sides.

Hence, the equation of line is [tex]\boxed{y = 2x + 2 \ }[/tex]  

Step-2: make a linear inequality  

Since the test point (0, 0) is not in the blue shaded area, which means the test results must be false (or 0 > 2), then linear inequality is arranged as follows:

[tex]\boxed{\boxed{ \ y > 2x + 2 \ }}[/tex]

Part-2: a dashed line that intersects the axes at points (¹/₂, 0) and (0, -1)..

Step-1: make a linear function  

[tex]\boxed{ \ ax + by = ab \ } \rightarrow \boxed{ \ (-1)x + \frac{1}{2}y = -1 \times \frac{1}{2} \ }[/tex]

[tex]\boxed{ \ -x + \frac{1}{2}y = -\frac{1}{2} \ }[/tex]

Multiply by 2 on both sides.

-2x + y = -1

Add by 2x on both sides.

Hence, the equation of line is [tex]\boxed{y = 2x - 1 \ }[/tex]  

Step-2: make a linear inequality  

Since the test point (0, 0) is not in the red shaded area, which means the test results must be false (or 0 < -1), then linear inequality is arranged as follows:

[tex]\boxed{\boxed{ \ y < 2x - 1 \ }}[/tex]

Thus the system of linear inequalities is represented by the  graph is y > 2x + 2 and y < 2x - 1.

The distance between the pair of points A(-1,8) and B(-8,4)​ is 15.

In geometry, the distance formula is:

√(x2-x1)2+(y2-y1)2

Now we can just plug in the x and y values:

√(-1-8)2+(8-(-4)2

√(-1-8)2+(8+4)2

√(-9)2+(12)2

√(81+144)

√(225)

15

So our distance is 15 units.

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Final answer:

The distance between points A(-1,8) and B(-8,4) is calculated using the distance formula derived from the Pythagorean Theorem and is approximately 8.06 units.

Explanation:

To find the distance between two points on the Cartesian plane, you can use the distance formula, which is derived from the Pythagorean Theorem. In this case, the points are A(-1,8) and B(-8,4). The formula is as follows:

d = √((x2 - x1)² + (y2 - y1)²)

Here's how it's done step-by-step:

Subtract the x-coordinates of the two points: -8 - (-1) = -7.

Subtract the y-coordinates of the two points: 4 - 8 = -4.

Square both differences: (-7)² = 49 and (-4)² = 16.

Add the squares of the differences: 49 + 16 = 65.

Take the square root of the sum:
√65 approx 8.06.

Therefore, the distance between points A and B is approximately 8.06 units.

Answer:

C

Step-by-step explanation:

The area (A) of a regular decagon is

A = [tex]\frac{1}{2}[/tex] perimeter × apothem

perimeter = 10 × 8 = 80 in, thus

A = 0.5 × 80 × 12.3 = 492 in² → D

Answer:

Option B 3,-3,-6 is correct.

Step-by-step explanation:

We need to find real zeroes of [tex]x^3+6x^2-9x-54[/tex]

Solving

[tex]x^3+6x^2-9x-54\\=(x^3+6x^2)+(-9x-54)[/tex]

Taking x^2 common from first 2 terms and -9 from last two terms we get

[tex]=(x^3+6x^2)+(-9x-54)\\=x^2(x+6)-9(x+6)\\[/tex]

Taking (x+6) common

[tex](x+6)(x^2-9)\\[/tex]

x^2-9 can be solved using formula a^2-b^2 = (a+b)(a-b)

[tex]=(x+6)((x)^2-(3)^2)\\=(x+6)(x+3)(x-3)[/tex]

Putting it equal to zero,

[tex](x+6)(x+3)(x-3) =0\\x+6 =0, x+3=0\,\, and\,\, x-3=0\\x=-6, x=-3\,\, and\,\,  x=3[/tex]

So, Option B 3,-3,-6 is correct.

Answer:

B. 3,-3,-6

Step-by-step explanation:

Answer:

Step-by-step explanation:

this the gemetric  sequence  because : -12/6 =24/-12=-48/24=-2 (common rat)

the sum is : S=  u1 ×(d^n - 1)(d-1)

d = -2     u1  = 6     S= -2046

6((-2)^n -1) /(-2 -1) = -2046

(-2)^n -1  =1023

(-2)^n = 1024      but 1024 = 2^10 = (-2)^10

so : (-2)^n = (-2)^10

n=10  conclusion : 10 terms

The number of terms of the sequence is 10.

A geometric sequence exists a sequence of numbers where each term after the first term exists found by multiplying the earlier one by a fixed non-zero number, named the common ratio.

The terms of the sequence 6, -12, 24, -48, ...

Sum = -2046

Geometric sequence:

-12/6 = 24/-12 = -48/24 = -2

Sum of terms:

[tex]$S = u_{1} *(d^n - 1)(d-1)[/tex]

Let, d = -2, [tex]u_{1} = 6[/tex] and S = -2046

[tex]6((-2)^n -1) /(-2 -1) = -2046[/tex]

[tex](-2)^n -1 =1023[/tex]

[tex](-2)^n = 1024[/tex]

But the number of terms = 10

[tex]1024 = 2^{10} = (-2)^{10}[/tex]

so,[tex](-2)^{n} = (-2)^{10}[/tex]

Therefore, the correct answer is 10.

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Step-by-step explanation:

Volume of a cone is [tex]\pi r^{2} .height[/tex]/3 so [tex](3x)^{3}[/tex] is equal to

[tex]\pi r^{2} .x[/tex]/3 .  Also  [tex](3x)^{3}[/tex] = [tex]27x^{3}[/tex]

[tex]27x^{3}[/tex] = [tex]\pi r^{2} .x[/tex]/3. Pi equals to 3 so pi and the 3 in the denominator will simplfy each other. lets simplfy the "x" so [tex]r^{2}  = 27x^{2}[/tex] so the radius is 9x.

The expression that represents the radius of the cone's base is →

{r} = 3/√π.

Volume is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write Volume as -

V = ∫∫∫ F(x, y, z) dx dy dz

Given is that the volume of a cone is {3x} cubic units and its height is {x} units.

The volume of a cone is -

V = 1/3 πr²h

We can write the volume as -

3x = 1/3 πr²x

3 = 1/3 πr²

πr² = 9

r² = 9/π

r = 3/√π

Therefore, the expression that represents the radius of the cone's base is → {r} = 3/√π.

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Answer: 4/8 or 1/2

Step-by-step explanation:

See attached photo. - my answer got deleted lol

Answer:

4/8 or 1/2

Step-by-step explanation:

got it right on preworks

Final answer:

The volume of the tilted solid is 1200 cubic feet.

Explanation:

The volume of the cube in the image is given as 1000 cubic feet. Let's call the height of the cube 'h'. The length and width of the cube are also 'h', so the volume of the cube is h x h x h = h³ = 1000. Solving for 'h', we find that h = 10 feet.

The tilted solid has the same base and height as the cube, but the length of each of its slanted sides is 2 units longer than the height. So the length of each slanted side is h + 2 = 10 + 2 = 12 feet.

To find the volume of the tilted solid, we can use the formula for the volume of a rectangular prism: volume = base area x height. The base area is h x h = h², and the height is 12 feet. Therefore, the volume of the tilted solid is h² x 12 = 10² x 12 = 1200 cubic feet.

Answer:

The answer is A and B.

Step-by-step explanation:

Answer:

[tex]\displaystyle 24x^{2} - 41x + 12 = 24\left(x - \frac{3}{8}\right) \cdot \left(x - \frac{4}{3}\right) = (8x-3)\cdot (3x - 4)[/tex].

Step-by-step explanation:

Apply the quadratic formula to find all factors. For a quadratic equation in the form

[tex]a\cdot x^{2} + b\cdot x + c = 0[/tex],

where [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are constants, the two roots will be

[tex]\displaystyle x_1 = \frac{-b + \sqrt{b^{2} - 4\cdot a \cdot c}}{2a}[/tex], and

[tex]\displaystyle x_2 = \frac{-b - \sqrt{b^{2} - 4\cdot a \cdot c}}{2a}[/tex].

For this quadratic polynomial,

Apply the quadratic formula to find any [tex]x[/tex] value or values that will set this polynomial to zero:

[tex]\displaystyle x_1 = \frac{-(-41) + \sqrt{(-41)^{2} - 4\times 24 \times 12}}{2\times 24} = \frac{3}{8}[/tex].

[tex]\displaystyle x_2 = \frac{-(-41) - \sqrt{(-41)^{2} - 4\times 24 \times 12}}{2\times 24} = \frac{4}{3}[/tex].

Apply the factor theorem to find the two factors of this polynomial:

Keep in mind that simply multiplying the two factors will not reproduce the original polynomial. Doing so assumes that the leading coefficient of [tex]x[/tex] in the original polynomial is one, which isn't the case for this question.

Multiply the product of the two factors by the leading coefficient of [tex]x[/tex] in the original polynomial.

[tex]\displaystyle 24\left(x - \frac{3}{8}\right) \cdot \left(x - \frac{4}{3}\right) = (8x-3)\cdot (3x - 4)[/tex].

Expand to make sure that the factored form is equivalent to the original polynomial:

[tex](8x-3)\cdot (3x - 4)\\ = (8\times 3)x^{2} + ((-3)\times 3 + (-4)\times 8)\cdot x + ((-3)\times (-4))\\ = 24x^{2} - 41x + 12[/tex].

Answer:

Treat the lesser than sign as an equal sign. What you do to one side, you do to the other. Isolate the variable x. Do the opposite of PEMDAS.

PEMDAS = Parenthesis, Exponents ( & roots), Multiplication, Division, Addition, Subtraction.

Solve -6x + 14 < -28

First, subtract 14 from both sides:

-6x + 14 (-14) < -28 (-14)

-6x < -42

Next, divide -6 from both sides to isolate the variable x. Note that when you divide (or multiply) by a negative number, you must flip the greater than or less than sign.

(-6x)/-6 < (-42)/-6

x > (-42)/(-6)

x > 7

x > 7 is your answer.

Solve 3x + 28 < 25

First, subtract 28 from both sides.

3x + 28 (-28) < 25 (-28)

3x < -3

Isolate the variable x. Divide 3 from both sides. Note that because you aren't dividing by a negative number (rather a positive 3), you do not flip the sign.

(3x)/3 < (-3)/3

x < (-3)/(3)

x < -1

x < -1 is your answer.

~

To solve the given inequalities, we found that x > 7 and x < -1. Since no number satisfies both conditions simultaneously, there is no solution to this system of inequalities.

We are given two inequalities to solve for x:

-6x + 14 < -28

3x + 28 < 25

Solving the first inequality:

Solving the second inequality:

Combining the two inequalities, we find:

x > 7 AND x < -1

Since there is no number that satisfies both conditions simultaneously, there is no solution to this system of inequalities.

nothing can further be done with this?

The solution to the system of equations given by the ordered pairs (7x+3y,2x+3y) and (24, 0) is x= -4.8 and y=3.2.

To solve for x and y, you need to equate each component of the ordered pairs and solve the resulting equations. In this case, you have:

Solving the second equation for x: x = -1.5y

Substitute x into the first equation: 7(-1.5y) + 3y = 24, which becomes -10.5y + 3y = 24, then -7.5y = 24

Solving for y, you get: y = -24 / -7.5 which equals y = 3.2.

Substituting y into the second equation 2x + 3(3.2) = 0, we get 2x = -9.6, so x = -9.6 / 2, so x = -4.8.

So, the values of x and y are -4.8 and 3.2 respectively.

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Answer:

Answer 1:4 or 1/4

Step-by-step explanation:

30/120 reduced is 1/4 which would equal 1:4.

I'm learning this right now too well relearning and i hope i have helped you!

Answer:

1/4

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

The only number that is a perfect square is 36

6*6 = 36

Answer:

Step-by-step explanation:

[tex]\sqrt{a}=b\iff b^2=a\ for\ a\geq0\ and\ b\geq0\\\\\\\sqrt5-not\ rational\\\\\sqrt8-not\ rational\\\\\sqrt{36}=6-rational\qquad(\sqrt{36}=6\ because\ 6^2=36)\\\\\sqrt{44}-not\ rational[/tex]

Answer:

Domain is {10,-16,18,19,5}

Range is {12,-10,-12,19,-9,22}

This is not a function because 18 is in the domain twice

The Domain is {10,-16,18,19,5}

The Range is {12,-10,-12,19,-9,22}

And, This is not a function because 18 is in the domain twice.

Here,

In the table is shown in figure.

We have to find the domain, range and determine if it is a function.

What is Function?

A function is a relation between inputs and outputs where each input is related to exactly one output.

Now,

Domain is the inputs (values of x) on the table.

Hence, The Domain is {10,-16,18,19,5}

And, Range is the outputs (values of y) on the table.

Hence, The Range is {12,-10,-12,19,-9,22}.

Since, In the table 18 is twice in the domain.

So, It is not a function.

Therefore,

The Domain is {10,-16,18,19,5}

The Range is {12,-10,-12,19,-9,22}

And, This is not a function because 18 is in the domain twice.

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The answer would be 5, - 8

Answer:5,-8

Step-by-step explanation:

The answer is C

Step-by-step explanation:

The pair of given triangles which satisfied the HL theorem of congruency is given by option C. Both right triangles with hypotenuse and one corresponding leg congruent.

HL theorem also named as Hypothenuse Leg theorem,

It states hypotenuse and any one leg of one right angled triangle is congruent to hypotenuse and corresponding leg of another right angled triangle.

This implies both the triangles are congruent using HL theorem.

To check which pair of triangles are congruent using HL theorem are as follow,

a. In the first pair of right angled triangles only hypotenuse is marked as congruent side of two different triangles.

So it is not true.

b. In the second pair of triangles,

Both the triangles are obtuse angled triangle.

It does not satisfied HL theorem.

So , it is also not true.

c. In the third pair of the right angled triangle,

Hypotenuse of both the triangle are marked congruent.

One of the corresponding leg is also congruent.

It satisfied the HL theorem.

And both the triangles are congruent to each other using HL theorem.

Option C. is true.

d. IN fourth pair of triangles,

Triangles are not right angled triangle.

It satisfied the SSS (Side -Side- Side) congruency theorem.

It is not a correct option for HL theorem.

Therefore, pair of triangles which satisfied the HL theorem of congruency is option C. Both right triangles.

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Answer:

The z-score for this kernel is -2.3

Step-by-step explanation:

* Lets revise how to find the z-score

- The rule the z-score is z = (x - μ)/σ , where

# x is the score

# μ is the mean

# σ is the standard deviation

* Lets solve the problem

- The popping-times of the kernels in a certain brand of microwave

  popcorn are  normally distributed

- The mean is 150 seconds

- The standard deviation is 10 seconds

- The first kernel pops is 127 seconds

- We want to find the z-score for this kernel

∵ z-score = (x - μ)/σ

∵ x = 127

∵ μ = 150

∵ σ = 10

∴ z-score = (127 - 150)/10 = -23/10 = -2.3

* The z-score for this kernel is -2.3

Answer:

-2.3

Step-by-step explanation:

Answer: 30+18x C is correct

Step-by-step explanation: You distribute the 6 to both of the values in the parenthesis.

Answer:

C 30 + 18x

Step-by-step explanation:

6(5 + 3x)

Distribute the 6 to both terms inside the parentheses

6*5 +6*3x

30 +18x

Answer:

A

Step-by-step explanation:

Hihi. So, this is a nice application of interest rates as well as properties of exponentials/logarithms. As you know, the basic equation for interest rates is A= Pe^(rt) where A is your final amount, P is your initial, r is your rate of interest, and t is the time the money was accumulating interest. After cleaning up, you get in a situation due to you having e still lying around. Luckily, if you take the natural log of e, all you have left behind is the previous exponent. Thus, you can take the natural log of both sides, divide by 4, and then simplify to see that your final interest rate is ~6%

Answer:

A. 6%

Step-by-step explanation:

Since, the given amount formula is,

[tex]A=Pe^{rt}[/tex]

Where, P is the initial amount,

r is the periodic rate of interest,

t is the number of periods,

Here, P = $ 2000,

t = 4 years,

A = $ 2543,

By substituting the values,

[tex]2543=2000e^{4r}[/tex]

[tex]1.2715=e^{4r}[/tex]

Taking ln on both sides,

[tex]ln(1.2715)=4r[/tex]

[tex]\implies r = 0.06004932647\approx 0.06 = 6\%[/tex]

Hence, the rate of interest is 6 %.

Option 'A' is correct.

Answer: 36 units

Step-by-step explanation:

once you plot out the points, it shows a polygon. cut the polygon into a square and a triangle, and count the units to get the lengths, widths, and heights.

you find that the height of the square is 6, and the width is 5. multiply those to get the area of the square: 30.

the width of the triangle is 2 units, and the height is 6. multiply those to get 12, then divide it in half to get the area: 6.

then you add the area of the square to the area of the triangle to get the total area of 36 units squared.

hope this is an understandable explanation!!

Answer:8 ,-8

Step-by-step explanation:the absolute value of a number is how far it is from 0 so 8 and -8 are both 8 spots from 0. Hope this helps!

Answer:

Third option. I am sure it!

Step-by-step explanation:

Mark other guy brainliest. He's a great answer and he helped me before

Answer:

The third option choice

Step-by-step explanation:

Here you have the term (n^-6)(p^3)

(n^-6)(p^3) = (n^-6)(p^3)/1

[And whole number can be written over 1. For example, 4 = 4/1.]

You can see that n has a negative exponent, -6.

My teacher taught it to me like this:

If this is our expression;

(n^-6)(p^3)

---------------  <------ [and thats a fraction bar]

       1

Think of the fraction bar as a bunk bed. Since the (n^-6) isn't happy being "on top of the bunk bed," [since its a negative exponent] move it to the bottom bunk.

So your new expression would be:

 (p^3)

--------------  <-------- [fraction bar]

 (n^6)

Moving n^6 to the bottom changes it into a positive exponent.

So, the third option choice would be correct.

That's the best way I can explain it! I hope this helps!!! :)

Answer:

0 and -5/2

Step-by-step explanation:

g is the first function we consider because that is the function we are first plugging in values into since the order is f o g and not g o f.

g has domain all real numbers meaning you can plug in any number into g and get a number back

So now let's look at plugging in g(x) into f(x)

that is f(g(x))=f(2x^2+5x)=5/(2x^2+5x)

Here you are dividing by a variable

You have to watch out dividing by 0

The variable, 2x^2+5x, is 0 when....

2x^2+5x=0

x(2x+5)=0

x=0 or x=-5/2

So The domain is all real numbers except x=0 or x=-5/2

[tex](f \circ g)(x)=\dfrac{5}{2x^2+5x}\\\\2x^2+5x\not =0\\x(2x+5)\not=0\\x\not =0 \wedge x\not =-\dfrac{5}{2}[/tex]

Answer:

x=7

Step-by-step explanation:

slope formula: (y2-y1)/(x2-x1)

(-8-9)/(x-(-3))=-17/10

-17/x+3=10

-17/7+3=10

-17/10=10

To find the missing value so that the two points have a slope of -17/10, we can use the slope formula. Substituting the coordinates into the formula, we get an equation -17/(x + 3) = -17/10. Solving for x, we find x = 7.

To find the missing value so that the two points have a slope of −17/10, we can use the slope formula. The slope formula is (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, the first point is (-3, 9) and the second point is (x, -8).

Substituting the coordinates into the slope formula,

we have (-8 - 9) / (x - (-3)) = -17/10.

Simplifying this equation,

we get -17 / (x + 3) = -17/10.

Cross multiplying, we find x + 3 = 10.

Solving for x, we subtract 3 from both sides, giving x = 7.

Therefore, the missing value is 7.

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The formula for slope is [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

In this case:

[tex]y_{2} = 1\\ y_{1} }= -3\\x_{2} = -4\\x_{1} = 0[/tex]

so...

[tex]\frac{1 - (-3)}{-4 - 0}[/tex]

[tex]\frac{4}{-4}[/tex]

-1 <<<The slope

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

m = -1

Step-by-step explanation:

The slope is also called the gradient, m.

m=(y2-y1)/(x2-x1)

x1 = 0

y1 = 3

x2 = -4

y2 = 1

we therefore substitute for the values in the formula

m = (1-⁻3)/(⁻4-0)

m = -1