Solve for x. x2 = 64

Answer:

x = 14

Step-by-step explanation:

3(x + 3) - 2x = 23

3x + 9 - 2x = 23

x + 9 = 23

x = 14

Answer:divide the diameter by 2 and plug the values for volume, pi, and radius into the formula for volume of a cylinder. Next, square the radius and multiply the values together. Then, divide both sides by 200.96 for the answer, remembering to include the appropriate unit of measurement

Step-by-step explanation:

Finding A Diameter Of A Cylinder Is Easy.

If You Know The Radius, Multiply The Radius By 2 To get Your Diameter,

Have A Great Day!

Answer: SECOND OPTION

Step-by-step explanation:

The area of a parallelogram can be calculated with this formula:

[tex]A=bh[/tex]

Where "b" is the of one base and "h" is the height.

You can observe in the figure that "b" and "h" are:

[tex]b=AB=4\sqrt{2}ft\\\\h=AX=3ft[/tex]

Then, substituting these values into the formula, you get that the area of the given parallelogram is:

[tex]A=(4\sqrt{2}ft)(3ft)\\\\A=12\sqrt{2}ft^2[/tex]

This matches with the second option.

Answer:

12√2 sq. ft.

Step-by-step explanation:

Hope this helps.

Answer:

1) vertex = (-2,4)

2) Focus = (-0.5,4)

3) x= -3.5

   y= 4

4)  y=4

Step-by-step explanation:

General equation of parabola that is parallel to a-axis and vertex at (h,k) is given as

(y - k)^2 = 4p (x - h)

where

vertex of parabola is at (h,k)

focus of parabola is given at (h + p, k)

the directrix of parabola is given as x = h - p.

Now

1)

finding vertex of parabola:

Given equation of parabola

(y-4)^2=6(x+2)

Comparing with the general form, we get

h=-2 ,k=4 and 4p=6

hence vertex = (-2,4)

2)

Finding focus

Comparing with the above standard form we get

k=4, h=-2, p=3/2

Since the given parabola is parallel to x-axis and also p is positive hence it will opens to the right.

As focus is inside the parabola and it is p units to the right of the vertex:

hence

focus of parabola (h + p, k)=(-2+3/2 , 4)

                                            =(-0.5,4)

3)

Comparing with the above standard form we get

k=4, h=-2, p=3/2

Since the given parabola is parallel to x-axis and also p is positive hence it will opens to the right.

As directrix is outside the parabola and it is p units to the left of the vertex:

hence

directrix x=h-p

                = -2-3/2

                =-7/2

                = -3.5

             y= 4

4)

Finding Axis of symmetry:

as the vertex is (-2,4) also the given parabola is parallel to x-axis so

the axis of symmetry is a horizontal straight line passing through the vertex  at y=4 !

Answer:

a(n) = 3*(2)^(n-1)

Step-by-step explanation:

Each new term is found by multiplying the previous term by 2.  The first term is 3.  Using the standard explicit formula for a geometric series, we get:

a(n) = a(1)*r^(n-1).  In this particular case we have a(n) = 3*(2)^(n-1).

Answer:

14

Step-by-step explanation:

2k - 1 is linear, so this is an arithmetic series.  The sum of an arithmetic series is:

S = (n/2) (a₁ + an)

Here:

S = 196

a₁ = 2(1) - 1 = 1

an = 2n - 1

Solving:

196 = (n/2) (1 + 2n - 1)

196 = (n/2) (2n)

196 = n²

n = 14

The student's question relates to the point P with the polar coordinates (3, -π/3). Polar coordinates are not unique, so we can find all coordinates of point P by adding multiples of 2π to the angle part of the coordinate, that is, (3, -π/3 + 2πn) where n is an integer.

The polar coordinates system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from the origin (point O) and an angle measured anti-clockwise from an arbitrary direction, usually the x-axis.

Each point is represented by the ordered pair (r, θ). Our point P has the polar coordinates (3, -π/3). However, polar coordinates are not unique for a given point. To find all polar coordinate pairs for point P, we add multiples of 2π to the angle part of the coordinate pair, as a complete revolution is 2π in radians. Therefore, alternative polar coordinate pairs for point P would include (3, -π/3 + 2πn) where n is an integer.

Examples include:

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ANSWER

The discriminant is 49.

EXPLANATION

The given quadratic equation is:

[tex]0 =2{x}^{2} + 3x - 5[/tex]

We can rewrite this as

[tex]2{x}^{2} + 3x - 5 = 0[/tex]

Comparing this to

[tex]a{x}^{2} + bx + c = 0[/tex]

We have a=2,b=3, c=-5.

The discriminant is given by:

[tex]D = {b}^{2} - 4ac[/tex]

We plug in the values to get:

[tex]D = {3}^{2} - 4(2)( - 5)[/tex]

[tex]D =9 + 40[/tex]

[tex]D = 49[/tex]

Answer:

D IS THE ANSWER (49)

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Note that the sum of the coefficients of g(x)

1 + 2 - 3 = 0

Hence x = 1 is a root of g(x) and (x - 1) is a factor

Note the sum of the coefficients of f(x)

1 - 3 - 13 + 15 = 0

hence x = 1 is a root of f(x) and (x - 1) is a factor

Since (x - 1) is a factor of both

Then f(x) is also divisible by x² + 2x - 3

Answer:

48

Step-by-step explanation:

12x8=96

96/2=48

you can check this on a calculatot

they threw in the angel to confuse you

Here is the answer, you can use the formula to find the area

Answer:

[tex]\frac{\tan 60\degree}{\cos45 \degree}= \sqrt{6}[/tex]

Step-by-step explanation:

We want to evaluate

[tex]\frac{\tan 60\degree}{\cos45 \degree}[/tex]

We use special angles or the unit circle to obtain;

[tex]\frac{\tan 60\degree}{\cos45 \degree}=\frac{\sqrt{3}}{\frac{\sqrt{2}}{2}}[/tex]

This implies that;

[tex]\frac{\tan 60\degree}{\cos45 \degree}=\sqrt{3}\div \frac{\sqrt{2}}{2}[/tex]

[tex]\frac{\tan 60\degree}{\cos45 \degree}=\sqrt{3}\times \sqrt{2}[/tex]

[tex]\frac{\tan 60\degree}{\cos45 \degree}= \sqrt{6}[/tex]

Answer:

[tex]\sqrt{6}[/tex].

Step-by-step explanation:

[tex]\frac{tan(60)}{cos(45)}[/tex]

[tex]= \frac{\frac{sin(60)}{cos(60)}}{cos(45)}[/tex]

[tex]= \frac{sin(60)}{cos(60)*cos(45)}[/tex]

[tex]= \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}*\frac{\sqrt{2}}{2}}[/tex]

[tex]= \frac{\frac{\sqrt{3}}{2}}{\frac{\sqrt{2}}{4}}[/tex]

[tex]= \frac{4\sqrt{3}}{2\sqrt{2}}[/tex]

[tex]= \frac{2\sqrt{3}}{\sqrt{2}}[/tex]

[tex]= \frac{2\sqrt{3}\sqrt{2}}{2}[/tex]

[tex]=\sqrt{3}\sqrt{2}[/tex]

[tex]=\sqrt{6}[/tex].

Should be 160 chairs

To determine the total number of chairs in the restaurant, multiply the count of tables with 2 chairs (20 tables) by 2, and those with 4 chairs (30 tables) by 4, and sum the two products to get a total of 160 chairs.

To calculate the total number of chairs in the restaurant, we first need to find out how many tables are there with 2 chairs and how many with 4 chairs. Since 40% of the tables have 2 chairs, we multiply 40% (or 0.4) by the total number of tables (50) to find the number of tables with 2 chairs, which equals to 20 tables.

The remaining 60% of the tables have 4 chairs, so we multiply 60% (or 0.6) by the total number of tables (50) to find the number of tables with 4 chairs, which equals to 30 tables.

To find the total number of chairs, we multiply the number of tables with 2 chairs (20) by 2 and the number of tables with 4 chairs (30) by 4, then we add the two results together:

Tables with 2 chairs: 20 tables imes 2 chairs/table = 40 chairs

Tables with 4 chairs: 30 tables imes 4 chairs/table = 120 chairs

So, the total number of chairs in the restaurant is:

40 chairs + 120 chairs = 160 chairs

Answer:

The volume of the prism = 300 units³

Step-by-step explanation:

* Lets study the triangular prism

- The triangular prism has 6 faces

- Two right triangular bases

- Four rectangular side faces

- The volume of the prism = area of its base × its height (altitude)

* Now lets solve the problem

∵ The base is a right triangle with a hypotenuse of 13 units and

   a leg of 12 units

∵ The area of the right triangle = 1/2 × leg1 × leg2

- You can find the length of other leg by using Pythagoras theorem

∵ (hypotenuse)² = (leg1)² + (leg2)²

∵ hypotenuse = 13 units

∵ leg1 = 12 units

∴ (13)² = (12)² + (leg2)²

∴ 169 = 144 +  (leg2)² ⇒ subtract 144 from both sides

∴ 25 =  (leg2)² ⇒ take √ for both sides

∴ leg2 = 5 units

- The area of the right triangle = 1/2 × leg1 × leg2

∴ The area of the base = 1/2 × 12 × 5 = 30 units²

∴ The volume of the prism = 30 × 10 = 300 units³

Answer:

A. 0.5

B. 4.5

C. 1.5

D. 0.5

Step-by-step explanation:

y varies inversely with x can be written as:

y = k/x

where k is constant of variation.

1. value of A

x=A, y = 9 and k = 4.5 (given)

y = k/x

9 = 4.5/A

=> A = 4.5/9

=> A=0.5

2. Value of B

x =1, y= B, k = 4.5

y = k/x

B = 4.5/1

B= 4.5

3. Value of C

x=C, y=3. k=4.5

y = k/x

3 = 4.5/C

3C = 4.5

C = 4.5/3

C = 1.5

4. Value of D

x= 9, y=D, k=4.5

y = k/x

D = 4.5/9

D = 0.5

Answer:

[tex]A=0.5[/tex]

[tex]B=4.5[/tex]

[tex]C=1.5[/tex]

[tex]D=0.5[/tex]

Step-by-step explanation:

The form an the equation of inverse variation is:

[tex]y=\frac{k}{x}[/tex]

Being "k" the constant of variation.

Since we know "k" and we have the values given in the table, we can find the missing values:

To find A we need to substitute the [tex]y=9[/tex], the value of "k" and [tex]x=A[/tex] into the equation and solve for "A":

[tex]9=\frac{4.5}{A}[/tex]

[tex]A=\frac{4.5}{9}=0.5[/tex]

To find B we need to substitute the [tex]x=1[/tex], the value of "k" and [tex]y=B[/tex] into the equation:

[tex]B=\frac{4.5}{1}=4.5[/tex]

To find C we need to substitute the [tex]y=3[/tex], the value of "k" and [tex]x=C[/tex] into the equation and solve for "C":

[tex]3=\frac{4.5}{C}[/tex]

[tex]C=\frac{4.5}{3}=1.5[/tex]

To find D we need to substitute the [tex]x=9[/tex], the value of "k" and [tex]y=D[/tex] into the equation:

[tex]D=\frac{4.5}{9}=0.5[/tex]

Answer:

1

Step-by-step explanation:

In each set, there is a difference of 1 between the two x's.

I just did it its 2 4 and 8 i think

Answer:

3/2x

Step-by-step explanation:

Find the slope of the original line.

3x + 2y = 19

2y = -3x + 19

y = -2/3x + 19

Use the reciprocal with the opposite sign.

3/2x

Final answer:

To find the slope of a line perpendicular to 3x+2y=19, first find the original line's slope (-1.5) and then calculate its negative reciprocal, which is 2/3.

Explanation:

The question asks about the slope of a line perpendicular to the given line 3x + 2y = 19. To find this, we first need to find the slope of the given line. We rearrange the equation into slope-intercept form, which is y = mx + b, where m is the slope. For 3x + 2y = 19, subtract 3x from both sides and divide by 2 to get y = -1.5x + 9.5. Thus, the slope of the given line is -1.5. The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. Therefore, the slope of the line perpendicular to the given line is 2/3.

Answer:5

Step-by-step explanation:

To solve the expression 2 + 3x16 - 2x21 - 3, we apply the order of operations rule (PEMDAS) without any parentheses or exponents to handle. The expression simplifies to 5.

The student is asking to solve a mathematical expression using the correct order of operations. The proper order to solve math expressions is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This rule is often remembered by the acronym PEMDAS.

Let's solve the expression step by step:

First calculate any operations inside parentheses. In the given problem, there are none.

Next, perform all multiplication and division operations from left to right. 3x16 equals 48, and 2x21 equals 42.

Subtract and add from left to right. So, 2 + 48 - 42 - 3 = 5.

Therefore, the expression

2 + 3x16 - 2x21 - 3= 5

.

Answer:

no

Step-by-step explanation:

the first 7, 7000, is 1000 times greater than the first 7. If the first seven is the one in the ones value and the second is in the 7, than it it 1000 smaller.

The value of the first 7 is a thousand times as great as the value of the second 7 in 7,027.

Place value is the basis of our entire number system. This is the system in which the position of a digit in a number determines its value.

Given, a number 7,027 that has two 7 we need to compare the values of 7 in the form of place values.

thus,

Place value of first seven (right to left) = 1

Place value of 2 = 10

place value of 0 = 100

place value of second 7(right to left) = 1000

the first 7 or 7000, is 1000 times greater than the first 7. If the first seven is the one in the one's value and the second is in the 7, then it is 1000 times smaller.

therefore, The first 7's value is 1,000 times more than the second 7's value of 7,027.

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The answer is -12 and 9. You have to factor the equation first. Once you do this, than you can set each problem equal to zero and solve. I hope this helps.

Answer:

Final answer is [tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x[/tex].

Step-by-step explanation:

Given problem is [tex]\sqrt[3]{x}\cdot\sqrt[3]{x^2}[/tex].

Now we need to simplify this problem.

[tex]\sqrt[3]{x}\cdot\sqrt[3]{x^2}[/tex]

[tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}[/tex]

Apply formula

[tex]\sqrt[n]{x^p}\cdot\sqrt[n]{x^q}=\sqrt[n]{x^{p+q}}[/tex]

so we get:

[tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=\sqrt[3]{x^{1+2}}[/tex]

[tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=\sqrt[3]{x^{3}}[/tex]

[tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x[/tex]

Hence final answer is [tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x[/tex].

The original expression ∛x * ∛[tex]x^2[/tex] simplifies to x.

This means that the cube root of x times the cube root of [tex]x^2[/tex] is equal to x.

To simplify the expression ∛x * ∛[tex]x^2[/tex], we can apply the rules of exponents and radicals.

The cube root of x is equivalent to raising x to the power of 1/3.

Similarly, the cube root of [tex]x^2[/tex]  is equivalent to raising [tex]x^2[/tex] to the power of 1/3.

So, we have:

∛x = [tex]x^{(1/3)[/tex]

∛[tex]x^2 = (x^2)^{(1/3)} = x^{(2/3)[/tex]

Now, let's multiply these two expressions:

[tex]x^{(1/3)}\times x^{(2/3)[/tex]

To simplify, we add the exponents when multiplying like bases:

[tex]x^{(1/3 + 2/3)} = x^{(3/3)} = x^1[/tex]

So, the simplified expression is just x.  

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186-140=46/2=23 weeks -2/23=slope

Answer:

Equation is W = -2t+186

It will take 23 weeks to achieve the goal.

Slope = -2 pounds per week

Step-by-step explanation:

Here  current Weight  is 186 pounds

and her goal is to weigh 140 pounds

she can safely lose 2 pounds per week which is the slope

for t =0 , W =186 pounds  (Y intercept )

    slope = 2 pounds per week

since its decreasing therefore its negative

W = -2t+186 is the equation

To achieve the desired goal W = 140

plugging W = 140 and solving for t

140 = -2t+186

2t = 186-140

2t = 46

t = 23

It will take 23 weeks to achieve the goal.

Slope = -2 pounds per week

Answer:

The length of the hypotenuse is [tex]h = 6.71\ units[/tex]

Step-by-step explanation:

For a straight triangle it is true that

[tex]h = \sqrt{a ^ 2 + b ^ 2}[/tex]

Where has is the hypotenuse of the right triangle and a and b are the lengths of the other two sides.

In this case we know that:[tex]a = 3\\b = 6[/tex]

So the hypotenuse is:

[tex]h = \sqrt{3 ^ 2 + 6 ^ 2}[/tex]

[tex]h = \sqrt{3 ^ 2 + 6 ^ 2}[/tex]

[tex]h = 3*\sqrt{5}[/tex]

[tex]h = 3*\sqrt{5}[/tex]

[tex]h = 6.71[/tex]

ANSWER

The hypotenuse is 3√5 units.

EXPLANATION

We use the Pythagoras Theorem.

Let h be the hypotenuse.

The Pythagoras Theorem says that, the hypotenuse square is equal to the sum of the squares of the two shorter legs.

[tex] {h}^{2} = {3}^{2} + {6}^{2} [/tex]

[tex]{h}^{2} = 9+ 36[/tex]

[tex]{h}^{2} = 45[/tex]

Take positive square root.

[tex]h = \sqrt{45} [/tex]

[tex]h = 3 \sqrt{5} units[/tex]

Answer:

x = 34; y = 14

Step-by-step explanation:

Step 1: Make the equations

x + y = 48

x - y = 20

Step 2: Solve the equations

x + y = 48

x - y = 20

2x = 68

x = 34

34 + y = 48

y = 14

Answer:

5x+y=-3

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = 5x - 3   it's a slope-intercept form

y = 5x - 3         subtract 5x from both sides

-5x + y = -3          change the signs

5x - y = 3     it's a standard form

5x - y = 3          subtract 3 from both sides

5x - y - 3 = 0         it's a general form

In the equation: -6x - 19 - 4x replace x with -2

-6(-2) - 19 - 4(-2)

Use your rules of PEMDAS to evaluate

12 - 19 + 8

-7 + 8

1

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer

1

Step-by-step explanation:

Step 1: Replace all x's with -2

-6(-2)-19-4(-2)

Step 2: Multiply

12-19+8

Tip: Remember that a double negative is a positive.

Step 3: Add and Subtract

12-19+8

-7 + 8

1

Answer:

The volume of the smaller solid is [tex]339\ yd^{3}[/tex]

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z----> the scale factor

x----> surface area of the larger solid

y----> surface area of the smaller solid

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

we have

[tex]x=361\ yd^{2}[/tex]

[tex]y=121\ yd^{2}[/tex]

substitute

[tex]z^{2}=\frac{361}{121}[/tex]

[tex]z=\frac{19}{11}[/tex]

step 2

Find the volume of the smaller solid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z----> the scale factor

x----> volume of the larger solid

y----> volume of the smaller solid

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]z=\frac{19}{11}[/tex]

[tex]x=1,747\ yd^{3}[/tex]

substitute

[tex](\frac{19}{11})^{3}=\frac{1,747}{y}\\ \\(\frac{6,859}{1,331})=\frac{1,747}{y} \\ \\y=1,331*1,747/6,859\\ \\y=339\ yd^{3}[/tex]

For this case we have that by definition, a polynomial in its standard form is given by:

[tex]P (x) = ax ^ {n} + bx ^ {n-1} + ... + cx ^ 3 + dx ^ 2 + ex + f[/tex]

Where:

a, b, c, d, e, f: They are the coefficients

n, n-1,3,2,1: They are the exponents. The degree of the polynomial is "n" because it is the largest exponent.

x: It is the variable

The given polynomial is:

[tex]4m-2m ^ 4-6m ^ 2 + 9[/tex]

Rewriting it in its standard form:

[tex]P (x) = - 2m ^ 4-6m ^ 2 + 4m + 9[/tex]

It is a polynomial of degree 4

ANswer:

[tex]P (x) = - 2m ^ 4-6m ^ 2 + 4m + 9[/tex]

Answer:

For this case we have that by definition, a polynomial in its standard form is given by:Where:a, b, c, d, e, f: They are the coefficientsn, n-1,3,2,1: They are the exponents. The degree of the polynomial is "n" because it is the largest exponent.x: It is the variableThe given polynomial is:Rewriting it in its standard form:It is a polynomial of degree 4ANswer:

Step-by-step explanation:

Answer:

Population will be approx 1606300.

Step-by-step explanation:

Given that a city’s population is about 763,000 and is increasing at an annual rate of 1.5%. Now we need to predict the population of the city in 50 years.

We can use growth formula

[tex]A=P\left(1+r\right)^t[/tex]

Where P=763000

rate r=1.5% = 0.015

time t = 50 years

Plug these values into above formula

[tex]A=763000\left(1+0.015\right)^{50}[/tex]

[tex]A=763000\left(1.015\right)^{50}[/tex]

[tex]A=763000\left(2.10524242061\right)[/tex]

[tex]A=1606299.96692[/tex]

Hence population will be approx 1606300.

Therefore, the predicted population of the city in 50 years is approximately [tex]$1,586,997$[/tex].

To predict the population of the city in 50 years, we can use the formula for compound interest, where the principal is the initial population, the interest rate is the annual growth rate, and the time is 50 years.

Given:

- Initial population = 763,000

- Annual growth rate = 1.5% = 0.015

Step 1: Calculate the total growth factor after 50 years using the compound interest formula.

Growth factor = [tex](1 + r)^_t[/tex]

Growth factor =[tex](1 + 0.015)^_{50}[/tex]

Growth factor = [tex]$1.015^{50} = 2.079$[/tex]

Step 2: Calculate the final population by multiplying the initial population with the growth factor.

Final population = Initial population × Growth factor

Final population = 763,000 × 2.079

Final population = [tex]$1,586,997$[/tex]

Answer:

15 yards, 45 feet and 540 inches are equal.

Step-by-step explanation:

To know if the measurements are equal, we first need to convert all the measures to the same unit. In this case, I will convert them all to feet.

a.6 feet

b.15 yards ≈ 45 feet

c.45 feet

d.600 inches ≈ 50 feet

e. 12 feet

f. 540 inches  ≈ 45 feet

Therefore, b, c and f are equal.

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{5}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{8+5}{2}~~,~~\cfrac{2+6}{2} \right)\implies \left( \cfrac{13}{2}~,~\cfrac{8}{2} \right)\implies \left(6\frac{1}{2}~,~4 \right)[/tex]