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Answer:

The correct answer option is x = 4.

Step-by-step explanation:

We are given the following logarithmic equation and we are to determine whether which of the given options shows its extraneous solution:

[tex] log _ 7 ( 3 x ^ 3 + x ) - log _ 7 ( x ) = 2 [/tex]

We can rewrite it as:

[tex]log7[\frac{3x^3+x}{x} ]=2[/tex]

But we know that [tex]log_7(49)=2[/tex]

So, [tex]log7[\frac{3x^3+x}{x} ]=log_7(49)[/tex]

Cancelling the log to get:

[tex]\frac{3x^3+x}{x} =49[/tex]

Further simplifying it to get:

[tex]3x^2+1=49[/tex]

[tex]3x^2=48[/tex]

[tex]x^2=\frac{48}{3}[/tex]

[tex]x^2=16[/tex]

x = 4

Answer:

The extraneous solution to the logarithmic equation is [tex]x=-4[/tex]

Step-by-step explanation:

We have the equation:

[tex]Log_{7} (3x^3+x)-Log_7(x)=2[/tex]

By properties of logarithms:

[tex]LogA-LogB=Log(\frac{A}{B})[/tex]

So, with the equation we have:

[tex]Log_{7} \frac{(3x^3+x)}{x}=2[/tex]

[tex]Log_{7}( \frac{3x^3+x}{x})=2\\Log_{7}( \frac{3x^3}{x}+\frac{x}{x})=2\\Log_{7}( \frac{3x^3}{x}+1)=2\\Log_{7}(3x^2+1)=2[/tex]

This logarithm base is 7 and this equation is equal to 2,  the number 7 passes as the base on the other side of the equation and the two as an exponent, after that we just to find x:

[tex]7^2=(3x^2+1)\\49=3x^2+1\\49-1=3x^2\\\frac{48}{3} =x^2\\16=x^2[/tex]

Now, we can find x with square root

[tex]16=x^2\\\sqrt{16} =\sqrt{x^2} \\x_1=4\\x_2=-4[/tex]

This equation has two answers because it is a quadratic equation, so with this logic the strange solution is -4

Answer:

13 ft

Step-by-step explanation:

The volume of a rectangular prism is the product of its length, width, and height. To find the height, divide the volume by the product of the other two dimensions.

V = LWH

1144 = 11·8·H

1144/88 = H = 13 . . . . feet

Answer:

13 ft is your answer

Step-by-step explanation:

Hope it helped...

Answer:

[tex]\large\boxed{x=\dfrac{5-\sqrt5}{4},\ x=\dfrac{5+\sqrt5}{4}}[/tex]

Step-by-step explanation:

[tex]\text{The quadratic formula for}\ ax^2+bx+c=0\\\\\text{if}\ b^2-4ac<0,\ \text{then the equation has no real solution}\\\\\text{if}\ b^2-4ac=0,\ \text{then the equation has one solution:}\ x=\dfrac{-b}{2a}\\\\\text{if}\ b^2-4ac,\ ,\ \text{then the equation has two solutions:}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\==========================================[/tex]

[tex]\text{We have the equation:}\ 4x^2-10x+5=0\\\\a=4,\ b=-10,\ c=5\\\\b^2-4ac=(-10)^2-4(4)(5)=100-80=20>0\\\\x=\dfrac{-(-10)\pm\sqrt{20}}{2(4)}=\dfrac{10\pm\sqrt{4\cdot5}}{8}=\dfrac{10\pm\sqrt4\cdot\sqrt5}{8}=\dfrac{10\pm2\sqrt5}{8}\\\\=\dfrac{2(5\pm\sqrt5)}{8}=\dfrac{5\pm\sqrt5}{4}[/tex]

Answer:

D. -1

Step-by-step explanation:

We have been given a set of data points and the slope of the line of best fit as 2.5.

The equation of the line of best fit, in slope-intercept form, can be thus written as;

y = 2.5x + c

where c is the  y-intercept of this line.

We can then use any of the points given to determine c. Using the point

( 2, 4);

4 = 2.5(2) + c

4 = 5 +c

c = 4-5 = -1

The answer will be -1

Answer:

see below

Step-by-step explanation:

The number of columns of A is equal to the number of rows of B, so multiplication is possible. It works well to have a calculator do this for you. It involves 27 multiplications and 18 additions, tedious at best.

Each product term is the sum of products ...

p[row=i, column=j] = a[i, 1]b[1, j] +a[i, 2]b[2, j] +a[i, 3]b[3, j]

For example, the product term in the 3rd row, 2nd column is ...

p[3, 2] = a[3, 1]b[1, 2] +a[3, 2]b[2, 2] +a[3, 3]b[3, 2]

= (-4)(-5) +(-1)(3) +(-9)(4) = 20 -3 -36

p[3, 2] = -19

the answer is d.a function only

Answer:

It's a relation only.

Step-by-step explanation:

Answer:

D. 15P15 * 10P5

Step-by-step explanation:

Since you have to place all first-grade students in the first three rows, and nowhere else, we have to make a special calculation for that, then another for the rest of the bus.

These are permutations since the order is important. If we sit John, Paul, Ringo, George and Pete in this order in the first row it's a different way than seating them (in the same order) in the second row for example.

For the 15 first-graders of the first three rows (15 seats), we have 15P15 since all 15 places have to be occupied by all 15 first-graders.

Then we have 10 remaining seats left to be assigned to the 5 second-graders.  That is 10P5.

We then multiply the permutation numbers of those two arrangements to get the total ways:

15P15 * 10P5, answer D.

Answer:

The correct answer option is D. 15P15 x 10P5.

Step-by-step explanation:

We know that there are 15 students in first grade and we have 5 rows of 5 seats to accommodate them. So first grade students can be arranged to occupy the seats in [tex]15P15[/tex].

Also, we have 5 students in the second grade with a total of 25 seats from which 15 seats are already occupied so we are left with 10 seats now.

Therefore, the students can be seated in 15P15 x 10P5 ways.

Answer:

Step-by-step explanation:

[tex]4x+2y=8\qquad\text{subtract 4x from both sides}\\\\4x-4x+2y=-4x+8\\\\2y=-4x+8\quad\text{divide both sides by 2}\\\\\dfrac{2y}{2}=\dfrac{-4x}{2}+\dfrac{8}{2}\\\\y=-2x+4[/tex]

Answer:

b = 29.4 units , m∠A = 122.9 , m∠C = 21.1°

Step-by-step explanation:

* To solve a triangle we can use cosine rule and sin rule

* In ΔABC

- If a, b, c are the lengths of its 3 sides, where

# a is opposite to angle A

# b is opposite to angle B

# c is opposite to angle C

- By using the cosine rule:

# a² = b² + c² - 2bc cos(A)

# b² = a²² + c² - 2ac cos(B)

# c² = a² + b² - 2ab cos(C)

- By using sin rule

# c/sinC = a/sinA = b/sinB

* Lets solve the problem

∵ a = 42 , c = 18 , m∠B = 36°

* We will use the cosine rule

∴ b² = (42)² + (18)² - 2(42)(18) cos(36) =864.766 ⇒ take √ for both sides

∴ b = 29.4

* Now we will use the sin rule to find m∠C

∵ 29.4/sin(36) = 18/sin(C) ⇒ by using cross multiplication

∴ sin(C) = 18 × sin(36°)/29.4 = 0.3598685

∴ m∠C = 21.1°

* The sum of the measure of the interior angle of a triangle is 180°

∴ m∠A = 180° - (36° + 21.1°) = 122.9°

* b = 29.4 units , m∠A = 122.9 , m∠C = 21.1°

Let's call them: W and L

Then area: A = W × L

We can replace: L = 2 × W

So: A = W × 2W=98→

2W^2=98 →W^2=98/2=49

→W=√49=7

→L=2×W=2×7=14

Conclusion: The rectangle is 7*14 ft

Hope this helps :)

Answer:

7 and 14 in simple terms, i got this right.

HAVE A BLESSED DAY!!!!!!

Explanation:

By checking the table for when y=0, Jose was looking for the number of rows such that the total number of seats is zero. Jose needed to check the table for when y = 416.

Doing that, Jose would find the number of rows to be -13 or +16. He would determine that the auditorium has 16 rows of seats.

Answer:

c. zero

Step-by-step explanation:

The expression on the left of the equal sign is a polynomial of degree 2. (The highest power of x is 2.) A polynomial of degree 2 is called a "quadratic." Values of the variable (x, in this case) that make the value of the quadratic be zero are called "zeros" or "roots" of the quadratic.

Every polynomial has as many roots as its degree. So, a second degree polynomial (quadratic) will have two roots. The roots may be real numbers, or they may be complex numbers. For polynomials of degree higher than 2, there may be some roots of each kind.

This question is asking, "How many roots of this quadratic are real numbers?"

___

There are several different ways you can figure out the answer to this question. One of the simplest is to graph the quadratic. (See attached.) You can see that the graph of the quadratic never has a y-value of zero, so there are no (real) values of x that will be solutions to this equation.

The two solutions are -0.25±i√1.1875. The "i" indicates that portion of the number is imaginary, and the entire number (real part plus imaginary part) is called a "complex" number. Both solutions for this quadratic are complex, not real.

__

Another way you can answer this question is to compute what is called the "discriminant." The roots of every quadratic of the form ax^2+bx+c can be found using the formula ...

x = (-b±√(b^2-4ac))/(2a)

For this quadratic, the values of a, b, and c are 4, 2, and 5, respectively. Then the formula becomes ...

x = (-2±√(2^2 -4·4·5))/(2·4) = (-2±√-76)/8

The value under the radical sign is the "discriminant." When it is negative, as here, the value of the square root is an imaginary number (not a real number), so the roots are complex. When the discriminant is zero, the two roots have the same value; when it is positive, there are two distinct roots.

There are zero real number solutions to this equation.

Answer:

see below

Step-by-step explanation:

Plot the points on the given graph. The ones that fall in on a solid line at the edge of the doubly-shaded area, or fall in the doubly-shaded area, are part of the solution set.

(0, 4) on the dashed line — not a solution

(-2, 4) on red line in blue area — solution

(0, 5) in doubly-shaded area — solution

(–2, 7) in doubly-shaded area — solution

(–4, 1) in blue area — not a solution

(–1, 1) on red line outside blue area — not a solution

(–1.5, 3.5) in doubly-shaded area — solution

Answer:

either 76 or 19

Step-by-step explanation:

76 if it's 1/5 of the original amount as well as 3/4 the original amount

1/5+3/4=19/20

3.80=1/20x

3.80+19/20x=76

3.8*20=76

19 if it's 1/5 of the original amount and 3/4 of the new amount

3.80=1/4y

3.80+3/4y=15.20

15.20=4/5x

15.20+1/5x=19

Answer:

[tex]\frac{1}{15}[/tex]

Step-by-step explanation:

Multiples of 3 (from 1 to 10) are 3, 6, and 9.

Multiples of 4 (from 1 to 10) are 4 and 8.

First,

Probability of selecting multiple of 3 from 10 total slips are 3/10

now since it is not replaced, we have to now think that there are 9  total slips.

Second,

Probability of selecting multiple of 4 from 9 total slips are 2/9

in probability "AND" means multiplication. Hence,

selecting 3 "AND" then selecting 4 means, we need to multiply the individual probabilities found.

So,

3/10 * 2/9 = 1/15

Answer:

1/15

Step-by-step explanation:

I just took the test

will you receive the grade immediately?

Answer:

21

Step-by-step explanation:

√(35x)

The prime factorization of 35 is 5×7.  To simplify the radical, the expression underneath must be a multiple of a perfect square.  So we need to choose a value of x that has either 5 or 7 as a factor.

21 has a factor of 7.  Let's see:

√(35×21)

√(5×7×3×7)

√(15×7²)

7√15

Answer:

  D)  y = 1/4 x^2

Step-by-step explanation:

For these functions, the leading coefficient can be considered to be either ...

  the vertical scale factor (larger ⇒ narrower)

  the square of the inverse of the horizontal scale factor.

In the latter case, the horizontal scale factor will be larger (wider) when its inverse and the square of its inverse are smaller.

Either way, you're looking for the smallest leading coefficient: 1/4.

Answer:

Sheridan is correct.

Step-by-step explanation:

She is correct because there is no B squared listed only A and C are provided, Jayden put 13 cm as B instead of listing it as C but she listed it correctly and answered everything else correctly.

Hope this helps!

Answer:

6

Step-by-step explanation:

If we are raising to the 5th power we have to allow for the constant at the end of it all.

Answer:

The answer is 6.

Answer:

Box 2

Step-by-step explanation:

Volume= l*w*h

            =2*3*1

            = 6ft3

Answer:

Box 2 is your answer

Step-by-step explanation:

Answer:

h(height)= 40cm

Step-by-step explanation:

V= h x w x l

(10000)= h x (25) (10)

h= (10000)/ ((25) (10))

h= (10000)/ ((250))  

h=40

You can verify if this is right by working the problem backwards.

V= (25) (10) (40)

V= 10, 000 cm^3

Answer:

h = 40 cm

Step-by-step explanation:

the formula for the volume of a rectangular box of width w, height h and depth d is V = w·h·d (the order in which you write these doesn't matter).

We want to find out how tall this box is.  Thus, we solve V = w·h·d for h:

            V

h = -------------

          w·d

Here, h = vertical measurement of box = ( 10000 cm³) / [ (25 cm)(10 cm) ], or

h = 40 cm

Answer:4

Step-by-step explanation:

The equation of a vertical parabola is:

y = a (x − h)² + k,

where (h, k) is the vertex and a is the coefficient.

We know the vertex is (-5, -2), so:

y = a (x − (-5))² + (-2)

y = a (x + 5)² − 2

We also know the parabola passes through (-4, 2).

2 = a (-4 + 5)² − 2

2 = a (1)² − 2

2 = a − 2

a = 4

So the coefficient of the squared expression is 4.

Answer:

The recursive rule is a1 = 3 , an = (1/6) a(n-1)

Step-by-step explanation:

* Lets revise the recursive formula for a geometric sequence:

1. Determine if the sequence is geometric (Do you multiply, or divide,

  the same amount from one term to the next?)

2. Find the common ratio. (The number you multiply or divide.)

3. Create a recursive formula by stating the first term, and then

   stating the formula to be the common ratio times the

   previous term.

# a1 = first term;

# an= r • a(n-1)

- Where:

- a1 = the first term in the sequence

- an = the nth term in the sequence

- an-1 = the term before the nth term  

- n = the term number

- r = the common ratio

* Lets solve the problem

∵ an = 3(1/6)^(n-1) ⇒ geometric sequence

∵ The explicit rule is an = a1(r)^n-1

∴ a1 = 3 and r = 1/6

- Lets write the recursive rule

∵ a1 = first term;

∵ an= r • a(n-1)

∴ a1 = 3

∴ an = (1/6) a(n-1)

* The recursive rule is a1 = 3 , an = (1/6) a(n-1)

Answer:

a1 = 3
an = 1/6a n-1

Step-by-step explanation:

i took the test

Answer:

The flux of F across S is 8.627.

Step-by-step explanation:

Given,

F(x, y, z) = xy i + yz j + zx k

or F=(xy, yz, zx)

S is the part of the paraboloid [tex]z=8-x^{2} -y^{2}[/tex] above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1

By differentiating z with respect to x we get:

fx=-2x

By differentiating z with respect to y we get:

fy=-2y

So, Surface integral is given by:

[tex]=\int\limits^1_0\int\limits^1_0( {(xy)*(2x)+y(8-x^{2} -y^{2} *(2y)+x(8-x^{2} -y^{2})} \, )dx \, dy[/tex][tex]=\int\limits^1_0\int\limits^1_0 (2x^{2} y+16y^{2} -2x^{2} y^{2} -2y^{4}+8x-x^{3}-xy^{2} } \,) dx \, dy[/tex]

Integrating with respect y:

[tex]=\int\limits^1_0(x^{2} y^{2} +\frac{16}{3} y^{3} -\frac{2}{3} x^{2} y^{3} -\frac{2}{5} y^{5}+8xy-x^{3}y-\frac{1}{3} xy^{3} } \, )dx \,[/tex]

After Substituting limits of y, we get:

[tex]=\int\limits^1_0(x^{2} +\frac{16}{3} -\frac{2}{3} x^{2} -\frac{2}{5}+8x-x^{3}-\frac{1}{3} x } \,) dx \,[/tex]

Integrating with respect x:

[tex]=(\frac{1}{3} x^{3} +\frac{16}{3}x -\frac{2}{9} x^{3} -\frac{2}{5}x+4 x^{2} -\frac{1}{4} x^{4}-\frac{1}{6} x^{2} } \,)[/tex]

After Substituting limits of x, we get:

[tex]=(\frac{1}{3} +\frac{16}{3} -\frac{2}{9} -\frac{2}{5}+4 -\frac{1}{4} -\frac{1}{6} } \,)\\\\=\frac{1553}{180}[/tex]

[tex]= 8.627[/tex]

Learn more: https://brainly.com/question/3607066

To evaluate the surface integral of the given vector field F across the given surface S, we need to use the formula: Φ = ∫∫S F · dS. In this case, the vector field F(x, y, z) = xy i + yz j + zx k and the surface S is the part of the paraboloid z = 8 - x^2 - y^2 that lies above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, with upward orientation. We can parametrize the surface S and calculate the normal vector to evaluate the surface integral using the given formula.

To evaluate the surface integral of the given vector field F across the given surface S, we need to use the formula:

Φ = ∫∫S F · dS

In this case, the vector field F(x, y, z) = xy i + yz j + zx k and the surface S is the part of the paraboloid z = 8 - x2 - y2 that lies above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, with upward orientation.

We can parametrize the surface S as r(u, v) = (u, v, 8 - u2 - v2), where 0 ≤ u ≤ 1 and 0 ≤ v ≤ 1.

Next, we calculate the normal vector to S by taking the cross product of the partial derivatives of r(u, v) with respect to u and v: N = (-∂r/∂u) x (-∂r/∂v) = (2u, 2v, 1).

Now, we can evaluate the surface integral using the formula:

Φ = ∫∫S F · dS = ∫∫R F(r(u, v)) · (N · (∂r/∂u) x (∂r/∂v)) du dv

Substituting the values for F and N, we get:

Φ = ∫∫R (u2v + 4uv + 4uv) (2u, 2v, 1) · (2u, 2v, 1) du dv

Calculating this integral over the region R: 0 ≤ u ≤ 1 and 0 ≤ v ≤ 1, we find the flux of F across S.

Answer:

0.19

Step-by-step explanation:

μ = 160 and σ = 50.  Find the z scores for 180 and 210.

z = (x - μ) / σ

z = (180 - 160) / 50 = 0.40

z = (210 - 160) / 50 = 1.00

So we want P(0.40<z<1.00).  This can be found as:

P(0.40<z<1.00) = P(z<1.00) - P(z<0.40)

Now use a calculator or table to find each probability:

P(0.40<z<1.00) = 0.8413 - 0.6554

P(0.40<z<1.00) = 0.1859

Rounded to the nearest hundredth, P ≈ 0.19.

Final answer:

The probability of a Major League Baseball game lasting between 180 and 210 minutes is approximately 0.19 when assuming normal distribution with a mean of 160 minutes and a standard deviation of 50 minutes.

Explanation:

The probability of a Major League Baseball game duration being between 180 and 210 minutes can be calculated using the Z-score formula, which is Z = (X - μ) / σ, where X is the value in question, μ is the mean, and σ is the standard deviation. In this case, the mean (μ) is 160 minutes, and the standard deviation (σ) is 50 minutes.

First, we find the Z-score for 180 minutes:

Z1 = (180 - 160) / 50 = 0.4

Then, we find the Z-score for 210 minutes:

Z2 = (210 - 160) / 50 = 1.0

Using a Z-table or a calculator with normal distribution functions, we can find the probabilities corresponding to these Z-scores:

P(Z < Z1) = P(Z < 0.4)

P(Z < Z2) = P(Z < 1.0)

To find the probability of a game duration between 180 and 210 minutes, subtract the probability of Z1 from the probability of Z2:

P(180 < X < 210) = P(Z < Z2) - P(Z < Z1)

Assuming the probabilities from Z-table or calculator:

P(Z < Z2) = 0.8413 (approximately)

P(Z < Z1) = 0.6554 (approximately)

Therefore:

P(180 < X < 210) = 0.8413 - 0.6554 = 0.1859

So the probability, rounded to the nearest hundredth, that a game will last between 180 and 210 minutes is approximately 0.19.

Answer:h

Step-by-step explanation:

Answer:

Volume of the Right Triangular Prism is 1771 m³.

Step-by-step explanation:

Given:

A Right Triangular base Prism.

Length of the legs of the right triangle of the base is 14 m , 23 m

Hypotenuse of the triangle is 26.9 m

Height of the Prism is 11 m

To find: volume of the Prism.

We know that Volume of the Prism = Base Area × Height

Volume of the Right Triangular Prism = Area of Base Triangle × Height

                                                              = 1/2 × 14 × 23 × 11

                                                              = 7 × 23 × 11

                                                              = 1771 m³

Therefore, Volume of the Right Triangular Prism is 1771 m³.

Answer:

1,771

Step-by-step explanation:

When you mark up a price, multiply the original price by 1 plus the amount of the mark up as a decimal.

15% = 0.15 + 1 = 1.15

$60 x 1.15 = $69

The correct answer is $69 Start by putting 15 into a decimal

Answer:

x ≈ 6.6 cm

Step-by-step explanation:

The Pythagorean theorem applies. The sum of the squares of the legs of this right triangle equals the square of the hypotenuse:

x^2 + 13.5^2 = (x+8.45)^2

x^2 +182.25 = x^2 +16.9x +71.4025

110.8475 = 16.9x . . . . . subtract x^2 +71.4025

6.559024 = x . . . . . . . .divide by 16.9

The value of x is about 6.6 cm.

Answer:

D. 7

Step-by-step explanation:

The given expression is

[tex]\frac{5x-18}{x-7}[/tex]

This is a rational expression.

This expression undefined, when the denominator is zero.

We equate the denominator to zero  to get;

[tex]x-7=0[/tex]

This implies that;

x=7

Answer:

The correct answer option is 7.

Step-by-step explanation:

We are given the following expression and we are to determine whether which of the given options for the value of x would the expression become undefined:

[tex] \frac { 5 x - 1 8 } { x - 7 } [/tex]

We know that the expression is undefined when the denominator equals zero. So to make the denominator zero, the value of x should be 7.