Which of the following is equivalent to the expression below ? log 3 -log 15

Answer:

m<PQR = 37°

Step-by-step explanation:

7x - 19 = x + 16 + 2x -3  Combine like terms

7x -19 = 3x +13  Subtract 3x from both sides

4x -19 = 13  Add 19 to both sides

4x = 32  Divide both sides by 4

x = 8

m<PQR = 7x - 19  Substitute in 8 for x

7(8) - 19

56 - 19 = 37

Answer:

∠PQR = 37°

Step-by-step explanation:

In this problem, ∠PQR is the exterior angle of ΔOPQ.

⭐What is an exterior angle of a triangle?

We are given the expressions for ∠OPQ and ∠QOP, which are opposite of the external angle.

Therefore, we can follow these steps to find ∠PQR:

1. Utilize the exterior angle theorem to solve for x

2. Substitute x into the expression for ∠PQR to solve for ∠PQR

⭐What is the exterior angle theorem?

1. Utilize the exterior angle theorem to solve for x

∠PQR = ∠OPQ + ∠QPO

(7x-19) = (2x-3) + (x+16) . . . . . substitute the given expressions

7x - 19 = 3x + 13 . . . . . . . . . . . add like terms (terms with the same variable and exponent)

4x = 32 . . . . . . . . . . . . . . . . . . subtract 3x from the LHS and RHS and add 19 on the LHS and RHS

∴ x = 8 . . . . . . . . . . . . . . . . . . . . divide the LHS and RHS by 4 to isolate x

2. Substitute x into the expression for ∠PQR to solve for ∠PQR

∠PQR = 7x-19

∠PQR = 7(8) - 19

∠PQR = 56 - 19

∴ ∠PQR = 37°

⭐if this response helped you, please mark it the "brainliest"!⭐

hence , 2√5 = √20

The equation of the Parabola in vertex form that has a vertex of (4, -2) and a y-intercept of (0, -66) is:y = -4(x - 4)^2 - 2

The vertex form of a parabola is given by:y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola.

We are given that the vertex is (4, -2), so we can substitute these values in the equation to get:y = a(x - 4)^2 - 2

Now, we need to find the value of "a". To do this, we can use the fact that the y-intercept is (0, -66). Since the point (0, -66) lies on the parabola, we can substitute x = 0 and y = -66 in the equation above to get:-66 = a(0 - 4)^2 - 2

Simplifying this, we get:-66 = 16a - 2

Adding 2 to both sides, we get:-64 = 16a

Dividing both sides by 16, we get:a = -4

Substituting this value of "a" in the equation above, we get the equation of the parabola in vertex form:y = -4(x - 4)^2 - 2

Therefore, the equation of the parabola in vertex form that has a vertex of (4, -2) and a y-intercept of (0, -66) is:y = -4(x - 4)^2 - 2

To know more abut Parabola .

https://brainly.com/question/21414275

#SPJ11

The number that can complete the equation 5y + 2(3y − 1) = ⬜y − (y + 2) is

5y + 2(3y − 1) = 12 y − (y + 2)

The number that can complete the equation is computed by simplifying the equation at the left hand side of the equality sign and comparing with the right side of the equality side

The comparison will show the number that can fit in the blank

Simplifying the equation at the left hand side of the equation

= 5y + 2(3y − 1)

= 5y + 6y − 2

= 11y - 2

Simplifying the equation at the right hand side of the equation

=  ⬜y − (y + 2)

let x represent the missing number

=  xy − (y + 2)

=  xy − y - 2

comparing both equations

11y - 2 =  xy − y - 2

11y =  xy − y

11y + y =  xy

12y = xy

x = 12

The missing value = 12

Learn more about equations at:

https://brainly.com/question/18831322

#SPJ1

Answer:

A

Step-by-step explanation:

For a right triangle

\(A=\frac{ab}{2} \\\frac{(10.4)(15.3)}{2} =79.56\)

This is the same as the other triangle because they are the same size because of congruency

Area of the rectangle

\(a^2+b^2=c^2\\\)

\(\sqrt{(10.4^2+15.3^2} =c\)

\(c= 18.5\)

18.5 x 7 = 129.5

Add them all up

129.5+79.56+79.56= 288.62

Step-by-step explanation:

This is a geometric series where our common ratio is -1/2, and a is -4

Since r is less than -1, this series converges so

The sun is

\( \frac{ - 4}{1 + 0.5} \)

\( \frac{ - 4}{1.5} = - \frac{8}{3} \)

The sum is -8)3

Answer:

y = 5

Step-by-step explanation:

\(14y-7y=35\\7y=35\\y=5\)

14 minus 7 is 7

7Y is equal to 35

divide both sides by 7 is equal to 5

When Henry ran 1 5/8 miles in the morning and 9/10 miles in the afternoon, In all he a total of 2 21/40 miles

The number of miles Henry ran is calculated by addition operation

The sum of the miles Henry ran in the morning plus the number of miles he ran in the afternoon gives the what Henry ran in all

The procedure involves addition of tractions and done as follows

= 1 5/8 + 9/10

= 13/8 + 9/10

adding both fractions will result to

= 101/40 miles

= 2 21/40 miles (as a mixed number)

Henry ran a sum of 2 21/40 miles

Learn more about addition of fractions:

https://brainly.com/question/29321903

#SPJ1

Answer:

If you want to use the Rational Zeros Theorem, as instructed, you need to use synthetic division to find zeros until you get a quadratic remainder.

P: ±1, ±2, ±3, ±6  (all prime factors of constant term)

Q: ±1, ±7              (all prime factors of the leading coefficient)

P/Q: ±1, ±2, ±3, ±6, ±1/7, ±2/7, ±3/7, ±6/7  (all possible values of P/Q)

Now, start testing your values of P/Q in your polynomial:

f(x)=7x4-9x3-41x2+13x+6

You can tell f(1) and f(-1) are not zeros since they're not = 0Now try f(2) and f(-2):

f(2)=7(16)-9(8)-41(4)+13(2)+6

       112-72-164+26+6 ≠ 0

f(-2)=7(16)-9(-8)-41(4)+13(-2)+6

       112+72-164-26+6 = 0  OK!! There is a zero at x=-2

This means (x+2) is a factor of the polynomial.

Now, do synthetic division to find the polynomial that results from

(7x4-9x3-41x2+13x+6)÷(x+2):

-2⊥ 7   -9   -41    13     6

         -14   46   -10    -6          

      7  -23   5       3     0     The remainder is 0, as expected

The quotient is a polynomial of degree 3:

7x3-23x2+5x+3

Now, continue testing the P/Q values with this new polynomial.  Try f(3):

f(3)=7(27)-23(9)+5(3)+3

      189-207+15+3 = 0  OK!!  we found another zero at x=3

Now, another synthetic division:

3⊥ 7   -23    5     3

          21   -6   -3_

    7    -2    -1    0  

The quotient is a quadratic polynomial:

7x2-2x-1  This is not factorable, you need to apply the quadratic formula to find the 3rd and 4th zeros:

x= (1±2√2)÷7

The polynomial has 4 zeros at x=-2, 3, (1±2√2)÷7

Step-by-step explanation:

Step-by-step explanation:

Here you go i think its good

Answer:

7

Step-by-step explanation:

:)

Answer:

D: 7

Explanation: after the decimal, its tenths, hundredths, thousandths

Answer:

See below for explanation

Step-by-step explanation:

The area of an isosceles triangle is \(A=\frac{1}{2}bh\), so let's write the base as an equation of y:

\(\displaystyle 9x^2+4y^2=36\\\\4y^2=36-9x^2\\\\y^2=9-\frac{9}{4}x^2\\\\y=\pm\sqrt{9-\frac{9}{4}x^2\)

As you can see, our ellipse consists of two parts, so the hypotenuse of each cross-section will be \(\displaystyle 2\sqrt{9-\frac{9}{4}x^2\), and each height will be \(\displaystyle \sqrt{9-\frac{9}{4}x^2}\).

Hence, the area function for our cross-sections are:

\(\displaystyle A(x)=\frac{1}{2}bh=\frac{1}{2}\cdot2\sqrt{9-\frac{9}{4}x^2}\cdot\sqrt{9-\frac{9}{4}x^2}=9-\frac{9}{4}x^2\)

Since we'll be integrating with respect to x because the cross-sections are perpendicular to the x-axis, then our bounds will be from -2 to 2 to find the volume:

\(\displaystyle V=\int^2_{-2}\biggr(9-\frac{9}{4}x^2\biggr)\,dx\\\\V=9x-\frac{3}{4}x^3\biggr|^2_{-2}\\\\V=\biggr(9(2)-\frac{3}{4}(2)^3\biggr)-\biggr(9(-2)-\frac{3}{4}(-2)^3\biggr)\\\\V=\biggr(18-\frac{3}{4}(8)\biggr)-\biggr(-18-\frac{3}{4}(-8)\biggr)\\\\V=(18-6)-(-18+6)\\\\V=12-(-12)\\\\V=12+12\\\\V=24\)

Therefore, this explanation confirms that the correct volume is 24!

Answer:

42/11

Step-by-step explanation:

11/7 = 6/v

cross multiply:

11v = 6x7 = 42.

v = 42/11 ≈ 3.81

The most appropriate choice for arithmetic and geometric series will be given by-

P = 0, Q = 4 , R = 8, S = 16 or P = 15, Q = 9, R = 3, S = 1 are the required numbers

What is arithmetic and geometric series?

Arithmetic series are those series whose difference between two consecutive terms are same.

Geometric series are those series whose ratio between two consecutive terms are same.

Here,

P, Q and R forms an Arithmetic sequence

Let P = a - d , Q = a, R = a + d, Where a is the first term of the Arithmetic sequence and d is the common difference of the sequence.

Let S = b

Q, R and S forms a Geometric sequence

\(\frac{a + d}{a} = \frac{b}{a +d}\)

\((a + d)^2 = ab\\a^2 + d^2 + 2ad = ab\\\) ............... (1)

Now the sum of first and fourth number is 16

a - d + b = 16

b = 16 - a + d

Putting the value of b in (1),

\(a^2 + d^2 + 2ad = a(16 - a +d)\\a^2 + d^2 + 2ad = 16a -a^2+ad\\a^2+a^2 + d^2+2ad - ad - 16a = 0\\2a^2 + ad+d^2 -16a = 0\)............ (2)

Sum of second and third number is 12

\(a + a + d = 12\\2a +d = 12\\d = 12-2a\)

Putting the value of d in (2)

\(2a^2 + a(12 - 2a)+(12 - 2a)^2-16a = 0\\2a^2 + 12a - 2a^2+144-48a+4a^2 - 16a = 0\\4a^2-52a+144=0\\4(a^2-13a+36)=0\\a^2 -13a+36=0\\a^2-9a-4a+36=0\\a(a - 9)-4(a-9)=0\\(a-4)(a-9) = 0\\\)

\(a - 4 = 0\) or \(a - 9 = 0\)

\(a = 4\) or \(a = 9\)

When a = 4,

\(d = 12 - 2\times 4\\d = 12 - 8\\d = 4\)

\(b = 16 - 4+4\\b = 16\)

P = 4 - 4 = 0

Q = 4

R = 4 + 4 = 8

S = 16

When a = 9,

\(d = 12 - 2\times 9\\d = 12 - 16\\d = -6\)

\(b = 16 - 9-6\\b = 1\)

P = 9 - (-6) = 15

Q = 9

R = 9 + (-6) = 3

S = 1

To learn more about arithmetic and geometric series, refer to the link:

https://brainly.com/question/24643676

#SPJ9

Answer:

24 minutes

Step-by-step explanation:

t=d/s

t=30mi/75mph

t=0.4h

0.4×60=24 minutes

Answer:

\(w^{22}\)

Step-by-step explanation:

\((w^3)^4\cdot(w^5)^2=w^{3*4}\cdot w^{5*2}=w^{12}\cdot w^{10}=w^{12+10}=w^{22}\)

The solution to the equation 10+4y=-4y+2 is -1 because the variable y represents the same value.

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

10+4y=-4y+2

8y=-8

y=-1

The solution of equation 10+4y=-4y+2 is -1 as the variable y represents the same value.

To know more about equation,

https://brainly.com/question/2228446

#SPJ1

Based on the information provided, the missing number would be number 6.

When it comes to finding missing numbers, the first step is to decipher or identify the pattern. This can be either a sequence of numbers or the application of a specific mathematical operation such as subtraction or addition.

In this case, we can see there is a sequence of numbers that seems to go from 1 to 9. However, if you check carefully, the number 6 is missing, which is the number you need to add.

Learn more about numbers in https://brainly.com/question/24908711

#SPJ1

Answer:

The answers are 5 10

Step-by-step explanation:

Answer:

5.10!!!

Step-by-step explanation:

Answer:

1, 4, 6.

Step-by-step explanation:

\(\left(2n+8\right)\left(n+4\right)=2n^2+16n+32\)

1. \(2(x+4)^2=2n^2+16n+32\)

2. \(2\left(n+4\right)\left(n+4\right)=2(n+4)^2\)

3. \(16n+32=16n+32\)

4. \(2n^2+16n+32=2n^2+16n+32\)

5. \(2n^2+8n+32=2n^2+8n+32\)

6. \(2(n^2+8n+16)=2n^2+16n+32\)

As you can see from the answers it is 1, 4, and 6.

Answer:

534 is the mean.

Step-by-step explanation:

to calculate the mean you add all the numbers together (for example this set of numbers):

785, 585, 465, 409, 495, 465

=3204

then divide the number of numbers that you added together , (in this case 6)

3204/6

=

534

The length of each side of the wood is 5 centimetres.

Doug has 8 square pieces of wood. Each piece of wood have a side length of s cm. The total area of all 8 pieces of wood is 200 cm².

Hence, using quadratic equation let's find the length of each side of the wood.

Therefore,

8s² = 200

Hence,

8s² = 200

divide both sides of the equation by 8

s² = 200 / 8

s² = 25

s = √25

s = 5 centimetres

learn more on quadratic equation here: https://brainly.com/question/22364785

#SPJ1

Answer:

31

Step-by-step explanation:

replace the values of a and b in the given term

=2a x 3 + b

2(5) x 3 + (1)

2x5 x 3 + 1

10 x 3 + 1

30 + 1

31

Answer:11

Step-by-step explanation:

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

For more such questions on homework

https://brainly.com/question/28521601

#SPJ8

Answer:

<N is corresponding to <P   and  <P and <L correspond

Step-by-step explanation:

Corresponding angles: any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal.

To improve understanding of this topic look up corresponding angles and go to pictures. I believe it shows a more clear example

Hope this helps :D

Answer:2200 seats per minute

Step-by-step explanation:

draw a line from 6 minutes upwards till your line and the line on the graph meet then where the line meets draw another line going across(left)

Read across (left side) and the number will be your answer

Answer: The surface area of the rectangular prism is approximately 4 square yards.

Step-by-step explanation: Given that the volume of the rectangular prism is 160 cubic yards, we can find the dimensions of the prism using the formula:

V = lwh

where V is the volume, l is the length, w is the width, and h is the height.

So, we have:

160 = lwh

Now, we need to find two other measurements in order to calculate the surface area of the rectangular prism. However, we do not have enough information to find all three dimensions. Therefore, we will assume one dimension and find the other two.

Let's assume that the height of the rectangular prism is 10 yards. Then, we can rearrange the formula for the volume to solve for the product of the length and width:

lw = V/h = 160/10 = 16

Now, we have two equations:

lw = 16

wh = 160/10 = 16

Solving for w in the first equation, we get:

w = 16/l

Substituting this expression for w in the second equation, we get:

l(16/l)h = 16

Simplifying, we get:

h = 1

Therefore, the dimensions of the rectangular prism are:

length = l

width = 16/l

height = 10

Now, we can calculate the surface area of the rectangular prism using the formula:

SA = 2lw + 2lh + 2wh

Substituting the values we found, we get:

SA = 2(l(16/l)) + 2(l(10)) + 2((16/l)(10))

SA = 32/l + 20l + 160/l

To find the minimum value of this expression, we can take its derivative with respect to l and set it equal to zero:

dSA/dl = -32/l^2 + 20 + (-160/l^2)

0 = -32/l^2 + 20 - 160/l^2

52/l^2 = 20

l^2 = 52/20

l ≈ 1.44

Substituting this value of l back into the expression for SA, we get:

SA ≈ 4 square yards

Therefore, the surface area of the rectangular prism is approximately 4 square yards.