Solve the equation. Give the solution in exact form.
log 4[(x + 7)(x - 5)] = 3

Answer:

\(\frac{50}{7}\)

Step-by-step explanation:

\(5\div \frac{7}{10}\)

Convert to fraction:

Apply fraction rule: \(\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}\)

Multiply fraction:

Multiply :

OAmalOHopeO

Answer:

my favorite christmas song is white christmas

Step-by-step explanation:

This looks simple I belive the answer would be 35 because 4^x + 31^x = 35^x

Answer:

Let's assume the first number is represented by the variable 'x'.

According to the given information, the second number is 4 less than three times the first number. In other words, the second number can be represented as 3x - 4.

The sum of the two numbers is 44, so we can set up the equation:

x + (3x - 4) = 44

Now, we can solve this equation to find the value of 'x':

4x - 4 = 44

Adding 4 to both sides of the equation:

4x = 48

Dividing both sides by 4:

x = 12

So the first number is 12.

To find the second number, we can substitute the value of x back into the equation:

3x - 4 = 3(12) - 4 = 36 - 4 = 32

Therefore, the second number is 32.

Step-by-step explanation:

Points $a$, $b$, $c$, and $d$ are the midpoints of the sides of the larger square. If the larger square has an area of 60, the smaller square's area is 15 square units.

A square's midpoints connect, making it possible to divide the square into four equal squares. Each of these four squares has a side length of half that of the larger square.

Consider the fact that the area of the larger square is 60, with sides of $s$ units. \($s^2=60$\\\). Now, the smaller square is created by connecting the midpoints of the larger square. Each side of the smaller square has a length of \($s/2$\) units.

Since the area of a square is \($s^2$\), the area of the smaller square is \($\left(\frac{s}{2}\right)^2$\). Simplifying gives \($\left(\frac{s}{2}\right)^2=\frac{s^2}{4}$\). So, the area of the smaller square is \($\frac{1}{4}$\) of the larger square's area.

We know that the area of the larger square is 60. Therefore, the area of the smaller square is \($\frac{1}{4}$\) (60) = 15 square units.

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Answer:

D.

Step-by-step explanation:

4.526 x 10^6 = 4,526,000.

55,246,900 is greater than this.

Answer: Hi!

First, we will find value of the equation given, 4.526 * 10^6.

We will solve the exponent first.

10^6 = 10*10*10*10*10*10 = 1,000,000

Now, we will multiply 1,000,000 by 4.526.

4.526 * 1,000,000 = 4,526,000

4,526,000 is the value of 4.526 * 10^6.

We can automatically tell that d), 55,264,900 is greater than 4,526,000. Therefore, d) is your answer.

Hope this helps!

Answer:373248

Step-by-step explanation:

72^3 = 373248

Answer:

9/8

Step-by-step explanation:

divide 3/4 by 2/3

use the KCF method

so your gonna get 3/4 divided 2/3 then change the division to multiplcation and then flip the 2/3 to 3/2

now multiply across: 3/4 × 3/2=9/8

Answer:

B

Step-by-step explanation:

took test on edg

Based on the amount paid per $1,000 of face value, the face value of a 10-year term insurance policy on a 24-year-old male will be a. $75,000.

This can be found by the formula:

= 1,000 x (Annual premium / Amount paid per $1,000 coverage for 24 year old male for 10 year policy)

Solving gives:

= 1,000 x (359.25 / 4.79)

= 1,000 x 75

= $75,000

In conclusion, option A is correct.

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The value of m<1 based on the given diagram is 53°

Let

m<1 = y

So,

(20x + 7) + y = 180°

Angles on a straight line

20x + 7 + y = 180

20x + y = 180 - 7

20x + y = 173

79° + 8x + y = 180° (sum of angles in a triangle)

8x + y = 180 - 79.

8x + y = 101

20x + y = 173

8x + y = 101

Subtract

12x = 72

x = 72/12

x = 6

Substitute into (1)

(20x + 7) + y = 180°

20(6) + 7 + y = 180

120 + 7 + y = 180

127 + y = 180

y = 180 - 127

y = 53°

Therefore, m<1 is 52° and x is 6

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Rows of chairs that are needed to make 48 musicians sit is 8 rows.

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers.

Given,

Number of musicians in orchestra

18 string musicians, 9 percussion musicians,

15 brass musicians, and 12 woodwind musicians

Total number of musicians

= 18 + 9 + 15 + 12

= 54

Six of the musicians cannot play in the next performance

Number of musicians playing in next performance

= 54 - 6

= 48

48 musicians will sit on 48 chairs

Number of chairs in one row = 6

Number of rows for 48 chairs = 48/6 = 8

Hence, 8 rows of chairs are needed to make 48 musicians sit.

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Answer: b the second answer

Step-by-step explanation:

Answer:

Tyler can swim 1.5 miles per hour

Step-by-step explanation:

The ratio of the circumferences of the bases of the two cylinders is; 25

Formula for lateral surface area of a cylinder is;

LSA = 2πrh

Thus,for first cylinder;

2πrh = 6π

Thus;

rh = 3 - - - - (eq 1)

Similarly;

2πr2h = 150π

r2h = 75 - - - (eq 2)

Divide eq 2 by eq 1 to get;

r2/r = 75/3

r2/r = 25

r2 = 25r

Thus;

Circumference of base of bigger cylinder = 2π(25r) = 50πr

Circumference of smaller cylinder = 2πr

Thus;

Ratio = 50πr/2πr

Ratio = 25

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Answer:

Circle

Step-by-step explanation:

Examples of conic sections are the circle, the ellipse, the parabola and the hyperbola. Parametric equations are used to express the x and y variables in terms of a less complicated manner using a third variable (t or θ).

The parametric equation for a circle with an equation \((x-h)^2+(y-k)^2=r^2\) is given by:

\(x=rcos(t)+h, y=rsin(t)+k\)

where r is the radius of the circle and (h, k) is the center of the circle.

A conic section with a parametric equations X=3cos(t)-1, y=3sin(t)+4 is a circle with center at (-1, 4) and radius of 3. The equation of the circle is:

(x + 1)² + (y - 4)² = 3²

The interval of convergence for the given power series is (2, 8).

To find the interval of convergence for the given power series. We have the power series:

∑(n=2 to ∞) ((x-5)ⁿ)/(3ⁿ)

To find the interval of convergence, we'll use the Ratio Test. For the Ratio Test, we need to compute the limit:

L = lim (n → ∞) |(a_(n+1)/a_n)|

For our series, a_n = ((x-5)ⁿ)/(3ⁿ). Therefore, a_(n+1) = ((x-5)(n+1))/(3(n+1)). Now, let's compute the ratio:

|(a_(n+1)/a_n)| = |(((x-5)(n+1))/(3(n+1))) / (((x-5)ⁿ)/(3ⁿ))|

Simplify the expression:

|(a_(n+1)/a_n)| = |(x-5)/3|

The series converges if L < 1. So we have:

|(x-5)/3| < 1

Now, we'll solve for x to find the interval of convergence:

-1 < (x-5)/3 < 1

Multiply each term by 3:

-3 < x-5 < 3

Add 5 to each term:

2 < x < 8

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Answer:

I'll give you some clues in the solution. Please read them so you can do the rest faster.

Solution:

First thing you do is write the vertex. The vertex is basically the last number in the absolute value bars and the number outside of them (to the right of the bars). The vertex is the opposite of the last number in the absolute value brackets and if there is no number to the right, assume it is 0.

We start at (2,0).

The domain is 99% of the time all real numbers. Write that for domain.

The range is the y value where things start to increase (the y value of the vertex). The range is 0.

The type of function is absolute value function btw

The individual events of drawing and eating two red pieces of candy in a row from a bag are dependent. The probability of the second event is influenced by the outcome of the first event, since one red candy has already been removed from the bag.

The probability of drawing a red candy from the bag on the first attempt is 6/37. Once the first red candy has been drawn and eaten, there are now 5 red candies left in the bag out of 36 total candies. Therefore, the probability of drawing and eating a second red candy from the bag is now 5/36.

The probability of the combined event of drawing and eating two red candies in a row can be found by multiplying the probability of the first event by the probability of the second event, since the events are dependent:

P(drawing and eating two red candies in a row) = P(drawing a red candy on the first attempt) x P(drawing a red candy on the second attempt, given that a red candy was drawn on the first attempt)

P(drawing and eating two red candies in a row) = (6/37) x (5/36)

P(drawing and eating two red candies in a row) = 5/222

Therefore, the probability of drawing and eating two red candies in a row from the bag is 5/222 or approximately 0.0226.

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As a result, there is a 23.3 degree depression in the angle between the balloon and its final location.

A person on the ground is 36° lower than a hot air balloon in the air at this angle of depression. The new angle of depression is 25° if the subject moves backwards by 10 feet.

The tangent function allows us to write:

tan θ = opposite / adjacent

Therefore:

tan θ = 7800 / 17952

tan θ ≈ 0.435

To find θ, we need to take the inverse tangent (or arctan) of both sides:

θ = arctan(0.435)

Using a calculator, we get:

θ ≈ 23.3 degrees

As a result, there is a 23.3 degree depression in the angle between the balloon and its final location.

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The value of 6 / 8 - 4/7  is 5/28.

what is fraction ?

A fraction is a numerical representation of a part of a whole or a ratio of two numbers. It is written as a number or expression in the form of a numerator and a denominator separated by a horizontal line or slash.

6/8 - 5/8

To subtract fractions with the same denominator, simply subtract the numerators and keep the denominator the same:

6/8 - 5/8 = (6 - 5)/8 = 1/8

Therefore, 6/8 - 5/8 = 1/8.

20/5 - 12/5

Again, we have fractions with the same denominator, so we can subtract the numerators and keep the denominator the same:

20/5 - 12/5 = (20 - 12)/5 = 8/5

Therefore, 20/5 - 12/5 = 8/5.

6/8 - 4/7

To subtract fractions with different denominators, we need to find a common denominator. In this case, we can use the least common multiple of 8 and 7, which is 56.

To get the equivalent fractions with a denominator of 56, we need to multiply the numerator and denominator of each fraction by the appropriate factor:

6/8 * 7/7 = 42/56

4/7 * 8/8 = 32/56

Now we can subtract the numerators and keep the denominator the same:

42/56 - 32/56 = 10/56

We can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:

10/56 = 5/28

Therefore, The value of 6/8 - 4/7  is 5/28.

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Answer:

Step-by-step explanation:

You want two methods of choosing points on the line with slope 1/2 through A(-1, 2).

Writing the equation in standard form, we can find the x- and y-intercepts. To get there, we can start from point-slope form:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -2 = 1/2(x -(-1)) . . . . . using given slope and point

  2y -4 = x +1 . . . . . . . . . . multiply by 2

  x -2y =  -5 . . . . . . . . . . . . add -1 -2y

Setting x=0 tells us the y-intercept is ...

  0 -2y = -5

  y = -5/-2 = 5/2

So, the y-intercept is (0, 5/2).

Setting y=0 tells us the x-intercept is ...

  x -2(0) = -5

  x = -5

So, the x-intercept is (-5, 0).

It will be convenient to choose an arbitrary y-value to find another point on the line. We can pick y = 6, for example, Then the corresponding x-value is ...

  x -2y = -5

  x = -5 +2y = -5 +2(6) = 7

Another point on the line is (7, 6).

__

Additional comment

If we were to choose an arbitrary value for x, we would want it to be odd, so the corresponding y-value would be an integer. We chose to pick an arbitrary value of y so we didn't have to worry about how to make the x-value an integer.

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Answer:

6,2

Step-by-step explanation:

The fourth point of the parallelogram will be (-6,1) so option (C) will be correct.

A basic quadrilateral with two sets of parallel sides is known as a parallelogram.

A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

There are 4 types of parallelograms, including 3 special types. The four types are parallelograms, squares, rectangles, and rhombuses.

The slope of the green lines and red line should be same for being it a parallelogram.

Slope of green line = (7-2)/(3-1) = 2.5

So the only coordinate is matching the slope 2.5 of red line is (-6,1).

Slope = (6-1)/(-4+6) = 2.5

Hence "The fourth point of the parallelogram will be (-6,1)".

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Answer:

-26!!!! :))))

Step-by-step explanation:

Answer: 941.33 inches squared

Step-by-step explanation:

You will find the area of each shape separately, then add them together.

The area of a square is s²

26² = 676

Area of a semicircle is 1/2(πr²)

1/2((3.14)(13)²)

1/2((3.14)(169))

1/2(530.66)

265.33

676 + 265.33 = 941.33 inches squared

Hope this helps!

Evidence points to the Egyptians using gypsum mortar – also known as plaster of Paris – in constructing pyramids during the Pharaonic period. The first Egyptologist to identify this method was Alfred Lucas in 1926.

The value of the angle m∠2 = 67°.

Angle may be defined as the space between two lines. An angle consists of a vertex with which the angle is extended. When sum of two angles is exactly 90°, they are called complementary angles. For example, if we have two angles a and b then, ∠a + ∠b = 90°. When sum of two angles is exactly 180°, they are called supplementary angles. For example, if we have two angles a and b then, ∠a +∠b =180°. According to the given question ∠1 is a complement of ∠2 and we know when two angles are complementary to each other sum of their angles is 90°. So,

m∠1 + m∠2 = 90°

Now, m∠1 = 23°

23° + m∠2 = 90°

m∠2 = 90° - 23°

m∠2 = 67° which is required angle.

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Answer:

is there an actual graph though that would really help

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

10 of 50 can be written as:1050To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 1001050 × 100100= (10 × 10050) × 1100 = 20100 Therefore, the answer is 20%

Answer:

A

Step-by-step explanation:

The equation representing a proportional relationship is

y = kx ← k is the constant of proportion

The only equation in this form is

y = 24x ( k = 24 ) → A