A scientist studied a population of 300 lizards. It was revealed that 25/300 lizards had red spots on their back. Based on the results of her study, how many lizards in the population did NOT have spots on their backs

Answer:

(10 + 11y)(10 - 11y)

Step-by-step explanation:

100 - 121y²

This is a special factoring called difference of squares. Since both of the numbers in the subtraction expression are perfect squares, we can use this rule:

a² - b² = (√a² - √b²)(√a² + √b²)

Take the square root of each number. Add them in one bracket, subtract them in the other bracket.

(10 + 11y)(10 - 11y)

100 is a perfect square because its square root is a whole number.

√100 = 10

121y² is a perfect square because its square root is a whole number, and its variable is squared.

√121 = 11

√y² = y

Answer:

(10 + 11y)(10 - 11y)

Step-by-step explanation:

difference of squares :)

Answer: 5 hours

Step-by-step explanation: 5 hours because 7/5 *5/1=35/5 and 35 divided by 5 equals 7

Answer:

7.3 divided by 4.38

Step-by-step explanation:

Answer:

[tex]8 {m}^{2} {n}^{3} - 24 {m}^{2} {n}^{2} + 4 {m}^{3}n = 4 {m}^{2} n(2 {n}^{2} - 6n + m)[/tex]

Step-by-step explanation:

The given expresion is

[tex]8 {m}^{2} {n}^{3} - 24 {m}^{2} {n}^{2} + 4 {m}^{3}n[/tex]

Observe that 4 is common to 8,-24, and 4

Observe also that, m²n is common to all the terms.

Hence the GCF is:4m²n

We factor the GCF to get;

[tex]8 {m}^{2} {n}^{3} - 24 {m}^{2} {n}^{2} + 4 {m}^{3}n = 4 {m}^{2} n(2 {n}^{2} - 6n + m)[/tex]

Answer:

-1 and 4

Step-by-step explanation:

multiply -1 and 4 to get -4.

-1 x 4 = -4

add 4 to -1 to get (positive) 3.

-1 + 4 = 3

hope this helps :)

Answer:

6 lots of 5 means 6×5=30

Step-by-step explanation:

Answer:

Multiplication - When we multiply we find 'lots of'

6 lots of 5 = 30

6×5=30

Answer:

  6(8x +7)(x -4)

Step-by-step explanation:

6(8x^2 -25x -28) = 6(8x^2 -32x +7x -28) . . . . rewrite the middle term

  = 6(8x(x -4) +7(x -4)) . . . . factor by grouping

  = 6(8x +7)(x -4)

_____

To rewrite the middle term, you are looking for factors of (8)(-28) that have a sum of -25. The sum will be odd only if one of the factors is odd. The only odd factor in the product is 7, so we choose (8)(-28) = (7)(-32). Those two factors, 7 and -32, have a sum of -25, so those are the ones we used.

Answer: [tex]y - 3 = 6 (x - 8 )[/tex]

Step-by-step explanation:

The equation of line in point slope form is given as :

[tex]y - y_{1} = m ( x - x_{1} )[/tex]

[tex]x_{1}[/tex] = 8

[tex]y_{1}[/tex] = 3

[tex]m = 6[/tex]

substituting into the formula , we have :

[tex]y - 3 = 6 (x - 8 )[/tex]

Yes, The expression [tex]\frac{1}{8} -10(\frac{3}{4}-\frac{3}{8}x)+\frac{5}{8} x[/tex] is equivalent to [tex]-\frac{1}{8} (59-35x)[/tex]

Explanation:

The given expression is [tex]\frac{1}{8} -10(\frac{3}{4}-\frac{3}{8}x)+\frac{5}{8} x[/tex]

Solving, we get,

[tex]\frac{1}{8} -\frac{30}{4}+\frac{30}{8}x+\frac{5}{8} x[/tex]

Adding the similar terms, we have,

[tex](\frac{1}{8} -\frac{30}{4})+(\frac{30}{8}x+\frac{5}{8} x)\\[/tex]

[tex]\frac{1-60}{8} +\frac{35}{8}x[/tex]

Adding, we get,

[tex]-\frac{59}{8} +\frac{35}{8}x[/tex]

Taking out the common term [tex]-\frac{1}{8}[/tex] , we have,

[tex]-\frac{1}{8} (59-35x)[/tex]

Thus, the expression [tex]\frac{1}{8} -10(\frac{3}{4}-\frac{3}{8}x)+\frac{5}{8} x[/tex] is equivalent to [tex]-\frac{1}{8} (59-35x)[/tex]

Step-by-step explanation:

Given,

f(x) = 2x - 8 and g(x) = x + 9

To find, the values of  f(g(x)) and g(f(x)) = ?

f(x) = 2x - 8

∴  f(g(x)) = 2(g(x)) - 8

= 2(x + 9) - 8

= 2x + 18 - 8

= 2x + 10

Also,

g(x) = x + 9

g(f(x)) = f(x) + 9

= 2x - 8 + 9

= 2x + 1

∴ f(g(x)) = 2x + 10 and g(f(x)) = 2x + 1

Answer:

1) x = 25    2) x = 23; m∠CBD = 80 degrees

Step-by-step explanation:

1) 5x + 15 = 6x - 10           Set both equations equal to each other

- 5x         - 5x                  Subtract 5x from both sides

15 = x - 10

+ 10    + 10                       Add 10 to both sides

25 = x

2) 2x + 14 + x + 7 = 90         Set the equations equal to 90

   3x + 21 = 90                     Combine like terms

         - 21  - 21                      Subtract 21 on both sides

3x = 69                                 Divide both sides by 3

x = 23

Plug 23 into the equation

2(23) + 14 = 60

Answer:4v+3

Step-by-step explanation:

-2v+3+6v

-2+6=4

The solution is [tex](x=\frac{-7}{2},\ y=\frac{-13}{2} )[/tex].

Solution:

Given system of equations are

[tex]-3 x+y=4[/tex] ---------- (1)

[tex]-9 x+5 y=-1[/tex] ---------- (2)

To solve the given system of equations by substitution method.

Let us take the equation (1) and find the value of y.

(1) ⇒ [tex]-3 x+y=4[/tex]

Add 3x on both sides of the equation, we get

⇒ [tex]y=4+3x[/tex]

Substitute y = 4 + 3x in equation (2), we get

[tex]-9 x+5 (4+3x)=-1[/tex]

[tex]-9 x+20+15x=-1[/tex]

Combine like terms together.

[tex]-9 x+15x=-1-20[/tex]

[tex]6x=-21[/tex]

Divide by 6 on both sides of the equation.

[tex]$x=-\frac{21}{6}[/tex]

Divide the numerator and denominator by the common factor 3.

[tex]$x=-\frac{21\div3}{6\div3}[/tex]

[tex]$x=-\frac{7}{2}[/tex]

Now, substitute x value in y = 4 + 3x, we get

[tex]$y=4+3\left(\frac{-7}{2} \right)[/tex]

[tex]$y=4+\left(\frac{-21}{2} \right)[/tex]

Take LCM of the denominators and make the same.

[tex]$y=\frac{8}{2} +\frac{-21}{2}[/tex]

[tex]$y=\frac{-13}{2}[/tex]

Hence the solution is [tex](x=\frac{-7}{2},\ y=\frac{-13}{2} )[/tex].

Answer:

1/24

Step-by-step explanation:

As you go fraction to the next fraction you divide by 2.

2/3 divided by 2 = 1/3

1/3 divided by 2 = 1/6

the rule is "divide by 2"

Final answer:

The next fraction in the sequence is 1/24, found by continuing the pattern of halving each successive fraction.

Explanation:

To determine the next fraction in the sequence 2/3, 1/3, 1/6, 1/12, we observe a pattern. The second fraction is half of the first, the third is half of the second, and the fourth is half of the third. By continuing this pattern, to find the next fraction, we need to take half of the last fraction in the sequence.

To solve the more difficult problem, multiply the numerator and denominator by a skillfully chosen factor: 1/2. For the fraction 1/12, we multiply both the numerator (1) and the denominator (12) by 1/2 to get our next fraction:

Therefore, the next fraction in the sequence is 1/2 divided by 6 which simplifies to 1/24.

Answer:  [tex]A=280\ in^2[/tex]

Step-by-step explanation:

As you can observe in the figure attached, when the slice is made perpendicular to the base of the right rectangular prism, the resulting two-dimensional cross-section is a Rectangle.

By definition, the area of a rectangle can be calculated with this formula:

[tex]A=lw[/tex]

Where "l" is the  length of the rectangle and "w" is the width.

In this case, looking at the figure attached, you can identify that the   length and the width of the rectangle are:

[tex]l=20\ in\\w=14\ in[/tex]

Now, knowing these values, you can substitute them into the formula:

[tex]A=(20\ in)(14\ in)[/tex]

Finally, you must evaluate in order to find area of this rectangle. You get that its area is the following:

[tex]A=280\ in^2[/tex]

Answer:

A which is 280mm

Step-by-step explanation:

Answer:

the correct answer for x is 8

Step-by-step explanation:

since:     1/2 ((4) (8) - 8) + (3) (8) = 36

The correct value for x that makes the equation true is 8.

To solve the equation [tex]\( \frac{1}{2}(4x-8)+3x=36 \)[/tex], follow these steps:

1. Distribute the [tex]\( \frac{1}{2} \)[/tex] to both terms inside the parentheses:

[tex]\[ \frac{1}{2} \cdot 4x - \frac{1}{2} \cdot 8 + 3x = 36 \][/tex]

2. Simplify the equation by multiplying:

[tex]\[ 2x - 4 + 3x = 36 \][/tex]

3. Combine like terms:

[tex]\[ 5x - 4 = 36 \][/tex]

4. Add 4 to both sides of the equation to isolate the term with x:

[tex]\[ 5x = 36 + 4 \][/tex]

[tex]\[ 5x = 40 \][/tex]

5. Divide both sides by 5 to solve for x:

[tex]\[ x = \frac{40}{5} \][/tex]

[tex]\[ x = 8 \][/tex]

Answer:

Therefore 9th term of the geometric sequence is [tex]\frac{2}{2187}[/tex]

Step-by-step explanation:

Given first term(a) = 6

and common ratio = [tex]\frac{1}{3}[/tex]

[tex]T_n= ar^{n-1}[/tex]

[tex]\therefore T_9=ar^{9-1}[/tex]

[tex]\Leftrightarrow T_9=a r^8[/tex]

[tex]\Leftrightarrow T_9=6\times ( \frac{1}{3}) ^8[/tex]

[tex]\Leftrightarrow T_9=\frac{2}{2187}[/tex]

Therefore 9th term of the geometric sequence is [tex]\frac{2}{2187}[/tex]

Answer:

27.8871 feet

Step-by-step explanation:

1 meter ≅ 3.28084

You need to multiply the meters by 3.28084 to get the answer in feet.

So, 8.5 * 3.28084 ≅ 27.8871

Answer:

f(x)=x^2+8

Step-by-step explanation:

To move a function upwards, you need to shift the function up the y axis. The function intersects the y axis at 3, so you need to add 5 to 3 to shift the graph up 5 units. I hope this helps you!

Answer:

12x + 2

Step-by-step explanation:

To find what the expression equals, you can collect like terms. This means to do the operations (add or subtract) the numbers that have the same variables.

(8x + 5) + (4x - 3)        Remove brackets to add a binomial (2-term brackets)

= 8x + 5 + 4x - 3        Collect like terms

= 8x + 4x + 5 - 3        I rearranged so you can see which terms are alike

= 12x + 5 - 3        Collected like terms with "x" (8x + 4x = 12x)

= 12x + 2        Collected like terms with no variables (5 - 3 = 2)

Therefore (8x + 5) + (4x - 3) is equal to 12x + 2.

If you want, you can also find another equal expression by factoring. Since "12x" and "2" are both divisible by the factor 2, you can take it out and put the other numbers in a bracket.

12x + 2

= 2(12x/2 + 2/2)

= 2(6x + 1)        This is equal, but in factored form.

Answer:

12x+2

Step-by-step explanation:

8x+4x=12x

5-3=2

12x+2

Answer:

its a triangle

Step-by-step explanation:

3 sides

Answer:

the shape is known as a triangle

Answer:

f(-7) = 24

Step-by-step explanation:

Step 1:  Identify the Function

f(x) = 17 - x is the function

Step 2:  Set x to -7 in the function

f(-7) = 17 - (-7)

f(-7) = 17 + 7

f(-7) = 24

Answer: f(-7) = 24

Answer:

the sum interior angles of a triangleis equal to 180

so (x + 13) +(x +23) + 90 = 180

2x + 36 + 90 = 180

2x = 180 - 126

2x = 54

x = 27

Answer:

2621

Step-by-step explanation:

We know how much they drink in 1 week, now we need to know how many they drink in 5 weeks.

To do so, multiply how much they drink in 1 week by 5 to get the value for 5 weeks.

524.2*5=2621

Answer:135 degrees

Step-by-step explanation: Pretend that the 2 circles are equal, and connect the lines that form the angle. You can draw a right triangle on the circle that is on the right, connecting 2 radii to form it. Then, because the two radii are of equal length, you know that it is a 45-45-90 triangle. Then draw a line that is from the top line and connect in to G. That line is perpendicular, so 45 degrees plus 90 degrees is 135 degrees. I hope this helps!

Answer:

27 hours

Step-by-step explanation:

1620 divided by 60 = 27

Answer:

27 Hours

Step-by-step explanation:

Divide 1620 by 60 and get.. 27 hours.

Answer:

Angle BDC is an inscribed angle.

The inscribed angle equals one half of the intercepted arc.

Therefore, the intercepted arc equals 130 degrees.

Step-by-step explanation:

The measure of BC should be 130 degrees.

The angle of d is 65 degrees:

Since angle of D is 65

So, the BC should be doubled i.e. 130 degrees.

Learn more about the circle here: https://brainly.com/question/14337527

Answer: [tex]\frac{1}{10} miles=0.1 miles[/tex]

Step-by-step explanation:

If the total distance [tex]D[/tex] Mick jogged is divided among five posts, we can write the following relation to find the distance [tex]x[/tex] between each post:

[tex]x=\frac{D}{5}[/tex]

Where [tex]D=\frac{1}{2} mile[/tex]

Then:

[tex]x=\frac{\frac{1}{2} mile}{5}[/tex]

[tex]x=\frac{1}{10} miles=0.1 miles[/tex] This is the distance between each marker post.

Answer:

The answer is 11

Step-by-step explanation: