Select the best answer for the question
17. A local supermarket sells shrimp for $4.50 per pound and lobster for $7.25 per pound.
You have a total budget of $95.75. If you buy 7 pounds of lobster, how many pounds of shrimp
can you purchase?​

Answer:

Triangle ABC is dilated is dilated with a scale factor of ⅓ with the center of dilation at the point (3,4) resulting in triangle DEC

Step-by-step explanation:

From triangle ABC,

|AC|=3 units

From triangle DEC,

|EC|= 1 unit

Since the two triangles are similar, we can find the scale factor using the ratio of the image length over the corresponding object length.

[tex]scale \: factor = \frac{ |EC| }{ |AC| } [/tex]

Let us substitute the values to get:

[tex]scale \: factor = \frac{1}{3 } [/tex]

When we trace through AD and EB, they will meet at C. Hence C(3,4) is the center of dilation.

Answer:

Step-by-step explanation:

Answer:

-32

Step-by-step explanation:

Divide both sides by 3/4 to solve for x.

－24/1*4/3 = -96/3

－96/3=－32

Answer:

641

Step-by-step explanation:

24,358 ÷ 38=641

Hope this helps!!

24,358 / 38 = 641

Use long division to find the answer :)

Hope this helps!

The equation that relates y, the amount of yellow paint in liters, and b, the amount of blue paint in liters, needed to make the Green Goober's special green paint is y + b = 888

Solution:

Given that the Green Goober mixes 333 liters of yellow paint with 555 liters of blue paint to make 888 liters of special green paint for his costume.

Let "y" be the amount of yellow paint in liters needed to make the Green Goober's special green paint

Let "b" be the amount of blue paint in liters needed to make the Green Goober's special green paint

The required equation is:

amount of yellow paint in liters +  amount of blue paint in liters = Green Goober's special green paint

y + b = 888

Where y = 333 liters and b = 555 liters ( from given information)

Thus the equation is found

Answer:

y=3/5b

Step-by-step explanation:

Answer: H-7

Step-by-step explanation: I got it right on test!  have a great day! :)

Answer:

1.13 repeated

Step-by-step explanation:

Answer:

1 and 100 over 750

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use the formula

[tex]A(t)=P(1+\frac{r}{n})^{(n)(t)}[/tex]

where A(t) is the amount after all the compounding is done, P is the initial investment, r is the interest rate as a decimal, n is the number of times the investment is compounded each year, and t is time in years.  For us,

P = 6050

r = .046

n = 4

t = 6

A(t) = ?

Filling in our given info:

[tex]A(t)=6050(1+\frac{.046}{4})^{(4)(6)}[/tex]

which simplifies to

[tex]A(t)=6050(1+.0115)^{24}[/tex]

which simplifies a bit more to

[tex]A(t)=6050(1.0115)^{24}[/tex] and

A(t) = 6050(1.31577397) so

A(t) = $7960.43

which is choice C

Final answer:

The balance after 6 years is $6810.53 that is option A is correct.

Explanation:

To find the balance after 6 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt).

Given that the initial principal (P) is $6050, the interest rate (r) is 4.6% (or 0.046 in decimal form), and it is compounded quarterly (n=4 times per year), we can plug in the values and solve for A.

A = $6050(1 + 0.046/4)^(4*6) = $6810.53

Therefore, the balance after 6 years is $6810.53, which corresponds to answer choice A.

Answer:

x = -5 + 5i, -5 - 5i

Step-by-step explanation:

The solution to the given equation (-20+5) (58-65) is 105. This is calculated by first simplifying the expressions within the brackets and then multiplying the resulting numbers.

The student's question relates to the calculations and simplifying of expressions in mathematics. This type of operation can be found in basic algebra, and its mastery is an essential part of succeeding in mathematics.

To solve the equation given, which is (-20+5) (58-65), we'll need to separate it into two steps. First, simplify the expressions in the brackets. Therefore, -20+5 equals -15 and 58-65 equals -7. Now, substitute these values back into the equation getting -15 * -7. Multiplying these two values will give a product of 105. That is the final answer. The provided list of numbers following the initial problem statement seems to be irrelevant to this specific calculation.

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Solve: 4(6x - 10) = 8x + 40

A 0

B.5/2

c. 23

D. 5​

Option D

The solution to given equation is x = 5

Given that we have to solve the given equation

4(6x - 10) = 8x + 40

Let us solve the above expression and find value of "x"

Multiplying 4 with terms inside bracket in L.H.S we get,

24x - 40 = 8x + 40

Move the variables to one side and constant terms to other side

24x - 8x = 40 + 40

Combine the like terms,

16x = 80

[tex]x = \frac{80}{16} = 5[/tex]

Thus solution to given equation is x = 5

Answer:

10. ○[tex]\displaystyle 4,85; 4\frac{17}{20}[/tex]

9. ○680%

8. ○40%

7. ○[tex]\displaystyle 60[/tex]

6. ○0,4, 40,5%, 11⁄25, 4⁄9

5. ○[tex]\displaystyle 0,928[/tex]

4. ○1%

3. ○76%

2. [tex]\displaystyle See\:above\:grid[/tex]

1. [tex]\displaystyle See\:above\:grid[/tex]

Step-by-step explanation:

10. To convert from a percentage to a decimal, move the decimal mark twice to the left; each 20 is worth 5, and since 5 by 17 is 85, you have your fractional part of 17⁄20, then attach the whole number of 4.

9. To convert from a mixed number\improper fraction to a percentage, first evaluate the fractional part for a decimal answer, then move the decimal mark twice to the right.

8. To convert from a fraction to a percentage, evaluate the fraction for a decimal answer, then move the decimal mark twice to the right.

7. [tex]\displaystyle \frac{132}{220} = \frac{3}{5} =[/tex]60%

Greatest Common Divisor [GCD]: 44

6. [tex]\displaystyle \frac{11}{25} =[/tex]44%

_

[tex]\displaystyle \frac{4}{9} =[/tex]44,4%

[tex]\displaystyle 0,4 =[/tex]40%

Now that these are all percentages, it is alot easier to order them from least to greatest.

5. To convert from a percentage to a decimal, move the decimal mark twice to the left.

4. To convert from a decimal to a percentage, move the decimal mark twice to the right.

3. Each 25 is worth 4, and since 4 by 19 is 76, you get 76%.

2. Each 25 is worth 4, and since 4 by 6 is 24, you get 24%, and this graph.

1. Each 36 is worth 2 7⁄9, and since 12 by 2 7⁄9 is 33⅓, you get 33⅓%, so you would choose this answer.

I am joyous to assist you anytime.

Answer:

The ordered pair is not a solution of the system of inequalities

Step-by-step explanation:

we know that

If a ordered pair is a solution of a system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)

we have the system

[tex]x+5y < 16[/tex] ----> inequality A

[tex]x< 8[/tex] ----> inequality B

substitute the value of x and the value of y of the ordered pair in each inequality

ordered pair (6,2)

Verify inequality A

For x=6, y=2

[tex]6+5(2) < 16[/tex]

[tex]16 < 16[/tex] ----> is not true

so

The ordered pair not satisfy the inequality A

therefore

The ordered pair is not a solution of the system of inequalities

a. She pays $100 for 5 sheets

b. 25+15x dollars for x sheets

c. 8 sheets

Step-by-step explanation:

Given

Sitting cost = $25

Per sheet picture cost = $15

Let p be the number of sheets of pictures

Then the cost can be written as a function of p

[tex]c(p) = 25+15p[/tex]

Now,

a. How much does she pay for 5 sheets of pictures?!

Putting p = 5 in the function

[tex]c(5) = 25 + 15(5)\\= 25+75\\=100[/tex]

She will pay $100 for 5 sheets of pictures

b. How much does she pay for "x" sheets?

Putting x in place of p

[tex]c(x) = 25+15x[/tex]

c. How many sheets can she buy for $145?

We know the cost now, we have to find p so,

[tex]145 = 25+15p\\145-25 = 25+15p-25\\120 = 15p[/tex]

Dividing both sides by 15

[tex]\frac{15p}{15} = \frac{120}{15}\\p = 8[/tex]

Hence,

She can buy 8 sheets for $145

Keywords: Linear equation, Algebraic functions

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Answer:

x=5, y=22. (5, 22).

Step-by-step explanation:

y-x=17

y=4x+2

----------

4x+2-x=17

3x+2=17

3x=17-2

3x=15

x=15/3

x=5

y-5=17

y=17+5

y=22

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y-x=17&(1)\\y=4x+2&(2)\end{array}\right\\\\\\\text{substitute (2) to (1):}\\\\(4x+2)-x=17\qquad\text{combine like terms}\\\\(4x-x)+2=17\qquad\text{subtract 2 from both isdes}\\\\3x+2-2=17-2\\\\3x=15\qquad\text{divide both sides by 3}\\\\\dfrac{3x}{3}=\dfrac{15}{3}\\\\x=5[/tex]

[tex]\text{Put the value of x to (2):}\\\\y=4(5)+2\\\\y=20+2\\\\y=22[/tex]

Answer:

6*(3/4) is 75% of 6.

Step-by-step explanation:

3/4 =0.75

Consider this:

6*1 =6, so 1=100%.

6*1/2 =6*0.5=3, so 1/2=50%.

You can then see that 6*0.75=4.5 is 75% of 6.

Answer:

Step-by-step explanation:

P = Q - 7.......Q is the quantity of baskets....and he makes 15 baskets....so sub in 15 for Q and solve for P, the price

P = 15 - 7

P = 8 <====

Answer:

D.$8

Step-by-step explanation:

Firstly, you replace Q with 15. Then you solve the equation.

P=15-7

P=8

Final answer:

The new balance in the checkbook register is $114.04.

Explanation:

To find the new balance in a checkbook register after a deposit and a check are processed, you need to add the deposit to the current balance and then subtract the amount of the check.

Initially, the checkbook register has a balance of $158.

A deposit of $35 is made, and a check for $78.96 is written.

Calculating the new balance involves the following steps:

After completing these steps, the new balance in the register would be $193 - $78.96 = $114.04.

Balancing your checkbook regularly is essential to manage your money efficiently and to avoid fees associated with overdrafts or insufficient funds.

Answer:

324

Step-by-step explanation:

Given:

[tex]g(x)=4x^2+2x\\ \\f(x)=\int\limits^x_0 {g(t)} \, dt[/tex]

Find:

[tex]f(6)[/tex]

First, find f(x):

[tex]f(x)\\ \\=\int\limits^x_0 {g(t)} \, dt\\ \\=\int\limits^x_0 {(4t^2+2t)} \, dt\\ \\=\left(4\cdot \dfrac{t^3}{3}+2\cdot \dfrac{t^2}{2}\right)\big|\limits^x_0\\ \\=\left(\dfrac{4t^3}{3}+t^2\right)\big|\limits^x_0\\ \\= \left(\dfrac{4x^3}{3}+x^2\right)-\left(\dfrac{4\cdot 0^3}{3}+0^2\right)\\ \\=\dfrac{4x^3}{3}+x^2[/tex]

Now,

[tex]f(6)\\ \\=\dfrac{4\cdot 6^3}{3}+6^2\\ \\=288+36\\ \\=324[/tex]

Answer:

Volume of the cone in ascending order.

[tex]V_{2}=270\pi\ units^{3}<V_{3}=300\pi\ units^{3}<V_{4}=363\pi\ units^{3}<V_{1}=400\pi\ units^{3}[/tex]

cone with DIAMETER of 18 & height of 10

cone with RADIUS of 10 & height of 9

cone with RADIUS of 11 & height of 9

cone with DIAMETER of 20 & height of 12

Step-by-step explanation:

Let [tex]V_{2}. V_{3}. and\  V_{4}.[/tex] be the volume of the cone.

Let d, r and h be the diameter, radius and height of the cone.

Given:

[tex]d_{1} = 20\ and\ h_{1}=12[/tex]

[tex]d_{2} = 18\ and\ h_{2}=10[/tex]

[tex]r_{3} = 10\ and\ h_{3}=9[/tex]

[tex]r_{4} = 11\ and\ h_{14}=9[/tex]

Arrange the cones in order from lease volume to greatest volume.

Solution:

The volume of the cone is given below.

[tex]V=\pi r^{2} \frac{h}{3}[/tex]----------------(1)

where: r is radius of the base of cone.

and h is height of the cone.

The volume of the cone for [tex]d_{1} = 20\ and\ h_{1}=12[/tex]

[tex]r_{1} = \frac{d_{1}}{2}[/tex]

[tex]r_{1} = \frac{20}{2}=10\ units[/tex]

[tex]V_{1}=\pi (r_{1})^{2} \frac{h_{1}}{3}[/tex]

[tex]V_{1}=\pi (10)^{2} \frac{12}{3}[/tex]

[tex]V_{1}=\pi\times 100\times 4[/tex]

[tex]V_{1}=400\pi\ units^{3}[/tex]

Similarly, for volume of the cone for [tex]d_{2} = 18\ and\ h_{2}=10[/tex]

[tex]r_{2} = \frac{d_{2}}{2}[/tex]

[tex]r_{2} = \frac{18}{2}=9\ units[/tex]

[tex]V_{2}=\pi (r_{2})^{2} \frac{h_{2}}{3}[/tex]

[tex]V_{2}=\pi (9)^{2} \frac{10}{3}[/tex]

[tex]V_{2}=\pi\times 81\times \frac{10}{3}[/tex]

[tex]V_{2}=\pi\times 27\times 10[/tex]

[tex]V_{2}=270\pi\ units^{3}[/tex]

Similarly, for volume of the cone for [tex]r_{3} = 10\ and\ h_{3}=9[/tex]

[tex]V_{3}=\pi (r_{3})^{2} \frac{h_{3}}{3}[/tex]

[tex]V_{3}=\pi (10)^{2} \frac{9}{3}[/tex]

[tex]V_{3}=\pi\times 100\times 3[/tex]

[tex]V_{3}=\pi\times 300[/tex]

[tex]V_{3}=300\pi\ units^{3}[/tex]

Similarly, for volume of the cone for [tex]r_{4} = 11\ and\ h_{4}=9[/tex]

[tex]V_{4}=\pi (r_{4})^{2} \frac{h_{4}}{3}[/tex]

[tex]V_{4}=\pi (11)^{2} \frac{9}{3}[/tex]

[tex]V_{4}=\pi\times 121\times 3[/tex]

[tex]V_{4}=\pi\times 363[/tex]

[tex]V_{4}=363\pi\ units^{3}[/tex]

So, the volume of the cone in ascending order.

[tex]V_{2}=270\pi\ units^{3}<V_{3}=300\pi\ units^{3}<V_{4}=363\pi\ units^{3}<V_{1}=400\pi\ units^{3}[/tex]

Answer:

Step-by-step explanation:

the amount of mark up = 23% of 80

= [tex]\frac{23*80}{100}[/tex]

= 23 * 0.8 = $18.4

There were 45 markers originally in each box.

Step-by-step explanation:

Given,

Boxes ordered = 3 large boxes

Markers given to one teacher = 15

Markers given to 3 teachers = 15*3 = 45 markers

Remaining markers = 90

Let,

x be the original number of markers in 3 boxes.

Total markers - markers given to teachers = markers left

[tex]x-45=90\\x=90+45\\x=135[/tex]

There were 135 markers in 3 boxes.

3 boxes = 135 markers

1 box = [tex]\frac{135}{3}=45\ markers[/tex]

There were 45 markers originally in each box.

Keywords: multiplication, addition

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Answer:

D and E

Step-by-step explanation:

Using the rule of radicals

[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]

Given

[tex]3^{\frac{4}{7} }[/tex]

= ([tex]\sqrt[7]{3}[/tex])^4 → D or

= [tex]\sqrt[7]{3^{4} }[/tex] = [tex]\sqrt[7]{81}[/tex] → E

The area common to both triangles is [tex]18\sqrt3[/tex] square centimeters.

In a 30-60-90 triangle, the ratio of the side lengths is [tex]1:\sqrt{3} :2[/tex]. Since the hypotenuse is 12 cm, we can determine the lengths of the other sides using this ratio.

The shorter leg (opposite the 30-degree angle) is (1/2) times the hypotenuse, which is (1/2) * 12 cm = 6 cm.

The longer leg (opposite the 60-degree angle) is [tex]\sqrt3[/tex] times the shorter leg, which is 6 * [tex]\sqrt{3[/tex] cm = [tex]6\sqrt3[/tex] cm.

Now, since the two triangles are congruent, the overlapping region forms an isosceles triangle with two sides measuring 6 cm (the shorter leg) and a base measuring [tex]6\sqrt3[/tex] cm (the longer leg).

The base of the isosceles triangle is [tex]6\sqrt3[/tex] cm, and since it's an isosceles triangle, the height is the same as the shorter leg, which is 6 cm.

Common Area = ([tex]6\sqrt3[/tex] cm * 6 cm) / 2 = [tex]36\sqrt3[/tex] cm² / 2 = [tex]18\sqrt3[/tex] cm².

Therefore, the area common to both triangles is [tex]18\sqrt3[/tex] square centimeters.

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The area common to both triangles is 144 square centimeters.

To find the area common to both triangles, we need to determine the overlapping region, which is a rhombus formed by the intersection of the two 30-60-90 triangles.

First, let's consider one of the 30-60-90 triangles. The sides of a 30-60-90 triangle are in the ratio 1:√3:2. In this case, the hypotenuse is 12 cm, so the sides of the triangle are:

Shorter leg (opposite the 30-degree angle) = 12 cm / 2 = 6 cm

Longer leg (opposite the 60-degree angle) = 6 cm * √3

Now, let's look at the overlapping region, which forms a rhombus. The diagonals of a rhombus are perpendicular bisectors of each other, so each diagonal will be twice the length of the shorter leg of the 30-60-90 triangle.

Diagonal of the rhombus = 2 * 6 cm = 12 cm

The area of a rhombus can be calculated using the formula: Area = (diagonal1 * diagonal2) / 2

In this case, both diagonals are equal (12 cm each), so the area of the rhombus (and hence the common area of the triangles) is:

Area = (12 cm * 12 cm) / 2

Area = 144 cm²

So, the area common to both triangles is 144 square centimeters.

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Final answer:

C paid Rs. 127,050 for the car.

Explanation:

To find out what C paid for the car, we need to consider the gains made by A and B. A bought the car for Rs.100,000 and spent Rs. 10,000 on repairs. This means A's total cost is Rs. 110,000. A then sells the car to B at a gain of 10%, which means B buys the car for 110% of Rs. 110,000, or Rs. 121,000.

Now, B sells the car to C at a gain of 5%. To find out what C paid, we need to calculate 105% of Rs. 121,000, which gives us Rs. 127,050. Therefore, C paid Rs. 127,050 for the car.

Step-by-step explanation:

You must write formulas regarding the volume and surface area of ​​the given solids.

[tex]\bold{\#1\ Rectangular\ prism:}\\\\V=lwh\\SA=2lw+2lh+2wh=2(lw+lh+wh)\\\\\bold{\#2\ Cylinder:}\\\\V=\pi r^2h\\SA=2\pi r^2+2\pi rh=2\pir(r+h)\\\\\bold{\#3\ Sphere:}\\\\V=\dfrac{4}{3}\pi r^3\\SA=4\pi r^2[/tex]

[tex]\bold{\#4\ Cone:}\\\\V=\dfrac{1}{3}\pi r^2h\\\\\text{we need calculate the length of a slant length}\ l\\\text{use the Pythagorean theorem:}\\\\l^2=r^2+h^2\to l=\sqrt{r^2+h^2}\\\\SA=\pi r^2+\pi rl=\pi r^2+\pi r\sqrt{r^2+h^2}=\pi r(r+\sqrt{r^2+h^2})\\\\\bold{\#5\ Rectangular\ Pyramid:}\\\\V=\dfrac{1}{3}lwh\\\\[/tex]

[tex]\\\text{we need to calculate the height of two different side walls}\ h_1\ \text{and}\ h_2\\\text{use the Pythagorean theorem:}\\\\h_1^2=\left(\dfrac{l}{2}\right)^2+h^2\to h_1=\sqrt{\left(\dfrac{l}{2}\right)^2+h^2}=\sqrt{\dfrac{l^2}{4}+h^2}=\sqrt{\dfrac{l^2}{4}+\dfrac{4h^2}{4}}\\\\h_1=\sqrt{\dfrac{l^2+4h^2}{4}}=\dfrac{\sqrt{l^2+4h^2}}{\sqrt4}=\dfrac{\sqrt{l^2+4h^2}}{2}[/tex]

[tex]\\\\h_2^2=\left(\dfrac{w}{2}\right)^2+h^2\to h_2=\sqrt{\left(\dfrac{w}{2}\right)^2+h^2}=\sqrt{\dfrac{w^2}{4}+h^2}=\sqrt{\dfrac{w^2}{4}+\dfrac{4h^2}{4}}\\\\h_2=\sqrt{\dfrac{w^2+4h^2}{4}}=\dfrac{\sqrt{w^2+4h^2}}{\sqrt4}=\dfrac{\sqrt{w^2+4h^2}}{2}[/tex]

[tex]SA=lw+2\cdot\dfrac{lh_1}{2}+2\cdot\dfrac{wh_2}{2}\\\\SA=lw+2\!\!\!\!\diagup\cdot\dfrac{l\cdot\frac{\sqrt{l^2+4h^2}}{2}}{2\!\!\!\!\diagup}+2\!\!\!\!\diagup\cdot\dfrac{w\cdot\frac{\sqrt{w^2+4h^2}}{2}}{2\!\!\!\!\diagup}\\\\SA=lw+\dfrac{l\sqrt{l^2+4h^2}}{2}+\dfrac{w\sqrt{w^2+4h^2}}{2}\\\\SA=\dfrac{2lw}{2}+\dfrac{l\sqrt{l^2+4h^2}}{2}+\dfrac{w\sqrt{w^2+4h^2}}{2}\\\\SA=\dfrac{2lw+l\sqrt{l^2+4h^2}+w\sqrt{w^2+4h^2}}{2}[/tex]

Answer:

Y = 5x + 2 . . . . . . . . . . (1)

3x = -y + 10 . . . . . . . . (2)

3x = -(5x + 2) + 10

3x = -5x - 2 + 10

3x + 5x = -2 + 10

8x = 8

x = 1

y = 5(1) + 2 = 5 + 2 = 7

Solution is (1, 7)

Step-by-step explanation:

The Solution is (1,7) is the solution to the system of equations:

y=5x+2, 3x=-y + 10

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

given that,

We need to find the solution of the system of following equations.

y= 5x + 2        eq(1)

3x = -y +10      eq(2)

We will solve the equations using Substitution method to find the values of x and y

we put value of y from eq (1) into eq (2), The eq(2) will be:

3x = - (5x + 2) + 10

3x = -5x -2 +10

3x+5x = -2+10

8x = 8

x= 1

Now, putting value of z in eq(1) to find value of y

y = 5x +2

y = 5(1) + 2

y = 5+2

y = 7

So, Solution is (1,7).

Hence, The Solution is (1,7) is the solution to the system of equations:

y=5x+2, 3x=-y + 10

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Answer:

Only 1 time

Step-by-step explanation:

When it is compound interest it can be added in the following ways:

Annually = 1 Time in a year

Semiannually = 2 Times in a year

Quarterly = 4 Times in a year

Monthly = 12 Times in a year

Answer:

2

Step-by-step explanation:

a.p.e.x

Solve for x in this equation.

x+(-9)=-36

x-9=-36

x=-27

answer: -27

Answer:

The answer should be C. 1 1/4

Step-by-step explanation:

Eliminate A and B because none of them work

Eliminate E because we are using 1/4s

Eliminate D because we aren't using decimals

You can also think of a clock with adding 1/4s: 0.75 + 1/4= 1

1 + 1/4 = 1 1/4

(you can divide 1/2 into 2 one fourths)

The answer is 1 1/4 option C.

What is the sum of 1/2 and 0.75?

Simply add these two terms i.e:

1/2 + 0.75

Write 0.75 as a 75/100 and take lcm and lcm is 100.

1/2 + 75/100

On solving we get,

= ( 50 + 75 )/100

= 125/100

= 5/4

= 1 1/4

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Answer:

see explanation

Step-by-step explanation:

A difference of 2 squares factors in general as

a² - b² = (a - b)(a + b)

(x - 1)² - 25 ← is a difference of squares

with a = x - 1 and b = 5, thus

(x - 1)² - 25

=(x - 1 - 5)(x - 1 + 5) = (x - 6)(x + 4), then

(x - 6)(x + 4) = 0

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 4 = 0 ⇒ x = - 4

Solutions are x = - 4, x = 6