In the following exercises, multiply the binomials. Use any method.
266. (3rs − 7)(3rs − 4)

Answer:

a view from the side.

"the parts are shown in the sectioned side view"

With the help of trigonometric function, the above problems have been calculated. See explanation below.

The term "trigonometric function" refers to functions that are periodic in nature and that shed light on how a right-angled triangle's angles and sides relate to one another.

The solutions to x in the respective problems is given as follows:

1) x = 5 /Sin(30°)

x = 10

!) Sin(45°) = 4/x

x = 4/sin(45°)

x = 4√2

I) Cos(45°) = √3 / x

x = √3 / Cos(45°)

x = √6

E) Tan(60°)

= (3√3) / x

x = (3√3) / 3

W) In trigonometry, every right-triangle that is isosceles in nature, the angle made by the legs and the hypotenuse will always equal 45°.

x = 45°

N) x² + x² = (7√2)²

x = 7

V) Tan(60°) = 7 / x

x = 7√3/3

K) x² + x² = (9)²

x = 9/√2

Y) Sin(60°) = 7√3/x

x = 14

M) Sin(30°) = x/11

x = 11/2

T) Sin(45°) = x/√10

x = √5

A) x + 2x + 90° = 180°

x = 30°

O) Sin(45°) = √2 / x

x = 2

R) Tan(30°) = x / 4

x = 4/√3

= 4√3 / 3

S) Sin(60°) = x / (10/3)

x = (5√3) / 3

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The measure of ∠STR in the isosceles triangle is 24°

What is an isosceles triangle?

A triangle having two sides of equal length is termed as an isosceles triangle. The base angles of an isosceles triangle are also equal in measure. The fact that the perpendicular bisector of the base and the angle bisector of the vertex angle are the same is another crucial characteristic of an isosceles triangle. We refer this as Isosceles Triangle Theorem.

What is the value of angle STR?

It is given that in isosceles triangle SQT,

∠STQ = 48°

Since, the line TR is the angle bisector of angle STQ, we have,

∠STR = ∠RTQ

And, ∠STR + ∠RTQ = ∠STQ

Let ∠STR be x, the, we get,

x + x = ∠STQ

⇒ 2x = 48°

⇒ x = 24°

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24 different ways can they line up to receive their championship rings.

What is a permutation mean in math?

What are permutations used for?

Given,

            No. of captains of the football team = 4

So,

         4 ways we can line up  their championship rings = (4,4)

                  4 ×3 ×2 ×1  = 24

Therefore, 24 different ways can they line up to receive their championship rings.

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Based on the polynomial function given, the lower bound can be found to be -14.

With f(x) being:
= x⁴ - 4x³ + 9x² - x - 14

Then f'(x) will be:
= 4x³ - 12x² + 18x - 1

If f'(x) is 0:

0 = 4x³ - 12x² + 18x - 1

x = 0.0578

So:
f(0.05) = -14.028

The lower bound is therefore -14.

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Answer: -5

Step-by-step explanation:

     Slope can be found with change in y over change in x.

           [tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

     Let (10, 4) be point 1 and (2, 44) be point 2.

           [tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

           [tex]\displaystyle \frac{44-4}{2-10}[/tex]

           [tex]\displaystyle \frac{40}{-8}[/tex]

           [tex]\displaystyle \frac{40}{-8}[/tex]

           -5

The direction of the vector is - 21.8 N of E , Option B is the answer.

A vector is an object with both magnitude and direction.

A vector is shown in the graph.

To determine the direction , The angle needs to be determined

The slope of the vector will give the direction of the vector

The vector starts from the point (1 , 1)

Another point on the vector (-4 , 3)

slope = -2 /5

It is making angle x with the line y = 1

tan x = -2 /5

x = - 21.8 N of E.

Therefore the direction of the vector is - 21.8 N of E , Option B is the answer.

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The total dollar amount of sales is $150,000

What is the sales amount achieved by the salesman to earn a commission of $3,000?

To compute the portion of total sales earned as commission, we simply  multiply the sales amount recorded  by the percentage of commission which is 2%

sales commission=sales amount*commission rate

sales commission=$3,000

sales amount=unknown(assume it is X)

commission rate=2%

$3,000=X*2%

X=$3000/2%

X=$150,000

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Answer:

43 °

Step-by-step explanation:

The ladder is the hypotenuse   13 feet is one leg of a a right triangle

   sin = opposite leg / hypotenuse

    sin (theta ) = 13 / 19

      theta = arcsin (13/19) = 43°

The solution to the linear expressions are:

The solution to linear expression is determined by taking into consideration the arithmetic operations used in each linear expression.

From the information given:

a. $18.79 + $2.11 + ‐$1.92 + $17.28

By rearrangement:

= $18.79 + $2.11 + $17.28 ‐$1.92

= $36.26

b. $7.45 + ‐$24.45 + $74.17 + ‐$76.52

By rearrangement:

= $7.45  + $74.17 ‐ $24.45 ‐ $76.52

= -$19.35

c.  $98.45 − $10.63 + $2.82 − $20.26

By rearrangement:

= $98.45 + $2.82 − $10.63 − $20.26

= $70.38

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Answer: 25,0.

Step-by-step explanation:

∡B=27°     ∡C=82°      b=12      a=?

∡A=180°-(27°+82°)=180°-109^°=71°.

[tex]\frac{a}{sinA} =\frac{b}{sinB} \\a=\frac{b*sinA}{sinB}=\frac{12*sin71^0}{sin27^0}=\frac{12*0,9455}{0,454} \approx25,0[/tex]

The expression of the decimal 0.139 in fraction form of p/q gives; 139/1000

We are given the decimal 0.139.

Now, when we want to convert to fraction, it means we want the decimal expression to have a numerator and a denominator.

Thus;

0.139 can also be expressed as; 139/1000

Therefore, the expression of the decimal 0.139 in fraction form of p/q gives; 139/1000

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Answer:

The sale price per piece of chicken was $0.69

Step-by-step explanation:

• We have to first calculate the price of 1 piece of chicken when 12 pieces cost $9.48.

Original price per piece = $9.48 ÷ 12

                                        = $0.79

• According to the question the price per piece decreased by $0.10 during the sale.

∴ Sale price per piece = $0.79 - $0.10

                                     = $0.69

Answer: The correct answer is choice A.

Step-by-step explanation:

This is because the triangles have the same angles, but are scaled differently.  Thus because of the scale, there can be no correlation between the sides. Because the triangles share point E you can see that both triangles share the same angle but also notice how lines CD and AB are parallel. This makes all angles identical proving the triangles are the same but different sizes. Concluding that choice A is correct.

Answer:

7[tex]\sqrt{2}[/tex]

Step-by-step explanation:

the diagonal d divides the square into 2 right angles.

using Pythagoras' identity in one of the right triangles , then

d² = 7² + 7² = 49 + 49 = 98 ( take square root of both sides )

d = [tex]\sqrt{98}[/tex] = [tex]\sqrt{49(2)}[/tex] = [tex]\sqrt{49}[/tex] × [tex]\sqrt{2}[/tex] = 7[tex]\sqrt{2}[/tex]

Answer:

c =7√2

Step-by-step explanation:

using the Pythagorean theorem we solve the diagonal ,where the two sides are given to find the hypotenuse.

c² =a² + b²

where c is the diagonal (hypotenuse fot thr triangle)

a and b are the legs (sides)

c² =7²+7²

c²= 98

c= √98

c=√49.√2

c=7√2

20) [tex]\overline{AC} \cong \overline{AC}[/tex] by the reflexive property, so SSS

21) [tex]\overline{CD} \cong \overline{CD}[/tex] by the reflexive property, so ASA

22) [tex]\overline{CE} \cong \overline{CB}, \overline{AC} \cong \overline{CD}[/tex] by the definition of a midpoint and [tex]\angle 1 \cong \angle 2[/tex], so SAS

23) [tex]\overline{AC} \cong \overline{AC}[/tex] by the reflexive property, so ASA

The point-slope form of a line with slope that contains the point

(-3, 6) is y-6=2(x+3)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The point-slope form of a line is given by y - y₁ = m(x - x₁)

where m is the slope of the line, and (x₁, y₁) is a point on the line.

We are given that the line has a slope, but we are not given what the slope is.

The given point is (-3, 6)

y - 6 = m(x - (-3))

y - 6 = m(x+3)

As per the given options which matches the point slope form is y-6=-2(x+3)

Hence, the point-slope form of a line with slope that contains the point

(-3, 6) is y-6=2(x+3)

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The equation of Daredevil Danny's jump in vertex form is y = -0.32(x - 25)^2 + 32

The graph of Daredevil Danny's jump is added as an attachment

A quadratic function is represented as:

y = a(x - h)^2 + k

From the graph, we have:

So, we have:

y = a(x - 25)^2 + 32

Substitute the value of the x-intercept

0 = a(15 - 25)^2 + 32

Subtract 32 from both sides

a(15 - 25)^2 = -32

Solve for a

a = -0.32

Substitute a = -0.32 in y = a(x - 25)^2 + 32

y = -0.32(x - 25)^2 + 32

Expand the exponent

y = -0.32(x^2 -50x + 625) + 32

Expand the bracket

y = -0.32x^2 + 16x - 200 + 32

This gives

y = -0.32x^2 + 16x - 168

Hence, the values of the coefficients a, b and c are -0.32, 16 and -168

Yes, he jumped successfully

This is so because his maximum height (i.e. the vertex of his jump) is higher than the vertex of the hoop

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Answer: -5/21.

Step-by-step explanation:

[tex]\frac{2}{5}*[\frac{-3}{7} +(\frac{-1}{6})]=\frac{2}{5} *(-\frac{3}{7} -\frac{1}{6}) =\frac{2}{5}*(-\frac{3*6+1*7)}{7*6} )=\frac{2}{5}*(-\frac{18+7}{42})=\frac{2}{5}*(-\frac{25}{42})=-\frac{5}{21} .[/tex]

Good luck an' have a nice day!

Answer:

Step-by-step explanation:

Answer: Option (2)

Step-by-step explanation:

There is a double root at x=-1, so there is a factor of [tex](x+1)^2[/tex].

Also, as x approaches both positive and negative infinity, the graph approaches negative infinity, so the leading coefficient is negative.

John must scan more than 862 images before his total cost is less than getting scanned images at the computer center.

To determine how many images John must scan before his total cost is less than getting scanned images at the computer center, we can set up an equation.

Let's denote the number of images John needs to scan as "x."

The total cost for John to scan x images is given by:

John's total cost = cost of scanner + cost of supplies + cost per image scanned

John's total cost = $215.70 + ($0.34 * x)

The total cost for scanning x images at the computer center is given by:

Computer center's cost = cost per image scanned * x

Computer center's cost = $0.59 * x

We want to find the point at which John's total cost is less than the computer center's cost. In other words, we want to find the value of x for which John's total cost is less than the computer center's cost:

John's total cost < Computer center's cost

$215.70 + ($0.34 * x) < $0.59 * x

Now, we can solve for x:

$215.70 + ($0.34 * x) < $0.59 * x

$215.70 < $0.59 * x - $0.34 * x

$215.70 < $0.25 * x

Divide both sides of the inequality by $0.25:

$\frac{215.70}{0.25} < \frac{0.25 * x}{0.25}$

862.80 < x

Therefore, John must scan more than 862 images before his total cost is less than getting scanned images at the computer center.

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The system of linear inequalities to represent this situation. is given as-

9p <= 480

a >= 8s

p = a + s

Expressions with linear inequalities compare any two values using inequality symbols like "<," ">," "<=," or ">=." These values could be either numerical, algebraic, or both.

If the linear inequality is larger than or less than but not equal to, a dashed line appears on the graph. On the other hand, a solid line always appears in linear equations. Linear equations lack shaded sections, whereas linear inequalities do.

According to the question,

The buses can carry a maximum of 480 people.

These people include adults as well as students.

Let 'p' represents the total number of people in the bus.

Let 'a' represents the number of adults in the bus.

Let 's' represents the number of students in the bus.

Thus,

p = a + s.

As, there must be a minimum of one adult for every 8 students.

a >= 8s

and,

9p <= 480

Therefore, the system of linear inequalities are found.

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The inverse of the statement is M be the point on PQ since PM is congruent to QM than M is midpoint on the PQ.

Inverse of the statement means that explain the condition in reverse way or vice versa.

Since, M is the midpoint of PQ, then PM is congruent to QM.
Proving in reverse way, let m be the point between P and Q the distance M from P is equal to the distance from M to Q. Which implies that M lies as the mid of the P and Q.

Thus, the inverse of the statement is M be the point on PQ since PM is congruent to QM than M is midpoint on the PQ.

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The Central Carbon

It is a method that represents the three-dimensional structures of molecules on a single page. These are a convenient way to represent the molecules and distribute them between the pairs of enantiomers. These are very often used to represent isomers of sugars.

The Fischer Projection consists of horizontal and vertical lines, the horizontal lines represent atoms that are pointed out of the plane and the vertical line represents atoms that are pointed away from the plane. The intersection point of the horizontal line and the vertical line represents the central carbon.

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Answer:

Hence, 0.041 can be expressed as [tex]$4.1 \times 10^{-2}$[/tex].

Step-by-step explanation:

- Given 0.041

- Use given, move the decimal point so that first factor is greater than or equal to 1 but less than 10 .

- Then count n and write in scientific notation.

Step 1 of 1

Consider 0.041

[tex]$$\Rightarrow 4.1$$[/tex]

Decimal has moved to 2 places at right.

The power will be negative as original no. is less than 1 .

So, [tex]$4.1 \times 10^{-2}$[/tex]

[tex]$$0.041=4.1 \times 10^{-2} \text {. }$$[/tex]

Using the Speed-Distance-Time relation, the Dolphin's rate in Feet per hour is 221,760 ft/hr.

Given, we have the distance travelled by dolphin is 665,280 feet and time is 3 hours.

s = d/t = 665.280/3 = 221,760 feet per hour

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Answer:

None of these

Step-by-step explanation:

None of this expressions are equivalent. But if the original polynomial is 9x^2-4, then answer would be (3x+2)(3x-2).

Using formula (a+b)(a-b)=a^2-b^2 , it follows:

(3x+2)(3x-2)=(3x)^2-2^2=9x^2-4