The binomial (x + 5) is a factor of x2 + 8x + 15. What is the other factor? (x + 3) (x + 7) (x + 12) (x + 13)

Answer:

1843:6754.9709254546.,657675

Step-by-step explanation:

The measure of the angle of the triangle is calculated by the law of sines and m∠S = 59.7°

The relationship between a triangle's sides and angles is provided by the Law of Sines. Trigonometry's law of sines can be expressed as a/sinA = b/sinB = c/sinC, where a, b, and c are the lengths of the triangle's sides, and A, B, and C are the triangle's respective opposite angles.

Law of Sines :

a / sin A = b / sin B = c / sin C

Given data ,

Let the triangle be represented as ΔRST

Now , the measure of s = 620 cm

The measure of side r = 210 cm

And , the measure of angle m∠R = 17°

From the law of sines , we get

a / sin A = b / sin B

On simplifying , we get

sin ( 17 )° / 210 = sin ( S ) / 620

Multiply by 620 on both sides , we get

sin ( S ) = ( 620 / 210 ) x 0.2923717

On further simplification , we get

sin S = 0.86319265203

Taking inverse on both sides , we get

S = sin⁻¹ ( 0.86319265203 )

S = 59.68°

S = 59.7°

Therefore , the value of S is 59.7°

Hence , the measure of angle m∠S = 59.7°

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Answer:

Step-by-step explanation:

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".

Answer:

35/ 18

(Decimal: 1.944444)

Step-by-step explanation:

Answer

Step-by-step explanation:35/18

Sa Of Rectangular Prism - 65

Sa Of Pyramid - 85

TOTAL SURFACE AREA - 150

Answer:

y= x+4

y=–4–2x

Step-by-step explanation:

using the formula (x–x1)/(x1–x2)= (y–y1)/(y1–y2)

Answer:

2,827.43

Step-by-step explanation:

Answer:

x=30

Step-by-step explanation:

x/5-16=-10

x/5=-10+16

x/5=6

x=6×5

x=30

Answer:600

Step-by-step explanation:

Answer:

20

___ x X = 120

100

x100       x 100

20x = 120

divide by 20 on both sides.

x = 6

Answer:

Real number

Rational number

Step-by-step explanation:

Answer:

2.1 kilometers

Step-by-step explanation:

Pythagoras' Theorem

a^2 + b^2 = c^2

2^2 + b^2 = 2.9^2

2.9^2 - 2^2 = b^2

8.41 - 4 = 4.41

b = √4.41

b= 2.1

Answer:

54°

Step-by-step explanation:

Because p and q are parallel, angle 3 equal to angle 6 as they are alternative angles.

So angle 6 is 54°.

Alternative

Line p and line q is parallel, so that the sum of a pair of interior angles (angle 3 and angle 5, angle 4 and angle 6) are equal to 180°.

So angle 4 + angle 6 = 180°.

Find angle 4 first:

180° - angle 3 = angle 4

180° - 54° = 126°

So the measure of angle 6 is

180° - 126° = 54°

Answer:

54 degrees

Step-by-step explanation:

Here,

ADDITIONALL,both two equation.

we get that,

so,

Applying the Pythagorean theorem, we have ΔPQR ≅ ΔABC. then we would have: ∠ACB = ∠PRQ = 90°

The pythagorean theorem states that the square of the longest side (hypotenuse) of a right triangle is always equal to the sum of the squares of the other two sides (legs) of the right triangle.

Since we know that ΔPQR is a right triangle, then:

x² + y² = PQ²

We are also given that x² + y² = z², so by substitution, we have:

z² = PQ², which makes both triangles have corresponding congruent sides. Therefore, ΔPQR ≅ ΔABC.

Using the corresponding parts of the congruent triangles, we can conclude that: ∠ACB = ∠PRQ = 90°.

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Answer:

associative property

Step-by-step explanation:

happy to help :)

Answer:

Associative Property

Step-by-step explanation:

The property says you can regroup the three numbers being added.

(a + b) + c = a + (b + c)

Either add a and b first, then add c, ...

or, add b and c first, then add that result to a.

Given:

The logarithmic equation is:

[tex]\log x+\log (x-3)=1[/tex]

To find:

The value of x.

Solution:

Properties of logarithm used:

[tex]\log a+\log b=\log (ab)[/tex]

[tex]\log 10=1[/tex]

[tex]\log x[/tex] is defined for [tex]x>0[/tex].

We have,

[tex]\log x+\log (x-3)=1[/tex]

Using properties of logarithm, we get

[tex]\log [x(x-3)]=\log 10[/tex]

[tex]x^2-3x=10[/tex]

Splitting the middle term, we get

[tex]x^2-5x+2x-10=0[/tex]

[tex]x(x-5)+2(x-5)=0[/tex]

[tex](x-5)(x+2)=0[/tex]

[tex]x=5,-2[/tex]

In the given equation, we have a term [tex]\log x[/tex]. It means the value of x must be greater than 0 or positive. So, the only possible value of x is:

[tex]x=5[/tex]

Therefore, the value of x is 5.

Answer:

[tex]x = \frac{5a-2} {7+5a}\\[/tex]

Step-by-step explanation:

Given the expressions

[tex]x = \frac{5}{9y+5}....1\\y = \frac{5}{5a-2} ...2[/tex]

Substitute 2 into 1

[tex]x = \frac{5}{9(\frac{5}{5a-2} )+5} \\x = \frac{5}{(\frac{45}{5a-2} )+5} \\x = \frac{5}{\frac{45+5(5a-2)}{5a-2} } \\x= \frac{5}{\frac{35+25a}{5a-2} }\\x = \frac{5(5a-2)} {35+25a}\\x = \frac{5(5a-2)} {5(7+5a})\\\\x = \frac{5a-2} {7+5a}\\[/tex]

Answer:

Angle AGC

Step-by-step explanation:

Two angles are called complementary if their measures add to 90 degrees, and called supplementary if their measures add to 180 degrees. ... For example, a 50-degree angle and a 40-degree angle are complementary; a 60-degree angle and a 120-degree angle are supplementary

Answer:

378 cm

Step-by-step explanation:

Answer:

<1 = 113

<2 = 67

<3 = 113

Step-by-step explanation:

m<2 = 67 (because of vertical angles)

<1 + 67 = 180

<1 = 113

<1 = <3 because of vertical angles

Answer:

carrots and cauliflower: 6

peas: 12

cabbage, sweetcorn: 18

Step-by-step explanation:

10 percent is 1/10, which is 6/60. Multiplied by two it's 12/60. Multiplied by 3 is 18/60.

Answer:

Step-by-step explanation:

The potential energy of a body can be found by using the formula

PE = mgh

where

m is the mass

h is the height

g is the acceleration due to gravity which is 9.8 m/s²

From the question we have

PE = 15 × 9.8 × 5

We have the final answer as

Hope this helps you

Answer:

2/6  or 33.3%

1/6 or 16.65%

3/6 or 50%

0/6 0r 0%

Step-by-step explanation:

Answer:

110 square centimeters.

Step-by-step explanation:

The area for a trapezoid can be figured out with the equation (a + b)h/2.

(9 * 5) + (9 + 4)10/2 {Work inside the parentheses first.}

45 + (13)10/2 {Divide 10 by 2 to get 5.}

45 + 13(5) {Multiply 13 by 5 to get 65.}

45 + 65 {Add 45 & 65 to get 110.}

110 square centimeters.

The area of the figure is 110 square centimeters.

The Percentage increase in the purchase price each year is 4.5%.

The given function is:

[tex]V(t)=P(1.045)^t[/tex]

Where P is the purchase price of the baseball card and t is the time.

A function is a rule that establishes a relation between two variables.

[tex]V(1)=P(1.045)^1\\V(1)=1.045P[/tex]

[tex]V(2)=P(1.045)^2\\V(2)=1.092025P[/tex]

Percentage increase in the purchase price each year

=[tex]\frac{V(2)-V(1)}{V(1)} *100[/tex]

[tex]=\frac{1.092025P-1.045P}{1.045P} *100[/tex]

[tex]=4.5%[/tex]%

Hence, the Percentage increase in the purchase price each year is 4.5%.

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Answer:

D. 4 units to the left

The transformation of the function will be 4 units to the left. The correct option is D.

A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They've simply shifted in one or more directions.

Given that the functions are f(x) = x³ and g(x) = ( x + 4 )³. The translation of the function will be at 4 units to the left.

When the functions are plotted on the graph the translation is seen to the left of the origin at the coordinate (-4,0).

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