PLEASE LAST FEW SETS OF QUESTIONS FOR SEMESTER PLEASE HELP 3

[tex]5^x = 3^{2x-1}\\\\\implies \ln(5^x) = \ln\left(3^{2x-1}\right)\\\\\implies x \ln 5 = (2x-1) \ln 3\\\\\implies x \ln 5 = 2x \ln 3 - \ln 3\\\\\implies 2x \ln 3 - x \ln 5 = \ln 3\\\\\implies x(2 \ln3 - \ln 5) = \ln 3\\\\\implies x =\dfrac{\ln 3}{2 \ln 3 - \ln 5} = 1.87[/tex]

The solution to the equation is x ≈ 1.864 (correct to 3 significant figures).

To solve the equation 5ˣ = 3²ˣ⁻¹ using logarithms, we'll take the logarithm of both sides to bring down the exponent. Since the bases are different (5 and 3), we can use either the natural logarithm (ln) or the common logarithm (log base 10). Let's use the natural logarithm (ln):

Take the natural logarithm (ln) of both sides:

ln(5^x) = ln(3²ˣ⁻¹)

Apply the logarithm rule: ln(a^b) = b * ln(a):

x * ln(5) = (2x - 1) * ln(3)

Expand the equation:

x * ln(5) = 2x * ln(3) - ln(3)

Move the terms with "x" to one side of the equation:

x * ln(5) - 2x * ln(3) = -ln(3)

Factor out "x" from the left side:

x * (ln(5) - 2 * ln(3)) = -ln(3)

Solve for "x":

x = -ln(3) / (ln(5) - 2 * ln(3))

Now, we can calculate the value of "x" using a calculator:

ln(3) ≈ 1.099

ln(5) ≈ 1.609

x ≈ -1.099 / (1.609 - 2 * 1.099) ≈ -1.099 / (1.609 - 2.198) ≈ -1.099 / (-0.589) ≈ 1.864

Therefore, the solution to the equation is x ≈ 1.864 (correct to 3 significant figures).

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Answer:

C) 84

Step-by-step explanation:

Use the Fundamental Counting Principle, which states that if there are p ways to do one thing, and q ways to do another thing, then there are p×q ways to do both things. In this case, we have 2 ways to select one object from the first set, 3 ways to select one object from the second set, and 14 ways to select one object from the third set. So, we multiply and do 2*3*14=84

Therefore, there are 84 unique combinations

Answer: [tex]2c^9[/tex]

Step-by-step explanation:

I'm assuming this is the expression: [tex]6a^3b^2c^{10}+\:20c^{10}\:-\:8a^3b^2c^9[/tex]

[tex]\mathrm{Factor\:}6a^3b^2c^{10}[/tex] (Expand using 2's and 3's as they are the common factor in all terms)

[tex]2\cdot \:3\cdot \:a\cdot \:a\cdot \:a\cdot \:b\cdot \:b\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c[/tex]

[tex]\mathrm{Factor\:}20c^{10}[/tex] (5 needed to expand the coefficient)

[tex]2\cdot \:2\cdot \:5\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c[/tex]

[tex]\mathrm{Factor\:}8a^3b^2c^9[/tex]

[tex]2\cdot \:2\cdot \:2\cdot \:a\cdot \:a\cdot \:a\cdot \:b\cdot \:b\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c[/tex]

Common factors (terms that are in all expressions):

[tex]2\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c\cdot \:c[/tex]

Simplify:

[tex]2c^9[/tex]

Answer:

126

Step-by-step explanation:

There are 126 different ways he can wear the outfit.

The definition of the combination is "An arrangement of objects where the order of the objects is irrelevant." Combining these two words indicates "Selection of things," where the order of the items is irrelevant.

Given:

Number of pairs of shoes= 7

Pants= 3 pairs

Shirts= 6

So, different outfits can he​ wear

= 7 x 3 x 6

= 21 x 6

= 126

Hence, there 126 different ways he can wear the outfit.

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Answer:

The first one

Step-by-step explanation:

SAS postulate says that if two sides and the included angle of a triangle are equal to two sides and the included angle of another triangle, then the one triangles are said to be congruent.

Answer:

-4x+8=24

24-8

16/-4x

x= -4

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

-4x + 8 = 24

Subtract 8 from both sides to isolate the x.

-4x + 8 = 24

       -8    -8

-4x       = 16

Divide -4 from both sides to solve for x.

-4x = 16

/-4    /-4

x = -4

Answer:

Divide each term in  Y i  =  4  +  1.5 X i  by  i  and simplify.

Y  =  −  4 i  +  1.5 X

Step-by-step explanation:

Answer: 4.5

Step-by-step explanation:

S= ut + 1/2(at)

S= 10(1/2) + 1/2(-2x1/2)

S= 5 + 1/2(-1)

S= 5 + (-.5)

S= 4.5

The statement, The hypotenuse is NOT located across from the right angle is false.

A right-angled triangle is a type of triangle that has an angle that measures 90 degrees. The triangle has three sides. The hypotenuse is the longest side of a right-angled triangle. Other sides are the base and the length. The sum of sides in a a right-angled triangle is 180 degrees.

Please find attached an image of a right-angled triangle. To learn more about  a triangle, please check: https://brainly.com/question/9329354

Answer:

79 inches

Step-by-step explanation:

1 foot equals 12 inches

6 feet = 6*12 = 72 inches

72+7=79

79 inches

Answer:

35

Step-by-step explanation:

Let me know if I got it right

Answer:

D

Step-by-step explanation:

The first equation would have to have a y-intercept of 4, and the second equation would have to have a y-intercept of -1.

-hope it helps

Answer: what the actual fudge is this?? i am a former harvard professer for math and I have never seen such a monstrocity of a math question, but the answer is the first one.

Step-by-step explanation:

Answer:

21 above is the answer

Step-by-step explanation:

Answer:

12,448.9

Step-by-step explanation:

i'm sorry if this is wrong

Answer:

24/35

Step-by-step explanation:

Hope this helps!:)

Answer:

Step-by-step explanation:

2 1/2 + x = 5 1/3                Change the mixed numbers to improper fractions

5/2 + x = 16/3                   The lowest common multiple is 6. Multiply by 6

5*3 + 6x = 16*2

15 + 6x = 32                      Subtract 15 from both sides.

6x = 32 - 15

6x = 17                              Divide by 6

6x/6 = 17/6

x = 2 5/6

Check

5/2 + 17/6 = 16/3

15/6 + 17/6 = 32/6

32/6 = 32/6                    The question checks.

Answer: 13

Step-by-step explanation:

Distribute t.

Multiply 3 by each value in parentheses to get

3t - 12 = 2t + 1

Add 12 to both sides

3t = 2t + 13

Subtract 2t from both sides

t = 13

Answer:

t = 13

Step-by-step explanation:

[tex]3(t-4)=2t+1\\\\3t-12=2t+1\\\\t-12=1\\\\t=13[/tex]

hi how have you been and i think u did get it right

91929229

7373738292929202010100110010110

Answer:

[tex]x=\frac{3+\sqrt{6} }{3}, \frac{3-\sqrt{6} }{3}[/tex]

Step-by-step explanation:

Let's see

[tex]\\ \rm\rightarrowtail 3x^2-6x+1=0[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{6\pm \sqrt{36-12}}{6}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{6\pm \sqrt{24}}{6}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{6\pm 2\sqrt{3}}{6}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{3+\sqrt{3}}{6}[/tex]

Answer:

1.5

Step-by-step explanation:

Hope this helped!

Answer:

No it does not

Step-by-step explanation:

Two points simplify to 1/6 whilst the other, 1/5

Answer:

93.5

Step-by-step explanation:

Answer:

A 3x10^-6

Step-by-step explanation:

The given equations are 3x + y - 1 = 0 and 6x + 2y - 2 = 0.

So,

Equation I = (3x + y = 1) and

Equation II = (6x + 2y = 2)

= { 2(3x + y) = 2}

= 3x + y = 2/2

= 3x + y = 1

So, The given equations are 3x + y = 1 and 3x + y = 1.

Thus, there is one equation in two variables.

So, the given equations have an infinite number of solutions.

Answer:

1st option; 3x-y=-1

Step-by-step explanation:

-3x + y = 1

we can divide through by -1 so that the 'x' value is positive:

3x - y = -1

Answer:

Let's add more steps.

step 6: angle AEB measures 360 - 90 -90 - 70 - 39 = 71° Reason, AECF is a quadrangonal and three of its angle measures 90, 90, and (70+39)

step 7: angles AEB and ABE are congruent: reason triangle ABE is isosceles since AE is conruent to AB

step 8 Angle BAE measures 180 -71-71 = 38°: by difference from the sum of the internal angles.

step 9: Angle BAD measures 90 - BAE = 90 - 38 = 52° Reason angles BAD and BAE are complementary.

QED