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4 years ago

Find the missing measures

Mathematics

1 answer:

Yanka [14]4 years ago

7 0

The middle right is 145-90, so 55°. I'm not sure about the others

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3.3^(2x+1)-103^x+1=0 need value of x

photoshop1234 [79]

Answer:

The value of $x$ is approximately -1.531.

Step-by-step explanation:

Let $3.3^{2\cdot x + 1}-103^{x+1} = 0$ , we proceed to solve this expression by algebraic means:

1) $3.3^{2\cdot x + 1}-103^{x+1} = 0$ Given

2) $3.3^{2\cdot x}\cdot 3.3 -103^{x}\cdot 103 = 0$ $a^{b}\cdot a^{c} = a^{b+c}$

3) $(3.3^{x})^{2}\cdot 3.3 -\left[\left( \sqrt{103} \right)^{2}\right]^{x}\cdot 103 = 0$ $(a^{b})^{c} = a^{b\cdot c}$

4) $(3.3^{x})^{2}\cdot 3.3 - \left[\left(\sqrt{103}\right)^{x}\right]^{2}\cdot 103 = 0$ $(a^{b})^{c} = a^{b\cdot c}$ /Commutative property

5) $\left[\left(\frac{3.3}{\sqrt{103}}\right)^{x}\right] ^{2}-\frac{103}{3.3} = 0$ Existence of multiplicative inverse/Definition of division/Modulative property/ $a^{b}\cdot a^{c} = a^{b+c}$

6) $\left(\frac{3.3}{\sqrt{103}} \right)^{2\cdot x}=\frac{103}{3.3}$ Existence of additive inverse/Modulative property/ $(a^{b})^{c} = a^{b\cdot c}$

7) $\log \left(\frac{3.3}{\sqrt{103}} \right)^{2\cdot x}=\log \frac{103}{3.3}$ Definition of logarithm.

8) $2\cdot x\cdot \log \left(\frac{3.3}{\sqrt{103}} \right)= \log \frac{103}{3.3}$ $\log_{b} a^{c} = c\cdot \log_{b} a$

9) $2\cdot x \cdot [\log 3.3-\log \sqrt{103}] = \log 103 - \log 3.3$ $\log_{b} \frac{a}{d}$

10) $x\cdot (2\cdot \log 3.3-\log 103) = \log 103 - \log 3.3$ $\log_{b} a^{c} = c\cdot \log_{b} a$ /Associative property

11) $x = \frac{\log 103-\log 3.3}{2\cdot \log 3.3-\log 103}$ Existence of multiplicative inverse/Definition of division/Modulative property

12) $x \approx -1.531$ Result

The value of $x$ is approximately -1.531.

4 0

3 years ago

Parallel / Perpendicular Practice

deff fn [24]

The slope and intercept form is the form of the straight line equation that includes the value of the slope of the line

Neither
║
Neither
⊥
║
Neither
Neither
Neither

Reason:

The slope and intercept form is the form y = m·x + c

Where;

m = The slope

Two equations are parallel if their slopes are equal

Two equations are perpendicular if the relationship between their slopes, m₁, and m₂ are; $m_1 = -\dfrac{1}{m_2}$

1. The given equations are in the slope and intercept form

$\ y = 3 \cdot x + 1$

The slope, m₁ = 3

$y = \dfrac{1}{3} \cdot x + 1$

The slope, m₂ = $\dfrac{1}{3}$

Therefore, the equations are neither parallel or perpendicular

Neither

2. y = 5·x - 3

10·x - 2·y = 7

The second equation can be rewritten in the slope and intercept form as follows;

$y = 5 \cdot x -\dfrac{7}{2}$

Therefore, the two equations are parallel

3. The given equations are;

-2·x - 4·y = -8

-2·x + 4·y = -8

The given equations in slope and intercept form are;

$y = 2 -\dfrac{1}{2} \cdot x$

Slope, m₁ = $-\dfrac{1}{2}$

$y = \dfrac{1}{2} \cdot x - 2$

Slope, m₂ = $\dfrac{1}{2}$

The slopes

Therefore, m₁ ≠ m₂

$m_1 \neq -\dfrac{1}{m_2}$

The lines are Neither parallel nor perpendicular

Neither

4. The given equations are;

2·y - x = 2

$y = \dfrac{1}{2} \cdot x +1$

m₁ = $\dfrac{1}{2}$

y = -2·x + 4

m₂ = -2

Therefore;

$m_1 \neq -\dfrac{1}{m_2}$

Therefore, the lines are perpendicular

5. The given equations are;

4·y = 3·x + 12

-3·x + 4·y = 2

Which gives;

First equation, $y = \dfrac{3}{4} \cdot x + 3$

Second equation, $y = \dfrac{3}{4} \cdot x + \dfrac{1}{2}$

Therefore, m₁ = m₂, the lines are parallel

6. The given equations are;

8·x - 4·y = 16

Which gives; y = 2·x - 4

5·y - 10 = 3, therefore, y = $\dfrac{13}{5}$

Therefore, the two equations are neither parallel nor perpendicular

Neither

7. The equations are;

2·x + 6·y = -3

Which gives $y = -\dfrac{1}{3} \cdot x - \dfrac{1}{2}$

12·y = 4·x + 20

Which gives

$y = \dfrac{1}{3} \cdot x + \dfrac{5}{3}$

m₁ ≠ m₂

$m_1 \neq -\dfrac{1}{m_2}$

Neither

8. 2·x - 5·y = -3

Which gives; $y = \dfrac{2}{5} \cdot x +\dfrac{3}{5}$

5·x + 27 = 6

$x = -\dfrac{21}{5}$

Therefore, the slopes are not equal, or perpendicular, the correct option is Neither

Learn more here:

brainly.com/question/16732089

6 0

3 years ago

Cheryl is planning to go to a four-year college in two years. She develops a monthly savings plan using the estimates shown. Wha

Alik [6]

Answer:

$541.67 per month

Step-by-step explanation:

Tuition and other expenses = $8,250 per semester.

There are two semesters in a year

She has 4 years to spend

Total semester=4years*2semesters

=8 semesters

4 years in college which is a total of 8 semesters.

Total Tuition and other expenses = $8,250 * 8

= $66,000

She needs a total of $66,00 to complete her college

Assistance from parents=$15,000

Financial aid(per semester)=$4750

Total financial aid=$38,000

Total assistance=

Assistance from parents+ financial aid

=$15000+$38,000

=$53,000

Total savings=Total amount needed - Total assistance

=$66,000 - $53,000

=$13,000

She needs to save $13,000 in two years

There are 12 months in one year

2 years=2*12=24 months

Monthly savings=Total savings/24 months

=$13,000/24

=$541.666666

To the nearest cent

=$541.67

3 0

3 years ago

4.23×10 to the third power in standard notation/4.23×10 to the third power equals 4.23 times blank equals blank

vredina [299]

9514 1404 393

Answer:

4230

Step-by-step explanation:

4.23×10³ = 4.23×1000 = 4230

6 0

3 years ago

Fareed wants to add 1/4 +5/8 Add the fractions by using the giant one to create a common denominator

saul85 [17]

Hi!

This question is about math.

$\frac{1}{4}+\frac{5}{8}$

Least Common Factor 4 or 8: 8

Factors of 4 : 1, 2, 4 (prime factorization) (2*2)

Factors of 8: 1, 2, 4, 8 (prime factorization) (2*2*2)

Least Common Factor of a,b is the smallest positive number that divisible by both a and b.

Multiply each factor the greatest number of times it occurs in either 4 or 8.

Then multiply by the numbers.

$2*2*2$

$=8$

Multiply each numerator by the same amount needed to multiply its corresponding denominator to turn it into the Least Common Factor of 8.

For 1/4 multiply the denominator and numerator by the 2.

$\frac{1}{4}=\frac{1*2}{4*2}=\frac{2}{8}$

$\frac{2}{8}+\frac{5}{8}$

Since the denominator are equal, combine the fractions.

$\frac{2+5}{8}$

Add the numbers 2+5=7

$=\frac{7}{8}$

Hope this helps! Thank you for posting your question at here on Brainly. Have a great day.

-Charlie

6 0

3 years ago