-Exponential and Logarithmic Functions- Graph y = log (x + 1)

To prove that line segment a is parallel to line segment d, based on the given information, we can utilize the properties of perpendicular and parallel lines.

Given that a is perpendicular to b and b is perpendicular to c, we know that angles formed between a and b, as well as between b and c, are right angles. Let's denote these angles as ∠1 and ∠2, respectively.

Now, since c is parallel to d, we can conclude that the corresponding angles ∠2 and ∠3, formed between c and d, are congruent.Considering the fact that ∠2 is a right angle, it can be inferred that ∠3 is also a right angle.

By transitivity, if ∠1 is a right angle and ∠3 is a right angle, then ∠1 and ∠3 are congruent.Since corresponding angles are congruent, and ∠1 and ∠3 are congruent, we can deduce that line segment a is parallel to line segment d.

Thus, we have successfully proven that a is parallel to d based on the given information and the properties of perpendicular and parallel lines.

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Check the picture below.

so let's recall that the area of a circle is just πr² where r = radius, so since the sizes of each pizza are 10, 14, 18 and 22, that's simply their diameter, so that means they each have a radius half of that, or namely 5, 7, 9 and 11, as you see in the picture, so, hmmm which radius gives us the most area per the fraction provided, namely per slices provided?

\(\cfrac{4}{8}\pi 5^2\implies \cfrac{25\pi }{2} ~~ \approx ~~ 39.26~in^2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{3}{8}\pi 7^2\implies \cfrac{147\pi }{8} ~~ \approx ~~ 57.73~in^2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{2}{8}\pi 9^2\implies \cfrac{81\pi }{4}~~ \approx ~~ 63.62~in^2 ~~ \textit{\LARGE \checkmark} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1}{8}\pi 11^2\implies \cfrac{121\pi }{8}~~ \approx ~~ 47.52~in^2\)

Answer: Large

Step-by-step explanation:  Hope it helps Good luck!!!

Answer:

sorry

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

f(4) means to use 4 in place of x.

f(x) = 3(5)^(x-2)

fill in 4 for

f(4) = 3(5)^(4-2)

do the 4-2 subtraction first

f(4) = 3(5)^2

do the 5 to the 2nd power next.

f(4) = 3(25)

last, multiply.

f(4) = 75

This is just following the typical order of operations.

The equation of the line that passes through the point (3,2) and has a slope of 4 is; y = 4x - 10

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

Point (3,2)

Then Slope m = 4

Now Write the equation as;

y - 2 = 4(x - 3)

y = 4x - 10

Hence, The equation of the line is; y = 4x - 10

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Answer:

Step-by-step explanation:

Let one angle be x

Another angle will be 24+x

x+24+x=90

2x+24=90

2x=66

x=66/2=33

Now,

x= 33

x+24= 33+24= 57

Answer:

x + x - 45 = 90

2x - 45 = 90

2x = 135

x = 67.5, so x - 45 = 22.5

The other two angles measure 22.5° and 67.5°.

The size of angle ACB to the nearest degree is 88 degree.

Construction Steps:

Create a line segment BC with the property AC = 4 cm.

Draw two arcs that meet at point A by using B as the centre and a radius of 4 cm, and C as the centre and a radius of 7 cm.

Join AB and AC now. Consequently, the necessary triangle is ABC.

With the use of a compass, draw a line segment AB = 7 cm from A, cutting an arc AC = 4 cm.

Cut an arc of 3 cm from point B.

Embrace BC and AC

Triangle with  angle ABC is necessary.

< ACB = 88 degree

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Step-by-step explanation:

chicken nuggets are so bussing that the answer is c

Given the final amount of money available in Maddy's account, the interest rate and the time elapsed, the initial money her aunt invested was $15,000.

Interest is simply the amount of money a lender or financial institution receives for lending out money or pays for receiving money.

The formular for calculating compound interest is expressed as;

A = P(1 + r/n)^(n*t)

Where A is final amount, P is initial principal balance, r is interest rate, n is  number of times interest applied per time period and t is number of time periods elapsed.

Given the data in the question;

We substitute our given values into the expression above.

$39322  = P(1 + 0.055/1)^(1*18)

$39322  = P(1 + 0.055)^(18)

$39322  = P(1.055)^(18)

P = $39322 / (1.055)^(18)

P = $39322 / 2.621466

P = $15,000

Therefore, given the final amount of money available in Maddy's account, the interest rate and the time elapsed, the initial money her aunt invested was $15,000.

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Answer:

20

Step-by-step explanation:

\(15^2+b^2=25^2\\225+b^2=625\\625-225=b^2\\b^2=400\\\sqrt{400}=20\)

The required sample sizes are given as follows:

a) Previous estimate of 0.52: n = 1839.

b) No previous estimate: n = 1842.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of 0.995, so the critical value is z = 2.575.

The margin of error is given as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

For an estimate of 0.52, the parameters are given as follows:

\(M = 0.03, \pi = 0.52\)

Hence the sample size is obtained as follows:

\(0.03 = 2.575\sqrt{\frac{0.52(0.48)}{n}}\)

\(0.03\sqrt{n} = 2.575\sqrt{0.52 \times 0.48}\)

\(\sqrt{n} = \frac{2.575\sqrt{0.52 \times 0.48}}{0.03}\)

\((\sqrt{n})^2 = \left(\frac{2.575\sqrt{0.52 \times 0.48}}{0.03}\right)^2\)

n = 1839.

Without a previous estimate, the sample size is given as follows:

\(0.03 = 2.575\sqrt{\frac{0.5(0.4)}{n}}\)

\(0.03\sqrt{n} = 2.575\sqrt{0.5 \times 0.5}\)

\(\sqrt{n} = \frac{2.575\sqrt{0.5 \times 0.5}}{0.03}\)

\((\sqrt{n})^2 = \left(\frac{2.575\sqrt{0.52 \times 0.5}}{0.03}\right)^2\)

n = 1842.

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The correct option regarding the given sets is option(b)  which shows that A ∩ B' = {3}.

What is set theory?

The area of mathematical logic known as set theory examines sets, which are essentially collections of objects. Set theory is an area of mathematics that primarily focuses on items that are pertinent to mathematics as a whole, despite the fact that any form of an object can be grouped into a set.

Given,

      U = {a,b,c,1,2,3,4}

      A = {b,2,3}

      B = {a,b,2,4}

      C = {4}

      D = {c,3}

      E = {a,b,1,2,3}

      B' = U - B =  {a,b,c,1,2,3,4} -  {a, b,2,4} = {c,1,3}

     A ∩ B' = {b,2,3} ∩ {c,1,3} = {3}

Therefore the correct option regarding the given sets is option(b).

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The range of whole numbers between which the decimal falls is 0 yards to 1 yard.

The whole number is set to positive integers including 0. i.e 0, 1, 2, 3, and so on.

To find the total amount of fabric Mary Beth needs to make a pillow, we first need to convert 7/12 yards into a decimal. To do this, we can divide the numerator by the denominator:

7/12 = 7 / 12 = 0.5833...

So, Mary Beth needs approximately 0.5833 yards of fabric to make a pillow.

To determine the range of whole numbers between which the decimal falls, we can round up to the next whole number (1 yard) and round down to the previous whole number (0 yards). Therefore, the range of whole numbers between which the decimal falls is 0 yards to 1 yard.

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Therefore the result of adding the system of equations  2x + y = 4  ,

6=3x-y is 5x =10

Equations are statements in mathematics containing the equals (=) sign flanked on either side by two algebraic expressions. The relationship between the expressions printed on the left and right sides is shown to be equal in this way. In all mathematical equations, LHS = RHS  is used. You can solve equations to find the value of an unknown variable that stands in for an unknown quantity. If a sentence lacks a "equal to" sign, it is not considered an equation. It will be considered to be a phrase.

Here,

Given:

we have to solve the system of equations given. .Each equation is added together to remove the variable Y.

2x + y = 4  

+

3x - y = 6

________

=> 5x =10

Therefore the result of adding the system of equations  2x + y = 4  ,

6=3x-y is 5x =10

The value of x :

x =10 / 5 = 2

⇒ x=2

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Answer:

A and D are correct. This is a parallelogram, which is a quadrilateral. B is not correct because not all the sides are congruent. C is not correct. E and F are not correct because this parallelogram does not have any right angles.

The area of the triangle FGH is equal to  13√10 unit²

Given that the vertices;

F(-5,-7), G(-2,-5), and H(-6,-2)

We have to find the area of the triangle as;

Area of triangle = 1/2bh²

Here,

Area of triangle FGH = 1/2 (GH) (FG)²

Now,

Length of FG =  √26

Length of GH =  √10

Then,

Area of triangle FGH = 1/2 (GH) (FG)²

Area of triangle = 1/2 × √10 × √26²

Area of triangle = 1/2 × √10 × 26

Area of triangle FGH = 13√10

Therefore,

The area of the triangle FGH = 13√10 unit²

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Answer:

t = 2 and t = 3.

Step-by-step explanation:

To solve the equation 2^(2t) - 12(2^t) + 32 = 0, we can use a substitution to simplify the equation. Let's set u = 2^t:Substituting u = 2^t, the equation becomes:u^2 - 12u + 32 = 0Now we have a quadratic equation in terms of u. We can solve it by factoring or using the quadratic formula. Let's try factoring:(u - 4)(u - 8) = 0Setting each factor equal to zero, we have:u - 4 = 0 or u - 8 = 0Solving for u:u = 4 or u = 8Now, substitute back u = 2^t:For u = 4:

2^t = 4Taking the logarithm base 2 of both sides:

t = log2(4)

t = 2For u = 8:

2^t = 8Taking the logarithm base 2 of both sides:

t = log2(8)

t = 3

Answer:

Amount of discount =80-70=10$

percentage:-

\({:}\longrightarrow\)\(\sf {\dfrac{10}{80}}\times 100 \)

\({:}\longrightarrow\)\(\sf {\dfrac {10}{4}}5 \)

\({:}\longrightarrow\)\(\sf {\dfrac {50}{4}}\)

\({:}\longrightarrow\)\(\sf 12.5\% \)

Answer: the answer is 12.5

Step-by-step explanation:

3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

Let's start by breaking down the information given:

- Three-fourths of the yard is covered with grass.

- One-fourth of the yard is used as a garden.

- The sprinkler could only water 1/5 of the yard.

To find out how much of the grass died, we need to determine the portion of the grass that was not watered by the sprinkler.

Let's assume the total area of the yard is represented by the value 1. Therefore, we can calculate the area of the grass as 3/4 of the total yard, which is (3/4) * 1 = 3/4.

The sprinkler can only water 1/5 of the yard, so the portion of the grass that was watered is (1/5) * (3/4) = 3/20.

To find the portion of the grass that died, we subtract the watered portion from the total grass area:

Portion of grass that died = (3/4) - (3/20) = 15/20 - 3/20 = 12/20.

Simplifying, we get:

Portion of grass that died = 3/5.

Therefore, 3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

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10, 40, 400.

20, 30, 600.

25, 25, 525.

40, 60, 2400.

I think.

=======================================================

Explanation:

C = set of people skilled at communication

M = set of people skilled at handling money

Refer to the Venn Diagram shown below.

The blue region refers to the set of employees that are in circle C and in circle M.

Add up the numbers in the blue region to get 22+25 = 47

Answer:

The Highest common factor of 120,140,180 is  ( HCF) = 20

Step-by-step explanation:

Explanation:-

Given numbers  120,140,180

120 = 60 × 2

     = 30 × 2× 2

     = 15 × 2×2×2

    = 5×3× 2×2×2

140 =  70 × 2

      = 10 × 7× 2

      = 5× 2× 7× 2

180 = 90 × 2

      = 30×3×2

     = 5 × 6 × 3× 2

    = 5 × 2× 3× 2 × 3

The Highest common factor of 120,140,180 is   5 ×2×2 = 20

Answer:

-45

Step-by-step explanation:

Answer:

((−5)(−3))(−3)

=−45

hope this was helpful!

Answer:

2.5

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

Option B is the correct answer.

We have,

The null hypothesis states that the population mean for the number of hours spent studying by full-time students at 4-year colleges in the United States is equal to 14 hours per week,

while the alternative hypothesis states that it is different from 14 hours per week.

By using a two-tailed test, we are checking for any significant change in either direction, whether the average number of hours spent studying has increased or decreased from 14 hours per week.

Thus,

The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

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