10 degrees, 80 degrees, 90 degrees

Answer:

x = 20

Step-by-step explanation:

We know that the vertically opposite angles are equal.

Accordingly,

41 = 2x + 1

Subtract 1 from both sides.

41 - 1 = 2x

40 = 2x

Divide both sides by 2.

x = 20

(21)⁹ . (15)⁹ is the equivalent expression using the same bases.

What are power and exponent?

One can represent extremely big or extremely small numbers in a more straightforward fashion by using exponents and powers. For instance, we can write 3 x 3 x 3 x 3 as 34, where 4 is the exponent and 3 is the base, to demonstrate 3 x 3 x 3 x 3 in a straightforward manner.

                            It is claimed that the entire statement 34 possesses power. How many times you should multiply a number depends on its power. Other names for powers include exponents and indices.

using (a.b )ⁿ = (a)ⁿ . (b)ⁿ

 ( 21.15)⁹ = (21)⁹ . (15)⁹

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Answer: 31

Step-by-step explanation:

Answer:

$22.49

Step-by-step explanation:

5 pounds of nectarines costs $8.65

8.65/5 = 1.73

1 pound of nectarines costs $1.73

1.73 times 13 = 22.49

Answer:2249/100

Step-by-step explanation:

13 x 8.65/5

calculate : 13 x 8.65/5

2249/100

Answer:

The formula for the function g(x) obtained when the graph of f(x) = √x is shifted up 1 unit and to the left 6 units is g(x) = √(x + 6) + 1.

Step-by-step explanation:

To obtain the formula for the function g(x) when the graph of f(x) = √x is shifted up 1 unit and to the left 6 units, we can use the following transformations:

A vertical shift up by 1 unit is represented by adding 1 to the function: f(x) + 1

A horizontal shift to the left by 6 units is represented by replacing x with (x + 6): f(x + 6)

Therefore, the formula for the function g(x) is:

g(x) = f(x + 6) + 1

Substituting the expression for f(x), we get:

g(x) = √(x + 6) + 1

So, the formula for the function g(x) obtained when the graph of f(x) = √x is shifted up 1 unit and to the left 6 units is g(x) = √(x + 6) + 1.

From the given polygon, The measure of angle K is 115 degrees.

A polygon is a two-dimensional shape made up of straight lines (segments) that are connected to form a closed shape. A polygon can have any number of sides (or edges), and the sides must not cross each other.

We know that the sum of the interior angles of a triangle is 180 degrees. We can use this fact to find the measure of angle J, which is opposite to angle K:

Angle J = 180 - 70 - 25 = 85 degrees

Now, we can use the fact that the sum of the interior angles of a quadrilateral is 360 degrees.

Angle K + 85 + 90 + 70 = 360

Simplifying the equation:

Angle K = 360 - 85 - 90 - 70 = 115 degrees

Therefore, the measure of angle K is 115 degrees.

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The correct statement regarding the limit of f(x) as x -> 1 is given as follows:

lim x -> 1 f(x) = -∞.

To obtain lateral limits, we need to take the limit of a function as it approaches a point from the left-hand side and the right-hand side separately.

If the two limits are equal, then this is the limit of the function, while if the lateral limits are different, then the limit of the function does not exist for the value of x.

From quadrant 2, the function approaches x = 1 on quadrant 4, hence the limit to the left is given as follows:

lim x -> 1^- f(x) = -∞.

A graph approaches x = 1 in quadrant 1, and curves down and approaches the x-axis in quadrant 1, hence the limit to the right is given as follows:

lim x -> 1^+ f(x) = -∞.

As the lateral limits are equal, the limit of the function is given as follows:

lim x -> 1 f(x) = -∞.

The problem describes the graph of the function.

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Step-by-step explanation:

This figure is made up of a cone and a semi sphere. Let's find the area of the cone

Volume of a cone

[tex] \frac{1}{3} \pi {r}^{2} h[/tex]

The height is 34 cm.

The radius is half the diameter of the sphere ,

this the radius is 14

[tex] \frac{1}{3} \pi( {14}^{2} )(34)[/tex]

Hint: Do not round mid calculations, only when you are done.

Volume of the semi sphere is

[tex] \frac{1}{2} ( \frac{4}{3} \pi {r}^{3} )[/tex]

The radius is 14

[tex] \frac{1}{2} ( \frac{4}{3} \pi(14) {}^{3} )[/tex]

Add both areas

[tex] \frac{1}{3} \pi( {14}^{2} )(34) + \frac{2}{3} \pi(14) {}^{3} [/tex]

Use 3.14 for pi

Which gives us

12719 to the nearest whole number

x= 3 and y = 4

so :

x + y = 3 + 4 = 7

Answer : 7

The prove that triangle ABE is congruent to triangle CDE is given below

Generally, To prove that triangle ABE is congruent to triangle CDE, we need to show that they have the same size and shape.

First, we can see that angle AED and angle CEB are opposite angles and therefore congruent, since AB || DC.

Also, since line AB = line DC, we know that segment AE is congruent to segment CE and segment BE is congruent to segment DE.

Using these congruent sides and the congruent angle, we can apply the Side-Angle-Side (SAS) congruence criterion to conclude that triangle ABE is congruent to triangle CDE.

Therefore, we have proven that triangle ABE is congruent to triangle CDE.

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Answer:

I think is D'C becausse everything goes back words

The time at which Neo reaches the work destination is A = 8 : 15 AM

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It displays the similarity of the connections between the phrases on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.

Given data ,

Let the time at which Neo reaches the work destination be A

Now , the time at which Neo leaves home = 6 : 45 AM

And , the distance between Neo and work = 45 miles

where the speed of Neo is S = 30 miles per hour

So , the distance traveled by Neo in 1 hour = 30 miles

The distance traveled by Neo in 1.5 hours = 45 miles

Therefore , the time required by Neo to reach office is 1.5 hours

And , the time at which Neo reaches the work destination A = 6 : 45 AM + 1.5 hours

On simplifying the equation , we get

The time at which Neo reaches the work destination A = 8 : 15 AM

Hence , the equation is A = 8 : 15 AM

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The graph of the function is added as an attachment

From the question, we have the following parameters that can be used in our computation:

g(x) = 6, -7 < x ≤ -2

          2, -2 < x ≤ 3

          -2, 3 < x ≤ 8

The above is a piecewise function that has three linear functions, and three domains

Using the above as a guide, we have the following:

We plot each function in each domain

See attachment for the graph of the function

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The pοssible decimals that satisfy the given cοnditiοns are:5.20, 5.22, 5.24, 5.26, 5.28, 5.60, 5.62, 5.64, 5.66, 5.68, 7.20, 7.22, 7.24, 7.26, 7.28, 7.60, 7.62, 7.64, 7.66, 7.68

Decimals are a way οf expressing numbers that fall between whοle numbers, using a decimal pοint tο separate the whοle number and the fractiοnal part. Each digit tο the right οf the decimal pοint represents a decreasing pοwer οf 10, starting frοm tenths, hundredths, thοusandths, and sο οn.

Since the digit in the tenths place is οdd, it can οnly be 5 οr 7. Similarly, since the digit in the hundredths place is even, it can οnly be 0, 2, 4, 6, οr 8.

Therefοre, the pοssible decimals that satisfy the given cοnditiοns are:

5.20

5.22

5.24

5.26

5.28

5.60

5.62

5.64

5.66

5.68

7.20

7.22

7.24

7.26

7.28

7.60

7.62

7.64

7.66

7.68

Nοte that these are the οnly pοssible decimals that satisfy all the given cοnditiοns.

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The polynomial expressions when simplified are 2g² + 3g - 1, 24c⁵d - 8cd² + 12c³d³ + 4cd, (m² + 5m + 4) ÷ (m + 1) = m + 4.

Others are added below

Expression 1

The expression is given as

(14g³ + 21g² - 7g)/7g

Divide the numerator by the denominator

So, we have

2g² + 3g - 1

Expression 2

Here, we have

24c⁵d - 8cd² + 12c³d³ + 4cd

The expression is in its simplified state

Expression 3

Given that

(m² + 5m + 4) ÷ (m + 1)

By long division, we have

           m + 4

m + 1 | m² + 5m + 4

           m² + m

-------------------------------------

              4m + 4

              4m + 4

-------------------------------------

                0

This means that (m² + 5m + 4) ÷ (m + 1) = m + 4

Expression 4

Given that

(c² - 2c - 15)(c + 3)⁻¹

By long division, we have

           c - 5

c + 3 | c² - 2c - 15

          c² + 3c

-------------------------------------

              -5c - 15

              -5c - 15

-------------------------------------

                0

This means that (c² - 2c - 15)(c + 3)⁻¹ = c - 5

Expression 5

Here, we have

(2y² + 10y + 17) ÷ (y + 3)

By synthetic division, we have

-3 | 2  10  17

    |__-6_-12______

      2  4   5

This means that (2y² + 10y + 17) ÷ (y + 3) = 2y + 4 + 5/(y + 3)

Expression 6

Here, we have

(2p³ - p² - 10p + 8)(p - 2)⁻¹

By synthetic division, we have

2 | 2    -1   -10    8

    |___4__6__-8____

      2    3   -4     0

This means that (2p³ - p² - 10p + 8)(p - 2)⁻¹ = 2p² + 2p - 4

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The range of values for length when the perimeter is between 82 feet and 124 feet is: 27 ≤ l ≤ 48

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. The area encircling a two-dimensional figure is known as its perimeter. Whether it is a triangle, square, rectangle, or circle, it specifies the length of the shape. The two primary characteristics of a 2D shape are area and perimeter. The perimeter of the shape can be calculated by summing the measurements of its sides and edges. A rectangle's perimeter is equal to twice the product of its length and width.

Given a rectangular fence.

The perimeter P is at least 82 feet and is no more than 124 feet.

82 ≤ P ≤ 124

The width is 14 feet.

The range of values of the length is to be found.

Now,

Perimeter of rectangle = 2( length + width)

The lowest value of the perimeter is 82

82 = 2(l + 14)

82 = 2l + 28

54 = 2l

l = 27

The highest value of perimeter is 124

124 = 2(l + 14)

124 = 2l +28

96 = 2l

l = 48

Therefore the range of values for length when the perimeter is between 82 feet and 124 feet is:

                  27 ≤ l ≤ 48

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Answer: We can use the formula for future value of an annuity to calculate how much will be saved for retirement:

FV = Pmt x (((1 + r)^n - 1) / r)

where:

FV is the future value of the annuity

Pmt is the payment made each period (in this case, the annual profit of $22,000)

r is the annual interest rate (9% or 0.09 as a decimal)

n is the number of periods (7 years)

Substituting the given values into the formula, we get:

FV = $22,000 x (((1 + 0.09)^7 - 1) / 0.09)

FV = $22,000 x (1.9904 / 0.09)

FV = $22,000 x 22.116

FV = $485,552

Therefore, the amount saved for retirement after 7 years will be $485,552.

Step-by-step explanation:

The prοbability that nο mοre than fοur cοmmittee members are technοlοgically adept is 0.9851, rοunded tο fοur decimal places.

c) By dividing the tοtal number οf applicants whο are nοt technically prοficient (9) by the likelihοοd that any οne οf them wοuld be selected fοr the cοmmittee, it is pοssible tο calculate the anticipated number οf instructοrs οn the cοmmittee whο are nοt technically prοficient:

Number anticipated: 9 * (12/30) = 3.6

Tο the nearest whοle number, we estimate that there will be fοur prοfessοrs οn the cοmmittee whο lack technical prοficiency.

d) We can use the binοmial distributiοn with n=12 (the number οf trials) and p=0.3 tο determine the likelihοοd that at least three members οf the cοmmittee lack technical prοficiency (prοbability οf success, which is defined as selecting a vοlunteer whο is nοt technically prοficient). When X is the number οf technically incοmpetent prοfessοrs οn the cοmmittee, we want tο determine P(X>=3).

P(X>=3) = 1 - P(X<3)

= 1 - P(X=0) - P(X=1) - P(X=2)

[tex]\mathrm{=1 - (12\ choose\ 0)(0.3^0)(0.7^{12}) - (12\ choose\ 1)(0.3^{1})(0.7^{11}) - (12\ choose\ 2)(0.3^2)(0.7^{10)}}[/tex]

[tex]= 1 - 0.00744 - 0.0563 - 0.1667[/tex]

[tex]= 0.7696[/tex]

The likelihοοd that at least three members οf the cοmmittee lack technical prοficiency is 0.7696, rοunded tο fοur decimal places.

e) Using the same binοmial distributiοn as in part d), we can calculate the likelihοοd that at mοst 4 members οf the cοmmittee are nοt technically adept by adding the prοbabilities fοr X=0, 1, 2, 3, and 4:

P(X<=4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)

[tex]\mathrm{= (12\ choose\ 0)(0.3^0)(0.7^{12}) + (12 \ choose\1)(0.3^1)(0.7^|{11}) + (12 \ choose\2)(0.3^2)(0.7^{10})}\\\mathrm{ + (12 \ choose\3)(0.3^3)(0.7^9) + (12 \ choose\4)(0.3^4)(0.7^8)}[/tex]

[tex]= 0.9851[/tex]

Rounding tο four decimal places, the likelihood that no more than four committee members are technοlogically savvy is 0.9851.

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The answers to each part context to similar triangles is given above.

A proportional relationship between two variables {x} and {y} means that if {x} increases, then {y} increases with it proportionally.

Given are two similar triangles as shown in the image.

{ 1 } -

We can write the scale factor as -

{k} = ZX/AC

{k} = 39/13

{k} = 3

{ 2 } -

m∠X = m∠A = 67°

m∠X = 67°

{ 3 } -

ZW/CD = k

CD = ZW/k

CD = 36/3

CD = 12 units

{ 4 } -

Area of triangle ABC = 1/2 x 5 x 12 = 30 square units.

A{ΔABC} = 30 square units

{5} -

Ratio of area of triangle ABC to triangle XYZ = (30)/(15 x 36) = 1/18

A{ΔABC}/A{ΔXYZ} = 1/18

Therefore, the answers to each part context to similar triangles is given above.

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Answer:

48.2 degrees

Step-by-step explanation:

look at photo

Based on proportional multiplication, the quantity of medication in grams that the patient, who weighs 63 kg needs in 12 hours is 1,224.3 mg.

Proportional multiplication involves the cross-multiplication of two fractional ratios, which are equated to each other.

Proportions involve the equation of two ratios.

The dosage required by a patient in 4 hours with a weight of 9 kg = 58.3 mg

Proportionately, the dosage required by a patient in 12 hours with a weight of 63 kg = 1,224.3 mg (58.3 x 63/9 x 12/4).

Thus, if a patient weighing 9 kg receives 58.3 mg of medicine in 4 hours, proportionately, in 12 hours, a patient weighing 63 kg will receive 1,224.3 mg.

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Answer:

[tex]\cos \dfrac{\theta}{2}(1-\cos \theta)=\sin \dfrac{\theta}{2} \sin \theta[/tex]

Step-by-step explanation:

[tex]\textsf{To show that}\;\;\cos \dfrac{\theta}{2}(1-\cos \theta)=\sin \dfrac{\theta}{2} \sin \theta:[/tex]

[tex]\textsf{Let}\;\;u=\dfrac{\theta}{2} \implies 2u=\theta[/tex]

Therefore:

[tex]\implies \cos \dfrac{\theta}{2}(1-\cos \theta)=\cos u(1-\cos 2u)[/tex]

 cos(A±B) = cosA cosB ∓ sinA sinB

 cos(2θ) = cos²θ - sin²θ

 cos(2θ) = 2cos²θ - 1

 cos(2θ) = 1 - 2sin²θ

Use the cos double angle identity cos(2θ) = 1 - 2sin²θ to rewrite cos(2u) in terms of sin:

[tex]\begin{aligned}\implies \cos \dfrac{\theta}{2}(1-\cos \theta)&=\cos u(1-\cos 2u)\\&=\cos u(1-(1-2 \sin^2 u))\end{aligned}[/tex]

Simplify:

[tex]\begin{aligned}\implies \cos \dfrac{\theta}{2}(1- \cos \theta)&=\cos u(1- \cos 2u)\\&=\cos u(1-(1-2 \sin^2 u))\\&=\cos u(1-1+2 \sin^2 u)\\&= \cos u(2 \sin^2 u)\\&=2 \sin u \cos u \sin u\end{aligned}[/tex]

 sin(A±B) = sinAcosB ± cosAsinB

 sin(2θ) = 2sinθcosθ

Using the sine double angle identity to rewrite 2sin(u)cos(u) as sin(2u):

[tex]\begin{aligned}\implies \cos \dfrac{\theta}{2}(1-\cos \theta)&=\cos u(1- \cos 2u)\\&=\cos u(1-(1-2 \sin^2 u))\\&= \cos u(1-1+2 \sin^2 u)\\&= \cos u(2 \sin^2 u)\\&=2 \sin u \cos u \sin u\\&= \sin(2u) \sin u\end{aligned}[/tex]

Finally, substitute u = θ/2 back in:

[tex]\begin{aligned}\implies \cos \dfrac{\theta}{2}(1-\cos \theta)&=\cos u(1-\cos 2u)\\&=\cos u(1-(1-2 \sin^2 u))\\&=\cos u(1-1+2 \sin^2 u)\\&= \cos u(2\sin^2 u)\\&=2\sin u\cos u \sin u\\&=\sin(2u) \sin u\\&=\sin\left(2 \cdot \dfrac{\theta}{2}\right) \sin \dfrac{\theta}{2}\\&=\sin \theta \sin \dfrac{\theta}{2}\\&=\sin \dfrac{\theta}{2} \sin \theta \end{aligned}[/tex]

If you don't want to substitute u = θ/2, the full calculation using the same double angle identities is:

[tex]\begin{aligned}\implies\cos\dfrac{\theta}{2}(1-\cos\theta)&=\cos\dfrac{\theta}{2}\left(1-\left(1-2\sin^2\dfrac{\theta}{2}\right)\right)\\\\&=\cos\dfrac{\theta}{2}\left(1-1+2\sin^2\dfrac{\theta}{2}\right)\\\\&=\cos\dfrac{\theta}{2}\left(2\sin^2\dfrac{\theta}{2}\right)\\\\&=2\sin \dfrac{\theta}{2}\cos \dfrac{\theta}{2} \sin \dfrac{\theta}{2}\\\\&=\sin\left(2\cdot\dfrac{\theta}{2}\right)\sin\dfrac{\theta}{2}\\\\&=\sin\theta\sin\dfrac{\theta}{2}\\\\&=\sin\dfrac{\theta}{2}\sin\theta \end{aligned}[/tex]

The interval which is function increasing and decreasing is  

A) x = -3.5 and x = -1.5.

What is function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Here we know that The slope determines if the function is an increasing linear function, a decreasing linear function, or a constant function. f(x)=mx+b is an increasing function if m>0. f(x)=mx+b is an decreasing function if m<0

Then according to the graph ,

The highest point = x=-3.5

The lowest point = x=-1.5

Then the interval which is function increasing and decreasing is  

A) x = -3.5 and x = -1.5.

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The cost of Shai's haircut is $25 and the cost of his shave is $30, so the subtotal before tax and tip is:

$25 + $30 = $55

The sales tax is 8.25%, so the tax amount is:

$55 * 0.0825 = $4.54

The total cost before tip is:

$55 + $4.54 = $59.54

If Shai tips 25% on the subtotal, the tip amount is:

$55 * 0.25 = $13.75

So the total cost including tax and tip is:

$59.54 + $13.75 = $73.29

Therefore, Shai must pay a total of $73.29 if he gets his hair cut and beard shaved and he tips the barber 25%. The answer is option (B).

Answer:

15 miles in 120 minutes

Step-by-step explanation:

We can start by using the unit rate of Alex's running speed:

5 miles / 40 minutes = 0.125 miles per minute

This means that Alex runs at a speed of 0.125 miles per minute.

To find out how many miles he can run in 120 minutes, we can multiply his speed by the number of minutes:

0.125 miles/minute × 120 minutes = 15 miles

Therefore, if Alex runs at the same rate, he can run 15 miles in 120 minutes.

A good book is one that makes the reader feel. It takes the reader on a compelling journey. .

A book is a medium for recording information in the form of writing or images, typically composed of many pages bound together and protected by a cover

Given is to understand what are the characteristics of good book.

A good book is one that makes the reader feel. It takes the reader on a compelling journey.

Calling a book “good” is an opinion that can be applied to any book.

Therefore, a good book is one that makes the reader feel. It takes the reader on a compelling journey.

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The algebraic expression for Thabo is, Thabo's age in 6 years' time is x + 6.

There are three primary categories of algebraic expressions, including:

Numeral Expression. Binary Expression. Expression of a Polynomial

Monomial Expression: A monomial is an algebraic expression that only has one term.

Monomial expressions include 3x4, 3xy, 3x, 8y, etc. as examples.

A binomial expression is an algebraic expression with two terms that are opposite each other.

Binomial examples are 5xy + 8; xyz + x3; etc.

Polynomial Expression: In general, a polynomial expression is one that has several terms with non-negative integral exponents of a variable.

Given that, Thabo is x years old and Lizzie is y years old.

In 6 years, Thabo's age will be:

x + 6

Hence, Thabo's age in 6 years' time is x + 6.

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Answer:

376.8

Step-by-step explanation:

Area of circle: A = πr^2 = π12^2 = 144π

Area of shade: A = (θ/360º) x πr^2 = (60/360) x 144π = 24π

Area not shaded = 144π - 24π = 120π = 120(3.14) = 376.8