What is the measure of ∠w, rounded to the nearest degree? 19° 19° 32° 32° 56° 56° 71° 71° a horizontally-aligned scalene triangle u v w. side u v is labeled as 35 meters. side v w is labeled as 30 meters. side u w is labeled as 30 meters.

[tex]\huge \mathbb{ \underline{EXPLANATION:}}[/tex]

▪ [tex] \bold{\: x + y + z = 20}[/tex]

[tex]\\[/tex]

◆ As we have a [tex]\small\bold{sum \: of \: three \: integers}[/tex] equal to 20 and less than 10, we know the integers have to be between 2 and 9 (1 and 0 don't apply because the sum wouldn't be equal to 20 between three integers.

[tex]\large\tt{Note:}[/tex]

The first value would be X value, second Y value and third Z value.

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

[tex] \large\boxed{ \sf 36 \: solution}[/tex]

The value of x from the given diagram is -10

Two triangles are known to be similar if the ratio of their similar sides is equal. The diagram shown is similar to the required diagram.

Given the following parameters

<ABC = 2x

<BAC = 3x + 10

Equate the expression since both angles are equal. Substitute;

2x = 3x + 10

Subtract 3x from both sides

2x-3x = 3x-3x+10

-x = 10

x = -10

Hence the value of x from the given diagram is -10

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This number in expanded form 200 + 5 + 5/10 + 9/100  .

What is expanded form in math example?

Given  : 205.95 centimeters.

the number in a expanded form.

200 + 5 + 9/10 + 5/100

we have given 205.95 centimeters.

We can see 2 is at hundred place = 200.

0 is at tens place = 00.

5 is at ones place  = 5.

9 after decimal is at tenth place =  [tex]\frac{9}{10}[/tex].

5 is at hundredth place  = [tex]\frac{5}{100}[/tex] .

Therefore , Expanded form : 200 + 5 + 5/10 + 9/100 .

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Step-by-step explanation:

clearly divergent.

the elements of the series are getting bigger and bigger intercepted by some constant "1" (but they don't help here - after every intercepting "1" are 2 numbers that are larger by 1 than the 2 numbers before the intercepting "1", and that continues into infinity, so, the numbers will go to infinity, and that shows that the series is divergent).

The graph of the linear equation can be seen in the image below.

Here we have a linear equation:

y = -x

To graph it, we just need to find two points and the line, and then connect the points with a line.

Evaluating in x = 0, we get:

y = -0 = 0

Then we have the point (0, 0).

Evaluating in x = 1 we get:

y = -1

So we have the point (1, -1)

Now we just need to graph these two points and connect them with a line, the graph can be seen below.

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Answer:

180.

Step-by-step explanation:

100 contains 2  zero digits.

101 - 109 have 9 numbers,  110 to 200 have 11 numbers

so for 101 to 200 its 20 numbers

Its also 20 for 201 to 300  and for all sets of 100 up to 900.

- that is 7 * 20 = 140 numbers

Finally from 901 to 999 we have 18.

Total = 20 + 140 + 18

= 2 + 20 + 140 + 18

= 180.

The missing reason in step 8 is the substitution property.

It should be noted that according to substitution property, if x = y, then x can be substituted for y in any equation.

When a variable is equal to another variable, then the variables can be interchangeable.

In this case, the missing reason in step 8 is the substitution property.

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Solving a system of equations we can see that:

Let's define:

When the airplane travels against the wind, the total speed is:

(A - W)

In this way, we know that the airplane travels 1350 miles in 5 hours, then:

(A - W) = 1350mi/5h

When the airplane travels with the wind, it takes 3.75 hours to travel the same distance, then:

(A + W) = 1350mi/3.75h

We have now a system of equations:

(A - W) = 1350mi/5h

(A + W) = 1350mi/3.75h

If we isolate A on the first equation, we get:

A = 270mi/h + W

Replacing that in the other equation we get:

270mi/h + W + W = 360 mi/h

Solving for W we get:

2*W = 360mi/h - 270mi/h = 90mi/h

W = 90mi/h = 45mi/h

And the airplane rate is:

A =  270mi/h + W = 270mi/h + 45mi/h = 315 mi/h

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If adding only twelve, you must leave out three of the fifteen, and the number of ways is = 15! / (3! * 12!).

1∗2∗3∗4∗5∗6∗6∗8∗9∗10∗11∗12∗13∗14∗15 over

(1∗2∗3)∗(1∗2∗3∗4∗5∗6∗6∗8∗9∗10∗11∗12) =

13∗14∗15 over

(1∗2∗3)

27306 = 455

Answer: If all toppings are distinct, then you have C 4 15 combinations. If there are three distinct toppings, you have 3 ⋅ C 3 15 combinations (because we have C 3 15 choices for toppings and then 3 choices for which of those three toppings is doubled).

Step-by-step explanation:

Answer: [tex]\Large\boxed{B.~\displaystyle 75~m^3}[/tex]

Step-by-step explanation:

Given information

Height = 2 m

Base = 5 m

Length = 15 m

Given the formula for Triangular Prism Volume

[tex]V~=~\displaystyle \frac{1}{2}\times ~b~\times~h~\times~l[/tex]

[tex]\to V=Volume\\\to b=base\\\to h = height\\\to l = length[/tex]

Substitute values into the formula

[tex]V~=~\displaystyle \frac{1}{2}\times ~(5)~\times~(2)~\times~(15)[/tex]

Simplify by multiplication

[tex]V~=~\displaystyle \frac{5}{2}~\times ~30[/tex]

[tex]\Large\boxed{V~=~\displaystyle 75~m^3}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

the area and volume of the Pyramid of Gaza are  139, 840 m²

and 52950 m³ respectively.

The formula for volume and area of a square pyramid are given thus;

Volume, V= [tex]a^2\frac{h}{3}[/tex]

Area , [tex]A=a^2+2a \sqrt{\frac{a^2}{4}+ h^2 }[/tex]

Where

Substitute the values;

Area = [tex]230^2 + 2(230) \sqrt{\frac{230^2}{4}+ 150^2 }[/tex]

Area = [tex]52900 + 460 + \sqrt{13225 + 22500}[/tex]

Area = [tex]52900 + 460(189)[/tex]

Area = 52900 + 86, 940

Area = 139, 840 m²

Volume , v = [tex]230^2 + \frac{150}{3}[/tex]

Volume = 52900 + 50

Volume = 52950 m³

Thus, the area and volume of the Pyramid of Gaza are  139, 840 m²

and 52950 m³ respectively.

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answer is in the attachment below

goodluck!!

Answer:

Step-by-step explanation:

2x + 1 = 4x - 19

Solve for x

2x + 1 = 4x - 19

2x - 4x = -19 - 1

-2x = -20

x = 20 : 2

x = 10

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

check

2 * 10 + 1 = 4 * 10 - 19

21 = 21

the answer is good

Answer: [tex]\Large\boxed{x=10}[/tex]

Step-by-step explanation:

2x + 1 = 4x - 19

Add 19 on both sides

2x + 1 +19 = 4x - 19 + 19

2x + 20 = 4x

Subtract 2x on both sides

2x + 20 - 2x = 4x - 2x

20 = 2x

Divide 2 on both sides

20 / 2 = 2x / 2

[tex]\Large\boxed{x=10}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Step-by-step explanation:

sin∅=-3/4 in 4 quadrant which sine is negative there

using soh cah toa

sin=opp/hyp

where our opp=-3 and our hyp=4

using pythagoras theorem

hyp²=opp²+adj²

(4)²=(-3)²+adj²

16=9+adj²

16-9=adj²

adj²=7

adj=√7

from soh cah toa

cos∅=adj/hyp

cos∅=√7/4

Answer:

I think its -10 or -8

Step-by-step explanation:

The x-intercept and the asymptote of g(x) are x = 5 and x = 4, respectively

The equation of the function is given as:

g(x)  = log3 (x - 4)

Set the function to 0, to determine the x-intercept

log3 (x - 4) = 0

Express the function as an exponential function

x - 4 = 3^0

Evaluate the exponent

x - 4 = 1

Add 4 to both sides

x = 5

Set the radical to 0, to determine the asymptote

x - 4 = 0

Add 4 to both sides

x = 4

Hence, the x-intercept and the asymptote of g(x) are x = 5 and x = 4, respectively

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the area of the shaded part is 30. 89 cm²

We have the shape to be a rectangle

The area of the shaded part should be;

Area of rectangle - 2 ( area of a semi circle)

The formula for area of a rectangle

Area = length × width

Area = 12 × 12

Area = 144 cm²

Area of a semicircle = 1/2 πr²

Area = 1/ 2 × 3. 142 × 6²

Area = 56. 56 cm²

Area of shaded part = area of rectangle - 2( area of semicircle)

Area of shaded part = 144 - 2(56. 56)

Area of shaded part = 144 - 113. 11

Area of shaded part = 30. 89 cm²

Thus, the area of the shaded part is 30. 89 cm²

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The value of the function g(-3) from the given piecewise function is 1

A piecewise-defined function is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain.

From the given piecewise function, we are to find the value of the function when x is -3 that is g(-3)

In order to determine the equivalent function, we need to determine the function where x = -3

The equivalent function is g(x) = x+ 4

Substitute x = -3 into the resulting function

g(x) = x + 4

g(-3) = -3 + 4

g(-3) = 1

Hence the value of the function g(-3) from the given piecewise function is 1

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[tex]\qquad \qquad \textit{sum of an infinite geometric sequence} \\\\ \displaystyle S=\sum\limits_{i=0}^{\infty}\ a_1\cdot r^i\implies S=\cfrac{a_1}{1-r}\quad \begin{cases} a_1=\stackrel{\textit{first term}}{\frac{1}{8}}\\ r=\stackrel{\textit{common ratio}}{\frac{2}{3}}\\ \qquad -1 < r < 1 \end{cases}[/tex]

[tex]\displaystyle\sum_{k=0}^{\infty} ~~ \underset{a_1}{\frac{1}{8}}\underset{r}{\left( \frac{2}{3} \right)}^k\implies S=\cfrac{ ~~ \frac{1}{8} ~~ }{1-\frac{2}{3}}\implies S=\cfrac{ ~~ \frac{1}{8} ~~ }{\frac{1}{3}}\implies S=\cfrac{3}{8}[/tex]

The sample at option B, {0, 2} is not a part of the sample space of a spinner when spun two times.

The set consists of all the possible outcomes of an event called sample points, which is said to be a sample space.

It is given that,

a spinner has 5 sections of equal area and each section is numbered from 1 to 5.

If the spinner is spun two times, then the possible outcomes are 25. They are:

{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5)}

So, from the given options, the sample {0, 2} is not possible since there is no such a section on the spinner named 0.

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Answer:

0.012

Step-by-step explanation:

We know the standard notation of table salt is 0.003, so we simply multiply 40 by this.

answer - 0.0003 X 40 = 0.012

Answer:

100

Step-by-step explanation:

to turn whole numbers to a fraction it is whatever numbers out of 100

Answer:

99

Step-by-step explanation:

Domain and Range of f(x) is given by:

Domain: {x | all real numbers} ;

Range: {y | y > 0}

The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation. A function's range is its potential output, whereas its domain is the set of all possible input data.

The function can be written as :

[tex]f(x)=\sqrt[\frac{2}{3} ]{108^{2x} } \\f(x)=108^{\frac{3}{2}^{2x} }[/tex]

Now that x is an exponent, all real values are possible for it. Therefore, all real numbers make up its domain for f(x). But value of f(x) cannot be less than 1 because for x = 0 the value of f(x) is 1 and also for any values of x, the value of f(x) can never be less than 1

So, Range of f(x) is all real numbers greater than 0

Hence, Domain and Range of f(x) is given by:

Domain: {x | all real numbers} ;

Range: {y | y > 0}

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The general solution of the given higher-order differential equation y''' − 8y'' − 9y' = 0 is ,    [tex]y = C_{1} + C_{2} e^{8x} + C_{3}e^{-x}[/tex]

Given higher-order differential equation = y''' − 8y'' − 9y' = 0

We have to find the general solution of the above differential equation

The auxiliary equation for the above differential equation will be :                             [tex]m^{3} - 8m^{2} - 9m = 0[/tex]

Solve the equation :- [tex]m^{3} - 8m^{2} -9m = 0[/tex]

                                  [tex]m ( m^{2} - 8m - 9 ) = 0[/tex]

                                  m ( m - 8 ) ( m + 1 ) = 0

                                  m = 0 , m = 8 , m = -1

Then the general solution will be like :

[tex]y = C_{1} e^{0x} + C_{2} e^{x} +C_{3}e^{-1x}[/tex]

The above solution can be written as:

[tex]y = C_{1} +C_{2} e^{8x} +C_{3} e^{-x}[/tex]

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Answer:

The value of

[tex]a {}^{b} - c \: b {}^{c} - a \: c {}^{a} - b \: [/tex]

is

[tex] \frac { 19}{8} [/tex]

Step-by-step explanation:

[tex]a {}^{b} - c \: b {}^{c} - a \: c {}^{a} - b[/tex]

where,

Thus, substitute these values to the given equation to find the values.

[tex]a {}^{b} - c \: b {}^{c} - a \: c {}^{a} - b ... \: substitute \: \\ given \: values \\ (1) {}^{2} - ( - 3)(2) {}^{ - 3} - 1( - 3) {}^{1} - 2 \\ 1 + 3 \: ( \frac{1}{8} ) - 1( - 3) - 2 \\ 1 + \frac{3}{8} + 3 - 2 \\ \frac{11}{8} + 3 - 2 \\ \frac{35}{8} - 2 \\ \frac{19}{8} = 2 \frac{3}{8} [/tex]

Hope it helps

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

As we can see in the figure, lines m and n are parallel to each other. so we can apply Angle pair properties ~

So,

[tex]\qquad \sf  \dashrightarrow \: \angle1 \cong \angle2[/tex]

[ they form corresponding angle pair ]

and it's given that :

[tex]\qquad \sf  \dashrightarrow \: \angle2 \cong\angle 3[/tex]

therefore, by using above information. we can conclude that :

[tex]\qquad \sf  \dashrightarrow \: \angle1 \cong \angle3[/tex]

The 95% confidence interval for the population standard deviation will be,

[tex]$\sqrt{\frac{(n-1) s^{2}}{\chi^{2}} \frac{\alpha}{2}} & < \sigma < \sqrt{\frac{(n-1) s^{2}}{\chi^{2}}} \\[/tex]

simplifying the equation, we get

[tex]$\sqrt{\frac{2551.5}{26.1}} & < \sigma < \sqrt{\frac{2551.5}{5.63}} \\9.887 & < \sigma < 21.288[/tex]

The 95% confidence interval exists (9.887, 21.288).

A random sample of 15 men exists selected. The mean weight exists at $165.2 pounds and the standard deviation exists at $13.5 pounds. The population exists normally distributed.

So, [tex]$n=15, \bar{X}=165.2, s=13.5$[/tex]

where n exists the sample size, [tex]$\bar{X}$[/tex] exists the sample size

s exists the sample standard deviation.

The degrees of freedom will be n - 1 i.e.15 - 1 = 14.

For a 95% confidence interval, the level of significance will be [tex]$\alpha=0.05$[/tex].

The 95% confidence interval for the population standard deviation will be,

[tex]$\sqrt{\frac{(n-1) s^{2}}{\chi^{2}} \frac{\alpha}{2}} & < \sigma < \sqrt{\frac{(n-1) s^{2}}{\chi^{2}}} \\[/tex]

substitute the values in the above equation, we get

[tex]$\sqrt{\frac{(15-1)(13.5)^{2}}{\chi^{2}} 0.05} & < \sigma < \sqrt{\frac{(15-1)(13.5)^{2}}{\chi_{0}^{2}}} \\[/tex]

[tex]$\sqrt{\frac{(15-1)(13.5)^{2}}{\chi_{0.975}^{2}}} & < \sigma < \sqrt{\frac{(15-1)(13.5)^{2}}{\chi_{0.025}^{2}}} \\[/tex]

simplifying the above equation, we get

[tex]$\sqrt{\frac{2551.5}{26.1}} & < \sigma < \sqrt{\frac{2551.5}{5.63}} \\9.887 & < \sigma < 21.288[/tex]

The 95% confidence interval exists (9.887, 21.288).

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a) The equation represents an ellipse.

b) The equation represents a circle.

c) The equation represents a parabola.

In this problem we have general equations of the form A · x² + B · y² + C · x + D · y + E = 0, which have to be modified into standard form to infer its graphical form. This procedure can be done by algebra properties:

16 · x² + 4 · y² + 96 · x - 8 · y + 84 = 0

[(4 · x)² + 2 · 12 · (4 · x)] + [(2 · y)² - 2 · 2 · (2 · y)] = - 84

[(4 · x)² + 2 · 12 · (4 · x) + 144] + [(2 · y)² - 2 · 2 · (2 · y) + 4] = 64

(4 · x + 12)² + (2 · y + 2)² = 64

4² · (x + 3)² + 2² · (y + 2)² = 64

(x + 3)² / 4 + (y + 2)² / 16 = 1 : Ellipse

x² + y² + 8 · x - 6 · y - 15 = 0

(x² + 8 · x) + (y² - 6 · y) = 15

(x² + 2 · 4 · x + 16) + (y² - 2 · 3 · y + 9) = 40

(x + 4)² + (y - 3)² = 40 : Circle

x² + 6 · x + 4 · y + 5 = 0

x² + 6 · x + 5 = - 4 · y

y = - (1 / 4) · x² - (3 / 2) · x - (5 / 4) : Parabola

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The statement; In western culture, 4 to 12 feet is considered public space whereas personal space is 1½ to 4 feet is false.

These refers to culture which is related to the people of the west.

Culture

This can be defined as the beliefs, values, behaviour and material objects that constitute a people's way of life.

Therefore, it is b false that in western culture, 4 to 12 feet is considered public space whereas personal space is 1½ to 4 feet.

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Justine only goes when her friend goes [Conditional probability].

Mom going to PROM and Justine going to PROM are separate events. [Independent events].

Mom can't go until she finishes the housework is dependent on events

independent events. [Dependent events]

The probability exists in the analysis of the possibilities of happening of a result, which exists acquired by the ratio between favorable cases and possible cases.

Conditional probability directs to the possibility that some outcome happens given that another possibility contains also occurred.

Justine only goes when her friend goes [Conditional probability]

Independent events exist as those possibilities whose occurrence exists not dependent on any other event.

Mom going to PROM and Justine going to PROM are separate events. [Independent events]

Dependent events exist that depend upon what occurred before.

Mom can't go until she finishes the housework is dependent on events

independent events. [Dependent events]

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The midpoint of PQ is (1, -0.5)

The coordinates of the point 2/3 of the way from p to q are (-0.2, 0.4)

What is the midpoint of a line segment?

the midpoint is the middle point of a line segment. It is equidistant from both endpoints.

The midpoint of PQ

To calculate this, we use the midpoint formula;

(x,y) = {(x1 + x2)/2 , (y1 + y2)/2}

From the question; (x1,y1) = (-5,4) and (x2,y2) = (7,-5)

So (x,y) = (-5+7)/2 , (4-5)/2 = 2/2, -1/2 = (1,-0.5)

The coordinates of the midpoint of PQ are (1,-0.5)

What is the internal division of the line segment?

we will use here the internal division formula of the section formula;

Mathematically the coordinates can be calculated using the formula;

(x,y) = (mx2 + nx1)/m+ n , (my2 + ny1)/m + n

in this case, m = 2 and n = 3

(x1,y1) = (-5,4)

(x2,y2) = (7,-5)

So substituting these values, we have;

(x,y) = (2(7)+ 3(-5))/(2+3) , 2(-5) + 3(4)/(2+3)

(x,y) = (14 -15)/5 , (-10 + 12)/5

= (-1/5, 2/5) = (-0.2, 0.4)

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