a water bottle has a capacity of 25oz.. How many cups of water will the water bottle hold.

The relationship between the variables x, y and z is an illustration of similar triangles

The values of x, y and z are 6, [tex]\sqrt{117}[/tex] and [tex]\sqrt{52[/tex]

Right triangles are triangles with an angle measure of 90 degrees, and we have the following equivalent ratio from the triangle

[tex]x : 9 = 4 : x[/tex]

Express as fraction

[tex]\frac x9 = \frac 4x[/tex]

Cross multiply

[tex]x^2 = 36[/tex]

Take the square root of both sides

[tex]x = 6[/tex]

The value of y is then calculated using the following Pythagoras theorem

[tex]y = \sqrt{9^2 + x^2[/tex]

This gives

[tex]y = \sqrt{9^2 + 6^2[/tex]

[tex]y = \sqrt{117[/tex]

The value of z is then calculated using the following Pythagoras theorem

[tex]z = \sqrt{4^2 + x^2[/tex]

This gives

[tex]z = \sqrt{4^2 + 6^2[/tex]

[tex]z = \sqrt{52[/tex]

Hence, the values of x, y and z are 6, [tex]\sqrt{117}[/tex] and [tex]\sqrt{52[/tex]

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Given that ST = RT and PS and QR are produced to meet at T, the

congruency of the angles and the included side proves;

The given parameters are;

The given cyclic quadrilateral = PQRS

The produced side that meet at point T = PS and QR

ST = RT

Required:

To prove that PRS = QRS

Solution:

A two column proof is presented as follows;

Statement        [tex]{}[/tex]                               Reason

1. ST = RT        [tex]{}[/tex]                                 1. Given

2. ΔSRT is an isosceles triangle  [tex]{}[/tex]  2. Definition of isosceles triangle

3. ∠TSR ≅ ∠TRS     [tex]{}[/tex]                        3. Base angles of an isosceles triangle

4. ∠TSR = ∠TRS      [tex]{}[/tex]                        4. Definition of congruency

5. ∠TSR and ∠PSR, ∠TRS and ∠QRS are linear pair angles 5. Definition of linear pair angles

6. ∠TSR + ∠PSR = 180° and ∠TRS +∠QRS = 180°   6. Property of linear pair angles

7. ∠TSR + ∠PSR = ∠TRS +∠QRS,     7. Substitution property of equality

8. ∠PSR = ∠QRS      [tex]{}[/tex]                         8. Subtraction property of equality

9. ∠RQS in ΔRQS = ∠SPR in ΔSPR [tex]{}[/tex]                              9. Angle subtending the same arc formed at the circumference of a circle

10. ΔPRS ≅ ΔQRS           [tex]{}[/tex]                        10. By ASA rule of congruency

The Angle-Side-Angle rule of congruency states that if two angles and

an included side of one triangle are congruent to two angles and the

included side of another triangle, then the two triangles are congruent.

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Step-by-step explanation:

just add all the given angles and equate it with 540° and then find x

x/2 + x/2 + x - 25 + 100 + x - 15 = 540°

3x + 60 = 540°

3x = 540 - 60

x = 480/3

x = 160°

on checking, the given shape values of x-25 and x - 15 are both still obtuse angles thus the answer is correct.

Answer:

3n - 15

Step-by-step explanation:

3 multiplied by n which is 3n

Then 3 multiplied by 5 which is 15

So your answer is 3n - 15

Hope I helped :)

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Step-by-step explanation:

since x=3

1. substitute into the equation

g(3) = 1/5 x (1/3)^3

2. solve

g(3) = 1/5 x (1³/3³)

= 1/5 x (1/27)

= 1/5 x 1/27

= 1/135 (0.00740740741)

Answer:

The solution of (2,5) indeed equals the solution of the equation y=2x+1

Step-by-step explanation:

to solve just plug in the values.

y=2(2)+1 which gives us the y value of y=5

to solve for x, plug in y. 5=2x+1.

subtract 1 from both sides, and you get 4=2x

then divide 2 on both sides to get x, which is 2. therefore this is true.

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Answer:

App. percent decrease of 29.41%

Step-by-step explanation:

60-85/85=0.2941- 29.41%

Answer:

false

Step-by-step explanation:25.9cm is too big to connect to 15.9cm and 10 cm

Answer:

B $13,660.27

Step-by-step explanation:

Answer:

[x - 5]² + [y + 7]² = 6²

Step-by-step explanation:

It should be noted:

"h" represents the x coordinate of the center point, "k" represents the y coordinate of the center point, and "r" represents the radius of the circle.

When the values are substituted:

[x - 5]² + [y - (-7)]² = 6²

⇒ [x - 5]² + [y + 7]² = 6² = 36

ANSWER

14.3

EXPLANATION

angle = 21⁰

opposite side = 5.5

adjacent side = x

Knowing this, we must use tangent (opposite / adjacent)

tan (21⁰) = 5.5 / x

x = 5.5 / tan (21⁰) (use calculator)

x= 14.3

Answer:

3, 4, and 5, i think

Step-by-step explanation:

because its continious and the other ones arent

Answer:

2,3,5, and 6

Step-by-step explanation:

Answer:

Hey there!

9) Answer: D. :---- (x +8)(x-8)

10) Answer: P. :------(x-2y)^2

11) Answer: D. :-----(2a+3b)*(2a-3b)

12) Answer: P. :-----(a+4b)^2

13) Answer: P. :-----(x-3)^2

14) Answer:. D. :----(5xy+9z)*(5xy-9z)

15) Answer: P. :-----(2a+1)^2

16)Answer: D. :---(4ab+5)*(4ab-5)

Answer:

could you add more details? you only put ¨ if M¨

Step-by-step explanation:

Answer:

[tex]if \: m \: then \: m \: can \: be \: any \: variable.[/tex]

Answer:

the median is 36

Step-by-step explanation:

31, 34 , 34 , 35 37, 38 ,38 39

1.     2.    3.    4.  5.   6.   7.  8

(i put the numbers below because i like umm doing this weird technique where i count it)

since theres no median there then you have to add 35 and 37 then divide by 2

Answer:

[tex]=\frac{27}{125}[/tex]

Step-by-step explanation:

[tex]0.216[/tex]

[tex]\mathrm{Multiply\:and\:divide\:by\:10\:for\:every\:number\:after\:the\:decimal\:point.}[/tex]

[tex]\mathrm{There\:are\:}3\mathrm{\:digits\:to\:the\:right\:of\:the\:decimal\:point,\:therefore\:multiply\:and\:divide\:by\:}1000[/tex]

[tex]=\frac{0.216\cdot \:1000}{1000}[/tex]

[tex]=\frac{216}{1000}[/tex]

[tex]216,\:1000[/tex]

[tex]\mathrm{The\:GCD\:of\:}a,\:b\mathrm{\:is\:the\:largest\:positive\:number\:that\:divides\:both\:}a\mathrm{\:and\:}b\mathrm{\:without\:a\:remainder}[/tex]

[tex]2,\:3\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}[/tex]

[tex]=2\cdot \:2\cdot \:2\cdot \:3\cdot \:3\cdot \:3[/tex]

[tex]2,\:5\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}[/tex]

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

[tex]\mathrm{The\:prime\:factors\:common\:to\:}216,\:1000\mathrm{\:are\:}[/tex]

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

[tex]\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2\cdot \:2=8[/tex]

[tex]=8[/tex]

[tex]=\frac{8\cdot \:27}{8\cdot \:125}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:8[/tex]

[tex]=\frac{27}{125}[/tex]

Hence, the correct answer is [tex]=\frac{27}{125}[/tex]

Answer:

prime numbers between 20-30 are 23,29

prime numbers between 10-20 are 11,13,17,19

No,Steve is not right

Reason-there are two prime numbers between 20 to 30.Whereas there are 4 prime numbers between 10 to 20.

Answer:

they are

Step-by-step explanation:

the simplest form 8/18 is 4/9

250 - 250 * 12% = 250 * (1 - 12%) = 250 * 0,88

with x = fish number

=> P = 250 * 0,88 * x

Answer: A. P=250(0.12)x

Step-by-step explanation:

12%= 0.12

250 x 0.12 = the amount decreased by each week

Using it's concept, it is found that there is a 0.3482 = 34.82% probability that a randomly selected student in this class did not earn an A on the final exam and did not earn an A for the entire course.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that 13 out of 28 students did not earn an A on the final course, and 21 out of 28 students did not earn an A for the entire course, hence:

[tex]p = \frac{13}{28} \times \frac{21}{28} = 0.3482[/tex]

0.3482 = 34.82% probability that a randomly selected student in this class did not earn an A on the final exam and did not earn an A for the entire course.

More can be learned about probabilities at https://brainly.com/question/14398287

Answer:

-2.9, -2 3/5, -2.4

Step-by-step explanation:

Convert 3/5 in -2 2/5 to a decimal (3/5x2=6/10=0.6)

Sort it from least to greatest (-2.9, -2 3/5, 2.4)

Answer:

6 liters

Step-by-step explanation:

The ratio of lemons to water is 4:3. When the amount of lemons is 8, that menas the ratio is doubled, so then it is 8:6. The answer is 6 litres.

1/2(2 + 8)(4) and (2 + 3)(4)

area of trapezoid:

[tex]\sf \dfrac{1}{2} (a + b) *h[/tex]

Here:

So area of this trapezium:

[tex]\sf \dfrac{1}{2} (2 + 8) *4[/tex]

[tex]\sf 20 \ units[/tex]

area of rectangle:

length * width

5 * 4

20 units²

Area of trapezoid:-

Put the values

Answer: 7x + 6

Step-by-step explanation:

Use distribution property

(3x + 12)+(4x - 6)

Combine like terms

7x + 6

Answer:

7x + 6

Step-by-step explanation:

I hope this helps!

Answer:

The pyramid consists of 4 triangles having bases of 3 km and height of 4 km (measured along the face)

A = 4 * 3 / 2 * 4 = 24 km^2

Each triangle has an area of 1/2 * bottom length * height

3 cannot refer to the length of one of the isosceles triangles because a slant height of 4 km is given and is less than one such side

The surface area of the square pyramid is 24 km².

The surface area of a square pyramid with a slant height can be determined by the product of the base perimeter with the slant height divided by two.

Mathematically, it can be expressed as:

Surface Area S.A = P × l/2

where;

Surface Area (S.A) = 12 × (4/2)

Surface Area (S.A) = 24 km²

Learn about calculating the surface area of a square pyramid here:

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#SPJ6

Answer:

0.77

Step-by-step explanation:

correct me if im wrong this is just what i got

Answer: x > [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

-4x + 5 < -5

Subtract 5 from both sides

-4x < - 10

Divde each side by -4

x < -10 / -4

Dividing each side by a negative number flips the inequality

x > - 10 / -4

- 10 / -4 = 10 / 4 = 5/2

x > 5/2

Answer:

-4x+5<-5

-4x<-5-10

-4x<-15

-4x/-4>-15/-4

x>15/4

The division of x4-3x3-5X2-7x-9 by x + 1. yields; x²-4x²-x-6 with a remainder of -3.

From the task content;

The division of the polynomial x⁴-3x³-5x²-7x-9 by (x+1) therefore yields; x²-4x²-x-6 with a remainder of -3.

Read more on polynomial division;

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Answer: 15

Step-by-step explanation: