find the value of x & z plz and give an explanation ( :

Answer:

Step-by-step explanation:

It is convenient to use the Pythagorean theorem to find XY to start with. That theorem tells you ...

  XZ² = YZ² + XY²

Solving for XY, you find ...

  XY² = XZ² - YZ²

  XY = √(XZ² - YZ²) = √(7.5² -6²) = √(56.25 -36) = √20.25

  XY = 4.5

The mnemonic SOH CAH TOA is very helpful here. It reminds you that ...

  Sin = Opposite/Hypotenuse

  sin(X) = 6/7.5

  Cos = Adjacent/Hypotenuse

  cos(X) = 4.5/7.5

  Tan = Opposite/Adjacent

  tan(X) = 6/4.5

_____

Comment on the triangle and ratios

The side lengths of this triangle are in the ratios ...

  XY : YZ : XZ = 3 : 4 : 5

If you recognize that the given sides are in the ratio 4 : 5, this tells you that you have a "3-4-5" right triangle with a scale factor of 1.5. At least, you can find XY = 1.5·3 = 4.5 with no further trouble.

The trig ratios could be reduced to sin(X) = 4/5; cos(X) = 3/5; tan(X) = 4/3, but the wording "don't simplify" suggests you want the numbers shown on the diagram, not their reduced ratios.

Answer:

The answer is 4x^3 + 2x^2 + 2x

Step-by-step explanation:

To find a subtracted function, simply change all of the signs in the second function and then combine like terms.

f(x) - g(x) = 9x^3 + 2x^2 - 5x + 4 - 5x^3 + 7x - 4

f(x) - g(x) = 4x^3 + 2x^2 + 2x

Answer:

4.25 Liters

Step-by-step explanation:

Edge of Cubical tank

= 20 cm

= 20 (0.01 m)……………..1 meter = 100 cm

= 0.2 m

Volume of Tank

= ( Edge ) ^ 3

= ( 0.2 m ) ^3

= 0.008 m^3

= 8 liters…………….. 1 m^3 = 1000 Liters

Volume required to fill the tank

= 8 - 3.75

= 4.25 Liters

Answer:

x+5=m

Let x be the number of miles that were run the first time.

Add five to the original number

M is the total number of miles for both weeks

To express the area of a rectangle with a perimeter of 14 in terms of one side, use the function S = 7a - a² where S is the area and a is one side length.

To find the function that describes the area of a rectangle in terms of one of its sides with a given perimeter, we can follow these steps. Let's say one side length is a; we will then call the other side length b. The perimeter of a rectangle is given by the formula P = 2a + 2b, where P is the perimeter, and a and b are the lengths of the sides of the rectangle.

Given that the perimeter is 14, we can express b in terms of a as follows:

b = (14 - 2a) / 2

Next, to find the area (S) in terms of a, we multiply the two side lengths together.

S = a × b

Substitute b into the area formula:

S = a × ((14 - 2a) / 2)

Simplifying the formula gives us the function for the area in terms of side a:

S = (14a - 2a²) / 2

Which simplifies further to:

S = 7a - a²

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Answer:

A) The y-coordinates have the same value.

Step-by-step explanation:

Answer:

D) Both points are 4 units above the y-axis.

Step-by-step explanation:

Consider the points (3, 4) and (−3, 4). When the two points are compared, which statement is NOT TRUE?

A) The y-coordinates have the same value. TRUE. The y-coordinates have the value 4.

B) The x-coordinates have the same absolute value. TRUE. 3 and -3 have the same absolute value, |-3| = |3| = 3.

C) The x-coordinates are opposite numbers. TRUE. 3 and -3 are opposite numbers.

D) Both points are 4 units above the y-axis. NOT TRUE. Both points are 4 units above the x-axis.

Answer:

  $2.25

Step-by-step explanation:

Let c represent the cost of a cup of coffee. Then the total amount paid for 3 cups is ...

  3c + 3c·0.08 = 7.29

  3.24c = 7.29

  c = 7.29/3.24 = 2.25

A cup of coffee costs $2.25.

_____

Comment on "I will give you 100 pointd"

I don't know what a "pointd" is, but I suggest you not make promises you cannot keep.

Answer:  [tex]\bold{x=\dfrac{1\pm \sqrt5}{2}}[/tex]

                both zeros are irrational numbers

Step-by-step explanation:

Note: The question would have made more sense if if it was 2/x = x - 1 but I will answer it as written.

[tex]\dfrac{1}{x}=x-1\qquad \text{Restriction: }x\neq 0\\\\\\\text{Cross multiply, simplify, and set equal to zero:}\\1=x(x-1)\\\\1=x^2-x\\\\0=x^2-x-1\\\\\\\text{This is not factorable so you will need to use Quadratic Formula:}\\\\x=\dfrac{-(-1)\pm \sqrt{(-1)^2-4(1)(-1)}}{2(1)}\\\\\\x=\dfrac{1\pm \sqrt5}{2}[/tex]

[tex]\bf \textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 64x^2-25y^2~~ \begin{cases} 64=8\cdot 8\\ \qquad 8^2\\ 25=5\cdot 5\\ \qquad 5^2 \end{cases}\implies 8^2x^2-5^2y^2\implies (8x)^2-(5y)^2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (8x-5y)(8x+5y)~\hfill[/tex]

Answer:

50

Step-by-step explanation:

20% is the same as 0.2 times something.

So you can create the equation 0.2x = 10. The solution of this equation is x=50.

Answer:

The total volume of the snowman is [tex]6\pi\ ft^{3}[/tex]

Step-by-step explanation:

we know that

The volume of a sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

step 1

Find the volume of the spherical snowball with a diameter of 3 feet

Find the radius

[tex]r=3/2=1.5\ ft[/tex] ----> the radius is half the diameter

substitute

[tex]V=\frac{4}{3}\pi (1.5)^{3}[/tex]

[tex]V1=\frac{9}{2}\pi\ ft^{3}[/tex]

step 2

Find the volume of the spherical snowball with a diameter of 2 feet

Find the radius

[tex]r=2/2=1\ ft[/tex] ----> the radius is half the diameter

substitute

[tex]V=\frac{4}{3}\pi (1)^{3}[/tex]

[tex]V2=\frac{4}{3}\pi\ ft^{3}[/tex]

step 3

Find the volume of the spherical snowball with a diameter of 1 feet

Find the radius

[tex]r=1/2=0.5\ ft[/tex] ----> the radius is half the diameter

substitute

[tex]V=\frac{4}{3}\pi (0.5)^{3}[/tex]

[tex]V3=\frac{1}{6}\pi\ ft^{3}[/tex]

step 4

Find the total volume

[tex]V=V1+V2+V3[/tex]

substitute the values

[tex]V=\frac{9}{2}\pi+\frac{4}{3}\pi+\frac{1}{6}\pi=\frac{27+8+1}{6}\pi=6\pi\ ft^{3}[/tex]

Answer: 100 cookies approximately.

Step-by-step explanation:

To round to the nearest ten:

- If the digit located in the units place of the number is [tex]<5[/tex], then you must round the number down.

 - If the digit located in the units place of the number is [tex]\geq5[/tex], then you must round the number up.

The digit located in the units place of the number 11 is 1 and [tex]1<5[/tex], therefore you must round the number down to: 10

The digit located in the units place of the number 12 is 2 and [tex]2<5[/tex], therefore you must round the number down to: 10

Multiply 10 by 10 to estimate the total number of cookies:

[tex]Total_{(cookies)}=10*10\\Total_{(cookies)}=100[/tex]

(100 cookies approximately)

Answer:

vertically stretched by a factor of 5

Step-by-step explanation:

Multiplying the function value by 5 makes each vertical coordinate 5 times the value it was, so it is 5 times as far away from the x-axis. This has the appearance of stretching the graph vertically by a factor of 5.

_____

Comment on the answer choices

The stretch factor is a "pure number", a ratio of new units to old units. It is "5", not "5 units."

For example, if f(x) is 1 ft (1 unit, where the unit is a foot), then g(x) = 5 ft, the value of f(x) multiplied by 5. It is not 5 ft^2, as you would get if f(x) were multiplied by 5 units, or 5 ft.

Answer:

D. y + 4 = 2x  

Step-by-step explanation:

The graph has a y-intercept at (0, -4).

A. y=16 - 3x/4

if x = 0, y = 16. FALSE.

B. 24 + 3y = 6x

If x = 0, 24 + 3y =     0

                     3y = -24

                       y =    -8. FALSE.

C. 4y + x = 16

If x = 0, 4y = 16

              y =   4. FALSE.

D. y + 4 = 2x

If x = 0, y + 4 =  0

           y       = -4. TRUE.

y = 4 + 2x has the same y-intercept as the graphed line.

Answer:

He will take 1.5 seconds to hit the water

Step-by-step explanation:

* The formula h(t) = -16t² + vt + s

- h is the his height above the water

- v is his initial up-word velocity

- s is his starting height

- t is the time

* When he hits the water h(t) = 0

- because h is his height above the water

∴ -16t² + vt + s = 0

∵ v = 8 ft/s

∵ s = 24 ft

∴ -16t² + 8t + 24 = 0 ⇒ × (-1)

∴ 16t² - 8t - 24 = 0 ⇒ ÷ 8

∴ 2t² - t - 3 = 0 ⇒ by using factorization

∴ (2t - 3)(t + 1) = 0

∴ 2t - 3 = 0 ⇒ 2t = 3 ⇒ t = 3/2 = 1.5 sec

∴ t + 1 = 0 ⇒ t = -1 ⇒ rejected the time is positive value

* He will take 1.5 seconds to hit the water

Answer: The answers is 1.5 second

Answer:

252 square inches

Step-by-step explanation:

Georgia needs 4 triangles, each of which has a base of 9 inches and a height of 14 inches. The area of a triangle is ...

A = (1/2)bh

so one face of Georgia's pyramid will have an area of ...

A = (1/2)(9 in)(14 in) = 63 in^2

Then all four faces will have a total area of ...

(63 in^2) · 4 = 252 in^2

_____

Comment on the pattern

The pattern shown includes the base of the pyramid. The problem text says the base is not included. We have assumed that the base is not included. (For Georgia's pyramid, a different pattern would be more to the point: see attachment.)

252 square inches of  cardboard she needed if a = 14 in. and b = 9 in

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The square pyramid will not have a bottom.

We have to find the lateral surface area as the base area is not included.

Georgia needs 4 triangles, each of which has a base of 9 inches and a height of 14 inches.

The area of lateral face is A = (1/2)bh

A = (1/2)(9 in)(14 in)

= 63 square inches

There are four faces so, 4×63 = 252 square inches

Lateral surface area is  252 square inches

Hence, 252 square inches of  cardboard she needed if a = 14 in. and b = 9 in

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The center of the circle is (-4, 5) while the radius is 11 units.

The diagonals of kite KITE intersect at point P. This would be at 44 degrees then.

Answer: 44 degrees

..._..._..._..._..._..._

appreciate

Answer:

c

Step-by-step explanation:

Answer:

p = w - 8

Step-by-step explanation:

I can find 1p or p by subtracting 8 on both sides of the equation.

We need to isolate the variable p here, so we subtract 8 from both sides.

Answer:

f(x) = 3(x -4)^2 +1

Step-by-step explanation:

Usually you start by factoring the leading coefficient from the first two terms:

f(x) = 3(x^2 -8x) +49

Now, you add the square of half the x-coefficient inside parentheses, and subtract the same quantity outside.

f(x) = 3(x^2 -8x +(-4)^2) -3(-4)^2 +49

= 3(x -4)^2 -48 +49

f(x) = 3(x -4)^2 +1 . . . . . . . . the vertex form you desire

Answer:

B) linear function with a positive rate of change

Step-by-step explanation:

Each increase by 1 m^2 in area produces the same 0.2 kW increase in power, so the relationship between area and power is linear. Since they both go up (or both go down), the "rate of change" is positive. (If it were negative, one would go down when the other went up.)

The best description is that of B.

Answer:

  D.  N = w² + 8w + 12

Step-by-step explanation:

The current size is w by w+4, so the area is ...

  A = w(w+4)

When each dimension is increased by 2, the new size is (w+2) by (w+4+2). The latter dimension can be simplified to (w+6). Now, the new area is ...

  N = (w+2)(w+6) = w² +8w +12 . . . . . . . matches choice D

3(20×9)+3((24-9)×8)+(10×8)+(9×10)+((20-8)×10)+((24-9)×10)

=3(180)+3(15×8)+80+90+(12×10)+(15×10)

=540+3(120)+170+120+150

=920+360

=1280

Answers

[tex] {1280cm}^{2} [/tex]

Answer:

[tex]S=1964 in^{2}[/tex]

Step-by-step explanation:

The surface of a rectangular prims is defined as

[tex]S=2lw+2wh+2lh[/tex]

Where [tex]l[/tex] is length, [tex]w[/tex] is width and [tex]h[/tex] is height.

In this case, we have a figure formed by two rectangular prism. We are gonna call Surface 1 to the bottoming prism.

Its diemensions are:

[tex]l=24in\\w=10in\\h=8in[/tex]

So, the Surface 1 is

[tex]S_{1}=2(24)(10)+2(10)(8)+2(24)(8)= 480+160+384=1024in^{2}[/tex]

Now, the dimensions of Surface 2 are

[tex]l=9in\\w=10in\\h=20in[/tex]

Replacing all values, its surface is

[tex]S_{2}= 2(9)(10)+2(10)(20)+2(9)(20)=180+400+360=940in^{2}[/tex]

Therefore, the total surface of the whole figure is

[tex]S=1024+940=1964 in^{2}[/tex]

Answer: [tex]\frac{32}{35}[/tex]

Step-by-step explanation:

We need to convert the mixed numbers into fractions.

The new numerator will be the sum of the numerator of the fractional part and the product obtained by multiplying the denominator of the fractional part by the whole number part.

The new denominator will the the same denominator of the fractional part.

Then:

[tex]2\ \frac{2}{7}=\frac{2+(2*7)}{7}=\frac{16}{7}[/tex]

[tex]2\ \frac{1}{2}=\frac{1+(2*2)}{2}=\frac{5}{2}[/tex]

Dividing the fractions, we get:

[tex]\frac{\frac{16}{7}}{\frac{5}{2}}=\frac{16*2}{7*5}=\frac{32}{35}[/tex]

Answer:

30°

Step-by-step explanation:

If the measure of the arc KL is 25°, then the central angle KOL has measure 25° and the inscribed angle KML subtended on the arc KL has the measure 12.5°.

If the measure of the arc MJ is 85°, then the central angle MOJ has measure 85° and the inscribed angle MLJ subtended on the arc MJ has the measure 42.5°.

Thus, the measure of the angle ELM is 180°-42.5°=137.5°.

Consider triangle EML. In this triangle,

m∠MEL=180°-137.5°-12.5°=30°.

Thus, m∠MEJ=30°.

Answer:

30°

Step-by-step explanation:

x=(a-b)/2 because of secants exterior angles

x=(85-25)/2 Substitution

x=60/2 Algebra

x=30° Answer

Answer:

$120

Step-by-step explanation:

✯Hello✯

↪  If we know that the original price was 20% more than what was payed for it we can form an equation

↪  80%(x)=96 when we solve this x=120

↪ The original price was 120

↪  We can check this by working out 20% of 120 which is 24 and 120-24-96

HOPE THIS HELPS

❤Gianna❤

Answer:

Step-by-step explanation:

Call the point of intersection of AA' and BC point X. Then ...

  CX = AC·cos(90°-x) = AC·sin(x)

and the area of AA'C is ...

  area = AC·CX·sin(90°-x) = AC²·sin(x)cos(x) = (1/2)AC²·sin(2x)

Obviously, area is maximized for 2x = π/2, or x = π/4 when AC is fixed.

___

On the other hand, ...

  AC = AB·tan(x)

so the area of the triangle is ...

  area = (1/2)AC²·sin(2x) = (1/2)(AB·tan(x))²·sin(2x) = AB²·sin(x)³/cos(x)

For fixed AB, area approaches infinity as x approaches 90°.

_____

Comment on the attachments

The attached diagrams show AC=1 and B free to move. Values of x around 45° are shown. The number in the middle of the figure is the approximate area of ΔAA'C.

Answer:

8/3

Step-by-step explanation:

Let S represent the value of 2.666...(repeated). Then 10S will have the value 26.666...(repeated). Subtracting S from 10S, we have ...

10S -S = 26.666... - 2.666... = 24

9S = 24

S = 24/9 = 8/3

The improper fraction equivalent of 2.666...(repeated) is 8/3.

_____

In general, if the number of repeated digits is n, you do this procedure multiplying the number by 10^n before you do the subtraction. The result is a fraction with (10^n)-1 as a denominator. That is, for a 2-digit repeat, the denominator will be 99; for a 6-digit repeat, 999999.

Knowing this, you can immediately recognize that 0.6...(repeated) = 6/9 = 2/3. Then your number 2.666...(repeated) is 2 2/3 = 8/3.

The repeating decimal 2.6 (2.66...) can be simplified as a fraction by setting it equal to a variable, multiplying by a power of 10 to eliminate the decimal, subtracting the original equation, and solving for the variable. This process results in the simplified fraction 8/3.

The number 2.6 repeated refers to the number where the digit 6 repeats indefinitely. To simplify it as a fraction, we can do the following steps:

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Answer:

10.) 116.6

Step-by-step explanation:

10.) add 100^2 + 60^2 = c^2

10,000 + 3600 = c^2

√13,600 = √c^2

116.6 = c

hope this helps!!