Two square based pyramids are joined, total volume is 2700mm, perpendicular height of top pyramid is 16mm, perpendicular height of bottom pyramid is 20mm, length and width of joint base area both x, find x. Please help me

Answer:

(1 + sin x)(1 – sin x) = cos^2x

1 - sin^2x = cos^2x

cos^2x = cos^2x

Step-by-step explanation:

Simplify the left hand side:

(1 + sin x)(1 – sin x) = cos^2x

1 - sin^2x = cos^2x

Using the Pythagorean Identity, we can see that the two sides are equivalent if you subtract sin^2x from both sides:

sin^2x + cos^2x = 1

cos^2x = 1 - sin^2x

Lastly, write it out:

(1 + sin x)(1 – sin x) = cos^2x

1 - sin^2x = cos^2x

cos^2x = cos^2x

Answer:

[tex]x=7\text{ and } m\angle KLM = 34^\circ[/tex]

Step-by-step explanation:

We are given ethat KM and JN are parallel.

And we want to find the value of x.

Notice that ∠JKM and ∠LKM form a linear pair. Linear pairs total 180°. Therefore:

[tex]m\angle JKM + m\angle LKM = 180[/tex]

We know that ∠JKM measures (14x + 8). Substitute:

[tex](14x+8)+m\angle LKM =180[/tex]

Solve for ∠LKM:

[tex]m\angle LKM = 172-14x[/tex]

Next, since KM and JN are parallel, by the Corresponding Angles Theorem:

[tex]\angle JNM \cong \angle KML[/tex]

Since we know that ∠JNM measure (10x + 2), we can conclude that:

[tex]m\angle KML = 10x+2[/tex]

Next, recall that the three interior angles of a triangle must total 180°. Therefore:

[tex]m\angle KLM + m\angle LKM + m\angle KML = 180[/tex]

Substitute:

[tex](5x-1)+(172-14x)+(10x+2)=180[/tex]

Solve for x. Rewrite:

[tex](5x-14x+10x)+(-1+172+2)=180[/tex]

Combine like terms:

[tex](1x)+(173)=180[/tex]

Therefore:

[tex]x=7[/tex]

To find ∠KLM, substitute in 7 for x and evaluate. So:

[tex]m\angle KLM = 5(7) - 1 =34^\circ[/tex]

Answer:

IJKUKOKLIOLIOOOIOLI

Step-by-step explanation:

IOIUOIUOIOIOIOIOIOIOIOIOIOIOIOIOIOIOIOOIOIOIOIOIOIOIOIOIOIOIO

Answer:

[tex]\implies \dfrac{ -4x+7}{2(x-2) }[/tex]

Step-by-step explanation:

The given expression to us is ,

[tex]\implies \dfrac{\frac{ 3}{x-1} -4 }{ 2 -\frac{2}{x-1}}[/tex]

Now take the LCM as ( x - 1 ) and Simplify , we have ,

[tex]\implies \dfrac{\frac{ 3 -4(x-1) }{x-1} }{ \frac{2-2(2x-1)}{x-1}}[/tex]

Simplifying further , we get ,

[tex]\implies \dfrac{ -4x+7}{2(x-2) }[/tex]

Hence the second option is correct .

Step-by-step explanation:

[tex] \frac{ \frac{3}{x - 1} - 4}{2 - \frac{2}{x - 1} } \\ = \frac{ \frac{3 - 4(x - 1)}{x - 1} }{ \frac{2(x - 1) - 2}{x - 1} } \\ = \frac{3 - 4x + 4}{2x - 2 - 2} \\ = \frac{7 - 4x}{2x - 4} = \frac{ - 4x - 7}{2(x - 2)} \\ thank \: you[/tex]

[tex]option \: b \\ thank \: you[/tex]

Answer:

B

Step-by-step explanation:

B was missed. You have to convert this from hours into minutes before you can deal with seconds.

Answer:

126

Step-by-step explanation:

There are 9 city council members.

We have to choose 4 of them.

We have to use the combination as :

[tex]$^9C_4$[/tex]

where, 9 is the population size

4 is the sample size.

Therefore, the total number of possible samples without replacement is given as :

[tex]$^9C_4=\frac{9!}{4!(9-4)!}$[/tex]

      [tex]$=\frac{9!}{5! \ 4!}$[/tex]

     [tex]$=\frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1}$[/tex]

    = 126

Answer:

[tex]y=4x+6[/tex]

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope (also called the gradient) and b is the y-intercept (the value of y when x is 0)

1) Plug the gradient into the equation (b)

[tex]y=mx+b[/tex]

We're given that the gradient of the line is 4. Plug this into [tex]y=mx+b[/tex] as m:

[tex]y=4x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=4x+b[/tex]

Plug in the given point (1,10) as (x,y) and solve for b

[tex]10=4(1)+b\\10=4+b[/tex]

Subtract 4 from both sides to isolate b

[tex]10-4=4+b-4\\6=b[/tex]

Therefore, the y-intercept of the line is 6. Plug this back into [tex]y=4x+b[/tex] as b:

[tex]y=4x+6[/tex]

I hope this helps!

answer = y = 4x + 6

y = mx + b

gradient = slope = m = 4

(1,10) = (x,y)

plug in the values

10 = 4 (1) + b

10 = 4 + b

b = 6

y = 4x + 6

Answer:

Q = G

Step-by-step explanation:

We are already given that angle P = angle H

We are also given that side QP = side GH

Remember if two sides are congruent then so are their opposite angles meaning that the opposite angle of GH ( which would be angle F ) would be congruent to the opposite angle of QP ( which would be angle R )

The remaining angles would be angle q and angle g so the additional information needed would be G = Q

Answer:

a)

x=4, y=-2

b)

x=2, y=2

c)

x=0, y=0

d)

x=1, y=1

e)

x=3, y=3

f)

x=4, y=4

Step-by-step explanation:

a) (x,-2) = (4,y)

x=4

y=-2

b) (3x, 4) = (6, 2y)

3x=6 => x=2

2y=4 => y=2

c) (2x-1, y + 2) = (-1,2)

2x-1 =-1 => x=0

y+2 = 2 => y=0

d) (2x + 4, y + 5) = (3x + 3,6)

2x+4 = 3x+3 => x=1

y+5 = 6 => y=1

e) (x + y,y + 3) = (6, 2y)

x+y = 6 => x+3 = 6 => x=3

y+3 = 2y => y=3

f) (x + y, x - y) - (8,0)​

x+y = 8 => 2x=8 => x=4

x-y = 0 => x=y => y=4

The equivalent equation solved for h is [tex]\frac{P}{mg} = h[/tex]

From the question, we are to determine the equivalent equation solved for h

From the given information,

The amount of potential energy, P, is modeled by the equation

P = mgh

To determine the equivalent equation solved for h, we will make h the subject of the equation,

From,

P = mgh

Divide both sides of the equation by mg

That is,

[tex]\frac{P}{mg} = \frac{mgh}{mg}[/tex]

∴ [tex]\frac{P}{mg} = h[/tex]

Hence, the equivalent equation solved for h is [tex]\frac{P}{mg} = h[/tex]

Learn more on Subject of formula here: https://brainly.com/question/24155675

#SPJ1

Answer

B

Step-by-step explanation:

Edge 2022

Answer:

y=2-3

Step-by-step explanation:

using a calculator

Answer:

-7x and -2x

Step-by-step explanation:

because -7x and -2x are on the same side of the equation. the equal sign in the equation, -7x+12-2x = 23+13x is basically a different way of writing -7x+12-2x and 23+13x.

they're kind of like 2 separate equations. hope this helped! :)

Answer:

[tex]40\ cm^3[/tex]

Step-by-step explanation:

Let the actual volume is V.

The measured volume of an object is 46 cubic cm  which was 15% high from the actual volume.

According to the given condition,

[tex]V+\dfrac{15V}{100}=46\\\\\dfrac{115V}{100}=46\\\\V=\dfrac{4600}{115}\\\\V=40\ cm^3[/tex]

So, the actual volume was [tex]40\ cm^3[/tex].

Answer:

h(x) = 3^(x + 1)

Step-by-step explanation:

The exponential function is;

g(x) = 3^(x)

Now, in transformation of exponential functions of say f(x) = b^(x), when the new function g(x) is created by stretching by a factor of say c along the y-axis, we have;

g(x) = c•b^(x)

In this question, we are told it is stretched by a factor of 3 along the y-axis.

Thus, new function h is;

h(x) = 3 × 3^(x)

Using law of indices, we have;

h(x) = 3^(x + 1)

Answer:

D.

Step-by-step explanation:

She cannot buy a negative number of notebooks. She can buy 0 notebooks, or 1 notebook, or 2, or 3, etc. The number of notebooks she buys must be a non-negative integer.

Answer: D.

Answer:

3x

Step-by-step explanation:

We need to find the HCF of given two numbers .HCF is the Highest Common factor for two or more than two numbers . The given numbers are ,

[tex]\implies Numbers = 3x \ and \ 6x [/tex]

Let's factorise the numbers , we get .

[tex]\implies 3x = 3 \times x [/tex]

[tex]\implies 6x = 3\times 2 \times x [/tex]

The common factors are 3 and x . Therefore the HCF is 3 × x = 3x .

[tex]\implies\underline{\underline{ HCF = 3x }}[/tex]

Answer:

The answer is c=5,-5

Answer:

Correct answer 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Sequence = 120

Step-by-step explanation:

Given

6 rolls of a die;

Required

Determine the possible sequence of rolls

From the question, we understand that there were three possible outcomes when the die was rolled;

The outcomes are either of the following faces: 1, 2 and 3

Total Number of rolls = 6

Possible number of outcomes = 3

The possible sequence of rolls is then calculated by dividing the factorial of the above parameters as follows;

Sequence = \frac{6!}{3!}

Sequence = \frac{6 * 5 * 4* 3!}{3!}

Sequence = 6 * 5 * 4

Sequence = 120

Hence, there are 120 possible sequence.

Step-by-step explanation:

Hope this helps

Answer:

Step-by-step explanation:

Six liters of paint will cover 50 square meters.

  6L ⇒ 50m²

then,

  1L ⇒ 50/6 m²

  9L ⇒ 50 × [tex]\frac{9}{6}[/tex] m²

       ⇒ 75 m²

Answer:

See below

Step-by-step explanation:

Let side AB equal x. Since triangle ABC is equilateral, sides AB, BC, and Ac are all the same length, x. In any isosceles triangle(equilateral is a type of isosceles triangle) the median is the same as the altitude and angle bisector. This means we can say that AD is also a median. A median splits a side into two equal sections, so we can say BD = DC = x / 2. We are given that DC = CE, so we can also say CE = DC = x / 2. Now, we can use the pythagorean theorem to find the length of AD. So we get the equation:

AB^2 - BD^2 = AD^2

We have the values of AB and BD, so we can substitute them and solve for AD:

x^2 - (x/2)^2 = AD^2

x^2 - x^2 / 4 = AD^2

AD^2 = 3x^2 / 4

AD = x√3 / 2

DE is equal to the sum of DC and CE because of segment addition postulate, so we can say DE = DC + CE = x / 2 + x/ 2 = x. We can again use the pythagorean theorem to find the length of AE:

AD^2 + DE^2 = AE^2

(x√3 / 2)^2 + x^2 = AE^2

3x^2 / 4 + x^2 = AE^2

AE^2 = 7x^2 / 4

AE = x√7 / 2

Now, we know(from before) that AE squared is 7x^2 / 4. We can say EC squared is x^2 / 4 because EC is x / 2 and x / 2 squared is x^2 / 4. We can also notice that AE squared is 7 times EC squared because 7x^2 / 4 = 7 * x^2 / 4

Therefore, we can come to the conclusion AE^2 = 7 EC^2

Answer:

[tex]-3\frac{1}{3}[/tex]

Step-by-step explanation:

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

Given:

[tex](-4)+\frac{2}{3}[/tex]

--------------->>>>

Make the denominators the same.

[tex](-4*\frac{3}{3} )+\frac{2}{3}=[/tex]

--------------->>>>

Multiply inside the parenthesis.

[tex]-\frac{12}{3} +\frac{2}{3}=[/tex]

--------------->>>>

Join the denominators.

[tex]\frac{-12+2}{ 3}=[/tex]

--------------->>>>

Add the numerators.

[tex]-\frac{10}{3}[/tex]

--------------->>>>

Convert to mixed fraction.

[tex]-3\frac{1}{3}[/tex]

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

Hope this is helpful.

Answer:

-10/3.

Step-by-step explanation:

(-4). 2

----- + ------

1 3

we have to make the denominator same:

so.,

-4. ×. 3. -12

---- ---- = ------

1. ×. 3. 3

-12 2. -12+2

---. + ---- =. -----------

3. 3. 3

-10

=. ----

3

Answer:

240

Step-by-step explanation:

well do *

so 8x6x5 = 240 there's your answer

Answer:

[tex]S.A=1/2(8+8)(9^{2})+8\times 6+8\times 5[/tex]

[tex]=26\times2+48+40[/tex]

[tex]=140 ~cm^{2}[/tex]

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

HOPE IT HELPS

HAVE A GREAT DAY!!

Answer:

∆a = 1/2

Step-by-step explanation:

parabolas cross the x-axis at (-4, 0) and (6, 0)

y = a(x + 4)(x - 6)

At the y-intercept x = 0

y =  a(0 + 4)(0 - 6)

y = -24a

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

y-intercept of the first parabola is (0,–12)

-12 = -24a

a = 1/2

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

y-intercept of the second parabola is (0, -24)

-24 = -24a

a = 1

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

What is the positive difference between the a values

∆a = 1 - 1/2

∆a = 1/2

Answer:

The number of FM listereners are 24000.

Step-by-step explanation:

Let the listeners of FM are p and thus the istereners of AM are 5p.

According to the question,

p + 5 p = 144000

6 p = 144000

p = 24000

The number of FM listereners are 24000.

Answer:

7 cajas grandes y 3 cajas pequeñas  

Step-by-step explanatio:

Answer:

C.) AA

Step-by-step explanation:

AA is a similarity theorem

hope this helps stay safe :)

Answer:

The answer would be C.

Step-by-step explanation: Hope this helps :)