Find the value of x in the isosceles triangle shown

Answer:

Step-by-step explanation:

Look at the picture.

We have the triangles 30° - 60° - 90° and 45° - 45° - 90°.

The sides are in proportions:

30° - 60° - 90° ⇒ 1 : √3 : 2

45° - 45° - 90° ⇒ 1 : 1 : √2

======================================================

[tex]SR=ST\sqrt3\to ST\sqrt3=2\sqrt3\qquad\text{divide both sides by}\ \sqrt3\\\\ST=2\\\\TR=2ST\to TR=2(2)=4\\\\RQ=TR\to RQ=4\to x=4[/tex]

Answer:

The volume of the irregular figure is [tex]470\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the irregular figure is equal to

[tex]V=BL[/tex]

where

B is the area of the front of the L-shaped figure

L is the length of the figure

Find the area B

The area of of the front of the L-shaped figure is equal to the area of two rectangles

[tex]B=(9)(3)+(9-5)(8-3)[/tex]

[tex]B=(9)(3)+(4)(5)[/tex]

[tex]B=27+20=47\ cm^{2}[/tex]

we have that

[tex]L=10\ cm[/tex]

Find the volume

[tex]V=BL[/tex]

[tex]V=(47)(10)=470\ cm^{3}[/tex]

Answer:

Possible, but very unlikely

Step-by-step explanation:

In a school of 150 students, the probability that at least two people have the same birthday is possible but very unlikely.

In a year, we have 365 total possible birthdays. If one student was born on 1st of January say, then the second student has 364 possible birth-dates assuming that they have different birthdays. This implies there is a higher probability that the second student has a different birthday.

Moreover, considering the school has only 150 students which is less than the total possible birth-days in a year, 365, the chances of two or more students sharing a birthday is possible but would be very unlikely.

Final answer:

The event that at least two people have the same birthday in a school of 150 students is possible and likely, according to the principles of probability theory and the 'birthday paradox'.

Explanation:

In considering whether it is possible and likely that at least two people have the same birthday in a school of 150 students, we can refer to the birthday paradox. This mathematical probability phenomenon shows that, with just 23 people, there is a roughly 50% chance of two individuals sharing a birthday.

The probability increases significantly with each additional person to the point that in a group of 150 students, it is highly likely that at least two people will share the same birthday. This scenario is an interesting application of probability theory where our intuition might not align with the mathematical reality due to the non-intuitive properties of combinatorics and probability.

We do not arrive at this conclusion by adding probabilities of non-mutually exclusive events incorrectly, which would exceed 100% certainty. Instead, we calculate the probability of all students having unique birthdays, and subtract this from 1 to find the complement probability that at least two students share a birthday. This approach correctly keeps the calculated probability between 0 and 1, as per probability theory's third law.

In the case of 150 students, the calculated likelihood is so close to 1 (almost certain) that we can confidently classify the event as possible and likely.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x=3y&\text{subtract}\ 3y\ \text{from both sides}\\3x-2y=14\end{array}\right\\\\\left\{\begin{array}{ccc}x-3y=0&\text{multiply both sides by (-3)}\\3x-2y=14\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-3x+9y=0\\3x-2y=14\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad7y=14\qquad\text{divide both sides by 7}\\.\qquad\qquad y=2\\\\\text{put the value of y to the first equation:}\\x=3(2)=6[/tex]

Since the sum of the opposite angles of a cyclic quadrilateral are supplementary, the value of d is equal to 80°.

In Mathematics, the measure of the sum of two (2) adjacent angles would be equal to 180º when a quadrilateral is inscribed in a circle. Generally speaking, any cyclic quadrilateral would have all of its vertices on the circumference of a circle.

This ultimately implies that, the sum of the opposite angles of a quadrilateral that is inscribed in a circle (cyclic quadrilateral) are supplementary;

m∠c + 96 = 180°

m∠d + 100 = 180°

Now, we can solve for the value of d by by subtracting 100 from both sides of the equation as follows;

m∠d + 100 - 100 = 180° - 100

m∠d = 80°

Answer: 91,445,760 ft³

Step-by-step explanation:

You know that the base of this pyramid is a square, then you can use the following formula to calculate its volume:

[tex]V=\frac{s^2h}{3}[/tex]

Where "s" is the lenght of any side of the base of the pyramid and "h" is the height of the pyramid.

You know that:

[tex]h=480ft\\s=756ft[/tex]

Then, you can substitute these values into the formula. So, you get that the volume of The Great Pyramid is:

[tex]V=\frac{(756ft)^2(480ft)}{3}=91,445,760ft^3[/tex]

This answer should be found using the distance formula. Steps are attached. Answer is 7.

Simple! All you need to do is graph the coordinates and then count the spaces in between, and the answer should be seven! Or, try -5 + 7, which would equal 2.

Answer:

52 sodas

Step-by-step explanation

h=hotdogs

s= sodas

1.5h+.5s=78.5

You know that Emily sold 35 hotdogs so you replace h with 35.

Therefore, 1.5(35)+.5s=78.5

52.5+.5s=78.5

.5s=26

s=52

The answer is:

We will have to fill 226.194 cubic inches.

To solve the problem, we need to find the volume of the flower vase, and then, calculate the two third parts of its volume. Also, from the statement we know that the shape of the flower vase is a right cylinder, since the only given information about it, is its diameter and height.

We can calculate the volume of a right cylinder using the following equation:

[tex]V_{Cylinder}=\pi radius^{2}*height[/tex]

So, we are given the following information:

[tex]diameter=6in\\radius=\frac{diameter}{2}=\frac{6in}{2}=3in\\height=12in[/tex]

Then,

Substituting the given information, and calculating, we have:

[tex]V_{Cylinder}=\pi *(3in)^{2}*12in=108\pi=339.292in^{3}[/tex]

Now, calculating how many cubic inches are [tex]\frac{2}{3}[/tex] of the flower vase volume, we have:

[tex]VolumeToFill=CubicInchesToFill=\frac{2}{3}*Volume\\\\CubicInchesToFill=\frac{2}{3}*339.292in^{3} =226.194in^{3}[/tex]

Hence, we have that we will have to fill 226.194 cubic inches.

Have a nice day!

Answer:

[tex]72\pi\ in^{3}[/tex]

Step-by-step explanation:

step 1

Calculate the volume of the cylinder (flower vase)

The volume is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]r=6/2=3\ in[/tex] -----> the radius is half the diameter

[tex]h=12\ in[/tex]

substitute the values

[tex]V=\pi (3)^{2}(12)=108\pi\ in^{3}[/tex] ------> exact value

step 2

Calculate  2/3 of the volume

[tex]V=(2/3)108\pi=72\pi\ in^{3}[/tex]

Answer:

The correct answer is C) 7,200.

Step-by-step explanation:

In order to find the answer for this, start by using the formula for momentum.

Mo = M*V

Mo = 120 * 60

Mo = 7,200

The momentum is 7200 kg-m/s.

Given: An object

Mass = 120 kg

Velocity = 60 m/s

We have to find the momentum of an object.

We know, momentum is given by:

⇒ Momentum = Mass × Velocity

⇒ Momentum = 120 × 60

⇒ Momentum = 7200 kg-m/s

Therefore, the momentum of an object is 7200 kg-m/s.

Hence, option (C) is correct.

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Answer:

From the information we can conclude that the triangle is a isosceles triangle.

First, we can calculate the hypotenuse by using pythagorean theorem:

√(6² + 6²) = √(36 + 36) =√64 = 8 (cm)

To calculate the area of the triangle, we first need to know the height of it.

Since this is a isosceles triangle, the altitude (which is also the height) will also  be the median of that triangle.

Then we also have a 90° angle, this triangle is also a right triangle, and in right triangle, the median will equal half of the hypotenuse.

From the reasoning above, we can now calculate the height of the triangle:

8/2 = 4(cm)

The area of the triangle should be:

S = hb/2 = (4 . 6)/2 = 12 (cm²)

Answer:

25.

The question is on  kinematic equations and free fall

An expression for h, displacement is given by;

h=v.t +1/2 at²................... where v is initial velocity, t is time and a is acceleration due to gravity

Given v=10ft/s d=-50 and a= -32.2 ft/s²..............................substitute the values in

h=v.t +1/2 at².

-50=10t + 1/2( -32.2)t²

-50=10t-16.1t²

16.1t²-10t-50=0..........................the function for height h in feet

b)  Solve 16.1t²-10t-50=0 using the quadratic formula

t= (-b ± √b² - 4ac )/2a

a=16.1  b= -10   and c= -50

t=( 10 ± √ (-10)² - 4 × 16.1 × -50 ) / 2×16.1

t= (10± √3320 )/ 32.2

t= (10± 57.62 ) / 32.2

t=67.62/32.2 = 2.1 sec or  - 47.62/32.2 = -1.5 sec

26.

a)The question is on  kinematic equations and free fall

An expression for h, displacement is given by;

h=v.t +1/2 at²................... where v is initial velocity, t is time and a is acceleration due to gravity

Given v=3ft/s  h= -1.3 ft and a= -32.2 ft/s²

substitute vales in;

h=v.t +1/2 at²

1.3=3t+1/2(32.2)t²

1.3=3t+16.1t²

16.1t²+3t-1.3=0...........................the function for h

b) Solve for t in 16.1t²+3t-1.3=0 using the quadratic formula

a=16.1        b=3      c= -1.3

t= (-3 ± √ -3² - 4×16.1× -1.3) / 2×16.1

t= ( -3 ± √ 9 + 83.72 ) / 32.2

t= (-3 ± 9.6 )/32.2

t= (-3+9.6)/32.2  = 6.6/32.2 = 0.2049 or

t= (-3-9.6)/32.2 = -12.6/ 32.2 = -0.391

c)  if the ball hit the rim at one half foot above the ground, find the distance it covered before hitting the rim

1.3-0.5=0.8 ft......................displacement

applying h=v.t +1/2 at²

0.8=3t+16.1t²

16.1t²+3t-0.8=0.......................solve using the quadratic formula

a=16.1  b=3    c= -0.8

t=(  -3 ± √3²- 4×16.1×-0.8  )/2×16.1

t=( -3±√9+51.52 )/ 2× 16.1

t = (-3 ± √60.52 )/32.2

t=( -3±7.78 )/ 32.2

t= (-3+7.78 )/32.2 =0.148 sec   or  t= (-3-7.78)/32.2 = -0.335 sec

Answer:

d. x= +-11.18

Step-by-step explanation:

The value of x in the quadratic equation  3x² = 375 is  ± 5√5.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Given, An equation 3x² = 375.

x² = 375/3.

x² = 125.

x = ± 5√5.

So, the value of x in the equation  3x² = 375 is 5√5.

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Answer:

Step-by-step explanation:

We know: the sum of the measures of triangle angles is 180°.

Therefore we have the equation:

[tex]2x+(3x-10)+50=180\\\\(2x+3x)+(-10+50)=180\\\\5x+40=180\qquad\text{subtract 40 from both sides}\\\\5x+40-40=180-40\\\\5x=140\qquad\text{divide both sides by 5}\\\\\dfrac{5x}{5}=\dfrac{140}{5}\\\\x=28[/tex]

The sum of all the angles of a triangle is 180°

This means you have to add all the angles together and set it equal to 180. Here is the formula:

50 + 2x + 3x - 10 = 180

Now you solve for x

Step 1: Combine like terms

(50 + (-10) ) + (2x + 3x) = 180

40 + 5x = 180

Step 2: Subtract 40 to both sides

(40-40) + 5x = 180 - 40

5x = 140

Step 3: Isolate x by dividing 5 to both sides

[tex]\frac{5x}{5}  = \frac{140}{5}[/tex]

x = 28

Check: 50 + 2(28) + 3(28) - 10 = 180

50 + 56 + 84 - 10 = 180

180 = 180

Therefore your value of x is 28!

Hope this helped!

Answer:

cosA/cosB =  1

Step-by-step explanation:

We know that cos = Adjacent Side/hypothenuse.

Then Cos(A)= AC/AB = 3/4.24 = 0.707

Cos(B) = BC/AB = 3/4.24 = 0.707

Then cosA/cosB = 0.707/0.707 = 1

Answer:

The correct answer is

CosA/CosB =1

Step-by-step explanation:

Points to remember

Trigonometric ratios

Cos θ = Adjacent side/Hypotenuse

From the figure we can see a right angled triangle.

To find the value of CosA/CosB

CosA = Adjacent side/Hypotenuse

 =AC/AB = 3/4.24

Cos B =  Adjacent side/Hypotenuse  

 = BC/AB = 3/4.24

CosA/CosB = (3/4.24)/(3/4.24) = 1

Therefore the value of CosA/CosB = 1

Answer:

put the united states population over the world population you will get a simplified fraction to the ratio between them which is 1/23   easily you can multiply 23 by the USA population to get the world population so it is more than USA population 23 times  

3*10^8 / 6.9*10^9 = 1/23

then   23  *  3*10^8  = 6.9*10^9  

The world population is approximately 23 times larger than the population of the United States.

The question is asking us to determine how many times larger the world's population is compared to the population of the United States. It gives us the population of the United States as 3 x 108 and the world's population as 6.9 x 109. To solve this, we'll divide the world population by the US population.

The calculation is as follows: (6.9 x 109) / (3 x 108) which equals to 23

This means that the world population is approximately 23 times larger than the United States population.

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The answer is:

D. [tex]8\sqrt[3]{5}[/tex]

To solve the problem, we need to remember the following roots properties:

[tex]a^{\frac{m}{n} }=\sqrt[n]{a^{m} }[/tex]

[tex]a\sqrt[n]{b} =\sqrt[n]{a^{n}*b} \\\\\sqrt[n]{ab}=\sqrt[n]{a}*\sqrt[n]{b}[/tex]

So, we are given the expression:

[tex](8.320)^{\frac{1}{3} }[/tex]

Then,  writing its equivalent expression, we have:

[tex]\sqrt[3]{8.320}[/tex]

Now, simplyfing, we have:

[tex]\sqrt[3]{8.320}=\sqrt[3]{2560}=\sqrt[3]{512*5}\\\\\sqrt[3]{8.320}=\sqrt[3]{512*5}=\sqrt[3]{8^{3} .5}\\\\\sqrt[3]{8.320}=\sqrt[3]{8^{3} .5}=\sqrt[3]{8}*\sqrt[3]{5} \\\\\sqrt[3]{8.320}=\sqrt[3]{8}*\sqrt[3]{5}=8*\sqrt[3]{5}[/tex]

Hence, we have that the correct option is:

D. [tex]8\sqrt[3]{5}[/tex]

Have a nice day!

Answer:

A

Step-by-step explanation:

To calculate the scale factor k, find the ratio of corresponding sides

[tex]\frac{XZ}{AC}[/tex] = [tex]\frac{18}{3}[/tex] = 6

[tex]\frac{YZ}{BC}[/tex] = [tex]\frac{24}{4}[/tex] = 6

Hence the scale factor k = 6 → A

Answer:  The correct option is (A) 6.

Step-by-step explanation:  We are given to find the scale factor of dilation from triangle ABC to triangle XYZ.

From the figure, we note that

The lengths of the sides of triangles ABC and XYZ are as follows :

AB = 5 units, BC = 4 units, AC = 3 units, XY = 30 units, YZ = 24 units and XZ = 18 units.

We know that

[tex]\textup{Scale factor}=\dfrac{\textup{length of a side of the dilated figure}}{\textup{length of the corresponding side of the original figure}}.[/tex]

Therefore, for the given triangles, we get

[tex]\textup{Scale factor}=\dfrac{XY}{AB}=\dfrac{30}{5}=6.[/tex]

Thus, the required scale factor of dilation is 6.

Option (A) is CORRECT.

4x - 8, 4x just means four of x, and eight less means to subtract 8.

Final answer:

The algebraic expression for 'eight less than four times a number' is '4x - 8', where x represents the number.

Explanation:

To write an algebraic expression for "eight less than four times a number," we first consider what the expression tells us:

Four times a number hints at a multiplication of some number, let's call it x, by 4, which we write as 4x.

Eight less than something means we need to subtract 8 from that something.

Therefore, combining these two steps, the algebraic expression that represents "eight less than four times a number" is 4x - 8.

The answer is 9424.78

Reason:

Answer:

Ans: -5

Step-by-step explanation:

__ + 3 = -2

You bring the 3 to the other side

-2 - 3 = -2 + -3 = -5

-5 is the answer for your problem

Answer:

The width of the original rectangle on the left is [tex]5\ m[/tex]

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

so

Let

z -----> the scale factor

a ----> perimeter of the reduced rectangle on the right

b ----> perimeter of the original rectangle on the left

[tex]z=\frac{a}{b}[/tex]

we have

[tex]a=24\ m[/tex]

[tex]b=30\ m[/tex]

substitute

[tex]z=\frac{24}{30}=0.8[/tex]

step 2

Find the width of the reduced rectangle on the right

we know that

The perimeter of rectangle is equal to

[tex]P=2(L+W)[/tex]

we have

[tex]L=8\ m[/tex]

[tex]P=24\ m[/tex]

substitute and solve for W

[tex]24=2(8+W)[/tex]

[tex]12=(8+W)[/tex]

[tex]W=12-8=4\ m[/tex]

step 3

Find the width of the original rectangle on the left

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

so

Let

z -----> the scale factor

y ----> the width of the reduced rectangle on the right

x ----> the width of the original rectangle on the left

[tex]z=\frac{y}{x}[/tex]

we have

[tex]y=4\ m[/tex]

[tex]z=0.8[/tex]

substitute and solve for x

[tex]0.8=\frac{4}{x}[/tex]

[tex]x=\frac{4}{0.8}[/tex]

[tex]x=5\ m[/tex]

Answer: E

Step-by-step explanation:

Answer E hope this helped

Answer:

[tex]x1=\frac{-2+\sqrt{26/3}}{2}[/tex]

[tex]x2=\frac{-2-\sqrt{26/3} }{2}[/tex]

Step-by-step explanation:

To find the zeros of the quadratic function f(x)=6x^2 + 12x – 7 we need to factorize the polynomial.

To do so, we need to use the quadratic formula, which states that the solution to any equation of the form ax^2 + bx + c = 0 is:

[tex]x=\frac{-b±\sqrt{b^{2}-4ac}}{2a}[/tex]

So, the first thing we're going to do is divide the whole function by 6:

6x^2 + 12x – 7 = 0 -> x^2 + 2x - 7/6

This step is optional, but it makes things quite easier.

Then we using the quadratic formula, where:

a=1, b= 2, c = -7/6.

Then:

[tex]x=\frac{-2±\sqrt{2^{2}-4(1)(-7/6)}}{2}[/tex]

[tex]x=\frac{-2±\sqrt{4 +14/3}}{2}[/tex]

[tex]x=\frac{-2±\sqrt{26/3}}{2}[/tex]

So the zeros are:

[tex]x1=\frac{-2+\sqrt{26/3}}{2}[/tex]

[tex]x2=\frac{-2-\sqrt{26/3}}{2}[/tex]

Answer:

[tex]\lim_{x \to \infty} \frac{2500+17(x-100)}{x}=17[/tex]

Step-by-step explanation:

Let the theme park sold number of tickets = x

Theme park charges $500 for group booking more than 25 tickets.

In addition to this theme park charges $20 per ticket for up to 100 tickets.

So charges of 100 tickets = 500 + (100×20) = $2500

For more than 100 tickets theme park charges $17, so charges for x tickets will be = 500 + (100×20) + 17(x - 100)

= 2500 + 17(x - 100)

Cost of one ticket of the theme park = [tex]\frac{2500+17(x-100)}{x}[/tex]

Now we have to write the limit equation when number of tickets purchased becomes very high.

[tex]\lim_{x \to \infty} \frac{2500+17(x-100)}{x}=17[/tex]

[By solving limit as below

[tex]\lim_{x \to \infty} \frac{2500+17(x-100)}{x}= \lim_{x \to \infty}\frac{2500}{x}+17-\frac{1700}{x}[/tex]

since [tex]\lim_{x \to \infty}(\frac{1}{x})=0[/tex]

Therefore, [tex]\lim_{x \to \infty}\frac{2500}{x}+17-\frac{1700}{x}=0+17-0[/tex]

= 17 ]

Answer:

A  36[tex]\pi[/tex] [tex]cm^{3}[/tex]

Step-by-step explanation:

The formula for the volume of a sphere is [tex]\frac{4}{3}\pi r^{3}[/tex]. Because we are given the radius, 3 (centimeters), of the sphere, all we would need to do is plug 3 in for [tex]r[/tex], and solve.

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

Using the order of operations (Parentheses, Exponents), we can solve for [tex](3)^{3}[/tex], which is 27 (think 3*3*3).

Then, we simply Multiply [tex](\frac{4}{3})(\pi)(27)[/tex], to get [tex]36\pi[/tex].

With our unit, centimeters cubed ([tex]cm^{3}[/tex]), our sphere's volume is 36[tex]\pi[/tex] [tex]cm^{3}[/tex].

The answer is provided in the image attached.

Answer:

x ≈ 11.7

Step-by-step explanation:

When 2 secants are drawn from an external point to a circle then

The products of the measures of one secant's external part and the entire secant is equal to the product of the measures of the other secant's external part and that entire secant, that is

3(3 + x) = 4(4 + 7)

9 + 3x = 4 × 11 = 44 (subtract 9 from both sides )

3x = 35 ( divide both sides by 3 )

x ≈ 11.7

Answer:

a.

Step-by-step explanation:

The key thing to look for here is the vertex. The vertex is the middle of the graph. In the graph, the vertex is located as (2,3)

To write your equation, use the formula y = a|x-h|+k. (h,k) is your vertex [h is the x-coordinate k is the y-coordinate]. So, substitute your vertex into the equation.

[Notice the equation says -h, not h. That's why you have to put -2 into the equation, not positive 2.]

So, your equation will be y=|x-2|+3.

I hope this helps!

Answer:

the rule is add 7 i thinso it would be m+7

Step-by-step explanation:

Answer:

? = 7

Step-by-step explanation:

We know it's 7 because,

2 + 7 = 9

4 + 7 = 11

8 + 15 = 7

11 + 7 + 18

Hey, this is easy! Why not ask your parents?

Answer:

A - f

Step-by-step explanation:

Break each term down into its prime factors

7f^2 = 7 *f*f

12f = 2*2*3*f

The common term is f

Factor out the f

f(7f-12)