Of 240 stamps that Harry and his sister collected, Harry collected 3 times as many as his sister. How many did each collected.

9514 1404 393

Answer:

  x = 36

Step-by-step explanation:

The interior angle at E is (180-2x). The interior angle at F is (180-4x). The sum of the interior angles of the triangle is 180, so we have ...

  (180 -2x) +x +(180 -4x) = 180

  180 = 5x . . . . . . add 5x-180 to both sides

  36 = x . . . . . . . divide by 5

__

Additional comment

This value of x makes the exterior angles at E and F be 72° and 144°, respectively. The internal angles at E, F, G are then 108°, 36°, 36°, making the triangle isosceles with EF = EG.

The solution of the equation 3x² + 17x - 6 = 0 are, x = 1/3 and x = - 6.

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The quadratic equation is,

⇒ 3x² + 17x - 6 = 0

Now, We can solve the equation as;

⇒ 3x² + 17x - 6 = 0

⇒ 3x² + (18 - 1)x - 6 = 0

⇒ 3x² + 18x - x - 6 = 0

⇒ 3x (x + 6) - 1 (x + 6) = 0

⇒ (3x - 1) (x + 6) = 0

This gives two solutions,

⇒ 3x - 1 = 0

⇒ x = 1/3

And, x + 6 = 0

⇒ x = - 6

Learn more about the quadratic equation visit:

brainly.com/question/1214333

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Answer:

6 samples

Step-by-step explanation:

Given :

Sample size, = n

Standard deviation, = 6000

Margin of Error = 2000

Confidence interval, α = 95%

Zcritical at 95% = 1.96

n = (Zcritical * σ) / margin of error

n = (1.96 * 6000) /2000

n = 11760 / 2000

n = 5.88

n = 6 samples

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

It is given that,

→ 10(2x-3) = 10

Then find required value of x,

→ 10(2x-3) = 10

→ 20x-30 = 10

→ 20x = 10+30

→ 20x = 40

→ x = 40/20

→ [x = 2]

Hence, the value of x is 2.

Answer:

99, 113

Step-by-step explanation:

X-the first bus

X+14-the second bus

5x+5(x+14)=1060

10x+70=1060

10x=990

X=99-the first bus

99+14=113-the second bus

Answer:

3 e^t/2 + 4 = 27

e^t/2 = 23 / 3

Taking natural log of both sides

t/2 = ln 23/3 = ln 7.667 = 2.037

t = 4.074

Check:

3 e^4.074/2 + 4 = 27

27 = 27

Answer:

b) LeBron is relatively taller because he has a larger z-score.

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

LeBron James:

Height of 81 inches, while the average 30- to 39-year old man is 69.5 inches tall, with a standard deviation of 2.7 inches, which means that we have to find Z when [tex]X = 81, \mu = 69.5, \sigma = 2.7[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{81 - 69.5}{2.7}[/tex]

[tex]Z = 4.26[/tex]

Candace Parker:

Height of 76 inches, while the average 30- to 39-year old woman is 64.2 inches tall, with a standard deviation of 3.2 inches. This means that we have to find Z when [tex]X = 76, \mu = 64.2, \sigma = 3.2[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{76 - 64.2}{3.2}[/tex]

[tex]Z = 3.69[/tex]

Who is relatively taller?

Due to the higher z-score, LeBron James, and thus, the correct answer is given by option b.

Answer:

2 sqrt(2) = x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin 45 = x/4

4 sin 45 = x

4 ( sqrt(2)/2) =x

2 sqrt(2) = x

Answer: D

Use sine to find the x-value:

[tex]sin(45)=\frac{x}{4} \\\\4*sin(45)=x\\\\x=\frac{\sqrt{2} }{2} *4=2\sqrt{2}[/tex]  

Answer:

11, 18, 25, 32, .....

Option D

Step-by-step explanation:

The formula for the nth term of an AP is a+(n-1)d

a+(n-1)d=a+(n-1-1)d+7

a+nd-d=a+nd-2d+7

d=7

As the common difference is 7.

The only option given which is in an AP is the 4th option

Answer:

Option (C)

Step-by-step explanation:

Surface area of a right prism = 2(Area of the triangular base) + Ph

Here, P = Perimeter of the base

h = Height of the prism

Area of the triangular base = [tex]\frac{1}{2}(\text{Height})(\text{Base})[/tex]

                                             = [tex]\frac{1}{2}(5)(12)[/tex]

                                             = 30 cm²

Height of the prism = 15 cm

Perimeter of the base = (5 + 12 + 13)

                                     = 30 cm

Surface area of the right prism = 2(30) + 30(15)

                                                   = 60 + 450

                                                   = 510 cm²

Therefore, Option (C) will be the correct option.

Step-by-step explanation:

One easy way to find a number that has all of these numbers as factors is to multiply them all together, so 2 * 5 * 7 = 10 * 7 = 70, which is one number.

To find the other number, we can multiply the number we already have by any integer greater than 1, e.g. 2, to get 70* 2= 140 as our other number, making our numbers 70 and 140

Answer:

17d/20

Step-by-step explanation:

100-25=85

85/100×d

=17/20×d

=17d/20

measure horizontally

measure vertically

measure depth..

Answer: B. X It passes the vertical line test :)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:  [tex]-\infty < y < \infty[/tex] which is choice A

This is the set of all real numbers.

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

Explanation:

If you were to graph this function, then it spans infinitely upward and infinitely downward as well. That means that we can land on any y value we want, and that's why the range is the set of all real numbers.

Another approach we could take is to swap x and y to get [tex]x = \sqrt[3]{y+8}[/tex] which solves to [tex]y = x^3-8[/tex] . This is the inverse of the original function your teacher gave you. Recall that the domain and range swap roles when going from the original function to the inverse. What this means is that because the domain of

Domain of inverse = set of all reals

Range of original = set of all reals

Answer:

FnH = {Meagan}

Step-by-step explanation:

Given the following sets and events:

S = {Albert, Betty, Abel, Jack, Patty, Meagan}

F = {Betty, Patty, Meagan},

H = {Abel, Meagan}

P = {Betty, Abel}.

In order to get FnH

The intersection of F and H is the element that is common to both sets. Hence for the set given, we can see that Meagan is common to both sets, therefore:

FnH = {Meagan}

Answer:

Move triangle ABC over 2 and up 1

Step-by-step explanation:

A transformation in geometry is to essentially move a shape. To move ABC onto A1B1C1 you would move triangle ABC over 2 and up 1.

Answer:

x = 14.4

Step-by-step explanation:

x is sin(angle 24/30)×24

how do we get the angle at 24/30 ?

by using the extended Pythagoras for baselines opposite other than 90 degrees.

c² = a² + b² - 2ab×cos(angle opposite of c)

in our example the angle 24/30 is opposite of the side 18.

so,

18² = 24² + 30² - 2×24×30×cos(angle 24/30)

324 = 576 + 900 - 1440×cos(angle 24/30)

324 = 1476 - 1440×cos(angle 24/30)

1440×cos(angle 24/30) = 1152

cos(angle 24/30) = 1152/1440 = 576/720 = 288/360 = 144/180 = 72/90 = 36/45 = 12/15 = 4/5

angle 24/30 = 36.9 degrees

x = sin(36.9) × 24 = 14.4

Answer:

Following are the solution to the given points:

Step-by-step explanation:

Normal Distribution:

[tex]\mu=50\\\\\sigma= 6\\\\Z=\frac{X-\mu}{\sigma} \sim N(O,l)[/tex]

For point a:

[tex]P(X< 56)=\frac{(56-50)}{6}= \frac{6}{6}=1\\\\[/tex]

[tex]=P(Z<1)\ From\ \sigma \ Table=0.8413\\\\P(X>= 56)=(1-P(X< 56))=1-0.8413=0.1587\\\\[/tex]

For point b:

[tex]P(X< 49)=\frac{(49-50)}{6}=-\frac{1}{6} =-0.1667\\\\=P(Z<-0.1667)\ From\ \sigma \ Table\\\\=0.4338[/tex]

For point c:

To Find [tex]P(a\leq Z\leq b)= F(b) - F(a)\\\\[/tex]

[tex]P(X< 45)=\frac{(45-50)}{6}=\frac{-5}{6} =-0.8333\\\\P (Z<-0.8333) \ From \ \sigma \ Table\\\\=0.20233\\\\P(X< 55)=\frac{(55-50)}{6} =\frac{5}{6}=0.8333\\\\P ( Z< 0.8333) \ From \ \sigma\ Table\\\\=0.79767\\\\P(45 < X < 55) =0.79767-0.20233 =0.5953[/tex]

Answer:

C    

If x = o then f(0) = 4(2) * 0 = 0

If f(x) = 4(2) 0 - 13

then f(x) = -13 at x = 0

Answer:

it will indeed be c

Step-by-step explanation:

deesnuts

9514 1404 393

Answer:

Step-by-step explanation:

Let x and y represent the cost of a hot dog and a hamburger, respectively. The the two purchases can be described by ...

  3x +2y -9.75 = 0

  2x +3y -10.25 = 0

We can list the coefficients of these general-form equations in 2 rows, listing the first one again at the end:

  3, 2, -9.75, 3

  2, 3, -10.25, 2

Now, we can form differences of cross-products in adjacent pairs of columns:

  d1 = (3)(3) -(2)(2) = 9 -4 = 5

  d2 = (2)(-10.25) -(3)(-9.75) = -20.50 +29.25 = 8.75

  d3 = (-9.75)(2) -(-10.25)(3) = -19.50 +30.75 = 11.25

Then the solutions are found from ...

  1/d1 = x/d2 = y/d3

  x = d2/d1 = 8.75/5 = 1.75

  y = d3/d1 = 11.25/5 = 2.25

The cost of one hot dog is $1.75; the cost of one hamburger is $2.25.

_____

Additional comment

This is my simplification of the "cross-multiplication method" of solving a pair of linear equations. That method can be found described on web sites and in videos. This version, and the versions described elsewhere, are variations on Cramer's Rule and on the Vedic Maths method of solving equations. Each of those do similar differences of cross products, perhaps in less-easily-remembered fashion.

For a given pair of columns with coefficients ...

  a b

  c d

The cross-product we form is ad -cb.

Answer:

Answer:

Solution given:

f(x)=5x-3

let

y=f(x)

y=5x-3

interchanging role of x and y

x=5y-3

x+3=5y

y=[tex]\frac{x+3}{5}[/tex]

$o,

f-¹(x)=[tex]\frac{x+3}{5}[/tex]

we conclude that

f-¹(x)≠g(x)

Each pair of function are not inverses.

g(x)=x/5+3

let g(x)=y

y=x/5+3

interchanging role of x and y

x=y/5+3

x-3=y/5

doing crisscrossed multiplication

5(x-3)=y

y=5x-15

g-¹(x)=5x-15

So

g-¹(x)≠f-¹(x)

Each pair of function are not inverses.

Step-by-step explanation:

there are two answers for a

Answer:

The ANSWER IS 1/6

Step-by-step explanation:

Answer:

t=55+6w

Hope This Helps!!!

Answer:

24

Step-by-step explanation:

6 x 4 = 24

Answer:

Step-by-step explanation:

4⁶=4096

Answer:

x = -2: y = 8.5

x = -1: y = 4

x = 0: y = -0.5

x = 1: y = -5

x = 2: y = -9.5

Step-by-step explanation:

We find the numeric values for the function from x = -2 to x = 2.

x = -2:

[tex]y = -4.5(-2) - 0.5 = 9 - 0.5 = 8.5[/tex]

x = -1:

[tex]y = -4.5(-1) - 0.5 = 4.5 - 0.5 = 4[/tex]

x = 0:

[tex]y = -4.5(0) - 0.5 = 0 - 0.5 = -0.5[/tex]

x = 1:

[tex]y = -4.5(1) - 0.5 = -4.5 - 0.5 = -5[/tex]

x = 2:

[tex]y = -4.5(2) - 0.5 = -9 - 0.5 = -9.5[/tex]

Answer:

[tex]x=0,x=-2[/tex]

Step-by-step explanation:

From the question we are told that:

[tex]y=2x^5+5x^4-19[/tex]

Generally the equation if differentiated is mathematically given by

[tex]y'=10x^4+20x^3-0[/tex]

Where

y'=0

[tex]10x^4+20x^3=0[/tex]

Factorizing,We have

[tex]x=0,x=-2[/tex]

Therefore

The critical points are

[tex]x=0,x=-2[/tex]

Excellent question, but let's rephrase it.

Suppose you have a square of surface area of 2851.

What would be a hundredth of such square?

What would be surface area of that hundredth.

Why hundredth? Because percent denotes hundredths cent is a latin word for hundred. You would usually encounter similar word that describes 100 years: century.

Well it is actually very easy. Just divide 2851 into 100 pieces and look at what is the area of one piece.

[tex]2851/100=285.1=y[/tex]

So a single piece has an area of 258.1.

Hope this helps. :)

Option A

Answered by GauthMath if you like please click thanks and comment thanks