EB.AACB = ADCE. AB = 8 and AC = 6DE = [?]

You can see the three points where the result is equal to an integer in the photo below. Good luck!

Using the Pythagorean Theorem, it is found that:

A. The straight line distance between the school and the fire station is of 4.62 miles.

B. The distance between the school and the hospital is of 2.08 miles.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following rule:

[tex]h^2 = l_1^2 + l_2^2[/tex]

In the context of this problem, the distance between the school and the fire station is the hypotenuse of a right triangle with sides 4.3 and 1.7, hence:

d² = 4.3² + 1.7²

d = sqrt(4.3² + 1.7²)

d = 4.62 miles.

The hospital is 3.1 miles west of the fire station, hence the distance between the school and the hospital is the hypotenuse of a right triangle of sides 1.7 and 4.3 - 3.1 = 1.2, hence:

d² = 1.2² + 1.7²

d = sqrt(1.2² + 1.7²)

d = 2.08 miles.

The complete problem is given by the image at the end of the answer.

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All the possible amounts that Anna may have spent at the bowling alley are presented on the number line.

In mathematics, a numbered line is a straight line with numbers organized at regular intervals or sections throughout its breadth. The beginning of period is frequently shown laterally and may be shifted in any position.

Anna visited a bowling alley. She did not spend less than or equal to $30, but she did spend more than $25.

The inequality is given as,

$25 < x ≤ $30

All the possible amounts that Anna may have spent at the bowling alley are presented on the number line.

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Answer:

x=15

Step-by-step explanation:

5x+25=100

Subtract 25 from both sides.

5x+25−25=100−25

5x=75

Divide both sides by 5.

5x÷5=75÷5

x=15

[tex]5x+25=100\\x=[/tex]

Subtract 25 from both sides:

[tex]5x+25-25=100-25\\5x=75[/tex]

Divide both sides by 5:

[tex]\frac{5x}{5} =\frac{75}{5}[/tex]

[tex]\fbox{x=15}[/tex]

t(x) = x² + 8x - 20

Coordinate(s) of the solutions/roots

x² + 8x - 20 = 0 ==> (x -2)(x + 10) = 0

roots: x= 2 and x = -10

coordinate of the y-intercept

y-intercept is when x = 0 ==> t(x) = x² + 8x - 20 when x = 0: t(0) = -20

y-intercept: y = -20

location of the line of symmetry

x = -4

y = (x + 4)² - 36, therefore coordinates of the vertex (-4, 36) and line of symetry x = -4

coordinate of the vertex

(-4, -36)

y = (x + 4)² - 36, therefore coordinates of the vertex (-4, 36)

whether the graph opens up or down and how you know

Opens up

Because the coefficient of x² is positive

The equation of the the ellipse with a vertical major axis, center at (1, -3), a = 7, and b = 5 is [tex]\frac{(x-1)^2}{49}+\frac{(y+3)^2}{25}[/tex]

Equation of the ellipses:

The Equation of the ellipse with center at (h, k)

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}[/tex]

where,

a = length of semi-major axis

b = length of semi-minor axis

Given,

Here we have the value of center as (1, -3) and the values of a = 7 and b = 5.

Here we need to find the equation of the ellipse.

According to the formula we we have the following values are given,

We know the value of center of ellipses is written as,

(h, k) = (1, -3)

And the values of

a = 7 and b = 5

Therefore, when we apply the values on the formula then we get,

[tex]\frac{(x-1)^2}{7^2}+\frac{(y-(-3))^2}{5^2}[/tex]

When we simplify the term then we get,

[tex]\frac{(x-1)^2}{49}+\frac{(y+3)^2}{25}[/tex]

Therefore, the equation of the ellipse is [tex]\frac{(x-1)^2}{49}+\frac{(y+3)^2}{25}[/tex].

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sin (pi/12)cos(7pi/12) -cos(pi/12)sin(7pi/12) is equivalent to sin(-pi/2)

Define Trigonometric functions

A right-angled triangle's angle can be related to side length ratios using real-world trigonometric functions.

We know the formula of sin(A - B) = sinAcosB - cosAsinB

And the given expression is

sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12)

Which is in the form of given formula of sin(A - B)

where,  A = π/12  and B = 7π/12

put A and B values in sin(A - B),

sin(π/12 - 7π/12) =  sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12)

sin(-6π/12) =  sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12)

sin(-π/2) =  sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12)

Hence, sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12) is equivalent to sin(-π/2).

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Answer:

A)  8/15

Step-by-step explanation:

3 / 5 x 8/9

(3/5)(8/9)

(3*8)/(5*9)

(24/45)

8/15

Answer:

8/15

Step-by-step explanation:

3 / 5 x 8/9

Multiplying fractions

Rewriting

3/9 * 8/5

Simplify

1/3 * 8/5

Multiply the numerators

1*8 =8

Multiply the denominators

3*5 = 15

8/15

Answer:

B

Step-by-step explanation:

before finding the sum we require to find first term and common difference.

the nth term of an AP is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₁₀ = - 5 and a₁₅ = - 7 [tex]\frac{1}{2}[/tex] = - 7.5 then

a₁ + 9d = - 5 → (1)

a₁ + 14d = - 7.5 → (2)

subtract (1) from (2) term by term to eliminate a₁

0 + 5d = - 2.5

5d = - 2.5 ( divide both sides by 5 )

d = - 0.5

substitute d = - 0.5 into (1) and solve for a₁

a₁ + 9(- 0.5) = - 5

a₁ - 4.5 = - 5 ( add 4.5 to both sides )

a₁ = - 0.5

the sum to n terms of an AP is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

here a₁ = - 0.5 and d = - 0.5 , then

S₂₀ = [tex]\frac{20}{2}[/tex] [ (2 × - 0.5) + (19 × - 0.5) ]

      = 10 (- 1 -9.5)

     = 10 × - 10.5

    = - 105

The correct inequality to solve for x will be;

⇒ $20.03x + $125.99 < $200.00

Where, 'x' is the number of shirts.

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

Lisa buy new clothes for spring under $200.00

She spent $125.88 for buying some shirts that has each cost $20.80.

Let the number of shirts = x

Then, We can formulate for the given condition is;

The inequality for solution of the value of x is,

⇒ $20.03x + $125.99 < $200.00

Because we can solve for x, which is the number of shirts Lisa can buy with the money she has left.

Therefore,

The correct inequality to solve for x will be;

⇒ $20.03x + $125.99 < $200.00

Where, 'x' is the number of shirts.

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Answer:

5x-4

Step-by-step explanation:

Answer: so there for the answer is 498

Step-by-step explanation:

Answer: 642 Digits have been used to print 250 Pages

Step-by-step explanation:

A book has 250 pages

1 - 250  Numbers will be used

Single Digit number  -  9   ( 1- 9)

Two Digit Numbers   90  ( 10 - 99)

Three Digit Numbers  151  ( 100 - 250)

Number Of Digits used  = 9 * 1  + 90 * 2  + 151 * 3

= 9 + 180 + 453

= 642

642 Digits have  been used to print 250 Pages

Answer:

The probability that exactly 4 of them favour the new building project is 0.0768

what is Probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Step-by-step explanation:

We would assume a binomial distribution for the number of people that are in favour of a new building project. The formula is expressed as

P(x = r) = nCr × p^r × q^(n - r)

Where

x represents the number of successes.

p represents the probability of success.

q = (1 - r) represents the probability of failure.

n represents the number of trials or samples.

From the information given,

p = 40% = 40/100 = 0.4

q = 1 - p = 1 - 0.4

q = 0.6

n = 5

x = r = 4

Therefore,

P(x = 4) = 5C4 × 0.4^4 × 0.6^(5 - 4)

P(x = 4) = 5 × 0.0256 × 0.6

P(x = 4) = 0.0768

Hence, The probability that exactly 4 of them favour the new building project is 0.0768.

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Let's call x to the height. The inequality that represents an acceptable range is:

|x - 35| ≤ 1

Solving it, we get:

x - 35 ≤ 1 or x - 35 ≥ -1

x ≤ 1 + 35 x ≥ -1 + 35

x ≤ 36 x ≥ 34

which is equivalent to 34 ft ≤ x ≤ 36 ft

The standard form of the equation of f(x) is option a -x² - 6x + 7

Given,

The graph shows a downward open parabola.

The vertex points are:

(-3, 16), (-7, 0), (1, 0), (-6, 7), (0, 7)

Now,

We have to find the standard form of the function f(x):

As from the graph:

Parabola opens downward, so the function will be negative.

We have the options with:

a = -1, b = -6 and c = 7

Now,

Use x = -b/2a

x = 6/2 × -1 = 6/-2 = -3

Now,

f(x) = -x² - 6x + 7

f(-3) = -(-3)² - 6(-3) + 7

f(-3) = -9 + 18 + 7

f(-3) = 9 + 7

f(-3) = 16

That is, the points for the vertex in this equation is (-3, 16)

Then, the standard form of the equation of f(x) is option a -x² - 6x + 7

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Answer:

either 11 or 21

Step-by-step explanation:

tho I might be 2

Answer:

x<-2, x>-7

Step-by-step explanation:

1st one

add 7 to 3 =10

-5 divide by 10 = -2

2nd one

add 7 to -42 = -35

-35 divided by 5 = -7

Answer:

x = 30

Step-by-step explanation:

The sum of the interior angles of a triangle is 180

x + 65 + x + 55 = 180  Combine line terms

2x + 120 = 180  Subtract 120 from both sides

2x = 60  Divide both sides by 2

x = 30

The system of quadratic equations obtained on solving general equation of parabola are

a. 5=36a - 6b +c

   -2=64a+8b+c

    3=16a+4b+c

b. 1=289a+17b+c

   -1=81a-9b+c

  2=11025a+105b+c

the equation parabola

the general equation of Parabloa is written as-

y=a[tex]x^{2}[/tex]+bx+c

if the parabola passes through the point. then this point must satisfy the equation of the parabola. so, by putting the value of points we get a set equations-

5=a[tex]6^{2}[/tex]+b(-6)+c

5=36a - 6b +c

and for other two points we get equations

-2=64a+8b+c

and 3=16a+4b+c

and for other three points we get the equations

1=289a+17b+c

-1=81a-9b+c

2=11025a+105b+c

so on solving we get these three set of quadratic equations.

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We will multiply by 26 / 31 in the first number to get second number for fraction in simplest form.

What is mean by Fraction?

A fraction is a part of whole number, and a way to split up a number into equal parts.

Given that;

In the fraction,

The first number = 62

The second number = 52

Let the number which can be multiply by the fraction = x

Since, The given condition is,

Multiply the first number by to get the second number.

So, We can formulate;

⇒ 62 × x = 52

Solve for x, as;

⇒ 62 × x = 52

⇒ 62x = 52

Divide by 62, we get;

⇒ x = 52 / 62

Multiply and divide by 2;

⇒ x = 26 / 31

Therefore,

We will multiply by the number 26 / 31 in the first number to get second number for fraction in simplest form.

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The amount Ali will pay is  £25.80

Define Multiples

A number that can be divided by another number without a remainder.

Multiples of 8 and 12

8 : 8 , 16, 24, 32, 40, 48, 56, 64, 72

12 : 12, 24, 36, 48, 60, 72

common element is 72

72 cakes cost for 12 cakes in each box = 72/12

                                                                 = 6 packs

cost of 6 packs = 6 * £2.50 = £15

72 sausage rolls for 8 sausage in each box = 72 / 8

                                                                       = 9 packs

cost of 9 packs = 9 * £1.20 = £10.80

Total cost will be = £15 +  £10.80 =  £25.80

Hence, the amount Ali will pay is  £25.80

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Let's begin by identifying key information given to us:

Principal (p) = $690

Interest rate (r) = 7% = 0.07 per year

Time (t) = 8 years

The amount of money that Ji-yoon has in 8 years is calculated as shown below:

The eqations are 149=19/9 (10) +b and 130=19/9(1)+b

Given that,

As part of her work, Loren found the solution to the equation 10 = start fraction 19 over 9 end fraction (149) b for b and the points are  (1, 130) and (10, 149)

Finding the slope of a line that goes through two locations for Loren is as follows: m=y2-y1/x2-x1

=149-130/10-1

=19/9 

m=19/9

There are two ways to solve for b in the equation y=mx+b for the location (1,130), where y=130, x=1, and m=19/9, and for the position (10,149), where 149=19/9 (10) +b.

Therefore, the equation of a trend line that passes through the points (1, 130) and (10, 149) are 149=19/9 (10) +b ,130=19/9(1)+b

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EXPLANATION

The area of the figure can be obtained by applying the following relationship:

Where b=base and height=h

In order to find the height, we need to apply the trigonometric relationship:

Multiplying both sides by 6.4:

Solving the argument:

Switching sides:

Now that we have the height, we can compute the area as follows:

The answer is 53.24 squared inches.

Answer:

-88

Step-by-step explanation:

8 x -11 = 88

The quantity of salt in the tank at period t equivalents A(t) = 200 - 130 e(-t/40).

Initially, the tank has A(0) = 50 g of salt.

The rate of salt entryway is (1 g/L) × (5 L/min) = 5 g/min

And a rate of (A(t) ÷ 200 g/L) × (5 L/min) = (A(t) ÷ 40) g/min,

As an outcome, the quantity of salt in the tank modifications as

A'(t) = (5 - A(t)) ÷ 40.

Solve ODE for A(t):

A'(t) + (A(t) ÷ 40) = 4

[tex]e^{\frac{(t)}{40} }[/tex] A'(t) + ([tex]e^{\frac{(t)}{40} }[/tex] ÷ 40 A(t)) = 4[tex]e^{\frac{(t)}{40} }[/tex]

([tex]e^{\frac{(t)}{40} }[/tex] A(t))' = 4[tex]e^{\frac{(t)}{40} }[/tex]

[tex]e^{\frac{(t)}{40} }[/tex] A(t) = 160[tex]e^{\frac{(t)}{40} }[/tex] + C

A(t) = 160 + C[tex]e^{\frac{(t)}{40} }[/tex]

Given A(0) = 30, conclude that

30 = 160 + C

C = -130,

This denotes that the quantity of salt in the tank at period t equivalents

A(t) = 200 - 130 e(-t ÷ 40).

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