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△ABC is cοngruent tο bοth △ACD and △CBD.

Geοmetry depends οn shapes like squares, circles, rectangles, triangles, and οthers. Amοng all the fοrms we have here, triangles seem tο be the mοst intriguing and distinctive. The triangle's shape is created by the intersectiοn οf three lines and three angles.

△ABC is a right triangle, right angled at C.

CD is altitude drawn tο hypοthesis AB.

Tο prοve, △ACD ~ △CBD

In △ACD and △CBD.

∠ACB= ∠ADC=90°  

∠CAB=∠DAC (Cοmmοn angle)

By AA similarity we can say that, △ACD and △CBD.

Anοther side,

Need tο prοοf ∣AC∣²+∣BC∣²=∣A B∣²

If  is a right triangle at C with a prοjectiοn tο  as shοwn, then

BC²=BD*AB

AC²= AD*AB

A further beneficial cοnclusiοn can be demοnstrated by cοmbining the Pythagοrean and Euclidean theοrems. The Pythagοrean Theοrem prοvides us with

CD²= BC²-BD²

By putting the value οf BC²,

CD²= BD*AB-BD²

OR, CD²= BD*(AB-BD)

OR, CD²= BD*AD

AB²= (AD*AB)+(BD*AB)

Or, AB(AD+BD)=AB²

Or, AB²=AB²

Or, ∣AC∣²+∣BC∣²=∣A B∣² (prοved)

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The greatest common factor (GCF) of the polynomial ab+8a+2b+16 is 2.

To factor the given polynomial ab + 8a + 2b + 16 by grouping, follow these steps:

1. Group the terms in pairs: (ab + 8a) + (2b + 16).

2. Factor out the Greatest Common Factor (GCF) from each group. - For the first group (ab + 8a), the GCF is "a". So, factor out "a" from the group: a(b + 8).

-For the second group (2b + 16), the GCF is "2". So, factor out "2" from the group: 2(b + 8).

3. Notice that both groups have a common factor of (b + 8). So, factor out (b + 8) from the entire expression: (b + 8)(a + 2).

Thus, the factored form of the polynomial ab + 8a + 2b + 16 by grouping is (b + 8)(a + 2).

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Answer: It is and answer that is not known yet

Step-by-step explanation: so 5x5=x x would be 25

The vertices of the given hyperbola are (-1, -1 + sqrt(21)) and (-1, -1 - sqrt(21)), the foci are (-1, -1 ± sqrt(66)), the center is (-1, -1), and the asymptotes are y = -1 ± (sqrt(21)/sqrt(45))(x + 1).

To find the vertices, foci, center, and asymptotes of the given hyperbola, we need to use the standard form of a hyperbola equation:

(y - k)^2 / a^2 - (x - h)^2 / b^2 = 1

First, we need to find the center (h, k) of the hyperbola. From the given equation, we can see that h = -1 and k = -1, so the center of the hyperbola is (-1, -1).

Next, we need to find the values of a and b. From the given equation, we can see that a^2 = 21 and b^2 = 45, so a = sqrt(21) and b = sqrt(45).

Now, we can find the vertices of the hyperbola. The vertices are located at (h, k ± a), so the vertices are (-1, -1 ± sqrt(21)). This gives us the vertices (-1, -1 + sqrt(21)) and (-1, -1 - sqrt(21)).

Next, we need to find the foci of the hyperbola. The foci are located at (h, k ± c), where c = sqrt(a^2 + b^2). So, c = sqrt(21 + 45) = sqrt(66), and the foci are (-1, -1 ± sqrt(66)).

Finally, we need to find the asymptotes of the hyperbola. The equations of the asymptotes are y = k ± (a/b)(x - h). So, the equations of the asymptotes are y = -1 ± (sqrt(21)/sqrt(45))(x + 1).

So, the vertices of the given hyperbola are (-1, -1 + sqrt(21)) and (-1, -1 - sqrt(21)), the foci are (-1, -1 ± sqrt(66)), the center is (-1, -1), and the asymptotes are y = -1 ± (sqrt(21)/sqrt(45))(x + 1).

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Answer:

1. YES

2.NO

3. NO

4. YES

Step-by-step explanation:

Answer:

yes, no,no,yes

Step-by-step explanation:

So the length of the shorter diagonal is 3 inches. The length of the longer diagonal is  7 inches.

Let d1 and d2 be the lengths of the longer and shorter diagonals, respectively. We know that d1 = d2 + 4, and that the area of the rhombus is given by A = (d1*d2)/2 = 10.5.

Substituting d1 = d2 + 4 into the area equation, we get:

(d2+4)*d2/2 = 10.5

Multiplying both sides by 2 and simplifying, we get:

d2²+ 4d2 - 21 = 0

Using the quadratic formula, we can solve for d2:

d2 = (-4 ± [tex]\sqrt{4^2-4(-21)}[/tex]/2

d2 = (-4 ± [tex]\sqrt{100}[/tex]  /2

d2 = (-4 ± 10)/2

d2 = -7 or 3

Since the length of a diagonal cannot be negative, we reject the negative solution and conclude that d2 = 3. Therefore, d1 = d2 + 4 = 7, and the length of the longer diagonal is 7 inches.

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Answer: 171

Step-by-step explanation:

If r=20 and q=76 and they're directly proportional, multiply r×3.8

20×3.8=76

The multiplication factor is 3.8, so apply it to when r=45

45×3.8=171

Answer:

36.87o

Step-by-step explanation:

Since ABC is a right triangle

cos(x) = adjacent/hypotenuse

cos(x) = 12/15

x = cos^-1 (12/15) = 36.87o

All the integers between -102 and 105 including the two satisfy the expression.

What are integers?

All whole numbers and negative numbers are considered integers. This indicates that if we combine negative numbers with whole numbers, a collection of integers results.

The meaning of integers: An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.

The given expression is:

-102 ≤ x ≤ 105

All the numbers between -102 and 105 including the two satisfy the expression.

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how many integers satisfy

a) -102

b)-102≤ x≤  105

Answer:

x = 32

Step-by-step explanation:

(41)² - (40)² = 1681 - 1600

= 81

[tex] \sqrt{81} = 9[/tex]

|EC| = 9

x = 41 - 9

x = 32

The 2 triangles share 2 sides of common lengths and a common angle between these sides, therefore they are congruent.

11+ 3q = 12 + 2q

subtract 11 from both sides

3q = 1 + 2q

subtract 2q from both sides

q = 1

The initial value obtained using the slope-intercept relation is 3 gallons.

We need to obtain the rate of change which gives the amount of gas entering into his car per second :

Rate of change = Rise / Run

Rate of change = - 11 - 3) / (48 - 0)

Rate of change = 8/48 = 1/6 gallons

Using the slope intercept relation :

y = bx + c

b = slope ; c = initial amount of gas

Choosing any pair of (x, y) point on the table :

(0, 3)

3 = 1/6x + c

3 = 1/6(0) + c

3 = 0 + c

c = 3

Therefore, the initial value is 3 gallons.

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Answer: $1080

Step-by-step explanation:

First, find the area of the wall.

The area of a rectangle is length x width.

Area = 12 x 20 = 240 square feet

Multiply 4.50 by 240 to find the total cost.

4.50 x 240 = 1080 dollars

It would cost $1080 to cover the wall.

Hope this helps!

Step-by-step explanation:

For solving this problem, we will use √ab=√a√b. Therefore, the value of 3√27 is 9√3. Note: In the above solution, we factored 27 which is inside the root.

yp(t) = Aexp(2t) + Bexp(-2t) + Cexp(5t) + Dexp(-5t)

To find the solution to these two differential equations, we must use the technique of complex exponential forcing. The general solution for these types of equations is:

yp(t) = Aexp(2t) + Bexp(-2t) + Cexp(5t) + Dexp(-5t)

We can then use the given equations to substitute for y′ and y′′, and solve for the four constants A, B, C, and D. Doing so for equation (i), we get:

Aexp(2t) + Bexp(-2t) + Cexp(5t) + Dexp(-5t) = 5e2tsin(t) - 6[Aexp(2t) + Bexp(-2t)] - 7[Aexp(2t) + Bexp(-2t) + Cexp(5t) + Dexp(-5t)]

We can then solve this equation using algebraic manipulation to determine the four constants, and thus find the solution to this equation.

We can then use a similar method to solve equation (ii). The same general solution is used, and the constants can be determined using the same algebraic manipulation. The solution to this equation is then:

yp(t) = Aexp(2t) + Bexp(-2t) + Cexp(5t) + Dexp(-5t)

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Answer:

me no habla ingles?

Step-by-step explanation:

If the divisor contains 2 or more terms, (6x^(2)y+18x^(2)y^(2)-xy^(2))/(6xy) it can simplifies to x+3xy-y.

To divide the given expression, we need to factor out the common term from the numerator and then simplify by canceling out the common terms from the numerator and denominator. Here is the step-by-step explanation:

Step 1: Factor out the common term from the numerator:
(6x²y+18x²y²)-xy²)/(6xy) = 6xy(x+3xy-y)/(6xy)

Step 2: Cancel out the common terms from the numerator and denominator:
6xy(x+3xy-y)/(6xy) = (x+3xy-y)

Step 3: Simplify the expression:
(x+3xy-y) = x+3xy-y

Therefore, the final answer is x+3xy-y.

So, the given expression (6x²y+18x²y²-xy²)/(6xy) simplifies to x+3xy-y.

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Step-by-step explanation:

4y = - 4x +20 (2x) + 4y = 12

4y = -4x + 40x + 4y = 12

36x = 4y - 4y _12

36 x = 12

÷12

36x ÷ 12 = 12 ÷ 12

3x = 1

÷3

3x ÷ 3 =1

x = 1 over 3

The domain is the set of all t-value (inputs) used by the function/graph.

The least t-value is 0.  The greatest is 4.

The domain is [0,4].

The domain of graph for function h(t) is [0,4].

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values of a function like f(x) are part of this collection. A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

We have,

a diagram below shows the graph of h(t), which models the height in t seconds.

we know that the domain are the input values.

Here the domain is the set of all t-value used in the graph.

So, from the graph we can see that the least t-value is 0 and the greatest is 4.

Thus, the domain of graph is [0,4].

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The meaning of the symbol |415| is absolute value and the value of |415| is equal to 415.

Symbols | |  represent the absolute value function in mathematics.

The absolute value function returns the distance between a number and zero on the number line.

Absolute value of a number is always positive or zero.

Compute the absolute value of 415 using the absolute value function,

Replace the number within the bars with the given value as no sign is given,

415 > 0

⇒ Absolute value of |415| = 415

Since 415 is already a positive number

This implies absolute value is itself.

Therefore, the symbol | | represents absolute value of 415 and is equal to 415.

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The result would be:
a) (og)(4) = 294
b) (gof)(2) = 433
c) (fof)(1) = 36
d) (gog)(0) = 4

Given f(x) = 6x and g(x) = 3x² + 1, we can find the following expressions:

a) (og)(4)
To find (og)(4), we first need to find g(4).
g(4) = 3(4)² + 1 = 3(16) + 1 = 49
Now we can find (og)(4) by plugging in 49 for x in f(x):
(og)(4) = f(49) = 6(49) = 294

b) (gof)(2)
To find (gof)(2), we first need to find f(2).
f(2) = 6(2) = 12
Now we can find (gof)(2) by plugging in 12 for x in g(x):
(gof)(2) = g(12) = 3(12)² + 1 = 3(144) + 1 = 433

c) (fof)(1)
To find (fof)(1), we first need to find f(1).
f(1) = 6(1) = 6
Now we can find (fof)(1) by plugging in 6 for x in f(x):
(fof)(1) = f(6) = 6(6) = 36

d) (gog)(0)
To find (gog)(0), we first need to find g(0).
g(0) = 3(0)² + 1 = 1
Now we can find (gog)(0) by plugging in 1 for x in g(x):
(gog)(0) = g(1) = 3(1)² + 1 = 4

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The equation of the parabola in intercept form is y = -6(x+ 16 )(x + 2).    

A parabola is a type of curve that is formed when a point called the focus moves along a straight line called the directrix.

In other words a parabola is defined as the set of all points in a plane that are equidistant to the focus and the directrix.

The shape of a parabola is similar to a U or a V shape, and it can either be open upwards or downwards, depending on the orientation of the curve.

The Intercept form of a parabola is given by

                             y = a(x - p)(x - q)  

Where p and q are the x - coordinates at which the parabola crosses the x-axis (i.e, the x-intercepts).

Here we have

The parabola in intercept form that passes through (-18,72) with x-intercepts of -16 and -2

Let y = a(x-p)(x-q) is the equation of parabola    

From the data, x-intercepts p = - 16 and p = -2

=> y = a(x+ 16 )(x + 2)  ---- (1)

Given that the parabola passes through (-18, 72)

=> 72 = a(- 18 + 16 )(-8 + 2)  

=> 72 = a(-2)(-6)  

=> 72 = - 12a

=>  a = - 6

Substitute a = -6 in equation (1)

=> y = -6(x+ 16 )(x + 2)        

Therefore,

The equation of the parabola in intercept form is y = -6(x+ 16 )(x + 2).    

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The zeros of the function are: x = 1, x = -3, and the other two zeros may be irrational or complex.

A function is a mathematical rule that assigns a unique output value for each input value. It is a set of ordered pairs where the first element is the input and the second element is the output.

Using the Rational Root Theorem, the possible rational roots of the polynomial function F(x) = x⁴ - 2x³ - 6x² + 22x - 15 are:

±1, ±3, ±5, ±15

Using synthetic division, we can find that x = 1 and x = -3 are zeros of the function. Therefore, the zeros of the function are:

x = 1, x = -3, and the other two zeros may be irrational or complex.

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Answer:

Step-by-step explanatio

The value of the constant "k", which make the given pdf valid is 6/17 .

Let x be the amount of water flowing through the Dabney dam;

The Probability Density Function(pdf) of x is given as

⇒ f(x) = {  k           , 0≤x≤2

             (1/3)k       , 2<x≤4

             (1/6)k       , 4<x<5

We know that for a valid p.d.f. [tex]\int\limits^{\infty}_{-\infty} {f(x)} \, dx[/tex] = 1 ;

Substituting the functions for the different intervals ,

We get;

⇒ [tex]\int\limits^{0}_{-\infty} {0} \, dx[/tex] + [tex]\int\limits^{2}_{0} {k} \, dx[/tex] + [tex]\int\limits^{4}_{2} {\frac{1}{3} k} \, dx[/tex] + [tex]\int\limits^{5}_{4} {\frac{1}{6} k} \, dx[/tex] + [tex]\int\limits^{\infty}_{5} {0} \, dx[/tex] = 1 ;

⇒ 0 + [kx]²₀ + [kx/3]⁴₂ + [kx/6]⁵₄ + 0 = 1 ;

⇒ 2k + (k/3)(4-2) + (k/6)(5-4) = 1 ;

⇒ 2k + 2k/3 + k/6 = 1 ;

⇒ (12k + 4k + k)/6 = 1;

⇒ 17k/6 = 1;

⇒ k = 6/17.

Therefore, the value k=6/17 will make the pdf valid.

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The given question is incomplete, the complete question is

A water valve controls the amount of water flowing through the Dabney dam. The probability for the water flow is uniform between 0 and 4 b/s (barrels per second), uniform between 4 and 9 b/s, and uniform between 9 and 14 b/s. The water flow cannot be 14 b/s or greater. The probability of being in the second range is half of the first range. The probability of being in the third range is a fifth of of being in the first range.

In other words, the pdf looks like this:

f(x) = {  k           , 0≤x≤2

           (1/3)k    , 2<x≤4

           (1/6)k    , 4<x<5.

Find the value of k , that will make the pdf valid.

The measure of each angle of the triangle is 30 degrees, 60 degrees, and 90 degrees.

Let's assume that the three angles of the triangle are x, 2x, and 3x, respectively. We are given that these angles are in the ratio of 1:2:3. This means that:

x : 2x : 3x = 1 : 2 : 3

To solve for x, we need to add the three angles together and equate them to 180 degrees (since the sum of the angles in a triangle is 180 degrees). Therefore:

x + 2x + 3x = 180

6x = 180

x = 30

Now that we know the value of x, we can substitute it back into our original equation to find the measure of each angle. Therefore:

First angle: x = 30 degrees

Second angle: 2x = 60 degrees

Third angle: 3x = 90 degrees

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Complete Question:

The angles of a triangle are in the ratio of 1:2:3. Find the measure of each angle of the triangle

Answer: 1.64. To find the difference in orders of magnitude between the two distances, we first need to convert both distances to the same unit of measurement. We'll convert both distances to kilometers.

The distance from Boone to Charlotte is already in kilometers, so we don't need to do any conversion for that distance.
The distance from Boone to Anchorage is in miles, so we'll need to convert that distance to kilometers. To do this, we'll multiply the number of miles by the conversion factor 1.61 km/mi:
4,212.7 mi × 1.61 km/mi = 6,782.45 km

Now that both distances are in kilometers, we can compare them to find the difference in orders of magnitude. An order of magnitude is a factor of 10, so we'll divide the larger distance by the smaller distance and then take the base 10 logarithm of the result:
log10(6,782.45 km / 156.6 km) = log10(43.3) ≈ 1.64
So the distance from Boone to Anchorage is about 1.64 orders of magnitude larger than the distance from Boone to Charlotte.

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Answer: no

Step-by-step explanation:

1         2       3      4    5     6      7    8     9   10    11    12    13   14  15 16   17
13.4 12.8   12.2 11.6 11  10.4  9.8 9.2 8.6  8    7.4  6.8  6.2  5.6 5 4.4  3.8

18  19    20  21

3.2  2.6  2    1.4

With this table, you can see that Diego and his family would only make it to 21 days before the warning light comes on.

Answer:

The brain of the newborn baby has a mass of about 377 grams.

Step-by-step explanation:

Fractions are written as a ratio of two integers. For instance, a/b is a fraction.

Given the following parameters

Body mass = 2900 grams.

If the Brain mass of a newborn baby is about 13% of the mass of the newborn, then the mass of the brain is given as;

mass of brain = 13% of 2900

Mass of brain = 0.13 * 2900

Mass of brain = 377grams

The statement Im(T) ker(T) - T.T=Z is not necessarily true for all linear operators T.

To prove that Im(T) ker(T) - T.T=Z, we must first understand the terms "operator," "transformation," and "linear."

An "operator" is a function that maps one vector space to another. A "transformation" is a function that maps one set to another. A "linear" transformation is a transformation that satisfies the properties of linearity, meaning that it preserves addition and scalar multiplication.

Now, let's look at the equation Im(T) ker(T) - T.T=Z. The term "Im(T)" refers to the image of the linear operator T, which is the set of all vectors that can be obtained by applying T to any vector in V. The term "ker(T)" refers to the kernel of the linear operator T, which is the set of all vectors that are mapped to the zero vector by T.

To prove that Im(T) ker(T) - T.T=Z, we must show that the difference between the image of T applied to the kernel of T and the composition of T with itself is equal to the zero linear transformation.

First, let's consider the image of T applied to the kernel of T. Since the kernel of T is the set of all vectors that are mapped to the zero vector by T, applying T to any vector in the kernel of T will result in the zero vector. Therefore, Im(T) ker(T) = 0.

Next, let's consider the composition of T with itself, T.T. Since T is a linear operator, the composition of T with itself will also be a linear operator. However, there is no guarantee that T.T will equal the zero linear transformation.

Therefore, Im(T) ker(T) - T.T=Z can be simplified to 0 - T.T=Z. Since T.T is not necessarily equal to the zero linear transformation, the equation does not hold true for all linear operators T.

In conclusion, the statement Im(T) ker(T) - T.T=Z is not necessarily true for all linear operators T.

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