2
Name the intersection of plane P and plane ABD.
C
P
B.
.
D
E
BD
Point D
AD
Point B and Point D

The simplified expression in mathematical form is -45.36.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The expression given is -

(-15 + (-1.6 + 9.34) / 6) × (3² - 5.7)

Simplifying the terms inside the parentheses first, we get -

(-15 + 7.74 / 6) × (9 - 5.7)

Next, we simplify 7.74 / 6 by dividing the numerator by the denominator -

(-15 + 1.29) × (9 - 5.7)

We add -15 and 1.29 inside the first set of parentheses -

(-13.71) × (9 - 5.7)

We subtract 5.7 from 9 inside the second set of parentheses -

(-13.71) × 3.3

Multiplying these two terms, we get -

-45.363 ≈ -45.36

Therefore, the value is obtained as -45.36.

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Tan(x/2) = (1 + cosx)/sinx is equivalent to the trigonometric identity cscx

An equation is an expression that can be used to show the relationship between variables and numbers.

Trigonometric identities are based on the six trigonometric ratios. They are sine, cosine, tangent, cosecant, secant, and cotangent.

It is given as:

tanФ = sinФ/cosФ, cotФ = 1/tanФ = cosФ/sinФ, cosecФ = 1/sinФ and secФ = 1/cosФ

According to half angle formula:

tan(x/2) = (1 + cosx)/sinx

Hence:

tan(x/2) + cotx = [(1 - cosx)/sinx] + (cosx/sinx)

tan(x/2) + cotx = (1 - cosx + cosx)/sinx

= 1/sinx

= cscx

Therefore tan(x/2) = (1 + cosx)/sinx is equivalent to cscx

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In the figure, the length of any line segment in the image is longer the length of the corresponding line segment in the preimage. The scale factor of the dilation is 2

The scale factor of dilation is defined as the change in size of a figure. Thus, a scale factor that is greater than 1 is referred to as an enlargement while a scale factor that is greater than 0 but less than 1 is referred to as a reduction.

Now, we are told that ΔABC has been dilated from center D to form ΔRST, This means that the lengths in ΔRST are longer than the lengths in ΔABC.

Secondly, by close inspection we can see that it was dilated by a scale factor of 2.

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Lucio is 64 meters from the starting point.

The square has four sides of equal length, so Lucio has walked half the length of one side.

To return to the starting point, he needs to walk the other half of the side, which is 64 meters.

The angle Lucio turns is irrelevant, as long as he turns 180 degrees in total.

With this in mind, it can be seen that based on the parameters and the conditions, Lucio is 64 meters from the starting point because the angle to which he turns is irrelevant.

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The question in English:

In a square Lucio walks in straight sections, starting from the flagpole, at one point he changes direction turning 150º to his left, advances 64 meters and stops. To return to the pole you have to turn 75º to the left. How far are you from the starting point?

maybe 61km from northeast

The relation that can not be supported by the evidence in the image is option B

Corresponding angles are those that are located on the same side of the transversal and in identical relative positions to the parallel lines. Angles that correspond to one another have the same measure.

Alternate interior angles are those that are located on the transverse and within the area between the parallel lines, respectively. Congruent alternate interior angles exist.

Alternate external angles are those that are outside of the space between the parallel lines and on the opposing sides of the transversal. Congruent external angles exist between the two.

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Answer:

P is the amount borrows

R is the rate of interest

T is time

SI is the simple interest

A is the total amount to give

P= 1900

R= 7%

T= 7 years

Step-by-step explanation:

simple interest = PRT/100

=1900×7×7/100

=19×49

SI=931

A = SI + P

A = 931 + 1900

A = 2831

Answer:

w = 120

x = 60

y = 120

z = 60

Step-by-step explanation:

w = 120 (vertically opposite angles)

sum of co interior angles is 180

⇒ w + x = 180 and x + y = 180

w + x = 180

⇒ 120 + x = 180

⇒ x = 180 - 120

⇒  x = 60

x + y = 180

⇒  60 + y = 180

⇒   y = 180 - 60

⇒   y = 120

z = x (corresponding angles)

z = 60

Answer: is A

Step-by-step explanation:

Answer:

6 gallons

Step-by-step explanation:

25÷200= 0.125

0.125×48= 6

There are six possibilities for the first digit, as any of the six digits can be selected with replacement.

A fundamental combinatorial rule called the principle of counting, sometimes referred to as the counting principle or multiplication principle, enables us to determine the total number of outcomes in a series of occurrences. According to the principle, there are m n methods to perform both events sequentially if we have m ways to perform one event and n ways to perform another.

Consider that the numbers 1, 2, 3, 4, 5, and 6 are all distinct and equally likely to be chosen in order to understand why. When we choose a digit with replacement, it indicates that, regardless of the digits that were previously chosen, we can choose any of the six digits on the initial draw. Thus, the first digit has six potential values.

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Answer:

\( \huge{ \boxed{ \tt{75.9}\sf \: {m}^{2} }}\)

Step-by-step explanation:

\( \underline{ \sf{Given}} : \)

\( \star{ \sf{ \: Height \: of \: a \: parallelogram \: (h) \: = 11m}}\)

\( \star{ \sf{ \: Base \: of \: a \: parallelogram \: (b) \: = 6.9m}}\)

\( \underline{ \sf{Finding \: the \: area \: of \: the \: parallelogram \: having \: height \: of \: 11m \: and \: base \: of \: 6.9m}} : \)

\( \boxed{ \sf{Area \: of \: parallelogram = base \: ∗ \: height}}\)

\( \mapsto{ \sf{Area \: of \: parallelogram = 6.9m \: ∗ \: 11m}}\)

\( \mapsto{ \sf{Area \: of \: a \: parallelogram = 75.9 \: {m}^{2} }}\)

Hope I helped!

Best regards! :D

~\( \sf{TheAnimeGirl}\)

\( \huge\sf {\dag Question} \)

If the height of a parallelogram is 11m and the base is 6.9m, what is the area of the parallelogram?

\( \huge\sf {\dag Solution } \)

\( {\underline {\underline {\rm { Given:}}}} \)

\( {\underline {\underline {\rm { To \: find :}}}} \)

\( {\underline {\underline {\rm { Calculation :}}}} \)

We know that,

\( {\underline {\underline {\rm {\red { Ar. \: of \: parallelogram = h \times b}}}}} \)

Substituting values-

\( \sf {\implies Ar. \: of \: parallelogram = 11 \times 6.9}\)

\( \sf {\implies Ar\: of \: parallelogram = 75.9{m}^{2}}\)

Answer: Each friend ran 3.75 miles.

Step-by-step explanation:

Cecil and three friends is equal to 4 people. There are fifteen miles in the full relay. 15 divided by 4 is equal to 3.75.

15/4=3.75

So, the answer is each friend ran 3.75 miles.

What is a Right Angle Triangle?

A Right Angle Triangle is a triangle where one of the angles is equal to 90 degrees.

To calculate the values using SOHCAHTOA

 SOHCAHTOA calculate the angles and sides of the right triangle, using trigonometric function sine, cosine, and tangent. There are two triangles in which the adjacent and opposite changes based on which angle is in question, the hypotenuse always stays the same.

Where Sin A = Opposite/ Hypotenuse

            Cos A = Adjacent / Hypotenuse

   And  Tan A = Opposite / Adjacent

For question 1,

If Opposite = PR

Adjacent = PQ

Hypotenuse = QR

Sin A = 14/50

Cos A = 48/50

Tan A = 14/48

For question 2,

If Opposite = PQ

Adjacent = PR

Hypotenuse = QR

Sin A = 48/50

Cos A = 14/50

Tan A = 48/14

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Answer:

  [A]  Multiply the bottom equation by -3/2, then add the equations.

  [C]  Multiply the top equation by -3, then add the equations.

Step-by-step explanation:

You want to know a suitable "elimination" strategy for the two equations ...

The result of an elimination strategy is that one of the variables in the combined equations has a coefficient of 0. If we add the equations as a final step, the coefficients must be opposites for that to happen.

The ratios of variable coefficients in the top equation to those in the bottom equation are ...

A suitable elimination strategy will multiply one of the equations by a value that makes this ratio -1. Let's look at the choices.

Multiplying the bottom equation by -3/2 makes the ratio of x-coefficients be ...

  \(\dfrac{1}{3}\times\dfrac{1}{\left(-\dfrac{3}{2}}\right)}=-\dfrac{2}{9}\ne -1\)

Multiplying the bottom equation by -3/2 makes the ratio of y-coefficients be ...

  \(\dfrac{3}{2}\times\dfrac{1}{\left(-\dfrac{3}{2}\right)}=-\dfrac{6}{6}=-1\)

This is a suitable strategy for eliminating the y-variable.

This strategy is equivalent to multiplying the bottom equation by -3, then adding. This will make the x-coefficient ratio be ...

  \(\dfrac{1}{3}\times\dfrac{1}{\left(-3}\right)}=-\dfrac{1}{9}\ne -1\)

Multiplying the bottom equation by -3 makes the ratio of y-coefficients be ...

  \(\dfrac{3}{2}\times\dfrac{1}{-3}=-\dfrac{3}{6}\ne-1\)

Not a suitable strategy for elimination.

Multiplying the top equation by -3 makes the ratio of x-coefficients be ...

  \(\dfrac{1}{3}\times\dfrac{-3}{1}}=-\dfrac{3}{3}= -1\)

This is a suitable strategy for eliminating the x-variable.

Choices A and C are suitable strategies for eliminating a variable.

Answer:

-36

-3y

Step-by-step explanation:

F

Answer:

(4,-7)

Step-by-step explanation:

y=4x-9

y+3=x

y=4(y+3)-9

y=4y+12+9

y=4y+21

y-4y=21

-3y=21

y=-7

Now use y to find x

y+3=x

-7+3=4

x=4

Answer:

(3/5 times 5/6 = 1/2)

Step-by-step explanation:

Answer:

It will cost 12p a one apple

Answer:

The equation of the line, using the point-slope form, through (-4,6) that is parallel to the line will be:

\(y=-5x-14\)

Step-by-step explanation:

We know that the slope-intercept form is

\(y=mx+b\)

Where m is the slope and b is the y-intercept

Given the equation

\(y=-5x+2\)

comparing with the slope-intercept form

slope = m = -5

y-intercept = b = 2

We know that the parallel lines have the same slopes.

so , the slope of the parallel line will be: -5

Thus, the equation of the line, using the point-slope form, through (-4,6) that is parallel to the line will be:

\(y-y_1=m\left(x-x_1\right)\)

\(y-6 = -5(x-(-4)\)

\(y-6 = -5 (x+4)\)

\(y-6 = -5x-20\)

\(y=-5x+6-20\)

\(y=-5x-14\)

Answer:

y=-x+2

Step-by-step explanation:

i already did it and your welcome in advance

The equation of logarithm are solved and

a) A = 2 + 3 log x + 4 log b

b) B = ( 36 + x + y ) ( log 6 )

c) C = ( 1/2 )x log 5

d) D = ln ( x⁴ / y² )

Given data ,

Let the logarithmic equation be represented as A

Now , the value of A is

a)

A = 2 log 10 + 3 log x + 4 log b

The base of the logarithm is 10 , so

A = 2 + 3 log x + 4 log b

b)

B = log 6³⁶ + log 6ˣ - log 6^ ( y )

From the properties of logarithm , we get

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

B = 36 log 6 + x log 6 + y log 6

On taking the common term , we get

B = ( 36 + x + y ) ( log 6 )

c)

C = ( 1/2 )log 5ˣ

From the properties of logarithm , we get

C = ( 1/2 )x log 5

d)

D = 4 ln x - 2 ln y

From the properties of logarithm , we get

D = ln x⁴ - ln y²

On further simplification , we get

D = ln ( x⁴ / y² )

Hence , the logarithmic equations are solved

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(i) The first term (a) is 24 and the common difference (d) is -2.

(ii) The sum of the progression is 2520.

i) Finding the first term and common difference:

Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).

The nth term formula is: An = a + (n-1)d

Using the given information, we can substitute the values:

-54 = a + (40-1)d

-54 = a + 39d

We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:

S15 + S30 = 0

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values for S15 and S30:

[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0

Simplifying the equation:

15(2a + 14d) + 30(2a + 29d) = 0

30a + 210d + 60a + 870d = 0

90a + 1080d = 0

a + 12d = 0

a = -12d

Substituting this value into the equation -54 = a + 39d:

-54 = -12d + 39d

-54 = 27d

d = -2

Now we can find the value of a by substituting d = -2 into the equation a = -12d:

a = -12(-2)

a = 24

Therefore, the first term (a) is 24 and the common difference (d) is -2.

ii) Finding the sum of the progression:

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values:

S40 = (40/2)(2(24) + (40-1)(-2))

S40 = 20(48 - 39(-2))

S40 = 20(48 + 78)

S40 = 20(126)

S40 = 2520

Therefore, the sum of the arithmetic progression is 2520.

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The probability that the mean of this sample is less than 105.4 is 14.46%

The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

\(z=\frac{x-\mu}{\sigma/\sqrt{n} } \\\\x=raw\ score, \sigma=standard\ deviation, \mu=mean,n\ is\ sample\ mean\\\\\\Given\ that\ \sigma=45,\mu=124.5,n\ =36,hence:\\\\For\ x<105.4:\\\\z=\frac{105.4-124.9}{45/\sqrt{36} }=-1.06\)

From the normal distribution table, P(x < 105.4) = P(z < -1.06) = 0.1446 = 14.46%

The probability that the mean of this sample is less than 105.4 is 14.46%

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Relative frequency of A = 0.50

Relative frequency of B = 0.21

Relative frequency of C = 0.29

As per the given data the response to a question has three alternatives namely A, B, and C.

A sample of 120 responses provides 60 A, 25 B, and 35 C responses.

That means:

Frequency of A is 60.

Frequency of B is 25.

Frequency of C is 35.

Relative frequency can be calculated by using Class frequency and Total frequency.

Relative frequency = Class frequency ÷ Total frequency

Total frequency will be sum of all three Class frequencies.

Total frequency = 60 + 25 + 35

= 120.

Relative frequency of A = 60 ÷ 120

= 0.50

Relative frequency of B = 25 ÷ 120

= 0.21

Relative frequency of C = 35 ÷ 120

= 0.29

Therefore the complete table is given by:

Class Frequency Relative Frequency

A              60                  0.50

B              25                   0.21

C              35                   0.29

(Total)      120                  

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The response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 60 A, 25 B, and 35 C responses. Show the frequency and relative frequency distributions (use 0 decimals for the frequency column and 2 decimal for the relative frequency column).

Class Frequency Relative Frequency

A              ___                   _______

B              ___                   _______

C              ___                   _______

(Total)      ___                  

Step-by-step explanation:

(1 + ax)⁴(2 - x)³ = (1 + 2ax + a²x²)²(8 - 12x + 6x² - x³) =

(1 + 4a²x² + a⁴x⁴ + 4ax + 2a²x² + 4a³x³)(8 - 12x + 6x² - x³) = ... 6x² + 32a²x² - 48ax² + 16ax² ...

= ... x²(6 + 32a² - 32a) ...

32a² - 32a + 6 = 6

32a(a - 1) = 0 → 32a = 0 → a = 0 OR a - 1 = 0 → a = 1

Answer: For Y the rate of change is +4

For the rate of x its +5

Step-by-step explanation:

Answer:

The first one is the correct answer because it has the same value when you solve them.

Answer:

A) 3 + 36 ÷ 4 • 3

Step-by-step explanation:

Answer:

79/8

Step-by-step explanation:

\(\sf{9 \frac{7}{8} }\)

\(\sf{ = \frac{(9 \times 8 )+ 7}{8} }\)

\(\sf{ = \frac{72 + 7}{8} }\)

\( = \purple{\sf{ \frac{79}{8} }}\)

Apologies, but your questions seem to have errors and incomplete information.

For the first question about Jessica and Melissa sharing 12 pieces of dried pears, it is unclear how much Jessica ate as the fraction is missing. Similarly, information about how many pears Melissa ate is also missing. To answer the question accurately, I need the missing information.

For the second question about the children playing in the park, you mentioned that one-third of the children returned home, but you didn't provide the total number of children initially in the park. Without that information, I cannot determine how many children stayed in the park.

Please provide complete and accurate information for a precise answer.

The value of intergal  \(y=\int_{-2}^{x} \sqrt{3 t^{4}-1} d t\) is

\(y=\frac{1}{6} \sqrt{(3x^{2}-1)^{2}} - \frac{1}{6} \sqrt{(3(-2)^{2}-1)^{2}} \)\)

In mathematics, an integral is a mathematical object that can be interpreted as an area or a generalization of area. Integrals, together with derivatives, are the two main tools used in calculus and are used to calculate areas, volumes, and their generalizations.

The integral \(y=\int_{-2}^{x} \sqrt{3 t^{4}-1} d t\)  can be evaluated by first completing the square and then using the substitution method.

Completing the square gives us \(( 3 t^{4} -1 = (3t^{2} -1)^{2} \)\).

We can now make the substitution \(( u = 3 t^{2} -1 \)\)).

Differentiating, we get \(( du = 6t dt \)\)).

Therefore, the integral can be written as\(y=\int_{-2}^{x} \sqrt{(3t^{2}-1)^{2}} \frac{du}{6t} \)\).

Solving the integral, we get:

\(y = \frac{1}{6} \sqrt{(3t^{2}-1)^{2}} +C \)\)

Substituting back into the equation, we get the answer as:

\(y=\frac{1}{6} \sqrt{(3x^{2}-1)^{2}} - \frac{1}{6} \sqrt{(3(-2)^{2}-1)^{2}} \)\)

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