The point A(7, 1) is reflected over the point (4, 0) and its image is point B. What are the coordinates of point B?

ASA Criterion means that the triangles are congruent if the corresponding Angle-Side-Angle is also congruent.

From the the Triangle ABC :

corresponds with ASA.

Likewise from the Triangle DEF :

Since the given figure already states that :

and BC = FE

The other item that will complete the ASA will be :

SAS criterion means that the triangle are congruent if the corresponding Side-Angle-Side are also congruent.

The following corresponds with SAS :

From the triangle ABC :

From the triangle DEF

Answer:

7^5 (7 to the fifth power)

Step-by-step explanation:

those sevens can be represented by 7^5 because there are five sevens to multiply together

you can check the answer by doing 7 x 7 x 7 x 7 x 7=16807

and making sure that 7^5 is also equal to 16807, which it is.

Hope this helps! :)

The value of x based on the triangle is 7 cm.

From the given figure, we know that the two corresponding lines are parallel and so the two given triangles are congruent to each other.

Therefore, the corresponding sides of these triangles will also be proportional so we can write it as:

5 / 45 = 3 / 2x + 10

10x + 65 = 135

Collect the like terms

10x = 135 - 65.

10x = 70

Divide

x = 70 / 10

x = 7

Therefore, the value of x is 7 cm.

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Total metal needed to cast a cubical metal box with exterior edge length 12 inches and thickness 3 inches is equal to 999cubic inches.

Length of the exterior edge of the cubical metal box = 12 inches

Thickness of the wall of cubical metal box = 3 inches

Length of the interior edge of the cubical metal box

= 12 inches - 3 inches

= 9 inches

Volume of the exterior cubical metal box = 12³

                                                                     = 1728 cubic inches

Volume of the interior cubical metal box = 9³

                                                                     = 729cubic inches

Total metal required to cast a cubical metal box

= (Volume of the exterior - Volume of the interior )cubical metal box

= (1728 - 729 )cubic inches

= 999 cubic inches

Therefore, the total metal required to cast a cubical metal box is equal to 999 cubic inches.

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Answer:

B. 8(2-y)

Step-by-step explanation:

22-10y+2(y-3)

22-10y+2y-6

22-6-10y+2y

16-8y

Using factorisation method

8(2-y)

Level of advertisement expenditure when x < 300, Q'(x) >0 units of product sold is increasing and when x > 300 ,Q'(x) < 0 product sold in decreasing.

Function is equal to ,

Q(x) = -x² + 600x + 25

'Q' represents the firm estimated number of units sells its product with an advertising expenditure.

To get the critical point get the first derivative of Q(x) ,

Q'(x) = -2x + 600

Now equate it to zero.

Q'(x) = 0

This implies

⇒ -2x + 600 = 0

⇒ 2x = 600

⇒ x = 300

For x < 300 , Q'(x) is positive.

Number of units of product sold is increasing for the level of advertising expenditure.

For x > 300, Q'(x) is negative .

Number of units of product sold is decreasing for the level of advertising expenditure.

Therefore, the level of advertising expenditure is x  < 300 then the number of units of product is increasing and when x > 300 then it is decreasing.

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The probability that you will get through the door without returning for more keys is 0.03.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

Probability door is locked = 0.7

The probability that you will get through the door without returning for more keys will be:

= (1 - P(locked)) × P(key)

= (1 - 0.7) × 0.1

= 0.3 × 0.1

= 0.03

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The value of P(B) when A and B are mutually exclusive is 0.4 and when A and B are independent is zero.

Mutually exclusive events are those events which do not occur at the same time. For a mutually exclusive event we have the formula,

P(A∪B) = P(A) + P(B) - P(A∩B)

Here P(A∩B) is equal to zero and P(A) = 0.3 and P(A∪B) = 0.7

Now when we substitute the values we get

0.7 = 0.3 + P(B)

=> P(B) = 0.7 - 0.3

=> P(B) = 0.4

Now, if the events are independent then we have the formula

P(A∩B) = P(A)×P(B)

Since we already know that P(A∩B) = 0 then

0 = 0.3×P(B)

=> P(B) = 0 which means that the event will not take place.

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As per the combination method, there are 84 different ways to fill the three offices from a group of nine eligible members.

A combination is a way of selecting objects from a larger set without regard to the order in which they are selected. In other words, combinations are a way of counting how many different groups can be formed from a set of objects, where the order of the objects in the group does not matter.

In our case, n = 9 (the number of eligible members) and r = 3 (the number of offices to be filled). So we can plug these values into the formula and get:

⁹C₃ = 9! / 3!(9-3)! = (9 × 8 × 7) / (3 × 2 × 1) = 84

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Shop A sells a dress for $79.50 with a 20% discount while Shop B sells the same dress for $69.50 with a 10% discount is $ 318 and $ 625.5.

The proportion of value in relation to the original value is measured using the percentage discount concept. In business, percentages are frequently employed to calculate a company's profit or loss percentage.

Let x be the actual cost of the dress in the store. A

20/100 ×x = 79.50 x = 79.50 ×100/20 xx = 7950/20

x = $ 397.5

The actual cost of clothing A is $397.5.

Discount of outfit A therefore equals 20%

$397.5-79.5$= $ 318

Let x represent the true cost of dress B.

(10/100)× x = 69.50$

x = $695

The actual cost of dress B is $695.

So, the dress B's discount is 10%.

$ 695 - 69.50 = $ 625.5

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The terminal point of the angle is located 3.5 cm to the right and 3.5 cm above the circle's center.

To determine the position of the terminal point of the angle, we need to consider its measurement in radians, the direction of the initial ray, and the properties of a circle with a radius of 3.5 cm.

Given that the angle measures 2.3 radians, we know that it spans 2.3 times the radius of the circle. Since the radius is 3.5 cm, the arc length of the angle is 2.3 * 3.5 = 8.05 cm.

Now, let's analyze the direction of the initial ray. The 3-o'clock direction is to the right on a standard clock face. In a circle, the positive x-axis is typically considered to be the 3-o'clock direction. Therefore, the initial ray of the angle is pointing directly to the right.

Since the terminal point of the angle lies on the circumference of the circle, we can determine its position relative to the circle's center using polar coordinates. The terminal point is located at a radial distance from the center, which is equal to the radius of the circle.

Hence, the terminal point is situated 3.5 cm to the right of the circle's center, as it lies on the positive x-axis.

Additionally, the terminal point is located on the circumference of the circle, so it is also 3.5 cm above the circle's center. Since the circle is centered at the angle's vertex, the vertical displacement of the terminal point is equal to the radius of the circle.

Therefore, the terminal point of the angle is located 3.5 cm to the right and 3.5 cm above the circle's center.

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Thomas is 49 years old.

What is equation?

Two expressions joined by an equal sign form a mathematical statement known as an equation. An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.

Given:

Huilan is 11 years older than Thomas.

The sum of their ages is 109.

We have to find the Thomas's age in years.

Let x be the Thomas age.

Then the age of Huilan is x + 11.

As the sum of their ages is 109.

⇒ x + (x + 11) = 109

         2x + 11 = 109

               2x = 98

                 x = 49

Hence, Thomas is 49 years old.

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Answer:

Step-by-step explanation:

(3+1)/2= 4/2 = 2

(-8+2)/2= -6/2= -3

(2, -3)

The domain and range of F is F={(x, y) Ix+y=10] is: 3. Domain: All Real Numbers Range: All Real Numbers

The given set F={(x, y) | x+y=10} represents a linear equation where the sum of x and y is always equal to 10.

To determine the domain and range of F, we need to consider the

possible values of x and y that satisfy the equation.

Domain: The domain represents the set of all possible values for the independent variable, which in this case is x. Since there are no restrictions on the value of x, the domain is All Real Numbers.

Range: The range represents the set of all possible values for the dependent variable, which in this case is y. By rearranging the equation x+y=10, we can solve for y to get y=10-x. Since x can take any real value, y can also take any real value. Therefore, the range is also All Real Numbers.

The correct answer is: 3. Domain: All Real Numbers Range: All Real Numbers

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Therefore, the endpoints of the latus rectum of the given parabola are (1, -5/2) and (1, -7/2).

The standard form of the equation for a parabola is given as \((x - h)^2 = 4p(y - k)\), where (h, k) represents the vertex of the parabola and "p" is the distance from the vertex to the focus and the directrix.

In the equation \((x - 1)^2 = -4(y + 3)\), we can see that the vertex of the parabola is (1, -3). Since the coefficient of (y + 3) is -4, we can determine that the distance from the vertex to the focus and the directrix is 1/4.

To find the endpoints of the latus rectum, we need to consider the points that are equidistant from the vertex and the focus. The latus rectum has a length equal to 4p, so in this case, it will have a length of 1 unit.

To find the endpoints, we can simply add and subtract 1/2 from the y-coordinate of the vertex (-3):

Endpoint 1: (1, -3 + 1/2)

= (1, -5/2)

Endpoint 2: (1, -3 - 1/2)

= (1, -7/2)

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In an arithmetic sequence, consecutive terms differ by a fixed number d :

\(a_8=a_7+d\)

\(a_9=a_8+d=a_7+2d\)

\(a_{10}=a_9+d=a_7+3d\)

and so on up to

\(a_{19}=a_7+12d\)

Solve for d :

\(140=32+12d\implies12d=108\implies d=9\)

Work backwards to find the first term in the sequence, and hence the n-th term:

\(a_6=a_7-d\)

\(a_5=a_6-d=a_7-2d\)

and so on down to

\(a_1=a_7-6d\)

So the first term is

\(a_1=32-6\cdot9=-22\)

which means the n-th term is

\(a_n=a_1+(n-1)d=-22+9(n-1)=9n-31\)

\(S_n\) denotes the n-th partial sum of the sequence, i.e. the sum of the first n terms. We want to find the number of terms such that this sum is 511:

\(\displaystyle S_n=\sum_{i=1}^na_i=\sum_{i=1}^n(9i-31)=511\)

Distribute the summation and recall the formulas,

\(\displaystyle\sum_{i=1}^n1=n\)

\(\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2\)

\(\implies S_n=\displaystyle9\sum_{i=1}^ni-31\sum_{i=1}^n1\)

\(\implies511=9\cdot\dfrac{n(n+1)}2-31n\)

\(\implies1022=9n^2-53n\)

\(\implies9n^2-53n-1022=0\)

\(\implies(n-14)(9n+73)=0\)

\(\implies n=14\text{ or }n=-\dfrac{73}9\)

n must be a positive integer, so we the sum is obtained from the first n = 14 terms.

Answer:

8sin(x)cos³(x)

Step-by-step explanation:

sin(4x) +2 sin(2x)  = 2sin(2x)*cos(2x) + 2sin(2x) = 2sin(2x)(cos2x + 1)=

= 2sin(2x)(cos²x - sin²x + cos²x + sin²x)=²2sin(2x)*(2cos²x)=

= 4*2sin(x)*cos(x)*cos²(x)= 8sin(x)cos³(x)

In the standard curve for nitrophenol generated for use in this experiment, the nitrophenol concentration is reported on the x - axis.

What is standard curve?

A calibration curve, sometimes referred to as a standard curve, is a common technique used in analytical chemistry to compare an unknown sample to a group of standard samples with known chemical concentrations.

In order to calculate the nitrophenol concentration in mole/ml based on absorbance readings, the standard curve is drawn.

Based on the optical density, or OD410, or absorbance at 410 nm, this standard curve of absorbance is used to calculate the quantity of nitrophenol.

Therefore, the nitrophenol concentration is displayed on the x axis of the standard curve.

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Answer:

loss % = 9.25%

Step-by-step explanation:

loss % = 100 × loss / cost price

loss % = 100 × ($780 - $707.85) / $780

loss % = 100 × $72.15 / $780

loss % = 9.25%

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Answer:

x = 7ft

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

7 times 4 is 28 minus 3 is 25.

7 times 2 is 14 plus 21 is 35. 25 plus 35 equal 60. DG equals 60.

Answer:

a) A = 36π in² ≈ 113.09 in²

b)  $0.98 per slice

c) $0.09 per square inch

Step-by-step explanation:

a) area = πr²

    r= diameter/2 = 12/2 = 6

    A = π(6)²

    A = 36π in² ≈ 113.09 in²

b) s = price per slice

   s = 9.75 ÷ 10

   s = $0.975 ≈ $0.98

c) price per square inch = price ÷ area

   = 9.75 ÷ 113.09

   = $0.086 ≈ $0.09 per square inch

To set up an integral for the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves y, we would use the method of cylindrical shells.

First, we need to identify the limits of integration. The region in the first quadrant is bounded by the curves y, which intersect at the point (1,1). So our limits of integration will be from 0 to 1.

Next, we need to determine the radius and height of each cylindrical shell. The radius will be the distance from the x-axis to the curve y, which is simply y. The height will be the length of the shell, which is the difference between the x-coordinates of the two curves at that value of y.

So our integral will be:

∫[0,1] 2πy(x2 - y2) dy

where x2 is the equation of the curve y=x2 and y2 is the equation of the curve y=x.

Note that we do not evaluate this integral, as the question specifically asks us to only set it up.

To set up, but not evaluate, an integral for the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves y, I need the equations of the curves and the axis of rotation.

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Answer:

x = 1 , y = -6

Step-by-step explanation:

-5x - 1 = -x - 5

-5 x + x = -5 + 1

-4 x = -4

x = 1

if x = 1

y = -x - 5

y = -1 - 5

y = -6

Answer:

x=1 , y=-6

Step-by-step explanation:

y=-5x-1 ..............1

y=-x-5 ...............2

1×y=-5x-1 .............3

5×y=-x-5................4

y= -5×-1

5y=-5×-5

-5-(-5)=0

y=-1

5y=-5

so; 4y=-1-(-5)

4y = 4

4

y = 1

sub y =1 into eqn................. 2

y=-x-5

y=-1-5

y= -6

The probability of spinning a yellow on the spinner in the diagram is 1/8.

Probability is the ratio of the required outcome to the total possible outcome. It gives a measure of how probable a certain item or event can be obtained from a series of events.

Mathematically,

Probability = Required outcome / Total possible outcomes

Here ,

Total possible outcomes = 8

Required outcome = Yellow segment = 1

Probability(Yellow ) = 1/8

Hence, probability of spinning a yellow is 1/8.

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Two two numbers whose difference is 88 and whose product is a minimum are -44 and 44.

Let the numbers be x and y where x is larger value and y is smaller number.

According to ques,

x - y =88

and we need to make product of numbers i.e 'xy' minimum.

So we can take x = 88 + y ------(2)

substituting value of x in xy, we get

(88 + y) (y) = y² + 88y ------(1) to make it minimum we need to equate its derivative equal to zero.

derivative of  (1) is 2y + 88

Equating it to zero, we get

2y + 88 = 0

subtracting 88 from both sides, we get

2y = -88

Dividing 2 from both sides, we get

y = -44 ------(3)

Substituting value of y from (3) in (2), we get

x = 88 - 44

x = 44

So, we get value of x as 44 and y as -44 to get their product as minimum.

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Answer:

9

Step-by-step explanation:

Use Exponent rule:

           \(\sf \boxed{(a*b)^m = a^m*b^n}\)

\(\sf \dfrac{4(3x)^2}{(2x)^2} = \dfrac{4 * 3^2*x^2}{2^2*x^2}\\\)

          \(\sf = \dfrac{4 * 9 *x^2}{4*x^2}\\\\= 9\)

Answer:

x = 30

Step-by-step explanation:

well from the theorem we have

\(\frac{15}{3}=\frac{x}{6}\)

yes i know you could say that the right way is

\(\frac{3}{15}=\frac{6}{x}\)

well if you notice they are the same only that in my way the x is in the numerator which means it will be far easier to know it's value :)

so

\(\frac{15}{3}=\frac{x}{6}\\\\5=\frac{x}{6}\\\\6[5]=6[\frac{x}{6}]\\\\30=x\)

The probability that the number pyramid will land on three and the spinner will stop on blue is 1/24.

To determine the probability that the number pyramid will land on three and the spinner will stop on blue, we need to know the total number of possible outcomes for both events and the number of favorable outcomes for the desired outcome.

Let's assume that the number pyramid has six sides numbered from one to six, and the spinner has four sections colored blue, red, green, and yellow. If both the number pyramid and spinner are fair and unbiased, each outcome is equally likely.

Number pyramid outcomes: There are six possible outcomes, namely numbers one to six.

Spinner outcomes: There are four possible outcomes, namely blue, red, green, and yellow.

To find the probability of both events happening together, we need to multiply the probabilities of each event occurring individually, assuming they are independent events (i.e., the outcome of one event does not affect the outcome of the other).

Probability of landing on three: Since the number pyramid has six sides, and we want to land on three, there is only one favorable outcome (three) out of the six possible outcomes. Therefore, the probability of landing on three is 1/6.

Probability of stopping on blue: Since the spinner has four sections, and we want it to stop on blue, there is only one favorable outcome (blue) out of the four possible outcomes. Therefore, the probability of stopping on blue is 1/4.

To find the probability of both events occurring, we multiply these probabilities:

Probability of landing on three and stopping on blue = (1/6) * (1/4) = 1/24

Therefore, the probability that the number pyramid will land on three and the spinner will stop on blue is 1/24.

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