Which triangles are congruent by ASA?
ABC and TUV
VTU and ABC
VTU and HGF
none of the above

The probability that the other side of the card is red is [tex]\frac{4}{5}[/tex].

The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood conditional, occurrence to determine the conditional probability.

Suppose you choose a red/black card:

The probability of choosing a red and black card is [tex]\frac{1}{6}[/tex].

Now, since this card has one side as red the probability of seeing a red side in this card is [tex]\frac{1}{2}[/tex].

Suppose you choose a red/red card:

The probability of choosing red and red card is 2/6.

Now, since the card has two red sides the probability of seeing red side in this card is [tex]\frac{2}{2}[/tex] .

Considering we see a single side of the card we have the following probability:

[tex]\frac{2}{6} * \frac{2}{2} = \frac{1}{3}[/tex]

The total probability of seeing a red side is [tex]\frac{1}{12} + \frac{1}{3} = \frac{5}{12}[/tex].

The probability that you pick red-red card and see a red side is [tex]\frac{1}{3}[/tex].

So, the conditional probability of both red sides is given as:

[tex]\frac{\frac{1}{3} }{\frac{5}{12} } = \frac{4}{5}[/tex]

Hence, the probability that the other side of the card is red is [tex]\frac{4}{5}[/tex].

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The length of ST is 16 units.

A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.

We have to given that;

Point P is the midpoint of ST.

SP = x + 4, and ST = 4x

Since, P is the midpoint of ST.

Hence, We get;

⇒ SP = PT

And, ST = 2 SP

Substitute all values we get;

⇒ 4x = 2 (x + 4)

⇒ 4x = 2x + 8

⇒ 4x - 2x = 8

⇒ 2x = 8

⇒ x = 4

Thus, The value of ST = 4x

                                  = 4×4

                                  = 16

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The solution for the given equation would be [tex]x=8+\sqrt{15},\:x=8-\sqrt{15}[/tex].

What is an equation?

An equation is a statement that two expressions are equal to each other. It is a mathematical sentence that asserts the equality of two expressions. An equation can be written in the form of:

expression_1 = expression_2

The given equation is √2x – 1- x = −8.

[tex]2x=x^2-14x+49[/tex]

[tex]x=8+\sqrt{15},\:x=8-\sqrt{15}[/tex]

Hence, the solution for the given equation would be [tex]x=8+\sqrt{15},\:x=8-\sqrt{15}[/tex].

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The equation that relates x and y for the given data is y = (3/4)x.

The relationship between the number of shutters (x) and the number of hours (y) is an inverse variation because as the number of shutters increases, the number of hours required to paint them decreases and vice versa.

An inverse variation is a relationship between two variables in which their product is always equal to a constant value. Mathematically, it can be represented by the equation: y = k/x where k is a constant and x and y are the variables in question.

Hence, the equation that relates x and y can be found using the information given:

y = (9 hours) / (12 shutters) * x shutters

y = (3/4)x is the required equation.

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Answer: Its B

Step-by-step explanation:

Answer:

4 sweets per friend

Step-by-step explanation:

so first you want to minus 10 sweets since she ate 10 leaving her with 40 sweets. then she gives 8 sweets to her brother leaving her with 32 sweets left. If you divide the remaining sweets ( 32 ) by 8 you get 4 sweets per friend

Answer:g

Step-by-step explanation:

g

Anytime one makes a traffic manoeuvre, such as changing lanes or passing another vehicle, a person put both himself and other drivers on the road in danger.

What are the methods for passing risky situations?

Avoid driving at intersections with railroads, railroad crossings, and entrances to shopping centres.

Only pass to the left if there are two lanes on the road. It is frequently illegal and dangerous to pass on the right. Only when the car in front of you flashes its left turn signal is there an exemption.

When there is a long line of traffic and an oncoming car is right ahead, it is advisable to wait until the incoming vehicle has passed before making a passing motion.

Therefore, it is best to wait until one can see fully ahead because there might be an approaching car right around the bend.

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The equation is 4x + 17 = 7. Then the value of the variable 'x' will be negative 2.5.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The triangles are congruent triangles. Then the ratio of the corresponding sides will be equal to one. Then the equation is given as,

4x + 17 = 7

Simplify the equation, then we have

4x + 17 = 7

4x = 7 - 17

4x = - 10

x = - 10/4

x = - 2.5

The equation is 4x + 17 = 7. Then the value of the variable 'x' will be negative 2.5.

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On solving the provided question, we can say that the sum of the two expressions will be -4n + 6

It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: (Mathematical Operator, Number/Variable, Expression) A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)It is possible to compare expressions and phrases.

Expression, Number/Variable, and Mathematical Operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted.

let the two expression be

-4nand 6 and the sum will be -4n + 6

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The value of b that needs to be simplified is indicated as 1.43. The correct response when the new population growth is specified is A.

A mathematical function known as an exponential function has the following formula: f (x) = an x, where x is a variable and an is a constant known as the function's base. The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base. Bacterial proliferation is an illustration of an exponential function. Some bacteria grow by twofolds per hour. After x hours, there will be twice as many germs present as there were when you started with just one. The formula for this is f(x) = 2x.

Given that,

When a fisherman unlawfully releases some fish into a pond, they immediately multiply (reproduce). P(x) = 6bx, where x is the number of weeks that have passed since the moment the fish was placed into the pond, and b is an unknown positive base, serves as a model for the population expansion of the new species.

According to the question,

P(x) = 6bˣ

Put p(x) = 51 and x = 6

51 = 6b⁶

17/2 = b⁶

b = [17/2]¹/⁶

b = 1.43

The b value that must be simplified is given as 1.43. A is the proper answer.

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Answer:

a. 1.05

b. 0.95

Step-by-step explanation:

a. 5 percent increase

5% = 0.05

Because it is increasing, so we add 1

1 + 0.05 = 1.05

b. 12 percent decrease

12% = 0.12

Because it is decreasing, so subtract 1

1 - 0.05 = 0.95

So, the answer is

a. 1.05

b. 0.95

Answer:

y ≤ [tex]\frac{1}{3}[/tex] x - 4

Step-by-step explanation:

the first step is to obtain the equation of the line.

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 4) and (x₂, y₂ ) = (3, - 3) ← 2 points on the line

m = [tex]\frac{-3-(-4)}{3-0}[/tex] = [tex]\frac{-3+4}{3}[/tex] = [tex]\frac{1}{3}[/tex]

the line crosses the y- axis at (0, - 4 ) ⇒ c = - 4

y = [tex]\frac{1}{3}[/tex] x - 4 ← equation of the line

----------------------------------------------

the shaded region below the line indicates the values that are less than y

the solid line indicates that y can equal the values on the line (≤ )

the solution is then

y ≤ [tex]\frac{1}{3}[/tex] x - 4

The graph of the given linear equation 2x+3y=6 cuts the Y-axis at A(0,2).

For the graph of linear equation to cut the Y-axis its X-co-ordinate should be zero as abscissa is zero on Y-axis or the equation of Y-axis is x=0. Also the set of coordinates should satisfy the equation.

From the given set of coordinates, A(0,2) B(4,0) C(2,6) D(2,0), it is clear that the graph of the equation 2x+3y=6 cuts the Y-axis at A as it’s X-co-ordinate or abscissa is zero. So, it satisfies the first condition.

To satisfy the second condition the points of a should satisfy the equation given

LHS= 2x+3y

RHS=6

A(0,2)

Substituting the values of x and y in 2x+3y,

2(0)+3(2)=6

Therefore LHS=RHS

Hence, at point A(0,2) the graph of the given equation cuts the Y axis.

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The inequality which shows that Shelby should work for h hours is given by 15.5 h - 300 ≥ 280.

Given that,

Rent = 300 dollars

Shelby wants to have at least $280 left over after paying rent.

The total earnings of Shelby calculated in a week are given as, 15.5 h

where,

h is the number of hours

To that we have to substract the rent amount, and we'll get how much does she have left after paying rent,

15.5 h - 300

And she wants this amount to be at least 280 dollars. The inequality can therefore be expressed as follows,

15.5 h - 300 ≥ 280

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The linear regression equation that represents the given set of data is y=0.2x+865.

Linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables. The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression.

The line of best fit is in the form y=bx+a

The slope is b= [tex]\frac{\sum (x-\bar x)\sum (y-\bar y)}{\sum (x-\bar x)^2}[/tex]

Here, [tex]\bar x[/tex] =(0+1+2+3+4)/5

= 1.8

[tex]\bar y[/tex] = (856+871+924+961+961)/5

= 914.6

∑(x-[tex]\bar x[/tex])=(0-2.5)+(1-2.5)+(2-2.5)+(3-2.5)+(4-2.5)

= -2.5-1.5-0.5+0.5+1.5

= -2.5

∑(y- [tex]\bar y[/tex]) =(865-914.6)+(871-914.6)+(924-914.6)+(961-914.6)+(961-914.6)

= -49.6-43.6+9.4+46.4+46.4

= 9

So, slope b= 1.8×9/9²

b=0.2

Substitute b=0.2 and (0, 865) in y=bx+a, we get

865=0.2×0+a

a=865

Substitute b=0.2 and a=865 in y=bx+a, we get

y=0.2x+865

Therefore, the linear regression equation that represents the given set of data is y=0.2x+865.

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"Your question is incomplete, probably the complete question/missing part is:"

The number of newly reported crime cases in a county in New York State is shown in the accompanying table; where X represents the number of years since 1995, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected number of new cases for 2003, rounded to the nearest whole number: Years since 1995 (x) New Cases (y) 856 871 924 961 961

In given right triangle ACB, the ratios for sin A and cos A :

sin(A) = 48/50

cos(A) = 14/50

Consider the following diagram.

In a right triangle ACB, the angle ACB = 90 degrees.

We know that in right triangle for an angle θ, the trigonmetric ratios are:

sin(θ) = opposite side of θ/ hypotenuse

cos(θ) = adjacent side of θ / hypotenuse

Here, side AC = 14 units, side CB = 48 units and the hypotenuse AB = 50 units

We need to find the ratios for sin A and cos A

In right triangle ACB for angle A,

sin(A) = opposite side of angle A/ hypotenuse

sin(A) = CB/AB

sin(A) = 48/50

And cos(A) = adjacent side of A / hypotenuse

cos(A) = AC/AB

cos(A) = 14/50

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if the y-intercept is (0,5), you have:

y = (3/4)x + 5

To graph a line with a slope of 3/4, you can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

Since the slope is 3/4, the equation of the line is y = (3/4)x + b.

To find the y-intercept, you can plug in the coordinates (0,b) into the equation. So if the y-intercept is (0,5), you have:

y = (3/4)x + 5

You can then plot the point (0,5) on the graph, and use the slope of 3/4 to find the next point by going up 3 and right 4.

Another way is to pick two points on the line and plot them, you can use the slope formula (rise over run) to find the next point on the line.

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Answer: 3x+4=34

Step-by-step explanation: let the number be x

A.T.Q

the number is 3 times i.e 3x

4 increase=3x+4.

and it says the equation is equal to 34.

3x+4=34

To list the sides of a triangle in order from shortest to longest, you can follow these steps - Measure the length of each side of the triangle using a ruler or measuring tape. Then, write down the lengths of each side in a list. Sort the list in ascending order. The shortest side will be at the top of the list, and the longest side will be at the bottom.

A triangle is a polygon with three sides. By the property of a triangle which is the sum of any two sides of a triangle is greater than the third side. This property is known as the "Triangle Inequality Theorem".

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Answer:

Step-by-step explanation:

2/9 + x = 11/18

x = 11/18 - 2/9

x = 63/162

x = 7/18

2/9 + 7/18 = 11/18

11/18 = 11/18

Answer:

m<BCD=60

Step-by-step explanation:

4x+6=7x-12

3x=18

x=6

4(6)+6

24+6

30

30+30=60

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

Reason:

Use the HL (hypotenuse leg) theorem to prove that triangle BCF is congruent to triangle DCF.

It then leads to the fact that angle BCF is congruent to angle DCF.

Set those angle expressions equal to one another. Solve for x.

angle BCF = angle DCF

4x+6 = 7x-12

4x-7x = -12-6

-3x = -18

x = -18/(-3)

x = 6

Then,

Both angles are the same measure to confirm the correct x value.

Lastly, add up those angles to get angle BCD.

30+30 = 60 degrees is the final answer.

Answer: HG = CD.

Step-by-step explanation: If you tilt the second triangle so it's flat like the first triangle, you can see that HG is equal to CD.

The problem can be solved using algebra. Let's say the discount rate is x, then the price after discount is:

60000 (1 - x/100)

The price after VAT is:

60000 (1 - x/100) (1 + y/100) = 58986

Where y is the rate of VAT.

Rearranging the equation we get:

(1 - x/100) (1 + y/100) = 58986/60000

Multiply both sides by 100 to get rid of the fractions:

100 (1 - x/100) (1 + y/100) = 981

Expanding and grouping like terms, we get:

100 - x + 100y - xy = 981

We can see that x is in two terms, so we can move one side of the equation and get:

100 - x + 100y = 981 + x

x = (981 + x - 100 + 100y)/100 = (981 + xy - 100y)/100

Now we have x in only one term and we know the value of x is 10%, so we can substitute it:

10 + 10y = 9.81

Solving for y we can find that y = 0.81 or 81%

So the VAT rate is 81%

The maximum profit she can make if each goose produces a profit of $6 and each pig a profit of $20.

Making the Most of Total Revenue and Total Cost Data. Just multiply the price by the quantity at each quantity to find the company's total revenue. Next, deduct the company's total cost at each quantity, which is provided in the table.

Let the number of geese be x and the number of pigs be y

From the given information, we can form the following inequalities:

x ≤ 10

y ≥ 05

x + 15y ≤ 180

Maximize 6x + 20y.

We want to find the intersection points of the first three equations since x and y are bounded within the area under these

These points are (0,0), ( 10,0), (0,12), (10,65/3).

At (0,0) , the profit is $0

At ( 10,0), the profit is $60

At (0,12) , the profit is $240

At (10,65/3) , the profit is $499.33

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Therefore , the solution of the given problem of slope comes out to be  

M = 1/2.

What determines a line's steepness is its slope. Gradient overflow is a mathematical expression for the gradient. The slant is the proportion of both the vertical difference (rise) over the distance between two locations to the lateral change (run) over the same distance. Hill form of an equation is used to express a straight line's equation, which is written as y = mx + b. A point on the line where the slope is m, b equals a, and the y-intercept is placed is (0, b). An illustration would be the slope and y-intercept of the formula y = 3x - 7 (0, 7). At the location of the y-intercept, the line has a slope of m, b, and c.

Here,

Given : (0,-3) and (-2,-4)

Thus,

To calculate the slope ,

We use formula:

=> M = y2 -y1 /x2-x1

=> M = -4 -(-3) / -2 - 0

=> M = -1 /-2

=> M = 1/2

Therefore , the solution of the given problem of slope comes out to be  

M = 1/2.

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An expression which is equivalent to given [tex]\frac{\frac{1}{z+5} }{\frac{z+3}{5z+15} }[/tex] is 5 / (z + 5)

The correct answer is an option (B)

Consider given quotient.

[tex]\frac{\frac{1}{z+5} }{\frac{z+3}{5z+15} }[/tex]

Consider expression 5z + 15

We can write this expression as 5(z + 3) by  taking out the common factor 5.

So given quotient would be,

[tex]\frac{\frac{1}{z+5} }{\frac{z+3}{5(z+3)} }[/tex]

As we know a fraction is put in lowest terms by cancelling out the common factors of the numerator and the denominator.

For fraction [tex]\frac{z+3}{5(z+3)}[/tex] , the common term is z + 3.

So, [tex]\frac{z+3}{5(z+3)} = \frac{1}{5}[/tex]

We know that for fractions a/b and c/d where b ≠ 0, d ≠ 0, if we take quotient of these fraction then that would be,

(a/b) / (c/d) = (a/b) × (d/c)

So, given quotient would be,

[tex]\frac{\frac{1}{z+5} }{\frac{1}{5} }\\\\\\=\frac{1}{z+5} \times \frac{5}{1} \\\\\\=\frac{1\times 5}{(z + 5)\times 1}[/tex]

= 5 / (z + 5)

Therefore, an equivalent expression is: 5 / (z + 5)

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Option (D) that is (3.5, 8.75) is the ordered pair of point S.

An ordered pair is a composite of the x coordinate (abscissa) and the y coordinate (ordinate), with two values expressed between parenthesis in a predetermined order. It aids visual comprehension by locating a point on the Cartesian plane. An ordered pair's numeric values can be integers or fractions. Two variables are frequently represented by ordered pairs. We mean x = 7 and y = -2 when we write (x, y) = (7, -2). The x-coordinate is the number that corresponds to the value of x, and the y-coordinate is the number that corresponds to the value of y.

Here,

The ordered pair of point S is option (D), which is (3.5, 8.75).

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Complete question: Pentagon OPQRS is shown on the coordinate plane below:

Pentagon OPQRS on a coordinate plane with ordered pairs at O negative 1, 2, at P negative 5, 3, at Q negative 3, negative 2, and R 2, 1, at S 2, 5.

If pentagon OPQRS is dilated by a scale factor of seven over four from the origin, to create O’P’Q’R’S’, what is the ordered pair of point S’?

The difference in the volumes of the sphere is 410.29 inches³.

A sphere is a three dimensional circle in which each point on the circumference is equidistant from its center. The volume of a three-dimensional object is the amount of space in the object.

The formula for the volume of the sphere = 4/3πr³

Where:

Difference in the volumes = volume of the larger sphere - volume of the smaller sphere

(4/3 x 5³ x 3.14) - (4/3 x 3³ x 3.14)

523.33 - 113.04 = 410.29 inches³

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