if triangles have two corresponding angles and one corresponding side congruent but the side is not between the angles then the triangles are

right,scalene,congruent,obtuse,acute

The equation of the parabola will be;

y = (x - 3)² + 1

What is mean by Parabola?

A parabola is a set of points in the plane which are equidistant from the directrix and focus.

Given that;

The vertex of the parabola = (3 , 1)

A parabola passes through the point (2,2).

Now,

Since, The equation of parabola in vertex form is;

y = a (x - h)² + k

Where, (h , k) are vertex of the parabola.

So, The equation of parabola with vertex (3, 1) will be;

y = a (x - 3)² + 1

And, It passes through the point (2,2).

So we substitute the value of (2, 2) in place of (x, y) as;

2 = a (2 - 3)² + 1

2 = a + 1

a = 2 - 1

a = 1

Substitute the value of a in above equation, we get;

The equation of parabola as;

y = (x - 3)² + 1

Therefore, The equation of the parabola will be;

y = (x - 3)² + 1

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The equation which forms the correct slope-point form equation is

y - 9 = 2( x - 5). Thus, option (1) is the answer.

The point-slope form is a method that uses the slope of the line and a random coordinate on any point of the line to create an equation of that line.

The equation in the point-slope form is written in the format: [tex]y-y_{1}=m(x-x_{1})[/tex] , where m is the slope and [tex]x_{1}[/tex] and [tex]y_{1}[/tex]are the coordinates of the point on the line.

The given slope is 2, the x-coordinate is 5, and the y-coordinate is 9. There will be no addition symbol in the equation. There is only a subtraction of the coordinates in the equation form. Since options 2, 3, and 4 have addition signs, they do not show the correct equation.

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The estimated standard deviation from the range rule is 145.5 cm3.As it is 29.8 cm3 smaller than the exact standard deviation, we consider that the estimation is not accurate enough.

Generally, brain volumes which are smaller than 921.1 cm3 can be considered significantly low and bigger than 1417.5 cm3 can be considered significantly high. Hence, brain volume of 1457.5 cm3 is bigger than the expected maximum, so it can be considered significantly high.

The calculation goes like this,

According to the range rule, the standard deviation and range, or the distance between the maximum and smallest value, are roughly inversely proportional:

[tex]s=R/4[/tex]

If we have a sample of 50 brains volumes, and they range from 910 cm3 to 1492 cm3, we can estimate the standard deviation as:

[tex]s=max-min/4[/tex]

s=1492-910/4=582/4=145.5

The exact standard deviation is 175.3 cm3.The difference is 175.3-145.5=29.8 cm3, so the estimation is not accurate enough.

The range rule of thumb states that we should anticipate a maximum value that is approximately two standard deviations above the mean and a lowest value that is approximately two standard deviations below the mean. The expected ranges are as follows given our mean volume of 1169.3 cm3 and standard deviation of 124.1 cm3:

Min= M-2s=1169.3-2*124.1=921.1

Max=M+2s=1169.3+2*124.1=1417.5

The brain capacity of 1457.5 cm3 can be regarded as significantly high because it is higher than the predicted maximum.

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The slopes for each couple of points are summarized below:

Geometrically speaking, slopes in lines indicates the grade of steepness of the line itself. The slope of the line can be determine by knowning the coordinates of two distinct points set on Cartesian plane and using the secant line formula, whose definition is shown below:

m = Δy / Δx

Where:

Now we proceed to answer on each case:

Case 1

m = [3 - (- 1)] / [3 - (- 3)]

m = 4 / 6

m = 2 / 3

Case 2

m = (- 2 - 1) / [2 - (- 2)]

m = - 3 / 4

Case 3

m = [2 - (- 4)] / [- 4 - (- 1)]

m = 6 / (- 3)

m = - 2

Case 4

m = Undefined, as Δx = 0.

Case 5

m = [3 - (- 1)] / (3 - 2)

m = 4

Case 6

m = 0, as Δy = 0

Case 7

m = (6 - 9) / (1 - 4)

m = - 3 / (- 3)

m = 1

Case 8

m = [- 5 - (- 1)] / [- 2 - (- 4)]

m = - 4 / 2

m = - 2

Case 9

m = (- 9 - 3) / (5 - 5)

m = - 12 / 0

m = Undefined

Case 10

m = (9 - 1) / (8 - 2)

m = 8 / 6

m = 4 / 3

Case 11

m = [- 6 - (- 8)] / (7 - 14)

m = 2 / (- 7)

m = - 2 / 7

Case 12

m = [- 3 - (- 3)] / (8 - 4)

m = 0 / 4

m = 0

Case 13

[8 - (- 4)] / (2 - x) = - 3

12 = - 3 · (2 - x)

12 = - 6 + 3 · x

18 = 3 · x

x = 6

Case 14

(4 - y) / (3 - 10) = - 2 / 7

(4 - y) / (- 7) = - 2 / 7

4 - y = - 2

y = 6

Case 15

(4 - 1) / (x - 7) = 3 / 4

3 / (x - 7) = 3 / 4

x - 7 = 4

x = 11

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Step-by-step explanation:

1. Transform by dividing both sides by Highest common factor which is 10 in this case.

2. Final answer is 50:1

72.3 - 39.1 = 4 tens - 7 ones - 2 tens is the correct order after rewriting.

Given the formula 72.3 + (-39.1)

removing the parentheses:

= 72.3 + (-39.1) (-39.1)

= 72.3 - 39.1

converting decimal numbers to place values

72.3 = 7tens plus 2units plus 3tenths

72.3 = 7(10) (10)

+2(1)+3(1/10)

72.3 =70+2+0.3

Similarly, 39.1

39.1 = 3tens plus 9units plus 1tenth

39.1 = 3(10)+9(1)+1(1/10)

39.1 =30+9+0.1

72.3 - 39.1 = 70+2+0.3 - (30+9+0.1)

72.3 - 39.1 = 70+2+0.3 - 30-9-0.1

72.3 - 39.1 = 70-30+2-9+0.3-0.1

72.3 - 39.1 = 40 - 7 +0.2

Hence after rewriting we get 72.3 - 39.1 = 4 tens - 7 ones - 2 tens

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As all the length of each side of given triangle are unequal so the given triangle is scalene triangle

A triangle's perimeter is defined as the total length of its boundary.

The perimeter of a triangle is the sum of all three sides.

Here given that there is a triangle name ABC and the triangle ABC has the perimeter of 90.

∴ Sum of sides of triangle ABC will equal to the perimeter of triangle ABC

∴ AB + BC + AC = 90

As we have AB = 5x + 1, BC = 2x + 13, AC = x + 4

∴ 5x + 1 +  2x + 13 + x + 4 = 90

∴ 8x + 18 = 90

∴ 8x = 90 - 18

∴ 8x = 72

∴ x = 72/8

∴ x = 9.

So we get AB = 5x + 1 = 5(9) + 1 =45 + 1 = 46.

BC = 2x + 13 = 2(9) + 13 = 18 + 13 = 31.

AC = x + 4 = 9 + 4 = 13.

As all the length of each side are unequal so the given triangle is scalene triangle as an scalene triangle is a triangle in which all three side lengths are different and all three angle measurements are different. However, the sum of all interior angles is always equal to 180 degrees. Therefore, it satisfies the angle sum property of triangles.

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Answer:

it is 25 or 35

Step-by-step explanation:

The number of apples in the bag are 6

What are algebraic equations?

Algebraic equation are the equation containing coefficients and variable Which can be solved by various method like substitution and elimination.

We are given that, Ms. Yoto is putting together bags of fruit that contain 1 pear for every 2 apples.

Also the total number of fruits in the bag are 9

Now mr. Yoto is putting 3 fruit at a time and the bag contains total of 9 fruits that means 3 such sets were put

in each set there were 2 apples and 1 pear

Hence there were 6 apples and 3 pear

Hence the number of apples in the bag is 6

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SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Represent the two coins

Let N represents Nickels

Let Q represents quarters

STEP 2: Get the first equation

Equation 1: Eric has 130 coins consisting of quarters and nickels. This is given as:

STEP 3: Get the second equation

The total value of all of the coins is $15.90. Each quarter represents .25 and each nickel represents .05, then the second equation is:

STEP 4: Multiply Equation 2 by 100 to remove the decimals

STEP 5: Make N the subject of Equation 1

Answer:

1,3,9,5

Step-by-step explanation:

Answer:

9, 5, 1, 3

Step-by-step explanation:

i forgot my vocabulary

But i still know decent engrish

Answer:

30 + x + x + x = 180

so, 30 + 3x = 180

sub 30 on both sides

3x = 150

divide 3 on both sides

x = 50

Using Linear equation, The total number of fishes in the aquarium is found to be 50.

Linear equation is an equation containing one unknown variable with power one and constants.

The standard form of an linear equation in one variable x is :

ax + b = 0 , where a, b are constants

x= -b/ a is solution if this equation or we can solve this equation by adding or subtracting, multiplying, dividing same number to both sides.

Given that number of fishes jake has in the aquarium = 30

And that number of fishes Emi has is 1/3 the number of fish that jake has .

Therefore, Number of fishes that Emi has = 1/3 (30) = 10

Also given that Emi has 1/2 the number of fish that Tobin has .

Let Tobin has x fishes

⇒  1/2(x) = Number of fishes Emi has

⇒ (1/2)x = 10, this is an linear equation in x

Multiplying both sides by 2, We get:

⇒ 2× (1/2)x = 2 ×10

⇒ x = 20

∴ Tobin has 20 fishes

If the three students combined all their fish in the school's aquarium,

the Total number of fishes = 30+20+10 = 50

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Answer:

60 tulips

Step-by-step explanation:

1 daffodils : 3 tulips

Since she planted 20 daffodils

20 × 3 = 60 tulips

Answer:

20 Combos

Step-by-step explanation:

6C3 = 6! / ( 3! * 3!) = 20 COMBOS

The average rate of change of the equation g(x) =−x²+2x−4 from x = 2 to x = 5  is -15  .

The average of change of the function f(x) from x=a to x=b is given by the formula

Average rate of change = (f(b)-f(a))/(b-a)

In the question ,

it is given that

the function is g(x) =−x²+2x−4

we need to find g(2) and g(5) .

g(2) = −(2)²+2(2)−4

= -4 + 4 -4

= -4

g(5) = −(5)²+2(5)−4

= -25 +10 -4

= -15 -4

= -19

So , Average rate of change = (g(5) - g(2))/(5-2)

Substituting the values , we get

Average rate of change = (-19 - (-4))/3

= (-19+4)/3

= -15/3

= -5

Therefore , the average rate of change of the equation g(x) =−x²+2x−4 from x = 2 to x = 5  is -15  .

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The value for g is 2, meaning that each family bowled 2 games.

How to solve linear equations?
Given that the largest power of the variable (or pronumeral) in these equations is 1, linear equations are also known as first-degree equations. A line on the quadratic system is represented by a linear equation. This equation's general form is axe + b = 0, where a, b, and x are all integers and x is the variable. The y-axis is parallel to this form of equation's single solution, which it symbolizes.
The steps that should be followed while solving linear equations are listed below:
1) We must first determine which variable we need to isolate.
2) Next, make a distinction between variables and constants.
3) Arrange the constants on the right and the variables on the left.
4) Using established axioms, we carry out algebraic operations to determine the variable's value.

Given, the equation is 6(8g + 2) + 45 = 153
Following the steps in the available literature, we have the equation as:
6(8g + 2) + 45 = 153 ⇒ 48g + 12 + 45 = 153 ⇒ 48g = 153 - 45 - 12 = 96
⇒ g = 96/48 ⇒ g = 2
Thus, g as suggested will determine number of times each family bowled.

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( 1 ) The y-intercept for the first graph is 50. The correct option is B.

( 2 ) The y-intercept for the second graph is 12. The correct option is C.

( 3 ) The y-intercept for the third graph is 0. The correct option is C.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

The y-intercept of the first graph:-

y = mx + c

m= ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 350 - 50 ) / ( 4 ) = 75

y = mx + c

50 = 75 x 0 + c

c = 50

The y-intercept of the second graph:-

y = mx + c

m= ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 30 - 12 ) / ( 4 ) = 4.5

y = mx + c

12 = 4.5 x 0 + c

c = 12

The y-intercept of the third graph:-

y = mx + c

m= ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 6 - 3 ) / ( ( 8 - 4 ) = 3 / 4

y = mx + c

3 = ( 3 / 4) x 4  + c

c = 0

Therefore, the y-intercept of all the graphs is calculated above.

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The function which can be the reflection along y-axis will be F(-x, y).

A function may be defined as an expression in which for every input variable x there is only one output variable y. The input variable is known as independent variable and output variable is known as dependent variable. Reflection may be defined as the changes which occur on a graph for a given curve. If reflection of a point occurs along x axis, then there will be change in the y coordinate and if reflection along y axis, then there will be change in the x coordinate. We have a function F(x, y) and we need to find reflection along y axis so there will be change in the x coordinate, so new function will be F(-x, y).

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It will take 6 seconds for the acorn to be 1 foot above the ground.

A linear equation is an algebraic equation of the form y=mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

A typical form linear equation is, for instance, 2x+3y=5. When an equation is provided in this format, finding both intercepts is rather simple (x and y).

Given:

acorn is falling from 13 feet

Every seconds it descends = 4.8 feet

let us assume that the equation for the distance between the acorn from the ground is

x =13 - 4.8 y

where is y is time in seconds and x is the distance

if x = 1 foot

1 = 13 -4.8y

-12  = -4.8y

y = -12 / -4.8

y = 2.5 seconds

Hence, it will take 6 seconds for the acorn to be 1 foot above the ground.

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The value of the mean is 155.96mm

Calculation of the mean is:

n=5

Mean= [tex]\frac{\sum fx}{n}[/tex]

Mean=[tex]\frac{156.9+153.2+153.6+157.5+158.6}{5}[/tex]

Mean=779.8/5

Mean=155.96mm

The question was incomplete, the complete question is given below:

Auto pistons at Wenming​ Chung's plant in shanghai are produced in a forging​ process, and the diameter is a critical factor that must be controlled. from sample sizes of 10 pistons produced each​ day, the mean and the range of this diameter have been as​ follows:

Day Mean X(mm) Range R (mm)

1   156.9          4.2

2   153.2         4.6

3   153.6         4.1

4   157.5         4.8

5   158.6         4.7

What is the value of mean in mm, (round your response to 2 decimal places)

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Answer:

[tex]y-6=7(x-1)[/tex]

Step-by-step explanation:

The equation of a line with slope [tex]m[/tex] and that passes through [tex](x_1, y_1)[/tex] in point-slope form is [tex]y-y_1=m(x-x_1)[/tex].

System of inequalities are :

y> [tex]x^{2} -4[/tex] and y > [tex]x^{2} +3[/tex]

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Answer:

a) 81

b) 16807

c) 1010000000

d) 390630

These are all correct. I checked.

Answer:

that's a good question

Step-by-step explanation:

Given:

Let's graph the the absolute value equation.

From the equation let's solve for x.

Since |x| = -2, there is no possible value of x that can satisfy this equation. This is because an absolute value can never be a negative number.

Therefore, we can say there is no solution.

This absolute value equation can not be graphed.

ANSWER:

No solution

We can conclude that the value of angle y is 70° and x is 35°.

So, a measure of 'x':

We can see that ∠BAC = ∠DAE (Inversely opposite angles)

Let 2x be y for instance:

Now, we know that y = 70 and similarly 2x = 70.

Now, solve for 'x' as follows:

Therefore, we can conclude that the value of angle y is 70° and x is 35°.

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Answer:

Chloe has 10 songs.

Step-by-step explanation:

40 ÷ 4 = 10

Answer: 1.28

Step-by-step explanation:

1. P(Z > 0.99) = 1 -Ф (0.99) = 1-0.8389 = 0.1611

2.P(Z <-0.99) = Ф(-0.99) = 0.161 (known that from [a] by symmetry)

3.P(Z <0.99) = Ф(0.99) = 0.8389

4. P(Z >0.99) = P(Z <-0.99) + P(Z > 0.99) = 2(0.1611) = 0.3222

The value z = 10.0 is out because it is too large. On comparing with the largest value, z = 3.99,

we get

5. P(Z < 10.0) > P(Z <3.99) = 1.0

6.P(Z > 10.0)<P(Z > 3.99) =10.0

7. On solving the equation

Ф(Z) = 0.9

for Z.

In Table A4, find the value of z corresponding to the probability 0.9. The  nearest value is Ф(1.28) = 0.8997. Therefore, z ≈ 1.28