a puzzle piece, in the shape of a triangle, has perimeter 30 cm. two sides of the triangle are each twice as long as the shortest side. find the length of each side.

The parabola with vertex (-1, 0), focus (-1/4, -1) and directrix x = 1/4. Therefore, option C is the correct answer.

The given equation is 3x+3y²+6y+3=0.

An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively.

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Left

Vertex: (0, -1)

Focus: (-1/4, -1)

Axis of symmetry: y=-1

Directrix: x = 1/4

The coordinate points to plot (2, 0.41), (-2, -2.41), (-1, 0), (-1, -2) and (0, -1).

The parabola with vertex (-1, 0), focus (-1/4, -1) and directrix x = 1/4. Therefore, option C is the correct answer.

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Hello!

So, we are given the following to solve:

[tex]\frac{1}{2}- \frac{9}{4}x=- \frac{2}{3}[/tex]

To solve this, subtract  [tex]\frac{1}{2}[/tex] from both sides.

[tex]\frac{1}{2} -\frac{9}{4}x- \frac{1}{2} =-\frac{2}{3} -\frac{1}{2}[/tex]

Simplify.

[tex]-\frac{9}{4}x= -\frac{7}{6}[/tex]

Multiply both sides by 4.

[tex]4(-\frac{9}{4}x)=4(-\frac{7}{6})[/tex]

Simplify.

[tex]-9x=-\frac{14}{3}[/tex]

Divide both sides by -9.

[tex]\frac{-9x}{-9}= \frac{-14/3}{-9}[/tex]

Finally, simplify.

[tex]x=\frac{14}{27}[/tex]

Hope this helps!

The evaluation of the composite function (g o f)(0) is -4

A composite function is generally a function that is written inside another function.

Therefore, let's solve the composite function below:

f(x) = 1x

g(x) = x - 4

Let's find (g o f)(0)

Therefore,

(g o f)(x) = g(f(x))

Hence,

(g o f)(0) = g(f(0))

f(0) = 1(0) = 0

Therefore, let's substitute f(0) in g(x)

(g o f)(0) = 0 - 4

(g o f)(0) =  - 4

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Answer:

Step-by-step explanation:

We are looking for a new number which is 350 more than 400.

We will get the new number by adding 350 to 400.

We write it down as:

400+350=750

Therefore your answer is; 750

Answer: 750

Step-by-step explanation: You add both of them 350+400...

Answer: 120

Step-by-step explanation:

[tex]\displaystyle\\10.8:0.09=\\\\\frac{10.8}{0.09}=\\\\\frac{10.8(100)}{0.09(100)}=\\\\\frac{1080}{9} =\\\\\frac{9(120)}{9}=\\\\120[/tex]

The best description for the sequence of transformation used is; Rigid Transformations.

In mathematics, a rigid transformation is defined as a geometric transformation of a defined Euclidean space that does not change or preserves the Euclidean distance that is between every pair of points. Examples of this rigid transformations are rotations, translations, reflections e.t.c

Now, from the given transformation, the first thing to notice is that the transformation does not change the distance between pair of points in the diagram. Secondly, it is neither only a translation nor reflection as it is more than  one transformation that was used and so it can be described as a rigid transformation.

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The distance from the midpoint to the origin is [tex]\sqrt{5}[/tex].

What is midpoint?

Midpoint is the point that is in the middle pf the line, and to calculate midpoint the formula is

[(x)1 + (x)2]/2, [(y)1 + (y)2]/2

given coodinates are (-2, -4) and (0, 8)

midpoint = (-2+0/2, 8-4/2)

=(-1, 2)

to find the distance from the midpoint to origin.

d= [tex]\sqrt{(x_{2}-x_{1} )^2+(y_{2} -y_{2} )^2} }[/tex]

the points are (-1,2) and (0,0)

d = [tex]\sqrt{(-1)^2+(2)^2}[/tex]

d = [tex]\sqrt{5}[/tex]

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Answer: 16x^2+144x+18

Step-by-step explanation:

The sum of two given expressions is 16x²-6x+14.

Addition of Algebraic Expressions is the process of collecting like terms and adding them. Identify and add the coefficients of like terms and sum them to find the final expression of given problems.

The given expressions are 8x²-x+9 and 8x²-5x+5.

Now, sum =8x²-x+9+8x²-5x+5

Group like terms and simplify, we get

(8x²+8x²)+(-x-5x)+(9+5)

= 16x²+(-6x)+14

= 16x²-6x+14

Therefore, the sum of two given expressions is 16x²-6x+14.

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Answer:

16

Step-by-step explanation:

→ Add the fractions

[tex]2\frac{1}{4} +\frac{1}{2} =\frac{9}{4} +\frac{1}{2} =\frac{9}{4} +\frac{2}{4} =\frac{11}{4}[/tex]

→ Equate to 44

[tex]\frac{11}{4} x=44\\[/tex]

→ Multiply both sides by 4

11x = 176

→ Divide both sides by 11

x = 16

The angle which the pendulum travels is 0.61 radian

Two parallel, identical bases connected by a curving surface form a 3D solid shape known as a cylinder. Similar to a disk in shape, these bases. The axis of the cylinder shape is a line drawn through the middle of, or connecting, two circular bases.

Given that :A pendulum is 45cm long. When the pendulum swings it travels along the arc of the circle and covers a distance of 27.5cm.

  Central Angle =[tex]\frac{length of arc}{Radius}[/tex]

= [tex]\frac{27.5}{45}[/tex]

=0.61 radian

The angle which the pendulum travels is 0.61 radian

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Answer:

88

Step-by-step explanation:

multiply 13 by 2 = 26

then add by 1 52 and 15

= 94

then subtract 94-6

88

Remember use Dmas while solving

A measure of the probability that the sample's average IQ is below 987 is 44.70 %.

The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean.

The Z-standard score's deviation measure, which the p-value is, can be regarded of as a percentile expression. So they do have p-values.

Given: IQ scores are frequently described as having a normal distribution with a mean of 100.0 and a standard deviation of 15.0. A sample of 57 persons is chosen at random.

Z-score = (X- μ)/σ

             = (98-100)/15

             = -0.1333

P value for this z score equals 0.4470 which is 44.70 %

Therefore, the probability that the average IQ of the sample's population is lower than 987 is 44.70 %.

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Triangle RST is rotated 180° about the origin, and then translated up 3 units.  Then , ΔRST ≅ ΔBAC

We know that  To rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y).

Thus, The coordinates of triangle RST becomes

R (1,1) → R'(-1,-1)

S (3,4) → S'(-3,-4)

T(-5,0) → T'(5,0)

Also ΔRST after rotation is translated up 3 units. , so we apply the rule (x,y)→(x,y+3)

R'(-1,-1)→R"(-1,-1+3)=R"(-1,2)→ B

S'(-3,-4) → S"(-3,-4+3) = R"(-3,-1) → A

C'(-5,0) → C"(-5,0+3) → C"(-5,3) → C

As rotation and translation both are rigid transformation that maps only congruent figures.

Therefore, ΔRST ≅ Δ BAC

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The quadrilateral named D, H, and E will be the scaled copies of the unlabeled rectangle.

A quadrilateral may be defined as a closed figure having four sides whereas a rectangle is a type of quadrilateral which has four sides in which any two sides are equal and the other two sides are also equal. The interior angles are 90°. The scale factor may be defined as the ratio of two dimensions such that one figure is large, and another is small. The scale factor is done due to the unpractical measurement of any figure. For example, if a figure is a scale copy of the scale factor of 6/2 it means 2 is converted into 6. Now, from the question If any figure is a scaled copy, then all dimensions must be enlarged with the same factor it means length and width both must be enlarged with the same factor. So, the unlabeled rectangle has 4 grid lengths and 2 grid widths. In H length is 8 grids and width are 4 which is the multiplication of 2 by 4 and 2. Quadrilateral D and E also follow the same.

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If the Great games company sells 9/20 of its games through its online stores, then the percentage of the games are sold online is 45%

The fraction of games sells through the online store = 9/20

Here we have to convert the simple fraction to the percentage

Simple fraction is a fraction that consist of whole number numerator and denominator. The top term in the simple fraction is called the numerator and bottom term is called denominator

The percentage is defined as the number that is expressed as the fraction of 100. It is represented by the percentage sign "%"

To convert  simple fraction to percentage, multiply the simple fraction by 100

The percent of games are sold online = (9/20)×100

= 45%

Hence, if the great games company sells 9/20 of its games through its online stores, then the percentage of the games are sold online is 45%.

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Answer:

0.026 is the value of x.

Step-by-step explanation:

sinx=p÷h

sinx=5.3÷8.2

sinx=sin0.02......

x=0.02°

Answer:

Yes, you have to distribute.

Step-by-step explanation:

2+5(x+3)-3(x-4)=x+2(2x+4)

2+5x+15-3x+12=2(2x+4)

Add the Numbers

2+5x-3x=2(2x+4)

Combine Like Terms, Then you can rearrange the terms for simplification. You should end up with an exation looking like this:

2x+29=5x+8

Subtract 29 from both sides. Simplify, then subtract 5x from both sides.
2x-5x=5x-21-5x
Simplify, then Divide both sides by the same factor. Simplify once more then you should have
x=7

Hope this helps ;)

Answer:

y = 5

Step-by-step explanation:

the equation of a horizontal line, parallel to the x- axis is

y = c ( c is the value of the y- coordinates the line passes through )

the line passes through (- 5, 5 ) and (0, 5 ) with y- coordinates 5 , then

y = 5 ← equation of line

The probability of getting heads is 1/2 which typically implies that the coin is fair. NO, procedure (b) does not give a fair coin flip outcome.

Given that, we want to generate the outcome of the flip of a fair coin, but that all we have at our disposal is a biased coin which lands on heads with some unknown probability p that need not be equal to1/2.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

The following procedure for accomplishing our task are:

1. Flip the coin.

2. Flip the coin again.

From here will know that the coin is first flipped twice

3. If both flips land on heads or both land on tails, it implies that we return to step 1 to start again. this makes the flip to be insignificant since both flips land on heads or both land on tails

But if the outcomes of the two flip are different i.e., they did not land on both heads or both did not land on tails , then we will consider such an outcome.

Let the probability of head = p

so P(head) = p

the probability of tail be = (1 - p)

This kind of probability follows a conditional distribution.

Therefore, the probability of getting heads is 1/2 which typically implies that the coin is fair. NO, procedure (b) does not give a fair coin flip outcome.

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

Suppose that we want to generate the outcome of the flip of a fair coin, but that all we have at our disposal is a biased coin which lands on heads with some unknown probability p that need not be equal to1/2. Consider the following procedure for accomplishing our task:

1. Flip the coin.

2. Flip the coin again.

3. If both flips land on heads or both land on tails, return to step 1. 4. Let the result of the last flip be the result of the experiment.

(a) Show that the result is equally likely to be either heads or tails.

(b) Could we use a simpler procedure that continues to flip the coin until the last two flips are different and then lets the result be the outcome of the final flip?

Answer:

1422.5778

Step-by-step explanation:

8.89x8.89=79.0321. 79.0321x18=1422.5778

Mandy must to walk a distance of 24.73 units towards Mark.

Given:

Mark is standing at 35th Street and 21st Avenue, so his location can be determined using the coordinates (35,21)

Mandy is positioned at 59th Street and 15th Avenue, hence her position's coordinates are as follows: (59,15).

We must now determine the distance Mandy must travel if Mark stays where he is and walks to meet him.

We can use the distance formula to determine this:

D = [tex]\sqrt{(x_{2}-x_{1} )^{2} + (y_{2} -y_{1})^{2} } }[/tex]

Here,

(x₁, y₁) =  (35, 21)

(x₂, y₂) = (59, 15)

Then,

D = [tex]\sqrt{(59-35)^{2}+(21-15)^{2} }[/tex]

D = [tex]\sqrt{24^{2} +6^{2} }[/tex]

D = [tex]\sqrt{576+36}[/tex]

D = √612

D = 24.73

That is,

Mandy must to walk a distance of 24.73 units towards Mark.

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This operation is equivalent to:

It is like a function inside a function. So, we can look for parts in h(x) that are common and call that the function inside.

As we can see, h(x) have terms with x + 4, so if we call:

We can see that h(x) becomes:

And if we substitute g(x) by x, we will get the expression of the ouside function f(x):

This way, we have:

So, the functions are:

Considering that R and S are points on the number line If RS= 10 and R lies at 13 then s will lie at

A number line is a sequence of numbers arranged at a particular pattern in a straight line

Information gotten form the question have it that"

RS= 10

R lies at 13

In a number line if R lies in point 13 and RS = 10 then we solve as follows

R + | 10 |

13 + 10 = 23

13 - 10 = 3

Hence R lies at point 3 or 13

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Answer:

y= -3x+1

Step-by-step explanation:

If she wants to meet her target distance 3/20 steps need to be taken.

Emily made the decision to walk 4/5 kilometers every day in order to keep healthy. She walked a distance of 2/5 miles to work and a distance of 1 mile for lunch.

The desired range is 4/5 miles.

walked for 2/5 miles and for 1/4 miles.

Total miles walked is [tex]\frac{2}{5} + \frac{1}{4}[/tex]

= [tex]\frac{13}{20}[/tex]

Mileage walked overall is +

LCD is 20

add the fractions after matching the denominators

The desired range is 4 to 5 miles.

Now deduct the distance you walked from the goal distance.

[tex]\frac{4}{5} - \frac{13}{20} \\\\\frac{16}{20} - \frac{13}{20} \\\\\frac{3}{20}[/tex]

the required walking distance is 3/20

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The student's first error was in step 1.

Step 1 should involve plotting a point at (0, 1).

Step 2 should involve plotting a point 3 units down and 4 units right from the point in step 1, at (4, -2).

Step 3, connecting the points with a line was correct.

In this question, we have been given an equation of line y + 5 = - 3/4 (x - 8)

We need to describe and correct the error a student made when graphing y + 5 = - 3/4 (x - 8).

Consider given equation.

y + 5 = - 3/4 (x - 8)

y + 5 = - 3/4 x - (-3/4) 8

y + 5 = -3/4 x + 6

y = (-3/4)x + 6 - 5

y = -3/4 x + 1

Here,

slope(m) = (-3/4)

and y-intercept (c) = (0, 1)

Therefore, the student's first error was in step 1.

Step 1 should involve plotting a point at (0, 1).

Step 2 should involve plotting a point 3 units down and 4 units right from the point in step 1, at (4, -2).

Step 3, connecting the points with a line was correct.

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There are 8 tenths in 4/5, There are five fifths in 1/10, there are 2 tenths in 1/5, there are 25 fifths in 5.

The digit that follows the decimal has the place value of tenth. It stands for the digit's 1/10 position.

The fifth of a number is obtained by multiplying five occurrences of the number n together: n5 = n n n n. A number's fourth power or its square by its cube can likewise be used to create fifth powers.

a) Given 4/5, multiply the numerator and denominator by 2 to obtain the tenths. We get =4/5 2/2 =8/10 =8(1/10). Similarly, in 1/5, calculate the tenths in 1/5.

c) 525/25 = 25 is the fifth in 5.

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The measure of angle A is found as 115 degrees.

For the given question, the values of the angles are given.

A=(3x-35)

B=(x-35)

c=x

We know that the sum of all angles in a triangle is 180.

A + B + C = 180

Put the values;

3x-35 + x-35 + x = 180

Simplifying;

5x - 70 = 180

5x = 250

x = 50

Put the values in the angles;

Angles A = 3×50 - 35

Angles A = 115

Thus, the measure of angle A is found as 115 degrees.

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