what is the measures of ∠x

Answer:

Step-by-step explanation:

This is trying to help you understand a method of factoring trinomials.

The first step is to look at the linear term (-5x) and the constant term (-24) and identify the coefficients and their signs: -5 and -24.

The next step is to identify factors of -24 (the constant) that have a sum equal to -5 (the linear term coefficient). We can look at the ways that -24 can be factored:

  -24 = 1(-24) = 2(-12) = 3(-8) = 4(-6)

The sums of these factor pairs are 1-24=-23, 2-12=-10, 3-8=-5, 4-6=-2. Of course, the pair we're looking for is +3 and -8.

The next step from here is to rewrite the linear term using these factors. (-5x=3x-8x) This is the first step of the sequence shown in the figure:

  x² +3x -8x -24

The next step is to group these terms in pairs:

  (x² +3x) +(-8x -24)

And then, to factor each pair using the distributive property:

  x(x +3) -8(x +3)

Finally, finish the factoring, again using the distributive property:

  (x +3)(x -8)

Answer:

x² - 9

Step-by-step explanation:

Given

(x + 3)(x - 3)

Each term in the second factor is multiplied by each term in the first factor, that is

x(x - 3) + 3(x - 3) ← distribute both parenthesis

= x² - 3x + 3x - 9 ← collect like terms

= x² - 9

Answer:

Step-by-step explanation:

[tex](x + 3)(x - 3)[/tex]

Multiply each term in the first parentheses by each term in the second parentheses ( FOIL )

[tex]x(x - 3) + 3(x - 3)[/tex]

Calculate the product

[tex] {x}^{2} - 3x + 3x - 3 \times 3[/tex]

Multiply the numbers

[tex] {x}^{2} - 3x + 3x - 9[/tex]

Since two opposites add up to zero, remove them from the expression

[tex] {x}^{2} - 9[/tex]

Hope this helps..

Best regards!!

Answer:

10

Step-by-step explanation:

f(x)=-x^2+6x+1

This is a parabola that opens downward( the - coefficient of x^2)

The maximumx is at the vertex

The x coordinate is at

-b/2a  where ax^2 + bx +c  a =-1  b=6 c=1

-6/(2*-1)

-6/-2 = 3

The x coordinate of the vertex is 3

f(3) = - (3)^2 +6(3)=1

    = -9+18+1

    = 10

The vertex is ( 3,10)

The maximum value is 10

Answer:

[tex]10[/tex]

Step-by-step explanation:

[tex]f(x)=-x^2+6x+1[/tex]

x coordinate:

[tex]\frac{-b}{2a}[/tex]

[tex]a=-1\\b=6[/tex]

[tex]\frac{-6}{2(-1)} \\\frac{-6}{-2}\\ =3[/tex]

y-coordinate:

[tex]f(3)=-(3)^2+6(3)+1\\f(3)=-9+18+1\\f(3)=10[/tex]

Answer:

The correct answer is:

Poisson (A.)

Step-by-step explanation:

A Poisson distribution is used to model the number of events occurring within a given time interval, when the average number of times that the event occurs within the time interval is given.

Lambda ( λ ) is a rate parameter in Poisson's distribution, and it is used to represent "event/time", and it simply represents the expected number of events in the interval.

here's your answer in the given attachment

Answer:

Solution: {(-1,-8), (0,-6)}

Step-by-step explanation:

y=x^2+3x-6 ............(1)

y=2x-6 ....................(2)

Solution:

by comparison, the right-hand sides of both equations are equal (to y)

x^2+3x-6 = 2x - 6

Transpose and simplify

x^2 -x = 0

x = -1 or x=0

Substitute  x = -1 in (2)

y = 2(-1) -6 = -8  ..............(-1,-8)

substitute x = 0 in (2)

y = 2(0) -6 = -6 ...............(0,-6)

So there are two solutions, corresponding to the intersection of the quadratic and the straight line.

Answer:

x = 1.25, y = 1.75

Step-by-step explanation:

The smaller and larger triangles are similar triangles. (the 2 triangles have the same angles).

We know that the smaller triangle has length 8 for it's bottom side when the larger triangle has length 10. This means the scale factor between the 2 is 10 / 8 which is 1.25. Therefore by multiplying the side lengths of the smaller triangle by 1.25 we get the side lengths of the larger triangle.

5 * 1.25 = 6.25

7 * 1.25 = 8.75

However we don't want the whole side lengths we want x and y, We need to subtract 5 and 7 respectively from the lengths of the larger triangles.

Therefore the lengths must be: 6.25 - 5 = 1.25

and 8.75 - 7 = 1.75

Therefore x and y equal 1.25 and 1.75

Answer:

Step-by-step explanation:

[tex]Opposite =f\\Hypotenuse = 9\\Adjacent = 5\\\alpha = 50\\Using \: Pythagoras \:Theorem \\Hypotenuse^2 = Opposite^2 +Adjacent^2\\9^2 = f^2+5^2\\81=f^2+25\\81-25=f^2\\56=f^2\\\sqrt{56} = \sqrt{f^2} \\f = 2\sqrt{14} \\f = 7.483\\\\f = 7.5[/tex]

The correct answer to this question is A. 9.4 x [tex]10^{-8}[/tex], 9.25 x [tex]10^{-6}[/tex], 2.5 x [tex]10^{3}[/tex], 7 x

Explanation:

These numbers are written in scientific notation. In this system, the exponent shows the number of spaces the period has been moved to make the number shorter. Additionally, a positive exponent shows the number has a certain number of digits to the right, while a negative exponent shows the number has digits to the left. In this way, the numbers presented can be converted as:

9.4 x [tex]10^{-8}[/tex] = 0.000000094 (Exponent indicates eight spaces to the left)

9.25 x [tex]10^{-6}[/tex] = 0.00000925 (Exponent indicates six spaces to the left)

2.5 x [tex]10^{3}[/tex] = 2500 (Exponent indicates three spaces to the right)

7 x [tex]10^{3}[/tex] =  7000 (Exponent indicates three spaces to the right)

Answer:

Step-by-step explanation:

If the second angle's measure is based on the first angle's measure, and the third angle's measure is also based on the first angle's measure, then the first angle is the main angle. We will call that x.

1st angle: x

2nd angle: x + 20%

3rd angle: x - 20%

By the Triangle Angle-Sum Theorem, all those angles will add up to 180, so:

x + (x + 20%) + (x - 20%) = 180 and

3x = 180 so

x = 60. That means that

2nd angle: 60 + (.2*60) which is

60 + 12 = 72 and

3rd angle: 60 - (.2*60) which is

60 - 12 = 48. Let's check those angles. If

∠1 = 60

∠2 = 72

∠3 = 48,

then ∠1 + ∠2 + ∠3 = 180 and

60 + 72 + 48 does in fact equal 180, so you're done!

Answer:

22.8

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. 6x + 12 = 3x - 27

   3x + 12 = -27

   3x = -39

    x = -13

2. 2p - 3 = 3p + 2

    -p - 3 = 2

     -p = 5

      p = -5

3. 6x - 2 - 35x -28 = 18x - 27

   -29x - 30 = 18x - 27

   -47x - 30 = -27

    -47x = 3

    x = -3/47

Answer:

B

Step-by-step explanation:

Answer:

Volume of the smaller cone = 8.34 cm³

Step-by-step explanation:

"If two figures are similar, their dimensions will be proportional.

Following this rule,

Ratio of the dimensions of two cones = [tex]\frac{\text{Radius of the large cone}}{\text{Radius of the small cone}}[/tex]

                                                               = [tex]\frac{r_2}{r_1}[/tex]

                                                               = [tex]\frac{5}{2}[/tex]

                                                               = 2.5

Similarly, "ratio of the volumes of two similar figures is cube of the dimensional ratio".

Ratio of the volumes = (ratio of the dimensions)³

[tex]\frac{V_1}{V_2}=(2.5)^3[/tex]

[tex]\frac{131}{V_2}=15.625[/tex]

[tex]V_2=\frac{131}{15.625}[/tex]

    = 8.384 cm³  

    ≈ 8.4 cm³

Therefore, volume of the smaller cone is 8.4 cm³.                          

Answer:

1: 90º

2: 25º

Step-by-step explanation:

Hey there!

Well we know that all the middle angles are 90º right angles,

so we can conclude that angle 1 is 90º.

All the angles in a triangle add up to 180 so we can set up the following,

65 + 90 + x = 180

Combine like terms

155 + x = 180

-155 to both sides

x = 25º

So angle 2 is 25º.

Hope this helps :)

Answer:

Below

Step-by-step explanation:

From the kite you easily notice that 1 is a right angle so its mesure is 90°.

2 is inside a triangle. This triangke has two khown angles: a right one and a 65° one.

The sum of a triangle's angles is 180°.

● (2) + 90+65 = 180

● (2) +155 =180

● (2)= 180-155

●(2) = 25°

Answer: A) The total cost of 2 candies is $6.00.

Step-by-step explanation:

Hi, the question is incomplete,  options are :

A) The total cost of 2 candies is $6.00. B) The total cost of 6 candies is $2.00. C) The total cost of 2 candies is $3.00. D) The total cost of 3 candies is $2.00.  

So, to answer this question we have to analyze the function given:

f(2)=6

Since the input value x (number of candles) is 2, and the output (cost in dollars ) is $6, the correct option is :

A) The total cost of 2 candies is $6.00.  

Answer:

Step-by-step explanation:

Due to the '+1', the graoph of x^2 is shifted 1 unit to the left.  The '+9' results in the entire graph being shifted downward 9 units.

Answer:

18 minutes

Step-by-step explanation:

1: Calculate how many minutes are in an hour

2: Take 3:16 and add until 3:34

The part of an hour  3/10

Elapsed time is the time taken by an event to occur between the start of the time and the end of the time. In simple words, we can say that the amount of time that has passed between the beginning and the end of an event is called the elapsed time. We can determine this time by subtracting the end time and the start time. The formula to calculate the elapsed time is simply to subtract the hours and minutes separately. It gives the duration of an event.

Elapsed time means the time that has elapsed between the start of the time and the end of the time.

For example, if a man starts traveling at 10:30 AM and ends the journey at 12:15 PM, the time elapsed is the duration of his journey, that is, the time between 12:15 PM and 10:30 AM. Elapsed time is an important concept as it helps us to learn to read the time on a clock and measure the time taken for an event to occur.

Formula:

Elapsed Time = End Time - Start Time

As, 3:16 p.m. shows 44  minutes before 4:00 p.m.

and, 3:34 p.m. shows 26 minutes before 3: 34 p.m.

As, there is difference of

=44-26

=18 minutes

Hence, the part of an hour = 18/60= 3/10

Learn more about this concept here:

https://brainly.com/question/11921928

#SPJ2

Answer:

the answer is XY = 24 units.

Step-by-step explanation:

Given:

XY is tangent to the circles with center P and O respectively.

OX=16 units

PY=6 units

OP=26 units

To find:

Side XY = ?

Solution:

As per given statement, the diagram of two circles and their tangent is shown in the diagram.

We need to do one construction here,

Draw a line parallel to tangent XY from P towards OX such that it meets OX at A .

Now, let us consider triangle [tex]\triangle OAP[/tex]. It is a right angled triangle.

With sides Hypotenuse, OP = 26 units  

Perpendicular, OA = 16 -6  = 10 units

Base AP is equal to XY.

If we find the value of Base AP, the value of XY is calculated automatically.

Let us use pythagorean theorem in [tex]\triangle OAP[/tex]:

According to pythagorean theorem:

[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow OP^{2} = AP^{2} + OA^{2} \\\Rightarrow 26^2=XY^2+10^2\\\Rightarrow XY^2 = 676- 100\\\Rightarrow XY = \sqrt{576}\\\Rightarrow XY = 24\ units[/tex]

Hence, the answer is XY = 24 units.

Answer:

306 mi^2

Step-by-step explanation:

surface area = area of base + lateral area

surface area = s^2 + 4bh/2

surface area = (10 mi)^2 + 4(10 mi)(10.3 mi)/2

surface area = 306 mi^2

Answer:

The maximum size of the smaller jars is 6 liters

Step-by-step explanation:

Container 1=174 liters of oil

Container 2=258 liters of oil

Same pours the entire content of container one and container 2 into the same number of smaller jars

The maximum size of the smaller jar can be found by finding the highest common factor of 174 and 258

Factors of 174=1,2,3,6,29

Factors of 258=1,2,3,6,43

Common factors of 174 and 258=1,2,3 and 6

Highest common factor=6

Therefore,

The maximum size of the smaller jars is 6 liters

Answer:

Step-by-step explanation:

If m∠CED = 30° and m∠CDE = 90° than triangle CED is half of equilateral triangle where CE is side of the equilateral triangle, DE is hight of equilateral the triangle and CD is half of side of the equilateral triangle.

[tex]\dfrac{CE\sqrt3}2=2\sqrt3\\\\CE\sqrt3=4\sqrt3\\\\CE=4=s\\\\CD=\dfrac s2=\dfrac42=2[/tex]

Answer:

9/13

Step-by-step explanation:

rise = y₂ - y₁ = -1 - (-10) = -1 + 10 =   9

run = x₂ - x₁ =   9 - (-4)   =   9 +   4 = 13

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

2x-xy

2(-1/2)-(-1/2)(8)

-1+4

=3

Answer:

a) 4.50m/s²

b) v= 21

c) 11.25m/s

Step-by-step explanation:

a) rate of change of speed in first 2 seconds

= gradient of graph from t=0s to t=2s

The two points are (0,0) and (2,9).

[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]

Rate of change of speed

[tex] = \frac{9 - 0}{2 - 0} \\ = \frac{9}{2} \\ = 4.50m/ {s}^{2} [/tex]

Total distance= area under graph

Distance travelled for first 6s

= area of traingle +area of rectangle

= ½(2)(9) +(6-2)(9)

= 9 + 4(9)

= 9 +36

= 45m

Distance travelled from t=6s to t=12s

= 135 -45

= 90m

Area under graph from t=6s to t=12s =90

Area of trapezium= 90

½(A +B)(h)= 90

½(9+ v)(6)= 90

3(9 +v)= 90 (simplify)

9 +v= 30 (÷3 throughout)

v= 30 -9

v= 21

c) Average speed

= total distance ÷total time

= 135 ÷12

= 11.25 m/s

Answer:

D

Step-by-step explanation:

x^2 - 4x + 4 = 36

Take the square root on both sides.

x - 2x + 2 = 6

Answer:

Bottom right on TTM/Imagine Math    on the question asked it is d.

Step-by-step explanation:

Answer:

AHH! Geometry!

Thanks for this problem. Needed to refresh my skill for similarity and rations.

First, notice the lines that are on sides of the triangles. Lines with the same number of marks are the same measure. You may have already known this, but I'll just tell you for reference.

That means both of those pair of sides have equal length. What does this mean though?

Imagine that each of the line segments(the ones with two marks) are... 1 cookie (Their lengths, also, I really want a cookie.)

Now, this is where ratios come into play. Consider only the top triangle to the entire triangle. The Top Triangle has a side with the length of one cookie. That corresponding side on the entire large one is 2 cookies (because they are the same measure, and 1*2=2).

Thus, we can make a ratio, comparing the lengths of a corresponding sides.

(BTW, these are similar triangles, meaning that they have all the same angle measures, but different side lengths.)

[tex]\frac{1Cookie}{2Cookies}[/tex]

Now. (Refer to above) Similar triangles have ratios of similarity. Meaning that: Corresponding sides have a 1/3 ratio. This means, also, that all the other corresponding sides have a 1/3 ratio. Neat, huh?

Putting into other words, we can compare CB and RT with the same 1/2 ratio!(Just cancel out the cookies, its still the same ratio)

Now, that we have all our needed information, let's solve!(Also, remember to match it up properly, or else it won't work: Small triangle side/Small Triangle side=Large Triangle Side/Large Triangle Side, or something like that).

[tex]\frac{1}{3x-8} =\frac{2}{2x+4} \\2x+4=6x-16\\4x=20\\x=5[/tex]

^ ANSWER

So there you go! X is equal to 5. I'm sure you can solve the rest on your own!

Hope this helps!

Stay Safe! I'm going to get that cookie now...

Answer: I. True

II. True

III. True

Step-by-step explanation:

Uniform probability distributions, this are probability distributions which have equally likely outcomes. There are two known types of uniform distributions:

1. discrete

2. continuous.

In the first type of distribution, each outcome is discrete. In a continuous distribution, outcomes are continuous this means they are usually infinite.

Answer:3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

y=2x+3, 2x represents the slope of the line and 3 represents the y-intercept