What is the measure of this line?
80 mm
840mm
84mm
80.4 mm

Answer:

The required linear equation satisfying the given points (2,4) and (4,10) is y=3x-2

Step-by-step explanation:

Two points are given in question, (2,4) and (4,10).

It is required to find out a linear equation satisfying the points (2,4) and (4,10).

To find it out, find the slope of a line passing through these two given points. Then consider one of the points to give the linear equation of the line in the

[tex]$$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$$[/tex]

Step 1 of 3

The slope of a line passing through the points (2,4) and (4,10) is given by

[tex]$$\begin{aligned}m &=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\m &=\frac{10-4}{4-2} \\m &=\frac{6}{2} \\m &=3\end{aligned}$$[/tex]

Step 2 of 3

Now use the slope m=3 and use one of the two given points and write the equation in point-slope form:

[tex]$$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$$\\ $$(y-4)=3(x-2)$$[/tex]

Distribute 3 ,

[tex]$$\begin{aligned}&y-4=3 x-3 \times 2 \\&y-4=3 x-6\end{aligned}$$[/tex]

Step 3 of 3

This linear function can be written in the slope-intercept form by adding 4 on both sides,

[tex]$$\begin{aligned}&y-4+4=3 x-6+4 \\&y=3 x-2\end{aligned}$$[/tex]

So, this is the required linear equation.

Based on the lateral area of the cylinder, the volume of the cylinder can be calculated to be 139.5 cm³.

When given the lateral surface area of a cylinder, you can find the volume as:

= Area of lateral surface x (radius / 2)

Solving gives:

= 55.8 x (5 / 2)

= 55.8 x 2.5

= 139.5 cm³.

Missing part of the question:

Radius of the cylinder is 5cm.

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The approximate solution of the system of equations is x = 0.75

The functions are given as:

f(x) = x^4 + 9x^2 - 3

g(x) = (1/2)^x - 2

Calculate the values of the function from -1 to 1

x             f(x)      g(x)

-1            7          8

-0.75    2.38   6.72

-0.5   -0.69     5.66

-0.25  -2.43   4.76

0          -3       4

0.25    2.43   3.36

0.5      -0.69   2.83

0.75    2.38   2.38

1          7        2

From the above table, we have:

f(0.75) = g(0.75) = 2.38

Hence, the approximate solution of the system of equations is x = 0.75

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Answer:

You didn't include any choices.....see below

Step-by-step explanation:

The product of the polynomials, (x + 2)(x - 2) = x² - 4.

Given the following expression, (x + 2)(x - 2), to find the product, apply the distributive property as shown below:

(x + 2)(x - 2)

x(x - 2) + 2(x - 2)

x² - 2x + 2x - 4

Combine like terms together

x² - 4

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Answer:

B or the second option

Step-by-step explanation:

We can label the diagram parts A-E to fully represent the situation in the question.

A: Julie's ascent up the mountain (moving/increasing)

B: Julie drinking hot chocolate (stationary/constant)

C: Julie's descent down the mountain (moving/decreasing)

D:  Julie rests (stationary/constant)

E:  Julie's final descent down the mountain (moving/decreasing)

Using proportions, it is found that Mason ran 620 meters.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Considering the ratio, the rule of three is given as follows:

2 laps for Mason - 3 laps for Laney.

n meters for Mason - 930 meters for Mason.

Applying cross multiplication:

3n = 930 x 2

n = 930 x 2/3

n = 620

Mason ran 620 meters.

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The spherical ball for the machine with a radius of 2 centimeters, has a mass of 278.1 grams and will have a density of 8.29 grams per cm³, which is identical to the density of Terbium's 8.23 grams per cm³.

Thus, we can say that Terbium is the material used to make the spherical ball.

The density of an object is given as the ratio of its mass and its volume.

Density = Mass/Volume.

In the question, we are informed that a spherical ball for a machine was made with a radius of 2 centimeters.

Thus, the volume of the spherical ball, using the formula for the volume of a sphere, V = (4/3)πr³, where r is its radius, can be calculated as:

V = (4/3)π(2)³ cm³ = 32π/3 cm³ = 33.51032 cm³.

The mass of the ball is given to be 278.1 grams.

Thus, its density = 278.1/33.51032 grams per cm³ = 8.2989355 grams per cm³.

We know that the density of Terbium is 8.23 grams per cm³.

Thus, the spherical ball for the machine with a radius of 2 centimeters, has a mass of 278.1 grams, will have a density of 8.29 grams per cm³, which is identical to the density of Terbium's 8.23 grams per cm³.

Thus, we can say that Terbium is the material used to make the spherical ball.

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Answer: copper

Step-by-step explanation:

The arithmetic sequences are as follow:

An arithmetic sequence in algebra is a sequence of numbers where the difference between every two consecutive terms is the same.

1) t(n) = 5n + 4

t(1) = 9, t(2) = 14, t(3) = 19

So,

9,14,19,...

d= 14-9 = 5

d= 19-14 =5

Hence, it is an AP

2) 1, 2, 4, 8 , 16

Hence, it is not an AP

3) 3, 6, 9 ,...

It is an AP

4)It is given that it is an AP

5) tn =  2*3^n

 t1= 6, t2= 18, t3= 54

So, 6, 18, 54,...

Hence, it is not an AP

6) 3 , 1, 1/3,...

It is not an AP

7) t(n+1)= 6*t(n)

t(1) = -1

t(2)=-6

t(3)= -36

Hence, it is not an AP

8) -3, 1, 5, 9

Hence, it is an AP.

9) 1, 4, 9,...

Hence, it not an AP

10) 2,1,0,1,2,...

It is not an AP

11) t(n)= -2n-5

t(1)= -7, t(2)= -9, t(3)= -11

Hence, it is an AP

12) tn= (1/2)^n

 t1= 1/2, t2= 1/4, t3= 1/8

It is not an AP

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based on the options given, one thing that isn't true of the box plot is that d. Half the data lies between 51 and 68.

the box plot has a range of 67:

= 90 - 23

= 67

the data point 5 lies outside the data set.

3/4 of the data is less than 68 which is the 3rd quartile.

this means that the false statement is that half of the data is between 57 and 68.

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Answer:

Volume = 96m^3

Step-by-step explanation:

If the length of the tank is 8 meters, then the width must be 4 meters, because the question said the width was half the length. Since the height, 3 meters, was also given, we can find the volume.

Vol = L × w × h

We multiply together the length, width and height.

Vol = 8 × 4 × 3

= 96

The volume is 96 meters^3

The area of a rectangle = Length × Breadth

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Answer:

B

Step-by-step explanation:

Answer:

Everything in the box currently is correct but the bottom two numbers are just -3 and -4

Step-by-step explanation:

Answer:

factor polynomial is x+q so x=-q

putting the value of x in both equations

eqn 1)a^2+p(-a)+q=0

a^2 -ap+q=0

eqn 2)a^2+m(-a)+n=0

a^2-am+n=0

Since both are equal to zero,we can write:

a^2-ap+q=a^2-am+n

-ap+am=n-q

a(-p+m)=n-q

a=(n-q)/(m-p)

Explanation:

Since (x + a) is a factor of the two polynomials, when x = -a, the polynomials should both equal 0 (this is known as the factor theorem).

• First equation:

[tex]x^{2} + px + q[/tex]

When x = -a:

[tex](-a)^{2} + p(-a) + q = 0\\\\a^{2} -pa + q = 0[/tex]

• Second equation:

[tex]x^{2} + mx + n[/tex]

When x = -a:

[tex](-a)^{2} + m(-a) + n = 0\\\\a^{2} -ma + n = 0[/tex]

• As both equations equal 0, we can equate them:

[tex]a^{2} -pa + q = a^{2} -ma + n \\\\-pa + ma = n - q\\\\a(m - p) =n -q\\\\a = (n - q)/ (m - n)[/tex][proven]

Answer:

Step-by-step explanation:

There are 26 letters, so there are 26

3

 possible 3-letter sequences.

the number of these which are palindromes can be computed as follows:

26 choices for the first letter

26 choices for the second letter

1 choice for the third letter ( it has to agree with the first)

number of ways  =26

2

Probability of a letter palindrome =26

2

/26

3

=1/26

there are 10 digits, so there are 10

3

 sequences of digits.

Reasoning as above, the number of digit-palindromes is (10)(10)(1)=10

2

so the probability of a digit-palindrome is 10

2

/10

3

=1/10

The events

D - digit palindrome

L - letter palindrome

are independent but not mutually exclusive.

So, P(LorD)=P(L)+P(D)−P(LandD)

P(LorD)=P(L)+P(D)−P(L)P(D)

=1/26+1/10−(1/26)(1/10)

=10/260+26/260−1/260

=35/360=7/52

Answer:

Yes, it's a rational number

Step-by-step explanation:

Answer:

y=49x

Step-by-step explanation:

As you can see from the graph, the distance from home increases by 49 miles per hour driven.

Therefore the distance driven for any given time in hours is 49x

Therefore y = 49x

The coordinate pair that is a solution of the linear equation -3x+4y=19 is (0, 19)

The linear equation is given as:

-3x + 4y= 19

Set x = 0

So, we have:

-3(0) + 4y = 19

Evaluate

4y = 19

Divide by 4

y = 19/4

Hence, the coordinate pair that is a solution of the linear equation -3x+4y=19 is (0, 19)

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Answer:

x = 15° , y = 125°

I hope this helps u

Answer:

Step-by-step explanation:

no, you don't have the measure of at least one side, so having the same angles is similar but not congruent

The equation which could be used to find the value of x is; (x+10) +(x-6) = 10.

According to the task content, it follows that the lines WX and WY both amount to the line XY which joins points X and Y.

Hence, it follows that the equation which can be used to find the value of x is; (x+10) +(x-6) = 10.

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The order of the numbers from the greatest to the least is

|-20| > |12.3| > |8| > |-6| > |-4| > |2 3/10|

From the question, we are to order the given numbers from the greatest to the least in magnitude

The given numbers are

|-20|, |-4|, |-6|, |8|, |2 3/10|, |12.3|

Since the modulo sign is included, the negative signs do not take effect.

Hence, the order of the numbers from the greatest to the least is

|-20| > |12.3| > |8| > |-6| > |-4| > |2 3/10|

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Answer:

I hope this is the right answer

The error that Bryan has done in this inequality is that he included –14 in his solution set.

What Bryan has to do would be to write this inequality in such a way that the variable would appear on the left.

But the symbol that he has chosen does not move in this same direction as the graph.

The -14 should not be inclusive in the graph because it is not a part of the graph solution.

He used the wrong number in this inequality.

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Answer:

its c

Step-by-step explanation:

on edge

Total length of iron edging needed to create the square frame is 43.5 inches

Important properties of square:

All four interior angles are equal to 90°

All four sides of the square are congruent or equal to each other.

The opposite sides of the square are parallel to each other.

The diagonals of the square bisect each other at 90°

The two diagonals of the square are equal to each other.

Diagonal of square = [tex]\sqrt{2}[/tex]a

9 = [tex]\sqrt{2}[/tex]a

a = [tex]\frac{9}{\sqrt{2}}[/tex]

a = 6.36 inches

Iron edging needed to create the square frame = 4*6.36 = 25.44 inches

iron edging needed to create two diagonals = 2*9 = 18 inches

total length = 18 + 25.44

                   = 43.44 ~ 43.5 inches

Thus, Total length required is 43.5 inches

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Answer:

1. Function

2. Not a function

3. Function

4. Not a function

Step-by-step explanation:

A function just means that for each input it outputs only 1 output. This output isn't necessarily unique. So for example if you're just given: f(2) = 3 and f(1) = 3, this is a function since each input only outputs 1 value, even though the output isn't unique, but if you're given: f(3) = 2, f(2) = 1, f(3) = 3. that's not a function since f(3) outputs both 2 and 3.

Anyways now that you hopefully understand this, let's look at each image.

Relation 1: (Function)

   So for each input (the domain) it's only pointing to one output (range), even if multiple input (the domain) are pointing to the same output (the range), it's still a function.

Relation 2: (Not a function)

   This is not a function, since if you look at the input 7 (the range), you'll see it outputs two things (range). It outputs -6 and -7. So this is not a function

Relation 3: (Function)

   This is a function since each x-value (input) has only one y-value (output). So it's a function

Relation 4: (Not a functio)

   This is not a function, since there are multiply coordinates with the same x-coordinate (input) and different y-coordinates (output). The x-coordinate 2 has the output b, y, and m, and since no value is given for these variables, it can be assumed they're different values, thus it's not a function.

The function of the linear equation shows that the slope(m) = -7, the x-intercepts is (-1/7,0), and the y-intercepts is (0,-1)

The function of a linear equation takes the form y = ax + b. In this situation, the values of y can be determined when x = 0, and the values of x can be determined when y = 0

From the given information:

y = f(x) = -7x - 1

We can determine the:

y = -7x - 1

Slope (m) = -7

Set the values of y = 0 to determine the x-intercepts.

0 = -7x - 1

7x = - 1

x = -1/7

x-intercepts = (-1/7, 0)

Set the values of x = 0 to find the y-intercepts.

y = -7(0) - 1

y = - 1

y-intercepts = (-1, 0)

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