Find the measure of

Here we are given the expression:

[tex]x^{2}+52[/tex]

Now let us equate it to zero to find x first,

[tex]x^{2}+52=0[/tex]

Now subtracting 52 from the other side,

[tex]x^{2}=-52[/tex]

taking square root on both sides,

So we will get two values of x as ,

[tex]x=+2\sqrt{-13}[/tex]

[tex]x=-2\sqrt{-13}[/tex]

Now we can write square root -1 as i,

So our factors become,

[tex]x=+2i\sqrt{13}[/tex]

[tex]x=-2i\sqrt{13}[/tex]

Answer:

The final factored form becomes,

[tex](x+2i\sqrt{13})(x-2i\sqrt{13})[/tex]

Answer: No.

Step-by-step explanation: No, as two of sides need to be equal.

Answer:

we cannot form a triangle using the given lengths.

Step-by-step explanation:

There are three conditions that must be satisfied in order to form a triangle.

Let's take a, b and c are the sides of a triangle.

Conditions are:

i) a + b > c

ii) b + c > a

iii) c + a > b

Here let's take a = 12.2, b = 6.0 and c = 4.2

Let's check the conditions

i) 12.2 + 6 > 4.2

18.2 > 4.2

Which is true.

ii) 6 + 4.2 > 12.2

10.2 > 12.2

Which is not true.

The condition fails.

Therefore, we cannot form a triangle using the given lengths.

Hope this will helpful.

Thank you.

It's in the tenths place.

Answer:

no. she can read 30

Remark

This is much the same as the last inequality that you posted. When it tells you that you have 1 condition that is more than and one condition that is less than, then you need a compound statement. One of A and B is correct. C or D never will be.

At Least 4

This is the more than condition. You need 4 or more pennies to add to the collection. The rule is the same. The pointy end always points towards the smallest amount

4 ≤ x

No more than 2

That means that you can have 2 or under. The pointy end points to the x

2 ≥ x The biggest number (open end of the arrow) points at the 2.

Answer

2 ≥ x or  4 ≤  x That means the answer is A

Solution

The general form of the equation is y = mx + b, where m is the slope and b is the y-intercept.

Given: m = 8/7 and b = -3

Plugin the given values into the formula.

y = 8/7x - 3

The answer is y = 8/7x - 3

Thank you :)

The correct equation representing the line with a slope of negative 8/7 and a y-intercept of negative 3 is y = -8/7x - 3. This was determined by substituting these values into the slope-intercept form of a line equation, y = mx + b.

The equation of a line in slope-intercept form is given as y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, we're looking for an equation with a slope (m) of -8/7 and a y-intercept (b) of -3.

Substituting these values into the slope-intercept form, we get: y = -8/7x - 3.

So, the correct answer is y = -8/7x - 3.

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Answer:

The graph B.

Step-by-step explanation:

1. As you can see in the table shown in the picture attached, the correct graph must have the following points (x,y): (-1,8); (0,6), (1,4); (2,2) and (3,0).

2. To draw the graph, you must plot each point. For example, the third point is (1,4). Then, you can draw an imaginay line vertically from 1 (x axis) and an imaginary line horizontally from 4 (y axis). The intersection of this lines is the point (1,4).

Answer:

B is the right answer

Step-by-step explanation:

I just did it and it was right

The solution is  

[tex]x\le 3 \:or \:x>18[/tex]

[tex]<b><u>EXPLANATION</u></b>[/tex]

[tex]6x-10\le 8\: or \frac{1}{3}x+6>12[/tex]

We group like terms, to obtain;

[tex]6x\le 8+10\: or \frac{1}{3}x>12-6[/tex]

Simplify to get,

[tex]6x\le 18\: or \frac{1}{3}x>6[/tex]

We further simplify to get;

[tex]x\le 3\: or x>18[/tex]

This can also be rewritten as;

[tex]x\le 3, x>18[/tex]

Or

[tex](-\infty 3] \cup (18,+ \infty)[/tex]

This can be represented on the number line as shown in the diagram.

Answer: (-∞,3)∪(18,∞)

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

1. You must solve for x, as following:

[tex]6x-10\leq8\\6x\leq18\\x\leq3[/tex]

[tex]\frac{1}{3}x+6>12\\x>3(6)\\x>18[/tex]

2. Therefore, you have that the result is:

(-∞,3]∪(18,∞)

Answer:

D. [tex]\left[\begin{array}{cc}4&5\\-3&2\\\end{array}\right][/tex]

Step-by-step explanation:

The reason it is called an "identity matrix" is that it doesn't change anything. The result is what you started with.

When the matrix A = [ [2, 3], [4, 5] ] is multiplied by the 2x2 identity matrix, the resulting matrix is still A itself: [ [2, 3], [4, 5] ].

When you multiply a matrix by the identity matrix, the result is the original matrix itself. In this case, matrix A is given as A = [ [2, 3], [4, 5] ], and you want to find A * I, where I represents the identity matrix.

The identity matrix is a square matrix with ones on the main diagonal and zeros everywhere else. In this case, since A is a 2x2 matrix, you would use a 2x2 identity matrix, which looks like:

I = [ [1, 0], [0, 1] ]

Now, when you multiply A by I:

A * I = [ [2, 3], [4, 5] ] * [ [1, 0], [0, 1] ]

You can perform matrix multiplication as follows:

[ (2*1 + 3*0), (2*0 + 3*1) ]

[ (4*1 + 5*0), (4*0 + 5*1) ]

Simplifying the calculations:

[ 2, 3 ]

[ 4, 5 ]

The resulting matrix is exactly the same as matrix A. So, A * I equals the original matrix A: [ [2, 3], [4, 5] ].

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The probable question maybe:

Given the matrix A = [ [2, 3], [4, 5] ], what is the resulting matrix when it is multiplied by the identity matrix of the appropriate size?

Answer:

125 minutes

Step-by-step explanation:

Answer:

The vertices of parallelogram ESTA  are E (10, 0), S (14, 3), T (6, 9), and A (2, 6).

As we know ,Area of parallelogram = Base × Height

As base can be determined by using distance formula because coordinates of the vertices are given.

Now to determine perpendicular, we will find the equation of line through E and perpendicular to ST.

Equation of line through S(14,3) and T(6,9) is

[tex]\frac{y-3}{x-14}=\frac{9-3}{6-14}\\\frac{y-3}{x-14} =\frac{6}{-8}[/tex]

[tex]\frac{y-3}{x-14}=\frac{-3}{4}\\4y -12=-3x+42[/tex]

⇒4y + 3x =12+42

⇒ 3 x + 4 y=54

Equation of line perpendicular to ST and passing through E(10,0) is

4 x-3 y + k=0

Put x=10, y=0 in above equation is

4×10 -3×0 +k=0

⇒ k= -40

The Equation of line through point E and perpendicular to ST is

4 x-3 y -40=0

Hey!!

A cell phone company charges $45 a month and hence, this would be constant and would be same the same value. And the company charges $0.25 for every text message.

Let's take the number of text messages as ' t '

The question asks us to find the number of text messages needed to make it $75 for the first month.

We know, the constant is $45 and we know the number of text messages as ' t ' and we also know the cost of each text messages is $0.25. And with all this given, we can find the total cost which is denoted by ' c '.

The total cost would be the price of a month added to the cost of text messages.

The total cost = c

The price of for month = $45

The price of text messages = $0.25t

Now, let's form the equation :

... c = 45 + 0.25t ( this is the equation )

The total cost given is $75  

Hence, the equation would be :

... 75 = 45 + 0.25t

Subtract 45 on both sides

... 30 = 0.25t

Divide 0.25 on both sides

... t = 120

Hence, the answer would be option ( D )

Hope my answer helps!!

Answer:

The fraction of the tank is filled with gasoline is [tex]\frac{3}{8}[/tex].

Step-by-step explanation:

Consider the provided information.

Jamal filled his gas tank and then use 7/16 of the tank for traveling to visit his grandfather.

After his first traveling the amount of gas left can be calculated as:

[tex]1-\frac{7}{16}[/tex]

[tex]\frac{16-7}{16}[/tex]

[tex]\frac{9}{16}[/tex]

He then used 1/3 of the remaining gas in the tank to run around town.

That means he left with 2/3 of gas.

[tex]\frac{9}{16}\times \frac{2}{3}[/tex]

[tex]\frac{3}{8}[/tex]

Hence, the fraction of the tank is filled with gasoline is [tex]\frac{3}{8}[/tex].

Answer:

1 and 4 are correct. 2 and 3 are not.

Step-by-step explanation:

1.

When x = 0 where does the horse start?

y = 1.5*sin(0 + 0.5)*2*pi + 1.5

y = 1.5*sin(0.5*2pi) + 1.5

y = 1.5*sin(pi) + 1.5 But sin pi = 0

y = 0 + 1.5 So the horse is starting at the midpoint of it's travel.

2.

This one is a trick question. You can reason it without exact answers. At some point the sin(x + 0.5)*2pi will equal 1. When it does 1.5 * 1 + 1.5 = 3.0 At some other point sin(x + 0.5)*2pi = -1. When that happens the whole thing goes to 0. So the total of the distance traveled is 6 not three.

3.

You can figure this one out by letting x = 0.01 When it does then the value of the function is

y = 1.5*sin [(0.01 + 0.5)*2pi] + 1.5

y = 1.5*sin(0.51*2*pi) + 1.5

y = 1.5*sin(3.204424) + 1.5

y = 1.5*(- .0623) + 1.5

y = -0.9418 + 1.5

y = 1.4058 so it is going downward The value is getting smaller.

4.

The horse starts out in the middle of the pole. What  does x need to equal so that x + 0.5 = 1 ? And why 1. The answer to why 1 is that then the sine function will equal sin(2*pi)

That happens when x = 0.5 which is 1/2 a minute. If it takes 1/2 a minute to execute 1 complete cycle, then in 5 minutes the cycle will be executed 10 times. This one is correct.

We know:

The sum of the measures of the angles of a triangle is equal 180°.

Therefore we have the equation:

[tex](3x-16)+x+(x+6)=180\\\\3x-16+x+x+6=180\\\\(3x+x+x)+(-16+6)=180\\\\4x-10=180\ \ \ \ |+10\\\\4x=190\ \ \ \ |:4\\\\x=47.5[/tex]

m∠M = (3x-16)°

Substitute:

[tex]m\angle M=(3\cdot47.5-16)^o=(142.5-16)^o=126.5^o[/tex]

Answer:

98

Step-by-step explanation:

I got it wrong when I typed in 126.5, its actually 98

Go forth and Conquer

Answer:

Distance traveled 17.5 kilometers

Step-by-step explanation:

We can use the following equation to find the distance traveled,

Distance traveled = Speed * Time

First we need to find the total time he walked = 2.30 p.m. - 11.a.m.

                                                                             =[tex]3.5[/tex] hours

Now we can substitute the values to the equation,

Distance traveled = [tex]5[/tex] kilometers per hour * [tex]3.5[/tex] hours

                              = [tex]5*3.5[/tex] kilometers

                              = 17.5 kilometers

Instead of y = g(x)^2, it should be y = g(x)+2

What this means that every point on g(x) will be shifted up 2 units. A point like (2,-1) which is the saddle point shown on the graph, will move up to (2,1) after you shift up 2 units. Every other point will follow the same path. Another example: The point (0,-5) -- which is the y intercept -- will move up to (0,-3).

Check out the attached image below for a visual of what's going on.

The graph of the translation to make it y = g(x) + 2 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

The graph of y = g(x)

Translating the graph to make it y = g(x) + 2, we simply move the given up by 2 units

This means that the curves are moved up by 2 units

The graph to make it y = g(x) + 2 is added as an attachment

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Answer: $2.84 per pint

Step-by-step explanation:

[tex]\frac{5.68 (dollars)}{4 (cups)} *\frac{2(cups)}{1(pint)} = \frac{5.68(2)dollars}{4 pints} = \frac{2.84 dollars}{1 pint}[/tex] = $2.84 per pint

Final answer:

To find the price per pint of sour cream from a 4-cup carton costing $5.68, divide the total cost by the number of pints, resulting in $2.84 per pint.

Explanation:

The question asks to find the price per pint for a 4-cup carton of sour cream that costs $5.68. Since there are 2 cups in a pint, a 4-cup carton is equivalent to 2 pints. To find the price per pint, we simply divide the total cost by the number of pints.

Calculation:

Thus, the price per pint of sour cream is $2.84.

Easiest way for me is to convert those mixed fractions and then divide.

Sorry for some bad handwriting! Hope it helps

move the decimal point 2 places to the right

note 1m = 100 cm

4450m = 4450 × 100 cm

multiplying by 100 is equivalent to moving the decimal point 2 places to the right

If the orbital period of planet Y is twice the orbital period of Planet X, by then the factor is the mean distance increased by 4.

Given

The equation T^2 = A^3 shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU.

The mean is defined as the sum of all data set numbers and the total number in the data set.

If the orbital period of planet Y is twice the orbital period of Planet X,

Therefore,

If the orbital period of planet Y is twice the orbital period of Planet X, by then the factor is the mean distance increased is;

[tex]\rm Factor \of\ increase =\dfrac{2&^3}{2 }\\\\ Factor \of\ increase =4[/tex]

Hence, If the orbital period of planet Y is twice the orbital period of Planet X, by then the factor is the mean distance increased by 4.

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Answer:

D: 2^3/2

Step-by-step explanation:

Right on Edgenui test

Answer:

D: 2^3/2

Step-by-step explanation:

Right on Edgenui test

A(-3, -2) and B(3, -8)

slope m = (-2 + 8)/(-3 - 3) = 6/-6 = -1

b = y intercept = -5

Equation

y = -x - 5

Answer

y = -x - 5

The equation of the linear system will be y = - x - 5.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The graph is given below.

If the graph is decreasing, then the slope of the linear system will be negative.

And the y-intercept is negative 5.

Then the equation of the linear system will be y = - x - 5.

Thus, the correct option is D.

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The number of ways can a group of three students be chosen is 20 ways

The number of ways of selecting r objects from n unlike objects is given by combinations

ⁿCₓ = n! / ( ( n - x )! x! )

where

n = total number of objects

x = number of choosing objects from the set

Given data ,

Let the number of ways of selecting students be A

Now , the total number of students = 6

And , to choose 3 students out of 6 without regard to order. The formula for combinations is

n C r = n! / r!(n-r)!

where n is the total number of items, and r is the number of items to choose

6 C 3 = 6! / 3!(6-3)! = 20

Hence , there are 20 ways to choose a group of three students out of six

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The correct number of ways to choose a group of three students from six is [tex]\boxed{20}.[/tex]

To solve this problem, we can use the concept of combinations from combinatorics. A combination is a way of selecting items from a collection, such that the order of selection does not matter. In our case, we have six students and we want to choose three of them to participate in the spelling bee. The order in which we choose the students does not matter since all three will participate equally.

 The formula for calculating combinations is given by:

[tex]\[ C(n, k) = \frac{n!}{k!(n-k)!} \][/tex]

where n is the total number of items to choose from, k is the number of items to choose, and ! denotes factorial, which is the product of all positive integers up to that number.

 For our problem:

[tex]- $n = 6$[/tex] (total number of students)

[tex]- $k = 3$[/tex] (number of students to choose)

 Plugging these values into the formula, we get:

[tex]\[ C(6, 3) = \frac{6!}{3!(6-3)!} \][/tex]

 Calculating the factorials, we have:

[tex]\[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \][/tex]

[tex]\[ 3! = 3 \times 2 \times 1 = 6 \][/tex]

[tex]\[ (6-3)! = 3! = 6 \][/tex]

 Now, we substitute these values into the combination formula:

[tex]\[ C(6, 3) = \frac{720}{6 \times 6} \][/tex]

[tex]\[ C(6, 3) = \frac{720}{36} \][/tex]

[tex]\[ C(6, 3) = 20 \][/tex]

 Therefore, there are 20 different ways to choose a group of three students from six for the spelling bee.

okay the answers are

Question 1 A survey was sent to GCA students asking the question "Who is your favorite teacher?"  

What type of data was collected?

Answer) Qualitative

Question 2 ) A survey was sent to GCA students asking the question "On a scale of 1 to 5, with 1 being the lowest and 5 being the highest, how would you rate your AMDM teacher?"  

The data collected was

Answer) Quantitative

Question 3)  You decided to attend the GCA outing at Stone Mountain. Before you left for the park, you entered the park address into a GPS/Traffic app on your phone. The app told you that Stone Mountain was 47.6 miles from your house.

47.6 miles is an example of...

Answer) Quantitative, continuous data

Question 4 ) While you were at the Stone Mountain outing, you played a game of corn hole. You counted the number times you tossed the beanbag into the hole.

The number of times you were able to sink the beanbag is an example of....

Answer) Quantitative, discrete data

Question 5) You recorded the time you left Stone Mountain and the time you arrived home. You calculated time it took you get home was 57.28 minutes.

57.28 minutes is an example of....

Answer) Quantitative, continuous data

Mitchel Unit rate is 15 hotdogs per minute we know this because it show 45 hotdogs in 3 minutes and 45 divided by 3 is 15 so the unit rate is 15.

Correct answer is: A) [tex]\frac{-15F}{13hours}[/tex]

Solution:-

Given that temperature of town increased 16 Fahrenheit in 5 hours and decreases 31 Fahrenheit in the next 8 hours.

If we assume T as temperature, it became T+16 in 5 hours and (T+16-31) in next 8 hours.

That is change in temperature in (5+8) hours is 16-31 = -15 Fahrenheit.

Rate of total change in temperature = [tex]\frac{change in temperature}{time}[/tex]

                                                            = [tex]\frac{-15}{5+8}=\frac{-15}{13}[/tex]

Hence rate of total change in temperature is [tex]\frac{-15F}{13hours}[/tex]

The correct expression that shows the rate of the total change in temperature is -15 hours / 13 hours. The Option A.

The rate of change in temperature refers to the speed at which the temperature is increasing or decreasing over a given period of time.

Total change in temperature is:

= Temperature increase - Temperature decrease

= 16°F - 31°F

= -15°F

Total time for the change:

= Time for increase + Time for decrease

= 5 hours + 8 hours

= 13 hours

Rate of total change in temperature:

= Total change in temperature / Total time for the change

= -15°F / 13 hours.

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