how many terms are in the expression
[tex] {x}^{2} + xy - {y}^{2} + 5[/tex]
​

The perimeter of tile which is 3 by 3 would be 12. If each side is 3 and the tile is a square which has four sides we can do 3 x 4 to determine the perimeter of the tile. To determine perimeter just add up all the sides. In this case since it’s a square you are able to multiply. 3 x 4 or 3 + 3 + 3 + 3 = 12

Answer:

The answer is 12

Step-by-step explanation:

Because it is lol and i just got it right

I could be wrong but

area=172.1

Area of the pentagon after rounding to the nearest tenth is 172.5 cm²

Given: a regular pentagon with sides measuring 10 cm and apothem measuring 6.9 cm

To find: area of the pentagon

We know that the area of a regular pentagon can be found by the formula:

[tex]\text{area}= \frac{1}{2} \times \text{perimeter of pentagon} \times \text{apothem}[/tex]

Before putting the values in the formula, we need to find the perimeter of the pentagon. It can be found by fining the sum of all of its side as follows:

[tex]\text{perimeter} = 10+10+10+10+10 = 5 \times 10 = 50[/tex] cm

Now we can put the values in the formula for area as follows:

[tex]\text{area}= \frac{1}{2} \times 50 \times 6.9\\[/tex]

[tex]\text{area}= 172.5[/tex] cm²

As the area is already rounded off to the nearest tenth we do not need to perform any additional calculations

So, area of the given pentagon is 172.5 cm².

Answer:

d) 18

Step-by-step explanation:

The question is on graphing linear functions

Given the table of values of x and y, plot the graph and observe the gradient of -2 and the y-intercept at (0,-5) as shown on the attached graph with blue color.

Use the given function y=7x+13 to formulate a table of values of x with corresponding values of y

x     y

-3   -8

0      13

1       20

With the above values, plot the graph of y=7x+13 and obtain the y-intercept at (0,13) as shown in the red line graph attached.

To find the distance between the y-intercepts of the two graphs we apply the expression for distance between two points;

[tex]D=\sqrt{(X2-X1)^2 +(Y2-Y1)^2 \\\\[/tex][/tex]

points are (0,-5) and (0,13)

D=√ (0-0)² + (13--5)²

D=√(18)²

D=18 units

The y-intercepts of the two functions y = 7x + 13 and y = 3x + 9 are 13 and 9 respectively. The distance between the y-intercepts is the absolute difference between them, which is 4, a result not listed among the options.

Firstly, we need to find the equation that fits the values in the table. With the given x and y values, applying a method such as 'point-slope,' we calculate the slope (m) and y-intercept (b). We find the equation is y = 3x + 9.

Then, we determine the y-intercepts of both functions. For the function y = 7x + 13, the y-intercept is 13 (the constant term). For the function y = 3x + 9, the y-intercept is 9.

The distance between the y-intercepts of the two functions is simply the absolute difference between them, which equals |13 - 9| = 4. However, none of the options a), b), c), or d) are identical to this value. There might be a mistake in the question.

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Answer: Light waves

Step-by-step explanation:

Used in the usual sense, radiant energy is just light. When you turn on your electric stove unit, it heats up and emits radio waves, infrared waves, and visible light waves. All of these waves are just light with different frequencies.

Answer:

light waves

Step-by-step explanation:

Answer:

The answer is A. 70 in^2

Step-by-step explanation:

trust me it is right :) hope this helps! I JUST TOOK THE TEST

ANSWER

A. 70 in^2

EXPLANATION

The area of a tra-pezoid is

[tex] = \frac{1}{2} (sum \: of \: parallel \: sides) \times height[/tex]

Substitute the side lengths into the formula to obtain,

[tex] = \frac{1}{2} (8 + 14) \times 7[/tex]

Simplify the parenthesis

[tex] = \frac{1}{2} (20) \times 7[/tex]

Cancel out the common factors,

=10×7

Simplify

[tex] = 70 {in}^{2} [/tex]

The correct answer is A

Answer: -8 square root of 3 (choice a)

Step-by-step explanation:

You have to find 2 numbers that multiply to 48 and in the same time, 1 of these numbers is a perfect square. In this case, the numbers are 16 and 3. So -2√16*3

Then since 16 is. A perfect square, and the square root is 4, you take out the 4 and multiply it by -2 so that is -8 and now you are left with -8√3. Hopefully that helped.

ANSWER

[tex] - 8 \sqrt{3} [/tex]

EXPLANATION

We want to simplify:

[tex] - 2 \sqrt{48} [/tex]

Remove the perfect square under the radical sign.

[tex] - 2 \sqrt{16 \times 3} [/tex]

Split the radical sign for the factors under it.

[tex] - 2 \sqrt{16} \times \sqrt{3} [/tex]

Simplify:

[tex] - 2 \times 4\times \sqrt{3} [/tex]

This finally gives us:

[tex] - 8 \sqrt{3} [/tex]

The first choice is correct.

[tex]

48=5t-7 \\

55=5t\Longrightarrow t=\frac{55}{5}=\boxed{11}

[/tex]

Answer:

Step-by-step explanation:

11

Answer:

8

Step-by-step explanation:

The question is on number of subsets

Number of subset is given by 2^n

n=3 in our question, A,B,C

2^n = 2^3 =8

They are; { }, A, B, C, AB, AC, BC, ABC

Answer:

8

Step-by-step explanation:

Answer:

x is greater than 5, so x could be anything more than 5.

Step-by-step explanation:

Hope my answer has helped you!

Answer:

The product of x and y is 8[tex]8[/tex]

Step-by-step explanation:

If [tex]\log_{5\sqrt{5}}125=x[/tex], then the exponential form is:

[tex]125=(5\sqrt{5})^x[/tex]

[tex]\implies 5^3=(5)^{\frac{3x}{2}}[/tex]

[tex]\implies 3=\frac{3x}{2}[/tex]

[tex]\implies 6=3x[/tex]

[tex]\implies x=\frac{6}{3}=2[/tex]

Also  if, [tex]\log_{2\sqrt{2}}64=y[/tex], then the exponential form is:

[tex]64=(2\sqrt{2})^y[/tex]

[tex]\implies 2^6=(2)^{\frac{3y}{2}}[/tex]

[tex]\implies 6=\frac{3y}{2}[/tex]

[tex]\implies 12=3y[/tex]

[tex]\implies y=4[/tex]

The product of x and y is [tex]xy=2\times 4=8[/tex]

Answer:

1112

Step-by-step explanation:

The specific heat capacity of the alloy is 0.423 cal/g°C: Option A is correct.

The formula for calculating the quantity of heat absorbed by the alloy is expressed as:

[tex]Q=mc\triangle \theta[/tex]

m is the mass of the substance = 45g

c is the specific heat capacity

Q is the quantity of heat required = 956J

[tex]\triangle \theta[/tex] = 37 - 25 = 12°C

Substitute the given parameters to get the specific heat capacity:

[tex]c=\frac{Q}{m \triangle \theta}\\c =\frac{956}{45 \times 12}\\c =\frac{956}{540}\\c = 1.77J/g^oC[/tex]

Convert J/g°C to  cal/g°C

c = 1.77/4.184

c = 0.423 cal/g°C

Hence the specific heat capacity of the alloy is 0.423 cal/g°C

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The specific heat of the alloy is 0.423 cal/g°C, which is calculated using the formula q = mcΔT and converting joules to calories. The final answer corresponds to option A.

The question involves finding the specific heat of an alloy using the concept of heat transfer. To calculate the specific heat, we use the formula q = mcΔT, where q is the amount of heat absorbed, m is the mass of the substance, and ΔT is the change in temperature. The specific heat c can be rearranged to be c = q/(mΔT). Given that the alloy absorbs 956 J of heat (q), has a mass of 45 g (m), and experiences a temperature increase from 25°C to 37°C (ΔT = 12°C), we plug these values into the formula.

Specific heat c will be: c = 956 J / (45 g × 12°C) = 956 J / 540 g°C = 1.77 J/g°C

To convert from joules to calories, note that 1 calorie = 4.184 joules. Thus, c in cal/g°C is calculated as: 1.77 J/g°C / 4.184 J/cal = 0.423 cal/g°C, which corresponds to option A.

Answer:

(i) 16 cm.

(ii) 37 pieces in total.

Step-by-step explanation:

Through determining each lengths factors, it can be determined that every ribbon can be equally divided into 16 cm. long ribbons, so we already have our first answer. A 160 cm. long ribbon divided into 16 cm. long pieces will create 10 ribbons from that one piece; the 192 cm. long ribbon cut into the same 16 cm. lengths will equal 12 pieces of equal length; and the 240 cm. long ribbon will divide its 16 cm. lengths into 15 pieces of equal length. So the 10 pieces, plus the 12 pieces, plus the 15 pieces, will equal 37 total pieces, each 16 cm. in length.  

Final answer:

This answer explains how to find the largest length of pieces and total number of pieces cut from different ribbon lengths. Therefore, the largest piece length is 16 cm. and  Total number of pieces of ribbons cut  is 37.

Explanation:

(i) Largest possible length of each piece of ribbons: To find the largest piece length, we need to determine the greatest common divisor (GCD) of the ribbon lengths. The GCD of 160, 192, and 240 is 16. Therefore, the largest piece length is 16 cm.

(ii) Total number of pieces of ribbons cut: To find the total number of pieces, divide each ribbon length by the largest piece length. For 160 cm, it gives 10 pieces. For 192 cm, it gives 12 pieces, and for 240 cm, it gives 15 pieces. Adding these, the total number of pieces is 37.

Answer:

[tex]\large\boxed{x=\dfrac{4a^2+3a}{9-2a}}[/tex]

Step-by-step explanation:

[tex]\dfrac{3x-a}{x+2a}=\dfrac{2a}{3}\qquad\text{cross multiply}\\\\(3)(3x-a)=(2a)(x+2a)\qquad\text{use the distributive property}\\\\(3)(3x)+(3)(-a)=(2a)(x)+(2a)(2a)\\\\9x-3a=2ax+4a^2\qquad\text{add}\ 3a\ \text{to both sides}\\\\9x=2ax+4a^2+3a\qquad\text{subtract}\ 2ax\ \text{from both sides}\\\\9x-2ax=4a^2+3a\qquad\text{distributive}\\\\(9-2a)x=4a^2+3a\qquad\text{divide both sides by}\ (9-2a)\neq0\\\\x=\dfrac{4a^2+3a}{9-2a}[/tex]

Answer:

Square

Step-by-step explanation:

Well, the options they have given you to choose from are a pentagon, a quadrilateral and a square. Let's first take a look at these options and eliminate which ones can't be possible. The first option, a pentagon, can be eliminated from the possibilities because a pentagon has five sides and figure ABCD has only four sides. The second option, quadrilateral, is true because a quadrilateral has four sides and so does figure ABCD. But, if you look at the third option, a square, this is the best way out of all the options to classify this figure because there are three things ALL squares must have:

- four sides

- all right angles

- all the sides MUST be equal

Knowing this, taking a look at the picture, you will see that there are indeed four right angles, four sides AND all congruent sides, proven by the four triangles inside the square. The answer isn't quadrilateral because, although that may be true, there are MANY types of quadrilaterals, trapezoids, rectangles, rhombuses and so on, each having different properties and characteristics. Therefore, the third option, SQUARE is the right answer.

HOPE THIS HELPED! Please contact me if you have any further questions about this topic and feel free to ask any more questions you need! :)

Answer:

Step-by-step explanation:

y=5+2(3+4x) - Multiply parenthesis by 2

0=5+6+8x - Add the numbers

0=11+8x - Move variable to left

-8x=11 - Divide both sides by -8

x=-1.375

Answer:

The temperatures were more consistent in Springville

Step-by-step explanation:

This question is on consistency of data

Generally, consistency of a data set is measured by determining the range, the variance or the standard deviation.In this case, we will use the standard deviation.

A small standard deviation means higher consistence.A lower standard deviation  will mean easy to predict a value because most of the values are closer to the average value.When the variations are less, a better analysis can be performed on a set of data.

Temperatures were more consistent in Springville that had a standard variation of 4F compared to Dakota that had a standard deviation of 6.8F

Answer:277.50

Step-by-step explanation:you do this than u do that

Answer: Option 'D' is correct.

Step-by-step explanation:

Since we have given that

On 1st June, amount in piggy bank = $2.00

On 2nd June, amount in piggy bank = $2.50

On 3rd June, amount in piggy bank = $3.00

So, it forms an arithmetic sequence:

Here, a = $2

d = 0.50

n = 30 days

So, Sum of 30 terms would be

[tex]S_{30}=\dfrac{30}{2}(2\times 2+(30-1)0.5)\\\\S_{30}=15(4+29\times 0.50)\\\\S_{30}=15(4+14.5)\\\\S_{30}=15(18.5)\\\\S_{30}=\$277.50[/tex]

Hence, Option 'D' is correct.

Answer:

13 min 40 sec

Step-by-step explanation:

656 copies *(1 min/48 copies)= 656 /48 min = 13  32/48 min = 13 2/3 min

2/3 min = 2/3 min * 60 sec/1 min = 40 sec

13 2/3 min = 13 min 40 sec

Answer:

The points corresponding to P=(3,4) and Q=(6,7), so the answer is D.

Step-by-step explanation:

Ok, in mathematics, given two sets X and Y, the collection of all the ordered pairs (X, Y), formed with a first element in X and a second element in Y, is called the Cartesian product of X and Y. The Cartesian product of sets allows define relationships and functions. In this case, it is a function that contains two points, denoted P and Q. Given, the ordered pair of each, first read the one corresponding to the X axis  and then to the Y axis.

For P: you read X and you see that it is on 3 (between 2 and 4), and then the Y axis is on 4 (between 3 and 5).

For Q: you read X and you see that it is on 6 (between 5 and 7) and then the Y axis is on 7 (between 6 and 8)

Answer:

[tex]\large\boxed{x=-\sqrt2,\ x=0,\ x=\sqrt2}[/tex]

Step-by-step explanation:

[tex]x^3-2x=0\qquad\text{distributive}\\\\x(x^2-2)=0\iff x=0\ \vee\ x^2-2=0\\\\x^2-2=0\qquad\text{add 2 to both sides}\\\\x^2=2\to x=\pm\sqrt2[/tex]

You can factor out an x:

x ( [tex]x^{2}[/tex] - 2)

Now set x equal to zero and the expression in the parentheses equal to zero

x = 0

[tex]x^{2}  - 2 = 0[/tex]

We don't need to do anything to x = 0 because x is already isolated, but you can further isolate x in the equation:

x^2 - 2 = 0

To do this add 2 to both sides

x^2 = 2

Take the square root of both sides to completely isolate x

x = ± √2

The zeros are:

0 and ±√2

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

the inter-quartile range will increase

Step-by-step explanation:

The initial data-set was;

20,32,32,45,50

Adding a new value 78 will have several effects;

The mean of the new set of values will increase since 78 is mostly likely to be an outlier.

The median of the new data set will increase. The median of the old data set is 32 while that of the new data set will be 38.5

The mode is the most frequent observation. Both the new and the old sets of values will have a mode of 32. The mode will therefore remain the same.

The inter-quartile range just like the range will increase

Answer:

The table in the attached figure N 1

The graph in the attached figure n 2

Step-by-step explanation:

we have

x+2=y

we know that

To graph a linear equation the best way is plot the intercepts

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

For x=0

0+2=y

y=2

The y-intercept is the point (0,2)

Find the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

For y=0

x+2=0

x=-2  

The x-intercept is the point (-2,0)

Find additional points to create a table (is not necessary for plot the line)

For x=1

1+2=y

y=3

For x=2

2+2=y

y=4

The table in the attached figure N 1

Graph the linear equation ------> plot the intercepts a joined the points

see the attached figure N 2

Creating a table of values for the equation \( x + 2 = y \):
To create a table of values, we can choose arbitrary values for \( x \), and then calculate the corresponding \( y \) values using the equation. Let's pick a few values for \( x \) and solve for \( y \).
Here's the table:
\[
\begin{array}{cc}
\textbf{x} & \textbf{y (= x + 2)} \\
\hline
-3 & -1 \\
-2 & 0 \\
-1 & 1 \\
0 & 2 \\
1 & 3 \\
2 & 4 \\
3 & 5 \\
\end{array}
\]
For each value of \( x \), taking the equation \( x + 2 = y \) we just add 2 to \( x \) to find \( y \).
Now, let's graph these points on a coordinate plane:
1. Draw a horizontal line for the \( x \)-axis and a vertical line for the \( y \)-axis, ensuring they intersect at the origin (0,0).
2. Mark the scale on both axes. For simplicity, we can choose each grid unit to represent 1.
3. Plot the points from the table onto the graph:
  - (-3, -1)
  - (-2, 0)
  - (-1, 1)
  - (0, 2)
  - (1, 3)
  - (2, 4)
  - (3, 5)
4. Once all the points are plotted, draw a straight line through the points, extending the line as far as the graph allows on both ends since the equation represents a linear relationship without bounds.
5. Label the line with the equation \( x + 2 = y \).
The graphical representation would show a straight line with a slope of 1 (since for every unit increase in \( x \), \( y \) increases by 1) and a \( y \)-intercept at \( y = 2 \) (since when \( x = 0 \), \( y = 2 \)).

Gradient= -3/2 Equation: Y=mx+c Y=2 , X=8

So you substitute the numbers in

2=(-3/2) x 2 + c (then you backtrack to solve for c which is the y intercept)

2=-3+c

5=c So the equation should be Y=-3/2x+5

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - [tex]\frac{3}{2}[/tex], thus

y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation

To find c substitute (8, 2) into the partial equation

2 = - 12 + c ⇒ c = 2 + 12 = 14

y = - [tex]\frac{3}{2}[/tex] x + 14 ← equation in point- slope form

(a): 18

(b): $792

Step-by-step explanation:

A: 900 - 576 = 324. 324/18 = 18.

18 * 18 = 324. 324 + 576 = 900.

B: 6 * 18 = 108. 900 - 108 = 792

Answer:

[tex]64^\frac{1}{12}[/tex]

Step-by-step explanation:

[tex]\sqrt[4]{64}[/tex]

has the meaning of [tex]64^\frac{1}{4}[/tex]

That means that what you have is

[tex]64^\frac{1}{4}*^\frac{1}{3}[/tex]

which means that your final answer is

[tex]64^\frac{1}{12}[/tex]

That would be the answer that I try first. In fact the question is set up in such a way that I would ignore the fact that 64^(1/3) = 4

Answer:

y = x² + 38x + 311

Step-by-step explanation:

If a polynomial has rational coefficients and irrational roots, then the roots must be conjugate pairs.

y = (x − (-19-5√2)) (x − (-19+5√2))

y = (x + 19+5√2) (x + 19−5√2)

Use FOIL to distribute:

y = x² + x (19−5√2) + x (19+5√2) + (19+5√2)(19−5√2)

y = x² + 19x − 5√2 x + 19x + 5√2 x + (19+5√2)(19−5√2)

y = x² + 38x + (19+5√2)(19−5√2)

Use FOIL to distribute the last term:

y = x² + 38x + 19² − 95√2 + 95√2 − 50

y = x² + 38x + 361 − 50

y = x² + 38x + 311

The required polynomial would be y = x² + 38x + 311.

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

Given that least degree with rational coefficients and with (-19-5√2)

We know that if a polynomial has both rational and irrational roots, the roots must be conjugate pairs.

y = (x − (-19-5√2)) (x − (-19+5√2))

y = (x + 19+5√2) (x + 19−5√2)

Apply the distributive property,

y = x² + x (19−5√2) + x (19+5√2) + (19+5√2)(19−5√2)

y = x² + 19x − 5√2 x + 19x + 5√2 x + (19+5√2)(19−5√2)

y = x² + 38x + (19+5√2)(19−5√2)

y = x² + 38x + 19² − 95√2 + 95√2 − 50

y = x² + 38x + 361 − 50

y = x² + 38x + 311

Thus, the required polynomial would be y = x² + 38x + 311.

Learn more about the polynomial here:

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since the cone's diameter is 6, its radius must be 3 then.

[tex]\bf \textit{total surface area of a cone}\\\\ SA=\pi rs+\pi r^2~~ \begin{cases} r=&radius\\ s=&slant~height\\ \cline{1-2} r=&3\\ s=&5 \end{cases}\implies SA=\pi (3)(5)+\pi (3)^2 \\\\\\ SA=15\pi +9\pi \implies SA=24\pi \implies SA\approx 75.398[/tex]

Answer:

24π or 75.4

Step-by-step explanation:

The equation for the surface area is SA=πr²+πrl

Since the diameter is 6, then the radius will be 3

Plug the values in:

π3²+π×3×5

9π+15π

24π =75.39822

Answer:

204,160,000

Step-by-step explanation:

Assuming the sample is a good representation of the people from the United States.

Since there were 1,000 surveyed... and 638 of them were wearing glasses,  that makes a proportion of 638 out of  1,000 people, or 63,8 / 100 people... so 63.8%... or 0.638

So, if we assume that the US population is of 320 million, how many people does that make wearing glasses.... we just have to multiply 320M by 0.638

G = 320,000,000 * 0.638 = 204,160,000

Answer:

39.68 million[

Step-by-step explanation:

Remember that the sample is 1000 people.

Of those 1000 people we know that 762 wear corrective lenses. 124 of these people wear contact lenses.

The probability that a randomly selected person will wear contact lenses is:

[tex]P = \frac{124}{1000}\\\\P = 0.124[/tex]

Then, the expected number of people who wear contact lenses is:

[tex]N = 320 * P[/tex]

Where N is given in units of millions.

[tex]N = 320 * 0.124[/tex]

[tex]N = 39.68\ million[/tex]