what is a rational number whose square root is a whole number?
​

Answer:

by substitution

Step-by-step explanation:

To check if the solution to an equation is valid

Substitute the solution into the equation and if both sides agree then the solution is correct.

left side = z + 22 = 42 + 22 = 64 = right side

Hence z = 42 is the correct solution

The equation is given as:

  [tex]z+22=64[/tex]

⇒[tex]z+22-22=64-22[/tex]

⇒[tex]z=42[/tex]

So, we have to put the value of z in the 1st equation then we can say whether Frieda's work is correct or not.

⇒[tex]42+22=64[/tex]

[tex]=RHS[/tex]

Hence, Frieda's work is correct.

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in maths when you do not know the exact number in a calculation.

What is an equation example?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

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since it has a diameter of 4, then its radius is half that, or 2.

[tex]\bf \textit{lateral area of a cone}\\\\ LA=\pi r\sqrt{r^2+h^2}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=2\\ h=10 \end{cases}\implies LA=\pi (2)\sqrt{2^2+10^2} \\\\\\ LA=2\pi \sqrt{104}\implies LA\approx 64.076[/tex]

Answer:[tex]A = 64.076\ units^2[/tex]

Step-by-step explanation:

The  lateral area of right cone is calculated by the following formula

[tex]A = \pi r *\sqrt{r^2 +h^2}[/tex]

Where r is the radius of the cone and h is the height

In this case we know that the diameter d of the base is:

[tex]d=2r[/tex]

So the radius is:

[tex]r=\frac{d}{2}\\\\r=\frac{4}{2}\\\\r=2\ units[/tex]

and

[tex]h=10\ units[/tex]

So the area is:

[tex]A = \pi*2 *\sqrt{2^2 +10^2}[/tex]

[tex]A = 64.076\ units^2[/tex]

The equation of an ellipse with a center at origin, a height of 12 units, and a width of 19 units is x^2/(9.5^2) + y^2/(6^2) = 1.

The student is asking for an equation of an ellipse. An ellipse has a standard form equation given by x^2/a^2 + y^2/b^2 = 1, where 'a' is the semi-major axis and 'b' is the semi-minor axis. The semi-major axis and the semi-minor axis are half of the major axis (width) and minor axis (height) respectively. Here, the width or major diameter of the ellipse is given as 19 units and the height or minor diameter as 12 units.

Thus, the semi-major axis is 19/2 = 9.5 and the semi-minor axis is 12/2 = 6. As the ellipse's center is at the origin, the equation of the ellipse is given by: x^2/(9.5^2) + y^2/(6^2) = 1.

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The equation of the ellipse in standard form with a center at the origin, a height of 12 units, and a width of 19 units is x²/(19/2)² + y²/(6)² = 1.

The equation of an ellipse in standard form with the center at the origin is given by x²/a² + y²/b² = 1, where a is the semimajor axis (half the width) and b is the semiminor axis (half the height).

Given a width of 19 units and a height of 12 units, the semimajor axis will be half of the width and the semiminor axis will be half of the height. So, the equation of the ellipse will be x²/(19/2)² + y²/(12/2)² = 1.

Simplifying, x²/(19/2)² + y²/(6)² = 1. This is the equation of the ellipse in standard form with a height of 12 units and a width of 19 units.

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Answer:

17. Scale Factor is  3:1

18. Scale Factor is  1:3

Step-by-step explanation:

Scale Factor: In two similar shapes, the ratio of their corresponding sides is called scale factor.

17. Give the scale factor of Figure A to Figure B

Figure A has sides:

Hypotenuse = 15

Perpendicular = 12

Base = 9

Figure B has sides:

Hypotenuse = 5

Perpendicular = 4

Base = 3

So, if we divide all sides of figure A by 3 we get Figure B

So, Figure A : Figure B

3:1

18. Give the scale factor of Figure B to Figure A

Figure B has sides:

Hypotenuse = 5

Perpendicular = 4

Base = 3

Figure A has sides:

Hypotenuse = 15

Perpendicular = 12

Base = 9

If we multiply 3 with the sides of Figure B we can get the sides of Figure A.

So scale factor is 3.

So, Figure B : Figure A

1:3

Answer:

17) 3 : 1

18: 1 : 3

Step-by-step explanation:

Figure A and Figure B are similar triangle.

Scale Factor of A : B

= 9 : 3

= 3 : 1

Scale Factor of B : A

= 3 : 9

= 1 : 3

Answer:

[tex]M^{2}=3.2[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

In this problem we have

[tex]P*M^{2}=k[/tex]

step 1

Find the value of k

For P=8, M=2

substitute

[tex]k=(8)(2)^{2}=32[/tex]

The equation is equal to

[tex]P*M^{2}=32[/tex]

step 2

Find the value of M²

when P=10

substitute the value of P in the equation

[tex]10*M^{2}=32[/tex]

[tex]M^{2}=3.2[/tex]

Answer: D) 36 Inches

Step-by-step explanation:

Answer:

D)36 inches

Step-by-step explanation:

3 feet × (12 inches/1 feet) = 36 inches

Answer:

1436.03 units³

Step-by-step explanation:

The formula for the volume of a sphere of radius r is

V = (4/3)πr³.  We'll use 3.14 for π.

Then:

V = (4/3)(3.14)(7 units)³.  To the nearest hundredth:  1436.03 units³

Answer:

Step-by-step explanation:

Given

r = 7

pi = 3.14

Formula

V = (4/3) pi * r^3

Solution

V = (4/3) * pi * 343

V = (1.3333) * 3.14 * 343

V = 1435.99 You are going to get a lot of variation in this question: Everything depends on what value you use for 4/3. I used 1.3333 but it does go on. I would try this yourself. Whatever you get, enter it.

You are better off using 3.14 than using pi. You are still going to have to problem of how to represent 4/3

Answer:

The answer in the procedure

Step-by-step explanation:

I will analyze two cases

see the attached figure to better understand the problem

case a) applying the Pythagoras Theorem

I assume that the hypotenuse is BC

[tex]AB^{2}=BC^{2}-AC^{2}[/tex]

substitute the given values

[tex]AB^{2}=17^{2}-15^{2}[/tex]

[tex]AB^{2}=64[/tex]

[tex]AB=8\ units[/tex]

case b) applying the Pythagoras Theorem

I assume that the hypotenuse is AB

[tex]AB^{2}=BC^{2}+AC^{2}[/tex]

substitute the given values

[tex]AB^{2}=17^{2}+15^{2}[/tex]

[tex]AB^{2}=514[/tex]

[tex]AB=\sqrt{514}=22.67\ units[/tex]

Answer:

Check attached graph

Step-by-step explanation:

Given equation is [tex]y=x-2[/tex].

Now we need to graph the given equation [tex]y=x-2[/tex].

To graph that we can find two points then join them by a straight line.

We are free to plug any number for x say x=0 and x=2

plug x=0

[tex]y=x-2=0-2=-2[/tex]

Hence first point is (0,-2).

plug x=2

[tex]y=x-2=2-2=0[/tex]

Hence first point is (2,0).

Now graph both points and joint them to get final graph as shown below.

Answer:

C=12.57 ft

Step-by-step explanation:

Answer: 12.56 feet.

Step-by-step explanation:

The minimum amount of water she needs to completely fill the sphere is; 904.32 inches³

The formula for Volume of a Sphere is given as;

V = ⁴/₃πr³

We are given;

Diameter; d = 12 inches

Thus;

Radius; r = 12/2 = 6

To get the minimum amount of water she needs to completely fill the sphere, we just plug in the relevant values into the volume equation to get;

V = ⁴/₃π(6)³

V = 904.32 inches³

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Answer:

The answer in the procedure

Step-by-step explanation:

Let

A1 ------> the area of the first square painting

A2 ---->  the area of the second square painting

D -----> the difference of the areas

we have

[tex]A1=81x^{2}-90x-25[/tex]

[tex]A2=25x^{2}+30x+9[/tex]

case 1) The area of the second square painting is greater than the area of the first square painting

The difference of the area of the paintings is equal to subtract the area of the first square painting from the area of the second square painting

D=A2-A1

[tex]D=(25x^{2}+30x+9)-(81x^{2}-90x-25)[/tex]

[tex]D=(-56x^{2}+120x+34)[/tex]

case 2) The area of the first square painting is greater than the area of the second square painting

The difference of the area of the paintings is equal to subtract the area of the second square painting from the area of the first square painting

D=A1-A2

[tex]D=(81x^{2}-90x-25)-(25x^{2}+30x+9)[/tex]

[tex]D=(56x^{2}-120x-34)[/tex]

Final answer:

To find the difference between the areas of two square paintings, subtract the second area from the first to get an expression. By direct subtraction and using the distributive property, both methods yield the expression[tex]56x^2 - 120x - 34[/tex].

Explanation:

To find an expression that represents the difference between the areas of two square paintings, we simply subtract the area of the second painting from the area of the first painting.

The area of the first painting is [tex]81x^2 - 90x - 25,[/tex] and the area of the second painting is [tex]25x^2 + 30x + 9.[/tex]To find the difference, calculate [tex](81x^2 - 90x - 25) - (25x^2 + 30x + 9).[/tex]

Here's the direct subtraction method:

Subtract the [tex]x^2[/tex] terms: [tex]81x^2 - 25x^2 = 56x^2[/tex].

Subtract the x terms: -90x - 30x = -120x.

Subtract the constant terms: -25 - 9 = -34.

Combining these, we get the expression representing the difference in areas:[tex]56x^2 - 120x - 34.[/tex]

Another way to find the solution is using the distributive property to first factor out a negative from the second polynomial, making it easier to subtract:

Rewrite as[tex]: (81x^2 - 90x - 25) - 1*(25x^2 + 30x + 9).[/tex]

Distribute the negative sign:: [tex](81x^2 - 90x - 25) - 1*(25x^2 + 30x + 9)..[/tex]

Now proceed as in the direct subtraction method above.

The final result is the same: [tex]56x^2 - 120x - 34.[/tex]

Answer:

2

Step-by-step explanation:

From X to the black dot it is 2 and from the black dot to Y it is 3

From X' to the black dot it is 4 and from the black dot to Y' it is 6

The lengths are getting twice as bigger

Answer:

2

Step-by-step explanation:

U can use this formula

Image 1/image 2

Answer:

95

Step-by-step explanation:

Week                Number of Beetles

0                               16

1                                16 + (16/4) = 20

2                                20 + (20/4 ) = 20 + 5 = 25

3                                25 + (25/4 ) = 25 + 6.25 ≈ 31

4                                31 + (31/4) = 31 + 7.75 ≈ 31+8 ≈ 39

5                                39 + (39/4) = 39 + 9.75 ≈ 39 + 10 ≈ 49

6                                 49 + (49/4) =  49+ 12.25 ≈ 49+12 ≈ 61

7                                 61 + (61/4) = 61 + 15.25 ≈ 61 + 15 ≈ 76

8                                 76 + (76/4) = 76 + 19 = 95

Hence there will be approximately 95 beetles by 8th week                  

Answer:B!!

Step-by-step explanation:

Answer a is incorrect because only the seniors were questioned and answer c is incorrect because nothing was mentioned in the question about only testing males.

Your answer is B

Answer:

See below in bold.

Step-by-step explanation:

Arrange in order first:

1 1 2 3 4 6 8 9 15

Median ( middle number) = 4.

Mode ( the number which occurs most) = 1.

Mean =  (1+1+2+3+4+6+8+9+15) = 49/9 = 5.4.

Range = 15 - 1 = 14.

List the numbers in order from smallest to largest:

1, 1 , 2, 3, 4, 6, 8, 9, 15

Median is the Middle value of the set = 4

Mode is  the number that appears the most = 1

Mean is the average add the numbers together and divide by the quantity of numbers:

1 + 1 +2 + 3+ 4+ 6 +8 + 9+15 = 49 / 9 = 5.44

Range is the difference between the largest number and smallest number: 15 -1 = 14

Answer: [tex]x=\frac{23}{4}[/tex] and  [tex]x=-\frac{17}{4}[/tex]

Step-by-step explanation:

Given the equation [tex]|4x - 3| = 20[/tex], you can set up two cases:

Case 1: [tex]4x-3>0[/tex]

[tex]4x-3=20[/tex]

Solve for the variable "x", therefore you get:

[tex]4x=20+3\\\\x=\frac{23}{4}[/tex]

Case 2: [tex]4x-3<0[/tex]

[tex]-4x+3=20[/tex]

Solve for the variable "x". Then, you  get:

[tex]-4x=20-3\\\\x=\frac{17}{-4}\\\\x=-\frac{17}{4}[/tex]

Therefore, the solution is:

[tex]x=\frac{23}{4}[/tex] and  [tex]x=-\frac{17}{4}[/tex]

Answer:

10.7

Step-by-step explanation:

√114 = 10.7   <----to the nearest tenth

Answer:

10.7 to the nearest tenth.

Step-by-step explanation:

It will be between 10 and 11 because 10^2 = 100 and 11^2 = 121.

Using a calculator. It is 10.67707825.

Answer:

n = - 3

Step-by-step explanation:

It's not cheating unless this question is from a quiz or test.

5+0.5(6n+14)=3                Subtract 5 from both sides.

5-5 + 0.5(6n+14) = 3 - 5   Combine

0.5(6n+14) = - 2                There are two ways to go. I prefer dividing by 0.5

0.5(6n+14)/0.5 = -2/0.5    Do the division

6n + 14 = - 4                      Subtract 14

6n+14-14= -4-14                 Combine

6n = - 18                             Divide both sides by 6

6n/6 = - 18/6                      Combine

n = - 3      

The solution to the equation 5+0.5(6n+14)=3 will be n = - 3      

WE are given the equation as;

5+0.5(6n+14)=3                

We need to find the value of n here;

Subtract 5 from both sides.

5-5 + 0.5(6n+14) = 3 - 5  

Combine

0.5(6n+14) = - 2                

0.5(6n+14)/0.5 = -2/0.5    

6n + 14 = - 4                      

6n+14-14= -4-14                

6n = - 18                            

Divide both sides by 6

6n/6 = - 18/6                      

n = - 3      

Therefore, the solution to the equation 5+0.5(6n+14)=3 is n = - 3      

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Answer:

r=5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

The independent variable is manipulated or controlled by the experimenter and is usually placed on the horizontal axis of a graph. The dependent variable is the variable that is measured to see the effect of the independent variable and is usually placed on the vertical axis of a graph.

In a scientific study, the independent variable is the variable that is manipulated or controlled by the experimenter, and it is usually placed on the horizontal axis of a graph. The dependent variable is the variable that is measured to see the effect of the independent variable, and it is usually placed on the vertical axis of a graph.

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Answer:

83.33%

Step-by-step explanation:

We first need to evaluate 80% of the first 15 matches in order to determine the number of watches out of 15 which they won.

80 % of 15 = 80/100 * 15 = 12

12 matches out of the first 15 were won.

Since the team won the rest of the 3 remaining matches, the total number of matches won becomes;

12 + 3 = 15

The team thus won 15 matches out of a total of 15 + 3 =18 matches .

The percent of all matches won is ;

15/18 * 100 = 83.33%

Answer:

1 whole and 1 over 12

Step-by-step explanation:

Answer:

Step-by-step explanation:

7

12

+

3

6

=

7

12

+

3

6

=

7

12

+

1

2

=

7

12

+

6

12

=

7+6

12

=

13

12

(Decimal: 1.083333)

Answer:

[tex]A=\$6,768.75[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=10\ years\\ P=\$5,600\\ r=0.019\\n=4[/tex]  

substitute in the formula above  

[tex]A=\$5,600(1+\frac{0.019}{4})^{4*10}[/tex]  

[tex]A=\$5,600(1.00475)^{40}=\$6,768.75[/tex]  

Answer:

"between 30 yards and 150 yards"

Step-by-step explanation:

Let one side of a triangle be x and another side be y. To find the possible lengths of the third side, it is given by:

Possible length of 3rd side would be between "x - y" and "x + y"

Here, given x = 90 and y = 60, so the possible length of 3rd side would be:

90 - 60 = 30,

90 + 60 = 150

Hence, in between 30 and 150

Answer:

its D between 30 and 150 just took test on ed got a 100

Step-by-step explanation:

Answer:

x²+2xy-x+y²-y-12

Step-by-step explanation:

(x+y+3)(x+y-4)

= x(x+y-4)+y(x+y-4)+3(x+y-4)

= x²+xy-4x+xy+y²-4y+3x+3y-12

= x²+2xy-x+y²-y-12

The answer is:

The simplified expression is:

[tex](x + y + 3)(x + y - 4)=x^{2} +y^{2} +2xy-x-y-12[/tex]

To solve the problem,  we need to remember how to use the distributive property and how to add like terms.

The distributive property can be defined as follow:

[tex](a+b)(c+d)=ab+ad+bc+bd[/tex]

The like terms are the terms that share the same variable and the same exponent, for example:

[tex]3x+x+ x^{2}=x^{2} +4x[/tex]

We were able to add the first and the second term because they share the same variable and the same exponent.

Now, we are given the expression:

[tex](x+y+3)(x+y-4)[/tex]

So, simplifying we have:

[tex](x + y + 3)(x + y - 4)=(x*x)+(x*y)-(4*x)+(y*x)+(y*y)-(4*y)+(3*x)+(3*y)-(3*4)\\\\(x + y + 3)(x + y - 4)=x^{2} +xy-4x+xy+y^{2}-4y+3x+3y-12\\\\(x + y + 3)(x + y - 4)=x^{2} +y^{2} +2xy-x-y-12[/tex]

Hence, we have that the simplified expression is:

[tex](x + y + 3)(x + y - 4)=x^{2} +y^{2} +2xy-x-y-12[/tex]

Have a nice day!

A. 10% of n is q;          n = 10q

B. 25% of x is 320;     x = 1280

C. 15% of y is q;          y = 6.666....7q

Answer:

a = 90

b = 7.81

c = 60

5 weeks

8×2.5=20

2×2.5=5

ANSWER

Option C and E

EXPLANATION

An arithmetic sequence has a constant difference among the consecutive terms.

The sequence

[tex]18,5.5,-7,-19.5,-32,...[/tex]

has a constant difference of -12.5

[tex]d = 5.5 - 18 = - 7 - 5.5 = - 19.5 - - 7 = - 32 - - 19.5 = - 12.5[/tex]

The sequence

[tex]16,32,48,64,80,...[/tex]

also has a common difference of 16

[tex]d = 32 - 16 = 48 - 32 = 64 - 48 =80 -64 = 16[/tex]

Therefore correct answers are C and E

Answer:

Step-by-step explanation:

An arithmetic sequence has a constant difference among the consecutive terms.

The sequence has a constant difference of -12.5

The sequence also has a common difference of 16

Therefore correct answers are C and E

Answer:

(7,5) is the vertex

Step-by-step explanation: