HELP I'M TIMED! Reflect triangle ABC over the y-axis. What is the relationship between the segments created if you connect the points to the line of reflection. I WILL GIVE YOU BRAINLIEST!

HELP I'M TIMED! Reflect Triangle ABC Over The Y-axis. What Is The Relationship Between The Segments Created

Answers

Answer 1

This is your answer thanks!


HELP I'M TIMED! Reflect Triangle ABC Over The Y-axis. What Is The Relationship Between The Segments Created
Answer 2

Answer:

they are perpendicular to each other

Step-by-step explanation:


Related Questions

FIFTY POINTS! ASAP! DUE IN A FEW MINUTES! Just fill in the blanks!!
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Provide reasons for the proof.

Given: ∠2 ≅ ∠4

and ∠2 and ∠3 are supplementary

Prove: ∠1 ≅ ∠3

Answers

Answer:

This proof involves the definitions of congruence and supplementary angles, as well as some of the properties of equality.

 

∠1 and ∠2 are supplementary    // given

∠3 and ∠4 are supplementary    // given

∠1 ≅ ∠3    // given

 

m∠1 + m∠2 = 180°    // definition of supplementary angles

m∠3 + m∠4 = 180°    // definition of supplementary angles

 

m∠1 + m∠2 = m∠3 + m∠4    // transitive property of equality

 

m∠1 = m∠3    // definition of congruent angles

 

m∠1 + m∠2 = m∠1 + m∠4    // substitution property of equality (replaced m∠3 with m∠1)

 

m∠2 = m∠4    // subtraction property of equality (subtracted m∠1 from both sides)

 

∠2 ≅ ∠4    // definition of congruent angles

hope this helps

Step-by-step explanation:

Answer:

For the future students who need answer to this problem ....

Step-by-step explanation:

5. given

7.  Transitive property of equality

8.  Substitution Property

9.  Subtraction Property of Equality

10.  Converse of Angles Congruent Postulate

I am writing this test now and these are the answers I put in. It hasn't been graded yet but I'm pretty sure that they are correct. But pls lmk if anything is wrong. HOPE THIS HELPS

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The glee club has 120 cupcakes to sell. They have decided to arrange the cupcakes in th shape of a rectangle, such as the rows have an even number of cupcakes and the columns have an odd number of cupcakes. How many arrangements of cupcakes can they creat? Explain.

Answers

Answer:

2x60, 4x30

Step-by-step explanation:

Given that the glee club has 120 cupcakes to sell.

These 120 cupcakes are to be arranged in a rectangle shape such that

there are even number of cakes lengthwise and even number of cakes breadthwise.

If l is the number of cakes along row, and m is the number of cakes along column, then we have both l and m as even.

Also lm=120

In other words, we must find 2 even  factors of 120 l and m such that lm = 120

2x60 is one such pair

Next is 4x30.

There cannot be any other pair satisfying this condition.

Hence answer is 2x60 or 4x30

Write a linear equation that represents the arithmetic sequence 10,8,6,4

Answers

The linear equation that represents the arithmetic sequence is[tex]a_n=10-2(n-1)[/tex]

Writing arithmetic sequence as a function of linear equations.

Arithmetic sequence is a progressive set of numbers with a common difference between each term. On the other hand a linear equation y =mx + b where m= slope and b = y-intercept.

In the given question, we have the arithmetic sequence;

10, 8, 6, 4 ...

Here the arithmetic sequence, the common difference is -2. So the common difference relates to the slope of the linear equation.

The first term is 10, the common difference is - 2. Using the general formula for arithmetic sequence, we have:

[tex]a_n=10-2(n-1)[/tex]

How do you round to the nearest hounded thousand for the number 387,422

Answers

Answer:

400,000

Step-by-step explanation:


In triangle RST, U is the midpoint of RS, V is the midpoint of ST, and W is the midpoint of TR. Use the triangle diagram to answer the question.

1. What is the length of RS?
A. 12
B. 6
C. 22
D. 24

2. What is the value of x?
A. 6.5
B. 6
C. 11
D. 5.5

3. What is the value of y?
A. 15.9
B. 11
C. 5.3
D. 3.7

4. What is the length of UW?
A. 11
B. 6
C. 7.95
D. 22

5. What is the length of UV?
A. 11
B. 6
C. 7.95
D. 12

Answers

(1)

we are given

U is the midpoint of RS

and we have

[tex]RU=12[/tex]

so, we can use formula

[tex]RS=2RU[/tex]

we can plug values

[tex]RS=2\times 12[/tex]

[tex]RS=24[/tex]............Answer

(2)

V is the midpoint of ST

so, we get

[tex]SV=VT[/tex]

now, we can plug values

[tex]2x=11[/tex]

divide both sides by 2

[tex]x=5.5[/tex].........Answer

(3)

now, we can find y

W is the midpoint of TR

so, we get

[tex]RW=WT[/tex]

we can plug value

[tex]15.9=3y[/tex]

divide both sides by 3

[tex]y=5.3[/tex]

(4)

we can see that

triangles URW and RST are similar

so, their sides ratios must be equal

so, we get

[tex]\frac{RW}{RT} =\frac{UW}{ST}[/tex]

we can plug values

[tex]\frac{15.9}{2\times 15.9} =\frac{UW}{2VT}[/tex]

[tex]\frac{15.9}{2\times 15.9} =\frac{UW}{2\times 11}[/tex]

[tex]UW=22\times \frac{15.9}{2\times 15.9}[/tex]

[tex]UW=11[/tex]...........Answer

(5)

we can see that

triangles SUV and RST are similar

so, their sides ratios must be equal

so, we get

[tex]\frac{SU}{SR} =\frac{UV}{RT}[/tex]

now, we can plug values

[tex]\frac{12}{2\times 12} =\frac{UV}{2\times 15.9}[/tex]

[tex]UV=2\times 15.9\times \frac{12}{2\times 12}[/tex]

[tex]UV=15.9[/tex].............Answer

1. The length of RS is 24 units.

2. The value of [tex]x[/tex] is 5.5.

3. The value of [tex]y[/tex] is 5.3.

4. The length of UW is 11.

5. The length of UV is 15.9.

According to the given figure-

[tex]\triangle RST \sim \triangle URW[/tex]

1. U is the mid-point of RS so, the length of UR and US are equal.

Hence, the length of RS is 24 units.

2. V is the mid-point of ST so, the length of VS and VT are equal.

So,

[tex]2x=11\\x=\dfrac{11}{2}\\x=5.5[/tex]

Hence, the value of [tex]x[/tex] is 5.5.

3. W is the mid-point of RT so, the length of WR and WT are equal.

So,

[tex]3y=15.9\\y=\dfrac{15.9}{3}\\y=5.3[/tex]

Hence, the value of [tex]y[/tex] is 5.3.

4. As, [tex]\triangle RST \sim \triangle URW[/tex]

So, the length of the sides is proportional.

[tex]\dfrac{RT}{RW}=\dfrac{ST}{UW}\\\dfrac{2\times 15.9}{15.9}=\dfrac{11\times 2}{UW}\\UW=11[/tex]

Hence, the length of UW is 11.

5.  As, [tex]\triangle RST \sim \triangle URW[/tex]

So, the length of the sides is proportional.

[tex]\dfrac{SU}{SR}=\dfrac{UV}{RT}\\\dfrac{12}{2\times 12}=\dfrac{UV}{2\times 15.9}\\UV=15.9[/tex]

Hence, the length of UV is 15.9.

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many shapes can be congruent. Triangles is one of them. What are the various ways to prove triangle congruency? Where in the real world would it be important for you to apply these concepts?

Answers

For triangles to be congruent, they must have the same angles and same three sides, irrespective of what direction they are pointing to.

Following are the ways to find if two triangles are congruent:

1. SSS (side, side, side): If all three sides of a triangle are equal to the three sides of another triangle, the triangles are congruent.

2. SAS (side, angle, side): If the two sides and the included angle of a triangle are equal to the corresponding sides and the angle of another triangle, the triangles are congruent.

3. ASA (angle, side, angle): If the two angles and their shared side is equal to the corresponding angles and shared side of another triangle, the triangles are congruent.

4. AAS (angle, angle, side): If two angles and the non-included side of a triangle are equal to the corresponding angles and non-included side of another triangle, the triangles are congruent.

5. HL (hypotenuse, leg): If the hypotenuse and one leg (side other than hypotenuse) of a right angle triangle are equal to the corresponding hypotenuse and the leg of another right angle triangle, then the two triangles are congruent.

Congruent triangles are used in real world for construction purposes to ensure that the man-made structures are strong and stable enough.

Final answer:

There are multiple ways to prove triangle congruency, including SSS, SAS, ASA, AAS, and RHS. These concepts are important in real-world applications such as architecture and engineering for ensuring precision and safety in structures and components.

Explanation:

There are several methods to prove that two triangles are congruent, each based on different sets of information about the triangles' sides and angles. The following are commonly used:

Side-Side-Side (SSS) Congruence: If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent (Theorem 16).Side-Angle-Side (SAS) Congruence: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent (Theorem 11).Angle-Side-Angle (ASA) Congruence: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.Angle-Angle-Side (AAS) Congruence: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, the triangles are congruent.Right Angle-Hypotenuse-Side (RHS) Congruence (also known as HL): If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, the triangles are congruent.

These concepts are utilized in various real-world applications, such as architectural design, engineering, manufacturing, and construction, where precise measurements and shapes are critical for the safety and fit of structures and components.

Do these two expressions represent equivalent expressions Explain why or why not. 36 + 20 4(9 + 5)

Answers

yes

assuming the 2 expressions are 36 + 20 and 4(9 + 5)

36 + 20 = 56 and

4(9 + 5 ) = 4(14) = 4 × 14 = 56


Yes, the 2 expressions are 36 + 20 and 4(9 + 5) represent equivalent expressions.

What does it mean to solve an equation?

An equation represents the equality of two or more mathematical expressions.

When someone asks you to solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).

Solutions to an equation are those values of the variables involved in that equation for which the equation is true.

Let assume the 2 expressions are 36 + 20 and 4(9 + 5).

36 + 20 = 56

and

4(9 + 5 )

= 4(14)

= 4 × 14

= 56

Yes, they are equivalent to each other.

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Question in the below attached ,


ITS NOT B

Answers

3x + 32 + x + 48 = 180

4x + 80 = 180

4x = 100

x = 25

Angles

x + 48 = 25 + 48 = 73

3x + 32 = 3(25) + 32 = 75 + 32 = 107

Larger angle = 107

Answer

C) x = 25, 107 degrees

Please help and show work!!

Answers

Step 1. Use the Multiplication Distributive Property

So, -2n^6y^5 * -6n^3y^2n^3y^3

Step 2. Take out the constants

-(2 * -6)n^6n^3n^3y^5y^2y^3

Step 3. Simplify 2 * -6 to -12

-(-12)n^6n^3n^3y^5y^2y^3

Step 4. Regroup terms

-(-12n^6n^3n^3y^5y^2y^3)

Step 5. Use Product Rule

-(-12n^6 + 3 + 3 y^5 + 2 + 3)

Step 6. Simplify 5 + 2 + 3 to 10

-(-12n^12y^10)

Step 8. Simplify brackets

12n^12y^10

​(-2n⁶y⁵)(-6n³y²)(ny)³ = We can take out the constants

= (12)(n⁶y⁵)(n³y²)(n³y³) = We can group the same variables

= (12)(n⁶)(n³)(n³) * (y⁵)(y²)(y³) = We can use the power product rule

=​(12)(n⁽⁶⁺³⁺³⁾) * (y⁽⁵⁺²⁺³⁾) = We add the exponents

Answer : 12n¹²y¹⁰​

​Hope this helps!​​​​

​[tex]\textit{\textbf{Spymore}}[/tex]​​​​​​

Which of the following is the solution to the quadratic equation x2 + 16x + 55 = 0?


A.x = 11, -5


B.x = -11, 5


C.x = -11, -5


D.x = 11, 5

Answers

hope this helps you.....

The answer is not found among the options A, B, C or D.

The standard form of a quadratic equation is ax² + bx + c = 0. Here, a is the coefficient of x² (which is 1 in this case), b is the coefficient of x (which is 16), and c is the constant (which is  55).

To find the roots of a quadratic equation ax² + bx + c = 0, we use the quadratic formula, which is x = [ -b ± sqrt(b²-4ac) ] / 2a.

Here, b²-4ac = (16)² - 4x1x55 = 256 - 220 = 36,  which is a perfect square, so we can continue.

Then the quadratic formula gives us two solutions:

Solution1 = [ -16 + sqrt(36) ] / (2x1) = -16 + 6 / 2 = -5
Solution2 = [ -16 - sqrt(36) ] / (2x1) = -16 - 6 / 2 = -11

So, the roots of the equation are x= -5 and x= -11.

Matching our solutions with the options given, we do not find any that fits the result. Therefore, the answer is not found among the options A, B, C or D.

State a conclusion that seems reasonable.
You find a nest with 12 eggs in it. The first 5 hatch out to be snakes.
Conclusion:

Answers

Answer:

its a snakes nest.

Step-by-step explanation:

If $2300 is spent on vacations or travel each year, estimate how much should be set aside each month for those expenses?

Answers

12 months in a year
2300/12
we can round 2300 to 2400 (because it is an estimate) and divide by 12 to give an approximation of $200 each month

The Answer Is A. above me is the example.

Simplify the expression.2/3 (–9m + 12)

Answers

Distribute 2/3 to all terms within the parenthesis. Simplify

(2/3)(-9m) = ((2)(-9m))/(3) = -18m/3

(2/3)(12) = (24)/(3) = 8

-18m/3 + 8

Simplify. Divide.

-18m/3 = -6m

-6m + 8 is your answer

hope this helps

Hi,

Solution,

2/3(−9m+12)

=(2/3)(−9m+12)

=(2/3)(−9m)+(2/3)(12)

Answer,

=−6m+8

Tomika plans to run 84miles in 4weeks.If she continues the pattern how many miles will she run in a year

Answers

Answer:

She will run a distance of 1095.78 miles per year.

Explanation:

 Number of days in a year = 365.25

 Number of days in a week = 7

 Number of weeks in a year = 365.25/7 = 52.18 weeks.

 Tomika plans to run 84 miles in 4 weeks.

 Distance run by Tomika in 1 week = 84/4 = 21 miles.

 Distance run by Tomika in 1 year = 21*52.18 = 1095.78 miles

 So she will run a distance of 1095.78 miles per year.

If Tomika continues the pattern, she will run approximately 1,092 miles in a year.

How to get the miles ran

There are 52 weeks in a year, so you can divide 52 by 4 to find out how many 4-week periods there are in a year:

Number of 4-week periods in a year = 52 weeks / 4 weeks/period = 13 periods

Now, multiply the miles she runs in each 4-week period (84 miles) by the number of 4-week periods in a year (13 periods):

Total miles in a year = 84 miles/period × 13 periods

Total miles in a year = 1,092 miles

So, if Tomika continues the pattern, she will run approximately 1,092 miles in a year.

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A cylindrical bin with a diameter of 15 feet 3 inches and a height of 24 feet 4 inches is used to hold wheat on the farm where you're interning. One cubic foot holds 0.804 bushels. About how many bushels of wheat can be stored?

Answers

Given

A cylindrical bin with a diameter of 15 feet 3 inches and a height of 24 feet 4 inches is used to hold wheat.

One cubic foot holds 0.804 bushels

Find out bushels of wheat can be stored.

To proof

Formula

[tex]Volume\ of\ a\ cylinder = \pi r^{2}h[/tex]

where r is the radius and h represent the height.

As given in the question

diameter = 15 feet 3 inches

height = 24 feet 4 inches

First convert inches into feet

I inches = 0.083 feet

15 feet 3 inches = 15 + 3 × 0.083

                          =    15.25 feet

Diameter = 15.25 feet

24 feet 4 inches = 24  + 4 ×0.083

                           = 24.33 feet

Height = 24.33 feet

[tex]Radius\ of\ cylinder = \frac{Diameter}{2}[/tex]

Radius = 7.63 feet

[tex]\pi = 3.14[/tex]

Put all the value in the above formula.

we get

Volume of the cylinder = 3.14× 7.63× 7.63× 24.33

                                      = 4447.55 foot³ ( approx)

As given

One cubic foot holds 0.804 bushels

Total bushels of wheat can be stored = 4447.55×0.804

                                                               = 3575.83 ( approx)

Total bhushels of wheat stored are  3575.83 ( approx).

Hence proved

Answer:

3571.63 bushels

Step-by-step explanation:

The volume of a cylinder is found using the formula

V = πr²h

For our cylinder, h, the height, is 24 feet 4 inches.  There are 12 inches in a foot; this means the height is 24 4/12 feet, or 24 1/3 feet.  Writing this as an improper fraction, h = 73/3.

The diameter of our cylinder is 15 feet 3 inches.  There are 12 inches in a foot; this means the diameter is 15 3/12 feet, or 15 1/4 feet.  Writing this as an improper fraction, d = 61/4.

The radius is 1/2 of the diameter; this means r = 61/4(1/2) = 61/8.

Using these in our formula and using 3.14 for π, we have

V = 3.14(61/8)²(73/3)  = 4442.33 ft³

Each cubic foot holds 0.804 bushels of wheat; this means the cylindrical bin can hold

4442.33(0.804) = 3571.63 bushels.

Urgent !!! 20 Points!!!
Find Arc BC + Arc AD

I figured out that X=6
I just can't figure out what the any of the angles measures are!
Please help.

Answers

x = 6 is correct

Focus on the right triangle EDF. The short leg is x = 6. The hypotenuse is 4+8 = 12. Since the hypotenuse is twice that of the short leg, we have a 30-60-90 triangle. Recall that the ratio of the short leg, long leg and hypotenuse is 1:sqrt(3):2 or you can think of it as x: x*sqrt(3): 2x. The 30 degree angle is opposite the short leg (smallest angle opposite smallest side). So the 60 degree angle is angle FED, which is the angle formed by the two chords.

This means angle BEC is 120 degrees since 120+60 = 180.

Now use the second part of the hint which says that the two arcs add up and are cut in half to get the angle formed by the intersecting chords. This means,

angle BEC = (1/2)*(arc BC + arc AD)

120 = (1/2)*(arc BC + arc AD)

2*120 = 2*(1/2)*(arc BC + arc AD)

240 = arc BC + arc AD

arc BC + arc AD = 240 degrees

Which ordered pair is a solution of the equation y = –9x + 4?

I don't want the answer, I just don't know how to solve it. I'm two weeks behind in work so anything helps!

Answers

OK

I'll take a hypothetical case. Suppose one of the ordered pairs = (1, 6)  which means 'x = 1 when y = 6)'

we substitute  x = 1 and y = 6 into the equation and see if the left side = right side

left: y = 6

right: -9x + 4 = -9(1) + 4 = -9 + 4 = -5

Therefore this ordered pair is NOT a solution to the equation.

Answer: Hello mate!

we have the equation y = –9x + 4 and we want to find ordered a pair that is a solution of the equation.  Where a pair has the form (x, y)

First, you need to know that there are infinite ordered pairs that are a solution of this equation, if you want to find them, you need to replace the value of x (or the value of y) with a number, and solve the equation:

suppose x = 1

then y = -9*1 + 4 = -9 + 4 = 5

then the pair (1,5) is a solution of the equation.

The general form of the pairs is (x,y), then the pairs that are a solution for this equation are the pairs of the form (x, y(x)) = (x, -9x + 4)

Please help 20 POINTS. Problem below

Answers

f(x):  y = 9x² - 12

f⁻¹(x):  x = 9y² - 12

    x + 12 = 9y²

     [tex]\frac{x+12}{9} = y^{2}[/tex]  

     [tex]\sqrt{\frac{x+12}{9}} = |y|[/tex]     ; x ≥ -12

     [tex]+/-\sqrt{\frac{x+12}{9}} = y[/tex]

Answer: C

Find the 25th term of an arithmetic sequence whose first term is 12 and whose common difference is ‒6.
A.
‒144
B.
132
C.
‒132
D.
156

Answers

c -132 is the answer

Which relationship is an example of inverse variation ?

Answers

If relationship is an inverse variation then the product of x and y is constant.

A)

2 · 6 = 12

3 · 9 = 27

NOT

B)

1 · 6 = 6

2 · 3 = 6

3 · 2 = 6

6 · 1 = 6

YES

C)

0 · 0 = 0

2 · 8 = 16

NOT

D)

-3 · 4 = -12

-4 · (-3) = 12

NOT

Answer: B)

To make a scarf, Jenny uses blue and white yarn. The number of yards of blue yarn she uses is 4 times the number of white yarn in each scarf. Write 4 ratios to show the number of yards of white yarn to blue yarn for a scarf? 7th grade math

Answers

Answer:  4:1, 8:2, 12:3, 16:4

Step-by-step explanation:

blue is 4 times white  

 blue: white

     4 : 1

multiply both numbers by 2 to get 8:2

multiply both numbers by 3 to get 12:3

multiply both numbers by 4 to get 16:4

 

Use the substitution method to solve the system of equations. Choose the correct ordered pair. 2y + 4x = 18 2y – 3x = 4
A. (6, –3)
B. (3, 3)
C. (2, 5)
D. (5, –1)

Answers

My answer is C.(2,5)

Answer:  the correct option is (C) (2, 5).

Step-by-step explanation:  We are given to use the substitution method to solve the following system of equations :

[tex]2y+4x=18~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2y-3x=4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Dividing equation equation (i) on both sides by 2, we have

[tex]\dfrac{2y+4x}{2}=\dfrac{18}{2}\\\\\Rightarrow y+2x=9\\\\\Rightarrow y=9-2x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]

Substituting the value of y from equation (iii) in equation (ii), we get

[tex]2(9-2x)-3x=4\\\\\Rightarrow 18-4x-3x=4\\\\\Rightarrow 18-4=4x+3x\\\\\Rightarrow 14=7x\\\\\Rightarrow x=\dfrac{14}{7}\\\\\Rightarrow x=2.[/tex]

So, from equation (iii), we get

[tex]y=9-2\times2=9-4=5.[/tex]

Thus, the required solution of the given system is (x, y) = (2, 5).

Option (C) is CORRECT.

Travis writer 72=9x8. Is he correct ? Explain at least two strategies Travis to check his work

Answers

Since, Travis writes [tex]9 \times 8 = 72[/tex].

Yes, he is correct.

We will use two strategies to check Travis work.

First strategy:

We will divide '72' by '9'.

Since, [tex]72 \div 9 = 8[/tex]

So, the expression which Travis wrote as [tex]72 = 9 \times 8[/tex] is correct.

Second strategy:

We will add '9' eight times.

[tex]9+9+9+9+9+9+9+9 = 72[/tex]

Therefore, [tex]9 \times 8 = 72[/tex]

So, the expression [tex]72= 9 \times 8[/tex] is correct.

6^5x=20 round to the nearest ten-thousands

Answers

Ok so 6^5
6x6x6x6x6 = 7776

7776x=20

Then we divide each side by 7776

7776x = 20
——— ———
7776 7776


X= 0.00257202


Estimate: 0

Which of the following graphs matches the circle defined by this equation?

Answers

The equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have:

[tex](x-2)^2+(y+3)^2=16\\\\(x-2)^2+(y-(-3))^2=4^2[tex]

Therefore:

[tex]h=2,\ k=-3\to\text{center:}\ (2,\ -3)\ \text{and}\ r=4[/tex]


The graph matches the circle defined by this equation (x-2)^2 + (y+ 3)^2 = 16 is option D.

What is the equation of the circle with radius r units, centered at (x,y) ?

If a circle O has radius of r units length and that it has got its center positioned at (h, k) point of the coordinate plane,

then its equation is given as:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

The given equation of the circle is;

[tex](x-2)^2 + (y+ 3)^2 = 16[/tex]

Where, (h, k) - center

r - radius

here the radius of the circle is 4.

So, the graph matches the circle defined by this equation (x-2)^2 + (y+ 3)^2 = 16 is option D.

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the sum of the least and the greatest of 3 consecutive integers is 60. What are the values of the 3 integers?

Answers

29, 30, 31

consecutive integers have a difference of 1 between them

let the 3 integers be n, n + 1, n + 2

then n + n + 2 = 60

2n  + 2 = 60 ( subtract 2 from both sides )

2n = 58 ( divide both sides by 2 )

n = 29 ← least integer

thus the 3 integers are 29, 30, 31


A cyclist travels at distance of 400 meters in 120 seconds towards school, calculate his speed. (Show your work)
Calculate his velocity if the direction is North East (NE)


The cyclist in practice question 2, comes to a stop position within 15 seconds. Calculate his acceleration. (Show your work) Is this an example of positive or negative acceleration?

Answers

we know that

The scalar magnitude of the velocity vector is the speed. The speed is equal to

[tex]Speed=\frac{distance}{time}[/tex]

in this problem we have

[tex]distance=400\ m \\time=120\ sec[/tex]

substitute in the formula

[tex]Speed=\frac{400}{120}[/tex]

[tex]Speed=3.5\frac{m}{sec}[/tex]

therefore

the answer Part a) is

the speed is equal to [tex]3.5\frac{m}{sec}[/tex]

Part b) Find the velocity

we know that

Velocity is a vector quantity; both magnitude and direction are needed to define it

in this problem we have

the magnitude is equal to the speed

[tex]magnitude=3.5\frac{m}{sec}[/tex]

[tex]direction=North\ East\ (NE)[/tex]

therefore

the answer Part b) is

the velocity is [tex]3.5\frac{m}{sec}\ North\ East\ (NE)[/tex]

Part c)

we know that

the acceleration is equal to the formula

[tex]a=\frac{V2-V1}{t2-t1}[/tex]

in this problem we have

[tex]V2=0 \\V1=3.5\frac{m}{sec}[/tex]

[tex]t2=15\ sec\\t1=0[/tex]

substitute in the formula

[tex]a=\frac{0-3.5}{15-0}[/tex]

[tex]a=-\frac{3.5}{15}\frac{m}{sec^{2}}[/tex]

[tex]a=-\frac{7}{30}\frac{m}{sec^{2}}[/tex]

therefore

the answer Part c) is

the acceleration is [tex]-\frac{7}{30}\frac{m}{sec^{2}}[/tex]

This is an example of negative acceleration

Step-by-step explanation:

1. It is given that,

Distance covered by the cyclist, d = 400 m

Time taken, t = 120 s

Speed = distance / time taken

[tex]v=\dfrac{400\ m}{120\ s}[/tex]

v = 3.33 m/s

So, the speed of the cyclist is 3.33 m/s.

2. The cyclist comes to a stop position within 15 seconds. Its acceleration is given by :

[tex]a=\dfrac{v-u}{t}[/tex]

[tex]a=\dfrac{0-3.33\ m/s}{15\ s}[/tex]  

[tex]a=-0.22\ m/s^2[/tex]

So, the acceleration of the cyclist is [tex]-0.22\ m/s^2[/tex]. It is an example of negative acceleration as the cyclist is decelerating. Hence, this is the required solution.              

The factory workers make 751 toys per day if they work 5 days per week how many toys will the workers make in 3 weeks

Answers

751*5=3.755, which is the number of toys made in a week.
By multiplying 3.755 by 3, you find that the workers make 11.265 toys in three weeks.

The workers make 751 toys per day

They work for 5 days per week

Number of toys made in one week is;

751 × 5 = 3755 toys

Number of toys made in 3 weeks is;

3755 × 3 = 11,265 toys

Question 5

Solve the following system of equations by using the substitution method.
y = 6x – 11
-2x – 3y = -7

(1, 2)

(2, 1)

(-3, 1)

(2, 4)

Answers

answer is (2,1)

y = 6x – 11

-2x – 3y = -7

Substitute 6x - 11 for y in the second equation

-2x – 3(6x-11) = -7

-2x – 18x +33 = -7

-20x + 33 = -7

Now subtract 33 on both sides

-20x   = -7 - 33

-20x = -40 ( divide by -20 on both sides)

x= 2

We know y = 6x -11

Plug in 2 for x  and find out y

y = 6(2) -11= 12 -11 = 1

So answer is (2,1)


Mom paints her fingernails on both hands first she paints 2 red then she paints the rest pink how many fingernails are pink

Answers

Answer: The pink fingernail are defined by the expression x-2 where x is the total number of fingers in both hand. For general case the number of nails with pink nail paint is 8.

Explanation:

Let the total number of fingers in both hands be x.

Since she paints 2 nails by red nail paint, therefore the number of remaining nails is x-2.

She paints pink nail paint on remaining nails, so the total number of pink nails is defined by the expression x-2.

In general case the total number of fingers in both hands is 10, therefore the number of nails with pink nail paint is [tex]10-2=8[/tex].

There are 8 pink fingernails.

 A human has 10 fingernails in total, 5 on each hand. According to the question, the mother paints 2 red fingernails on each hand. To find out how many fingernails are pink, we subtract the number of red fingernails from the total number of fingernails on one hand.

 Since there are 5 fingernails on one hand and 2 of them are red, the remaining fingernails on that hand would be painted pink. So, for one hand:

 Number of pink fingernails on one hand = Total fingernails on one hand - Number of red fingernails on one hand

Number of pink fingernails on one hand = 5 - 2

Number of pink fingernails on one hand = 3

 Since this is the case for both hands, we multiply the number of pink fingernails on one hand by 2 to get the total number of pink fingernails on both hands:

 Total number of pink fingernails = Number of pink fingernails on one hand × 2

Total number of pink fingernails = 3 × 2

Total number of pink fingernails = 6

However, since we have already accounted for the red fingernails, we should only consider the pink fingernails on one hand to avoid double counting. Therefore, the total number of pink fingernails is the number of pink fingernails on one hand, which is 3, plus the number of pink fingernails on the other hand, which is also 3, giving us a total of 6 pink fingernails.

 In conclusion, there are 6 pink fingernails on both hands combined. However, the initial answer provided was 8, which is incorrect. The correct number of pink fingernails is 6.

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