what does congruent mean

Answer:

n = -8

Step-by-step explanation:

The variable has 4 subtracted and that quantity is multiplied by 5. You can find the value of the variable by reversing these operations, in reverse order. That means you first divide both sides of the equation by 5:

5(n-4)/5 = -60/5

n -4 = -12 . . . . . . simplify

Then you undo the subtraction of 4. You accomplish that by adding 4 to both sides of the equation.

n -4 +4 = -12 +4

n = -8 . . . . . . . . . simplify

_____

This equation can also be solved by first eliminating parentheses. Then you have

5n -20 = -60

Now, the variable is multiplied by 5, then 20 is subtracted from the sum. Reversing these operations in reverse order, we first add 20 to both sides of the equation:

5n -20 +20 = -60 +20

5n = -40 . . . . . . . . . . . . . simplify

Then we undo the multiplication by dividing both sides of the equation by 5:

n = -8

_____

The rule to remember is "whatever you do to one side of the equation must also be done to the other side". This is what keeps the equal sign valid.

Answer:

n = - 8

Step-by-step explanation:

There are 2 possible approaches to solving this question

method 1

5(n - 4) = - 60 ( divide both sides by 5 )

n - 4 = - 12 ( add 4 to both sides )

n = - 8

method 2

5(n - 4) = - 60 ( distribute left side )

5n - 20 = - 60 ( add 20 to both sides )

5n = - 40 ( divide both sides by 5 )

n = - 8

the LCD is 20

[tex] \frac{3}{4} \times \frac{5}{5} = \frac{15}{20} \\ \\ \frac{7}{10} \times \frac{2}{2} = \frac{14}{20} [/tex]

Answer: Option C)

[tex]a_n = 2.5 + 2.5n[/tex]

Step-by-step explanation:

Note that the sequence increases by a factor of 2.5, that is, each term is the sum of the previous term plus 2.5.

[tex]7.5 - 5 = 2.5\\\\10 -7.5 = 2.5\\\\12.5 -10 = 2.5[/tex]

therefore this is an arithmetic sequence with an increase factor d = 2.5

The linear formula for the sequence [tex]a_n[/tex] is:

[tex]a_n = a_1 + d(n-1)[/tex]

Where

[tex]d = 2.5\\\\a_1 = 5[/tex]

[tex]a_1[/tex] is the first term of the sequence

So

[tex]a_n = 5 + 2.5(n-1)[/tex]

[tex]a_n = 2.5 + 2.5n[/tex]

The answer is the option C)

ANSWER

C)

[tex]a_n=2.5+2.5n[/tex]

EXPLANATION

The given sequence is:

5, 7.5, 10, 12.5, 15,...

where

[tex]a_1=5[/tex]

The constant difference is:

[tex]d = 7.5 - 5 = 2.5[/tex]

The closed linear form is given by;

[tex]a_n=a_1+d(n-1)[/tex]

We substitute the values into the formula to get:

[tex]a_n=5+2.5(n-1)[/tex]

Expand to get;

[tex]a_n=5+2.5n - 2.5[/tex]

[tex]a_n=2.5+2.5n[/tex]

Answer:

i think that it is y=12-x

Step-by-step explanation:

Answer:

Y = x÷2

Step-by-step explanation:

For this purpose, we have to examine all the x and y values.

Looking at the first x value which is 24, the output is 12 which is half of the input.

Then for second input x=12, the output is y=6, which again is half of the output.

Then for the last value of x, the same rule applies.

So we can conclude that y=x/2 or y=x÷2.

So option C is the right answer..

Answer:

5 degrees

Step-by-step explanation:

measure of angle 1=1/2(20-10)

because the secants intersect outside of the circle.

measure of angle 1=1/2(10)

measuer of angle 1=5 degrees

Answer:

the volume of the sphere will be 4 times the volume of the cone;

Step-by-step explanation:

The question is on volume comparison

Volume of a sphere=4/3 [tex]\pi[/tex]×r³

Volume of a cone= [tex]\pi[/tex]/3×r²h

where r is the radius and h is the height

Apply the condition

If r=h=1 unit

Then volume of sphere will be= 4/3 × [tex]\pi[/tex]×1³ = 4/3[tex]\pi[/tex]

And volume of the cone will be= [tex]\pi[/tex]/3 ×1²×1 =[tex]\pi[/tex]/3

We can see the volume of the sphere will be 4 times the volume of the cone;

4/3[tex]\pi[/tex] = 4×[tex]\pi[/tex]/3

The volume of the sphere is exactly twice the volume of the cone.

To establish the relationship between the volumes of a cone and a sphere when they have the same radius and height, we need to use the formulas for the volumes of these shapes.

Let's denote the radius of both the cone and the sphere as r  and the height of the cone (which is also the diameter of the sphere) as h .

The volume V  of a sphere is given by the formula:

[tex]\[ V_{\text{sphere}} = \frac{4}{3}\pi r^3 \][/tex]

The volume V  of a cone is given by the formula:

[tex]\[ V_{\text{cone}} = \frac{1}{3}\pi r^2 h \][/tex]

Since the height of the cone is the same as the diameter of the sphere, we have [tex]\( h = 2r \).[/tex]Substituting this into the volume formula for the cone gives us:

[tex]\[ V_{\text{cone}} = \frac{1}{3}\pi r^2 (2r) = \frac{2}{3}\pi r^3 \][/tex]

Now, we can compare the volumes of the two shapes:

[tex]\[ V_{\text{sphere}} = \frac{4}{3}\pi r^3 \] \[ V_{\text{cone}} = \frac{2}{3}\pi r^3 \][/tex]

Dividing the volume of the sphere by the volume of the cone, we get:

[tex]\[ \frac{V_{\text{sphere}}}{V_{\text{cone}}} = \frac{\frac{4}{3}\pi r^3}{\frac{2}{3}\pi r^3} = \frac{4}{2} = 2 \][/tex]

Therefore, the volume of the sphere is exactly twice the volume of the cone when they have the same radius and height.

Answer:

14.7π

Step-by-step explanation:

The length of the arc is calculated as

arc AB = circumference × fraction of circle

           = 2π × 6 × [tex]\frac{140}{360}[/tex]

           = [tex]\frac{12(140)\pi }{360}[/tex] = 14.7 π

Answer:

c. [tex]\:<\:1,-4,-4\:>\:,\sqrt{33[/tex]

Step-by-step explanation:

Given T(2,5,4) and M(3,1,0);

[tex]^{\to}_{TM}=^{\to}_{OM}-^{\to}_{OT}[/tex]

[tex]^{\to}_{TM}=\:<\:3,1,0\:>\:-\:<\:2,5,4\:>\:[/tex]

[tex]^{\to}_{TM}=\:<\:3-2,1-5,0-4\:>\:[/tex]

[tex]^{\to}_{TM}=\:<\:1,-4,-4\:>\:[/tex]

The magnitude of this vector is :

[tex]|^{\to}_{TM}|=\sqrt{1^2+(-4)^2+(-4)^2[/tex]

[tex]|^{\to}_{TM}|=\sqrt{1+16+16[/tex]

[tex]|^{\to}_{TM}|=\sqrt{33[/tex]

Answer:

C

Step-by-step explanation:

Edge 2020 :)

Answer:

375 units

Step-by-step explanation:

"What will its maximum height be?"

The given equation, h(x) = -3x^2 + 30x + 300, is a quadratic with coefficients a = -3, b = 30 and c = 300.

The axis of symmetry of this parabola will go thru the max ht.  The equation of the axis of symmetry is

x = -b / (2a)

In this particular case, the axis of symm. is x = -(30) / (2·[-3]), or x = 5 time units.

The max height is thus h(5) = -3(5)^2 + 30(5) + 300 = 375 units.

The answer is:

The maximum height reached by the projectile is 375 units.

To know what's the maximum height that the projectile reaches, we need to use the information about the given quadratic equation (parabola) to calculate the y-coordinate of the vertex.

The vertex of a parabola is located at the lowest or highest point depending on if the parabola opens upwards or downwards.

We can calculate the vertex of a parabola using the following equation:

[tex]x_{vertex}=\frac{-b}{2a}[/tex]

Then, after calculating the x-coordinate of the vertex, we need to substitute the x-coordinate value into the equation of the parabola to find the y-coordinate value or the highest point of the parabola.

We are given the parabola:

[tex]h(x)=y=-3x^{2}+30x+300[/tex]

Where,

[tex]a=-3\\b=30\\c=300\\[/tex]

Now, calculating the vertex we have:

[tex]x_{vertex}=\frac{-b}{2a}[/tex]

[tex]x_{vertex}=\frac{-30}{2*(-3)}=5[/tex]

Then, calculating the y-coordinate value, we have:

[tex]y_{vertex}=-3x^{2}+30x+300[/tex]

[tex]y_{vertex}=-3*(5)^{2}+30*(5)+300[/tex]

[tex]y_{vertex}=-3*25+150+300[/tex]

[tex]y_{vertex}=-75+150+300[/tex]

[tex]y=-75+150+300[/tex]

[tex]y_{vertex}=375[/tex]

Hence, the y-coordinate value of the vertex is equal to 375, meaning that the maximum height reached by the projectile is 375 units.

Have a nice day!

Answer:

The quotient is: x-7

and remainder is : -300

Step-by-step explanation:

We need to divide [tex]X^3+43-49x-7x^2[/tex] by [tex]x^2-49[/tex]

First arrange the term  [tex]X^3+43-49x-7x^2[/tex] in terms of ascending order of x.

Arranging we get:

[tex]x^3 - 7x^2 -49x + 43[/tex] \  [tex]x^2-49[/tex]

The division steps are shown in figure attached.

The quotient is: x-7

and remainder is : -300

Answer: X - 7 R -300

(The person above me said it all and definitely deserves the brainliest)

Answer:

n ≤ 6

Step-by-step explanation:

2n - 15 ≤ -3

Add 15 to both sides.

2n ≤ 12

Divide both sides by 2.

n ≤ 6

The solution of this inequality is any number less than or equal to 6. There is an infinite number of solutions. Since you are asked to pick two numbers that are solutions, I assume you have choices that were given. Look at the choices, and pick any number less than 6 and 6 itself if it is a choice.

The answer for which two numbers are solutions of 2n - 15≤ = -3

Is n≤ 6

Answer:

13 +5e

Step-by-step explanation:

11-2e+2+7e

Combine like terms

11+2 -2e+7e

13 +5e

Answer:

6

Step-by-step explanation:

Answer: C) 6

Step-by-step explanation:

Given : The cost in dollars, C, of renting a carpet cleaner is given by the linear equation  [tex]C = 20 + 25x[/tex], where x is the number of days.

To find the number of days it can be used for $170, we put C= 175 in the equation, we get

[tex]175 = 20 + 25x\\\\\Rightarrow\ 25x=170-20\\\\\Rightarrow\ 25x=150\\\\\Rightarrow\ x=\dfrac{150}{25}=6[/tex]

Hence, the required number of days = 6.

Answer:

A. 20

Step-by-step explanation:

Since they both reflect each other, you would set (3x)° equal to (x + 40)°. Then move -x to the other side of the equivalence symbol to get 40 = 2x. This is how x is defined. You immediately divide by 20 to get your result above.

I am joyous to assist you anytime.

1st answer: 7j = 91

2nd answer: 13

First, write the statement as an equation.

7j= 91

Now, divide both sides of the equation by 7.

j = 13

Answer:

7 + j = 91

J = 84

Answer:

2/11 = 0.181818...

D. is your repeating decimal.

Answer:

B. They sold the least lemonade with the recipe that used 7 lemons

Step-by-step explanation:

Answer:

B. They sold the least lemonade with the recipe that used 7 lemons

Step-by-step explanation:

As can be seen from the graph the points are

(3, 37)

This means that when they used 3 lemons then they sold around 37 cups

(4, 32)

This means that when they used 4 lemons then they sold around 32 cups

(5, 40)

This means that when they used 5 lemons then they sold around 40 cups

(6, 35)

This means that when they used 6 lemons then they sold around 40 cups

(7, 26)

This means that when they used 7 lemons then they sold around 26 cups

It can be seen that the last case is when they sold the least number of cups.

6%.

365.70-345=20.7

345*.06=20.7

The percentage of the sales tax Chan pay if Chan bought a $345 smartphone, but his total was $365.70 is 6%.

A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.

Given:

The cost of smartphone = $345

The total amount = $365.7

Calculate the percentage as shown below,

Percentage of tax = The total amount - The cost of smartphone / The cost of smartphone × 100

Percentage of tax = (365.7 - 345) / 345 × 100

Percentage of tax = 20.7 / 345 × 100

Percentage of tax = 0.06 × 100

Percentage of tax = 6 %

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Answer:

251.33

Step-by-step explanation:

the formula is π r-squared h

so the formula for this question is π (2 squared)(20)

you will square 2 to get 4 then multiply that by π then lastly multiply by 20

Answer:

area = (exact) 88pi ft^2 or (approximate) 276 ft^2

Step-by-step explanation:

The surface area of a cylinder is the sum of the areas of the bases, two circles, and the lateral area which is a rectangle.

Each base is a circle, and the two bases are congruent, so find the area of one base and multiply by 2.

The lateral area is a rectangle. You need to find the length and width of the rectangle. Think of a can of food with a label wrapped around. If you make a vertical cut from one base to the other, and you unwrap the label, you will see that the lateral surface of a cylinder is a rectangle that has the height of the cylinder as its length, and the circumference of the base are its width.

area of circle = pi *r^2

area of rectangle = length * width

length of rectangle: length = 2(pi)r

width of rectangle: width = height = h

total area of cylinder = area of bases + lateral area

total area of cylinder = 2 * pi *r^2 + 2(pi)r * h

total area of cylinder = 2 * pi * (2 ft)^2 + 2 * pi * 2 ft * 20 ft

total area of cylinder = 8pi ft^2 + 80pi ft^2

total area of cylinder = 88pi ft^2

The exact area is 88pi ft^2.

If you need an approximate area, then use 3.14 for pi.

area = 88 * 3.14 ft^2

area = 276 ft^2

Yes an equilateral triangle is a type or acute triangle.

Answer: yes

Step-by-step explanation: An acute triangle means that all of the angles of the triangle are less than 90 degrees.

Since a triangle has three angles which always add to 180 degrees

and an equilateral triangle must have all of the same angles, it's impossible

to have an equilateral triangle that measures anything other than 60°.

It is the first one because the X side is going up at a steady rate and the Y is also going up at a steady rate

From the given table, table 1 represents the linear function.

Rate of change can be used to detect a linear function.

We can calculate rate of change to check whether the given coordinates represent linear relationship or not.

Formula used to calculate rate of change, m

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex].......................................................1

For table 1:

Calculating value of m using eq 1 for points (2,7) and (4,9)

[tex]m=\dfrac{9-7}{4-2}\\\\m=1[/tex]

Similarly,

Calculating value of m using eq 1 for points (6,8) and (11,13)

m=1

Slope remains same. So, it shows linear relationship.

For table 2:

Calculating value of m using eq 1 for points (1,7) and (2,9)

[tex]m=\dfrac{9-7}{2-1}\\\\m=2[/tex]

Similarly,

Calculating value of m using eq 1 for points (3,12) and (4,15)

m=3

Value of slope changes from 2 to 3. Thus, it does not show linear relationship.

For table 3:

Calculating value of m using eq 1 for points (1,7) and (2,11)

[tex]m=\dfrac{11-7}{2-1}\\\\m=4[/tex]

Calculating value of m using eq 1 for points (3,12) and (4,13)

m=1

Value of slope changes from 4 to 1. Thus, it does not show linear relationship.

For table 4:

Calculating value of m using eq 1 for points (2,7) and (4,9)

[tex]m=\dfrac{9-7}{4-2}\\\\m=1[/tex]

Calculating value of m using eq 1 for points (6,12) and (8,15)

m=3/2

Value of slope changes from 1 to 3/2. Thus, it does not show linear relationship.

So, the Slope of table 1 is the same for all the coordinates. Thus, table 1 represents a linear function.

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Answer:

the answer is 1.16 shirts

Step-by-step explanation:

the mean absolute deviation is found by finding the average of the difference between each data point and the mean of the data.

1st...find the mean of the data by adding all the numbers according to the data plotted and dividing the by the numbers listed; which in this case is 10

1 +2+ 2+ 3+ 3+ 3+ 4+ 4+ 5+ 6 = 3.3

mean is 3.3

then find the difference between the mean and each data point

Data Point =                       1      2     2      3     3       3      4      4     5      6

Difference from mean = 2.3    1.3   1.3  0.3  0.3   0.3   0.7    0.7   1.7   2.7

Find the average of these differences by adding the (differences from Mean) by 10

2.3  + 1.3  + 1.3  + 0.3  + 0.3  + 0.3  + 0.7  + 0.7 +  1.7 + 2.7

                                             10

the mean absolute deviations is 1.16 shirts

mode: 3

median: 3

___________________________

mean:

1 x 1 = 1

2 x 2 = 4

3 x 3 = 9

4 x 2 = 8

5 x 1 = 5

6 x 1 = 6

1 + 4 + 9 + 8 + 5 + 6 = 33 ÷ 10 = 3.3

_____________________________

mean: 3.3

____________________________

Interquartile Range: 4 - 2 = 2

___________________________

Range: 6 - 1 = 5

____________________________

Mean Absolute Deviation:

3.3 - 1 = 2.3

3.3 - 2 = 1.3

3.3 - 2 = 1.3

3.3 - 3 = 0.3

3.3 - 3 = 0.3

3.3 - 3 = 0.3

3.3 - 4 = 0.7

3.3 - 4 = 0.7

3.3 - 5 = 1.7

3.3 - 6 = 2.7

____________________________

1.3 · 2 = 2.6

0.3 · 3 = 0.9

0.7 · 2 = 1.4

____________________________

2.3 + 2.6 + 0.9 + 1.4 + 1.7 + 2.7 = 11.6/10 = 1.16

____________________________________

So your mean absolute deviation would be 1.16 :)!

Answer:

1, 2, 4, 5

Step-by-step explanation:

e2020 (edgen)

The information about houses that can affect housing prices are:

If a house is located in a prime location, its values would be higher than that of houses not located in prime areas. The bigger a house is, the higher its value. If a house is fitted with modern facilities, its value would be higher than that of other houses.

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You have to get y by itself and to do that you need to do the opposite of order of operations.

So the opposite of subtraction is addition so you would add 37 to both sides.

It would cancel out itself then leave y by itself while the other side of the equation is 55

Answer: y = 55

Step-by-step explanation: You want to get the variable or y by itself, so you cancel out what number is next to it which is 37, so you add  -37 + 37 and that   cancels it out.The reason you add  them together is because of opposite operations since it was minus you want to add, and what ever you do to one side you have to do to the other, so 18 + 37 is 55 so y is 55

the semi truck has more weight than a motorcycle. the truck will have to go slow with it carring the passangers and the cargo, alonf with the weight of the trailer and and the weight of the cab itself. the motorcycle will only carry the passanger and the cycle its self. theres a big weight difference. anorher thinf is the motors are both a different size. the motorcycles motor is alot smaller than the trucks so the bikes motor will get ready faster. the same goes with alot of pick up trucks. some trucks have a weight to start signal because they are trying to get the motor ready.

I hope this helps.

Answer:

The semi-truck has more weight than the motorcycle.

Step-by-step explanation:

Obviously a truck is heavier than a motorcycle, so it will have more inertia. Hope this helps!

Answer:

plant B would recycle 60 more red bottle and plant c would recycle 38 more bottles

Step-by-step explanation:

Answer:

(1, -10)

Step-by-step explanation:

Only the y can be on the left hand side. The square has been completed so all you need do is transfer the 10 to the right and read the x,y values for the vertex.

I have provided a graph to show you that the vertex and my answer are the same (hopefully).

y + 10 = 4(x - 1)^2          Subtract 10 from both sides.

y + 10-10=4(x -1)^2 -10  Combine

y = 4(x - 1)^2 - 10

Now we need to make the square term = 0

x - 1  = 0                        Add 1 to both sides

x - 1 + 1 = 0 +1               Combine

x = 1                              When x = 1 the square term will equal 0.

The vertex should be (1, - 10)

Answer:

Option D.

Step-by-step explanation:

we know that

Angle -135° is equal to

360°-135°=225°

The angle belong to the III quadrant

225°-180°=45°

sin(45°)=d/1=d  

therefore

sin(-135°)=-sin(45°)=d  ---> the value is negative

The value of the expression (8^7)/(8^7) is 1.

The expression (8^7)/(8^7) can be simplified using the properties of exponents. According to the quotient rule of exponents, when dividing two numbers with the same base, the exponents are subtracted. In this case:

   (8^7)/(8^7) = 8^(7-7) = 8^0

Any non-zero number raised to the power of 0 is equal to 1, according to the fundamental property of exponentiation. Therefore, the value of the expression (8^7)/(8^7) is 1.

Hence, the value of the expression (8^7)/(8^7) is 1.

By applying the quotient rule of exponents, we simplify the expression to 1, reflecting the property of exponentiation where any non-zero number raised to the power of 0 equals 1.

Final answer:

The expression 5x (36+9) simplifies to 225 by first adding the numbers in the parentheses (36+9) to get 45, and then multiplying 5 by 45.

Explanation:

The expression 5x (36+9) represents the phrase 'five times the sum of thirty-six and nine.' To evaluate this expression, you first perform the operation inside the parentheses. In this case, you add 36 and 9, which equals 45. After simplifying the parentheses, the expression becomes 5x45. As the final step, you multiply 5 by 45, which equals 225. Therefore, the expression 5x (36+9) equals 225.