carlo is 175 cm tall while his friend reggie is 1680mm tall. after three years carlo grew by 40mm and reggie grew by 7cm. which of the two is taller after a year? how tall in centimeters

We can use the formula for the equation of a line to determine any missing values. The formula is:

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y=mx+b

where $m$ is the slope of the line and $b$ is the y-intercept.

We can use the given data points to calculate the slope of the line:

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change in y

change in x

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2

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1

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2

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m=

change in x

change in y

​

=

x

2

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−x

1

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y

2

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−y

1

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where $(x_1, y_1)$ and $(x_2, y_2)$ are any two points on the line. Let's use the points $(-9, 3)$ and $(-6, 2)$:

\begin{align*}

m &= \frac{y_2 - y_1}{x_2 - x_1} \

&= \frac{2 - 3}{-6 - (-9)} \

&= \frac{-1}{3}

\end{align*}

Now we can use the slope-intercept form of the equation of a line to determine any missing values. Let's go through each option:

a. Missing $x:-2$, Missing $y:0$

We can use the formula $y = mx + b$ with $m = -\frac{1}{3}$ and $b = 3$ (substitute the coordinates of the point $(-9, 3)$) to find the y-value when $x = -2$:

\begin{align*}

y &= mx + b \

&= -\frac{1}{3} \cdot (-2) + 3 \

&= \frac{7}{3}

\end{align*}

So the missing value of $y$ when $x = -2$ is $\boxed{\frac{7}{3}}$.

b. Missing $x:0$, Missing $y:1$

We can use the formula $y = mx + b$ with $m = -\frac{1}{3}$ and $b = 3$ (substitute the coordinates of the point $(-9, 3)$) to find the y-intercept:

\begin{align*}

y &= mx + b \

3 &= -\frac{1}{3} \cdot (-9) + b \

3 &= 3 + b \

b &= 0

\end{align*}

So the y-intercept is $0$. Now we can substitute $b = 0$ and $m = -\frac{1}{3}$ into the formula $y = mx + b$ to find the y-value when $x = 0$:

\begin{align*}

y &= mx + b \

&= -\frac{1}{3} \cdot 0 + 0 \

&= 0

\end{align*}

So the missing value of $y$ when $x = 0$ is $\boxed{0}$.

c. Missing $x:-2$, Missing $y:2$

We can use the formula $y = mx + b$ with $m = -\frac{1}{3}$ and $b = 3$ (substitute the coordinates of the point $(-9, 3)$) to find the y-value when $x = -2$:

\begin{align*}

y &= mx + b \

&= -\frac{1}{3} \cdot (-2) + 3 \

&= \frac{7}{3}

\end{align*}

So the missing value of $y$ when $x = -2$ is $\boxed{\frac{7

Answer:

Step-by-step explanation:

r=12 in

dr=±32

A=πr²

dA=2 πr×dr=2π×12×1/32=3π/4

Possible error in computing the area=3π/4 ~square~inches.

Answer:

Therefore, the height of the rectangular prism is approximately 13 meters.

Step-by-step explanation:

Let's call the height of the rectangular prism "h". We know that the base area is 54 m², which means that the product of the length "l" and the width "w" is 54. In other words:

l × w = 54

We also know that the volume of the rectangular prism is 702 m³, which means:

l × w × h = 702

We can use the first equation to solve for one of the variables, for example:

w = 54 / l

Substituting this expression for "w" into the second equation, we get:

l × (54 / l) × h = 702

Simplifying and canceling the "l" terms, we get:

54h = 702

Dividing both sides by 54, we get:

h = 702 / 54

Simplifying this expression, we get:

h ≈ 13

Therefore, the height of the rectangular prism is approximately 13 meters.

Answer:

AB = 14 units

BC = 11 units

CD = 14 units

AD = 11 units

Step-by-step explanation:

d=√((x2-x1)²+(y2-y1)²)

AB= (-7,6)-(7,6) √((7+7)²+(6-6)²)=√((14)²+(0)²)=√(196+0)=√(196)=14

BC= (7,6)-(7,-5) √((7-7)²+(-5-6)²)=√((0)²+(-11)²)=√(0+121)=√(121)=11

CD= (7,-5)-(-7,-5) √((-7-7)²+(-5+5)²)=√((-14)²+(0)²)=√(196+0)=√(196)=14

AD= (-7,-5,)-(-7,6) √((-7+7)²+(6+5)²)=√((0)²+(11)²)=√(0+121)=√(121)=11

Answer:

5x + 7(x + 10.80) = 210.00

Step-by-step explanation:

Let x be the cost of a pencil in dollars. Then, the cost of a notebook is 10.80 dollars more, which is x + 10.80 dollars.

Aldrin bought 5 pencils and 7 notebooks, so the total cost is:

5x + 7(x + 10.80) = 210.00

Simplifying and solving for x, we have:

5x + 7x + 75.60 = 210.00

12x = 134.40

x = 11.20

Therefore, a pencil costs 11.20 dollars and a notebook costs 10.80 dollars more, which is 22.00 dollars.

We can check that the total cost of 5 pencils and 7 notebooks at these prices is indeed 210.00 dollars:

5 pencils * 11.20 dollars/pencil + 7 notebooks * 22.00 dollars/notebook = 56.00 dollars + 154.00 dollars = 210.00 dollars

Linear Scale Factor:

1) Enlargement. Scale Factor = 18/6 = 3

2) Reduction. Scale factor = 6/12 = 1/2

Answer:

  (-1, 2) and (4, -8)

Step-by-step explanation:

You want the ordered pairs (x, f(x)) that satisfy both equations ...

Equating the two expressions for f(x), we have ...

  x² -5x -4 = -2x

  x² -3x -4 = 0

  (x -4)(x +1) = 0

  x = 4 or -1

Corresponding values of f(x) are ...

  f(x) = -2{4, -1} = {-8, 2}

Ordered pair solutions are ...

  (x, f(x)) = (-1, 2) and (4, -8)

Asymmetric: Since, for instance, (2,3) is in R but (3,2) is not, R is not asymmetric. No element in A is connected to itself under R, making R irreflexive.

The collection of output values that such a function of relation can produce is referred to as the range in mathematics. It is the distinction between the largest or smallest values within an ensemble of data or a collection of all conceivable function or relation output values.

In other terms, it is the range of possible values for a variable. For instance, the range is 21 - 3 = 18 if the integers are 3, 7, 12, 15, and 21. The set of all value of y which may be produced by a function f(x) for the given subject area of x values is known as the range.

given

We will now examine the many characteristics of the relation R:

As no element in A is connected to itself under R, R is not reflexive. For instance, R does not support (2,2).

R is not symmetric since, for instance, (3,2) is not in R yet (2,3) is.

R is transitive because, for instance, the existence of (2,3) and (3,5) in R entails the existence of (2,5) in R.

Equivalence: As R is not reflexive or symmetric, it is not an equivalence relation.

Asymmetric: Since, for instance, (2,3) is in R but (3,2) is not, R is not asymmetric. No element in A is connected to itself under R, making R irreflexive.

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Answer: $3.60

Step-by-step explanation: $30(Item Purchased)x0.12(Sales Tax)=$3.60(Sales Tax Rate for a 12% Sales Tax State.)

The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is: P(Correctly placed and Plastic #4) = 15/100 = 0.15 is 15% chance.

What is probability?

To find the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle, we need to divide the number of bottles that meet both conditions by the total number of bottles.

Let's say Sandra examined 100 bottles, and 60 of them were properly placed, and 25 of them were Plastic #4 bottles, and 15 of those Plastic #4 bottles were also properly placed.

Then, the number of bottles that meet both conditions is 15, and the total number of bottles is 100. Therefore, the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is:

P(Correctly placed and Plastic #4) = 15/100 = 0.15

So, there is a 15% chance that a randomly selected bottle is both correctly placed and a Plastic #4 bottle.

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Complete question is: Curious about people's recycling behaviors, Sandra put on some gloves and sifted through some recycling and trash bins. She kept count of the plastic type of each bottle and which bottles are properly dispensed. The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is: P(Correctly placed and Plastic #4) = 15/100 = 0.15 is 15% chance.

The area and the circumference of the circle would be 4π square kilometers and 4π kilometers respectively.

The area of a circle with a radius r is given by:

The circumference of a circle with a radius r is given by:

Given that the radius of the circle is 2km, we can substitute r = 2 into these formulas to find the area and circumference:

In other words, the area and the circumference of the circle are 4π square kilometers and 4π kilometers respectively.

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The correct graph of the function [tex]y=-1\sqrt{x-2-3}[/tex] is attached as picture below.

To graph a function, we need to first determine the domain and range of the function. The domain is the set of all possible input values for the function, while the range is the set of all possible output values. Once we have determined the domain and range, we can plot the points on a graph.

To plot the graph, we can choose a set of values for the independent variable (usually denoted as x) and use the function to find the corresponding values of the dependent variable (usually denoted as y). We can then plot these points on the graph and connect them to create a curve that represents the function.

Graph using the end point and a few selected points.

x       y

2    − 3

3     −4

4     −4.41

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Answer:

70°

Step-by-step explanation:

280°÷4x

what is x?

x=70°

Answer:

63

Step-by-step explanation:

we divided 18÷2=9

and we multiply 9×7=63

Answer:

[tex]p(a) = \frac{7}{100} [/tex]

Step-by-step explanation:

Given:

7 red marbles

18 blue marbles

Total number of marbles: 7 + 18 = 25

All outcomes:

[tex]n = \frac{25 \times 24}{2 \times 1} = 300[/tex]

Let's name the event A:

A - "both marbles are red"

Event's A favorable outcomes:

[tex]m(a) = \frac{7 \times 6}{2 \times 1} = 21[/tex]

[tex]p(a) = \frac{m(a)}{n} = \frac{21}{300} = \frac{7}{100} [/tex]

The average cost per day is $90 and the average cost per km is $0.655.

To calculate the average cost per day, we need to first calculate the total cost of renting the car for both occasions and divide it by the total number of days.

The total cost of renting the car for both occasions is $180 + $180 = $360. The total number of days is 4 (2 days for each occasion).

Therefore, the average cost per day is $360 ÷ 4 = $90.

To calculate the average cost per km, we need to first calculate the total cost of renting the car for both occasions and divide it by the total number of kilometers driven.

The total cost of renting the car for both occasions is $180 + $180 = $360. The total number of kilometers driven is 550km (150km for the first occasion + 400km for the second occasion).

Therefore, the average cost per km is $360 ÷ 550km ≈ $0.655.

Correct question is " Eleni rents a car on two separate occasions. The first time, she paid $180 for 2 days and 150km. The next time, she paid $180 for 2 days and 400km. What is the average cost per day? What is the average cost per km?"

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Answer:

9) x = 12 cm

10) x = 10.4 ft (Rounded)

11) y = 39.7 in (Rounded)

Step-by-step explanation:

Just use Pythagorean theorem

Answer and Explanation:

We can solve for x in these questions using the Pythagorean Theorem:

a² + b² = c²,

where a and b are the legs (shorter sides) of a right triangle, and c is its hypotenuse (longest side).

Applying this theorem to the problems at hand:

9. We are using (10 / 2) as one of the legs.

(10 / 2)² + x² = 13²

↓ simplifying division

5² + x² = 13²

↓ subtracting 5² from both sides

x² = 13² - 5²

↓ simplifying the right side

x² = 169 - 25

x² = 144

↓ taking the square root of both sides

x = 12

10.

6² + x² = 12²

↓ subtracting 6² from both sides

x² = 12² - 6²

↓ simplifying the right side

x² = 144 - 36

x² = 108

↓ taking the square root of both sides

x = [tex]\sqrt{108}[/tex]

↓ simplifying the square root

    [tex]\sqrt{108} = \sqrt{3 \cdot 3 \cdot 3 \cdot 2 \cdot 2} = (3\cdot 2)\sqrt{3} = 6\sqrt3[/tex]

x = 6[tex]\sqrt3[/tex]

11.

24² + 33² = y²

↓ simplifying the right side

576 + 1089 = y²

1665 = y²

↓ taking the square root of both sides

y = [tex]\sqrt{1665}[/tex]

↓ simplifying the square root

    [tex]\sqrt{1665} = \sqrt{3 \cdot 3 \cdot 5 \cdot 37} = 3\sqrt{5 \cdot 37} = 3\sqrt{185}[/tex]

y = 3[tex]\sqrt{185}[/tex]

Answer: would be great if you could give the options of the questions?

The vector b is [10, 5, 10] and the general solution for [A|b] is [1, 5, -3] + [-3, 2, -1]s

To find the vector b, we need to multiply the matrix A by the vector x and solve for b in the equation Ax = b.

So, we have:

[tex]\left[\begin{array}{ccc}1&3&-3&0&1&-2&3&5&-1\end{array}\right]\left[\begin{array}{c}1&1&-2\end{array}\right] &= \left[\begin{array}{c}10&5&10\end{array}\right][/tex]

Therefore, the vector b is [10, 5, 10].

To find the general solution of [A | b], we need to perform row reduction on the augmented matrix [A | b] and express the pivot variables in terms of the free variables.

[tex]\left[\begin{array}{ccc|c}1&3&-3&10&0&1&-2&5&3&5&-1&10\end{array}\right] &\rightarrow \left[\begin{array}{ccc|c}1&0&3&1&0&1&-2&5&0&0&0&0\end{array}\right][/tex]

The third column does not have a pivot variable, so we can express x3 in terms of the free variables.

Let s be the free variable, then we have:

x3 = -s - 3

We can now express the pivot variables in terms of s:

x1 = 1 - 3s

x2 = 5 + 2s

Thus, the general solution of [A | b] is:

[tex]\left[\begin{array}{c}x_1&x_2&x_3\end{array}\right] &= \left[\begin{array}{c}1 - 3s&5 + 2s&-s - 3\end{array}\right] \&= \left[\begin{array}{c}1&5&-3\end{array}\right] + s\left[\begin{array}{c}-3&2&-1\end{array}\right][/tex]

Therefore, the general solution of [A | b] is [1, 5, -3] + [-3, 2, -1]s

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The answer should be 2.The lower quartile of the number of absence is 2

0 is the lowest number and then 2 would be lower quartile, The 4 would be the Median or the middle of all the data 7 is the upper quartile and 10 would be the highest number of absences.

The lower quartile, also known as the first quartile, is a measure of central tendency that divides a dataset into four equal parts. It represents the point at which 25% of the data values fall below and 75% of the data values fall above. In other words, the lower quartile marks the boundary between the lowest 25% and the upper 75% of the data. It is often used in statistics to help summarize and analyze datasets, and can be helpful in identifying outliers or unusual values in the lower end of a dataset.

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the correct answer is (D) 8 units to the left. To find the translation direction and number of units, we need to find the vector that takes us from point R to point R'.

Vector RR' can be found by subtracting the coordinates of R from the coordinates of R':

RR' = R' - R = (-7, 4) - (1, 4) = (-8, 0)

This means that the translation moves 8 units to the left, since the x-coordinate of the vector is negative.

To determine the translation direction and number of units required to move R to R', we need to first find the distance between the x-coordinates of R and R'. We can do this by subtracting the x-coordinate of R from the x-coordinate of R': -7 - 1 = -8.

This tells us that we need to move R' 8 units to the left to get to R. However, the question is asking for the translation required to move R to R', not the other way around. Therefore, we need to reverse the direction and say that we need to move R 8 units to the right to get to R'.

We can confirm this by checking the y-coordinates of R and R'. We see that they are both 4, which means there is no vertical translation required. Therefore, the answer is C. 8 units to the right.

Therefore , the correct answer is (D) 8 units to the left.

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a) The temperature decreases at a rate of -4°C per km.

b) The temperature is 0°C at a height of 8km

Here we can see the graph of a relation between the height and the temperature.

We can see that the line goes downwards from left to right, this means that as the height increases, the temperature decreases.

Notice that the horizontal squares represent 1km, while the vertical ones represent 4°C, then, the temperature is decreasing at a rate of -4°C per kilometer, your answer is correct here.

At which height is the temperature zero?

the temperature is zero at the horizontal axis, we can see that the line meets the horizontal axis at a height of 8 km, so that is the answer here.

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Answer:

3.1) Para calcular la mediana de la lista de datos, primero debemos ordenarlos de menor a mayor:

2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 10, 10, 10, 10, 10, 10

Como la lista tiene un número impar de elementos (35), la mediana es el valor central de la lista, es decir, el elemento en la posición 18. En este caso, el valor de la mediana es 6.

3.2) Para calcular la media y la mediana mediante una tabla de frecuencias, primero debemos determinar las frecuencias de cada valor en la lista:

Valor Frecuencia

2 5

4 8

6 9

8 5

10 8

La media se calcula sumando todos los valores y dividiendo entre el número total de elementos:

media = (25 + 48 + 69 + 85 + 10*8) / 35 = 5.8

Para calcular la mediana, primero debemos determinar el valor que ocupa la posición central de la lista. Como el número total de elementos es impar, ese valor es el que ocupa la posición (n+1)/2, donde n es el número total de elementos. En este caso, ese valor es el que ocupa la posición (35+1)/2 = 18.

Luego, debemos encontrar el valor que ocupa la posición 18 contando los valores de la tabla de frecuencias. Podemos hacer esto sumando las frecuencias hasta alcanzar o superar la posición 18:

Valor Frecuencia Frec. Acumulada

2 5 5

4 8 13

6 9 22

8 5 27

10 8 35

Como la posición 18 está dentro del intervalo correspondiente al valor 6, la mediana es 6.

Step-by-step explanation:

The answer is (-2, -7)

Before rotated, the coordinates of P is (7,2)

Imagine if P is rotated 360° clockwise, it will come back to the initial place (7,2).

Now it is just rotated 180° clockwise, halfway of 360° clockwise. So the coordinates should be(-7,-2) after rotated 180° clockwise.

Answer:

I hope this helps :)

Step-by-step explanation:

its the correct answer

Answer:

Multiply the numerators first together then multiply the denominators together.

Step-by-step explanation:

example  1/2(4/2) =4/4 = 1

Answer:

To solve this problem, we can use the Pythagorean theorem, which relates the sides of a right triangle. Let's call the height "h" and the width "w". Then we have: w = h + 7 (since the width is 7 inches longer than the height) We also know that the diagonal measurement is 34 inches, so we can use the Pythagorean theorem to relate the height, width, and diagonal: h^2 + w^2 = d^2 Substituting the values we have: h^2 + (h+7)^2 = 34^2 Expanding and simplifying: 2h^2 + 14h - 795 = 0 Now we can solve for h using the quadratic formula: h = (-14 ± sqrt(14^2 - 4(2)(-795))) / (

When x is -10, the value of y is 38. This means that the point (-10, 38) is on the graph of the function y = -4x - 2.

We must determine the values of x and solve for the matching value of y in order to fill in the table using the function rule y = -4x - 2. The table can then be populated with the resulting values for x and y.

An illustration table with x values ranging from -3 to 3 is shown below:

x y

-3 10

-2 6

-1 2

0 -2

1 -6

2 -10

3 -14

We may easily change x in the function rule y = -4x - 2 to -10 to find the value of y when x is -10:

y = -4(-10) (-10) - 2 \sy = 40 - 2 \sy = 38

As a result, y equals 38 when x is -10. This indicates that the point (-10, 38) is located on the y = -4x - 2 function graph.

It's vital to remember that the numbers in the table are produced by inserting various x values into the function rule, and the resulting y-values represent the corresponding locations on the function's graph. The line passing through the point on the graph of the function y = -4x - 2 has a slope of -4 and a y-intercept of -2. (-10, 38).

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Answer:

-16x+28

Step-by-step explanation:

Using the 2nd and 1st term in the sequence, we can find the change.

4x+4, -x+10.  Using mental math, we can see that x decreases by 5 and 4 increases by 6.  Using this, the change is -5x + 6.

The easiest way to solve this is mental math because the 5th term is very close to the last term (the 3rd).

Solving:

-6x+16 = 3rd term, so -6x+16-5x+6 = -11x+22 | -11x+22-5x+6 = -16x+28.

Answer:

∠h = 61°

∠g = 119°

∠m = 59°

∠k = 121°

Step-by-step explanation:

According to the Vertical Angles Theorem, when two straight lines intersect, the opposite vertical angles are congruent.

Therefore, as angle g is opposite 119°:

⇒ ∠g = 119°

As angle k is opposite 121°:

⇒ ∠k = 121°

Angles on a straight line sum to 180°.

As angle h and 119° form a straight line:

⇒ ∠h + 119° = 180°

⇒ ∠h + 119° - 119° = 180° - 119°

⇒ ∠h = 61°

As angle m and 121° form a straight line:

⇒ ∠m + 121° = 180°

⇒ ∠m + 121° - 121° = 180° - 121°

⇒ ∠m = 59°

Answer:

Step-by-step explanation:

To find:-

Answer:-

From the given figure we can see that angles k and 121° are vertically opposite angles . Also we know that vertically opposite angles are equal to each other. Hence here we can say that,

[tex]\longrightarrow \boxed{ k = 121^o}\\[/tex]

Secondly, we know the the mesure of angle of a straight line is 180° . So the sum of angles on a straight line would be 180° . If two angles are present we call them linear pair . Hence here , we can see that m and 121° are linear pairs.

So that,

[tex]\longrightarrow m + 121^o = 180^o \\[/tex]

[tex]\longrightarrow m = 180^o-121^o\\[/tex]

[tex]\longrightarrow \boxed{m = 59^o } \\[/tex]

Similarly we can see that g and 119° are vertically opposite angles. Again they will be equal. So ,

[tex]\longrightarrow \boxed{g = 119^o} \\[/tex]

Again, 119° and h form linear pair.So their sum would be 180° .

[tex]\longrightarrow h + 119^o = 180^o \\[/tex]

[tex]\longrightarrow h = 180^o - 119^o\\[/tex]

[tex]\longrightarrow \boxed{ h = 61^o }\\[/tex]

These are the required values of the unknown angles.