Jonathan and Oscar began saving money the same week. The table shows the models for the amount of money Jonathan and Ove saved after x weeks.

Jonathan's Savings

F (x)=18x+5

Oscar's Savings

G(x)=8x + 25

Jonathan and Oscar will have the same amount of money saved after

The functions are p(x) = b² - 16b +32 and q(x) = -32b-32 the x value when the functions are equivalent to each other is 8.

Given that,

The functions are p(x) = b² - 16b +32 and q(x) = -32b-32

We have to find the x value when the functions are equivalent to each other.

We know that,

Take the functions

p(x) = b² - 16b +32 and q(x) = -32b-32

When the function are equivalent

p(x) = q(x)

b² - 16b +32 = -32b-32

b² - 16b +32 +32b+32=0

b² + 16b +64 = 0

Now find the factors for 64

64 =  8×8

b² + 8b + 8b +64 = 0

Taking common terms

b(b + 8) + 8(b + 8)=0

(b + 8)(b + 8)=0

b=8

Therefore, The functions are p(x) = b² - 16b +32 and q(x) = -32b-32 the x value when the functions are equivalent to each other is 8.

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The graph of the given line 2x+3y=6 intersects the Y-axis at (0,2).

For the graph of linear equation to intersect the Y-axis, its X-co-ordinate should be zero or the abscissa is zero as Y-axis as the equation of Y-axis is x=0. Also the set of coordinates should satisfy the equation.

According to the first condition the x-coordinate of the equation should be zero so in equation 2x+3y=6 substituting the value of x as zero  2(0)+3y=6

3y=6  

y=6/3=2

So at point (0,2), the graph of the given line 2x+3y=6 intersects the Y-axis.

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The linear function expressed by the table is y = -1x + 4.

What is a linear function?

A linear function is a type of mathematical function that represents a linear relationship between two variables, often represented by x and y. The general form of a linear function is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis). Linear functions are also called lines.

To find the equation of the line from a table of values, you can use the slope-intercept form, y = mx + b

where m is the slope and b is the y-intercept

In order to find the slope 'm' we use the following formula:

m = (change in y)/(change in x) = (y2 - y1) / (x2 - x1)

Here,

m = (-2 - 2) / (2 - (-2)) = (-4)/4 = -1

The slope is -1, which means that for every one-unit increase in x there's a corresponding one-unit decrease in y.

To find the y-intercept, you can use one of the points from the table and substitute the x and y values into the equation

y = mx + b

So now we know that m = -1,

plugging the first point (x,y) = (-2,2) in the equation

2 = -2 - b

b = 4

So the equation of the line is y = -1x + 4

Hence, the linear function expressed by the table is y = -1x + 4.

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[tex]10\frac{1}{12}[/tex]  is the distance between  [tex]-6\frac{1}{3}[/tex] and [tex]4\frac{5}{12}[/tex]

The length along a line or line segment between two points on the line or line segment.

Distance=√(x₂-x₁)²+(y₂-y₁)²

We need to find the distance between [tex]-6\frac{1}{3}[/tex] and [tex]4\frac{5}{12}[/tex]

The given fractions are mixed fractions we have to convert them to improper fractions

[tex]-6\frac{1}{3}[/tex] =-17/3

[tex]4\frac{5}{12}[/tex] =53/12

Now we have to find the difference

53/12-(-17/3)

53/12+17/3

53+68/12

121/12

[tex]10\frac{1}{12}[/tex]

Hence, [tex]10\frac{1}{12}[/tex]  is the distance between  [tex]-6\frac{1}{3}[/tex] and [tex]4\frac{5}{12}[/tex]

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At the given rate, we can say that they will walk 6 laps and run 10 laps for a total of 16 miles.

In a direct proportional relationship, we can say that the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

For the first question, we have that out of a total distance of 8 miles,  and we can see that;

Walk is 3/8 of the distance.

Run is 5/8 of the distance.

Thus, the proportional relationships for the distances are given as follows:

Walked = 3/8 x Total Distance.

Ran = 5/8 x Total Distance.

We are told that the total distance is 16 miles and so;

Walked: 3/8 * 16 = 6 laps

Ran: 5/8 * 16 = 10 laps

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Señor Ochoa draws the perimeter of the garden with actual length of the vertical and horizontal legs of his triangular garden 3 meters as 6cm in his initial drawing with 18.5cm third side. Then new drawing with the vertical and horizontal legs of 18 cm

A scale drawing is a representation of an object or space that is reduced or enlarged in proportion to the actual size. To make a new scale drawing of Señor Ochoa's garden with the new dimensions of 18 centimeters for the vertical and horizontal legs of the triangle, you would need to apply a scale factor of 18/6 = 3 to the original drawing.

So, you would multiply each original dimension by 3 to get the new dimensions for the scale drawing.

The new scale drawing would be:

6cm × 3 = 18cm

6cm × 3 = 18cm

8.5cm × 3 = 25.5cm

The new scale is

= scale dimension/ original dimension

= 18cm/ 3m

= 18cm/ 300cm

= 3/ 50

It is also worth noting that as you are changing the scale, the measurement of the hypotenuse of the triangle would be affected, which is the square root of 3 meters, that would be approximately 25.5cm, which is the same as the original measurement on the original drawing.

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Answer:

x

Step-by-step explanation:

(log to the base 3) of 27^x can be re-written as

x*(log to the base 3) of 27, which is equivalent to:

x*(log to the base 3 of 3^3)  =  x

So the answer is simply " x "

Answer:

(B)

Step-by-step explanation:

we can solve by using formula (1/2) x base x height to get the answer.

Answer:

  -4/17

Step-by-step explanation:

You want the slope of the line described by the equation 20x +85y = 120.

Putting the equation in slope-intercept form by solving for y gives ...

  20x +85y = 120

  85y = -20x +120

  y = -20/85x +120/85

  y = -4/17x +24/17

The slope is the coefficient of x: -4/17.

The rate of change is -4/17.

Answer: Yes that I correct.

Step-by-step explanation:

Because 25 times 4 is 100 and what you do to the bottom you have to do to the top so 7 times 4 is 28

Area of a parallelogram

= length × height

= 20 ft. × 8ft.

= 160 ft.²

Answer:

a) La probabilidad de que a una persona elegida al azar no le guste ver la tele es 0.61 0 61%.

b) La probabilidad de que a una persona elegida al azar le guste leer, sabiendo que le gusta ver la tele, es 0.68 o 68%.

c) La probabilidad de que a una persona elegida al azar le guste leer es 0.77 o 77%.

Step-by-step explanation:

La Probabilidad es la mayor o menor posibilidad de que ocurra un determinado suceso. En otras palabras, la probabilidad establece una relación entre el número de sucesos favorables y el número total de sucesos posibles. Entonces, la probabilidad de un suceso cualquiera A se define como el cociente entre el número de casos favorables (número de casos en los que puede ocurrir o no el suceso A) y el número total de casos posibles. Esta se denomina Ley de Laplace.

[tex]P(A)=\frac{numero de casos favorables}{numero de casos posibles}[/tex]

a) A 47 personas les gusta ver la tele. Si la encuesta fue hecha a 120 personas, entonces a 73 personas (120 - 47) no les gusta ver la tele. Por lo que la probabilidad de que a una persona elegida al azar no le guste ver la tele es calculada como:

[tex]P=\frac{73}{120}[/tex]

P= 0.61= 61 %

La probabilidad de que a una persona elegida al azar no le guste ver la tele es 0.61 0 61%.

b) A 32 personas les gusta leer y ver la tele. Entonces la probabilidad de que a una persona elegida al azar le guste leer, sabiendo que le gusta ver la tele, es calculada como:

[tex]P=\frac{32}{120}[/tex]

P= 0.68= 68%

La probabilidad de que a una persona elegida al azar le guste leer, sabiendo que le gusta ver la tele, es 0.68 o 68%.

c) A 92 personas les gusta leer. Entonces la probabilidad de que a una persona elegida al azar le guste leer es calculada como:

[tex]P=\frac{92}{120}[/tex]

P= 0.77= 77%

La probabilidad de que a una persona elegida al azar le guste leer es 0.77 o 77%.

Answer:

75,000

Step-by-step explanation:

15,000x5=75,000

Answer: -2(4*2+(1/2)2) = -18

Step-by-step explanation: In order to solve this problem, we just have to use the order of operations. This can be shortened to PEMDAS.

The first step is PARENTHESIS. There are two parenthesis within this problem, so we start from the smaller ones and then go to the bigger ones. So, 1/2. That's equal to 0.5, so now we have -2(4*2+(0.5)2).

There are no EXPONENTS within this problem, so we skip the E part of the order.

Next is MULTIPLICATION and DIVISION. There are two instances of multiplication within the parenthesis. 4*2 is equal to 8. Because 2 is right next to the parenthesis, its contents are being multiplied by it. So, 0.5*2 is equal to 1.

Next is ADDITION and SUBTRACTION. There's no subtraction, but we can add 1 and 8 to get 9. This was the final process within the parenthesis, so now we can focus on what's happening outside.

For the same reasons mentioned before, we know that 9 is being multiplied by -2. 9*-2 is equal to -18. This is because any positive number multiplied by a negative number will result in a negative product.

Thus, our final answer is -18.

Answer:

72 m²

Step-by-step explanation:

12 m × 8 m = 96 m²

(12 × 4) ÷ 2 = 24 m²

96 m² - 24 m²

72 m²

Answer:

x + 2y = -15

Step-by-step explanation:

simplify -3x - 6y = 12 by dividing a -3 from each term to get:

x + 2y = -4

now put into slope-intercept form to get:

2y = -x - 4

y = -1x/2 - 2

parallel lines have the same slope so we know our answer must have a slope of -1/2

now we can plug (1,-8) into y=mx + b to get the 'y-intercept', or 'b'

-8 = 1(-1/2) + b

-8 = -1/2 + b

b = -7 1/2 or -15/2

we now know the slope and the y-intercept so our answer is:

y = -x/2 - 15/2

re-write in standard form, which is ax + by = c

multiply each term by  2 to get:

2y = -x - 15

add 'x' to each side to get:

2y + x = -15

x + 2y = -15

No, 8,15 and 16 is not a Pythagorean triplet.

A set of three integers that can be the lengths of the sides of a right triangle is called a Pythagorean triple, it also defines the positive integers a, b, and c which is a right triangle that exists with legs a,b, and hypotenuse c.

By the Pythagorean theorem, this is equivalent to finding positive integers a, b, and c satisfying  a²+b²=c²

One of the simplest Pythagorean triples is the set “3,4,5.”

Now, substitute the values in the above equation:

16²=8²+15²

256=64+225

256[tex]\neq[/tex]289

Therefore, (8,15,16) is not a Pythagorean triplet.

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Answer:

No solution

Step-by-step explanation:

-(y² - 2) = y²-5-2y²

= y^2 - 5 - 2y^2 = - (y^2 - 2)

= -y^2 - 5 =  - (y^2 - 2)

= −(y^2 − 2)

= -y^2 - 5 = -y^2 + 2

-5 = 2

We know that -5 is not equal to 2

So, there is no solution

Answer:
2

Step-by-step explanation:

Answer:

*read explanation for both questions*

Step-by-step explanation:

So the first one asks ”the first number in a pattern is 6, the pattern follows the rule ’multiply by 4’ “

The question has the answer to it, so each number would be multiplied by 4. So we have the first one which is 6, next we multiply 6 x 4 = 24. Then we multiply 24 x 4 = 96. and finally you multiply 96 x 4 = 384.

That’s the pattern fo the first one

The second one asks “The shapes have been sorted into two groups. explain what attribute was used to sort the shapes.”

When we’re looking for attributes, look for what they have in common. For me, I see that Group 1 has the smaller versions of the same shapes in Group 2. So that could be the attribute the question is asking for.

The mirror image of (2,5) in y-axis is (-2,5)

The term mirror image of the point is a reflected duplication that appears identical but in reverse.

Here we have given point is (2, 5).

And we have to find the mirror image of this point with respect to the y-axis that is the mirror image is a point whose distance is same from the origin O (0, 0) and same from both axes as of the point (2, 5) is.

As we all know that (2, 5) lies on the first quadrant, then the mirror image with respect to the y-axis must lie on the second quadrant.

And we all also know that In second quadrant, here the x-coordinate of any point (x, y) is negative.

Therefore, while we looking into the given graph we have identified that the mirror image is (- 2, 5).

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Answer:

nwhbjwhr

Step-by-step explanation:

ewrwrwrwewe

A hat symbol (^) is used to represent an estimated value in regression analysis.

We know that in regression analysis, the predicted values are the y-hat values.

Here y is the output variable or dependent variable

A 'hat' symbol (^) is used to denote an estimator.

A ^ symbol is placed over the variable name to denote the estimated value.

In matrix system, a hat matrix is nothing but the projection matrix.

It projects the vector of observations, y, onto the vector of predictions, y^

We know that a vector has magnitude and direction. A ^ symbol is used is represent the direction of unit vector.

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Answer:

3x ( 4x-3 )( 2x - 5 )

Step-by-step explanation:

24x^3 - 78x^2 + 45x

factor out biggest common values

3x ( 8x^2 - 26x + 15 )

3x ( 4x-3 )( 2x - 5 )

y = 3/2x - 9/2

The equation of the line that passes through the points (4,-3) and (2,0) can be found using the point-slope form of a linear equation. The point-slope form of a linear equation is y-y1=m(x-x1), where m is the slope of the line and (x1,y1) is a point on the line.

To calculate the slope, we will use the formula m = (y2-y1)/(x2-x1). In this equation, (x1,y1) = (4,-3) and (x2,y2) = (2,0). Substituting these values into the slope formula, we get m = (0-(-3))/(2-4) = 3/(-2) = -1.5.

Now that we have the slope, we can plug the point (4,-3) and the slope (-1.5) into the point-slope form of a linear equation to get y-(-3)=-1.5(x-4). Simplifying this equation, we get y+3=-1.5x+6, which is the equation of the line that passes through the points (4,-3) and (2,0).

Answer:

15

Step-by-step explanation:

-/40 and 3/8 40/5=8 3x5=15

Answer:

15 out of 40 students have a part in the spring play.

Step-by-step explanation:

(3/8) * 40 = 15

Answer:

The equation is:

[tex]y =12x+5[/tex]

Step-by-step explanation:

Given

[tex](x,y) = (Pizza,Cost)[/tex]

So, we have:

[tex](x_1,y_1) = (4,53)[/tex]

[tex](x_2,y_2) = (5,65)[/tex]

[tex](x_3,y_3) = (6,77)[/tex]

Required

Equation to represent the scenario

First, calculate the slope

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, we have:

[tex]m = \frac{65 - 53}{5 - 4}[/tex]

[tex]m = \frac{12}{1}[/tex]

[tex]m=12[/tex]

So, the equation is:

[tex]y =m(x - x_1) + y_1[/tex]

This gives:

[tex]y =12(x - 4) + 53[/tex]

[tex]y =12x - 48 + 53[/tex]

[tex]y =12x+5[/tex]

Answer:

11.2

Step-by-step explanation:

If the rectangulars are similar then we can use similarity ratio to calculate value of x

CD is similar to RS and AB is similar to QP

4/6.4 = 7/x cross multiply expressions

4x = 44.8 divide both sides by 4

x = 11.2

Answer:

the answer would be 5/24 :)