giselle is 4 years older than her brother marco. the sum of their ages is 30. Write and solve a system of equations to find their ages

Answer: [tex]d)x=4[/tex]

Step-by-step explanation:

[tex]a)x=-1\\b)x=0\\c)x=3\\d)x=4[/tex]

By definition, a relation is a function if and only if each input value has one and only one output value.

It is important to remember that the input values are the values of "x" and the output values are the values of "y".

Observe the graph attached.

You can identify in the graph that the function f(x) and the function g(x) intersect each other at the following point:

[tex](4,3)[/tex]

Where the x-coordinate (input value) is:

[tex]x=4[/tex]

And the y-coordinate (output value) is:

[tex]y=3[/tex]

Therefore, you can conclude that the input value that produces the same output value for the  two functions on the graph, is:

[tex]x=4[/tex]

Answer:

1.25

Step-by-step explanation:

x+1/8=1.375

x=1.375-0.125

x=1.25

Answer: 1.25

Move all terms not containing  x  to the right side of the equation.

Exact Form:

x  =  54

Decimal Form:

x  =  1.25

Mixed Number Form:

x  =  1  1/4

Hope this helps

Answer:

False

Step-by-step explanation:

15-0=0

0-15=-15

Sequence by the given rule will be 0, 6, 12, 18, 24, 30, 36.

   Given rule for the sequence to be formed,

        Here, x = 0, 1, 2, 3, 4, 5

To write the sequence, substitute the values of x in the rule given,

1st term → 6 × 0 = 0

2nd term → 6 × 1 = 6

3rd term → 6 × 2 = 12

4th term → 6 × 3 = 18

5th term → 6 × 4 = 24

6th term → 6 × 5 = 30

   Therefore, sequence will be → 0, 6, 12, 18, 24, 30, 36.

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Answer:

False

Step-by-step explanation:

The only vertical angles shown are 1 and 3. The other pair is 2 and 4

Answer:

1. 3/5                        c

2. 7                           c

3. 2/5                       b

4. $3.24                   c  

5. -3.2                      b

Step-by-step explanation:

1.

2/5 + 1/5  =    3/5

2.

a negative + a negative = a positive

2+5 = 7

3.

terminating means the decimal ends. When u divide a & c they keep on going but 2/5 ends

4.

divide 16.8 by 5.19 = 3.23 round up so 3.24

5.

multiply the two together to get the answer

Answer:

3 ounces every 40 minutes

60 divided by 40= 1.5

3x1.5= 4.5 ounces

Answer:

required bank balance=$148

Step-by-step explanation:

simple interest=[tex](  \right )P\times R\times  T\left )\div 100[/tex]

where P=principle=$100

           R=rate of interest=4%

           T=time=12 year

simple interest=[tex](  \right )100\times 4\times  12\left )\div 100[/tex]

simple interest=[tex]\frac{4800}{100}[/tex]

simple interest=48

required bank balance=principle+simple interest

required bank balance=$100+$48=$148

required bank balance=$148

Answer:

w = d + r²

Step-by-step explanation:

Given

d = w - r² ( isolate w by adding r² to both sides )

d + r² = w

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have the equation i point-slope form.

Convert to the slope-intercept form:

[tex]y-4=-2(x-5)[/tex]    use the distributive property

[tex]y-4=-2x+(-2)(-5)[/tex]

[tex]y-4=-2x+10[/tex]             add 4 t oboth sides

[tex]y-4+4=-2x+10+4\\\\y=-2x+14[/tex]

Answer: base = 20 inches , height = 8 inches

Step-by-step explanation:

The formula fro calculating the area of  a triangle , given the base and the height is given as ;

A = [tex]\frac{1}{2}[/tex]bh

The ratio of its base to the height is given as 5: 2 , this means that

2b = 5h , that is

b = [tex]\frac{5h}{2}[/tex]

Substitute this into the formula for finding area , that is

80 = [tex]\frac{1}{2}[/tex] X [tex]\frac{5h}{2}[/tex] X h

80 = [tex]\frac{5h^{2}}{4}[/tex]

Therefore :

[tex]5h^{2}[/tex] = 80 x 4

[tex]5h^{2}[/tex] = 320

[tex]h^{2}[/tex] = 320 / 5

[tex]5h^{2}[/tex] = 64

h = 8 inches

Substitute h = 8 into b = [tex]\frac{5h}{2}[/tex] , then

b = 20 inches

Therefore , the base of the triangle is 20 inches and the height is 8 inches

Answer:

There are three decimal places in the final answer.

Step-by-step explanation:

We have to calculate the expression 4.2 × 12.3 × 14.6, in which the floor dimensions are 12.3 ft by 14.6 ft. which I have to cover with tiles and each square foot of tile costs $4.20.

So, the area of the floor is (12.3 × 14.6) sq. ft. = 179.58 square feet.

Now, the cost of covering the floor with tiles will be = $(179.58 × 4.2) = $754.236.

Therefore, there are three decimal places in the final answer. (Answer)

Answer:

No.

Explanation:

The term linear function refers to two distinct but related notions. This is just one point.

Answer:

y=4x

Step-by-step explanation:

The line goes through the points (0, 0) and (2, 8).

You can plug these in to the slope formula, and the slope is 4

Since the line intersects the y-axis at 0, the y-intersect is 0.

Using these two pieces of information, you now know that the equation is

y=4x+0, or y=4x.

Hope this helps!

Answer:

Y = mx + c

Step-by-step explanation:

Where

m = gradient or slope

c = intercept (value of y when x=0)

Y = how far up

x = how far along

Answer:

15%

Step-by-step explanation:

75/500=0.15=15%

Answer:

15%

Step-by-step explanation:

divide 75/500 by 25/25= 3/20

3/20 x 5/5= 15/100

Answer:

1.  x > 4

2.  m < 2

3.  x > 2

4.  x < -6

Step-by-step explanation:

These 4 inequalities will be solved the same way we solve equations. We take variables to one side and numbers to another and use algebra to solve. Each of them are solved shown below:

1.

[tex]4+6x<x+6x\\4+6x<7x\\4<7x-6x\\4<x[/tex]

so x is greater than 4, we can write (variable first):

x > 4

2.

[tex]m+16>8m+2\\16-2>8m-m\\14>7m\\\frac{14}{7}>m\\2>m[/tex]

so m is less than 2, we can write:

m < 2

3.

[tex]5x-1>13-2x\\5x+2x>13+1\\7x>14\\x>\frac{14}{7}\\x>2[/tex]

so x is greater than 2, we can write:

x > 2

4.

[tex]-3x-2>-x+10\\-2-10>-x+3x\\-12>2x\\\frac{-12}{2}>x\\-6>x[/tex]

so x is less than -6, we can write:

x < -6

The equation of the line in the point-slope form is y - 15 = [tex]-\frac{3}{2}[/tex] (x - 10)

Step-by-step explanation:

The point-slope form of a linear equation is [tex]y-y_{1}=m(x-x_{1})[/tex] , where

∵ Point A = (10 , 15)

∵ The x-coordinate of the second point is 125% of x-coordinate

  of point A

∴ x-coordinate of second point = [tex]\frac{125}{100}[/tex] × 10

∴ x-coordinate of second point = 12.5

∵ The y-coordinate of the second point is 75% of y-coordinate

  of point A

∴ y-coordinate of second point = [tex]\frac{75}{100}[/tex] × 15

∴ y-coordinate of second point = 11.25

∴ The coordinates of the second point are (12.5 , 11.25)

Let us find the slope of the line by using the rule of it above

∵ [tex](x_{1},y_{1})[/tex] = (10 , 15)

∵ [tex](x_{2},y_{2})[/tex] = (12.5 , 11.25)

∴ [tex]m=\frac{11.25-15}{12.5-10}=\frac{-3.75}{2.5}=-\frac{3}{2}[/tex]

Now we can write the equation

∵ The point-slope form is [tex]y-y_{1}=m(x-x_{1})[/tex]

∵ [tex]m=-\frac{3}{2}[/tex]

∵ [tex](x_{1},y_{1})[/tex] = (10 , 15)

- Substitute these values in the form of the equation

∴ y - 15 = [tex]-\frac{3}{2}[/tex] (x - 10)

The equation of the line in the point-slope form is y - 15 = [tex]-\frac{3}{2}[/tex] (x - 10)

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For this case we must find the solution set of the given inequalities:

[tex]-15x + 4 <109[/tex]

We subtract 4 from both sides of the inequality:

[tex]-15x <109-4\\-15x <105[/tex]

We divide between 15 on both sides of the inequality:

[tex]-x <\frac {105} {15}\\-x <7[/tex]

We multiply by -1 on both sides taking into account that the sense of inequality changes:

[tex]x> -7[/tex]

The solution is given by all values of x greater than -7.

[tex]-6x + 70> -2[/tex]

Subtracting 70 from both sides of the inequality:

[tex]-6x> -2-70\\-6x> -72[/tex]

We divide by 6 on both sides of the inequality:

[tex]-x> - \frac {72} {6}\\-x> -12[/tex]

We multiply by -1 on both sides taking into account that the sense of inequality changes:

[tex]x <12[/tex]

Thus, the solution set is given by:

[tex]x> -7\ U\ x <12[/tex]

Therefore the solution is all real numbers.

Answer:

All real numbers.

Answer:

[tex]\frac{8}{5} x^{2}  - \frac{16}{5} xy + 4x[/tex]

[tex]xy^{2} + \frac{2}{3}y - 8y^{2}z[/tex]

Step-by-step explanation:

We have to simplify the followings:  

1) [tex]- \frac{4}{5}x (- 2x + 4y - 5)[/tex]

= [tex]- \frac{4}{5}x \times (- 2x) +  - \frac{4}{5}x \times (4y) + - \frac{4}{5}x \times (- 5)[/tex]  

{By distributive property of multiplication}

= [tex]\frac{8}{5} x^{2}  - \frac{16}{5} xy + 4x[/tex] (Answer)

2) [tex]2y^{2}( \frac{1}{2} x + \frac{2}{6}y - 4z)[/tex]

= [tex]2y^{2} \times (\frac{1}{2} x) + 2y^{2} \times ( \frac{2}{6}y) - 2y^{2} \times (4z)[/tex]

{By distributive property of multiplication}

= [tex]xy^{2} + \frac{2}{3}y - 8y^{2}z[/tex] (Answer)

Answer:

linear equation in Standard form that can be used to determine how many of each prize Caleb can buy is [tex]1.25x+ 2.50y = 25[/tex]

Step-by-step explanation:

Given:

Total cost spent on prizes for games = $25

Cost of one lip balm = $1.25

Cost of one mini notebook  = $2.50

A) linear equation in STANDARD FORM that can be used to determine how many of each prize she can buy.

Let the number of lip balms be x and the number of mini note books be y. Then

[tex]1.25x+ 2.50y = 25[/tex]

B. Graph the equation using x- and y- intercepts.

Now by trial and error method

[tex]1.25(0)+ 2.50(10) = 25[/tex]

[tex]1.25(2)+ 2.50(9) = 25[/tex]

[tex]1.25(4)+ 2.50(8) = 25[/tex]

[tex]1.25(6)+ 2.50(7) = 25[/tex]

[tex]1.25(8)+ 2.50(6) = 25[/tex]

[tex]1.25(10)+ 2.50(5) = 25[/tex]

[tex]1.25(12)+ 2.50(4) = 25[/tex]

[tex]1.25(14)+ 2.50(3) = 25[/tex]

[tex]1.25(16)+ 2.50(2) = 25[/tex]

[tex]1.25(18)+ 2.50(1) = 25[/tex]

[tex]1.25(20)+ 2.50(0) = 25[/tex]

Thus Caleb can buy 0,2,4,6,8,9,10,12,14,1,6,18,20 lip balms and

0,1,2,3,4,5,6,7,8,9,10 mini note books respectively

Now plotting these value in the graph, we get the below graph

Answer:

Step-by-step explanation:

10 5/6 km...in 5 days

(10 5/6) / 5 =

(65/6) / 5 =

65/6 * 1/5 =

65/30 =

2 1/6 kilometers per day <===

Answer:

The midpoints are ( 6, 6.5 ).

Step-by-step explanation:

Given that the endpoints are  A ( 9, 8) and B (3,5)-

As we know that-

If a line segment AB is with endpoints ([tex]x_{1}, y_{1}[/tex]) and  ([tex]x_{2}, y_{2}[/tex] then the mid points C are-  

C = ([tex]\frac{x_{1} + x_{2}  }{2}[/tex] , [tex]\frac{y_{1} + y_{2}  }{2}[/tex] )

Here,

A ( [tex]x_{1} = 9, y_{1} = 8[/tex] and B ( [tex]x_{2} = 3, y_{2} =5[/tex]

then the  midpoints C are-

C = ( [tex]\frac{9 + 3 }{2}[/tex], [tex]\frac{8 + 5 }{2}[/tex]

C= ( 12/2 , 13/2 )

C = ( 6, 6.5 )

Hence the midpoints are (6, 6.5).

Answer:

The coordinates are (5.3)

Step-by-step explanation:

Answer:

Step-by-step explanation:

-2(-8x - 4y + 3/4) =

16x + 8y - 3/2 ....(-3/2 is the same as - 1 1/2)

errors.....

A. the first term should be positive

B. the second term should be positive

C. the last term should be - 1 1/2

Daniel expanded the expression . The errors made by Daniel are

A. The first term should be positive.

B. The second term should be positive.

C. The last term should be -1 1/2, not -1 1/4.

Given :

Daniel expanded the expression as shown

[tex]-2(-8x-4y+3/4)\\-10x-8y-1 1/4[/tex]

Lets multiply -2 inside the parenthesis and see what happens

[tex]-2(-8x-4y+3/4) \\-2 (-8x)-2(-4y)-2(\frac{3}{4} )[/tex]

we know that negative times negative is positive

Also to simplify the fraction ,we can cancel out 2  and 4

[tex]-2 (-8x)-2(-4y)-2(\frac{3}{4} )\\+16x+8y-\frac{3}{2} \\+16x+8y-1\frac{1}{2} \\[/tex]

So the first and second terms are positive

Also the constant term is -1 1/2

So the errors he make are

A. The first term should be positive.

B. The second term should be positive.

C.The last term should be -1 1/2, not -1 1/4.

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Answer:

x=-11

Step-by-step explanation:

11-3x=44

3x=11-44

3x=-33

x=-33/3

x=-11

Final answer:

The area of a rectangular field that is 400 meters long and 350 meters wide is calculated by multiplying the length and width in meters to get square meters and then converting to square kilometers. The field's area is 0.14 square kilometers.

Explanation:

To calculate the area of a rectangular field, you multiply the length by the width. The area is usually given in square units.

In this case, the field is 400 meters long and 350 meters wide. To find the area in square meters, we do the following calculation:

Area = Length × Width

Area = 400 m × 350 m

Area = 140,000 m2

To convert square meters to square kilometers, you need to remember that 1 square kilometer equals 1,000,000 square meters. Therefore, you divide the area in square meters by 1,000,000 to get the area in square kilometers:

Area in square kilometers = Area in square meters / 1,000,000

Area in square kilometers = 140,000 m2 / 1,000,000

Area in square kilometers = 0.14 km2

The area of the field is 0.14 square kilometers.

To find the area of the rectangular field in square kilometers, the measurements of 400 meters and 350 meters must first be converted to kilometers, resulting in an area of 0.14 square kilometers.

To calculate the area of a rectangular field in square kilometers, we can use the formula for the area of a rectangle which is length × width. First, we need to convert the measurements into the same unit, so we will convert meters to kilometers. We know that 1 kilometer is equivalent to 1000 meters. Therefore, a field that is 400 meters long is 0.4 kilometers long (400 ÷ 1000 = 0.4 km), and a field that is 350 meters wide is 0.35 kilometers wide (350 ÷ 1000 = 0.35 km).

Now, with both measurements in kilometers, we can find the area:

Answer:

d = 1.2 + 2.3t

Step-by-step explanation:

A backpacker parked his car and hiked a distance of 1.2 km on the first day. On the second day, he continued hiking away from his car with an average speed of 2.3 km/hr.

Now, on the second day he started from distance 1.2 km from his car and continues to hike with an average speed of 2.3 km/hr.

Therefore, the distance of the backpacker from his car on the second day is given by  

d = 1.2 + 2.3t

where d is the distance in km and t is the time in hours he hiked. (Answer)

Answer:

D

Step-by-step explanation:

To determine which ordered pair is a solution.

Substitute the x and y values into the inequalities.

Note that both must be true for the pair to be a solution of the system.

(4, 8)

8 > 2(4) → 8 > 8 ← False

8 > 7 ← True

(0, 0)

0 > 2(0) → 0 > 0 ← False

0 > 7 ← False

(3, 7)

7 > 2(3) → 7 > 6 ← True

7 > 7 ← False

(1, 9)

9 > 2(1) → 9 > 2 ← True

9 > 7 ← True

Thus (1, 9) is a solution to the system of equations. → D

The ordered pair (1,9) is the solution to the system of inequalities.

To determine which ordered pair is a solution to the system of inequalities, we need to check if each pair satisfies both inequalities. Let's check:

A. (4,8): For y > 2x, 8 > 2(4) = 8 > 8, which is false. For y > 7, 8 > 7, which is true. Therefore, (4,8) is NOT a solution to the system.

B. (0,0): For y > 2x, 0 > 2(0) = 0 > 0, which is false. For y > 7, 0 > 7, which is false. Therefore, (0,0) is NOT a solution to the system.

C. (3,7): For y > 2x, 7 > 2(3) = 7 > 6, which is true. For y > 7, 7 > 7, which is false. Therefore, (3,7) is NOT a solution to the system.

D. (1,9): For y > 2x, 9 > 2(1) = 9 > 2, which is true. For y > 7, 9 > 7, which is true. Therefore, (1,9) is a solution to the system.

Thus, the ordered pair (1,9) is the solution to the system of inequalities.

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Answer:

the square root of -1 is i

Step-by-step explanation:

Answer:

[tex]\large\boxed{\sqrt{-1}=i}[/tex]

Step-by-step explanation:

[tex]\sqrt{-1}=i\\\\i-\text{immaginary unit}\ \left(i^2=-1\right)\\\\\text{It's a complex number.}[/tex]