Javier asks his mother how old a tree in their yard is. His mother says, “The sum of 10 and two-thirds of that tree’s age, in years, is equal to 50.” 

Javier writes the equation , where a is the tree’s age in years. His equation is not correct. What error did he make? ​

The type of land form that Caleb most likely draws is a hill. The answer is option C- a hill.

Step-by-step explanation:

The correct answer is option C. He most likely drawing a hill.

Contour maps are used to represent the topography or elevation of an area using contour lines. Contour lines connect points of equal elevation above a reference level (usually sea level).

A hill is typically represented on a contour map by concentric closed contour lines, with higher elevations towards the center and lower elevations towards the periphery.

Answer:

C(F) = 5/9 F-160/9

Step-by-step explanation:

Answer:

C(F) =  

5/9

F −  

-16/9

⇒ 160/9

Step-by-step explanation:

Your Welcome :D

Answer:

5

Step-by-step explanation:

One step equation. You would subtract 7 from 12 to get 5 because x would be alone now.

[tex]

kx+12=3kx \\

12=2kx \\

x=\frac{12}{2k} \\

x=\frac{6}{k}

[/tex]

Hope this helps.

Answer: x=6/k

Step-by-step explanation:

kx + 12 = 3kx and subtract k from both sides

12=3kx-kx then simplify

12=2kx, now divide both sides by two

12/2=kx simplify again

6=kx divide next

6/k=x finally, switch sides to get x=6/k

Hope this helps, have a BLESSED and wonderful day, as well as a safe one!

-Cutiepatutie ☺❀❤

Answer:

The coordinate  to the given equations is (3,1)

Step-by-step explanation:

Given equation is [tex]2x+6y=12\hfill (1)[/tex]

and [tex]4x-3y=9\hfill (2)[/tex]

To find the coordinate of the given equations :

Multiply the equation (2) into 2 we get

[tex]8x-6y=18\hfill (3)[/tex]

Now adding the equations (1) and (3) we get

[tex]2x+6y=12[/tex]

[tex]8x-6y=18[/tex]

_______________

[tex]10x=30[/tex]

[tex]x=\frac{30}{10}[/tex]

Therefore x=3

Substitute x=3 in (1)

2(3)+6y=12

6y=12-6

[tex]y=\frac{6}{6}[/tex]

Therefore y=1

The coordinate  to the given equations is (3,1)

To find the coordinates of the intersection point of the equations 2x+6y=12 and 4x-3y=9, we can solve the system of equations using the method of substitution. The coordinates of the intersection point are (3, 1).

To find the coordinates of the intersection point of the equations 2x+6y=12 and 4x-3y=9, we can solve the system of equations by using the method of substitution or elimination. Let's use the method of substitution:

The coordinates of the intersection point are (3, 1).

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The solution to the inequality 2x<8 is x<4.

Step-by-step explanation:

Given inequality is;

2x < 8

For solving this inequality, we will divide both sides by 2 to find the value of x, therefore;

Dividing both sides by 2

[tex]\frac{2x}{2}<\frac{8}{2}\\x<4[/tex]

It means that x is less than four.

Thus,

The solution to the inequality 2x<8 is x<4.

Keywords: inequality, division

Learn more about division at:

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Answer: 81

Step-by-step explanation:

The pattern of the sequence is :

[tex]1^{2}[/tex] , [tex]3^{2}[/tex] , [tex]5^{2}[/tex] , [tex]7^{2}[/tex] , [tex]9^{2}[/tex] ...

Which will be :

1 , 9 , 25 , 49 , 81 , ...

Therefore , the next pattern in the sequence is 81

Answer:

y= 2(2x-1) -4

Step-by-step explanation:

you subtract 4 from both sides and it cancel outs at the y side(because 4-4 is 0) leaving just y.

Answer: [tex]SA=189\ mm^2[/tex]

Step-by-step explanation:

You need to use the following formula for calculate the Surface area of a Right triangular prism:

[tex]SA=ph+2B[/tex]

Where "p" is the perimeter of the base, "h" is the height of the prism and "B" is the area of the base.

You can identify that the height is:

[tex]h=9\ mm[/tex]

The area of a triangle can be found with this formula:

[tex]A=\frac{bH}{2}[/tex]

Where "b" is the height of the triangle and "H" is its height.

Knowing this formula, you can find the area of the base of the prism. This is:

[tex]B=\frac{6\ mm*4.5\ mm}{2}\\\\B=13.5\ mm^2[/tex]

Since the perimeter of a figure is the sum of the lenghts of its sides, "p" is:

[tex]p=4.5\ mm+6\ mm+7.5\ mm=18\ mm[/tex]

Therefore, substituting values into the formula, you get:

[tex]SA=(18 mm)(9} mm)+2(13.5} mm^2)\\\\SA=189\ mm^2[/tex]

Option C: 126° is the correct answer

Step-by-step explanation:

When two lines intersect, the four angles are formed. The angles vertically opposite with same vertex are called vertical opposite angles.

The opposite vertical angles are equal.

In the given figure, the pairs of vertically opposite angles are e,h and f,g.

Given

∠e = 126°

The measurement of e and h will be equal as they are vertically opposite

So,

m∠e = m∠h

m∠h = 126°

Hence,

Option C: 126° is the correct answer

Keywords: Vertical angles, lines

Learn more about angles at:

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Answer:

G

Step-by-step explanation:

The cost to rent the canoe for 7 hours is $ 104

Solution:

At eagle bay it cost $12 per hour to rent a Canoe

Nate and his friends rented a canoe for 4 hours and paid $68

Let "x" be the number of hours rented

We can solve use the point slope equation

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

Where, "m" is the rate of change

[tex](x_1, y_1)[/tex] is the sample point

From given,

m = 12

[tex](x_1, y_1) = (4, 68)[/tex]

Therefore,

[tex]y - 68 = 12(x-4)[/tex]

[tex]y - 68 = 12x -48\\\\y = 12x -48+68\\\\y = 12x + 20[/tex]

Thus the linear equation is found

Here, "y" represents the amount paid for "x" hours

Find the cost to rent the canoe for 7 hours

Substitute x = 7 in linear equation

y = 12(7) + 20

y = 84 + 20

y = 104

Thus cost to rent the canoe for 7 hours is $ 104

To find the cost to rent the canoe for 7 hours, we can use the equation: Cost = Rate x Time. Given that the rate is $12 per hour and the time is 4 hours, the cost can be calculated as $68. Therefore, the cost to rent the canoe for 7 hours would be $119.

To find the cost to rent the canoe for 7 hours, we can use the equation:

Cost = Rate x Time

Given that the rate is $12 per hour and the time is 4 hours, we can substitute these values into the equation:

68 = 12 x 4

Solving for the rate, we get:

Rate = 68 ÷ 4

Therefore, the rate is $17 per hour. To find the cost to rent the canoe for 7 hours, we can multiply the rate by the time:

Cost = Rate x Time = 17 x 7 = $119

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Answer:

two solutions : 9   ; -9

Step-by-step explanation:

x²=81

means : x² - 81 =0   but 81 = 9²

use identity ; a² - b² = (a-b)(a+b)

x² -9² = 0     : (x-9)(x+9)=0

x-9=0 or x+9 = 0

x =9 or x = -9

Each multiplication problem was evaluated individually, revealing that two products are greater than 1 and one is less than 1.

When evaluating whether each product is less than 1, equal to 1, or greater than 1, it's important to consider the values being multiplied. Let's examine each multiplication problem provided:

2 x 1/3: Multiplying 2 by one-third gives us 2/3, which is less than 1.

5 x 1/3: Multiplying 5 by one-third gives us 5/3, which simplifies to 1 and 2/3, meaning it is greater than 1.

1/2 x 3: Multiplying one-half by 3 gives us 3/2, which simplifies to 1 and 1/2, so this is also greater than 1.

The function is definately defined at x=0 but not x=1.

But its just one part of the coordinate (x,y).

If the value of y or f(x) is considered, you'll see that it is never possible to attain f(x)=0. In other terms (x,y)= (0,0) is not a defined point in the graph of the function because the graph doesnt pass through that point.

Now I hope you understood what I meant!

Conclusion- The above function is not defined at all points in the space having the abscissa or x=1 in the coordinate and also at ordinate or y=0 in the coordinate.nation:

The value of x for which the function g(x)=x/1-x is not defined is at x = 1.

A value of a function becomes not defined when the denominator of that function becomes zero.

The function is g(x)=x/1-x.

We can substitute the different values of x to find which makes the function not defined.

g(-1) = -1/1-(-1)

= -1/2

The function is defined.

g(0) = 0/1-0

= 0

The function is defined.

g(1) = 1/1-1

= 1/0 = not defined

The function is not defined.

g(2) = 2/1-2

= 2/-1 = -2

The function is defined.

Therefore, we have found that the value of x for which the function g(x)=x/1-x is not defined is at x = 1.

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Answer:

x=14.7

Step-by-step explanation:

use the law of sines

sinA = sinB= sinC

------ ------ ------

a b c

Answer:

The correct answer is 1/4(n - 64).

Step-by-step explanation:

1/4n - 16  Write Original expression

0.25n -16     Simplify the fraction

0.25(n - 64)      Distribute(take out) 0.25 from n-16

1/4(n - 64)      

Answers:

a. The domain of f is ]-∞ , ∞[

b. The range of f is [-4 , ∞[

c. f(1) = 5

d. The vales of x for which f(x) is -3 are 7 and 9

e. The points at which the graph crosses the x-axis are (6,0) and (10,0)

f. The point where the graph of f crosses the y-axis is (0,5)

g. The values of x for which f(x) < 0 are ]6 , 10[

h. f(-7) is positive

Explanation:

Part a:

The domain of the function refers to all the possible x-values that can be used as an input for this function.

Taking a look at the graph, we can see that the graph extends endlessly from both ends of the x-axis. This means that all x-values can be used as a domain for the function. In other words, the domain of the function is all the real numbers.

In interval notation, this is written as:

Domain = ]-∞ , ∞[

Part b:

The range of the function refers to all the possible y-values that can be used as an output for the function.

From the graph, we can note that the function extends endlessly in the direction of the positive y-axis while it stops at a value of -4 in the direction of the negative y-axis.

This means that the range of the function starts from -4 (included) and extends to positive infinity.

In interval notation, this is written as:

R = [-4 , ∞[

Part c:

f(1) means that we are looking for the output (the value of y) for which the input (the value of x) is 1.

From the graph, we start by searching for x=1 (first square edge after the origin) and then move vertically till we intersect the graph.

Doing this, we will find that the value of y at x=1 is 5

Therefore:

f(1) = 5

Part d:

f(x) = -3 means that the output value (the value of the y) for the certain input (value of x) is -3

To get the value of x, we go y=-3 and move horizontally till we intersect the graph.

Doing this, we will find that the value of y is -3 at x = 7 and x = 9

Part e:

The points where the graph crosses the x-axis are the points that have y-value equal to 0

Checking the graph, we can note that the function crosses the x-axis at two points which are (6,0) and (10,0)

Part f:

The point where the graph crosses the y-axis is the point that has x-value equal to 0

Checking the graph, we can note that the function crosses the y-axis at only one point which is (0,5)

Part g:

f(x) < 0 means that the output of the function (the y-value) is less than 0 (0 is not included)

Taking a look at the graph, we can note that the function has negative output on the interval from 6 (excluded) to 10 (excluded)

In interval notation, this is written as ]6 , 10[

Part h:

f(-7) means the output of the function (the y-value) at input (x-vale) equal to -7

From the graph, we can note that the function has a constant value of 5 starting from x=5 till -∞

This means that, at x=-7, the value of y is 5 which is a positive value

Hope this helps :)

Answer:

C. Negative three-fourths

Step-by-step explanation:

Step-by-step explanation:

Given two fractions -1 1/4 and 1/2, the sum of the fractions is expressed as shown below:

-1 1/4 + 1/2

Converting the improper fraction -1 1/4 to mixed fraction will give -5/4. The expression will now become:

-5/4 + 1/2

Taking the LCM of the expression

= (-5+2)/4

= -3/4

Hence the sum of fraction Negative 1 and one-fourth and one-half is negative three-fourths

Final answer:

To add negative three-fourths and one-half, we first convert 1/2 to 2/4 to have the same denominator as -3/4. Adding the numerators gives us -1/4 as the sum, which can be visualized on the number line.

Explanation:

The student has asked how to find the sum of the fractions negative three-fourths (-3/4) and one-half (1/2) using a number line and equivalent fractions. To solve this problem intuitively, we can use our understanding of fractions as parts of a whole. First, we need to find a common denominator which is the least common multiple of 4 and 2, which is 4 in this case. So, we convert 1/2 to 2/4 since one half of one-half is one quarter, and then add it to -3/4.

Now, we have -3/4 + 2/4, which simplifies to -1/4 when we add the numerators, -3 and +2. This result can be visually confirmed on a number line. If we start at -3/4 on the number line and move 2/4 (which is half) to the right, we'll end up at -1/4, between -1 and 0.

Through this intuition and number line visualization, we have determined that -3/4 plus 1/2 equals -1/4. This highlights how our intuition about everyday things like parts of a pie or quarters in a dollar can help us with fraction operations like addition and finding common denominators.

Answer:

Step-by-step explanation:

5/y + 7/x =24.........(1)

12/y + 2/x =24........(2)

Let 1/y = a and 1/x = b

5a + 7b = 24 ...........(3)

12a + 2b = 24...........(4)

Multiply (3) by 2 and (4) by 7

10a + 14b = 48..........(5)

84a + 14b = 168.........(6)

Substracting (5) from (6)

84a - 10a = 168 - 48

74a = 120

a = 120/74

a = 60/37

Putting a = 60/37 in (3)

5a + 7b = 24

5(60/37) + 7b = 24

300/37 + 7b = 24

Multiply each term 37

300 + 259b = 888

259b = 888 - 300

259b = 588

b = 588/259

And a = 1/y

60/37 = 1/y

Cross multiply

60y = 37

y = 37/60

Also

b = 1/x

588/259 = 1/x

Cross multiply

588x = 259

x = 259/588

The ratio of the variables 'x' and 'y' will be 5/7.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of equations is given below.

5/y + 7/x =24

12/y + 2/x =24

Let 1/x = X and 1/y = Y. Then the equation is given as

5Y + 7X = 24            ...1

12Y + 2X = 24          ...2

From equations 1 and 2, then we have

12[(24 - 7X) / 5] + 2X = 24

288 - 84X + 10X = 120

74X = 168

X = 168 / 74

1/x = 168/74

x = 74/168

The value of the variable Y is given as,

12Y + 2(168 / 74) = 24

12Y = 720 / 37

Y = 60/37

1/y = 60/37

y = 37/60

The ratio of the variable 'x' and 'y' will be given as,

Ratio = x / y

Ratio = (74 / 168) / (37 / 60)

Ratio = (74 / 168) x (60 / 37)

Ratio = 5/7

The ratio of the variables 'x' and 'y' will be 5/7.

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Answer:

Step-by-step explanation:

#1 the answer is 32lb

first you want to make an equation. My equation looks like this

x+4x=40

the x is the weight of the cat.

then solve for x  = 8

8*4 = 32

#2 the answer is 3:20 PM

Since it took 15 min to get home, we take 15 min away from 4:25 leaving us with 4:10

then we take away the length of practice 30min

4:10 - 30 min = 3:40

then we take away the 20 min of break time before the practice.

3:40 - 20 min = 3:20

Answer:

1.) the dog is 10

2.) 3:55

Step-by-step explanation:

1.)its just u dived by 4

2.) 15 + 20=35 35-4:25=3:55

=============================================

Explanation:

A triangle is only possible if you can add two sides and have that sum be larger than the third side. This is the triangle inequality theorem.

Choice A is ruled out because the second and third sides add to 7+7 = 14, but that's not larger than the first side 15.

Choice B is a similar story: 6+8 = 14 is not larger than 14 (the first side)

Choice C as well: 6+7 = 13 is not larger than 14

------

Choice D is the answer because

15+7 > 9

15+9 > 7

7+9 > 15

These three inequalities show that picking any two sides of this triangle, then adding them up, leads to a sum larger than the third side.

9514 1404 393

Answer:

  45 cm

Step-by-step explanation:

The ratio of length to width is the same for the drawing as for the field.

  length/width = L/(30 cm) = (120 yd)/(80 yd)

  L = (30 cm)(3/2) = 45 cm . . . . . . multiply by 30 cm and simplify

The field should be 45 cm long on the drawing.

Final answer:

The soccer field in Lexie's scale drawing should be 45 centimeters long, using a scale factor based on the given width of 30 centimeters and the real soccer field's dimensions.

Explanation:

Lexie is scaling a real soccer field to a drawing, with the real field's dimensions being 120 yards long and 80 yards wide. When converting these dimensions to a scale drawing where the width is 30 centimeters, we need to find the drawing's length. To do this, we will use a scale factor.

First, we find the actual scale factor based on the given dimensions:

Actual width of soccer field = 80 yards

Width in the drawing = 30 centimeters

To convert yards to centimeters, we need to know that 1 yard equals 91.44 centimeters. Given this, the actual width in centimeters is 80 yards * 91.44 cm/yard = 7312 centimeters.

Now, we calculate the scale factor:

Scale factor = Width in the drawing / Actual width in centimeters = 30 cm / 7312 cm

Using this scale factor, we can find the length for the drawing:

Actual length of soccer field = 120 yards

Actual length in centimeters = 120 yards × 91.44 cm/yard = 10972.8 centimeters

Length in the drawing = Actual length in centimeters × Scale factor = 10972.8 cm × (30 cm / 7312 cm)

Calculating this gives us:

Length in the drawing = 45 centimeters

Therefore, the length of the soccer field in Lexie's drawing should be 45 centimeters.

Answer:

B) 36 + 9 = 3(12 + 3)

Step-by-step explanation:

The distributive property of multiplication over addition is:

a(b + c) = ab + ac

This is demonstrated by switching the sides of option B) 36 + 9 = 3(12 + 3)

Answer:

B

Step-by-step explanation:

B  Because 12*3 = 36 and 3*3 =9

308 is greater than 215.06

Solution:

Given data: 215.6 ÷ 0.7

Let us first convert the fraction without decimal.

To remove a decimal point multiply and divide the fraction by 10.

[tex]\frac{215.6}{0.7}=\frac{215.6\times10}{0.7\times10}[/tex]

       [tex]=\frac{2156}{7}[/tex]

If we divide 2156 by 7, we get quotient as 308.

Now, to compare the quotient with the number 215.06.

308 > 215.06

Hence, 308 is greater than 215.06.

It is greater than 215.06.

[tex]= 215.06 \div 0.7[/tex]

= 308

This 308 should be more or greater than 215.06

Therefore we can conclude that It is greater than 215.06.

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Answer:

Its the first option.

Step-by-step explanation:

120 is not a perfect square.

Its close to one though - 121 is a perfect square ( 11 * 11 = 121).

Answer:

a

Step-by-step explanation:

I toolk the test (:  :)

Answer:

Explanation:

add 13 to both sides of the equation.

17+13=−8x.

30=−8x.

divde both sides by −8.

30−8=x⇒x=−308=−154.

As a check.

Step-by-step explanation:

Answer:

Step-by-step explanation:

17 = -13 - 8x....add 13 to both sides

17 + 13 = -13 + 13 - 8x

30 = -8x...now divide both sides by -8

-30/8 = (-8/-8)x

-30/8 = x.....reduce

- 15/4 = x <===