The top of a ladder is 4m up a vertical wall.The bottom is 2m from the wall.The coordinate axes are the wall and the horizontal ground.
a)Find the equation representing the ladder.
b)A square box just fits under the ladder.Find the coordinates of the point where the box touches the ladder.

Step-by-step explanation:

(208/409)*100%

50.85%

Step-by-step explanation:

To go from A to M you need to go 4 to the right and 3 down. If M is the middle you'll need to do the same to get from M to B. So (2+4,-2-3)=(6,-5)

The equation of the line perpendicular to y=1/2x-9 passing through the point (7,10) is y=-2x+24.

To find the equation of a line that is perpendicular to another line, we need to determine the slope of the given line and use the negative reciprocal of that slope for our new line. The line given is y = ½x - 9, so the slope (m) is ½. The slope of the perpendicular line will be the negative reciprocal of ½, which is -2.

The next step is to use the point given, (7,10), and the slope of the perpendicular line to write the equation in point-slope form, which is y - y1 = m(x - x1). Plugging in our values we get: y - 10 = -2(x - 7).

Finally, we can rearrange this into slope-intercept form, y = mx + b, by simplifying and solving for y:

Therefore, the equation of the line perpendicular to y = ½x - 9 that passes through the point (7,10) is y = -2x + 24.

Answer:

-26a - 25a^7

Step-by-step explanation:

Answer:

P ≡ [tex](- \frac{5}{4}, \frac{15}{4})[/tex]

Step-by-step explanation:

The point P divides the line segment from A(-2,3) and B(1,6) in the ratio of 1 : 3.

So, AP : PB = 1 : 3.

Now, the coordinates of point P will be given by [tex](\frac{1 \times 1 + 3 \times (- 2)}{1 + 3}, \frac{1 \times 6 + 3 \times 3}{1 + 3})[/tex]

= [tex](- \frac{5}{4}, \frac{15}{4})[/tex] (Answer)

Note: Let there are two points with known coordinates [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] and another a point having coordinates (h,k) divides the line joining the two above points internally in the ratio m : n, then (h,k) is given by

(h,k) ≡ [tex](\frac{mx_{2} + nx_{1}}{m + n}, \frac{my_{2} + ny_{1}}{m + n})[/tex]

Answer:

OPTION C: 2x - y = -1

Step-by-step explanation:

Equations of two straight lines do not have a solution when they do not meet. Also, two parallel lines never meet.

Given the equation of the first line is: 2x - y = 1. So, the line parallel to this line should be the answer.

Note that the equations of two parallel lines only differ by a constant.

i.e, If ax + by + c = 0 is an equation of a line then the equation of the line parallel to this would be ax + by + k = 0.

Hence, the required answer is: 2x + y = -1, which is OPTION C.

Answer:

Option (c) is correct.

68% of the data points lie between 10 and 18.

Step-by-step explanation:

Given :  a normal distribution with a standard deviation of 4 and a mean of 14

We have to choose the  sentence that correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14.

Since, given 68% data.

We know mean of data lies in middle.

And standard deviation is distribute equally about the mean that is 50% of values less than the mean  and 50% greater than the mean.

So, 68% of data lies

mean - standard deviation = 14 - 4 = 10

mean + standard deviation = 14 + 4 = 18

So, 68% of the data points lie between 10 and 18.

The correct sentence for a normal distribution with a standard deviation of 4 and a mean of 14, is that 68% of the data points lie between 10 and 18.

The correct answer is C.

About 68% of the data in a normal distribution lie within one standard deviation of the mean.

● 14−4=10 is one standard deviation below the mean, and

14+4=18 is one standard deviation above it.

Thus, the range of 68% of the data values is between 10 and 18. Option C, which states that "68% of the data points lie between 10 and 18," thus accurately sums up the dataset.

Will is 29% taller than Wanda, so Will's height is 77.5% of Wanda's height.

Solution:

Let x be Will's height, and y be Wanda's height.

Since Will is 29% taller than Wanda we have,

[tex]x=1.29y \rightarrow(y+29\% \text{ of y }\rightarrow1y+.29\rightarrow y\rightarrowy(1+.29)\Rightarrow1.29y)[/tex]

Then solving for y we get,

[tex]\Rightarrow y=\frac{x}{1.29}\rightarrow y=\frac{100x}{129}[/tex]

[tex]\Rightarrow y\approx0.7752x[/tex]

Therefore, Will is 77.5% of Wanda's height.

Will's height is 129% of Wanda's height.

To calculate the percentage of Will's height compared to Wanda's height, we need to determine how much taller Will is than Wanda. If Will is 29% taller, it means his height is 129% of Wanda's height. This can be calculated by adding 29% to 100%: 100% + 29% = 129%. Therefore, Will's height is 129% of Wanda's height.If Will is 29% taller than Wanda, then he is 100% of Wanda's height (which is Wanda's total height) plus an additional 29% of Wanda's height. Therefore, if you combine these percentages, you will find that Will's height is 129% of Wanda's height.

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Answer:Integer Part: 67

Fractional Part: 60

Step-by-step explanation: This is how to round 67.6 to the nearest whole number. In other words, this is how to round 67.6 to the nearest integer.

67.6 has two parts. The integer part to the left of the decimal point and the fractional part to the right of the decimal point:

Answer:67

Step-by-step explanation:

When you round 67.6 to the nearest whole number you take the  6 off and get 67

Answer:

orange : cranberry : apple : orange

9 : 5 : 6

Step-by-step explanation:

Given the following ratios (fraction):

[tex]\frac{apple}{total} =\frac{1}{4}[/tex]

[tex]\frac{orange}{total} =\frac{3}{10}[/tex]

in order to add/subtract fractions, we have to ensure that the denominators are the same, we can see that for the denominators listed above, the least common multiple for 4 and 10 = 20, hence we can re-write the above as :

[tex]\frac{apple}{total} =\frac{1}{4} =\frac{5}{20}[/tex]

[tex]\frac{orange}{total} =\frac{3}{10} =\frac{6}{20} [/tex]

Hence,

Fraction of cranberry juice of the total is,

1 - [tex]\frac{5}{20}[/tex] - [tex]\frac{6}{20}[/tex]

= [tex]\frac{20}{20}[/tex] - [tex]\frac{5}{20}[/tex] - [tex]\frac{6}{20}[/tex]

= [tex]\frac{9}{20}[/tex]

Because all the denominators are the same, we can assemble the ratios of each component by taking the ratios of the numerators

cranberry : apple : orange

= ratios of their numerators

= 9 : 5 : 6

Answer:

Step-by-step explanation:

It should be 2.3 because dividing by decimals is almost the same as dividing by normal numbers you just change the decimal point when you are done dividing.

Answer:

Step-by-step explanation:

We know:

1m = 100cm

therefore

1m 74cm = 1m + 74cm = 100cm + 74cm = 174cm

45cm + 1m 74cm = 45cm + 174cm = 219cm = 200cm + 19cm = 2m 19cm

Answer:its is 2m 19cm

Step-by-step explanation:

0.45+

1.74

______

2.19

Which is 2cm 19m. HOPE IT HELPS YOU!!!

Answer:

180 chickens and 40 pigs

Step-by-step explanation:

We are given;

We are required to determine the number of chickens and pigs in the farm;

To answer the question we need to know the following;

Assuming the number of chickens is x and the number of pigs is y

Then we can form two equations;

We can solve the two equations simultaneously to find the number of chickens and pigs;

x + y = 220

2x + 4y = 520

Multiplying the first equation by 2, we get

2x + 2y = 440

2x + 4y = 520

Eliminating x, we get;

- 2y = -80

    y = 40

Solving for x;

x = 220 - y

  = 220 - 40

x  = 180

Therefore, there are 180 chickens and 40 pigs at the farm

Answer:

Step-by-step explanation:

f(x) = 2x^3 - 4x.....find f(-2).....so sub in -2 for x

f(-2) = 2(-2^3) - 4(-2)

f(-2) = 2(-8) + 8

f(-2) = -16 + 8

f(-2) = -8 <==

We have [tex]f(x)=2x^3-4x[/tex], to find [tex]f(-2)[/tex] put -2 instead of x, [tex]f(-2)=2(-2)^3-4(-2)=-16+8=\boxed{-8}[/tex].

Hope this helps.

Answer:

The Discount would save $2.25 of the final purchase.

Step-by-step explanation:

If the cake originally costs $9, 25% of that would be $2.25 off the final purchase. So the discount would save $2.25

Answer:

With the discount, you are saving $2.25 on the cake that you want.

Answer:

-$110

Step-by-step explanation:

An overdrawn bank account would be -$180. you would have to add $70 .

given 70 is not large enough to fully bring the balance to 0. long story short, subtract 70 from 180. since 70 is < 180 the number is therefore negative since 180 is negative in this problem

I hope this helps!!^^

Answer:

He is overdrawn by $110

Step-by-step explanation:

-180+ -70=110

Answer:

look below

Step-by-step explanation:

To write a fraction or mixed number as a decimal, divide the numerator by the denominator. So, for example, if you had 5/2, then you'd do 5÷2, which gives you 2.5. Hope that helped!

Answer:

The volume of Solid A is 120 cm³.

Step-by-step explanation:

Given the area of the solids are in the ratio: 4 : 9

Let their actual areas be 4x² and 9x². We have assumed the common ratio as x² for easier computation.

We have area: [tex]$ A_A : A_B = $[/tex]    4x²       :     9x²

This implies, the length should have been of the ratio of the square root of these numbers.

Therefore, the ratios of the lengths is: [tex]$ \sqrt{4x^2} : \sqrt{9x^2} $[/tex]

[tex]$ L_A : L_B = 2x : 3x $[/tex]

Now, volume is cube of lengths. Therefore, the ratio of volumes would be:

[tex]$ V_A : V_B = 8x^3 : 27x^3 $[/tex]

Given [tex]$ V_B = 405 cm^3 $[/tex]

[tex]$ \implies 27x^3 = 405 \hspace{1mm} cm^3 $[/tex]

[tex]$ \implies x^3 = \frac{405}{27} = 15 $[/tex]

Hence, the volume of solid A, [tex]$ V_A = 8x^3 = 8 \times 15 = \textbf{120} \hspace{1mm} cm^3 $[/tex].

Hence, the answer.

Answer:

y = -5/12

Step-by-step explanation:

−3(y+3)=2y+3 (multiply -3 with inside the parenthesis)

➡

-3y -9 = 2y +3

➡

-3y -2y = 3+9 add like terms

➡

-5y = 12

➡

y = -5/12

The first step to solve the equation 11-3x=44 is to isolate the variable x by subtracting 11 from both sides of the equation.

To solve the equation 11-3x=44, the first step is to isolate the variable x.

To do this, we need to get rid of the constant term on the left side of the equation. We can do this by subtracting 11 from both sides:

Now we have -3x = 33 as our new equation.

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Answer:

Therefore x = 33° , y = 40° and z = 109°.

Step-by-step explanation:

i) from properties of parallel lines a pair of alternate interior angles are equal

  Therefore x = 33°

ii) from properties of parallelogram that a pair of opposite angles are equal, Therefore z = 109°.

iii) from the law of triangle that the sum of all angles in a triangle is 180° and also using the property of parallel lines that a pair of alternate interior angles is equal we can say that x° + y° + z° = 180°                                           ⇒ 31° + y° + 109° = 180°, therefore   y° =  180° - 140° = 40°.

Therefore x = 33° , y = 40° and z = 109°.

The values of x, y and z in the parallelogram is 52°, 38° and 90° respectively.

The angles on the same side of the transversal of a parallelogram are supplementary, that is, 180°

So,

33° + 109° + y° = 180°

142 + y = 180

y = 180 - 142

y = 38°

x° + y° = 90°

x + 38 = 90

Subtract 38 from both sides

x = 90 - 38

x = 52°

x° + y° + z° = 180°

52 + 38 + z = 180

90 + z = 180

z = 180° - 90°

z = 90°

Hence,

x = 52°

y = 38°

z = 90°

Read more on parallelogram:

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Answer:

The function to represent the area a of the section inside the border is [tex]A=12x-x^2[/tex]

Step-by-step explanation:

Given section inside the border is [tex]x[/tex] inches and [tex](12-x)[/tex] inches.

We need to write the function to represent the area of the section inside the border.

We can see the length of border is [tex]x[/tex] and width of the border is [tex](12-x)[/tex].

So, the area of the rectangle will be [tex]length\times width[/tex]

The area [tex](A)[/tex] will be

[tex]A=x(12-x)\\\\A=12x-x^2[/tex]

So, the function to represent the area a of the section inside the border is [tex]A=12x-x^2[/tex]

Answer:

x = 4 OR 1x + 0y = 4

Step-by-step explanation:

so if it is a line parallel to the y axis, it is a vertical line. A vertical line has an undefined slope, so it cant be written in y = mx + b form.

ur equation would be : x = 4....because no matter what y is, x will always be 4.

but if u need it in standard form Ax + By = C it is :

1x + 0y = 4

The equation representing a line that is parallel to the y-axis and passes through the point (4,3) is x = 4.

The question is asking for an equation of a line that is parallel to the y-axis and goes through the point (4,3). In a coordinate system, a line parallel to the y-axis is a vertical line. The equation for a vertical line in the coordinate plane is of the form x = c, where 'c' is the x-coordinate of any point the line passes through. In this case, since the line passes through the point (4,3), the x-coordinate is 4. Therefore, the equation of the line parallel to the y-axis that passes through (4,3) is x = 4.

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Good evening

Answer:

Step-by-step explanation:

Look at the photo below for the details.

:)

Answer:

x = 5 or x = -2

Step-by-step explanation:

See the attached image for the working out.

We have to trade 5 bunnies for a donkey.

Solution:

To calculate how many bunnies could be exchanged for a donkey, we have to multiply the exchange rates of each animal/bird.

One bunny = 3/4 chickens (0.75 chicken),

One chicken = 2/5 pigs (0.4 pigs)

One pig = 2/3 donkeys (0.67 donkeys).

On multiplying all of the above rates we get,

0.75*0.4*0.67=0.2

Since we now know a bunnies worth is 0.2 donkey

Therefore, (1/0.2=5) 5 bunnies to trade for a donkey.

Answer:

IT'S B

Step-by-step explanation:

i actually got it! i looked up this answer for 3 hours and never found it, but i got it, it's B on edge!!!

The system of linear inequalities that includes the point (3, -2) in its solution set is y less-than-or-equal-to two-thirds x minus 4.

The system of linear inequalities that has the point (3, -2) in its solution set is y less-than-or-equal-to two-thirds x minus 4.

The first dashed line in the coordinate plane represents the inequality y = -3, where everything below the line is shaded. The second solid line, with a positive slope and passing through (0, -4) and (3, -2), represents the inequality y ≤ (2/3)x - 4, where everything below the line is shaded.

Therefore, the correct option is y less-than-or-equal-to two-thirds x minus 4.

Final answer:

A total of 63 cars raced over the two days: 36 cars on Saturday (4 races × 9 cars) and 27 cars on Sunday (3 races × 9 cars).

Explanation:

The student is asking to calculate the total number of cars that raced over two days. There were 4 car races on Saturday and 3 on Sunday, with 9 cars racing in each race. To find the total number of cars that raced, you would multiply the number of races each day by the number of cars in each race and then add those two products together.

For Saturday: 4 races × 9 cars per race = 36 cars

For Sunday: 3 races × 9 cars per race = 27 cars

Adding the cars from Saturday to the cars from Sunday gives us the total: 36 cars + 27 cars = 63 cars.

Therefore, over the two days, a total of 63 cars raced.