PLEASE HELP!!!!!!!!!!!!!!

Answer:

A = 110.25

Step-by-step explanation:

add all the equations and equal it to 180 because all triangle angles add to 180:

4x+1 + 3x + 3x-1 = 180

10x =70

/10   /10

x = 7

Insert x into each equation and solve:

3(7)-1 = 20

4(7)-1 = 27

3(7) = 21

and then use A = 1/2 base*height formula:

A= 1/2 21* 20

A= 210

Area of triangle A is 210 cm²

Given that;

Perimeter of the triangle = 70cm

Sides of triangle = 3x, 4x + 1, 3x - 1

Find:

Area of triangle A

Computation:

3x + (4x + 1) + (3x - 1) = 70

3x + 4x + 3x = 70

10x = 70

x = 7

So,

Perpendicular = 3x - 1 = 21 - 1 = 20 cm

Hypotenuse = 4x + 1 =28 + 1 = 29 cm

base = 3x = 21 cm

Area of triangle A = (1/2)(b)(h)

Area of triangle A = (1/2)(21)(20)

Area of triangle A = (21)(10)

Area of triangle A = 210 cm²

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Answer:

All the zeroes of f(x) are x = 1, x = -1 + 4i and x = -1 - 4i.

Step-by-step explanation:

Given that f(x) = x³ + x² + 15x - 17

Now, we have to find all the zeroes of the function.

Given that x = - 1 + 4i is a zero of the function.

So, x = - 1 - 4i must be another zero of the function.

Therefore, (x + 1 - 4i)(x + 1 + 4i) will be factor of the function.

Hence,  (x + 1 - 4i)(x + 1 + 4i)

= x² + 2x + (1 - 4i)(1 + 4i)  

= x² + 2x + [1² - (4i)²]

= x² + 2x + 17

Assume that (x + a) is another factor of f(x).

Therefore, we can write f(x) = x³ + x² + 15x - 17 = (x + a)(x² + 2x + 17)

⇒ x³ + x² + 15x - 17 = x³ + (a + 2)x² + (2a + 17)x + 17a

Hence, comparing the coefficients we can write  

a + 2 = 1  

⇒ a = -1  

Therefore, f(x) =x³ + x² + 15x - 17 = (x - 1)(x² + 2x + 17)

So, all the zeroes of f(x) are x = 1, x = -1 + 4i and x = -1 - 4i (Answer)

Good evening ,

Answer:

D : y = -6

Step-by-step explanation:

A line D has a slope of 0 shouled be parallel to the x-axis then

it’s equation in slope intercept form should be y=a

And since, It passes through the point (-1,-6) then a=-6

finally:

the equation of D is y=-6.

:)

Answer:

1 function {(2,2),(4,4),(6,6),(8,8)} written is a function the other following coordinates are not functions due to it not being a straight line as a 'proper' function should be.

Answer:

The answer is:

{(2,2),(4,4),(6,6),(8,8)} is a function

{(0,3),(3,5),(5,6),(8,4)} is a function

{(1,2),(3,3),(4,8),(6,3)} is a function

{(3,4),(5,2),(5,6),(7,3)} is not a function

Step-by-step explanation:

Sorry I don't have an explanation, but I know these are correct because I took the test and got this correct. ;)

It will take John 2800 steps to walk from his house to James' house

Step-by-step explanation:

First of all we have to convert all the measurements in same unit.

Distance = 0.7 km

As 1 km = 1000 m

0.7*100 = 700m

And

1 m = 100 cm

700*100 = 70000cm

Now,

25 cm = 1 step

[tex]So,\\70000cm = \frac{70000}{25}\\=2800\ steps[/tex]

It will take John 2800 steps to walk from his house to James' house

Keywords: Conversions, Lengths

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Answer:

The vertex of the function is (2, -3).

Step-by-step explanation:

Given:

[tex]y=x^{2}-4x+1[/tex]

So, to find the vertex of the function we will get the equation in the form:

[tex]y=ax^{2} +bx+c[/tex]

[tex]y=1x^{2}+(-4)x+1[/tex]

So, [tex]a=1,b=-4,c=1[/tex]

Then, we calculate the x-coordinate of the vertex:

[tex]x=\frac{-b}{2a}[/tex]

[tex]x=\frac{-(-4)}{2\times1}\\x=\frac{4}{2}[/tex]

[tex]x=2[/tex]

And now, we get the [tex]y[/tex] value of vertex of the function:

[tex]y=1x^{2}-4x+1[/tex]

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

[tex]y=1\times 4-8+1[/tex] (when the opposite signs multiply the result is negative)

[tex]y=4-8+1[/tex]

[tex]y=-3[/tex]

Therefore, the vertex is at [tex](x,y)=(2,-3)[/tex].

Answer:

A on edge

Step-by-step explanation:

Answer:

Plug in the Pythagorean Theorem and you get 5[tex]\sqrt{3}[/tex]

Step-by-step explanation:

We know that 5 is half of ten, so square those two.

a+25=100

a=75

[tex]\sqrt{75}[/tex]=5[tex]\sqrt{3}[/tex]

The answer is A, 5[tex]\sqrt{3}[/tex].

Hope this helps :)

Answer:  5

Step-by-step explanation:

5x4=20 and you cant have half a pack of strings so it 5 packs.

Ron worked for 3.25 hours and the total payment is $29.25 for 11.25 hours of combined work, which equates to an hourly wage of $2.60. Therefore, Ron should receive $8.45.

To calculate Ron's share of the $29.25 payment for removing garden gnomes, we first need to determine the total amount of time worked by all three individuals. Since Steve and Jerry worked 4 hours each and Ron was 45 minutes late, Ron worked 3 hours and 15 minutes, or 3.25 hours. We can convert 45 minutes to a decimal by dividing 45 by 60, which gives us 0.75, and since Ron was late by that duration, we subtract it from 4 hours (4 - 0.75 = 3.25).

Total hours worked by all = (Steve's hours + Jerry's hours + Ron's hours) = 4 + 4 + 3.25 = 11.25 hours.

To find the hourly rate, we divide the total payment by the total hours worked: $29.25 / 11.25 hours = $2.60 per hour. Finally, we multiply Ron's hours worked by the hourly rate to find his share: 3.25 hours * $2.60 per hour = $8.45.

Answer:

16/15 or 1 1/15

Step-by-step explanation:

2/6/8=8/3

1/5/8=8/5

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

8/3-8/5=40/15-24/15=16/15=1 1/15

The question is incomplete. Here is the complete question:

A 20-foot ladder is leaning against a wall. The foot of the ladder makes an angle of 58 degrees with the ground. Find, to the nearest foot, the vertical distance from the top of the ladder to the ground.

Answer:

17 ft

Step-by-step explanation:

Let the height from the top of the ladder to the ground be 'x' feet.

Given:

The triangle for the given situation is shown below.

Now, from the triangle ABC, AB is the length of the ladder, A is the top of ladder, B is the foot of the ladder and AC is 'x'.

The length of the ladder is, [tex]AB=20\ ft[/tex]

The angle made by the foot of the ladder with the ground is, [tex]\angle ABC=58[/tex]°

Now, using the sine ratio for the angle ∠ABC, we have:

[tex]\sin(\angle ABC)=\frac{AC}{AB}\\\sin(58)=\frac{x}{20}\\x=20\times \sin(58)\\x=20\times 0.8480\\x=16.96\approx 17\textrm{ ft (Nearest foot})[/tex]

Therefore, the vertical distance from the top of the ladder to the ground is 17 feet.

Answer:

The y intercept is when x=0

When x=0,

y+3= 5(-3)

y+3= -15

y=-18

the y intercept is thus -18.

Step-by-step explanation:

Wahab has to donate at least 50 books to reach his goal

Given that, Wahab wants to donate at least $6000 in books and pairs of shoes.  

Let "B' represent the number of books

Let "S" represent the number of pairs of shoes that Wahab must donate to achieve his goal.  

20B+50S ≥ 6000 ⇒ this is the inequality for total donation.  

Wahab donates 100 pairs of shoes.  

Now, as he donated 100 pairs of shoes, S = 100, so substitute this in inequality.

20B + 50(100) ≥ 6000

20B + 5000 ≥ 6000

20B ≥ 6000 – 5000

20B ≥ 1000

B ≥ 50

Hence, wahab has to donate at least 50 books to reach his goal.

The length of ramp is 8.9 meters approximately.

Given that, the entrance of the old town library is 2.3 feet above ground level.  

A ramp from the ground level to the library entrance is scheduled to be built.  

The angle of elevation from the base of the ramp to its top is to be 15º

We have to find the length of the ramp.

Let the length of ramp be “n” feet.

Now, if we observe there forms a right angle triangle with ramp as hypotenuse and height of entrance as opposite side for angle of elevation 15 degrees.

The diagram is attached below

In the figure,

AC = length of ramp

AB = height above ground level = 2.3 feet

angle of elevation = 15 degree

Then, we know that,

[tex]\sin \theta=\frac{\text {opposite side}}{\text {hypotenuse}}[/tex]

where θ is angle of elevation.

[tex]\begin{array}{l}{\sin 15^{\circ}=\frac{2.3 \text { feet }}{n \text { feet }}} \\\\ {\rightarrow 0.2588=\frac{2.3}{n}} \\\\ {\rightarrow n=\frac{2.3}{0.2588}} \\\\ {\rightarrow n=8.8865}\end{array}[/tex]

Hence, the length of the ramp is 8.9 meters approximately.

Slope intercept form of line passing through midpoint of CD and perpendicular to CD is [tex]\Rightarrow y=-\frac{4}{7} x+2[/tex]

Need to find the slope intercept form for the line perpendicular to C(-4,-5) and D(4,9)

And passing through the midpoints of the line CD.

Lets first calculate slope of CD  

Let say slope of CD be represented by [tex]m_1[/tex]

General formula of slope of line passing through points [tex]\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right)[/tex] is as follows:

[tex]m=\frac{\left(y_{2}-y_{1}\right)}{\left(x_{2}-x_{1}\right)}[/tex]

[tex]\text { In case of line } \mathrm{CD} , x_{1}=-4, \quad y_{1}=-5 \text { and } x_{2}=4, y_{2}=9[/tex]

[tex]\text {So slope of line } \mathrm{CD} \text { that is } m_{1}=\frac{(9-(-5))}{(4-(-4))}=\frac{14}{8}=\frac{7}{4}[/tex]

Let’s say slope of required line which is perpendicular to CD be [tex]m_2[/tex]

As product of slope of the lines perpendicular to each other is -1

=> slope of line CD [tex]\times[/tex] slope of line perpendicular to CD = -1

[tex]\begin{array}{l}{=>m_{1} \times m_{2}=-1} \\\\ {\Rightarrow \frac{7}{4} \times m_{2}=-1} \\\\ {\Rightarrow m_{2}=-\frac{4}{7}}\end{array}[/tex]

Now let’s find midpoint of CD

[tex]\text { Midpoint }(x, y) \text { of two points }\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right) \text { is given by }[/tex]

[tex]x=\frac{x_{2}+x_{1}}{2} \text { and } y=\frac{y_{2}+y_{1}}{2}[/tex]

[tex]\text { So in case of line } \mathrm{CD} , x_{1}=-4, y_{1}=-5 \text { and } x_{2}=4, y_{2}=9[/tex]

And midpoint of CD will be as follows

[tex]x=\frac{x_{2}+x_{1}}{2}=\frac{4+(-4)}{2}=0 \text { and } y=\frac{y_{2}+y_{1}}{2}=\frac{9-5}{2}=2[/tex]

So midpoint of CD is ( 0 , 2 )

As it is given that line whose slope intercept form is required is perpendicular to CD and passing through midpoint of CD , we need equation of line passing through ( 0 , 2 ) and having slope as [tex]m_{2}=-\frac{4}{7}[/tex]

Generic equation of line passing through [tex]\left(x_{1}, y_{1}\right)[/tex] and having slope of m is given by

[tex]\left(y-y_{1}\right)=m\left(x-x_{1}\right)[/tex]

[tex]\text { In our case } x_{1}=0 \text { and } y_{1}=2 \text { and } m=-\frac{4}{7}[/tex]

Substituting the values in generic equation of line we get

[tex](y-2)=-\frac{4}{7}(x-0)[/tex]

As we required final equation in slope intercept form which is y = mx + c, lets rearrange our equation is required form:

[tex]\Rightarrow y=-\frac{4}{7} x+2[/tex]

Hence can conclude that slope intercept form of line passing through midpoint of CD and perpendicular to CD is [tex]\Rightarrow y=-\frac{4}{7} x+2[/tex]

To find the equation of the line perpendicular to the line passing through points C(-4,-5) and D(4,9) and passing through the midpoint (0, 2), follow these steps: 1) Find the slope of the given line. 2) Find the midpoint of the line. 3) Find the negative reciprocal of the slope. 4) Use the slope and midpoint to write the equation of the perpendicular line in slope-intercept form.

To find the equation of a line perpendicular to the line passing through points C(-4,-5) and D(4,9) and passing through the midpoint of the line, we need to follow these steps:

Let's go through these steps:

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

slope = (y₂ - y₁) / (x₂ - x₁)

In this case, the points are C(-4,-5) and D(4,9). So, we can substitute the values into the formula:

slope = (9 - (-5)) / (4 - (-4))

slope = 14 / 8

slope = 7 / 4

The midpoint of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

In this case, the points are C(-4,-5) and D(4,9). So, we can substitute the values into the formula:

midpoint = ((-4 + 4) / 2, (-5 + 9) / 2)

midpoint = (0 / 2, 4 / 2)

midpoint = (0, 2)

The negative reciprocal of a slope is found by changing the sign of the slope and taking its reciprocal.

In this case, the slope is 7 / 4. So, the negative reciprocal is -4 / 7.

Now that we have the slope (-4 / 7) and the midpoint (0, 2), we can use the slope-intercept form of a line to write the equation:

y = mx + b

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

Substituting the values, we have:

y = (-4 / 7)x + b

To find the value of b, we can substitute the coordinates of the midpoint (0, 2) into the equation:

2 = (-4 / 7)(0) + b

2 = 0 + b

b = 2

So, the equation of the line perpendicular to the line passing through C(-4,-5) and D(4,9) and passing through the midpoint (0, 2) is:

y = (-4 / 7)x + 2

Answer:

yes

Step-by-step explanation:

just solve for n

20 characters why

Answer:

Yes

Step-by-step explanation:

4n+1=n-8

4n-n+1=-8

3n+1=-8

3n=-8-1

3n=-9

n=-9/3

n=-3

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

3n=-9

n=-9/3

n=-3

The two equations are equivalent.

Answer:

C

Step-by-step explanation:

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

The formula of a slope:

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

We have two points A(4, 3) and B(-1, 3).

Substitute:

[tex]m=\dfrac{3-3}{-1-4}=\dfrac{0}{-5}=0[/tex]

The slope m = 0, therefore it's a horizontal line.

The equation of a horizontal line:

[tex]y=a[/tex] where a is any real number

The line passes through points A and B, where ordinates are equal 3.

Therefore the equation is

[tex]y=3[/tex]

Answer:

measure of angle K is 48° or m∠K = 48°

Step-by-step explanation:

Given:

ΔJKL= ΔPQR

m∠P = 52°

m∠Q = 48°

m∠R = 80°

When 2 triangles are equal or congruent to each other then their corresponding angles are equal or congruent by congruence property.

Hence ,

m∠P = m∠J

m∠Q = m∠K

m∠R = m∠L

But m∠Q = 48° hence m∠K = 48°

Hence measure of angle K is 48°

Creating parallel and perpendicular lines involves understanding that parallel lines share the same slope, while perpendicular lines have slopes that are negative reciprocals of each other. A line that is neither parallel nor perpendicular to a given line simply has a slope that does not meet these conditions.

Given the lines in your question, you're asked to create a parallel, perpendicular, and neither parallel nor perpendicular line. Let's consider the first line: y = 3x.

1) A line parallel to y = 3x will have the same slope, so the equation of such a line can be y = 3x + b. You can choose any value for b, as it shifts the line up or down but doesn't change its slope.

2) A line perpendicular to y = 3x would have a slope that is the negative reciprocal of 3, which is -1/3. So, such a line can be represented by the equation y = -1/3x + b. Again, any value of b will work.

3) A line that is neither parallel nor perpendicular to y = 3x could have any slope that's not equal to 3 or -1/3. For instance, the line y = 2x + b is neither parallel nor perpendicular to y = 3x.

Do the same for all the remaining lines by understanding these principles.

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There are 4 queens in a deck of cards.

You have 4 chances out of 52 total cards to get a queen.

The probability is 4 queens / 52 cards = 4/52, which can be reduced to 1/13

Answer:

m=-23/10

Step-by-step explanation:

-2 67/90=-247/90

m-4/9=-247/90

m=-247/90+4/9

m=-247/90+40/90

m=-207/90

m=-23/10

675 people will have score between 85 and 120

Step-by-step explanation:

Given

Mean = 100

SD = 15

If we have to find percentage of score between two values we have to find the z-score for both values and then area under the curve for both values

z-score is given by:

for a value x:

[tex]z-score = \frac{x-mean}{SD}[/tex]

So,

For 85:

[tex]z-score = z_1 = \frac{85-mean}{SD}\\ = \frac{85-100}{15}\\=\frac{-15}{15}\\=-1[/tex]

[tex]z-score = z_2 = \frac{120-mean}{SD}\\ = \frac{120-100}{15}\\=\frac{20}{15}\\=1.3333[/tex]

Now we have to find the area under the curve for both values of z-score. z-score tables are used for this purpose.

So,

For z1 : 0.1587

For z2: 0.9082

The area between z11 and z2:

[tex]z_2-z_1 = 0.9082-0.1587=0.7495[/tex]

So the probability of score between 85 and 120 is 0.7495

As the sample is of 900 people, the people with scores between 85 and 120 will be:

900*0.7495 = 674.55 people

Rounding off to nearest whole number

675 people will have score between 85 and 120

Keywords: Probability, SD

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Answer:

The pattern is that the decimal point moves the same number of decimal points to the right as zeros the power of ten has.

Step-by-step explanation:

To multiply a decimal number by a power of ten (such as 10, 100, 1,000, etc.), count the number of zero in the power of ten. Then go to the right the decimal point the same number of positions.

For example, 0.36 * 10 = 3.6. The multiplier 10 has one zero, so you move the decimal point in 0.36 one position to the right to get the product 3.6.

A second example, 0.36 * 100 = 36. The multiplier 100 has two zeros, so you move the decimal point in 0.36 two positions to the right to get the product 36.

So, the pattern is that the decimal point moves the same number of decimal points to the right as zeros the power of ten has.

Answer:

To multiply a decimal number by a power of ten (such as 10, 100, 1,000, etc.), count the number of zero in the power of ten. Then go to the right the decimal point the same number of positions.

Step-by-step explanation:

Using the blueprint scale of 5 inches to 25 feet, the width of the door on the blueprint at 1.5 inches translates to an actual width of 7.5 feet.

To find the actual width of the door in feet using a given scale, we use proportional relationships.

The scale provided is 5 inches : 25 feet.

This means that every 5 inches on the blueprint correspond to 25 feet in actual size.

To find the actual door's width, we calculate it using the following proportion:

5 inches / 25 feet = 1.5 inches / x feet

Now, we solve for 'x' to find the actual width:

5/25 = 1.5/x

Now, cross-multiply and divide to find 'x':

5x = 25 * 1.5

x = (25 * 1.5) / 5

x = 37.5 / 5

x = 7.5 feet

So the actual door's width is 7.5 feet.

Answer:

19 ft, 24 ft and 38 ft are the lengths of triangle.

Step-by-step explanation:

Let the length of second side be x.

Now given:

Given: Length of first side is 2 times length of second side = 2x

Given:Length of third side is 5 ft longer than the second side = 5+x

Perimeter of triangle = 81 ft.

Need to Calculate length of each side.

Now we know that sum of all three sides of triangle is equal to perimeter of triangle.

Hence,

[tex]x+2x+5+x =81\\4x= 81-5\\4x=76\\x=19 ft[/tex]

Also,

2x= 2×19 =38 ft.

5+x = 5+19 =24 ft.

Hence,

Length of first side  = 38 ft.

Length of second side = 19 ft.

Length of third side =24 ft.

Answer:

A

Step-by-step explanation:

1)The mole is a unit of measure that contains as many elementary entities as in atoms of 12 grams of Carbon  (12 AMU). The Carbon mass is the reference.

2)We have to specify which particle we are using when dealing with mole unit:

particle, atoms, molecules, ions, electrons, etc.

[tex]1\:mol \:C=6*10^{23} \:particles[/tex]

3) So If I have 6 moles of a substance, I am going to have six times the number of particles that are in 12 grams of carbon-12.

[tex]36*10^{23} \:particles[/tex]

Final answer:

To solve the problem, three equations can be used: 25 ÷ 5 = ?, 5 × ? = 25, and 25 ÷ ? = 5.

Explanation:

The correct equations to help solve the problem are:

To find the number of lettuce plants in each row, you need to divide the total number of lettuce plants, which is 25, by the number of rows, which is 5. So the first equation, 25 ÷ 5 = ?, will give you the answer. The second equation, 5 × ? = 25, can also be used to find the number of lettuce plants in each row by solving for the missing value. Finally, the third equation, 25 ÷ ? = 5, can be used as an alternative way to find the number of lettuce plants in each row.

Hello,

Much love for using Brainly Today.

We need to simplify the fraction, once done you solve it from there. It's the main step, when you're done figure out who made a mistake (if someone does) and fix it.

Here's a reminder on how to simplify a fraction,

Find a common factor of the numerator and denominator. A common factor is a number that will divide into both numbers evenly. Two is a common factor of 4 and 14.

Divide both the numerator and denominator by the common factor.

Repeat this process until there are no more common factors.

The fraction is simplified when no more common factors exist.

Another method to simplify a fraction

Find the Greatest Common Factor (GCF) of the numerator and denominator

Divide the numerator and the denominator by the GCF

Thanks again for using Brainly,

Have an amazing day!