Solve each system of the new equations by adding or subtracting

Answer:

y=9

Step-by-step explanation:

16y and 18y-18 are vertical angles. The definition of Vertical Angles states that both of the measures of the angles are equal to each other. Therefore,

18y-18=16y

2y-18=0

2y=18

y=9

The bottom of a 25 feet ladder is propped up against a wall, which is 7 feet away. When the ladder is 15 feet above the ground, 23.3 feet per second is the top of the ladder falling down the wall.

Given that,

The bottom of a 25 feet ladder is propped up against a wall, which is 7 feet away. A feet per second of the ladder's bottom begins to slide away from the wall.

We have to find when the ladder is 15 feet above the ground, how many feet per second is the top of the ladder falling down the wall.

Let us take x = height where the ladder hits the building

7 squared + x squared=25 squared

49+x squared=625

x squared=576

x=24 feet

Now,

If it slips 15 feet that 24-15=9 feet

Let x = distance from wall:

x² + 9² = 25²

x² + 81= 625

x² = 544

x = 23.3 feet

Therefore, when the ladder is 15 feet above the ground, 23.3 feet per second is the top of the ladder falling down the wall.

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The volume of the cone is:

The volume of a cone is given by the formula:

Given radius, r = 8, and height, h = 4, we have:

After simplification, 7h+(-9.1d)-13+6d-3.5h is 3.5h-3.1d-13.

According to the question,

We have the following expression:

7h+(-9.1d)-13+6d-3.5h

Now, we will simplify it by adding or subtracting the numbers or the numbers with the same variable together. For example, 3.5h can only be subtracted from 7h because both of them h as a variable. And 6d can be subtracted from 9.1d.

(More to know: when a positive and a negative number is multiplied then the result is always negative. In this case, we will multiply +1 into -9.1d.)

Now, let's simplify the given expression:

7h-3.5h-9.1d+6d-13

3.5h-3.1d-13

Hence, the expression obtained after solving the given expression is 3.5h-3.1d-13.

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Given data:

The number of red drops for first batch are r=100.

The number of blue drops for first batch are b=20.

The number of red drops for second batch are r'=75.

The number of blue drops for second batch are b'=15.

The expression for the red per blue drop for first batch is,

n=r/b

Substitute the given values in the above expression.

n=100/20

=5

The expression for the red drop per blue drop of the second batch is,

n'=r'/b'

Substitute the given values in the above expression.

n'=75/15

=5

Thus, yes the ratio of red to the blue drop is same for both batches.

The largest prime factor that always divides the sum of the terms in the sequence is 37.

The sequence is finite and consists of three-digit integers.

The tens and units digits of each term are, respectively, the hundreds and tens digits of the next term, and the tens and units digits of the last term are, respectively, the hundreds and tens digits of the first term.

From the above property of the sequence, we can see that each digit at the units, tens as well as hundreds place will appear the same number of times in the sequence.

Let "x" be the sum of the digits at unit place in all the terms.

The sum of all the terms is "S".

S = 111*x

S = 3*37*x

We can clearly see that the sum "S" is divisible by 37.

Hence, the largest prime factor that always divides the sum of the terms in the sequence is 37.

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Answer:

f(x)=x+2 Passes through

x-y=2 DOES NOT pass through

Step-by-step explanation:

Method- plug in x and see if the y matches the points. (1,3) (7,9)

f(x)=x+2

f(1)=1+2=3

f(7)=7+2=9

Matches!

x-y=2

1-y=2 --> y=-1

Does not match

The midpoints of the first and last parts are 4/5m units apart

The length of the line segment is given as

Length = m units

From the question, the number of partitions is given as

Partition = 5

So, the length of each partition is

Each partition = Length/Partition

This gives

Each partition = m/5

The midpoint of a partition is

Partition midpoint = m/5 x 1/2

Evaluate

Partition midpoint = m/10

The distance between the midpoints of the first and last segments is then calculated as

Distance = Length - 2 x Partition midpoint

So, we have

Distance = m - 2 x m/10

Evaluate

Distance = m - m/5

This gives

Distance = 4/5m

Hence, the distance is 4/5m units

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for the square root you must look for a number that multiplied with itself gives you the indicated value

for this case a number that multiplied by itself gives you 100

sothe square root of 100 is:

We will have that the relationship is proportional because each time he bought more sets they had the same cost, and the total cost added to the sum of the independent cost. And we have the following relationship for the 2 sets and 4 sets:

2 sets:

So, each individual set is $12.5.

4 sets:

So, each individual set is $12.5.

So, each individual set for each relationship has the same cost, therefore the relationship is proportional.

The curves are intersecting at (1, 1) and (-10, -4)

Nonlinear functions are the functions where the equations are not linear or the highest degree is more than 1. The following are some examples where the functions are not linear or non-linear. Ex. [tex]x^{2}[/tex] + 4x -1

In the above question, a graphical representation of non-linear system of equations is given

We need to find the solution of this non-linear system of equations based on the graphical representation

We can find the solutions from the graph, wherever the curves are intersecting, that intersection point is known as the solution of the non-linear system of equations

We can clearly see that, the curves are intersecting at

(1, 1) and (-10, -4)

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The curves are intersecting at (1, 1) and (-10, -4)

Nonlinear functions are the functions where the equations are not linear or the highest degree is more than 1. The following are some examples where the functions are not linear or non-linear. Ex. [tex]x^{2}[/tex] + 4x -1

In the above question, a graphical representation of non-linear system of equations is given

We need to find the solution of this non-linear system of equations based on the graphical representation

We can find the solutions from the graph, wherever the curves are intersecting, that intersection point is known as the solution of the non-linear system of equations

We can clearly see that, the curves are intersecting at

(1, 1) and (-10, -4)

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The slope-intercept form of the linear equation is

y = m x + b, where

m is the slope

b is the y-intercept

If the x-coordinates of the two points are equal, that means the line is vertical

A vertical line has no slope

Its equation is x = a, where a is the x-coordinate of any point on the line

13) The two points are (5, 3) and (5, 4)

They have the same x-coordinates, then its equation is

x = 5

The rule of the slope is

(x1, y1) and (x2, y2) are two points on the line

The line passes through points (0, 4) and (2, 3)

x1 = 0 and y1 = 4

x2 = 2 and y2 = 3

Substitute them in the rule above to find m

The equation is

b is the value of y at x = 0

at x = 0 y = 4

b = 4

The equation of the line is

Answer:

2×10^7

Step-by-step explanation:

cuz 3:6 is 2 and 10^2÷10^-5 equals 10⁷

Answer:

2×10^7

Step-by-step explanation:

6×10²/3×10^5

6/3×10²-10^-5

2×10²-^(-5)

2×10²+^5

2×10^7

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Answer:

w = 35

Step-by-step explanation:

To solve this problem, you will need to undo it in reverse order. The first thing done to w is to multiply it by 17 and then add 29 to it. You need to undo the addition of 29 with subtraction first.

624-28=595

Next, you need to undo the multiplication by 17 with division.

[tex]\frac{595}{17} =35[/tex]

Therefore, your answer is 35

Answer:

-20

Step-by-step explanation:

1- each of the two numbers are inside parenthesis and are beside each other which means they should be multiplied like this: -5.6 * 3.4

2- because 5.6 is negative, the rule in multiplying different signs would result to a negative number

3- and when you accurately multiply them, the answer is 19.04, and the options here are estimated so you should estimate the 19.04 too

4- 1 after it is 9 and nine is a great number, 1 turns to 2 and 9 turns into 0, which equals to 20, and DO NOT forget to add the sign, which is negative as i said previously

The slope of the line that is parallel to 8x + 9x = 3 is: -8/9.

If two lines are parallel to each other, their slope values is equal to each other. This means the value of "m" in their equation expressed in slope-intercept form as y = mx + b, is the same.

Given the equation of a line in standard form as, 8x + 9y = 3, rewrite this in slope-intercept form:

8x + 9y = 3

8x + 9y - 8x = -8x + 3 [subtraction property of equality]

9y = -8x + 3

9y/9 = -8x/9 + 3/9 [division property of equality]

y = -8/9x + 1/3

The slope of the equation is -8/9. Therefore, the slope of the line that is parallel to the equation 8x + 9y = 3 will also be: -8/9.

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We will have the following:

Inferring from the information presented in the diagram we can conclude that the measurements will be:

Base: 3ft * 12ft = 36f t^2

Side1: 3ft * 2ft = 6 ft^2

Side 2: 12ft * 2ft = 24 ft^2

So, the values that would represent the dimension will be:

Length: 12 ft.

Width: 3 ft.

Height: 2 ft.

88cm² is the area of the trapezoid in the diagram.

This question is incomplete, the missing diagram is uploaded along the answer below below.

A trapezoid is simply a quadrilateral with at least one pair of parallel sides.

The area of a trapezoid is expressed as;

A = 1/2 × ( a + b ) × h

Where a is length of base a, b is length of base b and h is the height.

Given the data in the diagram;

To determine the area of the trapezoid, plug the given lengths into the above formula and solve for A.

A = 1/2 × ( a + b ) × h

A = 1/2 × ( 8cm + 14cm ) × 8cm

A = ( 8cm + 14cm ) × 1/2 × 8cm

A = ( 22cm ) × 4cm

A = 88cm²

Therefore, the area is 88 square centimeters.

Option C is the correct answer.

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The formula written in symbols as T =UN. Solve the formula for U.​

we have

T=U*N

solve for U

so

isolate the variable U

step 1

divide by N both sides

T/N=U*N/N

T/N=U

therefore

Given data

Ammy has a piece of wood that measures 42 inches

Ammy cut from the 42-inch piece of wood is calculated as

Thus, Amy cut from the 42-inch piece of wood is 33 inches

In plan B the price rises by 10%.

Thus the price rise is per week is $0.8

In plan A the price rise per week is $0.1

In plan C the price rise per week is

In plan D the price rise per week is $0.25

Considering all the plan the maximum price rise for each week is 0.8.

So the plan that would lead to $12 fastest is plan B.

The answer is plan B.

In this kind of problem is better to work backwards. We have the number nine hundred twenty-eigh.

This means that the two last digits are a 2 and a 8, becasue we have a "twenty-eight" = 28

And then, we have "nine hundred" = 900

The number whole, then, is:

⇒Mathematically this means

[tex]\frac{1}{4} (r+10)= r-4\\\frac{r}{4} +\frac{10}{4} =r-4\\\frac{r}{4}(4) +\frac{10}{4} (4)=r(4)-4(4)\\r+10=4r-16\\r-4r=-16-10\\-3r=-26\\\frac{-3r}{-3} =\frac{-26}{-3} \\r=\frac{26}{3}[/tex]

Attached is the solution.

The probability that one or more of them tests negative is 0.85.

Probability is defined as the likeliness of an event to occur. The probability of any event to occur ranges from 0 to 1, and the sum of all the probabilities of all the events happening is 1.

If Marv and Patricia will each take a Covid test, then the events that will occur are : both will test positive, both will test negative, or one of them will test negative.

Based on the given information, the probability that both will test positive is 0.15. Subtract it from 1 to and get the probability that one or more of them tests negative.

probability = 1 - 0.15

probability = 0.85

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Answer: C. Four loaves, with flour left over.

Step-by-step explanation:

7/2 simplifies to 3 1/2

Do the math,

3/4 + 3/4 = 1 1/2        2 loaves

1 1/2 + 3/4 = 2 1/4      3 loaves

2 1/4 + 3/4 = 3           4 loaves

Now when we add 3/4 to 3, we get more than 3 1/2. Which means we do not have enough flour for another loaf of bread. So, we can make four loaves and still have some four left over. The answer is C.

Answer: 48 is the smaller integer

Step-by-step explanation: 48+49=97 48 and 49 are the two integers, 48 is smaller than 49.

Using the angle of elevation, the height of the tree is 71.57 feet.

The angles of elevation to a nearby tree from a point on the ground is measured to be 54 degrees.

The distance from the tree to the point on the ground is 52 feet.

The height of the tree can be found as follows:

The situation can be modelled to a right triangle.

Therefore, the height of the tree is the opposite side of the right triangle formed.

Hence,

tan ∅ = opposite / adjacent

where

∅ = angle of elevation

tan 54 = h / 52

cross multiply

h = 52 tan 54

h = 52 × 1.37638192047

h = 71.5718598645

Therefore,

height of the tree = 71.57 feet.

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