Solve the system of equation using elimination.



7x−12y=−3−7x+12y=2

Multiple choice question.
cross out

A)
(−114,112)

cross out

B)
(−1,−13)

cross out

C)
infinitely many solutions

cross out

D)
no solution

Answer: 5.2 cm

Step-by-step explanation:

4.8 squared + 2 squared is 23.04 + 4, which is 27.04. The square root of that is 5.2

Answer: 3.9

Step-by-step explanation:

[tex]\frac{x}{\sin 15^{\circ}}=\frac{12}{\sin 128^{\circ}}\\\\x=\frac{12 \sin 15^{\circ}}{\sin 128^{\circ}}\\\\x \approx 3.9[/tex]

If y equals 7 when x equal 2/3, so when x =7/3 the y is equal to 14/7

If y varies inversely with x, this means that the product of x and y is a constant. So if we know that y = 7 when x = 2/3, then we can set up the equation: x*y = k, where k is the constant.

Substituting the known values we get: (2/3)*7 = k.

So we know that k = 14/3

Now, we can use this value of k to find the value of y when x = 7/3.

x*y = k

(7/3)*y = 14/3

y = 14/7

So, when x = 7/3, y = 14/7

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Answer: 5 4/7

Step-by-step explanation: First, we need to change both 1 5/7 and 3 1/4 into an improper fraction. So:

[tex]1 \frac{5}{7}[/tex] = [tex]\frac{12}{7}[/tex]

[tex]3\frac{1}{4}[/tex] = [tex]\frac{13}{4}[/tex]

So, now we need to cross-multiply 12/7 and 13/4.

That'd be 156/28

But wait. We analyze that 156 and 28 can be reduced by 4

So, 156 divided by 4 is 39, and 28 divided by 4 is 7. So now our improper fraction is 39/7. To make it an improper fraction, we divide 39 by 7, which would give us 5 4/7. I hope this helped!

Answer: translation

Step-by-step explanation:

the shape got shifted which is a translation

You can use a compass and set its angle such that it the radius of the circle that it will draw is less than that of WX's length but longer than its half. Use it to make 4 arcs.

Making 4 arcs (2 arcs up and down from W and 2 arcs up and down from X which intersect the previous two arcs) with the circle of radius smaller than the length of  WX will give two points on a perpendicular bisector.

How to find the perpendicular bisector of a line segment with the help of a compass and a straightedge?

The construction steps are as follows:

Let the line segment to be bisected(divided into two equal parts) by a perpendicular line(that perpendicular bisecting line is called the perpendicular bisector of the given line segment) be WX

Take a compass and set its radius length smaller than the length of WX and longer than half of WX

Put the tip of the compass on W and make an arc upside of WX

Now make an arc downside of WX

Repeat the above two steps but now with the tip being on X such that two new arcs intersect the previous two arcs.

Use a straightedge and join both the points of intersection of arcs.

The obtained line is the perpendicular bisector of the line segment WX

Using the above method, we get the perpendicular bisector of WX  shown in the below-attached figure.

Thus,

Making 4 arcs (2 arcs up and down from W and 2 arcs up and down from X which intersect the previous two arcs) with a circle of radius smaller than the length of  WX will give two points on a perpendicular bisector.

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You can use a compass and set its angle such - 1

James can conclude about lack of carbon-14 is  ; ( E ) Without carbon-14, James can use relative dating to estimate the age of the fossil.

Relative dating, while it will not give an exact age, can estimate the age of the fossil. James could take a look at the relative order of past events and estimate the age of the fossil that way.

It is important to know that all animals have carbon-14. Carbon 14 is in the air in carbon dioxide molecules, which animals produce through cellular respiration.

James can utilize relative dating, which can be used as a substitute to determine the age of fossils in the absence of Carbon-14, which is essential for Carbon dating, as Carbon-14 is not present in the animal fossils he is studying.

A scientific method of identifying an object's age in relation to another is called relative dating ( i.e. determining the relative order of events ).

We may thus draw the conclusion that James can determine the age of the fossil using relative dating in the absence of carbon-14.

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Complete question:

Answer:

see explanation

Step-by-step explanation:

there isa common difference between consecutive terms, that is

[tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-3}{-2}[/tex] = [tex]\frac{3}{2}[/tex]

[tex]\frac{a_{3} }{a_{2} }[/tex] = [tex]\frac{-4\frac{1}{2} }{-3}[/tex] = [tex]\frac{3}{2}[/tex]

this indicates the sequence is geometric with nth term

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = - 2 and r = [tex]\frac{3}{2}[/tex] , then

[tex]a_{n}[/tex] = - 2 [tex](\frac{3}{2}) ^{n-1}[/tex] , thus

a₅ = - 2 ([tex](\frac{3}{2}) ^{4}[/tex] = - 2 × [tex]\frac{81}{16}[/tex] = - [tex]\frac{81}{8}[/tex]

and

a₇ = - 2 [tex](\frac{3}{2}) ^{6}[/tex] = - 2 × [tex]\frac{72 9}{64}[/tex] = - [tex]\frac{729}{32}[/tex]

Answer: x = 81

Step-by-step explanation:

Quite a straightforward question.

Given equation is 61+20=x

So you just need to add 61 and 20 to get the value of x,

x=81

The probability of a randomly selected integer from 1 to 40 being prime, given that it is odd, is 18/40.

Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 means the event will never happen, and 1 means the event is certain to happen. Probability is used to make predictions or calculated decisions about the outcome of a random event. Probability is used in many areas of life, from gambling and finance to science and engineering.

This is because there are 18 prime numbers between 1 and 40 that are odd: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, and 41. Thus, the probability of a randomly selected integer from 1 to 40 being prime, given that it is odd, is 18/40.

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According to the given information the area of the parallelogram is 300ft².

A geometric shape having parallel sides in two dimensions is called a parallelogram. It is a type of four-sided polygon where each parallel set of sides is the same length (commonly referred to as a quadrilateral). The adjacent angles of such a parallelogram add up approximately 180 degrees.

Width of parallelogram = 20 feet.

Base of triangle = 4 feet.

Height of triangle = 15 feet.

To figure out the parallelogram's surface area:

To begin with, we would calculate the triangles' surface areas.

Note: The parallelogram supplied can be divided into two (2) triangles.

the triangle's surface area formula.

The formula: yields the triangle's area mathematically.

[tex]\begin{matrix}\mathrm{\ Area\ }=\frac{1}{2}\times\mathrm{\ base\ } \times\mathrm{\ height\ } \\\mathrm{\ Area\ }=\frac{1}{2}\times4\times15\\\mathrm{\ Area\ }=2\times15\\\mathrm{\ Area\ }=\mathbf{30}f^2\\\end{matrix}[/tex]

For the two (2) triangles:

[tex]Area =2\times30\\Area =\mathbf{60}ft^2[/tex]

For the rectangle left:

[tex]Length =15ft.\\Width =20-4=16ft.\\Area = length \times width\\Area =15\times16\\Area =\mathbf{240}ft^2[/tex]

Now, the area of the parallelogram:

Area of parallelogram =60+240

Area of parallelogram [tex]=\mathbf{300}{\rm ft}^2[/tex]

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After 4 years of recycling and re-using, approximately average one-half of the original 350,000 cans produced by the soft drink company would still be in use.

1. 350,000 cans produced in 1 year

2. 50% of cans recycled each year

3. 50% of 350,000 cans = 175,000 cans

4. After 4 years, 175,000 cans still in use.

Each year, it is predicted that about half of all aluminum cans will be recycled. This means that if a soft drink company produces 350,000 cans one year, then after four years, approximately one-half of the original cans produced would still be in use. This can be calculated by taking the initial number of cans produced (350,000), multiplying it by fifty percent (50%), and then multiplying that number by four (4). The final result is that after four years of recycling and re-using, approximately 175,000 cans would still be in use.

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An acute angle has a smaller measure than an obtuse angle.

What is acute angle ?

Acute angle can be defined in which if it is in the range between 0 to 90 degrees.

An obtuse angle is more than 90deg but less than 180deg. An acute angle is an angle smaller than a right angle. The range of an acute angle is between 0 and 90 degrees. So the correct answer is the corresponding to optin C: An acute angle has a smaller measure than an obtuse angle (if we add together an obtuse and an acute angle it will always be more than 90deg).

Therefore, An acute angle has a smaller measure than an obtuse angle.

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The first and fourth functions agrees that have  y-intercepts have a difference of 3 and the slopes are both negative.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Let us find the slope of first graph

m=-3+2/2=-1

-1=-1(-2)+b

-1=2+b

b=-3

The first function is y=-1x-3

Second function is y=4x-6

Third function is y=4x-1

The fourth function is y=-3x-3

Hence, the first and fourth functions agrees that have  y-intercepts have a difference of 3 and the slopes are both negative.

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Step-by-step explanation:

2(x-1) = 3(x+2)

2x-2 = 3x+6

2x-3x = 6+2

-x = 8

If in parallelogram ABCD, AB = 14cm. The altitude corresponding to AB is 6 cm and the altitude corresponding to BC is 7 cm. The AD is 8.57.

Given data:

AB= 14cm

Altitude corresponding  AB =6cm

Altitude corresponding to BC =7cm

So,

1/2 × AB × altitude 1 = 1/2 × AD × altitude 2

AB × altitude 1 =AD × Altitude 2

10 × 6 = AD × 7

60 = AD × 7

AD = 60/7

AD = 8.57

Therefore we can conclude that AD is 8.57.

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The probability of picking a solid color on the 4th day is 8/10 = 4/5.

The probability of picking a solid color on the 4th day is calculated by taking the total number of solid color pairs remaining in the drawer and dividing by the total number of pairs remaining.

On the first three days, you picked 1 black pair and 2 blue pairs, so you have 3 black pairs, 3 blue pairs, 3 brown pairs and 2 multi-colored pairs left in your drawer.

The total number of solid color pairs remaining is 8, and the total number of pairs remaining is 8+2 = 10.

So, the probability of picking a solid color on the 4th day is 8/10 = 4/5.

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The area of one of the pentagons is about 6.9 inches^2

The area of a regular pentagon can be calculated by using the formula: A = (perimeter x apothem) / 2.

Since we know that the side length of one of the pentagons is 2 inches, we can calculate the perimeter by multiplying the side length by the number of sides: P = 2 inches x 5 sides = 10 inches.

The apothem of the pentagon is given as 1.38 inches.

Therefore, we can substitute these values into the formula: A = (10 inches x 1.38 inches) / 2 = 6.9 inches^2

So the area of one of the pentagons is about 6.9 inches^2.

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If g(x) is the inverse function of f(x)  and[tex]$f^{\prime}(x)=\frac{1}{1+x^4}$[/tex], then [tex]$g^{\prime}(x)$[/tex]  is [tex]1+[\mathrm{g}(\mathrm{x})]^4\end{aligned}[/tex]

Correct option is A)

[tex]& \mathrm{g}=\mathrm{f}^{-1} \\[/tex]

[tex]& \mathrm{f}(\mathrm{g}(\mathrm{x}))=\mathrm{x}[/tex]

Differentiate w.r.t.x

[tex]& \mathrm{f}^{\prime}(\mathrm{g}(\mathrm{x})) \cdot \mathrm{g}^{\prime}(\mathrm{x})=1 \\[/tex]

[tex]& \therefore \frac{1}{1+(\mathrm{g}(\mathrm{x}))^4} \cdot \mathrm{g}^{\prime}(\mathrm{x})=1 \\[/tex]

[tex]& \mathrm{~g}^{\prime}(\mathrm{x})=1+[\mathrm{g}(\mathrm{x})]^4\end{aligned}[/tex]

The complete question is,

If [tex]$\mathrm{g}(\mathrm{x})$[/tex]is the inverse function of [tex]$\mathrm{f}(\mathrm{x})$[/tex] and [tex]$\mathrm{f}^{\prime}(\mathrm{x})=\frac{1}{1+\mathrm{x}^4}$[/tex], then [tex]$\mathrm{g}^{\prime}(\mathrm{x})$[/tex]is

A [tex]$1+[\mathrm{g}(\mathrm{x})]^4$[/tex]

B [tex]$1-[g(x)]^4$[/tex]

C [tex]$1+[\mathrm{f}(\mathrm{x})]^4$[/tex]

D [tex]$\frac{1}{1+[\mathrm{g}(\mathrm{x})]^4}$[/tex]

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Answer:

B.

Step-by-step explanation:

You need to find a common denominator.  In this case, 40.  Convert 2/5 to 16/40 and 3/8 to 15/40.  Add the numerators (16 + 15) together.  The denominator stays the same.

On solving the provided question we can say that 50 vehicles, 11 of which are damaged, leave 39 intact. Conditions for inference are satisfied because both proportion number of successes and failures is greater than 10.

Relationships that consistently have the same ratio are referred to as proportionate. For instance, the average quantity of apples per tree determines how many trees there are in an orchard and how many apples are in a harvest of apples. In mathematics, proportional denotes a linear relationship between two numbers or variables. The other amount doubles when the first quantity does. The other lowers as well when one of the variables falls to 1/100th of its prior value.

Yes, the prerequisites for inference are satisfied.

Inference requirements:

The sample must have at least 10 successes and 10 failures in order to construct a confidence interval for a population proportion.

50 vehicles, 11 of which are damaged, leave 39 intact.

Conditions for inference are satisfied because both the number of successes and failures is greater than 10.

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The prime factorization of the radicand 2 is 9√15.

A number can be expressed as the product of its prime components through the process of prime factorization. A number with precisely two elements, 1 and the number itself, is said to be a prime number.

As an illustration, let's use the number 30. We know that 30 = 5 × 6, but 6 is not a prime number. The number 6 can further be factorized as 2 × 3, where 2 and 3 are prime numbers. Therefore, the prime factorization of 30 = 2 × 3 × 5, where all the factors are prime numbers.

Given that,

x= 3√135

Solving the equation further using the rule √A*B = √A*√B

x= 3√9*15

x= 3√9*√15

x=3*3*√15

x= 9√15

Therefore, the prime factorization of the radicand 2 is 9√15.

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Point D is the center of rotation in the given figure.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Triangle A'B'C' rotating about the point d. Observe the Positional relation between ABC and A'B'C' you can get the result. There is no more information given Otherwise i will prove it to you theoretically.

Therefore, Point D can be described as Center of rotation.

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Complete question:

Answer:

f = 40

Step-by-step explanation:

0.25f = 10

f = 40

Let's check

0.25(40) = 10

10 = 10

So, f = 40 is the correct answer.

Answer:

p = 11

q = 34

r = 91

Step-by-step explanation:

If each term (after the first two terms) is the sum of the previous two terms:

[tex]\implies p+23=q[/tex]

[tex]\implies 23+q=57[/tex]

[tex]\implies q+57=r[/tex]

Solve the second equation for q:

[tex]\implies 23+q=57[/tex]

[tex]\implies 23+q-23=57-23[/tex]

[tex]\implies q=34[/tex]

Substitute the found value of q into the first equation and solve for p:

[tex]\implies p+23=34[/tex]

[tex]\implies p+23-23=34-23[/tex]

[tex]\implies p=11[/tex]

Substitute the found value of q into the third equation and solve for r:

[tex]\implies 34+57=r[/tex]

[tex]\implies r=91[/tex]

Therefore:

Step-by-step explanation:

[tex] \frac{x}{ \sin(46) } = \frac{5}{ \sin(29) } \\ x = 5 \times \frac{ \sin(46) }{ \sin(29) } \\ x = 7.42[/tex]

Answer:

30.8 degrees

Step-by-step explanation:

First, find the missing angles on the triangle to the right:

*arccosine(4.5/7) = 49.99

This is the angle between sides 7 and 4.5.

Next, using 49.99 as a reference angle, find the missing side:

tan(49.99) x 4.5 = 5.36

Next, we use arctan to find the missing angle:

*arctan(5.36/9) = 30.7761482323

Or 30.8 degrees.

*A fraction, not division ;-;

Answer:

There are 60 pencils packed in 5 boxes.

Step-by-step explanation:

36/3 = 12

There are 12 pencils in each box

12 x 5 = 60

Answer:

60 pencils

Step-by-step explanation:

1 box = 36/3 =12

in 5 boxes=12*5=60

hope it helps

This proof shows that the zero vector is in Col A, the vector Ax C Aw is in Col A, and c.Ax/ is in Col A, given a scalar c. This proves Theorem 3, which states that an element in Col A has the form Ax for some x in Rn.

a. The zero vector is in Col A because it is the result of multiplying the zero vector in Rn by matrix A. Therefore, A(0) = 0, which is the zero vector in Col A.

b. To show that the vector Ax C Aw is in Col A, we need to show that Ax C Aw can be written in the form A(x + w) for some vectors x and w in Rn. Since Ax and Aw are in Col A, they can be written as A(x) and A(w) for some vectors x and w in Rn. Therefore, Ax C Aw = A(x + w). Thus, the vector Ax C Aw is in Col A.

c. Given a scalar c, we need to show that c.Ax/ is in Col A. We can rewrite c.Ax/ as cA(x). Since A(x) is in Col A, then cA(x) is also in Col A. Therefore, c.Ax/ is in Col A.

This proof shows that the zero vector is in Col A, the vector Ax C Aw is in Col A, and c.Ax/ is in Col A, given a scalar c. This proves Theorem 3, which states that an element in Col A has the form Ax for some x in Rn.

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Answer:

Manish covers more distance. He covers 960m whereas Santosh only covers 480m

Step-by-step explanation:

First we compute the perimeter of the square track

Perimeter of a square of side a = 4a

Here a = 80m

Perimeter of the square of side 80 =>  4 x 80 = 320 m

Since Manish runs 3 times around it, total distance covered = 3 x 320 = 960

The perimeter of a rectangle with length L and breadth B = 2(L + B)

So perimeter of the rectangular track = 2(80 + 40) = 2 x 120 = 240

Since Santosh ran twice around this, total distance covered = 2 x 240 = 480