Fill in the blank of the triangle below x=

Answer:

x = -2 and y = 3

Step-by-step explanation:

It is given that,

4x + 5y = 7    -----(1)

3x – 2y = –12   ----(2)

To find the value of x and y

eq(1) * 3 ⇒

12x + 15y = 21   ----(3)

eq(2) * 4 ⇒

12x - 8y = -48  ---(4)

eq(3) - eq(4) ⇒

12x + 15y = 21   ----(3)

12x - 8y = -48 ---(4)

 0 + 23y = 69

y = 69/23 = 3

Substitute the value of y in eq(1)

4x + 5y = 7    ----(1)

4x + 5*3 = 7

4x = 7 - 15 = -8

x = -8/4 = -2

Therefore x = -2 and y = 3

Answer:

x = -2 and y = 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of hours elapsed, which function represents the scenario?

f(x) = 1500(1.15)x  

f(x) = 1500(115)x

f(x) = 1500(2.15)x

f(x) = 1500(215)x

The answer to this problem is a f(x) = 1500(2.15)x

Answer:

[tex]f(x) = 1500(2.15)^x[/tex]

Step-by-step explanation:

Let the function that represents the population of bacteria after x hours is,

[tex]f(x)=ab^x[/tex]

For x = 0, f(x) = 1500,

[tex]1500=a(1+r)^0[/tex]

[tex]1500=a[/tex]

Now, the population increases at a rate of 115% each hour,

So, the population after 1 hour = (100+115)% of 1500 = 215% of 1500 = 3225,

That is, for x = 1, f(x) = 3225,

[tex]3225 =ab[/tex]

[tex]3225=1500(b)[/tex]

[tex]\implies b =2.15[/tex]

Hence, the function that represents the given scenario is,

[tex]f(x)=1500(2.15)^x[/tex]

Answer:Correct. He transformed the triangle according to the rule (x, y) → (-y, x).

Answer:

Option A.

Step-by-step explanation:

Consider the below diagram is attached with this question.

Quinton tried to transform triangle FGH according to the rule (x, y) → (–y, x).

From the below figure it is clear that the vertices of triangle FGH are F(3,2), G(1,2) and H(4,5).

The vertices of image after transformation are F'(-2,3), G'(-2,1) and H'(-5,4).

The relation between preimage and image is defined by the rule

[tex](x,y)\rightarrow (-y,x)[/tex]

Since Quinton transformed the triangle according to the rule (x, y) → (–y, x), therefore he is correct.

Thus the correct option is A.

Answer:

   = x^2 +4x +3

Step-by-step explanation:

f(x) = 2x^2 - 5

g(x) = x^2 - 4x - 8

(f - g)(x)=2x^2 -5 - (x^2 -4x-8)

Distribute the minus sign

    = 2x^2 -5 -x^2 +4x+8

Combine like terms

   = x^2 +4x +3

Answer: Last option.

Step-by-step explanation:

To find which expression in equivalent to the expression [tex]\frac{125^2}{125^\frac{4}{3} }[/tex], you need to remember  :

The Power of a power property:

[tex](a^m)^n=a^{(mn)}[/tex]

The Quotient of powers property:

[tex]\frac{a^m}{a^n} =a^{(m-n)}[/tex]

And the Product of powers property:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

Knowing that:

 [tex]125=5*5*5=5^3[/tex]

Then, you get:

[tex]\frac{125^2}{125^\frac{4}{3} }=\frac{(5^3)^2}{(5^3)^\frac{4}{3} }=\frac{5^6}{5^4}=5^{(6-4)}=5^2=25[/tex]

Answer:

-3/2

Step-by-step explanation:

(Y2-Y1)/(X2-X1)

(-4 - 5) / (4 - (-2))

-9 / 6

Simplified: -3/2

Answer:

-3/2

Step-by-step explanation:

Answer:

b) 3a + 5b = 3

Step-by-step explanation:

It is an exact replica of the Standard Formula [Ax + By = C]. The Standard Formula is an example of a linear equation.

Answer:

3a + 5b = 1 is a linear equation

Step-by-step explanation:

Required?

To state which equation is linear...

An equation is said to be linear if it obeys the following.

1. For Single variables: y = b

An example is y = 4

2. For 2 Variables; it can take any of the following form: Ax + By = C.

An example 3x + 5y = 4

.from option A through D, only option B fits the description.

Note that the arithmetic sign could take the negative form and the position of x and y or any other constraints can take an interchanged forms.

The key thing to watch out when naming a linear equation is that the highest power is 1.

Hence, the 3a + 5b = 1 is a linear equation

Answer:

That's incorrect. The simplest way to show this is by evaluating the functions at a given point. Let's say x=0, then:

Sin(-x) = Sin(0) = 0

-cos x = -cos (0) = -1

Therefore, Sin(-x)≠-cos x.

The given expression :

        [tex]\sin (-x)=-\cos x[/tex] is a false expression i.e. it is not true for all the values of x.

We are asked to check whether the trignometric expression is true for all the values of x or not.

The expression is given by:

[tex]\sin (-x)=-\cos (x)[/tex]

We consider x=0

Then on taking left hand side of the expression we have:

[tex]\sin (-0)\\\\i.e.\\\\\sin (0)\\\\=0[/tex]

and the right hand side of the expression is:

[tex]-\cos x\\\\i.e.\\\\-\cos 0\\\\i.e.\\\\-1[/tex]

i.e. we have:

[tex]0=-1[/tex]

which is false.

Hence the statement is not true for all the values of x.

Answer:

arrow going from 9 to -infinity (open circle)

Step-by-step explanation:

equalize equation by multiplying both sides by 3 to obtain the equation 9>t

then simply plug in numbers to see if they check out, ie: 3> 4/3 makes sense, but 3> 10/3 doesn't.

Draw the arrow to accommodate for the answers that DO fit.

open circle, because it doesn't work for t=9

Answer:

see below

Step-by-step explanation:

3 > t/3

Multiply each side by 3

3*3 > t/3 *3

9 > t

t < 9

There is an open circle at 9, since  the symbol is  less than

The line goes to the left.

Answer:

Option C. Seven was not multiplied by 5/8

Step-by-step explanation:

we know that

To determine the height of a stack of 7 books that are each 2 5/8  inches thick. multiply 7 by 2 5/8

so

[tex]7(2\frac{5}{8})\\ \\7(2+\frac{5}{8})\\ \\7*2+7*\frac{5}{8}\\ \\14+\frac{35}{8}\\ \\14+4+\frac{3}{8}\\ \\18\frac{3}{8}\ in[/tex]

therefore

Seven was not multiplied by 5/8

Answer:

Option B.

Step-by-step explanation:

Giovanna did the calculations to determine the height of a stacks of 7 books having [tex]2\frac{5}{8}[/tex] inches thickness of each book.

[tex]7(2\frac{5}{8})[/tex]

[tex]=7(2+\frac{5}{8})[/tex]

[tex]=(7\times 2)+7(\frac{5}{8})[/tex]

[tex]=14+\frac{35}{8}[/tex]

[tex]=14+4+\frac{3}{8}[/tex]

=18+[tex]\frac{3}{8}[/tex]

[tex]=18\frac{3}{8}[/tex]

Now when compare this solution with Giovanna's solution we find error in 3rd step, in which she hasn't mutiplied the fraction [tex]\frac{5}{8}[/tex] by 7.

Therefore, option B is the correct one.

Answer:

15

Step-by-step explanation:

term 1 is equal to 5.

term 2 is equal to 5  + (1)                 = 5 + 1   = 6

term 3 is equal to 6  + (1 + 2)             = 6 + 3   = 9

term 4 is equal to 9  + (1 + 2 + 3)         = 9 + 6   = 15

term 5 is equal to 15 + (1 + 2 + 3 + 4)     = 15 + 10 = 25

term 6 is equal to 25 + (1 + 2 + 3 + 4 + 5) = 25 + 15 = 40

Answer:

optain A or the first one

Step-by-step explanation:

hop this helps

Finding 80% of 630 doesn't require using a table and can be calculated by simply multiplying 0.80 by 630 which gives 504.

To determine 80% of 630, Allison doesn't necessarily need a table. However, we can illustrate the solution using a simple self-created table. The calculation is rather straightforward. If Allison wants to find 80% of 630, she can simply multiply 0.80 (which is the decimal equivalent of 80%) by 630.

Therefore, 80% of 630 is 504.

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Answer:

0 and 1 have the same y values for the x values.

Answer:

5/12 ≈ 0.41667

Step-by-step explanation:

If the first die rolls a 1 and the second die rolls a 1, then the sum is 2.

If the first die rolls a 1 and the second die rolls a 2, then the sum is 3.

Repeating this, we can build a table showing all the possible outcomes:

[tex]\left[\begin{array}{ccccccc}&1&2&3&4&5&6\\1&2&3&4&5&6&7\\2&3&4&5&6&7&8\\3&4&5&6&7&8&9\\4&5&6&7&8&9&10\\5&6&7&8&9&10&11\\6&7&8&9&10&11&12\end{array}\right][/tex]

As we can see, of the 36 possible outcomes, 15 are greater than seven.  So the probability is 15/36, which reduces to 5/12.

Answer:

(- 8, - 2)

Step-by-step explanation:

Assuming you mean the inverse function

Then any coordinate point (x, y ) in f(x) → (y, x) in the inverse

Given

(- 2, - 8 ) is on the graph of f(x), then

(- 8, - 2) is on the graph of [tex]f^{-1}[/tex](x)

The corresponding point on the graph of function f(x)-1 for a given point (-2,-8) from the graph of function f(x) is (-2, -9). All corresponding x-values remain the same, while the y-values are decreased by 1.

The given point (-2,-8) is on the graph of the function f(x). Now, you're asked to find the corresponding point for the function f(x)-1. When we modify a function like this, it affects the y-values (output) of the function. The x-values (input) remains constant.

In this case, for any x-value in the function f(x), the corresponding y-value in the function f(x)-1 is simply the y-value of f(x) minus one. So the corresponding point on the graph of f(x)-1 for the given point (-2,-8) from the graph of f(x) would be (-2, -9), because -8 (the y-value from f(x)) minus 1 equals -9 (the y-value for f(x)-1). Hence, the point (-2, -9) is on the graph of the function f(x)-1.

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Answer:  [tex]\bold{\dfrac{69}{16}}[/tex]

Step-by-step explanation:

[tex]4.3125=\dfrac{43125}{10000}\\\\\\\dfrac{43125}{10000}\div\dfrac{625}{625}=\large\boxed{\dfrac{69}{16}}[/tex]

Mike can determine the width of his scale model car by setting up and solving a proportion. Using the ratio of the actual car's dimensions, calculate an equivalent ratio for the model. The width of the model car should be 6 inches.

To solve this problem, you can set up a proportion based on the known dimensions of the actual car and Mike's model. Given the actual car's length and width are 8 feet and 4 feet, and Mike's model length is 12 inches, we can set up the proportion like this:

8 feet : 4 feet = 12 inches : X

First, we need to convert all measurements to the same unit. Let's use inches since Mike's model is in inches (remember that 1 foot equals to 12 inches). So, the car's length is 96 inches and its width is 48 inches. Now, the proportion would be:

96 inches : 48 inches = 12 inches : X

To find the value of X (the width of the model), we can cross-multiply:

(96 * X) = (48 * 12)

Solve for X by dividing each side by 96, we get:

X = 6 inches

So, Mike's model car should be 6 inches wide to maintain the same ratio as the actual car.

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Vertical Angles have to be congruent and have the same vertex.

The correct options are:

B.  Have the same vertex.

C.  be congruent.

Vertical Angles--

Answer:

Step-by-step explanation:

Parallel lines have the same slope.

The formula of a slope:

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

Substitute the coordinates of the given points G(-4, 1) and H(2, -2):

[tex]m=\dfrac{-2-1}{2-(-4)}=\dfrac{-3}{6}=-\dfrac{1}{2}[/tex]

J(1, 3). Let other point (x, y).

Substitute to the slope:

[tex]\dfrac{y-3}{x-1}=\dfrac{-1}{2}[/tex]            cross multiply

[tex]2(y-3)=-1(x-1)[/tex]    use the distributive property

[tex]2y+(2)(-3)=-x+(-1)(-1)[/tex]

[tex]2y-6=-x+1[/tex]        add 6 to both sides

[tex]2y=-x+7[/tex]      divide both sides by 2

[tex]y=-\dfrac{1}{2}x+\dfrac{7}{2}[/tex]

Check the equality for coordinates of each point:

[tex](-3, 5)\\\\5=-\dfrac{1}{2}(-3)+\dfrac{7}{2}\\\\5=\dfrac{3}{2}+\dfrac{7}{2}\\\\5=\dfrac{10}{2}\\\\5=5\qquad\bold{CORRECT}[/tex]

[tex](1,\ 5)\\\\5=-\dfrac{1}{2}(1)+\dfrac{7}{2}\\\\5=-\dfrac{1}{2}+\dfrac{7}{2}\\\\5=\dfrac{6}{2}\\\\5=3\qquad\bold{FALSE}[/tex]

[tex](3,\ -2)\\\\-2=-\dfrac{1}{2}(3)+\dfrac{7}{2}\\\\-2=-\dfrac{3}{2}+\dfrac{7}{2}\\\\-2=\dfrac{4}{2}\\\\-2=2\qquad\bold{FALSE}[/tex]

[tex](3,\ 2)\\\\2=-\dfrac{1}{2}(3)+\dfrac{7}{2}\\\\2=-\dfrac{3}{2}+\dfrac{7}{2}\\\\2=\dfrac{4}{2}\\\\2=2\qquad\bold{CORRECT}[/tex]

[tex](5,\ 1)\\\\1=-\dfrac{1}{2}(5)+\dfrac{7}{2}\\\\1=-\dfrac{5}{2}+\dfrac{7}{2}\\\\1=\dfrac{2}{2}\\\\1=1\qquad\bold{CORRECT}[/tex]

To identify which points could be on a line that is parallel to another and passes through a specific point, we need to know the slope of the original line or the coordinates of the given point. Without this information, it is impossible to accurately determine which points from the list might be on the parallel line.

The question asks, Which points could be on the line that is parallel to and passes through point J? This problem is a part of geometry in mathematics where we study about points, lines, and planes.

The location of point J was not specified, but the line that is parallel to another would have the same slope, regardless of its y-intercept. As such, to find the points that can lie on a line that is parallel, we must know the slope of the primary line. If we are given the slope 'm', any points that fall on the line would satisfy the equation of a line, y = mx + b, where 'b' is the y-intercept. The points whose 'y' value remains constant in the given x-y pairs would lie on the line parallel to the original line.

Without the proper information about the slope of the line or the position of point J, it is impossible to accurately determine which points from the given list can lie on the line that is parallel and passes through point J.

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Answer:

6m

Step-by-step explanation:

The area of the rectangular plot is

A = l*w

   = 4*9

    = 36 m^2

To find the area of the square plot

A = s^2

36 = s^2

Take the square root of each side

sqrt(36) = sqrt(s^2)

6 = s

The length of the side of the square plot is 6 m

Answer:

8

Step-by-step explanation:

8y-8=24

+8 +8

8y=32

32/8 = 4

y=4

4*2=8

Answer:

8

Step-by-step explanation:

8 y - 8 = 24

( + 8 )

8 y = 32

( ÷ 4 )

y = 4

Find the value of 2 y

y = 4 so 2 y = 8

Answer:

45.73 m

Step-by-step explanation:

Answer: 14

Step-by-step explanation:

Answer:

The y-intercept is: (0,14).

Answer:

5 blocks

Step-by-step explanation:

Since the triangle is right use Pythagoras' identity to solve for AC

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

AC² = AB² + BC² ← substitute values

AC² = 3² + 4² = 9 + 16 = 25 ( take the square root of both sides )

AC = [tex]\sqrt{25}[/tex] = 5

Answer:

common Joe is cheaper

Step-by-step explanation:

1500/200 =7.5 truckloads

7.5×50=$375

1500/90=16.666 truckloads

16.666×20=$333.

I really didn't know for sure what u we're looking for

Answer:Common Joe

Step-by-step explanation:

Given

Total weight of Raw material is 1500 tons

Big Red can transport 200 tons at a cost of $50 per truckload

so  Big Red need to do 8 rounds to completely transport the raw material

In first 7 round round it carries 200 tons and in last round it carry 100 tons

i.e. [tex]200\times 7+100[/tex]

so cost for Red bus=[tex]50\times 8=$400[/tex]

For Common Joe truck requires 17 round of loading to completely transport 1500 tons

In first 16 round it carries 90 tons and in last round it carries 60 tons

So cost for Common Joe is [tex]17\times 20=$340[/tex]

So Factory should choose Common Joe while considering Economy.

ANSWER

The base is 7 and the height is 9.

EXPLANATION

If we consider any two pairs of points and the y-coordinates of these two points are constant (are the same), then that side forms one of the bases of the rectangle.

Consider, Q(-1, 1) and R(6, 1)

The y-values are the same.

The base of the rectangle is the absolute value of difference in the x-values.

[tex]Base = |6 - - 1| = |7| = 7[/tex]

We could have also used S(6,-8), and T(-1,-8) to obtain the same result.

For R(6, 1) and S(6,-8), the x-coordinates are the same. The height is the absolute values of difference in the y-values.

[tex]Height= |1 - - 8| = |9| = 9[/tex]

Therefore, the base is 7 and the height is 9.

Answer:

Base is 7, and Height is 9.

Step-by-step - If we consider any two pairs of points and the y-coordinates of these two points are constant (are the same), then that side forms one of the bases of the rectangle.

Consider, Q(-1, 1) and R(6, 1)

The y-values are the same.

The base of the rectangle is the absolute value of difference in the x-values.

We could have also used S(6,-8), and T(-1,-8) to obtain the same result.

For R(6, 1) and S(6,-8), the x-coordinates are the same. The height is the absolute values of difference in the y-values.

Therefore, the base is 7 and the height is 9.

I will convert feet to inches.

4 feet, 6 inches = 54 inches

20 feet = 240 inches

5/x = 54/240

Let x = closest height of tree

54x = 5(240)

54x = 1,200

x = 1200/54

x = 22.2222222222

The tree is about 22 feet tall.

Answer:

22 inches

Step-by-step explanation:

Height of Mac = 5 feet

Height of shadow of Mac = 4 foot 6 inches = [tex]4+\frac{6}{12}= 4.5[/tex] inches .

We are given that At the same time, a nearby tree casts a 20  foot shadow .

Let the height of the tree be x

ATQ

[tex]\frac{5}{4.5}=\frac{x}{20}[/tex]

[tex]\frac{5}{4.5} \times 20=x[/tex]

[tex]22.22=x[/tex]

Hence the height of the tree is approximately 22 inches .

[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{9}) \\\\\\ \stackrel{\textit{average rate of change}~\hfill }{slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}}\implies \cfrac{9-6}{-5-(-2)}\implies \cfrac{9-6}{-5+2}\implies \cfrac{3}{-3}\implies -1[/tex]

Answer:

[tex]\sum_{n=1}^{10} 316.5 (1.055)^{n-1} [/tex]

Step-by-step explanation:

The amount (A) in a deposit after 1 year is calculated as follows:

A = P*(1 + r)

where:

P is the present value

r is the annual rate (decimal)

After the first year:

A = 300*(1 + 0.055) = $316.5

After the second year, the account will have a new amount of $316.5 due to the new $300 and the interest gained with the previous $316.5:

A = 316.5 + 316.5*(1 + 0.055)

After the third year:

A = 316.5 + [316.5 + 316.5*(1 + 0.055)]*(1 + 0.55)

A = 316.5 + 316.5*(1 + 0.055) + 316.5*(1 + 0.055)^2

After 10 years:

[tex]\sum_{n=1}^{10} 316.5 (1.055)^{n-1} [/tex]