What is the solution for the system of equations {9x+8y=3 6x−12y=−11?

Answer:

m∠ABC = 120°

Step-by-step explanation:

Consider the case where point C is on the circle and long arc AC has measure 240°. Then ∠ABC is an inscribed angle, and its measure is half the measure of the intercepted arc, so is 120°.

This is still true even when point B and point C are on top of each other and BC is a tangent to the circle. That is the case shown here, so m∠ABC = 120°.

Answer:

7x = 2x + r

Step-by-step explanation:

On the left side you have 7 boxes.  So let's call those boxes "x" and we have 7x.

On the right side we have 2 of them, 2x, and 1 r.

Putting them together gives you

7x = 2x + r

The P(draw a blue marble)=0.25

The bag has:

3 blue marbles, 4 green marbles, and 5 red marbles.

This means that the total number of marbles in bag are:

3+4+5=12 marbles.

We are asked to find the probability that the marble that is randomly drawn from a bag is: Blue marble.

Let P denote the probability of an event.

We know that the probability of drawing a blue marble is equal to the ratio that the marble drawn is blue to the total number of marbles in the bag.

Hence,

[tex]\text{P(blue\ marble)}=\dfrac{3}{12}\\\\i.e.\\\\\text{P(blue\ marble)}=\dfrac{1}{4}\\\\\\\text{P(blue\ marble)}=0.25[/tex]

Hence, the answer is:

        P(draw a blue marble)=0.25

Certainly! Let's solve this step by step.

**Step 1: Determine the number of blue marbles.**

We have 333 blue marbles in the bag.

**Step 2: Determine the total number of marbles in the bag.**

The bag contains:
- 333 blue marbles,
- 444 green marbles, and
- 555 red marbles.

To find the total number of marbles, we add these numbers together:
Total marbles = 333 (blue) + 444 (green) + 555 (red)

**Step 3: Calculate the total number of marbles.**

Now, we add up each type of marble to get the total:
Total marbles = 333 + 444 + 555

**Step 4: Calculate the probability of drawing a blue marble.**

The probability of an event is calculated by dividing the number of favorable outcomes by the number of total possible outcomes. In this case, the favorable outcomes are drawing a blue marble, and the total outcomes are the total number of marbles.

Thus, the probability P of drawing a blue marble is:
P(draw a blue marble) = Number of blue marbles / Total number of marbles

Using the numbers provided:
P(draw a blue marble) = 333 / (333 + 444 + 555)

**Step 5: Calculate the exact probability.**

To get the exact probability, we perform the addition in the denominator and then divide:
P(draw a blue marble) = 333 / (1332)

Now, let's execute this calculation.

**Step 6: Simplify the fraction (if necessary).**

In this case, the fraction 333/1332 is already in its simplest form, so we don't need to simplify it further.

**Step 7: Calculate the approximation to 2 decimal places.**

To round the probability to 2 decimal places, we will compute the exact division and then round the result:
P(draw a blue marble) ≈ 0.2500 (rounded to 4 decimal places for illustrative purposes)

However, since we need to round our answer to 2 decimal places, the result is:
P(draw a blue marble) ≈ 0.25

Therefore, the probability of drawing a blue marble, rounded to two decimal places, is 0.25.

[tex](f\cdot g)(x)=(9x+1)\cdot x^3=9x^4+x^3[/tex]

Answer:

Part 1: The polygon ABCDE reflected across y-axis to get the polygon MNOPQ. So, the polygon ABCDE congruent to polygon MNOPQ.

Part 2: The vertices of polygon VWXYZ are V(1, 3), W(-1, 7), X(-7, 7), Y(-5, 3), and Z(-3, 1).

Step-by-step explanation:

Part 1:

The vertices of the polygon ABCDE are A(2, 8), B(4, 12), C(10, 12), D(8, 8), and E(6, 6).

The vertices of the polygon MNOPQ are M(-2, 8), N(-4, 12), O(-10, 12), P(-8, 8), and Q(-6, 6).

We need to find the transformation or sequence of transformations that can be performed on polygon ABCDE to show that it is congruent to polygon MNOPQ.

The relation between the vertices of ABCDE and MNOPQ are defined as

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

It means the polygon ABCDE reflected across y-axis to get the polygon MNOPQ. So, the polygon ABCDE congruent to polygon MNOPQ.

Part 2:

If polygon MNOPQ is translated 3 units right and 5 units down, then

[tex](x,y)\rightarrow (x+3,y-5)[/tex]

[tex]M(-2,8)\rightarrow V(-2+3,8-5)=V(1,3)[/tex]

[tex]N(-4,12)\rightarrow W(-4+3,12-5)=W(-1,7)[/tex]

[tex]O(-10,12)\rightarrow X(-10+3,12-5)=X(-7,7)[/tex]

[tex]P(-8,8)\rightarrow Y(-8+3,8-5)=Y(-5,3)[/tex]

[tex]Q(-6,6)\rightarrow Z(-6+3,6-5)=Z(-3,1)[/tex]

Therefore the vertices of polygon VWXYZ are V(1, 3), W(-1, 7), X(-7, 7), Y(-5, 3), and Z(-3, 1).

Answer:

see explanation

Step-by-step explanation:

Using the exact values

sin45° = cos45° = [tex]\frac{1}{\sqrt{2} }[/tex]

Since the triangle is right use the sine/cosine ratios, that is

sin45° = [tex]\frac{TU}{TV}[/tex] = [tex]\frac{TU}{9\sqrt{2} }[/tex]

Multiply both sides by 9[tex]\sqrt{2}[/tex]

9[tex]\sqrt{2}[/tex] × [tex]\frac{1}{\sqrt{2} }[/tex] = TU, hence

TU = 9

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

cos45° = [tex]\frac{UV}{TV}[/tex] = [tex]\frac{UV}{9\sqrt{2} }[/tex]

Multiply both sides by 9 [tex]\sqrt{2}[/tex]

9[tex]\sqrt{2}[/tex] × [tex]\frac{1}{\sqrt{2} }[/tex] = UV, hence

UV = 9

Since TU = UV = 9 , then triangle is isosceles

and ∠T = ∠V = 45°

Answer:

∠4

Step-by-step explanation:

An angle of depression is measured from the horizontal downwards.

This is ∠4 in the diagram

Answer:

The angle of depression from the light house to the boat is  <4

Step-by-step explanation:

From the figure we can see a light house and a boat.

The angle of depression means that angle from the horizontal downward to an object.

From the figure we can see that, <4 is the angle of depression from the light house to the boat.

Therefore the answer is <a

Check the picture below.

so the parabola looks more or less like so, bearing in mind that the directrix is a horizontal line, thusu the parabola is a vertical one, so the squared variable is the "x".

The vertex is always half-way between the focus point and the directrix, as you see there, and the distance from the vertex to the focus is "p" distance, since the parabola is opening downwards, "p" is negative, in this case -2.

[tex]\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ \stackrel{\textit{we'll use this one}}{4p(y- k)=(x- h)^2} \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=0\\ k=0\\ p=-2 \end{cases}\implies 4(-2)(y-0)=(x-0)^2\implies -8y=x^2\implies y=-\cfrac{1}{8}x^2[/tex]

To find the standard form of the parabola with a focus at (0, -2) and a directrix at y = 2, the process involves identifying the vertex, determining direction, and substituting into the general equation to get x² = -8y.

To find the standard form of the equation of a parabola with a focus at (0, -2) and a directrix at y = 2, we start by identifying key properties of parabolas. The vertex of the parabola is midway between the focus and the directrix. Here, the distance between the focus and the directrix is 4, so the vertex is 2 units away from each, placing it at (0, 0) as the directrix and focus are symmetrically placed above and below the x-axis.

The general equation for a parabola opening upwards or downwards is (x - h)² = 4p(y - k), where (h, k) is the vertex of the parabola, and p is the distance from the vertex to the focus (positive if the parabola opens upwards, negative if downwards). Given the focus (0, -2) and the vertex (0, 0), p = -2, indicating the parabola opens downwards. Applying these values to the general equation yields: x² = -8y, which is the standard form of the equation for the described parabola.

Answer:

  (x < -1) ∪ (6 < x)

Step-by-step explanation:

Divide by 3

  |2x -5| > 7

"Unfold." That is, put the negative of the constant value on the other side of the absolute value expression, using the same inequality symbol.

  -7 > 2x -5 > 7 . . . . . . . . . . this notation is convenient for expressing the two disjoint inequalities, but is not strictly correct because it is not true that -7 > 7.

Add 5, then divide by 2

  -2 > 2x > 12

  -1 > x > 6 . . . . . . . . . . this should be interpreted as -1 > x OR x > 6. Usually a compound inequality is interpreted as having an AND connector.

The solution is ...

  (x < -1) ∪ (6 < x)

_____

The more correct (and less convenient) way to "unfold" the absolute value is to write it as two distinct inequalities:

Each of these is then separately solved (by adding 5 and dividing by 2) to get ...

Answer: Half of 1/3 would be 1/6 :)

The decimal form of it would be 0.166666

ANSWER

[tex] \frac{1}{6} [/tex]

EXPLANATION

The given fraction is

[tex] \frac{1}{3} [/tex]

We want to find half of this fraction.

We can write this expression mathematically as:

[tex] \frac{1}{2} \: of \: \: \frac{1}{3} [/tex]

The 'of' in this expression means multiplication.

This implies that

[tex] \implies \: \frac{1}{2} \: of \: \: \frac{1}{3} = \frac{1}{2} \: \times \: \: \frac{1}{3} [/tex]

[tex] \implies \: \frac{1}{2 } \: of \: \: \frac{1}{3} = \frac{1 \times 1}{2 \times 3} [/tex]

We multiply out to get

[tex] \implies \: \frac{1 }{2} \: of \: \: \frac{1}{3} = \frac{1}{6} [/tex]

Answer: b. $407.50

Step-by-step explanation:

Multiply 450 by 0.75= 337.5

add 60: 337.5+60=397.5

add 10: 397.5+10= 407.5

Therefore B) is the correct answer

Answer:

  The solutions to the equation are 1, 0.375.

Step-by-step explanation:

The equation is already in factored form.

The solutions to the system are the values of x that make one or the other of the factors be zero.

  x -1 = 0 . . . when x = 1

  8x -3 = 0 . . . when x = 3/8 = 0.375

There is only one variable, so no "ordered pairs" are involved.

The solutions are {1, 0.375}.

Answer:

1,14

0,375,12.75

Step-by-step explanation:

Answer:

B Step 2

Step-by-step explanation:

he was suppose to collect the like terms

5x +x = 5x + 1x

collect the like terms by adding their coefficients

(5 + 1)

add the numbers

(5+1)x = 6x

Answer:

  A.  Step 1

Step-by-step explanation:

The correct result of eliminating parentheses in Step 1 is ...

[tex]\dfrac{5x+10-8+x}{2}[/tex]

Distributing the minus sign in the second term changes the signs of both of the terms in parentheses:

  -(8 -x) = -8 +x

Answer:

Rebecca have 18 nickels coins and 27 dime coins

Step-by-step explanation:

Remember that

1 nickel =$0.05

1 dime=$0.10

so

Let

x -----> the number of nickel coins

y -----> the number of dime coins

we know that

x+y=45

x=45-y ------> equation A

0.05x+0.10y=3.60 -----> equation B

Solve the system by substitution

Substitute equation A in equation B and solve for y

0.05(45-y)+0.10y=3.60

2.25-0.05y+0.10y=3.60

0.05y=3.60-2.25

0.05y=1.35

y=27

Find the value of x

x=45-y ---->x=45-27=18

therefore

Rebecca have 18 nickels coins and 27 dime coins

Rebecca has 18 nickels and 27 dimes.

Solving the Problem

Rebecca has 45 coins, composed of nickels and dimes, with a total value of $3.60. We can set up a system of linear equations to solve this problem.

Step-by-Step Explanation

Therefore, Rebecca has 18 nickels and 27 dimes.

Answer is D using A = Pe^(rt).

Final answer:

To calculate the total amount of money in Seth's account after 2.5 years with compound interest, use the formula [tex]A = P(1 + r/n)^{(nt)[/tex], applying the given values to find a total of $2106.25 in the account.

Explanation:

To calculate the total amount of money in the account at the end of the 2.5 years with compound interest, we use the formula

[tex]A = P(1 + r/n)^{(nt)[/tex]

where A is the total amount, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time the money is invested for.

For this case, P = $1890, r = 3.5% = 0.035, n = 1, and t = 2.5 years.

Plugging in these values gives [tex]A = $1890(1 + 0.035/1)^{(1\times 2.5)[/tex] = $2106.25.

Therefore, the total amount of money in the account at the end of 2.5 years is $2106.25.

Answer:

If she gives all the earnings to her sister she would still own her $9.30

Step-by-step explanation:

Subtract the $25.63 (sisters' money) fromv $16.33(earnngs from her dad) then you get 9.30

Answer:

$9.30

Step-by-step explanation:

Answer:

3/10 or 0.3

Step-by-step explanation:

You have 3 red marbles and 10 marbles in total, so you put how many red marble in the numerator and your total marbles in the denominator.

Answer:

1. 30ft

2. 0.4 min

Step-by-step explanation:

In this question, apply sine law which states that sine Ф= opposite/hypotenuse

The general formulae; is SOHCAHTOA where ;

(SOH) sineФ=opposite/hypotenuse  ; (COH) cosine Ф= adjacent/hypotenuse and (TOA) tan Ф=opposite/adjacent

In the question the height of the two floors is the " c" and the angel at the base is 60° and distance the conveyor travels is the hypotenuse

Hence;

[tex]Sin 60= \frac{26}{H} \\\\\\H=\frac{26}{Sin60} \\\\\\H=30 ft[/tex]

If 75ft=1min

  30ft=?........................simple math

30/75 = 0.4 minutes

Answer:

i) 30 ft

ii) 0.4 min

Step-by-step explanation:

i)

The question will be modeled by a right-angled triangle where-by;

The length of the conveyor belt will represent the Hypotenuse

The vertical distance which is 26 feet high will be the Opposite side to the angle the belt makes the ground which is given as 60 degrees.

The horizontal distance which is the ground will be the Adjacent side to the angle 60 degrees.

Therefore, we have a right angled triangle in which one angle and the length of the opposite side are given. To determine the length of the conveyor belt, the hypotenuse, we use the sine definition of an acute angle;

Remember the mnemonic. SOHCAHTOA

sine 60 = (opposite side)/(hypotenuse)

Hypotenuse = (opposite side)/sin 60

Hypotenuse = 26/sin 60

Hypotenuse = 30.02

The supplies thus travel 30 ft from one end of the conveyor belt to the other.

ii)

The speed of the belt is given as 75 ft/min

The length of the belt has been found to be approximately 30 ft

We are required to determine the time it takes for the supplies to move to the second floor.

Distance, Time and speed are related according to the following equation;

Distance = Time * Speed

Time = Distance/Speed

Time = 30/75

Time = 0.4 min

Answer:

6,7,8,9,....

Step-by-step explanation:

the minimum width can be 5 because 9 times 5 is 45 the area using the formula length times width but the question is asking greater than 45 and 9 times any number greater than 5 is greater than 45

Answer:

W > 36

Step-by-step explanation:

i got it right on edgeinuity

[tex]\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2)~\hfill a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^3-125=0\implies x^3-5^3=0\implies (x-5)(x^2+5x+5^2)=0 \\\\[-0.35em] ~\dotfill\\\\ x-5=0\implies \boxed{x=5} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~~~~~~~\textit{quadratic formula}[/tex]

[tex]\bf \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+5}x\stackrel{\stackrel{c}{\downarrow }}{+25} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x=\cfrac{-5\pm\sqrt{5^2-4(1)(25)}}{2(1)}\implies x=\cfrac{-5\pm\sqrt{25-100}}{2} \\\\\\ x=\cfrac{-5\pm\sqrt{-75}}{2}~~ \begin{cases} 75=&3\cdot 5\cdot 5\\ &3\cdot 5^2 \end{cases}\implies x=\cfrac{-5\pm\sqrt{-3\cdot 5^2}}{2}[/tex]

[tex]\bf x=\cfrac{-5\pm 5\sqrt{-3}}{2}\implies x=\cfrac{-5\pm 5\sqrt{-1\cdot 3}}{2}\implies x=\cfrac{-5\pm 5\sqrt{-1}\cdot \sqrt{3}}{2} \\\\\\ x=\cfrac{-5\pm 5i\sqrt{3}}{2}\implies \boxed{x= \begin{cases} \frac{-5+ 5i\sqrt{3}}{2}\\\\ \frac{-5-5i\sqrt{3}}{2} \end{cases}}[/tex]

To solve the complex number equation x^3-125=0, we rearrange to x^3=125 and apply the rule for cube roots in the complex system. This yields three solutions: x = 5, x = 5*omega, and x = 5*omega^2.

The given equation is x^{3}-125=0. It belongs to the category of complex number equations within the complex system. We can solve this equation step-by-step by using the cube root of unity in the complex number system.

Firstly, move '125' to the right side of the equation: x^{3}=125. We find that x is the cube root of 125. The solutions to this kind of equation are given by a rule in the complex number system that the cube roots of a number a are given by [a^(1/3), a^(1/3)*omega, a^(1/3)*omega^2], where omega is a cube root of unity and equals -1/2+sqrt(3)i/2 and omega^2=-1/2-sqrt(3)i/2 .

Therefore for x^{3}=125, we get x = 5, 5*omega, and 5*omega^2. These are the solutions in the complex number system.

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Answer:

29

Step-by-step explanation:

Since they have given you x = 4, simply sub it into the equation,

(4)^2 + 3(4) - 7 + 8

=  29

Answer:

29

Step-by-step explanation:

Substitute 4 for x into the expression x^2+3x−7+8 and then simplify using the order of operations.

4^2+3(4)−7+8

16+12−7+8

29

Answer:

The answer is D (line symmetry and rotational symmetry; 180o; order 2.

Step-by-step explanation:

You can fold the figure in half and it would be the same on both sides.  The figure also has rotational symmetry because if you rotate the figure 180 degrees about the center, then it basically maps itself, or in other words, its the same.  So the ANSWER IS D

line symmetry and rotational symmetry; 180 degree; order 2. Correct option is D.

The figure described exhibits characteristics of both reflectional and rotational symmetry. Firstly, it possesses reflectional symmetry because you can fold it in half, and both sides of the fold will be identical, essentially mirroring each other. This demonstrates that the figure can be divided into two equal parts that are reflections of each other along the fold line.

Furthermore, the figure displays rotational symmetry, specifically a 180-degree rotational symmetry. When you rotate it by 180 degrees about its center, the figure aligns with itself, showing that it remains unchanged upon this rotation. This means that you can rotate the figure halfway, and it will still appear identical.

So, the correct answer is not just "D," but rather a more comprehensive explanation of the figure's symmetrical properties, encompassing both reflectional and rotational symmetry.

to know more about rotational symmetry;

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Answer:

Option A is correct.

Step-by-step explanation:

The following matrix represent the augmented matrix

In augmented matrix the left side represent the co-efficient of the variables and right side represent the value of variables.

Since the matrix has been solved and reduced so, the solution of variables x, y and z is written on right side of augmented matrix

The given matrix is:

[tex]\left[\begin{array}{cccc}1&0&5&-2\\0&0&3&0\\0&0&0&-1\end{array}\right][/tex]

Since the last row is all zero and we have a non zero entry for the solution, the matrix is inconsistent.

As the variables have zero values, there cannot be any solution

So, there is no solution.

So, Option A is correct.

Answer:

A) No solution!

Step-by-step explanation:

Edge 2021 :)

Answer:

Step-by-step explanation:

Let s represent the number of Senators in the Congress. Then the number of Representatives is (5s-20) and the total number of members is ...

  s + (5s -20) = 520

  6s = 540 . . . . . . . . . add 20, simplify

  s = 90 . . . . . . . . . . . divide by 6

The number of Senators is 90; the number of Representatives is 430.

_____

You can find the number of Representatives either as 520 -90 = 430 or as 5·90 -20 = 430.

Answer:

Step-by-step explanation:

1) add the total number of male student

=14

2) divide the number of juniors by the total

2/14 = 1/7 = 0.14285

3)Multiply by 100 to get percentage

0.14285*100=14.285

4)Round

this rounds down to 14%

Answer:

B The probability's are equal

Step-by-step explanation:

FOR  APEX Hope i helped

Option: B is the correct answer.

The probabilities are equal.

( Since, probability of landing on 1 and on 4 are equal i.e. 1/8 )

The spinner is divided into two sizes such that the larger wedges are twice the size of the smaller ones.

The numbers that come on the smaller wedge are: 1,3,4 and 6

and those who come on the large wedge are: 2 and 5

If we divide the wedge which ere twice into equal sections then the total number of sections are:

      8

We know that the probability of an event is defined as the ratio of number of favorable outcomes to the total number of outcomes.

( Since 1 is comprised of just one section out of total 8 sections)

Similarly,

( Since 2 is comprised of two sections out of total 8 sections)

( Since 3 is comprised of just one section out of total 8 sections)

Similarly,

To answer the question, we first need to understand the command:

The product = multiply the unknowns together

Therefore, the expression:

4ya x 5x

when simplified: 4ya x 5x= 20ayx

Hope it helps!

Answer:

4ya x 5x = ?

Step-by-step explanation:

Answer:

Option B is correct

Step-by-step explanation:

Remove the parentheses from the following expression (2y + x) ÷ z

When removing the parenthesis, z will be divided by both the numbers inside the parenthesis

i.e.

2y/z + x/z

So, Option B is correct.

Answer:

The answer in the procedure

Step-by-step explanation:

we have

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

[tex]x^{2}-x-4-2=0[/tex]

[tex]x^{2}-x-6=0[/tex]

we know that

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]x^{2}-x-6=0[/tex]

so

[tex]a=1\\b=-1\\c=-6[/tex]

substitute in the formula

[tex]x=\frac{-(-1)(+/-)\sqrt{(-1)^{2}-4(1)(-6)}} {2(1)}[/tex]

[tex]x=\frac{1(+/-)\sqrt{25}} {2}[/tex]

[tex]x=\frac{1(+/-)5} {2}[/tex]

[tex]x=\frac{1(+)5} {2}=3[/tex]

[tex]x=\frac{1(-)5} {2}=-2[/tex]

Answer:

  x = 5

Step-by-step explanation:

Taking logarithms to the base 5, we get ...

   [tex]\log_x{7}=\log_5{7}[/tex]

Comparing forms gives x = 5.

Answer:

x=5

Step-by-step explanation: