What ordered pair is a solution of the equation y = 4x?
A. (1, 3)
B. (-1, -4)
C. (-4, -1)
D. (1, -4)

Answer:

a. x=100 b. x=30

Step-by-step explanation:

A: <1 and <2 are supplementary by consecutive interior angles theorem

x + x-20 = 180

2x-20=180

2x=200

x=100

B: <1 and <2 are congrunt by corresponding angles postulate

3x-5=x+55

2x=60

x=30

By transforming the second order polynomial 5 · x² - 30 · x = 5 into its standard form, the polynomial is equivalent to (x - 3)² = 9.833. (Correct choice: A) #SPJ5

The standard form of a parabola is a synthetic form that brings useful information of the geometric locus. This form is derived by applying the method of completing a square, which is based on algebra properties to transform and reduce a part of a second order polynomial into a perfect square trinomial.

Now we proceed to show the procedure to obtain the expression equivalent to the polynomial described in the statement:

5 · x² - 30 · x = 5

x² - 6 · x = 5/6

x² - 6 · x + 9 = 59/6

(x - 3)² = 59/6

(x - 3)² = 9.833

By transforming the second order polynomial 5 · x² - 30 · x = 5 into its standard form, the polynomial is equivalent to (x - 3)² = 9.833. (Correct choice: A) #SPJ5

To learn more on completing the square, we kindly invite to check this verified question: https://brainly.com/question/4822356 #SPJ5

Answer:

3446

Step-by-step explanation:

3718-272

=3446

because the question says more you'll have to subtract David's bass from his father's bass

The Length AB of the triangle ABC is 31.079m

Area is the total amount of space filled by a flat (2-D) surface or an object's shape.

A planar figure's area is the space that its perimeter encompasses.  Square units like cm²and m² are used to measure area. The area of a form is a two-dimensional quantity.

Area of oblique triangle: S(CAB)=AC*BC*sin(ACB)/2

Substituting the values;

AC=8.4m

S(ΔCAB)=100m²

(∠ACB)=40°

S(ΔCAB)=(8.4×BC×Sin40°)/2

100=(8.4×BC×Sin40°)/2

BC=37.041m

Law of cosines:

AB²=AC²+BC²-2AC×BC×cos(∠ACB)

Substitute  the values,

AC=8.4m, ∠ACB=40 ° , BC=37.041 we get:

AB²=8.4²+37.041²-2×8.4×37.041×cos40°

AB=31.079m

Hence, The Length AB of the triangle ABC is 31.079m.

To know more about perimeter, visit:

https://brainly.com/question/6465134

#SPJ1

Answer:

\(\boxed {x = -\frac{1}{7}}\)

Step-by-step explanation:

Solve for the value of \(x\):

\(6(4x + 5) = 3(x + 8) + 3\)

-Use Distributive Property:

\(6(4x + 5) = 3(x + 8) + 3\)

\(24x + 30 = 3x + 24 + 3\)

-Combine like terms:

\(24x + 30 = 3x + 24 + 3\)

\(24x + 30 = 3x + 27\)

-Take \(3x\) and subtract it from \(24x\):

\(24x + 30 -3x = 3x - 3x + 27\)

\(21x + 30 = 27\)

-Subtract both sides by \(30\):

\(21x + 30 - 30 = 27 - 30\)

\(21x = -3\)

-Divide both sides by \(21\):

\(\frac{21x}{21} = \frac{-3}{21}\)

\(x = \frac{-3}{21}\)

-Reduce the fraction to the lowest term by extracting and canceling out \(3\):

\(x = \frac{-3\div3}{21 \div 3}\)

\(\boxed {x = -\frac{1}{7}}\)

Therefore, the value of \(x\) is \(-\frac{1}{7}\).

Answer:

49

Step-by-step explanation:

(2^2 + 3)^2

(4 + 3)^2

(7)^2

49

Yk cause of bidams you gotta do 2 to the power of 2 first, and then get 4 + 3. Then you add them, you get 7. Cube it and get 49. Ez ;>

*winks and runs off*

To show that {1, 2-t, 2-t-t²} are linearly independent, we need to show that the equation c₁(1) + c₂(2-t) + c₃(2-t-t²) = 0 only has the trivial solution c₁ = c₂ = c₃ = 0.

[1] To show that {1, 2-t, 2-t-t²} are linearly independent, we set up the equation c₁(1) + c₂(2-t) + c₃(2-t-t²) = 0, and solve for c₁, c₂, and c₃. If the only solution is c₁ = c₂ = c₃ = 0, then the vectors are linearly independent.

[2] To find the change-of-coordinate matrix from E to B, we express each vector in B as a linear combination of the vectors in E: 1 = 1(1) + 0(t) + 0(t²), 2 - t = 0(1) + 1(t) + 0(t²), and 2 - t - t² = 0(1) + 0(t) + 1(t²). We arrange the coefficients of E as columns of the matrix.

[3] To find the E-coordinates of q(t), we multiply the coordinate vector of [q]B by the change-of-coordinate matrix from B to E. The coordinate vector [q]B is obtained by expressing q(t) = α + α₁t + α₂t² as a linear combination of the vectors in B: q(t) = α(1) + (α₁-α) (2-t) + α₂(2-t-t²).

[4] To find the B-coordinates of p(t) = -4+t+t², we first find the E-coordinates of p(t) using the standard basis E: p(t) = -4(1) + 1(t) + 1(t²). Then, we multiply the coordinate vector of [p]E by the change-of-coordinate matrix from E to B to obtain the B-coordinates of p(t).

know more about linearly independent :brainly.com/question/30575734

#SPJ11

Answer:

\(-16\)

Step-by-step explanation:

\(f(5)=4(5)-1=19 \\ \\ g(5)=2^5+3=35 \\ \\ (f-g)(5)=f(5)-g(5)=19-35=-16\)

Answer:

Step-by-step explanation:

Okay, here we have this:

Considering the provided measures, we are going to identify the scale of the drawing so we obtain the following:

Measuring with the inch ruler, we have:

The space that they say measures 9 feet in inches measures you 0.75, and the one that measures 12 feet in inches measures one inch.

a) Then the scale is: One actual inch equals 12 drawing feet.

b) The student put them on his own and they were verified

Answer:

k = 5

Step-by-step explanation:

Given that (x - h) is a factor of f(x) then f(h) = 0

Given (x - 1) is a factor of f(x), then f(1) = 0, that is

3(1)³ - 8(1) + k = 0

3 - 8 + k = 0

- 5 + k = 0 ( add 5 to both sides )

k = 5

The value of k in the polynomial f(x) = 3x³ - 8x + k is 5.

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given,  f(x) = 3x³ - 8x + k, and (x - 1) ⇒ x = 1 is a factor of f(x),

∴ If we replace 1 in place x and make f(x) = 0 and equate we will have the value of k.

So, 0 = 3(1) - 8(1) + k.

0 = 3 - 8 + k.

k = 5.

learn more about factor of a polynomial here :

https://brainly.com/question/28315959

#SPJ2

300 kilogrammes is equal to about 661.39 pounds.

Weight = mass x gravity is the formula for relating mass and weight.

Such equation is known as Newton's Second Law of Motion.

The Latin word "libra," which means balance and weight, is where the name "pound sterling" comes from.

In Newtons, N, force (or weight) is measured.

the mass is measured in kilograms, kg.

You can use the conversion factor 1 kg = 2.20462 pounds to change kilogrammes to pounds.

Thus, 300 kg divided by 2.20462 pounds per kilogramme results in:

300 kg times 2.20462 pounds/kg equals 661.386 pounds (rounded to three decimal places).

300 kilogrammes is equal to about 661.39 pounds.

For such questions on Conversion of pound,

https://brainly.com/question/29329446

#SPJ4

Answer:

-2

Step-by-step explanation:

(x + 2)(x + 3) = (x-2)(x-3) + 10

2x+6=2x-6+10

2x+12=2x+10

x=-2

Only statements (a) and (e) must be true.

Let's start by tracking the number of candies each person has after each round:

* Round 1: Lizzy has $x$ candies, Megan has $x$ candies, Oscar has $x$ candies, and Patrick has $0$ candies.

* Round 2: Lizzy has $0$ candies, Megan has $2x$ candies, Oscar has $x$ candies, and Patrick has $0$ candies.

* Round 3: Lizzy has $0$ candies, Megan has $0$ candies, Oscar has $3x$ candies, and Patrick has $x$ candies.

As you can see, the number of candies Patrick has is always a multiple of 2. This is because in each round, the total number of candies is multiplied by 2. Therefore, statement (a) must be true.

Now, let's consider statement (e). If $x$ is even, then the number of candies Patrick has in the end will be divisible by 4. However, if $x$ is odd, then the number of candies Patrick has in the end will be 1 more than a multiple of 4, and therefore not divisible by 4. Therefore, statement (e) must be true.

The remaining statements (b), (c), and (d) are not necessarily true. For example, if $x$ is a multiple of 3, then statement (c) will be true, but if $x$ is not a multiple of 3, then statement (c) will not be true. Similarly, statements (b) and (d) are also not necessarily true.

to learn more about number click here:

brainly.com/question/29546604

#SPJ11

Answer: m = 4

Step-by-step explanation:

-3m(4) = -12

Answer:

4

Step-by-step explanation:

-3 x 4 = -12

the answer is not -4 because -3 x -4 would just be 12.

Answer:X= -4

Step-by-step explanation:

6 less than the product of a number and 3 is -18.

Make each part of the sentence into numbers:

"the product of a number and 3":  becomes X*(3), where X is the "number."

"6 less than":  is -6, so we have:

X*(3) - 6

"is -18"  means = -18

Put the segments into one equation and solve:

X*(3) - 6 = -18

3X-6=-18

3X = -12

X = -4

====

See if this works:  If X=-4, then the product of it and 3 is -12.  Six less than -12 is -18.  And that is correct.  X= -4

Yes, there will be a collision between Speedy Sue's car and the slow-moving van in the tunnel. The collision will occur at a distance of approximately 146.5 meters into the tunnel, and the time of the collision will be around 7.72 seconds.

To determine whether there will be a collision, we need to calculate the time it takes for Speedy Sue to reach the van and compare it with the time it takes for the van to exit the tunnel.

First, we calculate the time it takes for Sue to reach the van. The relative velocity between Sue and the van is (33.0 m/s - 5.40 m/s) = 27.6 m/s. Using the formula time = distance / velocity, the time it takes for Sue to reach the van is approximately 175 m / 27.6 m/s ≈ 6.34 seconds.

Next, we calculate the time it takes for the van to exit the tunnel. The distance the van needs to travel to exit the tunnel is the sum of the distance from its initial position to the end of the tunnel and the distance Sue needs to travel to reach the end of the tunnel. The total distance is 175 m + 175 m = 350 m. The velocity of the van is 5.40 m/s. Using the formula time = distance / velocity, the time it takes for the van to exit the tunnel is approximately 350 m / 5.40 m/s ≈ 64.81 seconds.

Since 6.34 seconds is less than 64.81 seconds, Sue will collide with the van before it exits the tunnel. To determine the distance into the tunnel where the collision occurs, we subtract the distance Sue travels in 6.34 seconds from the initial distance between Sue and the van. The distance Sue travels is (33.0 m/s - 1.90 m/s^2 * 6.34 s^2 / 2) * 6.34 s ≈ 146.5 meters.

Therefore, the collision between Sue's car and the van will occur at a distance of approximately 146.5 meters into the tunnel, and the time of the collision will be around 7.72 seconds.

Learn more about meters here:

https://brainly.com/question/29367164

#SPJ11

Answer:

ben

Step-by-step explanation: b e n

Answer:

40%

Step-by-step explanation:

assuming you actually mean 10^5 and 10^6, to find percentages you do

part/total x percent/100

you have (6x10^5/1.5x10^6) x (x/100)

cross multiply, and you have 6x10^7=1.5x10^6x

divide on both sides by 1.5x10^6

x=40

so the answer is 40%

Answer:

52°

Step-by-step explanation:

The measure of angle between the ladder and the ground is given as:

Sum of angles in a triangle

38° + x° + 90° = 180

128°+X° = 180°

X° = 180-128

X= 52°

Hence the angle x = 52°

To find a value of theta in the interval [0, 90] that satisfies sin(theta) = 0.87185 using a TI-30X calculator, you can use the inverse sine function, which is denoted as sin⁻¹.

Follow these steps:

For example, if you follow these steps on the TI-30X calculator, you should get the result:

So, one possible value of theta in the interval [0, 90] that satisfies sin(theta) = 0.87185 is 60 degrees.

Learn more about theta: https://brainly.com/question/15869413

#SPJ11

9514 1404 393

Answer:

Step-by-step explanation:

Adding 10 and dividing by 4, we have ...

  4x < 28

  x < 7

The comparison does not include the "equal to" case, so the circle at x=7 is open. Values of x less than 7 are in the solution set. Those values are found to the left of 7 on the number line.

Answer:

C. The graph has an open circle at 7.

and

E.The arrow points left.

Step-by-step explanation:

i took the quiz and got it right

Answer:

a) He used the machine on the right

b) 4

Step-by-step explanation:

a) whatever number you insert on the left machine (y=x²+3), we will always get a number even if you put 0. but on the right machine (y=sqrt•x -2) we have a value to make the output 0

b) if you insert 4 on the right machine,

y=sqrt•4-2

y=2-2

y=0

Answer: B. 4 × 10⁻⁵

Step-by-step explanation:

0.00003762 = 3.762 × 10⁻⁵ ≈ 4 × 10⁻⁵

Answer:

b

Step-by-step explanation:

\(4 \times {10}^{ - 5} = 4 \times \frac{1}{100000} \)

Answer:

1

Step-by-step explanation:

The required probability that she rolls a 1 both times is 1/36.

Fatima rolls a number cube 2 times. To find the probability that she rolls a 1 both times.

Probability can be defined as the ratio of favorable outcomes to the total number of events for a system of certain events.
Probability = frequency of favorable outcome / Sample space.

Fatima rolls a number cube 2 times.
For a roll sample space = { 1 2 3 4 5 6}
n(sample space) = 6
Favorable outcome (rolls a 1) =  1
Required probability for 1 = 1/6
Probability for rolls a 1 both times.= 1/6 *1/6
                                                          = 1/36

Thus, the required probability that she rolls a 1 both times is 1/36.

Learn more about probability here:

brainly.com/question/14290572

#SPJ6

Answer:

24.61%

Step-by-step explanation:

48÷195=0.24615385

convert that decimal to a percent

24.61%

*********if the question asks you to round up, then the answer is 24.62%

Answer:

Boki tego trójkąta mają 6 cm.

Step-by-step explanation: