As a certain engine's rotation speed increases, its temperature increases at a constant rate. The table compares the engine's rotation speed (in cycles per second) and its temperature (in degrees Celsius).

Explanation:

Triangles HIG and FED are similar triangles. We know this because we have two pairs of angles that are congruent (angle G = angle D; angle I = angle E). Use the AA (angle angle) similarity theorem.

Since angles G and D are congruent, computing sin(D) is equivalent to finding sin(G)

sin(angle) = opposite/hypotenuse

sin(G) = IH/HG

sin(G) = 77/85

sin(D) = 77/85

Answer:

c/3, the sequence is NOT geometric because 2/3 was added to each term to get the next term.

Step-by-step explanation:

geometric sequences are multiplying, arithmetic sequences are addition.

1/3

1/3+2/3= 1 (or 3/3)

3/3+2/3= 5/3

5/3+2/3= 7/3

this is arithmetic, not geometric

Answer: k = 4

Step-by-step explanation:

For this division, to determine the value of k, use the Remainder Theorem, which states that:

polynomial p(x) = dividend (x-a) * quotient Q(x) + remainder R(x)

Knowing the degree of quotient is

degree of Q = degree of p(x) - degree of (x-a)

For this case, Q(x) is a third degree polynomial.

Using the theorem:

[tex]x^{4}-3x^{2}+kx-2 = (x-2)(ax^{3}+bx^{2}+cx+d) + 10[/tex]

[tex]x^{4}-3x^{2}+kx-2 = ax^{4} + x^{3}(b-2a)+x^{2}(c-2a)+x(d-2c)-2d+10[/tex]

a = 1

b - 2a = 0 ⇒ b = 2

c - 2b = -3 ⇒ c = 1

-2d + 10 = -2 ⇒ d = 6

d - 2c = k ⇒ k = 4

Therefore, k = 4 and Q(x) = [tex]x^{4} -2x^{2} + 4x + 2[/tex]

Answer:

2x^2+x-1/x^2-1

x^2+11x+18/x^2-11x+18

2x^2-5x+3/x^2+4x+3

Step-by-step explanation:

1.2 and 5

Answer:

1st fig ans=12x ^2-7x-21.

2nd fig ans

i) ( x-15)(x+2)

ii) 2(x+7)(x-9)

iii) -3x(2x+1)(5x-3)

Hope it will help uh....

Answer:

1C 2 D 3 c

Step-by-step explanation:

1, X^2-13x-30

X^2-15x+2x-30

X(x-15)+2(x-15)

(X+2)(x-15)

2, 2x^+4x-126..... Simplified As

(2x-14)(x+9)

3, -30x^3+3x^2+9x ..... Simplified as

-3x(2x+1)(5x-3)

Answer:

A. Net

Step-by-step explanation:

Answer:

a. net

Step-by-step explanation:

The net of a 3D shape is how it looks unfolded. A net can easily be put back together.

Hope this helps! :)

Answer:

su respuesta sería 21521.3

Answer:

The third number is 195-3x

Step-by-step explanation:

Given:

sum of three numbers, a, b, c is 180.

a=2x-11

b=x-4

c= ?

Solution:

a+b+c = 180

2x-11 + x-4 + c = 180

c = 180 - (2x-11) - (x-4)

= 180 -2x+11 - x+4

= 180 + 11 + 4 -2x -x

= 195 -3x

Answer:

D

Step-by-step explanation:

To reflect a function across the x axis, we just stick a negative in front. This will make all point's y coordinates to go from positive to negative or vice versa. If the original function already has a negative out front, then remove it.

Answer:

[tex]3\sqrt{17}$ or \approx 12.37$ Units[/tex]

Step-by-step explanation:

In the attached diagram

CA=CO+OA

CO=DB

Therefore:

5=2+OA

OA=3 Units

The angle between a tangent line and a radius is 90 degrees. therefore triangle OAB is a right triangle with:

OB=12 units

OA=3 units

Using Pythagoras theorem

[tex]AB=\sqrt{3^2+12^2}\\ =\sqrt{153}\\=3\sqrt{17}$ or \approx 12.37$ Units[/tex]

Answer:

Explained below.

Step-by-step explanation:

(A)

The p-value is well defined as per the probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was the truly observed value of the test statistic.

The p-value of the test was, p = 0.3822.

That is the probability that Remedy B has a greater salvage rate than A is 0.3822, given that rates are the same for Remedy A and B.

(B)

The significance level of the test is: α = 0.05.

A small p-value (typically ≤ 0.05) specifies strong evidence against the null hypothesis (H₀), so you discard H₀. A large p-value (> 0.05) specifies fragile proof against the H₀, so you fail to discard H₀.

The p-value of the test is very large. The null hypothesis will not be rejected.

Concluding that salvage rates are the same for Remedy A and B.

(C)

A type II error is a statistical word used within the circumstance of hypothesis testing that defines the error that take place when one is unsuccessful to discard a null hypothesis that is truly false.

In this case a type II error could have been made as the null hypothesis was not rejected.

The type II error could have been made because of the following reasons:

As the sample selected is quite large, the only potential consequence of this error is that the significance level of the test must be small.

Answer:

Step-by-step explanation:

We know:

We have:

HCF(6, x) = 2 and LCM(6, x) = 60.

Substitute:

60 · 2 = 6 · x

120 = 6x             divide both sides by 6

20 = x → x = 20

Substitute to x² + 3x:

20² + 3(20) = 400 + 60 = 460

Answer:

1 and 3

Step-by-step explanation:

The lines 1 and 3 divide the shape into 2 identical parts so they are axes of symmetry

The line of symmetry for the given figure is 1 and 3.

We need to find the line of symmetry for the given figure.

Line symmetry is a type of symmetry where one-half of the object reflects the other half of the object across the line.

In the given figure we can see line 1 and 3 divides the figure into two halves.

Therefore, the line of symmetry for the given figure is 1 and 3.

To learn more about the line of symmetry visit:

https://brainly.com/question/1597409.

#SPJ2

Answer:

10

Step-by-step explanation:

This is an arithmetic sequence.  The common difference is -6, and the first term is 52.

a = 52 − 6(n − 1)

When n = 8:

a = 52 − 6(8 − 1)

a = 52 − 42

a = 10

Answer: subtract 85 with a hundred because you are trying to see how many students out of 100% are good students after that you should get your answer

Step-by-step explanation:

Answer:

77% (rounded)

Step-by-step explanation:

1. Find 85% of 100

           100 x 0.85 = 85

     SO 85 students out of 100 students are good students.

2. Add the 10 more students to the total number.

             100 + 10 = 110 total students

3. Find the percent of good students in the total number of current students.

          85/110 = 0.77 * 100 (to convert to percent) = 77%

Answer:

a = - 4, b = 5

Step-by-step explanation:

Expand the left side and compare the coefficients of like terms on the right side.

- 3(2x² + ax + b)

= - 6x² - 3ax - 3b

Comparing like terms with - 6x² + 12x - 15

x - term → - 3a = 12 ( divide both sides by - 3 )

                    a = - 4

constant term → - 3b = - 15 ( divide both sides by - 3 )

                               b = 5

Answer:

Solution,

[tex]5 \frac{3}{4} \div 1 \frac{1}{2} [/tex]

Convert the mixed number to an improper fraction

[tex] \frac{23}{4} \div \frac{3}{2} [/tex]

To divide by a fraction, multiply by the reciprocal of that fraction

[tex] \frac{23}{4} \times \frac{2}{3} [/tex]

Reduce the numbers with the GCF 2

[tex] \frac{23}{2} \times \frac{1}{3} [/tex]

Multiply the fraction

[tex] \frac{23}{6} [/tex]

Hope this helps...

Good luck on your assignment...

Answer:

0.5

Step-by-step explanation:

Let D be the event of selecting a marble with dots.

Let P be the event of selecting a purple marble.

The probability of selecting a marble with dots, P(D)=0.2

The probability of selecting a marble that is both purple and has dots, [tex]P(D \cap P)=0.1[/tex]

We want to determine the probability of selecting a purple marble given that the marble has dots on it, P(P|D)

By the definition of conditional probability:

[tex]P(P|D)= \dfrac{P(P \cap D)}{P(D)} \\= \dfrac{0.1}{0.2}\\ =0.5[/tex]

The probability of selecting a purple marble given that the marble has dots on it is 0.5.

Answer:

48 miles.

Step-by-step explanation:

Her average speed was 12 miles per hour. She traveled for 4 hours. We can set up a proportion that shows that she traveled 12 miles over 1 hour, so she traveled x miles over 4 hours.

[tex]\frac{12}{1} =\frac{x}{4}[/tex]

1 * x = 12 * 4

x = 48

So, the cyclist traveled 48 miles.

Hope this helps!

Answer: 48 miles

Explanation: Well obviously if you've been on the road for 4 hours and you're traveling at 12 miles per hour, you end up going 48 miles.

Mathematically speaking we get that

by multiplying 12 × 4 to equal 48.

This 12 represents our rate.

This 4 represents the number of hours or our time.

The 48 represents the 48 miles or our distance we've travelled.

So our rate × time = distance.

This formula is a very popular one in algebra.

Answer:1/4

Step-by-step explanation:

Each term is multiplied by 1/4 to get to the next

Therefore 1/4 is the common ratio

Answer:

2310cm³

Step-by-step explanation:

volume= πr²h

22/7× radius of circle × height

circumference= πd

44cm=22/7×d, diameter= 7 cm, radius= 3.5cm

v= 22/7× 3.5× 21 = 2310cm³

Step-by-step explanation:

V= π*r²*h

V/π = r²*h

v/(π*r²) = h

[tex]\frac{x+y}{3}[/tex] = 5

x+y = 15

x = 15-y

Answer:

the slope of the perpendicular bisector is -2/3

Step-by-step explanation:

The slope of the line joining the two points P1(0,3), P2(6,12) is given by

m1 = (y2-y1) / (x2-x1) = (12-3) / (6-0) = 9/6 = 1.5

The slope m2 of a line perpendicular to the previous line is given by

m1*m2 = -1

solving

m2 = -1/m1 = -1/ (3/2) = -2/3

THerefore the slope of the perpendicular bisector is -2/3

Answer:

6-3/0-(-4)

=3/4

Step-by-step explanation:

Given two points of a line to find the slope, we use the formula.y2-y1/x2-x1 hence the answer above. Our xs are x2=0 x=-4 y2=6 y1=3

Answer & Step-by-step explanation:

When we see the phrase "rate of change" then it means that we are looking for the slope. So, we will need to know the formula for finding slope or the rate of change.

[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

Now, let's use this equation to solve for the rate of change of each question.

Problem 1:

[tex]Slope=\frac{2-\frac{4}{3}}{0-(-1)}\\\\Slope=\frac{\frac{2}{3}}{1}\\\\Slope=\frac{2}{3}[/tex]

The rate of change of this equation is 2/3

Problem 2:

[tex]Slope=\frac{4-2}{1-0}\\\\Slope=\frac{2}{1}\\\\Slope=2[/tex]

The rate of change for this equation is 2

Problem 3:

[tex]Slope=\frac{10-4}{2-1}\\\\Slope=\frac{6}{1}\\\\Slope=6[/tex]

The rate of change for this equation is 6

Answer:

AB║CD and AD║BC

Step-by-step explanation:

By the property of a parallelogram,

" Consecutive angles of a parallelogram are supplementary"

In the figure attached,

∠DCB and ∠CDA are the supplementary angles. Therefore ABCD will be a parallelogram.

[Given: m(∠DCB) + m(∠CDA) = 180°]

And the pair of opposite sides of the parallelogram ABCD will be parallel.

AD║BC and AB║CD

Answer:

second option

Step-by-step explanation:

The volume (V) of a sphere is calculated as

V = [tex]\frac{4}{3}[/tex] πr³ ( where r is the radius )

Here r = 6 , thus

V = [tex]\frac{4}{3}[/tex]π(6)³

Answer:

Second option

Step-by-step explanation:

Volume of a sphere =  [tex]\frac{4}{3}*\pi *r^{3}[/tex]

→ Substitute in the value of radius

Volume of a sphere =  [tex]\frac{4}{3}*\pi *6^{3}[/tex]