Which ordered pair is a solution of the equation 2x − y = 9?

Answer: 8.55 minutes.

Step-by-step explanation: To find the time to run a mile, divide the total minutes by the total number of miles.

94/11=8.55

It will take 8.55 minutes to run one mile.

Answer:a and b

Step-by-step explanation:

Answer:

[tex]A\subset B[/tex]

Step-by-step explanation:

Let A and B, be two non-empty sets, then set A is a subset of set B if all elements in set A can be found in set B.

The given sets are:

A={1,2} and B={1,2,3,4}

We can observe that, all the elements in set A are also in set B.

This means that set A is a subset of B.

We write this as:

[tex]A\subset B[/tex]

The correct answer is option D.

Answer:

third graph (open circle on 518, colored to the right)

Step-by-step explanation:

The record is 518 cm. That means that 518 cm has already been accomplished. Anything less than 518 cm is not a record. 518 cm is also not a record. Only distances greater than 518 cm are records.

Answer: third graph (open circle on 518, colored to the right)

Answer:

The correct option for the graph is C.

Step-by-step explanation:

Consider the provided information.

The school record in the long jump is 518 cm.

Now we need to find the graph represents the set of jump distances in centimeters that would set a new school record.

Here, school already set a record in the long jump i.e 518 cm, it means anything less then or equal to the 518 cm is not a record.

As we need to exclude the numbers 518. So use an open dot at 518.

For record the distances should be greater than 518 cm. Thus, use the arrow moving right to 518.

Hence, the correct option for the graph is C.

For this case we have that by definition[tex]\pi[/tex] equals 180 degrees.

We must convert 135 degrees to radians, then:

[tex]135 * \frac {\pi} {180} =\\135 * \frac {3.14} {180} =\\\frac {423.9} {180} = 2.355[/tex]

Rounding off we have:

2.4 radians.

Answer:

2.4 radians

I think the answer is 1/10.

The probability that the brother and sister are both selected is 0.5052.

Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.

For the givens situation,

Total number of boys and a brother = 12

Total number of girls and a sister = 8

A brother is included among boys. So among 12 boys anyone can be a brother.

Similarly, a sister is included among girls. So among 8 girls anyone can be a sister.

The probability that the brother and sister are both selected is

⇒ [tex]P(e)=\frac{(12C_{1} )(8C_{1})}{(20C_{2})}[/tex]    

we know that [tex]nC_{r} =\frac{n! }{r!(n-r)!}[/tex]      

⇒ [tex]12C_{1}=12, 8C_{1} = 8[/tex] and [tex]20C_{2}=190[/tex]

⇒ [tex]P(e)=\frac{(12 )(8)}{190}[/tex]        

⇒ [tex]P(e)=\frac{48}{95}[/tex]

⇒ [tex]P(e)=0.5052[/tex]

Hence we can conclude that the probability that the brother and sister are both selected is 0.5052.

Learn more about probability here

https://brainly.com/question/484120

#SPJ2

Answer:

Geometric Sequence.

[tex]a_{n}=(2)^{n-1}[/tex]

Step-by-step explanation:

The x-coordinates represent the number of terms of the sequence while the y-coordinates represent the term of the sequence. So the series shown on the graph is:

1, 2, 4, 8

We can see that the ratio of two consecutive terms of the above sequence is constant. i.e.

2/1 = 2

4/2 = 2

8/4 = 2

Such a sequence in which the ratio of two consecutive terms is a constant is known as Geometric Sequence and this constant ratio is known as common ratio.

The general term of a geometric sequence is represented as:

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

Using the values for the given sequence we get:

[tex]a_{n}=1(2)^{n-1}[/tex]

[tex]a_{n}=(2)^{n-1}[/tex]

Where n represents the number of term.

y= mx+b ( equation for slope)

y= 4/5x-3

The slope (m)is 4/5

The y- intercept(b) is -3

Answer: slope is 4/5

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

In this case:

m = 4/5

b = -3

This means that 4/5 is the slope of this line.

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

1/81

Step-by-step explanation:

Answer: 1/81

Step-by-step explanation:

9 to the power of -2 = 1^2/9^2

1/81

Hope it helps

Answer:

{ - 1, 1, 7, 23 }

Step-by-step explanation:

To find the range substitute the values from the domain into g(x)

g(-2) = -2(- 2) + 3 = 4 + 3 = 7

g(- 10) = - 2(- 10) + 3 = 20 + 3 = 23

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

g(2) = - 2(2) + 3 = - 4 + 3 = - 1

Range is { - 1, 1, 7, 23 }

Answer:

a) 51 feet

b) 3.5 seconds

Step-by-step explanation:

The y-coordinate of the vertex of the given parabola is what we are looking for.

We first need to find the t-coordinate of the vertex.

The t-coordinate can be found using -b/(2a).

We need to compare

-16t^2+56t+2

to

at^2+bt+c

to identify a,b, and c.

a=-16

b=56

c=2

We are ready to compute -b/(2a).

-b/(2a)=-56/(2*-16)=-56/-32=7/4.

The vertex occurs at t=7/4.

To find y, we use y=2+56t-16t^2

y=2+56(7/4)-16(7/4)^2

y=51

So the maximum height is 51 feet.

Part b)

Hitting ground means the height between the ball and the ground is 0.

So we need to replace h(t) with 0.

0=2+56t-16t^2

I'm going to use quadratic formula.

a=-16

b=56

c=2

The quadratic formula is:

[tex]t=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]t=\frac{-56 \pm \sqrt{56^2-4(-16)(2)}}{2(-16)}[/tex]

Computing the thing inside the square root and the thing in the denominator using my handy dandy calculator:

[tex]t=\frac{-56 \pm \sqrt{3264}}{-32}{/tex]

I'm going to do the square root of 3264 now:

[tex]t=\frac{-56 \pm 57.131427428}{-32}[/tex].

I'm going to compute both

[tex]\frac{-56 + 57.131427428}{-32}[/tex] and [tex]-56-57.131427428}{-32}[/tex] using my handy dandy calculator:

[tex]-0.035357[/tex] while the other one is [tex]3.535357[/tex]

The negative value doesn't make sense for our problem so the answer is approximately 3.5 seconds.

Answer:

-9/8

Step-by-step explanation:

We simplify the fraction, then we isolate the variable

Answer:

Step-by-step explanation:

42) 9/4 = 2/x

You can solve it by cross multiplication:

In cross multiplication the numerator of first expression will be multiplied by th denominator of 2nd expression and the numerator of second expression will be multiplied by the   denominator of 1st expression.

So,

9/4 = 2/x

9*x = 2*4

9x=8

Divide both the sides by 9

9x/9 = 8/9

x= 8/9

44) -3/8 = r/3

Perform cross multiplication:

-3 *3 = 8* r

-9=8r

Divide both the sides by 8

-9/8 = 8r/8

-9/8 = r

46) -9/2n = -5/7

Perform cross multiplication:

-9 * 7 = 2n* -5

-63= -10n

negative signs will be cancelled out by each other.

63= 10n

Divide both the sides by 10

63/10 = 10n/10

63/10 = n ....

For this case we have that by definition, two magnitudes are directly proportional when there is a constant such that:

[tex]y = kx[/tex]

Where:

k: It is the constant of proportionality

We must find the value of "k" when [tex](x, y): (- 3,2)[/tex]

[tex]k = \frac {y} {x} = \frac {2} {- 3} = - \frac {2} {3}[/tex]

Answer:

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

Answer:

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

Step-by-step explanation:

We are to find the constant of variation, [tex] k [/tex], of the direct variation, [tex] y = k x [/tex] given the coordinates of the point [tex] ( - 3 , 2 ) [/tex].

Direct variation is represented by:

[tex] y = k x [/tex]

where  [tex] k [/tex] is the constant of variation.

Substituting the coordinates of the given point to find the value of [tex] k [/tex].

[tex] 2 = k (-3) [/tex]

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

Answer:

John's number is 1500

Step-by-step explanation:

* Lets explain how to solve the problem

- Factors of a number are the numbers you multiply to get the number

- Ex: Factors of 12 are 1 × 12 , 2 × 6 , 3 × 4

- The factors of a number smaller than or equal the number

- Multiple of a number is that number multiplied by an integer

- Ex: 2, 4, 6, 8, and 10 are multiples of 2

- The multiples of a number greater than or equal the number

* Lets solve the number

- John is thinking of a number

- He gives the following 3 clues

# The number has 125 as a factor

# The number is a multiple of 30

# The number is between 800 and 2000

∵ 125 is a factor of the number

- Assume that the number is 125 (its factors 1 , 5 , 25 , 125)

∵ The number is a multiple of 30

- Assume the number is 30 (the first multiple of 30)

- To solve the problem lets find the lowest common multiple of 125

  and 30 by using prime numbers only

∵ The prime factors of 125 = 5 × 5 × 5

∵ The prime factors of 30 = 2 × 3 × 5

- L.C.M of the two numbers is the product of their prime factors

 without reputation

∴ L.C.M = 5 × 5 × 5 × 2 × 3 = 750

∵ 750 has 125 as a factor

∵ 750 is a multiple of 30

- But 750 is not between 800 and 2000

∴ Find a multiple of 750 and between 800 and 2000

∵ 2 × 750 = 1500

* lets check the three clues

∵ 1500 has 125 as a factor

∵ 1500 is a multiple of 30

∵ 1500 is between 800 and 2000

∴ John's number is 1500

Answer:

Above the x-axis

Step-by-step explanation:

Lets assume a polygon that has coordinates at A(3,2), B(3,4),C(6,4),D(6,2).

This polygon is in the 1st quadrant

so rotate it clockwise 90° about the origin, you apply the rule that point of object (h,k) will change to (k,-h) hence

A (3,2) ⇒A'(2,-3)

B (3,4) ⇒ B'(4,-3)

C (6,4) ⇒C' (4,-6)

D (6,2) ⇒D' (2,-6)

the image is in the 4th quadrant

Reflecting the rotated figure on the x-axis we get

A''=(2,3)

B''=(4,3)

C''=(4,6)

D''=(2,6)

it is on the 1st quadrant

The translation is(-3,3)

The image will be

A'''=(-3+2,3+3) = (-1,6)

B'''=(-3+4,3+3)= (1,6)

C'''=(-3+4,6+3)= (1,9)

D'''=(-3+2,6+3)= (-1,9)

the final figure above x-axis

Answer: C

I believe the correct answer would be C: above x axis

Hope this helps : )

Step-by-step explanation:

Answer: 190°

Step-by-step explanation:

Angle CAE is 1/2 times the measure of arc CBA, therefore:

95° x 2=190°

The  measure of arc CBA =190°

To understand the relationship between angle CAE and arc CBA, we need to delve into the properties of angles and arcs in circles. Here is a step-by-step explanation:

Step 1: Understanding Inscribed Angles

In a circle, an inscribed angle is an angle formed by two chords that intersect on the circle. The measure of an inscribed angle is always half the measure of the intercepted arc.

Step 2: Relationship between Angle CAE and Arc CBA

Given:

- Angle CAE is inscribed in the circle.

- Arc CBA is the intercepted arc for angle CAE.

According to the properties of inscribed angles:

[tex]\[ \text{Measure of Angle CAE} = \frac{1}{2} \times \text{Measure of Arc CBA} \][/tex]

Step 3: Using the Given Information

Let's denote:

[tex]- \( \angle CAE \)[/tex] as the measure of angle CAE.

[tex]- \( \text{Arc CBA} \)[/tex] as the measure of arc CBA.

From the given information, the measure of arc CBA is 95°. Using the inscribed angle property:

[tex]\[ \angle CAE = \frac{1}{2} \times \text{Arc CBA} \][/tex]

[tex]\[ \angle CAE = \frac{1}{2} \times 95^\circ \][/tex]

[tex]\[ \angle CAE = 47.5^\circ \][/tex]

However, if we are interpreting the problem differently and consider that angle CAE is given as 95°, and we need to find the measure of the arc intercepted by this angle when doubled, then we would calculate:

[tex]\[ \text{Arc CBA} = 2 \times \angle CAE \][/tex]

[tex]\[ \text{Arc CBA} = 2 \times 95^\circ \][/tex]

[tex]\[ \text{Arc CBA} = 190^\circ \][/tex]

Therefore, if angle CAE is half the measure of arc CBA, and given the angle CAE as 95°:

[tex]\[ \text{Arc CBA} = 2 \times 95^\circ = 190^\circ \][/tex]

This shows that the measure of arc CBA is 190°.

Final answer:

To find the length of the pole, we can use the Pythagorean theorem.

Explanation:

To find the length of the pole, we can use the Pythagorean theorem. Since the base of the pole is 7 feet away from the wall and the top of the pole reaches 21 feet up the wall, we can envision a right triangle with the pole as the hypotenuse. Using the Pythagorean theorem, we can calculate:

c^2 = a^2 + b^2

Where c is the length of the pole, a is the base length (7 feet), and b is the height reached by the pole (21 feet).

Plugging in the values, we get:

c^2 = 7^2 + 21^2

Solving for c, we find that the length of the pole is √(7^2 + 21^2) feet.

Answer:

8.555 in.

Step-by-step explanation:

So the area of the square is x^2.

This makes that the area of the circle is x^2 - 20 pie.

The radius of the circle is half of the diameter, so it is 0,5x.

The formula for the circle area is:

Area = pie * r^2.

x^2 - 20 pie = pie * (0,5x)^2

x^2 - 20 pie = pie * 0,25x^2

x^2 - pie * 0,25x^2 = 20 pie

x^2 * (1 - 0,25 pie) = 20 pie

x^2 = 20pie / (1 - 0,25 pie)

x = square root (20pie / (1 - 0,25 pie)) = 17.11

So the radius is 0,5 * 17.11 = 8.555 in.

Answer:

m∠A = 45.86°

Step-by-step explanation:

A rough sketch of the triangle is shown in the attached pic.

When 3 sides are given and we want to solve for an angle, we use the Cosine Rule. Which is:

[tex]p^2=a^2 +b^2 -2abCosP[/tex]

Where a, b, p are the lengths of 3 sides (with p being the side opposite of the angle we are solving for) and P is the angel we want to solve for

Thus, we have:

[tex]p^2=a^2 +b^2 -2abCosP\\13^2=14^2 +18^2-2(14)(18)CosA\\169=520-504CosA\\504CosA=351\\CosA=\frac{351}{504}\\CosA=0.6964\\A=Cos^{-1}(0.6964)=45.86[/tex]

In △ABC,a=13, b=14, and c=18. Then angle, m∠A is is 46.654°

[tex]\frac{a}{sinA}=\frac{b}{sinB} =\frac{c}{sinC}[/tex]

[tex]a^{2} =b^{2} +c^{2} -2bcCosA[/tex] or

[tex]b^{2} =a^{2} +c^{2} -2acCosB[/tex] or

[tex]c^{2} =a^{2} +b^{2} -2abCosC[/tex]

In our case;

we are going to use Cosine rule to find m∠A

We are given;

a=13, b=14, and c=18

Therefore;

[tex]a^{2} =b^{2} +c^{2} -2bcCosA[/tex]

Replacing the variables;

[tex]13^{2} =14^{2} +18^{2} -2(14)(18)CosA[/tex]

Making CosA the subject;

[tex]CosA = \frac{(13^{2} -14^{2} -18^{2})}{-2(14)(18)}[/tex]

[tex]Cos A = \frac{-351}{-504}[/tex]

[tex]CosA = 0.6964[/tex]

[tex]A = Cos^{-1} (0.6864)[/tex]

[tex]A = 46.654[/tex]

Therefore; In △ABC,a=13, b=14, and c=18, m∠A is 46.654°

Keywords: Sine rule, Cosine rule

Level; High school

Subject: Mathematics

Topic: Triangles

Sub-topic: Cosine and sine rule

Answer:

27.778 hours

Step-by-step explanation:

just 2500 divided by 90 and that is 27.778

Final answer:

The time to drive 2500 km at a speed of 90 km/h would be 27.78 hours, but this is only a theoretical minimum as actual driving would include stops.

Explanation:

The question is asking about the time it would take to drive a certain distance at a constant speed. This is a straightforward application of the formula for calculating travel time, which is:

Time = Distance / Speed

Given the distance from Thunder Bay to Vancouver is approximately 2500 km and the car travels at a constant speed of 90 km/h, the calculation would be:

Time = 2500 km / 90 km/h

This simplifies to approximately 27.78 hours.

Answer:

[tex]\large\boxed{5\dfrac{1}{3}\ units}[/tex]

Step-by-step explanation:

ΔZYW and ΔWYX are similar. Therefore corresponding sides are in proportion:

[tex]\dfrac{ZY}{YW}=\dfrac{YW}{YX}[/tex]

We have:

[tex]ZY=3,\ YW=4,\ YX = a[/tex]

Substitute:

[tex]\dfrac{3}{4}=\dfrac{4}{a}[/tex]          cross multiply

[tex]3a=(4)(4)[/tex]

[tex]3a=16[/tex]          divide both sides by 3

[tex]a=\dfrac{16}{3}\\\\a=5\dfrac{1}{3}[/tex]

Answer:

Hello guys im also here for that answer

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

Let's find the answer by dividing [tex](-2m^{3}-m+m^{2}+1)[/tex] by  [tex](m+1)[/tex], like this:

[tex](-2m^{2})*(m+1)=-2m^{3}-2m^{2}[/tex] and:

[tex](-2m^{3}-m+m^{2}+1)-(-2m^{3}-2m^{2})=3m^{2}-m+1[/tex] then:

[tex](3m)*(m+1)=3m^{2}+3m[/tex] and:

[tex](3m^{2}-m+1)-(3m^{2}+3m)=-4m+1[/tex] then:

[tex](-4)*(m+1)=-4m-4[/tex] and:

[tex](-4m+1)-(-4m-4)=5[/tex] notice that the remainder is 5 so we need to subtract the remainder.

Based on the previous procedure we can define:

[tex](-2m^{3}-m+m^{2}+1)/(m+1)=(-2m^{2}+3m-4) + 5[/tex]

In conclusion the smallest integer that can be added to the polynomial is -5, so the polynomial will be [tex](-2m^{3}-m+m^{2}-4)[/tex].

Answer:

6

Step-by-step explanation:

30 x 40 x 50 x 60 x 70 = 252,000,000

There are six zeros at the end. So there are 6 terminal zeros.

Answer: -16

Step-by-step explanation:

input is x

output is y

9x-7=y

9(-1)-7=y

-9-7=-16

Answer:

The answer is -16

Step-by-step explanation:

input is x

output is y

9x-7=y

9(-1)-7=y

-9-7=-16

Answer:

y=1/6x+1 because the formula is written as y=mx+b

Answer:

y=1/6x+1

Step-by-step explanation:

slope is the change in y over the change in . 2-1 is 1 and 6-0 is 6 so the slope will be 1/6. the y intercept is given by the second coordinate (0,1) which is why you add 1.

Answer:

The second choice

Step-by-step explanation:

The histogram shows the following:

3 children are within the ages of 5-10

7 children are within the ages of 11-13

4 children are within the ages of 14-18

So all you need to do is find the set of data that shows that fit the intervals. So find the data that have three values within 5 to 10; seven values with the 11-13; and four values within 14 to 18.

Answer:

y = -7/4 + 5

Step-by-step explanation:

Parallel lines have the same slope.

Step 1: Identify the slope of the given equation.

From my understanding, the equation is actually

y= -7/4x - 2

slope is m from y=mx + c

slope = m= -7/4

Slope of parallel line = -7/4

Step 2: Find the y-intercept (c) from the coordinates (4, -2)

y=mx + c

-2 = -7/4(4) + x

-2 = -7 + c

c = 5

Step 3: Write the equation of the parallel line.

slope = m = -7/4

y-intercept = c = 5

y = mx + c

y = -7/4 + 5

!!

Answer:

[tex]=\frac{x^2}{16} +\frac{y^2}{49}=1[/tex]

Step-by-step explanation:

The equation of this ellipse is

[tex]\frac{(x-h)^2}{b^2} +\frac{y-k)^2}{a^2} =1[/tex]

for a vertical oriented ellipse where;

(h,k) is the center

c=distance from center to the foci

a=distance from center to the vertices

b=distance from center to the co-vertices

You know center of an ellipse is half way between the vertices , hence the center (h,k) of this ellipse is (0,0) and its is vertical oriented ellipse

Given that

a= distance between the center and the vertices, a=7

c=distance between the center and the foci, c=√33

Then find b

[tex]a^2-b^2=c^2\\\\b^2=a^2-c^2\\\\\\b^2=7^2-(\sqrt{33} )^2\\\\\\b^2=49-33=16\\\\\\b^2=16[/tex]

The equation for the ellipse will be

[tex]\frac{(x-0)^2}{16} +\frac{(y-0)^2}{49} =1\\\\\\=\frac{x^2}{16} +\frac{y^2}{49} =1[/tex]

Answer:

Given an exponential function of the form

y = a*(b)^x

The values of b that will result in the desired percentage values are:

Case 1

b = 23% decrease

1 - 0.23 = 0.77

y = a*(0.77)^x

Case 2

b = 8% increase

1 + 0.08 = 1.08

y = a*(1.08)^x

Case 3

b = 15% decrease

1 - 0.15= 0.85

y = a*(0.85)^x

Case 4

b = 120% increase

1 + 1.2 = 2.2

y = a*(2.2)^x

See attached picture for examples

The value of b in an exponential function is calculated as : For a 23% decrease = 0.77, For an 8% increase = 1.08, For a 15% decrease = 0.85, For a 120% increase = 2.20.

The student is trying to determine the corresponding exponential function base value (b) for a given percent rate of change.

In an exponential function y = abx, a positive b models exponential growth, while a value of b less than 1 models exponential decay.

We can convert the percent increase or decrease to a decimal and then add or subtract it from 1 to find the corresponding value of b.

For a 23% decrease, b = 1 - 0.23 = 0.77.

For an 8% increase, b = 1 + 0.08 = 1.08.

For a 15% decrease, b = 1 - 0.15 = 0.85.

For a 120% increase, b = 1 + 1.20 = 2.20.

Answer:

R(p) = -6p^2 + 60p....

Step-by-step explanation:

Revenue, R = quantity sold * price

Price = p

Quantity sold = q = -6p + 60

R(p) = q*p

where q=-6p + 60

= (-6p + 60) * p = -6p^2 + 60p

Answer: R(p) = -6p^2 + 60p....

Answer:

A, C, E

Step-by-step explanation:

substitute for x in each option and check if the value of y satisfies the inequality

Answer:

Option A, C and E

Step-by-step explanation:

We have to find points which are solution to the linear inequality ( y<0.5x + 2)

(a) For (-3, -2)

-2 < (0.5 × 3 + 2)

-2 < 1.5 + 2

-2 < 3.5

True, It's a solution.

(b) For (-2, 1)

1 < 0.5 × (-2) + 2

1 < -1 + 2

1 < 1

False, it's not a solution

(c) For (-1, -2)

-2 < 0.5 (-1) +2

-2 < -1 + 2

-2 < 1

True, It's a solution.

(d) For (-1, 2)

2 < 0.5 (-1) + 2

2 < -1 + 2

2 < 1

False, It's not the solution.

(e) For (1, -2)

-2 < 0.5 (1) + 2

-2 < 2.5

True It's a solution

Therefore, Option A, C and E are the solutions.