solve ABC
c=10, B=35°, C=65%​

We understand a linear inequality as an inequality involving a linear function. It's important to know that a linear inequality contains one of the symbols of inequality:

< less than

> greater than

≤ less than or equal to

≥ greater than or equal to

In this problem, we have:

[tex]2x-3y<12[/tex]

In this case, we use the symbol <, so this indicates that [tex]2x-3y[/tex] is less than 12. To solve this, let's write the linear equation in slope-intercept form:

Step 1: Write the expression as an equation:

[tex]2x-3y=12[/tex]

Step 2: Subtract -2x from both sides:

[tex]2x-3y-2x=12-2x \\ \\ -3y=12-2x[/tex]

Step 3: Multiply the entire equation by -1/3

[tex]-\frac{1}{3}(-3y)=-\frac{1}{3}(12-2x) \\ \\ y=\frac{2}{3}x-4[/tex]

The graph of this equation is shown in the firs figure below. To know what's the shaded region let's take point (0, 0) and test it in the inequality:

[tex]2(0)-3(0)<12 \\ \\ 0<12 \ TRUE![/tex]

Since this is true, the shaded region includes point (0, 0) and this is above the graph. We have to draw a dotted line since equality is not included in the solution and this is shown in the second figure below.

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

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:

y=8x+13

Step-by-step explanation:

Perpendicular Lines are those with the following condition:

y=a*x+b (1)

y=c*x+d (2)

Where 'a' and 'c' are the respective slope

If These two lines are perpendicular, then

a=- 1/c

Equation (1) for our case is written as y=-(1/8)x-2, meaning that a=-1/8 and b = 2

Using those principles we have that the slope for our needed line ('c') has to be 8.

Now we most use the given point to find the remaining term of the equation (d)

Evaluate it in eq (2) to have this:

-3=8*(-2)+d

resulting that d=13

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:

  82

Step-by-step explanation:

Alternate exterior angles where the transversal "e" crosses parallel lines "a" and "b" are congruent. x° ≅ 82°

Answer: second option.

Step-by-step explanation:

It is important to remember that  Vertical angles are defined as two non-adjacent angles formed by intersecting lines. These angles share the same vertex and they are congruent.

Observe the figure attached. Since lines "a" and "b" are parallel, you can notice that the angle 82° angle x° are Vertical angles. Therefore, they are congruent.

Then, the value of "x" is:

[tex]x=82\°[/tex]

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:

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.

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.

Answer:

[tex](x^2+5)*(x-3)[/tex]

Step-by-step explanation:

In grouping method factoring, you must have to split the middle term in a way that the product of two terms in middle must be equal to the product of two terms at the edges of equation. Remember you have to consider the resultant signs as well as the magnitude of both products.

Now in the case given above,

[tex]x^3-3x^2+5x-15[/tex]

the result is [tex]-15x^3[/tex]

Note that the magnitude is 15x^3 and sign is '-' for both products.

Now taking out the common terms, equation becomes;

[tex]x^2(x-3)+5(x-3)[/tex]

Taking out (x-3) as common, now the factorized version we have is:

[tex](x-3)(x^2+5)[/tex]

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:

(b-1)(b-1)

Step-by-step explanation:

If you don't see a perfect square here, then your objective since the coefficient of b^2 is 1 and this is a quadratic, is to find two numbers that multiply to be 1 and add up to be -2.

-1(-1)=1 and -1+(-1)=-2.

So the factored form is (b-1)(b-1) or (b-1)^2.

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.

[tex]\large\boxed{\text{About}\,4.836\,\,\text{meters}}[/tex]

In this question, we're trying to find the radius of the circle.

In this case, we would use the formula:

[tex]r=\sqrt\frac{A}{\pi}\,\,\text{or}\,\,r=\sqrt\frac{A}{3.14}[/tex]

"A" would represent the area, so you would plug in 73.48 in "A."

Your equation should look like this:

[tex]r=\sqrt\frac{73.48}{\pi}[/tex]

Now, you will solve:

[tex]r=\sqrt\frac{73.48}{\pi}\\\\\text{Divide the fraction}\\\\r=\sqrt23.3894104367849385445951\\\\\text{Square it by finding the square root}\\\\r= 4.836259963730\\\\\text{Lets make it shorter}\\\\r=4.836[/tex]

When you're done solving, you should get 4.836

This means that the radius is about 4.836 meters.

Answer:

r=4.84m

Step-by-step explanation:

If the area of a circle is 73.48 square meters, the radius is 4.84m.

Formula: A=πr^2

r = A/π = 73.48/π ≈ 4.83626m

[tex]3(2x-7)+2+ 2(x+y)=6x-21+2+2x+2y=8x+2y-19[/tex]

Answer:

[tex]\large\boxed{y\geq3x+21}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

[tex]-6x+2y\geq42\qquad\text{add}\ 6x\ \text{to both sides}\\\\2y\geq6x+42\qquad\text{divide both sides by 2}\\\\y\geq3x+21[/tex]

Answer:

330:1

Step-by-step explanation:

least common multiple of 180 and 594

180: 2×2×3×3×5

594: 2×3×3×11

LCM: 594×2×5 = 5940

GCF: 2×3×3 = 18

ratio:

5940:18

330:1

The ratio of the Least Common Multiple (LCM) of 180 and 594 to the Greatest Common Factor (GCF) of 180 and 594 is 330. This is found by first determining the LCM (5940) and GCF (18), then dividing the LCM by the GCF.

To find the ratio of the Least Common Multiple (LCM) of 180 and 594 to the Greatest Common Factor (GCF) of 180 and 594, first, we find the LCM and GCF separately.

Finally, we divide the LCM by the GCF:

5940 ÷ 18 = 330.

So, the ratio of the LCM of 180 and 594 to the GCF of 180 and 594 is 330. Therefore, the correct answer is (C) 330.

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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:

c. 21/32 inches

C. 1.992

b. 0.3125

Step-by-step explanation:

Given

The inside diameter = 1/2 inches

Wall thickness = 1/16 inches

clearance = 1/32 inches

As it is given that the outside diameter is twice the thickness and diameter.

So,

Outside diameter = 1/2 + 2(1/32)

= 1/2+2/16

= 1/2+1/8

=(4+1)/8

=5/8

We also have to give clearance of 1/32 inches so,

Diameter of hole = 5/8+1/32

=(20+1)/32

=21/32 inches

So the correct answer for question 1 is:

c. 21/32 inches

Rounding off 1.99235 to three decimal places:

1.992

C. 1.992

Expressing 5/16 as a decimal fraction:

0.3125

b. 0.3125

16 completely divides 5 so the answer is already 4 decimal places ..

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:

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:

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:

D:  one-to-many

Step-by-step explanation:

D:  one-to-many.  This is because there is more than one output associated with a single input.  For input 2, the output could be either 9 or 8.  Similar situation with input -3:  output could be 7 or 6.  This relation is NOT a function.

Option A, One to many

A set of collected ordered pairs is known as a relation. In each ordered pair the left-hand side is mapped with the right-hand side

As you can see the left-hand side of the ordered pair 2 is mapped to both 9,8 and -3 is mapped to 9 and 6 we can safely say that it is a one-to-many relation as the same left-hand side mapping has 2 different right-hand side mapping and there is no similar right-hand side mapping.

Learn more about types of relations here

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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 }

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.

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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.

Finding the slope using two points, (5, -1) and (-8, -4)

The formula for slope is

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

In this case...

[tex]y_{2} =-4\\y_{1} =-1\\x_{2} =-8\\x_{1} =-5[/tex]

^^^Plug these numbers into the formula for slope...

[tex]\frac{-4-(-1)}{-8-5}[/tex]

[tex]\frac{-3}{-13}[/tex]

[tex]\frac{3}{13}[/tex]

^^^This is your slope

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Step-by-step explanation:

The formula to find a slope using two points is:

[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\m = ((-4)-(-1))/((-8)-(5))\\m = -3 / -13\\m = 3/13[/tex]

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:

-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 ....

Answer:

of what? i know how to do these but tell me the equation

Step-by-step explanation:

you asked a very not telling question. need more info to give an answer