Find the equation of the line that passes through the point (−3, −4) and is parallel to the line that passes through the points (−5, 1) and (7, −3).

Answer:

y = x²/4 + x/2 + 21/4 ⇒ -9 ≤ x ≤ 7

Step-by-step explanation:

∵ x = 2t - 1

∴ 2t = x + 1 ⇒ t = (x + 1)/2

∵ y = t² + 5

∴ y = [(x + 1)/2]² + 5 = (x² + 2x + 1)/4 + 5

  y = x²/4 + x/2 + 1/4 + 5 = x²/4 + x/2 + 21/4

∵ -4 ≤ t ≤ 4

∴ -9 ≤ x ≤ 7

As the exercise says, the triangles are similar. So, we can set up proportions between correspondent sides.

In order to solve for x we can set up the proportion between the horizontal and vertical sides:

[tex]28\div 11.2 = 27+x \div x[/tex]

Solving this proportion for x implies [tex]x=18[/tex]

Now you can solve for m and p using the pythagorean theorem, because both triangles are right:

[tex]m = \sqrt{18^2+11.2^2} =21.2[/tex]

Then, we know that the hypothenuse of the big triangle is m+p, so we have

[tex]m+p=\sqrt{(18+27)^2+28^2} = 53[/tex]

which implies

[tex]p = 53-p = 53-21.2=31.8[/tex]

The ratio of the given to similar triangles is 0.4. value of the x, m, and p is 18, 21.2, and 31.8.

Similar triangles are triangles whose corresponding sides are in ratio, while the corresponding angles are of equal measure.

As the two sides of the triangles are already given, therefore, the ratio of these two triangles are,

[tex]\dfrac{11.2}{28} = \dfrac{2}{5}[/tex]

As we already know the ratio of the two triangles, therefore,

[tex]\dfrac{x}{27+x} = \dfrac{2}{5}\\\\5x = 54 + 2x\\\\5x-2x = 54\\\\3x = 54\\\\x = 18[/tex]

Hence, the value of x is 18.

As the given triangle is a right-angled triangle, therefore, we can use the Pythagorean theorem to find the value of m,

[tex](Hypotenuse)^2 = (Perpendicular)^2+(Base)^2\\\\m^2 = x^2 + (11.2)^2\\\\m^2 = 18^2 + 11.2^2\\\\m^2 = 324+125.44\\\\m^2 = 449.44\\\\m = 21.2[/tex]

Thus, the value of side m is 21.2 units.

The value of m and p can be found using the same ratio, we already have for similar triangles,

[tex]\dfrac{m}{m+p} = \dfrac{2}{5}\\\\\dfrac{21.2}{21.2+p} = \dfrac{2}{5}\\\\106= 42.4 + 2p\\\\p = 31.8[/tex]

Thus, the value of the x, m, and p is 18, 21.2, and 31.8.

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A power of 10 is the number 10 multiplied by itself by the number of times indicated by the exponent. Thus, shown in long form, a power of 10 is the number 1 followed by n zeros, where n is the exponent and is greater than 0; for example, 106 is written 1,000,000.

1/100,000,000 expressed as a power of 10 is 10-8, reflecting the movement of the decimal point 8 times to the left.

The question asks for the expression of 1/100,000,000 as a power of 10. To find the answer, we need to realize that this fraction is the same as moving the decimal point 8 places to the left from 1, making it 0.00000001. This operation is equivalent to the negative power of 10, because you're making the number smaller (or dividing). Remembering that the exponent represents how many times we move the decimal place, we can express 1/100,000,000 as 10-8.

Answer:

B. .12 is the decimal

Step-by-step explanation:

What you do is you divide 25 by 3. That will already give you a decimal and when you divide it out your answer is .12.

3/25=.12.

Answer:

The correct answer is 0.12

Step-by-step explanation:

3 = numerator

25 = denominator

Divide the numerator by the denominator to convert a fraction to a decimal.

3 ÷ 25 = 0.12  

as a decimal is  

0.12

.

Answer: The answer is B. 0.12

Step-by-step explanation:

Answer:

28 in

Step-by-step explanation:

6+2= 8 so therefore the length is eight.

To find perimeter, add up all the sides of the rectangle so 6+6+8+8=28

Final answer:

The perimeter of the rectangle is calculated using its length and width. With a width of 6 inches and 2 inches added to determine the length, the perimeter is found to be 28 inches.

Explanation:

To determine the perimeter of the rectangle, we first have to calculate both the width and the length. The width is given as 6 inches. The problem states that the length is 2 inches more than its width, which means the length is 6 inches + 2 inches = 8 inches.

The formula to compute the perimeter (P) of a rectangle is P = 2 * (length + width). Substituting our values, we get P = 2 * (8 inches + 6 inches) = 2 * 14 inches = 28 inches. Therefore, the perimeter of the rectangle is 28 inches.

Answer:

Part 1)

(1,H),(2,H)(1,T),(2,T)

Part 2)

1320

Part 4)

1/4

Part 5)

1/15

Step-by-step explanation:

Part 1)

Possible outcomes of cube={1,2,3,4,5,6}

Possible outcomes of coin=(H,t}

Now,  Andrew rolls the number cube once and flips the coin once

then possible outcome that contains only the outcomes in which the number cube lands on a number less than 3 are:

(1,H),(2,H)(1,T),(2,T)

Part 2)

Given:

population=1500 dogs

spots containing dogs= 15 out of every 125 dogs in the population have spots

spots containing dogs:

                                =1500/125

                                     =12    

                                     =12*15

                                     =180    

dogs in the population that do NOT have spots on their back

=1500-180=1320

Part 4)

Given:

classical songs=2

rock songs=13

rap=5

total songs= 2+13+5

                 =20

probability that the first song that Joel hears is a rap song= 5/20

                                     =1/4

Part 5)

Given:

3 Characters= elf, hobbit, or human

4 tools= magic, sword, shield, slingshot, or umbrella

Probability of first event , P(C)= 1/3

Probability of second event, P(T)=1/5

As both events are mutually exclusive so

P(magic elf)= P(C)*P(T)

                 =1/3+1/5

                 =1/15 !

Answer:  F) (x, y) → (x - 6, y  + 2)

Step-by-step explanation:

6 units to the left means subtract 6 from the x-value --> x - 6

2 units up means add 2 to the y-value --> y + 2

Given a quadratic equation [tex]ax^2+bx+c=0[/tex]

The discriminant is defined as

[tex]\Delta=b^2-4ac[/tex]

In your case, the equation is defined by the coefficients

[tex]a=3,b=0,c=-10[/tex]

So, the discriminant is

[tex]\Delta=0^2-4\cdot 3\cdot (-10) = 120[/tex]

The discriminant is involved in the solving formula as follows:

[tex]x_{1,2} = \dfrac{-b\pm\sqrt{\Delta}}{2a}[/tex]

Which implies that:

In your case, since the discriminant is positive, you have two distinct solutions. Since 120 is not a perfect square, however, you will not get rid of the square root, so you will have two distinct irrational solutions.

The equation 3x² - 10 = 0 has a discriminant of 120, which is greater than zero. This means that there are two distinct real roots for this equation.

To describe the roots of the equation 3x² - 10 = 0 using the discriminant, we must first understand that the discriminant (d) of a quadratic equation of the form ax² + bx + c = 0 is given by b2 - 4ac. For our equation, a = 3, b = 0, and c = -10, so the discriminant
would be:
= (0)2 - 4(3)(-10) = 0 + 120 = 120

Since  > 0, this indicates that there are two distinct real roots. When the discriminant is greater than zero, the quadratic equation has two real solutions. Therefore, in this case, 3x2 - 10 = 0 has two real roots, corresponding to the x-values where the parabola intersects the x-axis.

Answer: B, C, and D are all correct.

Step-by-step explanation:

Answer: B and D

Step-by-step explanation:

It would go between 7.32 and 7.37

Answer:

[tex]\large\boxed{y=\dfrac{1}{4}x^2,\ y=-\dfrac{1}{2}x^2,\ y=\dfrac{3}{2}x^2}[/tex]

Step-by-step explanation:

The equation of a parabola: y = ax²

The larger the value of |a|, the narrower the parabola.

We have the following coefficients a:

[tex]\left|\dfrac{1}{4}\right|=\dfrac{1}{4},\ \left|-\dfrac{1}{2}\right|=\dfrac{1}{2},\ \left|\dfrac{3}{2}\right|=\dfrac{3}{2},[/tex]

We arrange the coefficients from the smallest to the largest:

[tex]\dfrac{1}{4}\ <\ \dfrac{1}{2}\ <\ \dfrac{3}{2}[/tex]

Therefore you have the answer:

[tex]y=\dfrac{1}{4}x^2,\ y=-\dfrac{1}{2}x^2,\ y=\dfrac{3}{2}x^2[/tex]

Slower bike = X

Faster bike = X+9

They both ride for 2 hours, now you have 2x and 2(x+9)

The sum of the two cyclists is 66 miles:

2x +2(x+9) = 66

Use distributive property:

2x + 2x+18 = 66

Simplify:

4x +18 = 66

Subtract 18 from both sides:

4x = 48

Divide both sides by 4:

x = 48/4

x = 12

The slower bike was going 12 mi/h

The faster bike was 12+9 = 21 mi/h.

Answer:

24 x + 10 y >= 200

Step-by-step explanation:

as x represents centerpiece and y represent  bouquet and total number of roses should be atleast 200 which means we can use roses more than 200 but not less than 200,  the equation will be:

24 x + 10 y >= 200

Answer:

[tex]24x+10y\geq 200[/tex]

Step-by-step explanation:

Givens:

According to the problem, we can define the number of roses per a centerpiece: [tex]24x[/tex]

The number of roses per bouquet: [tex]10y[/tex]

So, the problem restricts the amount of roses, at least 200, that means, 200 or more than 200 roses. Therefore the expression that represent the amount of roses would be:

[tex]24x+10y\geq 200[/tex]

As you can observe, the inequality includes the 200 roses restriction, and the amount of roses per centerpieces and per bouquet.

Answer: its B

Step-by-step explanation:

Answer:

7*-5=-35

so your answer would be D

Answer:

The point of intersection is

(7,-2)

Step-by-step explanation:

We can easily solve this equation by plotting each graph in a graphing tool or calculator.

If we do this, we can find the intersection between the three lines and prove that it exists.

We are solving the system of equations

x+y=5

2x–y=16

x+2y=3

Please see attached picture.

The point of intersection is

(7,-2)

answer :

y=-1/4x+5

my work:

y=mx+b

2=-1/4(12)+b

2=-3+b

+3 +3

5=b

y=-1/4x+5

Answer:

y = - [tex]\frac{1}{4}[/tex] x + 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - [tex]\frac{1}{4}[/tex], hence

y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation

To find c substitute (12, 2) into the partial equation

2 = - 3 + c ⇒ c = 2 + 3 = 5

y = - [tex]\frac{1}{4}[/tex] x + 5 ← equation of line

Answer:

Step-by-step explanation:

Since the length of one of the longer sides, a, has been given to be 6.3, plug it into the equation.

2(6.3) + b = 15.7

12.6 + b = 15.7

b = 15.7 - 12.6

b = 3.1

Answer:

Equation that can be used to find length of the base is b + 12.6 = 15.7  and the length of the base we get from this equation is 3.1 cm

Step-by-step explanation:

Given:

Length of the equal side of the Isosceles Triangle = a

Length of the base of the triangle = b

Equal sides are longer than base of the triangle.

Perimeter of the triangle = 15.7 cm

Equation representing given information = 2a + b = 15.7

To find: Equation that represent or can be used to find length of the base if longer side = 6.3 cm

Given Equation is the Equation representing the perimeter of the isosceles triangle.

Longer side  = 6.3 cm = Length of the Equal Sides of the triangle.

So, a = 6.3 cm

Now,

2 × 6.3 + b = 15.7

b + 12.6 = 15.7

b = 15.7 - 12.6

b = 3.1 cm

Therefore, Equation that can be used to find length of the base is b + 12.6 = 15.7  and the length of the base we get from this equation is 3.1 cm

Answer:

Step-by-step explanation:

I think 9. 10/50

10. 6/50

11. 44/50

It’s (x-6)(x+4) so the first one and last one

For this case we must factor the following expression:

[tex]x ^ 2-2x-24[/tex]

We must find two numbers that when added together give "-2" and when multiplied by "-24"

These numbers are:

[tex]-6\ and\ +4\\-6 + 4 = -2\\-6 * + 4 = -24[/tex]

So:

[tex]x ^ 2-2x-24 = (x-6) (x + 4)[/tex]

Answer:

[tex](x-6) (x + 4)[/tex]

Option A and D

     Step-by-step explanation

i had to turn  my laptop just to read that

                 My

Both rectangles have the same dimensions and shape. P'Q'R'S' is a translated image of PQRS, shifted 3 units right and 3 units up. They are congruent but not identical due to their position.

Step-by-step comparison of rectangles PQRS and P'Q'R'S':

1. Original coordinates:

Assume specific coordinates for the vertices of rectangle PQRS. For example, let P = (1, 2), Q = (5, 2), R = (5, 6), and S = (1, 6).

2. Translation:

A translation moves every point in the shape the same distance and in the same direction. Since Rashid translated rectangle 3 units up and 3 units to the right, add 3 to x-coordinate and 3 to y-coordinate of each point in PQRS to find corresponding points in P'Q'R'S'.

3. New coordinates:

P' = (1 + 3, 2 + 3) = (4, 5)

Q' = (5 + 3, 2 + 3) = (8, 5)

R' = (5 + 3, 6 + 3) = (8, 9)

S' = (1 + 3, 6 + 3) = (4, 9)

4. Comparison:

Shape:

Both rectangles PQRS and P'Q'R'S' are rectangles because a translation preserves the shape of the original figure.

Size:

They have the same dimensions (length and width) as the translation only shifts the position without altering the size.

Orientation:

They maintain the same orientation relative to the axes, meaning their sides remain parallel and perpendicular to the x and y axes.

Position:

The key difference lies in their position. P'Q'R'S' is located 3 units to the right and 3 units above PQRS.

5. Rectangles PQRS and P'Q'R'S' are congruent (same size and shape) but not identical (different positions).

P'Q'R'S' is a translated image of PQRS, moved 3 units to the right and 3 units up.

Answer:

Ben had biked 8 miles

Step-by-step explanation:

You would need to take 12 and divide it by three . That would make 4. After that you would take 4 and multiply it by 2 since he rode 2/3 miles of 12.  Then you would end up with 8.

Final answer:

Ben has biked 8 miles of the 12 miles he wants to, as he has completed 2/3 of his intended distance.

Explanation:

To calculate the number of miles Ben has biked, we simply need to multiply the total distance he wants to bike by the fraction of the trip he has completed. Ben wants to bike 12 miles, and he has biked 2/3 of that distance. Multiplying these together gives us 2/3 * 12 = 8 miles. Therefore, Ben has biked 8 miles so far.

Answer:  x < -12

Step-by-step explanation:

[tex]-\dfrac{1}{2}x>6\\\\\\\text{Multiply both sides by -2}\\\\(-2)\dfrac{-1}{2}x>(-2)6\\\\\\\text{Simplify - remember to flip the inequality symbol}\\x<-12[/tex]

Graph: ←-----------o -12

Interval Notation: (-∞, -12)

Answer:

x<-3

Step-by-step explanation:

Yes there is because the change of rate for both the x and y-values is 2. It has a consistant rate of change.

The formula for lateral surface of a cylinder is:

SA = 2 *PI * r *h

Replace the letters with the given values:

400 = 2 * PI * r *40

Multiply the right side:

400 = r * 251.2

Divide both sides by 251.2:

r = 400 / 251.2

r = 1.59

The radius is 1.59 inches.

Answer: 1.59

Step-by-step explanation:

Answer:

Step-by-step explanation:

The formula of an area of a trapezoid:

[tex]A=\dfrac{b_1+b_2}{2}\cdot h[/tex]

We have:

[tex]b_1=12,\ b_2=5,\ h=5[/tex]

Substitute:

[tex]A=\dfrac{12+5}{2}\cdot5=\dfrac{17}{2}\cdot5=8.5\cdot5=42.5[/tex]

Answer:

The correct answer option is x = -16 and x = 16.

Step-by-step explanation:

We are given the following equation and we are to find the solution for this equation:

[tex] | \frac { x } { 2 } | = 8 [/tex]

For the given equation, involving the modulus, we will have a positive as well as a negative value for it in order to find its solution set.

[tex] \frac { x } { 2 } = - 8 [/tex] and [tex] \frac { x } { 2 } = 8 [/tex]

[tex] x = 8 \times 2 [/tex] and [tex] x = - 8 \times 2 [/tex]

x = -16 and x = 16

Answer:

The correct answer is last option

x = -16 or x = 16

Step-by-step explanation:

it is given that,

|x/2| = 8

To find the solution set

From this we can understand that , the value of x/2 = - 8 or x/2 = 8

If x/2 = -8 then  x = -8 * 2 = = -16

If x/2 = 8 then x = 8 * 2 = 16

Therefore the solutions are

x = -16 or x = 16

Find two "dots" where the line crosses the X and Y axis at real numbers.

(0,3) and (6,-1)

Now find the slope which is the difference in Y over the difference in x.

Slope = (-1 - 3) / (6-0) = -4 / 6 = -2/3

The answer is D.

Answer:

x= -2,-3

Step-by-step explanation:

ANSWER

[tex]f( - 1) = 0[/tex]

EXPLANATION

From the table the values of x, are on the left and the values of f(x) are on the right.

To find f(-1), we look for the value under f(x) that corresponds to x=-1.

This value is 0.

Therefore

[tex]f( - 1) = 0[/tex]

A function assigns the values. The correct option is C.

A function assigns the value of each element of one set to the other specific element of another set.

As per the given table the value of f(-1), or the value of f(x), when the value of x=-1, is 0. Thus, it can be written that the value of f(-1) is 0.

Hence, the correct option is C.

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Answer:

Step-by-step explanation:

Angles on one side of a straight line always add to 180°.

Therefore we have the equation:

[tex]35+(3x-15)+x=180[/tex]

[tex]35+3x-15+x=180[/tex]             combine like terms

[tex](35-15)+(3x+x)=180[/tex]

[tex]20+4x=180[/tex]           subtract 20 from both sides

[tex]4x=160[/tex]          divide both sides by 4

[tex]x=40[/tex]

∠DBE = 3x - 15. Substitute:

[tex]\angle DBE=\bigg(3(40)-15\bigg)^o=\bigg(120-15\bigg)^o=105^o[/tex]