1.

Write the equation of the line, in slope - intercept form, that goes through the point ( 12, 5 ) and is perpendicular to the line: y = - 6x - 14.

Answer:

All real numbers are solutions.

Step-by-step explanation:

Let's solve your equation step-by-step.

10−4v=−2−4(−3+v)

Step 1: Simplify both sides of the equation.

10−4v=−2−4(−3+v)

10+−4v=−2+(−4)(−3)+(−4)(v)(Distribute)

10+−4v=−2+12+−4v

−4v+10=(−4v)+(−2+12)(Combine Like Terms)

−4v+10=−4v+10

−4v+10=−4v+10

Step 2: Add 4v to both sides.

−4v+10+4v=−4v+10+4v

10=10

Step 3: Subtract 10 from both sides.

10−10=10−10

0=0

Answer:

There are a total of 25 marbles in the bag.

The probability of choosing a red marble first is 8/25 since there are 8 red marbles out of 25 marbles in the bag.

Since a marble is not replaced after the first selection, there are now 24 marbles in the bag. There are still 3 blue marbles in the bag.

The probability of choosing a blue marble second, after a red marble has already been selected, is 3/24 or 1/8 since there are 3 blue marbles left out of 24 marbles in the bag.

To find the probability of both events occurring together, we multiply their individual probabilities:

8/25 x 1/8 = 1/25

Therefore, the probability that a red marble is chosen first, followed by a blue marble, is 1/25.

There approximately 7133 books in the library;

Data;

To solve this problem, we simply need to use an equation to explain the word problem into mathematical statements.

Let the total number of books be represented by x

The number of fictional books = 3/4x

After 592 fictional books were donated;

\(\frac{3x}{4} + 592 = \frac{5}{6}x\)

Let collect like terms and solve

\(\frac{3x}{4} +592 = \frac{5}{6} x\\\frac{5}{6}x - \frac{3x}{4} = 592\\ 0.083x=592\\x = 592/0.083\\x = 7132.53\)

There approximately 7133 books in the library;

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Answer: 290 degrees

Step-by-step explanation:

subtract the minor arc's measure from 360 to get the major arc's measure

Answer:

the answer is D

both lines intersect at (2, -3)

hope this helps <3

The correct answer is: O Yes, distance and angle measure are preserved.

When a triangle ABC is reflected across the line y = x, the pre-image and image are congruent.

This is because the line y = x is the perpendicular bisector of the segment joining each corresponding point of the pre-image and image.

Reflection across the line y = x is a type of transformation known as an isometry, which preserves both distance and angle measure.

Here's why:

Distance preservation:

When a point is reflected across the line y = x, the distance between the original point and its reflection remains the same.

This holds true for all corresponding points of the triangle.

Therefore, the distance between any two corresponding points in the pre-image and image triangle will be equal, resulting in distance preservation.

Angle preservation: When a line segment is reflected across the line y = x, the angle between the line segment and the line y = x is preserved. This means that the corresponding angles in the pre-image and image triangle will be congruent.

Since both distance and angle measure are preserved during reflection across the line y = x, the pre-image and image triangles are congruent.

It's important to note that congruence under reflection across a line holds only when the line of reflection is the same for both the pre-image and image.

If the line of reflection were different, the triangles would not be congruent.

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Answer:11/12

Step-by-step explanation:

3 1/4=13/4. Change to improper

2 1/3=7/3^^^

13/4-7/3=? new equation

4*3=12, find the common denominator(if you're lazy just multiply the denominators with each other) but now you have to do the same with the numerator

13*3(because we multiplied 4 BY 3 in the first equation)

7*4(again because for this one we multiplied 3 BY 4)

39/12-28/12=11/12

The average rate of change over is 1.

Given that;

the function is,

⇒ g (t) = - (t - 1)² + 5

Hence, We need to determine the average rate of change over the interval - 4 ≤ t ≤ 5.

The value of G(-4):

The value of G(-4) can be determined by substituting t = -4 in the function

⇒ g (t) = - (t - 1)² + 5

Thus, we have,

⇒ g (t) = - (-4 - 1)² + 5

⇒ g (t) = - 20

Thus, the value of G(-4) = -20

The value of G(5):

The value of G(5) can be determined by substituting t = 5 in the function , we get,

⇒ g (t) = - (t - 1)² + 5

⇒ g (t) = - (5 - 1)² + 5

⇒ g (t) = - 11

Thus, the value of G(5) is, -11

Now, Average rate of change:

The average rate of change can be determined using the formula,

⇒ G(b) - G (a) / (b - a)

where, a = - 4 and b = 5

Substituting the values, we get,

⇒ G(5) - G (-4) / (5 - (-4))

⇒ ( - 11 - (- 20)) / 9

⇒ 9/9

⇒ 1

Thus, the average rate of change over the interval is. 1.

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Answer:

The triangle is an isosceles triangle

Step-by-step explanation:

Let's get some definitions out of the way:

A scalene triangle is a triangle in which all three sides are in different lengths, and all three angles are of different measures.

An  isosceles triangle is a triangle in which two  sides are equal lengths, and angles opposite to equal sides are equal

An equilateral triangle is a triangle in which all three sides are equal and all three angles are equal

Let's determine the lengths of each of the three sides in ΔXYZ

The distance formula for the distance between any two points (x1, y1) and (x2, y2) is given by

d² = (x2 - x1)² + (y2 - y1)²
So the distance = the square root of the above expression - d

To find length of XY, take points X(4, 2) and Y(2, -2)
Length XY

\(\sqrt{4-2)^2 + (2 - (-2)^2}\\\\= \sqrt {{4} + {16}}\\\\= \sqrt{20}\)

Length YZ with Y(2, -2) and Z(-2, 0):

\(= \sqrt {(-2 - 2)^2 + (0 - (-2))^2}\\\\ = \sqrt {(-4)^2 + (2)^2}\\\\ = \sqrt {{16} + {4}}\\\\= \sqrt{20}\)

length XZ with X(4, 2) and Z(-2, 0):
\(= \sqrt {(-2 - 4)^2 + (0 - 2)^2}\\\\= \sqrt {(-6)^2 + (-2)^2}\\\\= \sqrt {{36} + {4}}\\\\= \sqrt {40}\)

So in triangle XYZ we have two sides equal.
These are XY and YZ
The third side is different

So the triangle is an isosceles triangle

Answer:v=-4

Step-by-step explanation:We move all terms to the left:

-5v+6-(26)=0

We add all the numbers together, and all the variables

-5v-20=0

We move all terms containing v to the left, all other terms to the right

-5v=20

v=20/-5

The value of x is -1 which makes the model true

The equation from the given model will be 5x+6=1

We have to find the value of x

5x+6=1

Subtract 6 from both sides

5x=-5

Divide both sides by 5

x=-1

Hence, the value of x is -1 which makes the model true

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If rectangle has an area of 114cm squared and a perimeter of 50 cm, the dimensions of the rectangle are approximately 5 cm by 22.8 cm.

Let's assume the length of the rectangle is "l" and the width is "w". We can start by using the formula for the area of a rectangle, which is A = lw. From the given information, we know that the area is 114cm².

So, we have:

lw = 114

Next, we can use the formula for the perimeter of a rectangle, which is P = 2l + 2w. From the given information, we know that the perimeter is 50cm.

So, we have:

2l + 2w = 50

We now have two equations with two variables, which we can solve using substitution or elimination. Let's use substitution by solving the first equation for l:

l = 114/w

We can then substitute this expression for l in the second equation:

2(114/w) + 2w = 50

Multiplying both sides by w to eliminate the fraction, we get:

228 + 2w² = 50w

Rearranging and simplifying, we get a quadratic equation:

2w² - 50w + 228 = 0

We can solve for w using the quadratic formula:

w = [50 ± √(50² - 4(2)(228))]/(2(2)) ≈ 11.4 or 5

Since the length and width must be positive, we can discard the solution w = 11.4. Therefore, the width of the rectangle is approximately 5 cm. We can then use the equation lw = 114 to solve for the length:

l(5) = 114

l ≈ 22.8

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Answer:

7, 2, -3, -8

Step-by-step explanation:

y = -5x + 2  Substitute in -1 for x

y = -5(-1) + 2

y = 5 + 2

y = 7

y = -5x + 2  Substitute in 0 for x

y = -5(0) + 2

y = 0 + 2

y = 2

y = -5 + 2 substitutes in 1 for x

y = -5(1) + 2

y = -5 + 2

y = -3

y = -5x + 2  Substitute in 2 for x

y = -5(2) + 2

y = -10 + 2

y = -8

Helping in the name of Jesus.

find the area of the rectangle;

w x l = 8 x 10 = 80ft^2

circle;

pi(r)^2

r = 4

pi(4)^2

pi(16) = 50.24

80 + 50.24 = 130.24

Step-by-step explanation:

a) 11*5=55

15*5=75

8*5+5=45

b) No, because (55+75+45=175°) and the perimeter of a triangle is 180°

Answer:

  B.  x > -5

Step-by-step explanation:

It seems you have a number x such that ...

 \(\dfrac{2}{5}(x-1)<\dfrac{3}{5}(x+1)\\\\2x-2<3x+3\qquad\text{multiply by 5, eliminate parentheses}\\\\-5<x\qquad\text{subtract $2x+3$}\)

This matches choice B: x > -5.

The measure of angle DEF is 37 degrees.

What is chord in circle

In geometry, a chord is a straight line segment that connects two points on the circumference of a circle. More specifically, a chord of a circle is a line segment whose endpoints lie on the circle.

Every circle has infinitely many chords, but some of the most commonly discussed chords are the diameter (a chord that passes through the center of the circle), and the secant (a chord that intersects the circle at two distinct points).

Chords play an important role in geometry, as they can be used to determine various properties of circles, such as their radius, diameter, and area.

Since G is the center of the circle, the angle DGE is a central angle of the circle.

Therefore, the angle DGE is equal to twice the inscribed angle DEF that subtends the same arc DE.

Let x be the measure of angle DEF. Then, we have:

2x = 74

x = 37

Hence, the measure of angle DEF is 37 degrees.

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Answer:

715000

Step-by-step explanation:

1300000 • 55%,

55% = 0.55

1300000 • 0.55 = 715000

Answer:

12

Step-by-step explanation:

G(2)= 2^2 +4(2)

Solve via order of operations

G(2)=4 +8

G(2)=12

Answer:

3

Step-by-step explanation:

I think

Answer:

less than or equal to 3

Step-by-step explanation:

Answer:

B.

g= 10

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

\(\sqrt{(-4-0)^2 + (1-(-2))^2}=5\)

Answer:

1200000

Step-by-step explanation:

Esun as ma

Answer:

258.65 mg will be remain after 1000 years

Step-by-step explanation:

This problem can be solved several ways, I prefer the natural log approach for reasons I won’t go into here:

Activity final = Activity initial e^-kt, where

k = the decay constant, = ln2/half life = 0.693/1590, = 0.000436/year

t = the decay time, in the same time base as k

The problem can be worked in units of activity, mass, or number of atoms.

400 x e^-0.000436 x 1000 = 400 x e^-.436 = 258.65 mg

you can check this by estimating. There is about 2/3 of a half life, so there should be more than 200 mg, which would be the value at one half life.