Rewrite the equation in slope-intercept form by solving for y:2x+7y=42

Answer:

A. 20 N.

Step-by-step explanation:

The net force acting on an object is the sum of all the individual forces acting on it. In this case, the block is being pulled to the left with a force of 15 N and to the right with a force of 5 N at the same time.

The net force acting on the block is the sum of these two forces, which is 15 N + 5 N = 20 N.

Therefore, the correct answer is (A) 20 N.

Answer: Dividing by 4 is the inverse of multiplying by 4

A plane consists of an infinite set of points.

A point's location on the coordinate plane is indicated by an ordered pair, (x, y).

Step-by-step explanation:

The undefined terms in geometry are points, lines and planes.

The length of JK is 4

A line segment can be defined as the part of a straight line bounded by two different or separate end points, and also contains every point on the line between its endpoints.

Note that point K is the midpoint between points J and L

From the information given, we have the points:

The expression is given as;

JL = KL + JK

Now, substitute the values

x + 10 = 4x + 2x

collect like terms

10 = 5x

Make 'x' the subject of formula

x = 10/ 5

x = 2

But we have that;

JK = 2x

JK = 2(2)

JK = 4

Thus, the value of JK is 4

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The complete question:

Given JL=x+10, KL=4x and JK=2x determine the numerical length of \overline{JK}.

By proving that ΔEAB and ΔFDC have congruent corresponding angles and proportional corresponding sides, we can conclude that ΔEAB ≅ ΔFDC.

Given:

- Triangle ΔAEB and ΔDFC

- Line ABCD is straight (implies AC and BD are collinear)

- AE is parallel to DF

- EB is parallel to FC

- AC = DB

To prove: ΔEAB ≅ ΔFDC

Recall that:

AE || DF

EB || FC

AC = DB

AE || DF, EB || FC (Parallel lines with transversal line AB)

Corresponding angles are congruent:

  ∠AEB = ∠DFC (Corresponding angles)

  ∠EAB = ∠FDC (Corresponding angles)

Corresponding sides are proportional:

  AE/DF = EB/FC (Corresponding sides)

  AC/DB = BC/DC (Corresponding sides)

  AC = DB

  BC = DC (Equal ratios)

ΔEAB ≅ ΔFDC (By angle-side-angle (ASA) congruence)

∠EAB = ∠FDC

∠AEB = ∠DFC

AC = DB, BC = DC

Therefore, by proving that ΔEAB and ΔFDC have congruent corresponding angles and proportional corresponding sides, we can conclude that ΔEAB ≅ ΔFDC.

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Solution

The answer is

The standard form of the equation of the line passing through (8,-3) that is parallel to the line 3y=4x+8 is 4x - 3y = 41

The equation of the line in standard form can be represented as follows:

Ax + By = C

where

Therefore, the standard form of the equation of the line through (8,-3) that is parallel to the line 3y = 4x + 8 is a s follows;

Parallel lines have the same slope.

Hence,

3y = 4x + 8

y = 4  / 3 x + 8 / 3

The slope of the line is 4 / 3. Hence, the line passes through (8, -3). let's find the y-intercept.

y = 4 / 3 x + b

-3 = 4 / 3 (8) + b

b = -3 - 32 / 3

b =  -9 - 32/ 3

b = -41 / 3

Hence,

y = 4 / 3 x - 41 / 3

multiply through by 3

3y = 4x - 41

Therefore, the standard form is 4x - 3y = 41

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The csc(theta) = 1/sin(theta) = 1/(-2/√13) = -√13/2. So, the cosecant of theta is -√13/2.

To find the cosecant (csc) of theta when a point (-3, -2) lies on its terminal side, we need to determine the hypotenuse (r) of the right triangle formed by this point.

Using the Pythagorean theorem, r^2 = (-3)^2 + (-2)^2. So, r^2 = 9 + 4 = 13, and r = √13.

The csc(theta) is the reciprocal of sin(theta). Sin(theta) is calculated as the ratio of the opposite side (y-coordinate) to the hypotenuse, or sin(theta) = -2/√13.

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Answer:

\(g(x) = 3.5^{x} -2\)

Step-by-step explanation:

This is the answer because, the y-intercept has decreased by -2. After you graph the original equation, you will find that the intercept is 1. So if the new one has a y-interceptn of -1, it decreased by 2. So, it is \(g(x) = 3.5^{x} -2\)

The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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Answer:

Step-by-step explanation:

2x + 12 = 2 is wrong , ( the third one )

Because if x = 7 then 2x would be 14. Then when you add 12, it would be 26 not 2.

Your Welcome!

Only the equations 8x - 15 = 41 and 1.5x + 4 = 14.5 are true for [x] = 7.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We JP who was asked to place a check mark next to any equation in which x = 7 is a true statement.

We have the following equations -

8x - 15 = 41

For x = 7, we can write -

8 x 7 - 15 = 41

41 = 41

1.5x + 4 = 14.5

1.5 x 7 + 4 = 14.5

10.5 + 4 = 14.5

14.5 = 14.5

2x + 12 = 2

2 x 7 + 12 = 2

14 + 12 = 2

26 ≠ 2

Therefore, only the equations 8x - 15 = 41 and 1.5x + 4 = 14.5 are true for [x] = 7.

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We're looking for z such that 54 is equal to some multiple of the standard deviation, 8z, plus the given mean.

54 = 8z + 44

Solve for z :

z = (54 - 44)/8 = 10/8 = 5/4 = 1.25

Answer:

2:16

Step-by-step explanation:

Answer:

1. 12

2.16

Step-by-step explanation:

Substitute the value of the variable into the equation and simplify.

There are 260 students who attend Juniper Middle School. The average daily unexcused absences increased by 25% from September to October.

a. Let's assume that the total number of students at Juniper Middle School is "x."

Given that 55% of the students are in the 8th grade, we can write:

0.55x = number of 8th grade students

And since the remaining 117 students are in 7th grade, we can write:

x - 0.55x = 117

0.45x = 117

x = 260

Therefore, there are 260 students who attend Juniper Middle School.

b. To find the percent change from September to October, we can use the formula:

percent change = ((new value - old value) / old value) x 100%

Substituting the given values, we get:

percent change = ((6 - 4.8) / 4.8) x 100%

percent change = (1.2 / 4.8) x 100%

percent change = 25%

Therefore, the average daily unexcused absences increased by 25% from September to October.

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Step-by-step explanation:

\(( {m}^{15} )( {m}^{3} ) ^ {- 4} \\ = ( {m}^{15} )( {m}^{3 \times - 4} ) \\ = ( {m}^{15} )( {m}^{ - 12} ) \\ = {m}^{15 + ( - 12)} \\ = {m}^{15 - 12} \\ = {m}^{3} \\ {m}^{x} = {m}^{3} \\ x = 3\)

Answer:she has 4 weeks worth of lunch money

Step-by-step explanation:first 5×2=10

Then 10×4=40

The total weight of Rice that Mark buys is given as follows:

2.5 pounds.

The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.

The weight of each bag is given as follows:

5/8 pounds = 0.625 pounds.

The number of bags is given as follows:

4 bags.

Hence the total weight of Rice that Mark buys is given as follows:

4 x 0.625 = 2.5 pounds.

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Answer$ 2.73 per gallon

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) You can show that two pairs of angles of each triangle are equal, ∠SRP = ∠SRT = 90°, and the given ∠QPR and ∠STR

2) This means that ∠PQR and ∠TSR must be identical as well as the internal angles of a triangle must sum to 180°

3) Three angles of triangles identical is sufficient to say that the triangles are similar. (Actually you only need two equal pairs of angles for proof because  step 2 is rather redundant)

Answer:

y = (3/4)x-9/2

Step-by-step explanation:

We've got two points, (-2, -6) and (2, -3). That's more than enough info to construct a line. The slope of the line is the ratio between the change in y (Δy) and the change in x (Δx). Here, Δy = -3 - (-6) = -3 +6 = 3, and Δx = 2 - (-2) = 2 + 2 = 4, so the slope is Δy/Δx = 3/4. From here, we can use the point-slope form of a line to get a general equation. With the slope m = 3/4 and choosing the point (2, -3), we have

\(y-y_1=m(x-x_1)\\y-(-3)=(3/4)(x-2)\\y+3=(3/4)x-3/2\\y=(3/4)x-3/2-3\\y=(3/4)x-3/2-6/2\\y=(3/4)x-9/2\)

Answer:A

Step-by-step explanation:took it

Answer:

A

Step-by-step explanation:

whole circle pointing right

Answer:

gradient M = 4

Step-by-step explanation:

pick any two pairs

M= change in Y / change in X

considering the last pairs

3--1/0--1=4✓

considering first pair

-1--5/-1--2 is also 4✓

I hope it helps

The distance from the center of the Earth to the point where the net gravitational force is zero is one-ninth the distance from the Earth to the Moon.

Let's assume that the distance from the center of the Earth to this point is denoted as x.

Given:

Mass of the Moon (M\(_{moon}\)) = 1/81 × M\(_{earth}\)

Distance from Earth to Moon (d\(_{moon}\)) = distance on center

According to the principle of gravitational equilibrium, the gravitational force from the Earth and the gravitational force from the Moon acting on an object at that point must balance out. Mathematically, we can express this as:

F\(_{earth}\) = F\(_{moon}\)

The gravitational force between two objects can be calculated using Newton's law of universal gravitation:

F \(_{gravity}\)= G × (m₁ × m₂) / r²

Where:

G is the gravitational constant (approximately 6.67430 x 10⁻¹¹m²/kg/s²)

m₁ and m₂ are the masses of the two objects

r is the distance between the centers of the two objects

Considering the gravitational forces involved:

F\(_{gravity}\)\(_{earth}\) = G ₓ (M\(_{EARTH}\)  ₓ m\(_{OBJECT}\)) / (d\(_{earth}\))²

F\(_{gravity}\) \(_{moon}\) = G ₓ (M \(_{moon}\) ₓ m\(_{object}\)) / (d \(_{moon}\))²

Since we are looking for the point where the net gravitational force is zero, we set these two forces equal to each other:

G × (M\(_{earth}\) × m\(_{object}\)) / (d\(_{earth}\))²   =     G × (M \(_{moon}\) × m\(_{object}\)) / (d \(_{moon}\))²

Canceling out the common factors of G and m\(_object}\), and substituting the given values:

(M\(_{earth}\) × 1) / (d\(_{earth}\))² = (M \(_{moon}\) × 1) / (d \(_{moon}\))²

Rearranging the equation:

(d\(_{earth}\))²/ (M\(_{earth}\)) = (d \(_{moon}\))² / (M \(_{moon}\))

Taking the square root of both sides:

d\(_{earth}\) / √(M \(_{moon}\))) = d_moon / √(M \(_{moon}\))

Substituting the given values:

d\(_{earth}\) /√(M\(_{earth}\)) = d\(_{moon}\) / √(1/81 × M\(_{earth}\))

Simplifying further:

d\(_{earth}\)  / √(M\(_{earth}\)) =d\(_{moon}\)  / (1/9 × √(M\(_{earth}\)))

Multiplying both sides by √(M\(_{earth}\)):

d\(_{earth}\) = (1/9) × d\(_{moon}\)

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The value of x in the equation x^x = 4^(x + 16) is 16

From the question, we have the following parameters that can be used in our computation:

x^x = 4^(x + 16)

Take the logarithm of both sides

So, we have

xlog(x) = (x + 16)log(4)

At this point, we make use of a graphing calculator

From the calculator, we have

x = 16

Hence, the solution is x = 16

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Answer:

Step-by-step explanation:

The system of inequalities are : C + D ≤ 1300 ; C≥500 and D≥650

The graph can be made using these three inequalities.

How do you describe linear inequality with two variables?

The solution(s) of a linear inequality in two variables like mx + ny > p is value in pair (x, y) that satisfies the inequality when the values of x and y are substituted into that inequality. The graph of that inequality in two variables is the set of points that represents all roots to the inequality.

Let the commercial units be represented by C and Domestic units by D,

Given that both units are not more than 1300.

Means, C + D ≤ 1300

Also Given that, Commercial units are atleast 500 i.e, C≥500

Similarly, for domestic D≥650

a)The system of inequalities are:

C+D ≤1300

C≥500

D≥650

b)Graph for the above inequalities

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Refer to the graph attached with solution.

Answer:

u said 30 points

Step-by-step explanation:

Answer:

a) increase

b) true

Step-by-step explanation:

Hope this helps plz hit the crown:D

Answer:

46/273

Step-by-step explanation:

To add fractions, they must have a common denominator. To set one, find a common multiple of both denominators. Simply multiply them together if it proves difficult.

7 x 39 = 253

Now set the denominators to this number and multiply the numerators by the opposite fraction's denominator.

39/259 + 7/253 = 46/253
This simplifies to 2/11

So, 1/3 + 1/39 = 2/11