Plot the intercepts to graph the equation.
9x−4y=−36
Graph it

Answer:

y=12, x=6

Step-by-step explanation:

y+3=15

3x-6=12

Answer:

b

Step-by-step explanation:

\( {x}^{ - \frac{5}{3} } = = = > \\ \frac{1}{x} ^{ \frac{5}{3} } \)

So the root is 3 and the power is 5

finally your answer

\( \frac{1}{ \sqrt[3]{ {x}^{5} } } \)

A member of the senate will serve for (h+4) years.

An expression, in mathematics, is a finite set of combinations and/ or numbers and variables that accurately represents the the context in question. When two or more expressions are connected using the equality sign then an equation is formed.

Here, we are given that in the US government a member of the senate serves for 4 years longer than a member of the House of Representatives.

Also the House of Representatives serves for- h years

Thus, the number of years a member of the Senate will serve will be 4 more than the number h

= h + 4

Thus, a member of the senate serves for (h+4) years.

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The statement that are consistent with the guidelines for hitching trailers are:

A. Trailers must be connected to the tow vehicle before loading.

D. Customer vehicles must have at least a frame mounted Class 3 receiver hitch with a 2" or 2 5/6" ball.

Option A: Because it guarantees that the weight of the cargo is evenly distributed and attached to the trailer before the vehicle is driven this recommendation is consistent with safe hitching techniques.

Option D: Because it guarantees that the trailer is securely fastened to the tow vehicle and can support the weight of the cargo this recommendation is consistent with safe hitching techniques. A 2" or 2 5/16" ball ensures the trailer is firmly fastened to the hitch and a Class 3 hitch is made to support the weight of heavier trailers.

Therefore the correct option is A and D.

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Answer: $400

Step-by-step explanation:

Discount = 15%

The original price/value of an item is always 100%

So selling price (%) = original price - discount = 100%-15% = 85%

We got selling price as 85%

This implies that 85% = 340

Let's find 1% first, then 100%

1% = 340÷85 = 4

100% = 4 × 100 = $400

The usual (normal/original) price is $400

Juan sold a bicycle at a discount of 15% if the selling price was $340 then the usual price of the bicycle was $400.

percentage, a relative value indicating hundredth parts of any quantity.

Let's represent the usual price of the bicycle by P.

Since Juan sold the bicycle at a discount of 15%, the selling price (S) would be 85% of the usual price (P).

We can express this relationship as an equation:

S = 0.85P

We also know that the selling price of the bicycle was $340.

Substituting S = $340 into the equation above, we get:

$340 = 0.85P

To find P, we can solve for it:

P = $340 / 0.85

P = $400

Therefore, the usual price of the bicycle was $400.

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The number of mangoes that were originally present in the bowl will be 72.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

Lord found mangoes and ate 1/6 of the mangoes. Then, at that point, Sovereign Gia ate 2/5 of the mangoes left. Then, at that point, Princess Gia ate 3/4 of the excess mangoes. Sovereign Jacob ate 1/3 of the leftover mangoes. At long last Woman Stick ate 1/2 of what was left leaving 3 mangoes for the worker.

The number of mangoes originally in the bowl will be given as,

⇒ 3 x [1 / (1 - 1/2)] x [1 / (1 - 1/3)] x [1 / (1 - 3/4)] x [1 / (1 - 2/5)] x [1 / (1 - 1/6)]

Simplify the expression, then we have

⇒ 3 x [1 / (1 - 1/2)] x [1 / (1 - 1/3)] x [1 / (1 - 3/4)] x [1 / (1 - 2/5)] x [1 / (1 - 1/6)]

⇒ 3 x [1 / (1/2)] x [1 / (2/3)] x [1 / (1/4)] x [1 / (3/5)] x [1 / (5/6)]

⇒ 3 x 2 x (3/2) x 4 x (5/3) x (6/5)

⇒ 72

The number of mangoes that were initially present in the bowl will be 72.

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Answer:

1

Step-by-step explanation:

\(h {}^{ - 1} ( - 1)\)

means that what is the value of the inverse function of h(x) when x=-1. The inverse function x and y values swap with original functions. When x=1, y=-1 so the inverse of that will be when x=-1, y=1.

Applying the inverse function concept, it is found that \(h^{-1}(-1) = 1\)

The inverse function \(f^{-1}(x) = a\) means that \(f(a) = x\).

In this problem, it is asked \(h^{-1}(-1)\).

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Answer:4

Step-by-step explanation:

464565=753

Evaluating the function from the given graph, g(-9) = 1.

To find the value of a function for a given x-value using a given graph, trace the x-value against the corresponding y-value on the y-axis.

To evaluate the function from the graph given, for g(-9), find the y-value that corresponds to the x-value of -9.

The graph shows that when x = -9, the corresponding y-value is 1.

Therefore, g(-9) = 1.

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Answer:

hey

Step-by-step explanation:

The point of intersection of the lines given is (1,4,2) and the plane determined is -3y +2z+8 = 0.

Let us first define the lines as -

L1 = x=3t+1, y=4t+4, z = 6t + 2

L2 = X=s+2 y=2s+6, z = 3s - 1

We have to find the intersection so -

= 3t+1 = s+2 ⇒ 3t - s - 1 = 0

= 4t+4 = 4t+4 ⇒ 4t - 2s - 2 = 0

= 6t + 2 = 3s - 1 ⇒ 6t - 3s + 3 = 0

Now, if we input the values of t and s as given in the question i.e., t = 0 and s = -1, we get -

= x = 1

= y = 4

= z = 2

These are the points of intersections of the given lines.

Now, the direction vector of L1 = (3,4,6) and L2 = (1,2,3)

So, the normal vector to the plane can be calculated using the determinant method.

\(\left[\begin{array}{ccc}i&j&k\\3&4&6\\1&2&3\end{array}\right]\)

On solving this, we get  = -3j + 2k

The equation of the plane is -

= 0(x-1) - 3(y-4) + 2(z-2) = 0

= -3y +2z+8 = 0

The complete question that you might be looking for is given below -

Find the point of intersection of the lines given below and then find the plane determined by these lines x=3t+1, y=4t+4, z = 6t + 2, 0<t< 0 X=s+2 y=2s+6 2 = 3s - 1 , C < 5 < 0

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Answer: i just took the test

Step-by-step explanation:

The probability that Isaac grabs two quarters is 4/25. So, the correct answer is (D) 4/25.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.

No, your solution is not correct. The probability of drawing a quarter on the first draw is 4/10, or 2/5 since there are 4 quarters out of 10 total coins. After replacing the coin, the probability of drawing another quarter on the second draw is still 4/10, or 2/5, since the probabilities of the two draws are independent.

To find the probability of both events happening, we can multiply the probabilities:

P(both quarters) = P(first quarter) × P(second quarter)

= (4/10) × (4/10)

= 16/100

= 4/25

Therefore, the probability that Isaac grabs two quarters is 4/25. So, the correct answer is (D) 4/25.

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Answer: All real number

Step-by-step explanation:

Given

Quadratic equation is \(x^2-4x+3\)

There is no point in the expression where the function is not defined

So, the domain of the quadratic function is all real number

The expression which can be used to represent the total owed for 3 months given the cost per month and a one-time equipment fee is 3(c) + 25

The correct answer option is option C

The total owed = Number of months(Price of the cable per month) + One time equipment fee

The total owed = 3(c) + 25

I'm conclusion, the expression for the total owed is represented by 3(c) + 25

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Answer: option c

bc 3<c> is the fee for 25                                                                                                                  

Answer:

x = 9

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

14=14 so plus 0 is 14 i gues

The expression "F = {(x, y) : φ(x, y, p)}" represents a set of ordered pairs (x, y) that satisfy a condition defined by the function φ. The interpretation and nature of the set F depend on the specific function φ and the parameter p, which determine the relationship between the variables x, y, and p.

The expression "F = {(x, y) :  φ(x, y, p)}" represents a set F consisting of ordered pairs (x, y) that satisfy a particular condition defined by the function  φ, which takes the variables x, y, and p as inputs.

To fully understand the meaning of F, we need to delve into the function  φ and its relationship with the variables x, y, and p. The function φ could represent a wide range of mathematical relationships or conditions that determine the inclusion of certain pairs (x, y) in the set F.

For instance, let's consider a specific example where vraphi(x, y, p) is defined  φ(x, y, p) = \(x^2 + y^2 - p^2.\)In this case, F = {(x, y) : \(x^2 + y^2 - p^2\)= 0} represents a set of ordered pairs (x, y) that satisfy the equation \(x^2 + y^2 - p^2 = 0.\) This equation represents a circle with radius p centered at the origin (0, 0). Consequently, F corresponds to all the points lying on the circumference of this circle.

It is important to note that the specific meaning and implications of F heavily rely on the nature of the function  φ and the parameter p. Different functions and parameters will yield distinct sets F with their own unique characteristics and interpretations.

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Answer:

d is equal to 4

Step-by-step explanation:

to do this problem divide both sides by 0.5 to isolate the variable d

0.5d = 2

d = 4

Answer:

4

Step-by-step explanation:

You want to get d all by its self. So, divide both sides by 0.5.

2 ÷ 0.5 = 4

d ÷ 0.5 = d

Then you get:

d = 4

Hope this helps!

Answer:

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by  2  gives the next term.

.

Answer:

The null hypothesis is \(H_0: p \leq x\), in which x is the proportion tested.

The alternative hypothesis is \(H_1: p > x\)

Step-by-step explanation:

A recent article in a university newspaper claimed that the proportion of students who commute more than miles to school is no more than x.

This means that at the null hypothesis, we test if the proportion is of at most x, that is:

\(H_0: p \leq x\)

Suppose that we suspect otherwise and carry out a hypothesis test.

The opposite of at most x is more than x, so the alternative hypothesis is:

\(H_1: p > x\)

Rollaway Skates is cheaper when the number of people is less than or equal to 4. For example, the cost for 2 people at Rollaway Skates is $10, while the cost for 2 people at Wheelie's Skates and Stuff is $106.

Wheelie's Skates and Stuff is cheaper when the number of people is greater than or equal to 5. For example, the cost for 6 people at Rollaway Skates is $30, while the cost for 6 people at Wheelie's Skates and Stuff is $118.

I hope this helps! Do you have any other questions?

As given by the question

There are given that 4<6, so 204<216.

Now,

On the number line, 4 is less tha6 and 204 is also less than 216

Hence, the given reasoning is correct.

The maximum displacement is 5 centimeters.

The time required for one oscillation is π seconds.

The frequency is 1 / π Hz.

Equation to model the motion of the object is x(t) = 5 × cos(2t)

The maximum displacement from equilibrium can be determined by observing that the object is pulled down 5 centimeters from its rest position.

In simple harmonic motion, the amplitude represents the maximum displacement from equilibrium.

The period of oscillation is given as π seconds.

The period (T) is the time required for one complete oscillation.

The frequency (f) is the reciprocal of the period and represents the number of oscillations per unit time.

Thus, the frequency is the inverse of the period: f = 1 / T.

To model the motion of the object, we can use the equation for simple harmonic motion:

x(t) = A×cos(ωt + φ)

A = 5 centimeters (maximum displacement),

T = π seconds (period),

f = 1 / π Hz (frequency).

To find ω, we can use the relation ω = 2π / T:

ω = 2π / π = 2 radians/second.

The equation to model the motion of the object is:

x(t) = 5 × cos(2t)

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Answer:

a line with a gradient of

\( \frac{ - x}{3} \)

Step-by-step explanation:

parallel lines have equal gradients, i.e the value of m, has to be the same.

therefore:

\(x + 3y = - 21 \\ 3y = - x - 21 \\ y = \frac{ - x}{3} - 7\)

The values of six trig functions are:

sinθ=− √5/5, cosθ=2√5/5, tanθ=-1/2, cot θ=−2, secθ=√5/2, cscθ=−√5

The relationship between the angles and sides of a triangle is given by these trig functions.

There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

The point's coordinates are:

x=2, y=−4

To calculate the functions we have to calculate the distance between the point and the origin:

r=√x²+y²=√2²+(−4)²=√16+4=√20

r=2√5

Now we can calculate the functions:

sinθ=y/r=−2/2√5=−√5/5

cosθ=x/r=4/2√5=2/√5=2√5/5

tanθ=y/x=−2/4=−1/2

cotθ=x/y=4/−2=−2

secθ=r/x=2√5/4=√5/2

cscθ=r/y=2/√5−2=−√5.

Hence, the values of trig functions are calculated.

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When a circular cone is intersected by a plane that passes through the cone's vertex and is perpendicular to its base, a pair of intersecting lines is formed.

How to know what is formed from a line intersecting a cone?

The right circular cone is intersected by a plane that passes through the cone's vertex and is perpendicular to its base.

This means the intersecting line forms a right angle with the base of the right circular cone.

Therefore, from this interaction is a pair of intersecting lines.

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Answer:

The answer is B. 350 euros

Step-by-step explanation:

350 euros was the initial value of Luna's savings. Thus option B is correct.

Merging objects and identifying them since one big bunch is done through addition. In arithmetic, addition is the technique of adding two or more integers together. The product can meet are the quantities that are included, and the outcome of the operation, or the final response, is referred to as the sum.

The data that is presented suggests that there will not be a change in the first week this remains still at 315. They left out the amount that was 35.

Therefore the initial amount of the savings that the person has was the sum of both amounts.

= 315 + 35

= $350

Therefore, option B is the correct option.

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Luna brought all her savings with her to Rome, in euros. For the first week, she spent the same amount of money each day. The table shows how much Luna had left at the end of each day. What was the initial value of Luna's savings? Day Euros ? 315 1 2 280 3 245 4 210 5 175 6 140 7 105 35 euros 315 euros 80 euros 350 euros

Answer:

Solution:

(0.2)x = 2.

Taking log on both sides

log (0.2)x = log 2.

x log (0.2) = 0.3010, [since log 2 = 0.3010].

x log (2/10) = 0.3010.

x [log 2 - log 10] = 0.3010.

x [log 2 - 1] = 0.3010,[since log 10=1].

x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].

x[-0.699] = 0.3010.

x = 0.3010/-0.699.

x = -0.4306….

x = -0.4 (nearest tenth)

Answer is option (c) -0.4

The value of x to the nearest tenth is -0.4

Given the following expressions

(0.2)x = 2 and log 2 = 0.3010

Taking log of both sides of (0.2)x = 2

log (0.2)x = log 2.

x log (0.2) = 0.3010,

x [log 2 - log 10] = 0.3010.

Note that log2 2 = 1

x [log 2 - 1] = 0.3010

x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].

x[-0.699] = 0.3010.

x = 0.3010/-0.699.

x = -0.4306

Hence the value of x to the nearest tenth is -0.4

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Answer is option (c) -0.4