Solving a Real-World Problem
Mr. Martin is giving a math test next period. The test, which is worth 100 points, has 29 problems. Each problem is
worth either 5 points or 2 points. Write a system of equations that can be used to find how many problems of each
point value are on the test.
Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points.
O x + y = 29, 5x + 2y = 100
O x + y = 100, 5x + 2y = 29
0 5x + y = 29, 2y + x = 100
O 2x + y = 100, 5y + x = 29

Answer:

D be because 2 +4 -5

Step-by-step explanation:

Answer:

A traditional economy is a system that relies on customs, history, and time-honored beliefs. Tradition guides economic decisions such as production and distribution. Societies with traditional economies depend on agriculture, fishing, hunting, gathering, or some combination of them. They use barter instead of money.

Answer:

custom

Step-by-step explanation:

here is proof its correct

hope this helps :]

Answer:

4cx

hope this helps

have a good day :)

Step-by-step explanation:

\(\cfrac{6^{\frac{1}{4}}}{36^{-\frac{x}{2}}}=1\implies 6^{\frac{1}{4}}=36^{-\frac{x}{2}}\implies 6^{\frac{1}{4}}=(6^2)^{-\frac{x}{2}}\implies 6^{\frac{1}{4}}=6^{-2\cdot \frac{x}{2}} \\\\\\ \stackrel{\textit{same base, exponents must be the same}}{6^{\frac{1}{4}}=6^{-x}\implies \cfrac{1}{4}=-x}\implies -\cfrac{1}{4}=x\)

Part A:The sample space contains 20 possible outcomes.

Part B :there are 3 favorable outcomes.

Part C:The probability of selecting 2 cards that are consonants is 3/20.

The proportion (relative frequency) of times an event is anticipated to occur when an experiment is repeated a large number of times under identical conditions is known as the probability of the event.

Part A:  When two cards are selected from the pile, the set of all possible outcomes known as the sample space is created. Since one of the five cards has already been selected, there are five choices for the first card and four for the second.

As a result, the sample space contains 20 possible outcomes, or 5 x 4.

Part B: There are 3 consonants in the arrangement of cards: R, S, and T, so the number of ways to choose two consonants from the set of three is one of the favorable outcomes. The following combination formula can be used to find this:

f = (number of ways to choose 2 consonants from 3)

= C(3,2)

= 3

So there are 3 favorable outcomes.

Part C: The probability of selecting two consonant-containing cards in the sample space is the product of the number of favorable outcomes and the number of possible outcomes.

P(selecting two consonants) = f / n,

where n is the number of possible outcomes in the sample space and f is the number of favorable outcomes.

Substituting the values we found in parts A and B, we get:

P(selecting 2 consonants) = 3 / 20

Therefore, the probability of selecting 2 cards that are consonants is 3/20.

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Answer:

134

Step-by-step explanation:

26% of 515

.26 x 515 = 133.9 I cannot have .9 of a person.  Round to 134

The rows of small jars of salsa are increased by 4 times.

The rows of ounces of salsa are increased by 32 times.

The pattern in the column of the table is

y = 8x

Therefore x = 4 then y = 8(4) = 32

x = 8 then y = 8(8) = 64

x = 12 then y = 8(12) = 96

x = 16 then y= 8(16) = 128.

x = 20 then y = 8(20) = 160.

The pattern in the column of the table is

y = 8x

Therefore x = 4 then y = 8(4) = 32

x = 8 then y = 8(8) = 64

x = 12 then y = 8(12) = 96

x = 16 then y= 8(16) = 128.

x = 20 then y = 8(20) = 160.

The relationship between ounces of salsa and small jars of salsa using a unit rate is

4 ounces = 1 serving

y = 4x

If x = 1 then y = 4

If x = 2 then y = 4(2) = 8

If x = 3 then y = 4(3) = 12

If x = 4 then y = 4(4) = 16

If x = 5 then y = 4(5) = 20

The relationship using the unit rate is

48 ounces = 4 medium jars of salsa.

For 1 medium jars of salsa = 48/4 = 12 ounces.

1 medium jar of salsa = 12 ounces.

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Now,

The cube root of 7 = 7^1/3

= 1.912

I hope it's help you...

Mark me as brainliest...

The chance that the call arrived when the switchboard was not completely busy is 0.75.

Probability is a branch of mathematics that studies the likelihood of a random event occurring.

It is given that the switchboard is fully busy for the first 15 seconds, that means it is not busy for the next 15 seconds to 60 seconds

Therefore the probability that calls arrived when the switchboard was not fully busy is

P(15< x < 60) = ∫_15^60▒f(x)dx

= ∫_15^60▒〖1/60 dx〗

=1/60 ∫_15^60▒〖1.dx〗

= 1/60 [ x ]6015

= (60 – 15)/60

= 45/60

= ¾

= 0.75

Therefore the probability that the call arrived when the switchboard was not fully busy is 0.75

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The first step you have to follow is to find k(1) by replacing each x in k(x) for 1:

Now, find g(k(1)), it means, g(-7):

(g°k)(1)=573.

Answer:

18.3505

Step-by-step explanation:

To find:

The formula for the length, l, of the rectangle.

Solution:

The perimeter of the rectangle is given by P = 2w + 2l.

Now, we have to isolate l and solve:

Thus, the first option is correct.

The correct graph is the first one.

Graph is a data structure composed of nodes connected by edges, which represent a relationship between the two notes of are used to represent networks of communication that organized and even extract concept like thought or riders the nodes in the graph are often represent by Circle and it's by line but the other safe of the symbol are also use copper power Bluetooth for a organizing and understanding data and can be used to solve complex problem.

It represents the equation y = 20 + 10x, which means that the gymnast pays a flat fee of $20 for each month plus an additional $10 for each class he attends. Therefore, the graph will show a line going from the point 0, 20 through the point 1, 30.

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Using the principle of proportional relationship, the 42 L of gas can go for a further 165 km

Consumption rate = 8L for 100 km

Km per Litre :

8L = 100km

1 L = m

8m = 100

m = (100 ÷ 8)

= 12.5 kilometer per Litre

Number of kilometers for 42 L

12.5 km = 1 L

m = 42 L

Cross multiply

m = 12.5 × 42

m = 525 km

The difference in the distance = 525 - 360 = 165 km

Therefore, the gas can go for a further 165 km

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Hey there!

10x+y=7(x+y)=7x+7y

or 10x−7x=7y−y

or 3x=6y

or x=2y ........(1)

Number formed by reversing the digits is yx, i.e.,

10y+x=10x+y−18

Substituting x=2y, we get

10y+2y=10×2y+y18

or 2y=21y−18

or 21y−12y=18

or 9y=18

or y=2

∴x=2y=2×2=4

Therefore, the number is 42.

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

Let the two digit number be ' xy '

where, x is the ten's place digit, and y is one's place digit, now let's proceed further ~

The origin number can be written as :

\(\qquad \sf  \dashrightarrow \: 10x + y\)

[ because x is at ten's place ]

of the digits are swapped, the new number will be :

\(\qquad \sf  \dashrightarrow \: 10y + x\)

According to conditions provided in the question : -

\(\qquad \sf  \dashrightarrow \: 10x + y = 7 \times (x + y)\)

\(\qquad \sf  \dashrightarrow \: 10x + y = 7x + 7y\)

\(\qquad \sf  \dashrightarrow \: 10x - 7x + y - 7y= 0\)

\(\qquad \sf  \dashrightarrow \: 3x - 6y = 0 \: \: \: \: \: \: \)

\(\qquad \sf  \dashrightarrow \: x - 2y = 0 \: \: \: \: \: \: - (1)\)

here we got our first equation, let's find the other one ~

\(\qquad \sf  \dashrightarrow \: (10x + y) - 18= 10y + x\)

\(\qquad \sf  \dashrightarrow \: 10x - x + y - 10y = 18\)

\(\qquad \sf  \dashrightarrow \: 9x - 9y = 18\)

\(\qquad \sf  \dashrightarrow \: x - y = 2 \: \: \: \: \: \: - (2)\)

we got our second equation ~

Now it's time to subtract equation (1) from equation (2) :

\(\qquad \sf  \dashrightarrow \:( x - y ) - (x - 2y)= 2 - 0\)

\(\qquad \sf  \dashrightarrow \: \cancel{x }- y - \cancel{x} + 2y= 2 - 0\)

\(\qquad \sf  \dashrightarrow \: y= 2 \)

hence, value of y is 2, use this value in equation (2) to find x ~

\(\qquad \sf  \dashrightarrow \: x - y= 2 \)

\(\qquad \sf  \dashrightarrow \: x - 2= 2 \)

\(\qquad \sf  \dashrightarrow \: x = 4 \)

Therefore, the required number is xy = 42

Answer:

perimeter= 2(a + b) mi

area= a×b mi squares

Step-by-step explanation:

Answers:

24 mm², 26.5 mm

Step-by-step explanation:

Area of the triangle:

\(A=\frac{b*h}{2}\\\\A=\frac{12*4}{2}\\\\ A=\frac{48}{2}\\\\ \boxed{A=24}\)

Perimeter of the triangle:

\(P=a+b+c \text{ (The side measurements of the triangle.)}\\\\P=6+12+8.5\\\\\boxed{P=26.5}\)

Hope this helps.

The perimeter of the composite figure is: 60.6 units Explanation: Given that two semicircles and a rectangle are used to make up a composite figure. The diameter of each semicircle is given to be 10 units.

 Also, it is known that the rectangle has a length of 26 units and a width of 10 units. First, let's find the perimeter of the rectangle:

Perimeter of rectangle = 2(Length + Width) = 2(26 + 10) = 72 units  Next, let's find the circumference of the semicircles: Circumference of each semicircle = (πd)/2, where d is the diameter Circumference of each semicircle = (22 x 10)/7 = 31.4 units Total circumference of the semicircles = 2 x 31.4 = 62.8 units Finally, we can add the perimeter of the rectangle and the total circumference of the semicircles to find the total perimeter of the composite figure:

Total perimeter = Perimeter of rectangle + Total circumference of semicircles .Total perimeter = 72 + 62.8 = 134.8 units However, we need to use 22/7 as an approximation for π,

so: Total perimeter = 72 + 2(22/7 x 10/2) = 72 + 44/7Total perimeter = 72 + 6.28 = 78.28 units Therefore, the perimeter of the composite figure, made up of two semicircles and a rectangle is 78.28 units. The perimeter of the composite figure, made up of two semicircles and a rectangle is 78.28 units.

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Answer:

x is less than and equal to 2

Step-by-step explanation:

Do not know how to type the less than equals sing on a computer but its < with the _ under it!

Answer:

We see a line that has a filled in circle which means that we include that number.  We also know that we are going in the negative direction from the number 2.

Using the information we can determine that our inequality is the following

\(x \leq 2\) because our solutions are anything less than or equal to 2.

Answer:

B

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

brainliest?

The value of the given integral ∫[0 to 1]∫[x to 1]e^(y^2) dy dx, with the order of integration changed, is 1 - e.

To evaluate the given double integral ∫[0 to 1]∫[x to 1]e^(y^2) dy dx, we can change the order of integration.

Let's swap the order of integration by integrating with respect to x first and then y:

∫[0 to 1]∫[x to 1]e^(y^2) dy dx.

Integrating with respect to y first, keeping x constant:

∫[0 to 1] e^(y^2) ∣[x to 1] dx.

Now we evaluate the integral with respect to y:

∫[0 to 1] (e^(1^2) - e^(x^2)) dx.

Simplifying:

∫[0 to 1] (e - e^(x^2)) dx.

Integrating with respect to x:

(e - e^(x^2)) ∣[0 to 1].

Substituting the limits:

(e - e^(1^2)) - (e - e^(0^2)).

Simplifying further:

(e - e) - (e - 1).

The terms cancel out:

0 - (e - 1).

Final result:

1 - e.

Therefore, the value of the given integral ∫[0 to 1]∫[x to 1]e^(y^2) dy dx, with the order of integration changed, is 1 - e.

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By changing the order of integration, we end up with integrals that cannot be evaluated in terms of elementary functions.

To evaluate the integral ∫[0, 1] ∫[x, 1] e^(y^2) dy dx by changing the order of integration, we can rewrite the integral as:

∫[0, 1] ∫[x, 1] e^(y^2) dy dx

Now, let's reverse the order of integration:

∫[0, 1] ∫[x, 1] e^(y^2) dx dy

Since the limits of integration are constant, we can directly evaluate the inner integral with respect to x:

∫[0, 1] ( ∫[x, 1] e^(y^2) dx ) dy

The inner integral with respect to x gives us:

∫[x, 1] e^(y^2) dx = x * e^(y^2) evaluated from x = x to x = 1

= (1 * e^(y^2)) - (x * e^(y^2))

= e^(y^2) - x * e^(y^2)

Now, we can integrate the resulting expression with respect to y:

∫[0, 1] (e^(y^2) - x * e^(y^2)) dy

Integrating term by term:

= ∫[0, 1] e^(y^2) dy - ∫[0, 1] x * e^(y^2) dy

The first integral ∫[0, 1] e^(y^2) dy cannot be expressed in terms of elementary functions and requires special functions to evaluate accurately. This integral is closely related to the Gaussian integral and does not have a simple closed-form solution.

The second integral ∫[0, 1] x * e^(y^2) dy can be evaluated by treating x as a constant:

= x * ∫[0, 1] e^(y^2) dy

Again, this integral is non-elementary and does not have a simple closed-form solution.

Therefore, by changing the order of integration, we end up with integrals that cannot be evaluated in terms of elementary functions.

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Answer:

Zero!

Step-by-step explanation:

Graphically, a solution to a system is a point where all of the lines intersect. Since a system parallel lines never meets, it has no solutions.

Answer:Zero

Step-by-step explanation: because the lines are diagonals down not pass through

Answer:

1.) 14.09 m/s

2.) 6.9 m/s

Step-by-step explanation:

Given that the boat is pointing North and can typically move at a speed of 12.8 m/s in calm waters. The boat travels through water where there is a 5.9 m/s current flowing to the East.

The speed of the boat relative to a stationary observer on land will be achieved by using pythagorean theorem

V^2 = 12.8^2 + 5.9^2

V^2 = 198.65

Square root both sides

V = 14.09 m/s

2.) If the boat turns to face directly West.

Since the boat can move at speed 12.8 m/s in a calm water, the speed of the boat if it face west will be

12.8 - 5.9 = 6.9 m/s

Therefore, the boat is moving relative to land at 6.9m/s

Answer:

8. 67 sure 100% so it will be A

9. I am not sure but the answer will be 100 or 120 so it will A or B

Good luck XD

Step-by-step explanation:

The vector <-32, 44, 22> is parallel to the line of intersection of the two planes given by the equations 2x - 3y + 5z = 2 and 4x + y - 3z = 7.

To find a vector parallel to the line of intersection of the planes given by the equations 2x - 3y + 5z = 2 and 4x + y - 3z = 7, we first need to find the direction vector of the line of intersection.

We can find the direction vector by taking the cross product of the normal vectors of the two planes. The normal vector of the plane 2x - 3y + 5z = 2 is <2, -3, 5>, and the normal vector of the plane 4x + y - 3z = 7 is <4, 1, -3>. Taking the cross product of these two vectors, we get:

<2, -3, 5> × <4, 1, -3> = <-16, 22, 11>

This vector <-16, 22, 11> is the direction vector of the line of intersection of the two planes.

To find a vector parallel to this line, we can simply multiply the direction vector by a scalar. For example, we can choose a scalar of 2 to get:

2<-16, 22, 11> = <-32, 44, 22>

Therefore, the vector <-32, 44, 22> is parallel to the line of intersection of the two planes given by the equations 2x - 3y + 5z = 2 and 4x + y - 3z = 7.

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Answer:

gradient = slope = 1

Y =1X +1  is the equation

Step-by-step explanation:

x1 y1  x2 y2

4 5  1 2

(Y2-Y1) (2)-(5)=   -3  ΔY -3

(X2-X1) (1)-(4)=    -3  ΔX -3

slope= 1          

B= 1          

Y =1X +1    

To solve this problem, we need to use some trigonometry. We can use the tangent function to find the length of the magma below sea level.

Let's define the following variables:

• x: the length of magma below sea level (what we want to find)

• y: the total length of magma (which we don't know)

• θ: the angle of elevation, which is 40°

We can set up a right triangle with the hypotenuse representing the total length of magma (y), the opposite side representing the length of magma below sea level (x), and the adjacent side representing the distance from the volcano to the point where the magma rises above sea level (which we don't need to calculate).

Using the tangent function, we can write:

tan(θ) = x / y

Rearranging this equation, we get:

x = y * tan(θ)

Now we just need to plug in the values we know:

• θ = 40°

• y = 15 kilometers (since the magma reservoir is located 15 kilometers beneath the Chijiwa Bay)

Using a calculator, we can evaluate tan(40°) to be approximately 0.8391.

Plugging in these values, we get:

X = 15km*0.8391, X = 12.5865km

Therefore, the length of magma below sea level is approximately 12.5865 kilometers



Answer:

\(\dfrac{1}{729}\)

Step-by-step explanation:

\(\left(\dfrac{}{}(-3)^2\dfrac{}{}\right)^{-3}\)

First, we should evaluate inside the large parentheses:

\((-3)^2 = (-3)\cdot (-3) = 9\)

We know that a number to a positive exponent is equal to the base number multiplied by itself as many times as the exponent. For example,

\(4^3 = 4 \, \cdot\, 4\, \cdot \,4\)

       ↑1 ↑2 ↑3 times because the exponent is 3

Next, we can put the value 9 into where \((-3)^2\) was originally:

\((9)^{-3}\)

We know that a number to a negative power is equal to 1 divided by that number to the absolute value of that negative power. For example,

\(3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{3\cdot 3} = \dfrac{1}{9}\)

Finally, we can apply this principle to the \(9^{-3}\):

\(9^{-3} = \dfrac{1}{9^3} = \boxed{\dfrac{1}{729}}\)

Answer:

I think its store A.

Step-by-step explanation:

Correct me if I am wrong please