In the figure below, line l is perpendicular to line n. If m<3 = 520, what is the measure of <4?

Given:

The graph of system of inequalities.

To find:

The system of inequalities.

Solution:

From the given graph it is clear that the shaded region is lies below the line y=10 and the boundary line y=10 is a solid line. So, the sign of inequality must be \(\leq\).

\(y\leq 10\).

The shaded region lies on the right side of the y-axis. So, \(x\geq 0\).

Another boundary line passes through the point (0,1) and (1,2). So, the equation of the line is:

\(y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\)

\(y-1=\dfrac{2-1}{1-0}(x-0)\)

\(y=1(x)+1\)

\(y=x+1\)

The boundary line \(y=x+1\) is a dotted line and the shaded region lies above the boundary line, so the sign of inequality must be \(>\).

\(y> x+1\)

So, the required system of inequalities is:

\(y> x+1\)

\(y\leq 10\)

\(x\geq 0\)

Therefore, the correct option is B.

Answer:

100π

Step-by-step explanation:

V = (4/3)πr^3

(500/3)π = (4/3)πr^3

r^3 = 125

r = 5

Surface area of sphere = 4πr^2

= 4π(5^2) = 100π

Therefore , the solution of the given problem of area comes out to be each pound of seed can be sown on about 0.129 acres.

Its total size can be determined by figuring out how much room would be required to completely cover the outside. The surroundings are also taken into consideration when determining this same surface that has a trapezoidal shape. Something's total dimensions are determined by its surface area. The volume of water that a cuboid can contain inside depends on the number of edges that are present between its four trapezoidal extremities.

Here,

Divide the total number of acres by the total quantity of seed used to calculate the number of acres that can be sown per pound of seed:

Acres per pound of seed equals total acres divided by total seed.

We are informed that 31 pounds of seed are required to fully seed a

4-acre field. So,

Overall

=> acres = 4 acres.

=> 31 pounds of seed in total.

When we enter these numbers into the formula, we obtain:

=> Acres per seed pound = 4/31 or 0.129.

As a result, each pound of seed can be sown on about 0.129 acres.

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Answer: Draw a line from (2, 2) to (6, 2) for the run.

Draw a line from (6, 2) to (6, 8) for the rise.

The slope of the line is represented by rise/run, so in this case it would be 6/4.

Answer: no solution

Step-by-step explanation:

x = 4

it would be -1/2 = 0 so that's not right

x = 0

it would be 1 = -2

well the first and second won't work.

all real numbers doesn't seem like the right answer

so best answer would be no solution.

Answer:

Option B: 7x + y - 4 feet

Step-by-step explanation:  I got it right on the test. Trust me

The total perimeter of the triangular fence using the perimeter of a triangle formula is:

7x + y - 4 feet.

The perimeter of a form is the whole length enclosing it. It is the measurement of the perimeter or outline of any two-dimensional geometric shape. Many figures may have the same perimeter depending on their sizes.

The length that the shape's perimeter covers is known as the perimeter. Hence, the perimeter's units will be the same as its length units.

Now perimeter of a triangle =

Sum of all the sides of the triangular region:

= 4x + 5 + y -7 + 3x - 2

= 7x + y -4

Therefore, perimeter of the fence = 7x + y -4 feet.

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Answer:

Week 1 and Week 2.

Step-by-step explanation:

By SAS similarity, ΔKML and ΔRTL are similar triangles. Therefore, option A is the correct answer.

From the given figure, KR=9 units, RL=15 units, MT=7.5 units and TL=12.5 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Consider ΔKML and ΔRTL, we get

RL/KL =15/(15+9)

= 15/24

= 5/8

TL/ML =12.5/(12.5+7.5)

= 12.5/20

= 5/8

Here, RL/KL=TL/ML

Here, ∠KLM≅∠RLT

By SAS similarity, ΔKML and ΔRTL are similar triangles

So, ∠KMT≅∠RTL

By SAS similarity, ΔKML and ΔRTL are similar triangles. Therefore, option A is the correct answer.

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Answer:

a

Step-by-step explanation:

got it right in edmentum

if f has an absolute maximum value at c, then function f '(c) = 0 is True

This statement is true. This is because the first derivative of a function, f', is equal to 0 at the point of an absolute maximum. This is because the first derivative measures the rate of change of a function, and at a maximum, the rate of change of a function is 0. Therefore, if a function has an absolute maximum value at c, then f'(c) = 0.

The statement that if f has an absolute maximum value at c, then f '(c) = 0 is true. This is because the first derivative of a function measures the rate of change of a function. At an absolute maximum, the rate of change of a function is 0, so the first derivative of a function at that point must be 0. Therefore, if a function has an absolute maximum value at c, then f'(c) = 0.

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9514 1404 393

Answer:

  (B)  stretch & reflection

Step-by-step explanation:

The original function is multiplied by -1.7. This has a negative sign, so will cause the graph to be reflected across the x-axis. The magnitude is greater than 1, so the reflected function will be a stretch of the original.

The final solution is: u(x,t) = Σ (-1)^n (2L)/(nπ)^2 sin(nπx/L) exp(-k n^2 π^2 t/L^2).

To solve the heat equation:

k ∂²u/∂x² = ∂u/∂t

subject to boundary conditions u(0,t) = 0, u(L,t) = 0, and initial condition u(x,0) = x,

we can use separation of variables method as follows:

Assume a solution of the form: u(x,t) = X(x)T(t)

Substitute the above expression into the heat equation:

k X''(x)T(t) = X(x)T'(t)

Divide both sides by X(x)T(t):

k X''(x)/X(x) = T'(t)/T(t) = λ (some constant)

Solve for X(x) by assuming that k λ is a positive constant:

X''(x) + λ X(x) = 0

Applying the boundary conditions u(0,t) = 0, u(L,t) = 0 leads to the following solutions:

X(x) = sin(nπx/L) with n = 1, 2, 3, ...

Solve for T(t):

T'(t)/T(t) = k λ, which gives T(t) = c exp(k λ t).

Using the initial condition u(x,0) = x, we get:

u(x,0) = Σ cn sin(nπx/L) = x.

Then, using standard methods, we obtain the final solution:

u(x,t) = Σ cn sin(nπx/L) exp(-k n^2 π^2 t/L^2),

where cn can be determined from the initial condition u(x,0) = x.

For this problem, since the initial condition is u(x,0) = x, we have:

cn = 2/L ∫0^L x sin(nπx/L) dx = (-1)^n (2L)/(nπ)^2.

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When the water is 6 feet deep, then the water level rise at the rate of 0.22 feet per minute

Water runs into a conical tank at the rate of 9 ft^3 per min

The rate of change volume with respect to time dV / dt = 9 ft^3 per min

The height of the tank = 10 feet

The base radius of the tank = 5 feet

The volume of the cone = (1/3)πr^2h

The water is 6 feet deep

r/h = 6/10

r/h = 3/5

r = 3/5h

Substitute the values in the equation

The volume of the cone = (1/3) π(3/5h)^2 ×h

= (3/25)πh^3

Differentiate the equation

dV/ dt = (9/25)πh^2 × dh/dt

9 = (9/25)πh^2 × dh/dt

dh/dt = 9 / ((9/25)π×6^2

= 0.22 feet per min

Therefore, the water level is rising at the rate of 0.22 feet per minute

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The property of adaptive immunity enables a person to have the chicken pox when he or she is six years old and still be immune to chicken pox at age 45 exists Memory.

Specificity and memory are two crucial properties that determine adaptive immunity. Both specificity and memory pertain to the adaptive immune system's capacity to recognize and attack certain diseases, as well as to promptly react to pathogens to which it has already been exposed.

Adaptive immunity can offer an enduring defense, perhaps for the duration of a person's lifespan. In certain circumstances, such as with chickenpox, it does not confer permanent protection; for instance, a person who recovers from measles is now protected against measles for the rest of their life.

Specificity, diversity, specialization, memory, and self/non-self identification are the immunologic characteristics that define adaptive immunity, and these cells both create and show antigen-binding cell surface receptors.

The property of adaptive immunity enables a person to have the chicken pox when he or she is six years old and still be immune to chicken pox at age 45 exists Memory.

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Answer:

Option 1

Step-by-step explanation:

You can tell if a function is even if \(f(-x)=f(x)\):

\(f(x)=x^2-x+8\)

\(f(-x)=(-x)^2-(-x)+8\)

\(f(-x)=x^2+x+8\)

Since \(f(-x)\neq f(x)\), the function is not even. Therefore, option 1 is the best option.

Answer:

Okay.........so what's the problem???

The relative price is a useful measure for comparing the prices of different products or services, especially in the context of consumer preferences and demand.

Relative price refers to the price of a particular product or service in relation to other goods or services in the market.

It is calculated as the ratio of the price of a given product or service to the price of a reference product or service, commonly referred to as a base good or service.

Let the price of a pair of shoes be $5 and the price of a box of tea be $3.

Then the relative price of a pair of shoes is given by:

Relative price of shoes = Price of shoes / Price of tea

= $5 / $3

= 1.67

Thus, the relative price of a pair of shoes is 1.67.

Similarly,

The relative price of a box of tea can be calculated as follows:

Relative price of tea = Price of tea / Price of shoes

= $3 / $5

= 0.6

Therefore, the relative price of a box of tea is 0.6.

This means that the price of tea is relatively cheaper than that of shoes, as its relative price is less than one.

The relative price of shoes is greater than one, which indicates that shoes are relatively more expensive than tea.

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Answer:

Step-by-step explanation: This is just rearranging the formula. Divide by m on both sides, then find the square root. The answer is E

Given,

Rate of vegetables last week = 50 per kg

Rate of vegetables this week= 55 per kg

Percentage increase in price = \(\frac{Rate of \: veg \: this \:week-Rate \: of \: veg \: last \: week}{Rate \: of \: veg \: last \:week} \times 100\)

\( = \frac{55 - 50}{50} \times 100\)

\( = \frac{5}{50} \times 100\)

\( = 5 \times 2\)

\( = 10\%\)

\({{\bold{ \underline{ \underline{ \overline{ \overline{ \pink{The \: percentage \: of \: increased \: in \: the \: price \: is \: 10\%}}}}}}}}\)

v₁·v₂ is -18 which is correct option(D)

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

The operator that perform arithmetic operation are called arithmetic operators .

Operators which let do basic mathematical calculations

+ Addition operation : Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation : Subtracts right hand operand from left hand operand.

for example 4 -2 = 2

* Multiplication operation : Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation : Divides left hand operand by right hand operand

For example 4/2 = 2

Given that,

v1 = (3,-4) and v2 = (2,6)

To determine v₁·v₂

v₁·v₂ = 3·(2) - 4·(6)

v₁·v₂ = 6 - 24

v₁·v₂ = -18

Hence, the v₁·v₂ is -18.

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The final calculation revealed that the height of the mountain was approximately 350.1 meters.

Back in their workshop, Alex applied the tangent function to find the mountain's height. They knew that tangent is the ratio of the opposite side (the height) to the adjacent side (the horizontal distance). Setting up the equation, they plugged in the known values:

tangent(35 degrees) = height / 500 meters

Using trigonometric tables or a calculator, they found that the tangent of 35 degrees is approximately 0.7002. Now they could solve the equation:

0.7002 = height / 500 meters

To isolate the height, they multiplied both sides of the equation by 500:

0.7002 * 500 meters = height

The final calculation revealed that the height of the mountain was approximately 350.1 meters.

With this crucial information, Alex and Sarah could now design the bridge

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Answer:

148 feet squared

Step-by-step explanation:

Hope it's correct!<D

A = 2 (wl+hl+hw) = 2 x (4x6+5x6+5x4) = 148

To find the work done when moving the particle along the x-axis, we can use the formula for work, which is the integral of the force function F(x) with respect to x over the given interval. In this case, the force function is F(x) = 2x, and the interval is from x = 0 to x = 2 meters.

So, the work done can be calculated as:

Work = ∫(F(x) dx) from 0 to 2 = ∫(2x dx) from 0 to 2

To find the integral of 2x, we can use the power rule:

∫(2x dx) = x^2 + C

Now, we can evaluate the integral over the interval [0, 2]:

Work = (2^2 - 0^2) = 4 - 0 = 4

Therefore, the work done when the particle is moved from x = 0 to x = 2 meters is 4 Newton-meters. As a whole number answer without units, the answer is 4.

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The change in the nominal exchange rate, in Canada's perspective, is a depreciation of the Canadian dollar by 2.76%.

Nominal exchange rate is the price of one currency in terms of another currency. It represents the number of units of one currency that can be purchased with a single unit of another currency. In Canada's perspective, a change in nominal exchange rate means the value of the Canadian dollar in US dollars. So, to calculate the change in nominal exchange rate from Canada's perspective.

Nominal Exchange Rate = Real Exchange Rate x (1 + Inflation of Canada) / (1 + Inflation of US) Given, Real Exchange Rate of Canada

= 4.9% Inflation of Canada

= 8.5% Inflation of US

= 3.8%  Nominal Exchange Rate

= 4.9% x (1 + 8.5%) / (1 + 3.8%) Nominal Exchange Rate

= 4.9% x 1.085 / 1.038 Nominal Exchange Rate

= 5.3099 / 1.038 Nominal Exchange Rate

= 5.11 (rounded to two decimal places)

This means that if there were no inflation, the nominal exchange rate from Canada's perspective would have been 5.11 Canadian dollars per US dollar. But due to inflation, the Canadian dollar depreciated by 2.76% (calculated as (5.11 - 4.97) / 5.11 x 100%). Therefore, the change in the nominal exchange rate, in Canada's perspective, is a depreciation of the Canadian dollar by 2.76%.

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Answer:

The numbers are 4 and 8.

Step-by-step explanation:

First, you have to form equations for the given informations :

\(x + y = 12 - - - (1)\)

\(x - y = - 4 - - - (2)\)

Next, you have to solve the simultaneous equations :

\((1) - (2)\)

\(2y = 16\)

\(y = 16 \div 2\)

\(y = 8\)

\(substitute \: y = 8 \: into \: (1)\)

\(x + 8 = 12\)

\(x = 12 - 8\)

\(x = 4\)

Step-by-step explanation:

in ten minutes it goes 1 km in 60 minutes it goes 4 km

Answer:

The amount saved in June is;

$(2x + 4)

Step-by-step explanation:

Here, we want to get the amount saved in June

From the question, she saved $5 more than twice here usual amount

twice here usual amount is 2 * x = $2x

So, adding the extra $4; the amount saved will be;

2x + 4

Answer:

Angles 9 and 5 are corresponding angles.

Mr. Nelson took 35 students on the trip.

The equation that can be used to solve this problem is:

100 + 6.50n = 327.50

Where n is the number of students. To solve this equation, we need to subtract 100 from both sides of the equation:

6.50n = 227.50

Next, we need to divide both sides by 6.50:

n = 35

Therefore, Mr. Nelson took 35 students on the trip.

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Answer:

To determine the number of 4-digit numbers that are multiples of at least one of the numbers 2 and 5, we can use the principle of inclusion-exclusion.

First, let's find the number of 4-digit numbers that are multiples of 2. The first 4-digit multiple of 2 is 1000, and the last 4-digit multiple of 2 is 9998. To find the count of multiples, we can divide the difference between these two numbers by 2 and add 1 (since we're including both endpoints):

Number of multiples of 2 = (9998 - 1000) / 2 + 1 = 4500

Next, let's find the number of 4-digit numbers that are multiples of 5. The first 4-digit multiple of 5 is 1000, and the last 4-digit multiple of 5 is 9995. Similar to before, we divide the difference between these two numbers by 5 and add 1:

Number of multiples of 5 = (9995 - 1000) / 5 + 1 = 1800

However, if we simply add these two counts together, we will be counting the multiples of 10 twice (since 10 is a multiple of both 2 and 5). To correct this, we need to subtract the number of 4-digit multiples of 10.

To find the number of 4-digit multiples of 10, we divide the difference between the first and last 4-digit multiples of 10 (1000 and 9990) by 10 and add 1:

Number of multiples of 10 = (9990 - 1000) / 10 + 1 = 900

Now we can use the principle of inclusion-exclusion to calculate the final count:

Number of 4-digit numbers that are multiples of at least one of 2 or 5 = Number of multiples of 2 + Number of multiples of 5 - Number of multiples of 10

= 4500 + 1800 - 900 = 5400

Therefore, there are 5400 4-digit numbers that are multiples of at least one of the numbers 2 and 5.