a-20
b-135
c-24
d-25

Answer:

x=60°

Step-by-step explanation:

180 - 90 = 90

90 - 30 = 60

x=60

Therefore, to determine if a linear transformation is an isomorphism, we can check if the determinant is non-zero or if the kernel is only the zero vector.

An isomorphism is a bijective linear transformation, that is both one-to-one and onto. The determinant of a linear transformation can help determine if it is an isomorphism. If the determinant is non-zero, the linear transformation is invertible, and therefore an isomorphism. A linear transformation is an isomorphism if and only if its determinant is nonzero.
Additionally, another way to check if a linear transformation is an isomorphism is to check if the kernel, which is the set of all vectors that get mapped to zero, is equal to only the zero vector. If the kernel is only the zero vector, then the linear transformation is one-to-one and therefore an isomorphism.

Therefore, to determine if a linear transformation is an isomorphism, we can check if the determinant is non-zero or if the kernel is only the zero vector.

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Answer:

110 is the answer

Step-by-step explanation:

Step 1: (250 ÷ 50) × £1.89

= 5 × £1.89

= £9.45

The rest = £15 - £9.45

= £5.55

He now has 5.55 left to spend on paper plates.

We know that 100p = £1

so the equation would be

5.55 × 100 = 555p

555p ÷ 49p = 11

And since he wants to buy 10 paper plates, we do

10 × 11 = 110

So, he can buy 110 paper plates

AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

What is congruent ?

Congruent refers to having the same shape and size. In mathematics, two objects are said to be congruent if they are identical in shape and size, and can be superimposed onto one another. The symbol used to represent congruence is ≅. Congruence applies to various geometric objects, such as triangles, rectangles, circles, and more. When two objects are congruent, they have all corresponding angles equal and all corresponding sides equal in length.

Step 1: Statement: \($\angle DBE = \angle EBC$\)

Reason: Given that overline BE bisects \($\angle DBC$\)

Step 2: Statement: \($\angle DBC + \angle EBC = 180^\circ$\)

Reason: Angle sum property of a straight line.

Step 3: Statement: \($\angle ABC + \angle EBC = 180^\circ$\)

Reason: Angles on a straight line sum to \(180^\circ$, and $\overline{BE} || \overline{AC}$\) implies that \(\angle ABC$ and $\angle EBC$\) are co-interior angles.

Step 4: Statement: \($\angle ABC = \angle DBC$\)

Reason: From step 2 and step 3, \($\angle ABC + \angle EBC = \angle DBC + \angle EBC = 180^\circ$\). Thus, \($\angle ABC = \angle DBC$\).

Step 5: Statement: \($\triangle ABE \cong \triangle CBE$\)

Reason: By the angle-angle-side congruence criterion, since \($\angle DBE = \angle EBC$\) (from step 1) and \($\angle ABC = \angle DBC$\) (from step 4), and \($\overline{BE}$\) is common to both triangles.

Step 6: Statement: \($AB = BC$\)

Reason: By step 5, \($\triangle ABE \cong \triangle CBE$\), so corresponding sides are congruent, including \($\overline{AB} \cong \overline{BC}$\).

Therefore, AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

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Answer:82

Step-by-step explanation:

Answer:

∠ 7 = 82°

Step-by-step explanation:

∠ 2 and ∠ 7 are Alternate exterior angles and are congruent, then

∠ 7 = ∠ 2 = 82°

the answer would 2.35 bc or thw way its written

Step-by-step explanation:

its wrong dont put it

Part A:

I got the number of kids in the survey which is 130 and I found 70 which is the amount of kids who like playing on a pc/console. I took 130 and 70 and converted it into a fraction 70/130, I simplified it to 7/13 and used a calculator to get my percentage which I rounded and got 53%

Part B:

I drew a table and just focused on column two. I looked at how many people don't like phone or pc and I found that 10 is how many people like phone and not pc, 30 is people who dont like phone or pc, together its 40, so you need to find what the percentage 30 is of 40, or 3/4, I used a calculator and converted it into a percentage and I got 75%

They rented the small car $39/day for 3 days after they lost their insurance coupon

Insurance is a means of protection from financial loss in which, in exchange for a fee, a party agrees to compensate another party in the event of a certain loss, damage, or injury. It is a form of risk management, primarily used to hedge against the risk of a contingent or uncertain loss.

Given here: The available car rents as

small car rental fee-( seats 4 passengers):$39/day

full car rental fee:$49/day

Insurance : $21/day

Now total cost = $75×3

                          =$225

Now insurance fee=$21×5

                               =$105

Thus the required sum before insurance =$120

Hence,  They rented the small car $39/day for 3 days after they lost their insurance coupon

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The primal solution does not satisfy all the dual constraints, the solution to the dual problem is infeasible.

To construct the dual problem, we'll use the given primal problem and its constraints. The primal problem is as follows:

Maximize: z = x1 + 2x2

Subject to:

-2x1 + x2 + x3 + x4 = 7

-x1 + 2x2 + x5 = 3

x1, x2, x3, x4, x5 ≥ 0

Now, let's construct the dual problem:

Minimize: w = 7y1 + 3y2

Subject to:

-2y1 - y2 ≥ 1

y1 + 2y2 ≥ 2

y1 + y2 ≤ 0

y1, y2 ≥ 0

Note that the coefficients in the dual problem come from the coefficients in the primal problem, but the inequalities are flipped and the objective function coefficients are used as the right-hand side values.

Now, let's find the solution to the dual problem using the given primal solution [3, 5, 3, 0, 0]T.

We substitute the primal solution into the dual constraints and find the maximum value of the objective function:

For the constraint -2y1 - y2 ≥ 1:

-2(3) - 5 ≥ 1

-6 - 5 ≥ 1

-11 ≥ 1 (not satisfied)

For the constraint y1 + 2y2 ≥ 2:

3 + 2(5) ≥ 2

3 + 10 ≥ 2

13 ≥ 2 (satisfied)

For the constraint y1 + y2 ≤ 0:

3 + 5 ≤ 0

8 ≤ 0 (not satisfied)

Since the primal solution does not satisfy all the dual constraints, the solution to the dual problem is infeasible.

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f = -4

f = 3

f = -2

f < 4 means that f consists of all the values that are less than 4.

From the options:

Numbers that are less than 4 are -4, 3 and -2.

7 is greater than 4, therefore, f = 7 is an incorrect choice

Answer:

Jack and Jill would each be \(200\; {\rm ft}\) away from the trail guide.

Step-by-step explanation:

Refer to the diagram attached. Let \(\sf A\) denote Jack, \(\sf I\) denote Jill, and \(\sf G\) denote the trail guide.

The angle \(\angle {\sf GAI} = 60^{\circ}\) as it represents the depression angle of the trail guide from the perspective Jack. Likewise, \(\angle {\sf GIA} = 60^{\circ}\) for the angle from the perspective of Jill.

Note that in triangle \(\triangle {\sf AGI}\):

\(\begin{aligned}\angle {\sf AGI} &= 180^{\circ} - \angle {\sf GAI} - \angle {\sf GIA}\\ &= 180^{\circ} - 60^{\circ} - 60^{\circ} \\ &= 60^{\circ} \end{aligned}\).

Thus, triangle \(\triangle {\sf AGI}\) would be an equilateral triangle as all its interior angles are  \(60^{\circ}\). Therefore, the length of all three sides would be equal:

\(\overline {\sf AG} = \overline{\sf GI} = \overline{\sf AI}\).

The length of segment \(\sf{AI}\) represents the distance between Jack and Jill. This distance is supposed to be the same as the width of the canyon,  \(200\; {\rm ft}\). Thus, \(\overline{\sf AI} = 200\; {\rm ft}\).

The distance between Jack and the trail guide would be the same as the length of segment \({\sf AG}\), which is \(\overline{\sf{AG}} = \overline{\sf AI} = 200\; {\rm ft}\).

Similarly, the distance between Jill and the trail guide would be the same as the length of segment \({\sf GI}\), which is \(\overline{\sf{GI}} = \overline{\sf AI} = 200\; {\rm ft}\).

Answer:

michelle is 56 years old

Step-by-step explanation:

start with madeline you know she's 7, move on to fiona we know she is twice as old as madeline so we mulitply 7 times 2, we get 14. now we know fiona is 14 and in order to find michelles age we multiply times 4 because shes four time fionas age. 14x4=56.

First find fionas age

Fiona is 2x as old as madeline

madeline is 7

mulitply 7*2 which gives you 14

that means fiona is 14

multiply 14 by 4 which gives you 56

michelle is 56

the original purchase price was:

original purchase= 210,000- 0.4(210,000)=210,000-84,000=126,000

So the final answer will be that she paid $126,000, 10 years ago for her house.

we can check that our answer is correct by adding 126,000+84,000=210,000

Students shouldn't be missing homework for many reasons. Students shouldn't be missing homework because this is school and it is their responsibility to get this work done. Another reason is that students need to make an effort to learn and grow in a class subject by doing their homework. Homework is mandatory and shouldn't be dismissed. By not doing your homework, you aren't giving your future self a chance.

Step-by-step explanation:

Answer: x=11/36

Step-by-step explanation:

Step One-Subtract 1/6 from both sides.

2x+1/6-1/6=7/9-1/6

2x=11/18

Step Two-Divide both sides by 2.

2x/2=11/18/2

x=11/36.

My math might not be correct, sorry if it is. In addition, my explanation is a bit confusing, so sorry about that too.

Answer:

3

Step-by-step explanation: She has exactly 13 flowers and each bouquet uses 4 flowers. So you just divide 13/4. You get 3.25, but you can't have .25 of a bouquet, so you just round to 3 and then they would have to throw away the rest or get more flowers.

Answer:385

Formulate and substitute:F=350+350rt

Calculate the product or quotient:350x1+0.1

Calculate the sum or difference:350x1.1

Calculate the product or quotient:385

The otter takes approximately 12.10 seconds to get to the other side if it swims directly across the river. The current will have carried the otter approximately 30.25 meters downstream when it reaches the other side. The otter's velocity, relative to the bank from where it started, is 0.25 m/s.

a) To find the time it takes for the otter to get to the other side, we can use the concept of relative velocity. The otter's swimming speed is 2.75 m/s, and the current velocity is 2.5 m/s. Since the otter is swimming directly across the river, its swimming speed and the current speed are perpendicular. Using the Pythagorean theorem, we can find the resultant velocity of the otter:

Resultant velocity = √(swimming velocity² + current velocity²)

= √(2.75² + 2.5²)

≈ √(7.5625 + 6.25)

≈ √13.8125

≈ 3.72 m/s (rounded to two decimal places)

The time it takes to cross the river is given by the distance divided by the resultant velocity:

Time = Distance / Resultant velocity

= 45.0 m / 3.72 m/s

≈ 12.10 seconds (rounded to two decimal places)

b) To find how many meters downstream the current carries the otter when it gets to the other side, we can calculate the distance using the time it takes to cross and the current velocity.

Distance downstream = Time × Current velocity

= 12.10 s × 2.5 m/s

= 30.25 m

c) The otter's velocity, relative to the bank from where it started, can be calculated by subtracting the current velocity from the otter's swimming velocity.

Relative velocity = Swimming velocity - Current velocity

= 2.75 m/s - 2.5 m/s

= 0.25 m/s

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In this case, the maximum column load is 140 T, not including the self-weight of the footing. The ultimate bearing capacity of the soil is given as qult = 55 T/m2, and the footing diameter is 2.5 m. With a factor of safety (FS) of 3, the required area of the footing 90.02 square meters

The ultimate bearing capacity of the soil, qult, is given as 55 T/m2. To determine the required area of the footing, we first need to calculate the total ultimate load that the footing can support. This can be done by multiplying the ultimate bearing capacity by the area of the footing. The area of the footing can be calculated using the formula for the area of a circle, A = πr2, where r is the radius of the footing. Since the diameter of the footing is given as 2.5 m, the radius is half of that, which is 1.25 m.

So, the area of the footing, A, is calculated as follows:

A = π(1.25)2 = 4.91 m2

Now, we can determine the total ultimate load that the footing can support by multiplying the ultimate bearing capacity, qult, by the area of the footing:

Total ultimate load = qult × A = 55 T/m2 × 4.91 m2 = 270.05 T

Next, we need to consider the factor of safety (FS), which is given as 3. The factor of safety is used to ensure that the structure is designed to be stronger than the expected loads. To calculate the required area of the footing, we divide the total ultimate load by the factor of safety:

Required area = Total ultimate load / FS = 270.05 T / 3 = 90.02 T

Therefore, the required area of the footing is 90.02 square meters, considering the given maximum column load of 140 T and a factor of safety of 3. This ensures that the footing is designed to safely support the load from the column while accounting for the ultimate bearing capacity of the soil.

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In this case, the maximum column load is 140 T, not including the self-weight of the footing.

The ultimate bearing capacity of the soil is given as qult = 55 T/m2, and the footing diameter is 2.5 m. With a factor of safety (FS) of 3, the required area of the footing 90.02 square meters. The ultimate bearing capacity of the soil, qult, is given as 55 T/m2. To determine the required area of the footing, we first need to calculate the total ultimate load that the footing can support. This can be done by multiplying the ultimate bearing capacity by the area of the footing.

The area of the footing can be calculated using the formula for the area of a circle, A = πr2, where r is the radius of the footing. Since the diameter of the footing is given as 2.5 m, the radius is half of that, which is 1.25 m. So, the area of the footing, A, is calculated as follows: A = π(1.25)2 = 4.91 m2

Now, we can determine the total ultimate load that the footing can support by multiplying the ultimate bearing capacity, qult, by the area of the footing:
Total ultimate load = qult × A = 55 T/m2 × 4.91 m2 = 270.05 T

Next, we need to consider the factor of safety (FS), which is given as 3. The factor of safety is used to ensure that the structure is designed to be stronger than the expected loads. To calculate the required area of the footing, we divide the total ultimate load by the factor of safety:
Required area = Total ultimate load / FS = 270.05 T / 3 = 90.02 T

Therefore, the required area of the footing is 90.02 square meters, considering the given maximum column load of 140 T and a factor of safety of 3. This ensures that the footing is designed to safely support the load from the column while accounting for the ultimate bearing capacity of the soil.

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Answer:

Cumulative Frequency:

The sum of all the frequencies for all classes is equal to the number of elements in the given data and that summation is termed as the cumulative frequency which defines the number of entries of that statistical data.

The sum of relative frequencies is also equal to one, since the sum of all fractional parts must equal the whole.

Step-by-step explanation:

Answer:

14 mm squared is the area

Step-by-step explanation:

Answer: A) Option B

B) 22.3 minutes.

Step-by-step explanation:

The temperature decreases in an exponential decrease, this means that we can write the equation as:

T(x) = A*r^x + B

Where A is the difference between the initial temperature and the room temperature, B is the room temperature, and r is a positive number smaller than 1, that says "how fast" the temperature decreases (and x is the variable, in units of time)

We know that the initial temperature

A = 200° - 72° = 128°

B = 72°

T(x) = 128°r^x + 72°

The only option with those two values is option B.

T(x) =  128(0.989)^x + 72

We should check that when x = 2m, the temperature must be 197°

T(2m) = 128*(0.989)^2 + 72 = 197.2° (that we can round down to 197°)

So this equation is correct

Now we want to find the time such the temperature is 172°F

then:

172° = 128°(0.989)^x + 72°

100° = 128°(0.989)^x

100/128 = (0.989)^x

x = ln(100/128)/ln(0.989) = 22.3 minutes.

Let's check in our equation:

T(22.3) =  128°(0.989)^22.3 + 72 = 172°

The equation of the line in point slope form is y - b = -3/4 (x - a), where (a, b) is a point on the line.

Equation of a line in point slope form is y - y₁ = m(x - x₁), where m is the slope of the line and (x₁, y₁) is a point on the line.

Given that slope, m = -3/4.

It is not given a point that the line passes through.

Let (a, b) be a point that the line passes through.

Substituting these in the point slope form,

y - y₁ = m(x - x₁)

y - b = -3/4 (x - a)

After simplifying we can write it as,

y - b = -3/4x + 3/4a

y = -3/4 x + (3/4a + b)

Hence the equation of the line is found.

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Answer:

you would have to do 1,472

Step-by-step explanation:

this is correct because if you take the problem and solve it then that should be the answer :D

Answer:

A = 90.25pi sq m

OR = 361pi/4 sq m

Step-by-step explanation:

If the circumference is 19pi, then the diameter is 19.

C = pi•d

19pi = pi•d

19 = d

If the diameter is 19, then the radius is 9.5.

The radius is always half of the diameter.

Then we can find the area.

A = pi•r^2

=pi•9.5^2

=90.25pi

We don't often see a decimal number coefficient for pi. So as an improper fraction, 90.25 which is 90 1/4 is

(90×4)+1 over 4

= 361/4

Area = (361/4)pi

=361pi/4 sq meters

Answer: the endpoint is going to be  (-12,11)

Step-by-step explanation: sorry if it wrong

The system of equations that models the profit for each team is given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The slope and intercept for the functions in this problem are given as follows:

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Answer:

He can work a maximum of 2 8-hour days for the remainder of the week

Step-by-step explanation:

Firstly, from the question, we are made to know that the maximum work hours is 40 hours.

Now, we know that he has already worked 24 hours this week, the number of hours remains to work will be 40-24 = 16 hours

Now, given that his working hour is 8-hours per day, we want to know the number of days he has to work for the remainder of the week

Mathematically, that would be 16 hours divided by 8-hours days

That is 16/8 = 2

Answer:

2

Step-by-step explanation:

just took the test