Question 3 For each of the following, explain whether it is (always) true or (possibly) false. If true, you must explain why. If false, you must give a concrete counterexample (with numbers).
a) (1.5pts) If b is a linear combination of the columns of the matrix A, then the linear system Ax = b has a unique solution.
b) (1.5pts) If {u, v, w} is linearly independent, then {u+w, v + w} is linearly independent.
c) (1.5pts) If V = span{V1, V2, V3} and dim(V) = 2, then {V2, V3} is a basis of V.

Answer: 18

Step-by-step explanation:

9 kids each have two bags

9 x 2 = 18

9 + 9 = 18

By the properties of rhombuses, m∠1 = 90°, m∠2 = 41°, and m∠3 = 49°.

A quadrilateral with all equal sides is a rhombus.

Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal.

A rhombus has 360° of interior angles total.

A rhombus's adjacent angles add up to 180°.

A rhombus's diagonals are perpendicular to one another and cut each other in half.

From the given figure and properties of the rhombus, m∠1 = 90°, As the diagonals bisect each other perpendicularly.

Now, The two diagonals have created 4 congruent right-angled triangles,

Therefore, m∠2 = 41°.

And m∠3 = 180° - (41° + 90°).

m∠3 = 49°.

learn more about rhombuses here :

https://brainly.com/question/16547718

#SPJ1

Answer:

$1.50

Step-by-step explanation:

3 boxes = $4.50

1 box= $4.50÷3

1box= $1.50

Answer:$1.50

Step-by-step explanation:

Answer

10 is the answer

Please mark as brainliest HOPE IT HELPS!

Answer:

the answer is 22

Step-by-step explanation:

-22 x -22=22

Result in decimals: 3.625

Step-by-step explanation:

Answer:

29/8 or 3 5/8

Step-by-step explanation:

first turn 3 1/4 to 13/4

now change 13/4 to get 26/8

now add 26/8+ 3/8 and get 29/8 or 3 5/8

Answer:

$0.33

Step-by-step explanation:

5.11-3.79=1.32÷4=.33

The company deposited $1,487.88 at the end of each quarter during the first six years.

The amount deposited quarterly during the first six years can be calculated using the formula for the future value of an annuity:

[tex]PMT = (FV / ((1 + r)^{n-1}) * (1 + r)^{-n[/tex]

where PMT is the equal quarterly deposit, FV is the final value of the account, r is the quarterly interest rate (APR / 4), and n is the number of quarters (6 years * 4 quarters per year = 24 quarters).

Plugging in the given values, we get:

[tex]PMT = ($50,000 / ((1 + 0.068/4)^{28-1}) * (1 + 0.068/4)^{-28}[/tex]

PMT = $1,487.88 (rounded to the nearest cent)

Therefore, the company deposited $1,487.88 at the end of each quarter during the first six years.

The problem involves finding the amount deposited quarterly by a company for a period of six years, given the final value of the account four years after the company stopped making deposits. This can be solved using the formula for the future value of an annuity, which calculates the total value of a series of equal payments made at regular intervals over a specified period, taking into account compound interest.

By plugging in the given values into the formula, we can solve for the equal quarterly deposit made by the company during the first six years. The resulting amount is $1,487.88, which represents the total value of all the quarterly deposits made by the company during the six-year period. This answer assumes that the interest rate remained constant throughout the entire period and that the company made no withdrawals or additional deposits after the initial six years.

For more questions like Revenue visit the link below:

https://brainly.com/question/403876

#SPJ11

The robberies that took place this year to the nearest whole number is 104 robberies.

A value's percentage change from its initial value is expressed as a percent reduction, but the percentage difference between two values is expressed as a % change from their average.

Let us suppose the number of robberies this year = x.

Given that,

This year the number of robberies has gone down 39%.

x = 171 (1 - 39/100)

x = 171 (1 - 0.39)

x = 104.31

Hence, the robberies that took place this year is 104 robberies.

Learn more about percentage decrease here:

https://brainly.com/question/10168902

#SPJ1

Answer:

not sure but i think its 12

Step-by-step explanation:

if you look carefully one side witch is 6 is have of side x and 6 x 2 is 12

hope this helps.

Answer:I think its 15 but I'm not sure

Step-by-step explanation:

Answer:

[tex] \sf \: x = 5[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 11 + 2x = 3(x + 2)

Then the value of x will be,

→ 11 + 2x = 3(x + 2)

→ 11 + 2x = 3x + 6

→ 2x - 3x = 6 - 11

→ -x = -5

→ [ x = 5 ]

Hence, the value of x is 5.

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

The value of x is 5 !

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

Using the properties of the exponents, we solve the expression and found the result as  [tex]w^{15} y^{12}[/tex].

The exponent of a number indicates how many times a number has been multiplied by itself. Exponent is another name for a number's power. It could be an integer, a fraction, a negative integer, or a decimal. How many times we must multiply the reciprocal of the base is indicated by a negative exponent. When writing exponentiated fractions, negative exponents are employed. A fractional exponent is one where the exponent of a number is a fraction. Parts of fractional exponents include square roots, cube roots, and nth roots. The square root of a base is a number with a power of half.

Given,

[tex](w^5 * y^4)^3[/tex]

We have to solve this using the properties of the exponents.

Now, this can be written as:

[tex](w^5)^3 * (y^4)^3[/tex]

When the exponent is raised to another power, we can follow the power rule for exponents.

This rule states that multiply the exponent by the power to raise a number with an exponent to that power.

Then the above expression becomes

[tex]w^{(5*3)} * y^{(4*3)}[/tex] = [tex]w^{15} y^{12}[/tex]

Therefore using the properties of the exponents, we solve the expression and found the result as [tex]w^{15} y^{12}[/tex].

To learn more about exponents, follow the link.

https://brainly.com/question/11975096

#SPJ1

15/25 = x/90

25x = 1350

x = 54

54 papers

Missing number to make the binomial 9x² + X + 25 a perfect square is 30x.

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).

Given expression

9x² + X + 25

It can be written as

(3x)² + X + 5²

Comparing with a² + 2ab + b²

a = 3x

b = 5

X = 2ab

X = 2(3x)(5)
X = 30x

Hence, 30x is the missing number  to create a perfect-square binomial.

Learn more about quadratic equation here:

https://brainly.com/question/30098550

#SPJ9

The value of R is -10.

The polynomial p(x)=x^(3)-3x^(2)+4x-12 can be expressed as p(x)=q(x)*(x-1)+R. To find the value of R, we need to divide the polynomial p(x) by (x-1) using synthetic division.

Set up the synthetic division by writing the coefficients of the polynomial p(x) in a row and placing the divisor (x-1) to the left of the row.

1 | 1 -3  4 -12
 |_____________

Bring down the first coefficient (1) and multiply it by the divisor (1) to get 1. Place this value below the second coefficient (-3) and add them to get -2.

1 | 1 -3  4 -12
 |   1
 |_____________
   1 -2

Multiply the new value (-2) by the divisor (1) to get -2. Place this value below the third coefficient (4) and add them to get 2.

1 | 1 -3  4 -12
 |   1 -2
 |_____________
   1 -2  2

Multiply the new value (2) by the divisor (1) to get 2. Place this value below the fourth coefficient (-12) and add them to get -10.

1 | 1 -3  4 -12
 |   1 -2  2
 |_____________
   1 -2  2 -10

The final value (-10) is the remainder, or the value of R.

Therefore, the value of R is -10.

Learn about Polynomial

brainly.com/question/11536910

#SPJ11

The length of the midsegment of the given trapezoid is 16.

A trapezoid is necessarily a convex quadrilateral in Euclidean geometry. The parallel sides are called the bases of the trapezoid.

Given is a trapezoid TUVW, with bases UV and TW given by expressions, 3x-1, 8x and the midsegment XY is 3x+7.

We need to find the length of the midsegment,

We know,

Midsegment = (base 1 + base 2) / 2

Therefore,

XY = UV+TW / 2

3x+7 = 3x-1 + 8x / 2

6x+14 = 11x-1

5x = 15

x = 3

XY = 3(3)+7 = 16

Hence, the length of the midsegment of the given trapezoid is 16.

Learn more about trapezoid click;

https://brainly.com/question/12623349

#SPJ1

They should sell each T-shirt for $27.80 to make a profit of $320.

Profit is the financial gain that a company or individual makes after deducting all the expenses from the revenue earned. It is the positive difference between the total revenue generated from the sale of goods or services and the total cost of producing and selling those goods or services.

Profit is one of the key indicators of a company's financial performance, and it is calculated by subtracting the total expenses from the total revenue. The expenses include the cost of raw materials, labor, rent, taxes, and other overhead costs associated with producing and selling the goods or services.

To make a profit of $320, they need to sell all 25 shirts for a total of $320 + ($15 x 25) = $695.

Therefore, the price they need to sell each T-shirt for is $695 ÷ 25 = $27.80 (rounded to the nearest cent).

So they should sell each T-shirt for $27.80 to make a profit of $320.

To know more about price visit:

https://brainly.com/question/15779608

#SPJ1

Answer:

75:77

Step-by-step explanation:

5 is 2 more than 3

3+72=75

5+72=77

therefore: 3:5 = 75:77

If that's not what you meant, then I don't understand the question

[tex]\stackrel{ \textit{Partial Variation} }{V=aD+bD^2}\qquad \impliedby \begin{array}{llll} \textit{V\textit{ varies partly}}\\ \textit{with D and partly with }D^2 \end{array} \\\\[-0.35em] ~\dotfill\\\\ \textit{we also know that} \begin{cases} V=5\\ D=2\\[-0.5em] \hrulefill\\ V=9\\ D=3 \end{cases}\implies \begin{array}{llll} 5=a2+b2^2&\qquad &5=2a+4b\\\\ 9=a3+b3^2&&9=3a+9b \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{5=2a+4b}\implies 5-2a=4b\implies \cfrac{5-2a}{4}=b \\\\\\ \stackrel{\textit{using the 2nd equation}}{9=3a+9b}\implies \stackrel{\textit{substituting from above}}{9=3a+9\left( \cfrac{5-2a}{4} \right)}\implies 9=3a+\cfrac{45-18a}{4} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4(9)=4\left( 3a+\cfrac{45-18a}{4} \right)}\implies 36=12a+45-18a\implies -9=-6a[/tex]

[tex]\cfrac{-9}{-6}=a\implies \boxed{\cfrac{3}{2}=a}\hspace{5em}b=\cfrac{5-2\left( \frac{3}{2} \right)}{4}\implies \boxed{b=\cfrac{1}{2}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill V=\cfrac{3}{2}D+\cfrac{1}{2}D^2~\hfill[/tex]

Answer:

Customer A - 5 / 22.45 = $0.22 or 22 cents per quart

Customer B - 7 / 25.45 = $0.27 or 27 cents per quart

Answer: A

Area of a circle=[tex]\pi r^2\\[/tex]

Now that we have established this, we will now substitute the values in the equation.

[tex]\pi r^2\\=\frac{22}{7}\\ =\frac{396}{7}\\ =56.57 \\[/tex] OR 57 square yards

HOPE THIS HELPED PLEASE MARK BRAINLIEST IF IT DID!

Answer:

If your options are  110 square yards

220 square yards

3,850 square yards

15,400 square yards

then the correct answer is 3,850 square yards.

Step-by-step explanation:

I took the quiz and got it right.

The midline or midsegment theorem calculate the value of P. the value of the variable, P that base length in the trapezoid is equals to the 13.

A trapezoid is a 4-sided (square) shape in which some sides are parallels and others not. The midsection of a trapeze is the line that runs from the middle of one leg to the middle of the other. The midsection or Midsegment theorem of a trapezium states that if a line parallel to the two bases passes through the middle of one leg, it also passes through the middle of the other leg. Also, the length of the middle fragment is half the length of two bases. Now we see a trapezoid in the image above, the length of the midsegment = 25

One of the bases of the trapezium = 37

We need to calculate the value of the other base length P Using Midsigment or Midline Theorem, Midsigment = length of two bases/2

=> 25 = (37 + P)/2

=> 50 = 37 + P

=> P = 50 - 37

=> P = 13

Hence, required length is 13.

For more information about Midsegment , visit :

https://brainly.com/question/29512883

#SPJ4

Complete question:

Use the midline theorem to find the value of the variable in the trapezoid. See the above figure.

The magnitude and direction of the resultant force will be 7.829 N and the direction is opposite to the applied force.

A vector is an amount that has direction as well as magnitude and complies with the rule of vector addition.

A constant force of 18 newtons is supplied to an item at a constant angle of 56° while a constant force of 32 newtons is produced to the entity at a fixed angle of 124°.

Then the magnitude and direction of the resultant force are given as,

∑F = 0

∑F = 18 · cos 56° + 32 · cos 124°

∑F = 10.065 - 17.894

∑F = - 7.829 N

The magnitude and direction of the resultant force will be 7.829 N and the direction is opposite to the applied force.

More about the vector link is given below.

https://brainly.com/question/13188123

#SPJ9

By applying trigonometric function concept, it can be concluded that the solutions are:

31.  tan a = cot(a + 10°), a = 40°

32. cos θ = sin(2θ - 30°), θ = 40°

33. sin(2θ + 10°) = cos(3θ - 20°), θ = 20°

34. sec(B + 10°) = csc(2B + 20°), B = 20°

35. tan(3B + 4°) = cot(5B - 10°), B = 12°

36. cot(5θ + 2°) = tan(2θ + 4°), θ = 12°

Two angles are said to be complementary angles if their sum is 90°. Sin and Cosine are complementary, Tan and Cot are complementary, and sec and cosec are complementary.

Trigonometric functions of complementary angles:

sin(90° - θ) = cos θ

cos(90° - θ) = sin θ

tan(90° - θ) = cot θ

cot(90° - θ) = tan θ

sec(90° - θ) = csc θ

csc(90° - θ) = sec θ

31. To find one solution for the equation tan a = cot(a + 10°), we can use the fact that cot(90° - θ) = tan θ. Therefore, we can rewrite the equation as:

         tan a = cot(a + 10°)

cot(90° - a) = cot(a + 10°)

      90° - a = a + 10°

             2a = 80°

                a = 40°

32. To find one solution for the equation cos θ = sin(2θ - 30°), we can use the fact that sin(90° - θ) = cos θ. Therefore, we can rewrite the equation as:

        cos θ = sin(2θ - 30°)

 sin(90° - θ) = sin(2θ - 30°)

θ + 2θ - 30° = 90°

              3θ = 120°

                θ = 40°

33. To find one solution for the equation sin(2θ + 10°) = cos(3θ - 20°), we can use the fact that sin(90° - θ) = cos θ. Therefore, we can rewrite the equation as:

sin(2θ + 10°) = cos(3θ - 20°)

sin(2θ + 10°) = sin(90° - (3θ - 20°))

sin(2θ + 10°) = sin(110° - 3θ)

      2θ + 10° = 110° - 3θ

               5θ = 100°

                 θ = 20°

34. To find one solution for the equation sec (B + 10°) = csc(2B + 20°), we can use the fact that sec θ = csc(90° - θ). Therefore, we can rewrite the equation as:

          sec(B + 10°) = csc(2B + 20°)

csc(90° - (B + 10°)) = sec(2B + 20°)

                 80° - B = 2B + 20°

                        3B = 60°

                          B = 20°

35. To find one solution for the equation tan(3B + 4°) = cot(5B-10°), we can use the fact that tan a = cot(90° - a). Therefore, we can rewrite the equation as:

           tan(3B + 4°) = cot(5B - 10°)

cot (90° - (3B + 4°)) = cot(5B - 10°)

                86° - 3B = 5B - 10°

                         8B = 96°

                           B = 12°

36. To find one solution for the equation cot(5θ + 2°) = tan(2θ + 4°), we can use the fact that cot(90° - θ) = tan θ. Therefore, we can rewrite the equation as:

          cot(5θ + 2°) = tan(2θ + 4°)

tan (90° - (5θ + 2°)) = tan(2θ + 4°)

                 88° - 5θ = 2θ + 4°

                           7θ = 84

                              θ = 12°

To learn more about trigonometric functions, click here: https://brainly.com/question/3418378

#SPJ11

The ordered pair which the graph pass through include the following:

A) (4, 9.2)

E) (0, 0)

F) (1, 2.3)

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled by the following mathematical expression:

y = kx

Where:

In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 9.2/4

Constant of proportionality (k) = 2.3

Therefore, the required equation is given by:

y = kx

y = 2.3x

In conclusion, we would use an online graphing calculator to determine the ordered pairs that the line passes through.

Read more on proportional relationship here: brainly.com/question/28350476

#SPJ1

Answer: Stem-and-leaf plot, because you can see each individual data point.

Step-by-step explanation:im taking the test.

Answer:stem and leaf plot

The Variation of Parameters is a method used to find a particular solution for ordinary differential equations (ODES). The method involves finding the general solution to the homogeneous equation and then using that to find a particular solution to the non-homogeneous equation.

For the given ODES:

(a) y" - 2y' + y = et^2

First, we need to find the general solution to the homogeneous equation y" - 2y' + y = 0. The characteristic equation is r^2 - 2r + 1 = 0, which has a repeated root r = 1. Therefore, the general solution to the homogeneous equation is yh = c1e^t + c2te^t.

Next, we use the Variation of Parameters to find a particular solution. We assume that the particular solution has the form yp = u1e^t + u2te^t, where u1 and u2 are functions of t. We then find the first and second derivatives of yp and substitute them into the original equation. After simplifying, we obtain a system of equations for u1' and u2'. We solve for u1' and u2' and then integrate to find u1 and u2. Finally, we substitute u1 and u2 back into the equation for yp to find the particular solution.

(b) y" + y = sec(x)

Similarly, we first find the general solution to the homogeneous equation y" + y = 0. The characteristic equation is r^2 + 1 = 0, which has complex roots r = i and r = -i. Therefore, the general solution to the homogeneous equation is yh = c1cos(x) + c2sin(x).

Next, we use the Variation of Parameters to find a particular solution. We assume that the particular solution has the form yp = u1cos(x) + u2sin(x), where u1 and u2 are functions of x. We then find the first and second derivatives of yp and substitute them into the original equation. After simplifying, we obtain a system of equations for u1' and u2'. We solve for u1' and u2' and then integrate to find u1 and u2. Finally, we substitute u1 and u2 back into the equation for yp to find the particular solution.

(c) y" + y = sin^2(x)

The general solution to the homogeneous equation y" + y = 0 is the same as in part (b). We use the Variation of Parameters to find a particular solution in the same way as in part (b), but with the right-hand side of the equation being sin^2(x) instead of sec(x).

Know more about Variation of Parameters here:

https://brainly.com/question/13258421

#SPJ11

Milo is 8.09 miles from the dock.

Here we can use the Law of Cosines,

which states that c² = a² + b² - 2abcos(C),

Where c is the side opposite the angle C in a triangle.

Call the distance from the dock to the point where Milo changes direction "a", the distance Milo sails in the new direction "b", and the angle between these two sides "C".

We know that a = 7 miles and b = 4 miles.

To find C, we can use the fact that Milo changes direction by 5π/36 radians.

Since he turned to the right, we can say that he turned by,

⇒ 360 - 5π/36 = 355π/36 radians.

This is the angle between the two sides of the triangle.

Now we can plug these values into the Law of Cosines to find the distance from Milo to the dock:

⇒ c² = a² + b² - 2abcos(C)

⇒ c² = 7² + 4² - 2(7)(4)cos(355π/36)

⇒ c² = 49 + 16 - 56cos(355π/36)

⇒ c² = 65.47

Taking the square root of both sides, we get:

c = 8.09 miles (rounded to 2 decimal places)

Therefore, Milo is 8.09 miles from the dock.

To learn more about trigonometric ratios visit:

https://brainly.com/question/29156330

#SPJ12