b. If Aᵀy = c has a solution and Ax = 0, then x is perpendicular to ___.

The answer to question (a) that is if Ax = b has a solution and [tex]A^{T}[/tex] y = 0 then y is **perpendicular** to b

Answer to question (b) that is if [tex]A^{T}[/tex] y = c has a solution and Ax = 0 then x is perpendicular to c.

a) As Ax = b has a **solution** for x this means b lies in the column space of A. We also know that [tex]A^{T}[/tex] y = 0. This means y lies in the orthogonal complement of the **column space** of A or in the left null space of A. Therefore y is perpendicular to b

b) We see [tex]A^{T}[/tex] y = c has a solution. This tells us that c lies in the row space of A and also from the given Ax = 0 we can deduce that x lies in the null space of A or the **orthogonal **complement of** row space** of A. Therefore evidently x will be perpendicular to c

Determine whether AT has a **row space** same as column space of A

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Maggie's brother is 3 years younger than four times her age. The sum of their ages is 42.How old is Maggie?Maggie isyears old.

The **age **of Maggie is 9 years and her brother whose age 3 years less than four **times **Maggie's **age **is 33 years old.

**What is age?**

**Age **is the difference in days, months, and years between the day, month, and year of birth and the day, month, and year of the event, expressed in the largest completed unit of solar time, such as years for adults and children and months, weeks, days, hours, or minutes of life, as appropriate, for infants under one year of **age **(Gregorian calendar).

Let the ages of Maggie and her brother be X and Y.

There are two condition given in the question through which we can form a** system of equation **containing two equations.

First **condition**: The sum of their **ages **is 42.

Therefore,

X + Y = 42

Second **Condition**: Maggie's brother is 3 years younger than four times her age.

Therefore,

4X - 3 = Y

We get the **system of equation**:

X + Y = 42

4X - 3 = Y

Solving this** system of equation**

4X - 3 = Y

4X - 3 = 42 - X

X = 45/5

**X = 9**

Putting the value of X in one of the **equation**:

Y = 42 - X

Y = 42 - 9

**Y = 33**

Therefore, **age **of Maggie is 9 years and **age **of her brother is 33 years.

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Look at triangle ABC on the coordinate plane. 1 Which coordinate plane shows triangle ABC after a reflection over the y-axis?

We a figure is being reflected over the y-axis, the y-coordinates of its point will not change. However, the x-coordinates will be multiplied by **-1**.

Given points of the figure:

Point A: **-5,-2**

Point B: **-4,-4**

Point C: **-6,-4**

Let's now determine the new points of the figure once reflected over the **y-axis**.

Point A: -5,-2 ➜** Point A'**: (-5)(-1),-2 = **5,-2**

Point B: -4,-4 ➜** Point B'**: (-4)(-1),-4 = **4,-2**

Point C: -6,-4 ➜ **Point C'**: (-6)(-1),-4 = **7,-4**

Looking at the

While sailing a boat offshore, Bobby sees a lighthouse and calculates thatthe angle of elevation to the top of the lighthouse is 3°. When she sails her boat700 m closer to the lighthouse, she finds that the angle of elevation is now 5°.How tall, to the nearest tenth of a meter, is the lighthouse?

Given

While sailing a boat offshore, Bobby sees a lighthouse and calculates that

the angle of elevation to the top of the lighthouse is 3°.

When she sails her boat 700 m closer to the lighthouse, she finds that the angle of elevation is now 5°.

To find:

How tall, to the nearest tenth of a meter, is the lighthouse?

Explanation:

It is given that,

While sailing a boat offshore, Bobby sees a lighthouse and calculates that

the angle of elevation to the top of the lighthouse is 3°.

When she sails her boat 700 m closer to the lighthouse, she finds that the angle of elevation is now 5°.

That implies,

[tex]\tan3\degree=\frac{y}{x+700}[/tex]Also,

[tex]\begin{gathered} \tan5\degree=\frac{y}{x} \\ y=x\tan5\degree \end{gathered}[/tex]Therefore,

[tex]\begin{gathered} \tan3\degree=\frac{x\tan5\degree}{x+700} \\ (x+700)\tan3\degree=x\tan5\degree \\ x\tan3\degree+700\tan3\degree=x\tan5\degree \\ (\tan5\degree-\tan3\degree)x=700\tan3\degree \\ 0.0351x=36.6854 \\ x=1045.7m \end{gathered}[/tex]Then,

[tex]\begin{gathered} \tan5\degree=\frac{y}{1045.7} \\ y=1045.7\tan5\degree \\ y=91.5m \end{gathered}[/tex]**Hence, the height of the light house is, 91.5m.**

A fair die is rolled 4 times. What is the probability of having no 1 and no 3 among the rolls? Round your answer to three decimal places.

**Answer:**

**Step-by-step explanation:**

You have to assume each roll is independent. The probability of rolling a fair die is 1/6. When you roll the die, you only care about 2,4,5, and 6 since you do not want to get 1 or 3. So the probability is of getting a 2,4,5 and 6 is 4/6.

You could of also see it as the probability of NOT getting a 1 or 3 is:

[tex]1-\frac{2}{6} =\frac{4}{6}=\frac{2}{3}[/tex]

Now you roll the die 4 times with each success being 2/3

[tex]\frac{2}{3} \cdot \frac{2}{3} \cdot \frac{2}{3} \cdot \frac{2}{3} =(\frac{2}{3})^4=.197530864[/tex]

Which of the following is not a solution 3x-5<2

SIMPLIFY THE EQUALITY FIRST

[tex]3x \leqslant - 2 + 5 \\ 3x \leqslant 3 \\ \frac{3x}{3} \leqslant \frac{3}{3} \\ x \leqslant 1[/tex]

X CAN BE ALL THE NUMBERS LESS OR EQUAL TO 1

IN THE PICTURE THE ONLY OPTION THAT CONTRAST THE INEQUALITY IS **OPTION B BECAUSE IT IS GREATER THAN 1.**

**HOPE THIS HELPS**** **

**Answer:**

option B

**Step-by-step explanation:**

3x - 5 ≤ -2

add 5 to both sides

3x - 5 + 5 ≤ -2 + 5

3x ≤ 3

divided both sided by 3 to get x alone

3x/3 ≤ 3/3

x ≤ 1

option B is the only choice that is above 1.01 making it not a solution

I only need help with part "b." I have provided the answer for "a" to help.

Part b.

If we want to dilate a figure we simply multiply each x- and y-coordinate with the scale factor we want to dilate with. Therefore:

Factor of 3

[tex]3\begin{bmatrix}{2} & {4} & {1} \\ {-1} & {3} & {5} \\ {} & {} & {}\end{bmatrix}[/tex]Multiply:

[tex]\begin{bmatrix}{6} & {12} & {3} \\ {-3} & {9} & {15} \\ {} & {} & {}\end{bmatrix}[/tex]**Answer:**

HELP ASAP WILL GET THE BRAINLEST FOR THIS ANSWER PLEASE ANSWER CORRECTLY

**Answer:**

(x,y)->(x+4,y-5)

**Step-by-step explanation:**

Find a set of common points first, for example, A and A', or B and B'

Then, find the coordinates of the two points. I'm choosing B and B'.

B: (1,8) x = 1, y = 8

B':(5,3) x = 5, y = 3

from B to B', we see that the x increases by 4 and the y decreases by 5. So, the third option, (x,y)->(x+4,y-5) is correct

please help with this practice question, thank you

So the equation shown: y=x-6 is in slope intercept form (y=mx+b)

m is the slope and would be 1 in this equation.

b is the y intercept and would be -6 in this equation. Draw a dot at -6 on the y-axis and go right 1, up 1. Then down 1, left 1 to continue on the left side of the y axis

m is the slope and would be 1 in this equation.

b is the y intercept and would be -6 in this equation. Draw a dot at -6 on the y-axis and go right 1, up 1. Then down 1, left 1 to continue on the left side of the y axis

without graphing, describe the transformation of each parabola or absolute value function y = 2 |x|+ 1

Remember the following transformations of a function:

[tex]c\cdot f(x)[/tex]This transformation stretches the function over the vertical axis if c>1 and shrinks it if 0

If c is positive, the orientation is mantained, and if c is negative, the function is also flipped over (it shrinks if -1

[tex]f(x)+c[/tex]This transformation moves the function vertically *c* units. It goes up if c>0 and down if c<0.

Therefore, starting with the absolute value function:

[tex]\lvert x\rvert[/tex]Multiply the function by 2:

[tex]2\cdot\lvert x\rvert[/tex]Since 2>1, then this is a vertical stretching by a factor of 2.

Next, add 1:

[tex]2\cdot\lvert x\rvert+1[/tex]This will translate the stretched absolute value function one unit upwards.

Therefore, the complete description of the transfromation would be:

[tex]y=2\cdot\lvert x\rvert+1[/tex]**Is a vertical stretching of the absolute value function by a factor of 2, translated 1 unit upwards.**

The owners of the Movie Palace use the Illuminator 100 light bulb in their projectors, but are now considering switching to the Illuminator 100 Plus, a more powerful light bulb that projects movies onto larger screens farther away. The Illuminator 100 Plus projects movies onto screens 108 feet wide and 180 feet from the projector, while the Illuminator 100 projects movies onto screens only 81 feet wide, as shown in the figure below. How much farther from the projector, in feet, is the screen for the Illuminator 100 Plus than the screen for the Illuminator 100 ?

Given that the illuminator 100 plus bulb movies onto larger screen farther away as shown in the diagram attached then;

Illuminator 100 plus bulb

It movies onto screens ;

108 ft wide

180 ft away from the projector

Illuminator 100 bulb

81 ft wide

? : from the projector

Here apply the idea of similarity ratios where;

The ratio

Write an expression describing all the angles that are coterminal with 346°. (Please use the variable k in your answer. Give your answer in degrees, but do not include a degree symbol in your answer.)

______ degrees

**Answer:**

346 + 360k

You can get coterminal angles by adding intervals of 360 degrees

the probability that the mean salary of the sample is less than $60,000 is? round 4 decimals if needed.

**Answer:**

0.26599

**Step-by-step explanation:**

We will assume a normal distribution for the salaries

We have the following information

Mean μ = 64000

Standard deviation σ = 6400

And we are asked to find P(X < 60000)

First find the z score corresponding to X = 60000

The z score is given by (X - μ) / σ

z score for 60000 with μ = 64000 and σ = 6400 is

z = (60000 - 64000)/6400

z = -40000/6400 = -0.625

We can either look up the P value from the z-tables or simply use a calculator

P(X < 60000) and this works out to 0.26599

help me please if you can i need to know the equation

Following the instructions provided, we shall use a graphing calculator (Desmos) to determine the equation of the circle shown by the "colorful people."

The first step is to determine the radius which we can observe from the circle itself, whose diameter spans from 0 units to 10 units along the x-axis. The radius therefore is 5 units (half of the diameter).

Observe also that the center has now moved away from the origin (0, 0), and if we move the slider very carefully for h, that would be 5 units away from the origin towards the right (along the x-axis), andk would be 7 units away from the origin) towards the bottom (along the y-axis).

After following these steps, we can replicate the circle given in the question and if we now substitute the values of h, k and r into the equation of a circle, we would end up with;

[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{Where;} \\ h=5,k=-7,r=5 \\ \text{The equation becomes;} \\ (x-5)^2+(y-\lbrack-7\rbrack)^2=5^2 \\ (x-5)^2+(y+7)^2=25 \end{gathered}[/tex]C IS BETWEEN A AND D, B IS THE MIDPOINT OF AC . IF BD =15 AND BC= 7, FIND AD

BD= 12

BC=7

Is this from a graded quiz?

50 points for this one

**Answer:**

-1, 0

**Step-by-step explanation:**

Hello!

We can test each solution for by **substituting** the value for x, and see if the inequality is **true**.

This inequality is **true**.

This inequality is **not true** because 12/7 is greater than 1.

This is inequality is **true**.

This inequality is **not true** because 27/12 is greater than 1.

The solutions that work are **-1 and 0**.

**Answer: A**

**Step-by-step explanation:**

I'm In K12" Help me Pleeasee *I Will Give "Brainlyest to The First Person"

The **correct **inequality sign for the **first** number expression is** > **and for the **second** number, the expression is **<**.

**Fraction **number consists of **two** parts, one is the** top **of the **fraction** number which is called the **numerator** and the second is the **bottom** of the **fraction **number which is called the **denominator**.

The **mixed **fractions are:

-19 5/6 = -119/6 = -19.83

-20 1/6 = -121/6 = -20.166

-19 5/6 > -20 1/6

|-19 5/6| = |-119/6| = 19.83

|-20 1/6| = |-121/6| = 20.166

|-19 5/6| < |-20 1/6|

Thus, the **correct **inequality sign for the **first** number expression is** > **and for the **second** number, the expression is **<**.

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How many 2-liter bottles of soda will you need to fill ten 500 milliliter containers?1. 4 2. 2 3. 3 4. 1 How many milliliters are 1/5 liter?1. 5002. 2003. 1004. 50

Hello there. To solve this question, we have to remember some properties about conversion of values.

1. How many 2-liter bottles of soda will you need to fill ten 500 mililiter containers?

First, multiply the number of containers by its capacity, that is

[tex]10\cdot500=5000\text{ mililiters}[/tex]Notice that 1000 mililiters is equivalent to 1 liter, hence

[tex]5000\text{ mililiters }=5\text{ liters}[/tex]To fill these containers with 2-liter bottles of soda, you'll need at least 3 bottles.

**The answer to the first question is 3.**

2. How many mililiter are 1/5 liter?

Considering 1 liter = 1000 mililiters, we have that

[tex]\dfrac{1}{5}\text{ liter }=\dfrac{1}{5}\cdot1000\text{ mililiters }=200\text{ mililiter}[/tex]Hence the answer to this question is **2. 200**

2(3x - 1) + 2(4x + 5) = 8

**Answer:**

0

**Step-by-step explanation:**

2(3x -1) + 2(4x + 5) = 8 Distribute the 2's

2(3x) + 2(-1) + 2(4x) + 2(5) = 8

6x - 2 + 8x +10 = 8 Combine like terms

14x + 8 = 8 Subtract 8 from both sides of the equaion

14x = 0 Divide both sides by 14

x = 0

help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

**Answer: .25x + 75.00 = C(x)**

**Step-by-step explanation:**

Im not the best at word problems please help.Frank knows that his first four test grades were 74, 76, 77, and 84. Use the formula x‾=x1+x2+…+xnn to find Frank's grade on the fifth test if his test average is 80.6.

Given:

Frank knows that his first four test grades were 74, 76, 77, and 84

We will find Frank's grade on the fifth test if his test average is 80.6.

So, let the fifth grade = x,

The average is the sum of the grades over the number of the grades

So,

[tex]\frac{74+76+77+84+x}{5}=80.6[/tex]Solve the expression to find x:

[tex]\begin{gathered} 74+76+77+84+x=5\cdot80.6 \\ 311+x=403 \\ x=403-311=92 \end{gathered}[/tex]So, the answer will be: **the fifth grade = 92**

Find csco, cose, and tan , where is the angle shown in the figure.Give exact values, not decimal approximations.

Let 'a' represent the unknown side of the triangle.

To solve for the unknown side, we will apply the Pythagoras theorem.

[tex]a^2=b^2+c^2^{}[/tex][tex]\begin{gathered} b=4 \\ c=5 \end{gathered}[/tex][tex]\begin{gathered} a^2=4^2+5^2 \\ a=\sqrt[]{16+25} \\ a=\sqrt[]{41} \end{gathered}[/tex]Let solve for cscθ

[tex]\begin{gathered} \csc \theta=\frac{1}{\sin \theta} \\ \sin \theta=\frac{4}{\sqrt[]{41}} \\ \text{Therefore,} \\ \csc \theta=\frac{1}{\frac{4}{\sqrt[]{41}}}=\frac{\sqrt[]{41}}{4} \end{gathered}[/tex]Let us solve for cosθ

[tex]\cos \theta=\frac{5}{\sqrt[]{41}}[/tex][tex]\begin{gathered} \frac{5}{\sqrt[]{41}} \\ \text{Rationalising} \\ \frac{5}{\sqrt[]{41}}\times\frac{\sqrt[]{41}}{\sqrt[]{41}}=\frac{5\sqrt[]{41}}{41} \end{gathered}[/tex][tex]\cos \theta=\frac{5\sqrt[]{41}}{41}[/tex]Let us solve for tanθ

[tex]\tan \theta=\frac{4}{5}[/tex]1. Line Q goes through (-6,7) and (4,-2). Write the equation of line Q.

First, find the **slope** of the line using the slope formula:

Provided two points (a,A) and (b,B) on a line, its slope is given by:

[tex]m=\frac{A-B}{a-b}[/tex]For the points (-6,7) and (4,-2), we have:

[tex]\begin{gathered} m=\frac{7--2}{-6-4} \\ =\frac{7+2}{-10} \\ =\frac{9}{-10} \\ \therefore m=-\frac{9}{10} \end{gathered}[/tex]The equation of a line in slope-intercept form, of a line with slope *m* and y-intercept *b* is:

Substitute *m=-9/10* and the coordinates of one point to find the y-intercept. Use, for instance, the point (-6,7):

Substitute *b=8/5* and *m=-9/10* to find the equation of line Q:

Write a mathematical expression for the following statement

Four times x is more than 13

**Answer:**

4x>13

**Step-by-step explanation:**

4 × X=4x

>=more than symbol

I need help with this question but no one is helping me! Can someone please help me

**Answer:**

when rounding the answer it shouldn't be the exact answer so add or multiply then once you find your product round it off and add a decimal

the mean absolute

for the following set of Determine

deviation

data: 1, 1, 3, 5, 5, 6, 8, 11

The **mean absolute **deviation is 2.5.

The **average** **distance between **each **data **value and the **mean **is known as the mean **absolute deviation **(MAD) of a data collection. A **measure **of **variance **in a **data** **collection **is the mean absolute deviation. We may determine how "**spread** **out**" the **values **in a **data **collection are by looking at the mean absolute deviation.

How to calculate the **mean deviation** from the **mean**:

Given **data**:1, 1, 3, 5, 5, 6, 8, 11

So, **mean** of the **data **is

= 1+ 1 +3 +5 +5+ 6+ 8 +11 / 8

= 40 /8=

5

Now, Mean **absolute** **deviation **is

= | 1-5| + |1-5| + |3-5 | + |5-5| + |5-5| + |6-5| + |8-5| + |11-5|/ 8

= 4 + 4 + 2+ 0 + 0+ 1 + 3 +6 /8

= 20/8

=2.5

Hence, the **mean absolute** **deviation **is is 2.5.

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State the domain and range for the graph and tell if it is a function.

The arrows indicate that the graph of the function continues beyond what can be seen in the image.

Notice that the graph does not appear to have asymptotes; then, the domain of the function is:

[tex]\text{domain}=(-\infty,\infty)[/tex]And the range is:

[tex]\text{range}=(-\infty,\infty)[/tex]Since the graph seems to continue towards the +y-direction and the -y-direction

Finally, notice that for each value of x, the graph has only one value of y. This is the key characteristic of a function; **the graph is a function.**

If F(X) = 5x-7 and G(X)= -2x+9, what is G(F(X))?O A. -10x +23O B. -10X2 +59x-63O C. -10x+38O 10XD. 10x7 - 59x+63

f(x) = 5x - 7

g(x) = -2x + 9

g(f(x)) = -2(5x -7) + 9 = -10x + 14 + 9 = -10x + 23

g(f(x)) = -10x + 23

**Answer:**

**Option A: -10x + 23**

please help me solve,the question is A cylinder with a diameter of 8 feet is cut out of a cube that measures 8 feet on each side.What is the volume of the resulting shape? ( use Pi and round to the nearest tenth.) ______ ft3

Side of cube = 8 ft

Volume of cube = Side x Side x Side

Volume of cube = 8 x 8 x 8

Volume of cube = 512 feet^3

A cylinder with diameter 8feet is cute form the cube

Height of cylinder = Side of cube

Height of cylinder = 8 feet

Diameter of cylinder = 8 feet

Radius of cylinder = 4feet

[tex]\begin{gathered} \text{Volume of cylinder =}\Pi\times radius^2\times Height \\ \text{Volume of cylinder =}\Pi\times4\times4\times8 \\ \text{Volume of cylinder =}401.92ft^3 \end{gathered}[/tex]The volume of resulting shape = Volume of cube - Volume of cylinder

Volume of resulting shape = 512 - 401.92

Volume of resulting shape = 110.08 ft^3

**Answer: 110.08 ft^3**

I need help with this practice problem solving• I believe the subject is complex numbers and vectors I will send an additional picture that goes along with this, it is a graph, use the graph to answer this

Solution

a + b = (-2, -1)

Using Parallelogram method

Calculate the perimeter for each of the following

**a) **Perimeter = **17.4 cm**

**b) **Perimeter =**210.6 cm**

**How are the perimeters calculated?**

**a) The perimeter of an irregular polygon = Sum of all the sides of the polygon.**

Converting value of all sides to centimetres.

Perimeter = 3.4 +3.2 +4.3 +3.7+2.8

= **17.4 cm**

**b) The perimeter of an irregular polygon = Sum of all the sides of the polygon.**

Converting value of all sides to centimetres.

Perimeter = 29.1+25.3+30+28.6+32.6+36.5+28.5

=**210.6 cm**

**What is the perimeter of a polygon?**

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State one rational number between -0.45 and -0.46 (answer must be in decimal form.)
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