A
ABCD FECG
2
B
F
6
4
5
E
100°
120°
G
W
D
w = [?]°
5
60°
C

The dot product of the two matrices D and n is determine as (4, - 7).

The dot product of the two matrices is calculated as follows;

n = (-2, -1), and D = [-4   2]

                               [4    3]

D.n =  (-2, -1). [-4   2]  = (-2 x -4) + (-1 x 4) = 4

                     [4    3]  = (-2 x 2) + (-1 x 3) = -7

D.n = (4, - 7)

Thus, the dot product of the two matrices D and n is determine as (4, - 7).

Learn more about matrices here: https://brainly.com/question/1821869

#SPJ1

Answer:

x=6, y=4

Step-by-step explanation:

x - y = 2

2x = 3y => 2x - 3y = 0

x - y = 2 | ×(-2) => -2x + 2y = -4

2x - 3y = 0

-2x + 2y = -4

2x - 3y = 0

___________

0 - y = - 4 | ×(-1)

y = 4

Substitution in x - y = 2:

x - 4 = 2 | +4

x = 2+4 = 6

     If the question should read as the following, then I hope my answer will help;       -3 +7 _ -10 - 2

Answer: A. >

Step-by-step explanation:

  Given:

-3 + 7 _ -10 - 2

  Simplify both sides by combining like terms:

4 _ -12

  Compare, knowing that 4 is greater than -12:

4 _ -12

4 > -12

             A. >

Answer:

  318

Step-by-step explanation:

The rate of 5.3% is an annual rate, and specifies the amount of interest earned in a 12-month period by the principal amount of the CD. The interest amount is found by multiplying the interest rate by the principal amount.

__

The amount of the penalty is 5.3% of 6000:

  0.053 × 6000 = 318

Wendy paid a penalty of 318 for her early withdrawal.

Answer:

6

Step-by-step explanation:

Answer:

2 or A

Step-by-step explanation:

Correct on edge22

If these coordinates are translated two units down, we will subtract 2 units from the y axis to have A(2, -1), B(0, -3) and C(2, -3)

Translation is a transformation technique of changing the position of an object on the xy-plane.

Given the following coordinate of a triangle expressed as:

A(2, 1)

B(0, -1)

C(2, -1)

If these coordinates are translated two units down, we will subtract 2 units from the y axis to have:

A(2, -1)

B(0, -3)

C(2, -3)

Learn more on translation here; https://brainly.com/question/1046778

#SPJ1

The amount of money that Phyllis invested at each given rate of 4 and 6 percent is = $394.57 and $591.86 respectively.

The time the investment lasted= 12 years.

Simple interest = 1579.05 - 800= $779.05

The principal capital= $800

Rate of the both capital invested;

= SI × 100/P ×T

= 779.05 × 100/800 × 12

= 77,905/9600

= 8.11%

To find the amount of money that Phyllis invested at each given rate,

Rate 1 = 4/8.11× 800

= 3200/8.11

= $394.57

Rate 2 = 6/8.11× 800

= 4800/8.11

= $591.86

The amount of money that Phyllis invested at each given rate of 4 and 6 percent is = $394.57 and $591.86 respectively.

Learn more about simple interest here:

https://brainly.com/question/20690803

#SPJ

Volume is a three-dimensional scalar quantity. The volume of the rectangular prism is 200 in³.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of the rectangular prism of the length of 8 inches, the width of 2 inches, and the height of 12 1/2 inches can be written as,

The volume of the rectangular prism = 8in × 2in × 12.5in

                                                               = 200 in³

Hence, The volume of the rectangular prism is 200 in³.

Learn more about Volume:

https://brainly.com/question/13338592

#SPJ1

The option that correctly replaces the question mark in Aisha's proof is SAS (Option C). See it explained below.

Mathematical proofs are statements that are used to demonstrate that a mathematical expression or logic of true.

Since the portion of the question that shows the question mark is missing, we can rewrite the proof as follows:

Step 1

AB Dissects BC

AE ║ BD

Reason - It is given

Step 2

BC ≅ BE

Reason -  Definition of Segment Bisector

Step 3

∠ABE ≅ ∠CBD

Step 4

∠BCD ≅ ∠BEA

Reason

Alternative Interior Angles

Step 5

ΔBCD ≅ ΔBEA

Reason

SAS Postulate

Step 6

QED

Learn more about mathematical proofs at:
https://brainly.com/question/13259961

#SPJ1

The ABEF is a parallelogram because DC is extended to point F; AB ≅ FE and FA ≅ BE.

In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.

We have ABCD is a parallelogram.

BE is perpendicular to FC

FA is perpendicular to FC

As we know in the parallelogram ABCD:

AB ≅ DC

AD ≅ CB

As the DC is extended to F

So, AB ≅ FE

And BE is perpendicular to FC

       FA  is perpendicular to FC  (given)

∴ FA ≅ BE

∴ ABEF is a parallelogram.

Thus, the ABEF is a parallelogram because DC is extended to point F; AB ≅ FE and FA ≅ BE.

Learn more about the parallelogram here:

brainly.com/question/1563728

#SPJ1

Answer:

12.5

Step-by-step explanation:

divide 43.75 by 3.5 to get your answer

Answer:

40 dollars

Step-by-step explanation:

We can use a ratio to solve the problem

5 pounds         50 pounds

----------------  = -----------------

4 dollars            x dollars

Using cross products

5 * x = 4 * 50

5x = 200

Divide by 5

5x/5 = 200/5

x = 40

40 dollars

Step-by-step explanation:

[tex]\sf 5 \: pounds \longrightarrow 4 \: dollars[/tex]

[tex]\sf 1\: pounds \longrightarrow \dfrac{4}{5} \: dollars[/tex]

[tex]\sf 50\: pounds \longrightarrow \dfrac{4}{5}×50 \: dollars[/tex]

[tex]\sf \longmapsto 40 \: dollars[/tex]

The midpoint theorem simply states that the line segment that joins the two sides of the triangle is parallel to the third side.

Your information is incomplete. Therefore, an overview of the theorem will be given. It should be noted that the midpoint theorem states that the line drawn through the mid point of one side of the triangle is parallel to another side.

To find the midpoint, one can measure the distance between the two end points and divide the results by 2.

Learn more about theorem on:

https://brainly.com/question/343682

#SPJ1

The choice in the solution set of the equation 4x = 30 is x = 7.5

The equation is given as:

4x = 30

Divide both sides of the equation by 4

4x/4 = 30/4

Evaluate the quotients

x = 7.5

Hence, the choice in the solution set of the equation 4x = 30 is x = 7.5

Read more about equations at:

https://brainly.com/question/2972832

#SPJ1

Answer:

[tex]31.8\%[/tex]

Step-by-step explanation:

The area of the circle is [tex]A=\pi r^2=\pi(4)^2=16\pi[/tex]

The area of the triangle is [tex]A=\frac{bh}{2}=\frac{8*4}{2}=\frac{32}{2}=16[/tex]

Hence, the probability of a randomly selected point within the circle falls in the red shaded area is [tex]\frac{16}{16\pi}=\frac{1}{\pi}\approx0.318\approx31.8\%[/tex]

Answer:

See below for answers and explanations

Step-by-step explanation:

Part A

Assuming that conditions have been met for the interval, we use the formula [tex]\displaystyle CI=\bar{x}\pm t\frac{s}{\sqrt{n}}[/tex] where [tex]\bar{x}[/tex] represents the sample mean, [tex]t[/tex] represents the critical value, [tex]s[/tex] represents the sample standard deviation, and [tex]n[/tex] is the sample size.

The critical value of [tex]t[/tex] for an 80% confidence level with degrees of freedom [tex]df=n-1=25-1=24[/tex] is equivalent to [tex]t=1.317836[/tex]

Thus, we can compute the confidence interval:

[tex]\displaystyle CI=\bar{x}\pm t\frac{s}{\sqrt{n}}\\\\CI=32.64\pm1.317836\biggr(\frac{9.39}{\sqrt{25}}\biggr)\\\\CI\approx\{30.17,35.11\}[/tex]

Therefore, we are 80% confident that the true mean age of all customers is between 30.17 and 35.11 years.

Part B

The margin of error is [tex]\displaystyle t\frac{s}{\sqrt{n}}=1.317836\biggr(\frac{9.39}{\sqrt{25}}\biggr)\approx2.47[/tex]

Answer:

19i

Step-by-step explanation:

note that [tex]\sqrt{-1}[/tex] = i

[tex]\sqrt{-361}[/tex]

= [tex]\sqrt{361(-1)}[/tex]

= [tex]\sqrt{361}[/tex] × [tex]\sqrt{-1}[/tex]

= 19 × i

= 19i

Step-by-step explanation:

please mark me as brainlest

Answer:

10:

7/4π = 5.5(1decimql place)

11:

50π = 157.1(1 decimal place)

Step-by-step explanation:

the equation is (angle/360) X πr^2

Answer:

  133 miles

Step-by-step explanation:

The limited budget gives rise to an inequality that can be solved for the maximum number of miles.

__

The rental cost for m miles will be the sum of the fixed charges and the product of the mileage charge and the number of miles.

  cost = 19.95 +0.15m

We want this to be no greater than 40, so we have the inequality ...

  40 ≥ 19.95 +0.15m

This two-step inequality can be solved in the usual way:

  20.05 ≥ 0.15m . . . . . step 1, subtract 19.95 from both sides

  133.667 ≥ m . . . . . . . step 2, divide by the coefficient of the variable

The maximum whole number of miles Gabrielle can drive is 133.

Answer:

There were 67 coins in the bag, 36 of which were 50-cent coins and 31 of which were 20-cent coins.

Let x be the number of 50-cent coins in the bag,

And y be the number of 20-cent coins.

From the problem,

we know that y = x - 5,

Since there were 5 fewer 20-cent coins than 50-cent coins.

We can also set up an equation for the total value of the coins in the bag,

⇒ 0.5x + 0.2y = 24.20

Now we can substitute y = x - 5 into the equation,

⇒ 0.5x + 0.2(x - 5) = 24.20

Simplifying, we get,

⇒ 0.7x - 1 = 24.20

⇒ 0.7x = 25.20

⇒ x = 36

So there were 36 50-cent coins in the bag.

Using y = x - 5,

We can find that there were 31 20-cent coins.

Therefore, there were a total of 67 coins in the bag (36 + 31 = 67).

To learn more about equations visit:

https://brainly.com/question/29174899

#SPJ2

The point at which three or more lines intersect is the point of concurrency.

The point were three lines meet or intersect is a point of concurrency.

In other words, a point of concurrency is where three or more lines intersect in one place.

This point of concurrency is a single point shared by three or more lines.

Perpendicular bisectors, and altitudes are concurrent in every triangle.

learn more on intersection here: https://brainly.com/question/14293086

#SPJ1

Answer:

concurrency

Step-by-step explanation:

Look above for more

The only key feature that these functions have in common is that they have the same y-intercept. So the correct option is D.

Here we have the functions:

[tex]f(x) = -x^2 + 2x + 1\\\\g(x) = 2^x[/tex]

f(x) is quadratic, and g(x) is exponential.

Notice that the exponential function has a positive base, so it is increasing. For the quadratic equation we can see a negative leading coefficient, so it opens downwards.  So first and second options are false.

Also, g(x) never intersects the x-axis, so third option is false.

Finally, the y-intercepts of the given functions are:

[tex]f(0) = -0^2 + 2*0 + 1 = 1\\\\g(0) = 2^0 = 1[/tex]

So the y-intercepts are equal, meaning that the correct option is D.

If you want to learn more about y-intercepts:

https://brainly.com/question/24363347

#SPJ1

Answer:

Both f(x) and g(x) have the same y-intercept of (0, 1).

Step-by-step explanation:

I got it right on the test.

Answer:

x = 23.0

Step-by-step explanation:

To solve, you have to make the equation:

[tex]cos(64)=\frac{9}{x}[/tex]

Now multiply x to both sides:

[tex]cos(64)*x=9[/tex]

Next divide both sides by cos(64):

[tex]x=\frac{9}{cos(64)}[/tex]

x = 22.9675486404

Round to the tenth:

x = 23.0

Hope it helps and have a nice day!

By finding the minimum of the given function, we conclude that the lowest average temperature that year is 57°F.

We know that the average temperature is given by the equation:

f(x)=31cos(0.0055πx)+88

And it is in Fahrenheit degrees.

To get the lowest average temperature, we just need to find the minimum of the above function.

Remember that the minimum of the cosine function is:

cos(x) = -1

Then the lowest value of the above function is:

f(x₀) = 31*(-1) + 88 = 57

From this, we conclude that the lowest average temperature that year is 57°F, so the correct option is A.

If you want to learn more about cosine functions:

https://brainly.com/question/8120556

#SPJ1

Answer:

your answer will be 85 1/3ins

Step-by-step explanation:

16x 5 1/3 = 85.3333333333

then I took the 85 and the 1/3

and just put em together

The total volume of this squared-base pyramid based on the information provided is 2666 micrometers.

The general formula to calculate the volume of a squared-based pyramid is:

Base area: 20 x 20 = 400

400 micrometers x 20/ 3 = 2666 micrometers.

Learn more about volume in: https://brainly.com/question/14996332

#SPJ1

Step-by-step explanation:

it is not important that the triangle is right-angled.

but the distance between each pair of points is calculated via Pythagoras

c² = a² + b²

with c being the Hypotenuse (baseline opposite of the 90° angle) = distance between the end points, and a and b are the legs (= the x and y coordinate differences of the 2 end points) of the virtual right-angled triangles between each pair of points.

so,

AB² = (6 - -3)² + (-4 - -4)² = 9² + 0² = 81

AB = 9 ft

BC² = (6 - 6)² + (8 - -4)² = 0² + 12² = 144

BC = 12 ft

and now for AC, which is because of the special case of how the main triangle is placed and oriented, the same calculation as with Pythagoras for the main right-angled triangle. but I keep showing you the point distance calculation, because this is what you will need in the future for more general triangle or other shapes calculations :

AC² = (6 - -3)² + (8 - - 4)² = 9² + 12² = 81 + 144 = 225

AC = 15 ft

so, Nasir will need

9 + 12 + 15 = 36 ft

of fencing.

Answer:

Step-by-step explanation:

a)  Sum of nine and two ⇒ 9 + 2

Four multiplied by (9+2) :  

       4* (9+2)

[tex]b) \dfrac{(18-6)}{4}[/tex]

[tex]c) \dfrac{45}{3*(3+2)}[/tex]

2) a) Multiply the sum of five and eight by 6

   b) There 5 story books in 6 red bags and 8 art books in 6 blue bags. How many books are there?

3) a) 7*(8-3)

      Multiply the difference of eight and three by 7.