Find an equation of the plane. the plane through the point (2, 0, 5) and perpendicular to the line x = 7t, y = 6 − t, z = 4 + 5t

Answers

Answer 1
Given:
P: (2,0,5)
L: (0,6,4)+t(7,-1,5)
and required plane, Π , passes through P and perpendicular to L.

The direction vector of L is V=<7,-1,5>.
For &Pi; to be perpendicular to V, &Pi; has V as the normal vector.

The equation of a plane with normal vector <7,-1,5> passing through a given point P(xp,yp,zp) is
7(x-xp)-1(y-yp)+5(z-zp)=0

Thus the equation of plane &Pi; passing through P(2,0,5) is
7(x-2)-y+5(z-5)=0
or alternatively,
7x-y+5z = 14+25 
7x-y+5z = 39


Related Questions

Emily measures 3 pieces of string. The first piece measures 642 cm. The second piece measures 124 cm, and the third piece is 134 cm. How many meters of string does she have altogether? (hint: 1 meter equals 100 centimeters)

Answers

9 meters. 642 + 124 + 134 = 900, there are 100 centimeters in a meter, so 900 / 100 = 9.

Martha is standing on a street corner in a big city, facing south. She walks 5 blocks to the south. Then, she turns right and walks 3 blocks. Then, she turns right as walks 2 blocks. Then, she turns right again and walks 1 block. Finally, she turns left and walks 5 blocks. What direction is she facing when she is done?

Answers

In the north direction, Martha facing if the Martha is standing on a street corner in a big city, facing south.

What is direction?

The four cardinal directions, sometimes known as cardinal points, are the four principal compass directions: north, east, south, and west, which are frequently abbreviated as N, E, S, and W.

We have:

Martha is standing on a street corner in a big city, facing south. She walks 5 blocks to the south.

Then, she turns right and walks 3 blocks. Then, she turns right as walks 2 blocks. Then, she turns right again and walks 1 block.

If we draw a line diagram, we will see:

She will be facing at North.

Thus, in the north direction Martha facing if the Martha is standing on a street corner in a big city, facing south.

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Solve using the arrow way
430-230?

Answers

To substract the numbers shown by the method known as the "Arrow way" you must rewrite 430 and substract the hundredths (In this case, it is 200). Then you have to substract the tenths to that result (Result obtained-30). This explanation is shown below:

 430 --( -200 )---> 230 --( -30 )---> 200

 Therefore, the solution of the mathematical operation 430-230, using the arrow way, is: 200 

Jose and Sue are playing a board game. If they land on a red or blue square, they lose 1 point. The inequality statement compares the magnitude of their scores at the end of the game. |−2|<|−5| What does the inequality statement show?

Answers

Final answer:

The inequality statement |−2|<|−5| shows that 2 is less than 5.

Explanation:

In mathematics, an inequality compares two expressions or values, indicating their relative size. Symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to) represent inequalities.

The inequality statement |−2|<|−5| compares the magnitude of two numbers, -2 and -5. To find the absolute value of a number, we remove the negative sign. So, |−2| is equal to 2 and |−5| is equal to 5. Therefore, the inequality statement |−2|<|−5| means that 2 is less than 5.

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What does the random variable for a binomial experiment of n trials measure?the random variable measures the number of successes out of n trials.the random variable measures the number of failures out of n trials. the random variable measures the standard deviation of n trials.the random variable measures the mean of n trials?

Answers

My answer is the random variable measures the number of successes out of n trials.

A binomial random variable is defined as the number of successes x in n repeated trials of a binomial experiment. It is more feasible to measure the number of successes than the number of failures because the more successes you have, the nearer you are to your desired goal in a binomial experiment. 

Answer:

The random variable measures the number of successes out of n trials.

Let x be a random variable that takes integer values and is symmetric, that is, p(x = k) = p(x = âk) for all integers k. what is the expected value of y = cos(xÏ) and y = sin(xÏ)?

Answers

Without knowing how [tex]X[/tex] is distributed, or what its PMF happens to be, we can't completely answer the question. However, recall that

[tex]\cos(-kx)=\cos kx[/tex]
[tex]\sin(-kx)=-\sin kx[/tex]

If [tex]Y=\cos(\pi X)[/tex], then

[tex]\mathbb E[Y]=\displaystyle\sum_{k\in\mathbb Z}\cos(k\pi)\,\mathbb P(X=k)[/tex]

By the symmetry of [tex]X[/tex],

[tex]\mathbb E[Y]=\mathbb P(X=0)+2\displaystyle\sum_{k\ge1}\cos(k\pi)\,\mathbb P(X=k)[/tex]

Splitting on the even and odd [tex]k[/tex], and using the fact that [tex]\cos(k\pi)=(-1)^k[/tex] for [tex]k\in\mathbb Z[/tex], we can write this as

[tex]\mathbb E[Y]=\mathbb P(X=0)+2\displaystyle\sum_{\ell\ge1}\bigg(\mathbb P(X=2\ell)-\mathbb P(X=2\ell-1)\bigg)[/tex]

but without knowing how [tex]X[/tex] is distributed, we can't go any further as far as I'm aware.

For [tex]Y=\sin(\pi X)[/tex], we would have

[tex]\mathbb E[Y]=\mathbb E[\sin(\pi X)]=\displaystyle\sum_{k\in\mathbb Z}\sin(k\pi)\,\mathbb P(X=k)[/tex]

but [tex]\sin(k\pi)=0[/tex] for all integers [tex]k[/tex]. Thus [tex]\mathbb E[\sin(X\pi)]=0[/tex].
Final answer:

The expected value of y = cos(xÏ) is 0 and the expected value of y = sin(xÏ) is also 0, due to the symmetry of the random variable x.

Explanation:

The expected value (mean) of y = cos(x Ï) is 0.

The expected value (mean) of y = sin(x Ï) is also 0.

Since the random variable x is symmetric, the probability of both positive and negative values cancel out, resulting in an expected value of 0 for both cosine and sine functions.

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What is the circumference of circle p? Express your answer in terms of pi , ab = 14

Answers

C=2πr hope this helps have a great day

Answer:

14 pi in.

Step-by-step explanation:

hop this helps!

HELP SUPER FAST PLS A rectangular cardboard has dimensions as shown. The length of the cardboard can be found by dividing its area by its width. What is the length of the cardboard in inches?

Rectangle with width labeled on the right, width equals 4 and 1 over 2 inches. Below the rectangle, it says, length equals question mark. Inside the rectangle, it says area equals 36 and 3 over 4 square inches

Answers

ok, so area/width=length

then they gave you mixed fractions
they want you to practice converting mixed fractions into improper fractions and dividing them

rmember, improper fractions are a/b where a>b sometimes

and also remember that [tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{ad}{bc}[/tex]


okie dokie

width
4 and 1/2=width
4+1/2=width
8/2+1/2=width
9/2=width


area=36 and 3/4
area=36+3/4
area=144/4+3/4
area=147/4

so area/width=length
[tex]\frac{\frac{147}{4}}{\frac{9}{2}}=length[/tex]
[tex]\frac{(147)(2)}{(4)(9)}=length[/tex]
[tex]\frac{294}{36}=length[/tex]
[tex]\frac{49}{6}=length[/tex]
[tex]\frac{48}{6}+\frac{1}{6}=length[/tex]
[tex]8+\frac{1}{6}=length[/tex]

so the length is [tex] 8 \space\ and \space\ \frac{1}{6} \space\ in[/tex]

Answer:

8 1/6

Step-by-step explanation:

hope it helps

Find the solution of the differential equation that satisfies the given initial condition. du/dt = (2t+sec^2t)/2u, u(0) = -3

Answers

Consider, pls, this option (see the attachment) of 3 steps.

if possible find the area of the triangle defined by the following: a=32, b=24, y=75°

Answers

If y=75 degrees is the angle between sides a and b, then yes, it is possible to calculate the area of the triangle.

To answer further, we use the sine function to do the calculation.
The area is given by
Area = absin(y)/2 = 32*24*sin(75)/2 = 370.92 to two decimal places.

kenny wants to buy gifts for all 18 of his co workers. He can buy t shirts for $10 and hats for $12. He plans on spending $200 for all 18 gifts. If Kenny wants to spend all of his money, how many of each type of gift can he buy?

Answers

10 hats, 8 t shirts = 18
10X12=120       8X10=80     12+80=200

PLZ HELP!! 20 points!

Is (3,-2) the solution to this system of equations? show how you determined your answer.

-2x-4y=2
3x+4y=8

Answers

To find if a point is a solution to a system of equations, we need to plug in the x and y values of the point into each equation, and see if the equation is true.

Let's plug it into the first equation first:

-2(3) - 4(-2) might = 2
-6 + 8 = 2

The first equation is true. 

Now, we need to check the second equation:

3(3) + 4(-2) might =8
9 - 8 does not = 8

Therefore, even if the point satisfies one equation, it does not satisfy the other. We can conclude that this is not a solution. 

Hope this helps!

One positive integer is 6 less than twice another. The sum of their squares is 468. Find the integer

Answers

I think I deserve your points and brainliest :^)

The two integers are 12 and 18.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, one positive integer is 6 less than twice another.

Let positive integer be x and the other positive integer is 2x-6

x²+(2x-6)²=468

x²+4x²-24x+36=468

5x²-24x+36-468=0

5x²-60x+36x-432=0

5x(x-12)+36(x-12)=0

(x-12)(5x+36)=0

(x-12)=0

x=12

So, 2x-6=18

Therefore, the two integers are 12 and 18.

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A cab driver is paid $6 plus $0.45 per mile driven. Which expression shows the amount of money the cab driver earns in m miles?

Answers

No expressions are showing to choose from, but it should look like:

A= amount of money earned
m= # of miles driven

Amount earned equals $6 plus ($0.45 times the # of miles driven.)

EQUATION:
A= $6 + $0.45m

Hope this helps! :)

Answer:

C/ 0.45m + 6

Step-by-step explanation:

i did the quiz

Please help me with questions 8 and 9

Answers

Problem 8

Answer: Choice A
Coordinates have been multiplied by a scale factor of 0.5

For instance
A = (-3, 4)
Multiply the coordinates by 0.5 to get
-3*0.5 = -1.5
4*0.5 = 2
So the coordinates of A' are (-1.5, 2) which is what matches what we're given above. The same will happen with B and C as well. 

-----------------------------------------------------------

Problem 9

Answer: choice C) x = 25; larger angle is 107 degrees

Work Shown:
(3x+32)+(x+48) = 180
4x+80 = 180
4x = 100
x = 25
If x = 25, then,
3x+32 = 3*25+32 = 107
x+48 = 25+48 = 73
So the larger angle is 107

James Callahan has available a 10% alcohol solution and a 60% alcohol solution. Find how many liters of each solution he should mix to make 50 liters of a 40% alcohol solution?

Answers

Let
x-------------> liters of 10% alcohol solution
y-------------> liters of 60% alcohol solution

we know that
x+y=50----------------------> x=50-y-----------------> equation 1
0.10x+0.60y=0.40*50----------> 0.10x+0.60y=20---------> equation 2

substitute 1 in 2 
0.10*(50-y)+0.60y=20---------> 5-0.10y+0.60y=20
5+0.50y=20------------> 0.50y=15-----------------> y=30
x+y=50----------> x=50-30---------> x=20

the answer is
20 liters of 10% alcohol solution
30 liters of 60% alcohol solution

Which equivalent expression will be generated by applying the Distributive Property and combining like terms in the expression 11 + 4(x + 2y + 4)?

Answers

11 + 4(x + 2y + 4)
= 11 + 4x + 8y + 16 ..........distributive property
= 4x + 8y + 27  .................combine like terms

Hayden is a manager at a landscaping company. He has two workers to landscape an entire park, Cody and Kaitlyn. Cody can complete the project in 8 hours. Kaitlyn can complete the project in 6 hours. Hayden wants to know how long it will take them to complete the project together.

Write an equation and solve for the time it takes Cody and Kaitlyn to complete the project together. Explain each step.

Answers

Answer: 3.4 h

Explanation:

1) The basis to solve this kind of problems is that the speed of working together is equal to the sum of the individual speeds.

This is: speed of doing the project together = speed of Cody working alone + speed of Kaitlyin working alone.

2) Speed of Cody

Cody can complete the project in 8 hours => 1 project / 8 h

3) Speed of Kaitlyn

Kaitlyn can complete the project in 6 houres => 1 project / 6 h

4) Speed working together:

1 / 8 + 1 / 6  = [6 + 8] / (6*8  = 14 / 48 = 7 / 24

7/24 is the velocity or working together meaning that they can complete 7 projects in 24 hours.

Then, the time to complete the entire project is the inverse: 24 hours / 7 projects ≈ 3.4 hours / project.Meaning 3.4 hours to complete the project.

Denote all work that should be done as 1. Then if Cody can complete the project in 8 hours, he can do [tex] \frac{1}{8} [/tex] per hour and if Kaitlyn can complete the project in 6 hours, then she can do [tex] \frac{1}{6} [/tex] per hour. Together they complete [tex] \frac{1}{8}+\frac{1}{6} [/tex] per hour.

Simplify this expression:

[tex] \dfrac{1}{8} +\dfrac{1}{6} =\dfrac{3}{24} +\dfrac{4}{24}=\dfrac{7}{24} [/tex].

Then it will take them to complete the project together [tex] \dfrac{1}{\frac{7}{24}} =\dfrac{24}{7} =3\dfrac{3}{7} [/tex] hours

Answer: It will take them to complete the project together [tex] 3\dfrac{3}{7} [/tex] hours.

What is the approximate volume of the cylinder with a height of 5 and a diameter of 4? round to the nearest tenths place

Answers

Formula for volume of cylinder:
V=πr²h
Here height, h= 5 units
Diameter, d= 4 units
So, radius, r= d/2 = 4/2 =2 units
Put values in formula.
V= (3.14)(2)²(5)
V=62.8 Cubic units

Answer: 62.8 cubic units

108+621 is the same as 100+ what

Answers

I think the answer you looking for is 629

If one of the 99 test subjects is randomly​ selected, what is the probability of getting a subject who is​ pregnant?

Answers

Final answer:

To calculate the probability of selecting a pregnant subject from the 99 test subjects, the exact number of pregnant subjects in the group is needed. Without this data, the probability cannot be determined.

Explanation:

To ascertain the probability of randomly selecting a pregnant subject from a group of 99 test subjects, additional information is required regarding how many subjects are actually pregnant within the group. Without this information, we cannot compute an exact probability.

However, if we had data—let's say 15 out of the 99 subjects are pregnant—the probability would then be calculated using the formula for probability, which is the number of favorable outcomes divided by the total number of possible outcomes. In this scenario, the probability would then be 15/99.

Final answer:

Without specific information on the number of pregnant subjects among the 99 test subjects, it's impossible to compute the exact probability of randomly selecting a pregnant subject.

Explanation:

To answer the question about the probability of randomly selecting a pregnant subject from the 99 test subjects, we would need to know the number of pregnant subjects within the group. Without that information, we cannot calculate the exact probability. However, if we had that information, the probability (P) of selecting a pregnant subject would be calculated as P = (Number of Pregnant Subjects) / (Total Number of Subjects), which in this case is 99.

This is an example of a probability question that falls under the broader subject of mathematics, specifically within the topic of probability and statistics commonly covered at the high school level.

Quadrilateral ABCD ​ is inscribed in this circle.



What is the measure of ∠A ?

Enter your answer in the box.

Answers

Since angle A and angle C are across from each other, they add to 180 degrees.
Given that angle C is 43 degrees
180 = 43 + A
subtract 43 from both sides
137 = A

Hope this helps!

Applying the inscribed quadrilateral conjecture, the measure of m∠A = 137°.

What is the Inscribed Quadrilateral Conjecture?

The inscribed quadrilateral conjecture states that the opposite angles in any inscribed quadrilateral in a circle measures up to 180 degrees.

Thus:

43° + m∠A = 180°

m∠A = 180 - 43

m∠A = 137°

Thus, applying the inscribed quadrilateral conjecture, the measure of m∠A = 137°.

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A hiker maintains an average speed of 3 3 /4 km/h. How many kilometers will the hiker walk in 3/5 h

Answers

Answer:

2 1/4

Step-by-step explanation:

3 3/4 times 3/5= 15/4 times 3/5=45/20=9/4=2 1/4

I did this because speed times time equals distance and we are finding distance

HOPE THIS HELPS!!!!! :)

The distance walked in 3/5 hours is 2(1/4) km.

What is speed?

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

Average speed = 3(3/4) km per hour

This can be written as,

3(3/4) km = 1 hour

15/4 km = 1 hour

15/4 km = 1 hour

Multiply 3/5 on both sides.

3/5 x 15/4 km = 3/5 hours

9/4 km = 3/5 hours

2(1/4) km = 3/5 hours

Thus,

2(1/4) km is walk in 3/5 hours.

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x y
0 -3
2 5
3 9
4 13

Which equation matches the table?
A) y = x - 3
B) y = x + 3
C) y = 4x - 3
D) y = 4x + 3

Answers

Let's prove each one:
A) y=x-3
x=0→y=0-3→y=-3=-3 ok
x=2→y=2-3→y=-1 different to 5 No

B) y=x+3
x=0→y=0+3→y=3 different to -3 No

C) y=4x-3
x=0→y=4(0)-3=0-3→y=-3=-3 ok
x=2→y=4(2)-3=8-3→y=5=5 ok
x=3→y=4(3)-3=12-3→y=9=9 ok
x=4→y=4(4)-3=16-3→y=13=13 ok

D) y=4x+3
x=0→y=4(0)+3=0+3→y=3 different to -3 No

Answer: Option C) y=4x-3

How many quarter inches long is 7 3/4

Answers

The number of quarters in 7 is 28 and the number of quarters in 3/4 is 3. Then the total number of quarters is 33.

What is a fraction number?

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.

The quarter is written as one-fourth.

[tex]\rm quarter = \dfrac{1}{4}[/tex]

We have 7 + 3/4

We know that one has 4 quarters then 7 has

→ 7 × 4 = 28

And 3/4 has three quarters.

Then the total quarter will be

[tex]\rm Number\ of \ quarter = 7 \dfrac{3}{4} \times 4 = \dfrac{33}{4} \times 4 = 33[/tex]

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Final answer:

There are 31 quarter inches in 7 3/4 inches. This is determined by converting the mixed number into an improper fraction and then dividing by ¼, which gives us 31/4 or 31 quarter inches.

Explanation:

The question asks how many quarter inches there are in 7 3/4 inches. To find this, we can convert the mixed number into an improper fraction and then divide by the fraction representing a quarter inch (¼ inch).

First, convert 7 ¾ to an improper fraction by multiplying the whole number 7 by the denominator 4 and then adding the numerator 3. This gives us 28 + 3 = 31, so 7 ¾ inches is equivalent to ⅔31/4 or 31 quarter inches. Therefore, 7 3/4 inches is 31 quarter inches long.

Select the ratios that are equivalent to 3 boys and 5 girls

Answers

You have given no choices, but here are some.
6/10
9/15
12/20
15/25

Melinda has a map of her city the map uses a scale of 1 inch equals 8 miles when does house is 1 1/2 inches from the library on the map how far apart with her house in the library be on the map if the scale is 1 inch equals 6 miles

Answers

Melinda has a map of her city the map uses a scale of 1 inch equals 8 miles when does house is 1 1/2 inches from the library on the map how far apart with her house in the library be on the map if the scale is 1 inch equals 6 miles

So, the house is 12 miles away from the library because 1 1/2*8 is 12.  Now, Just divide 12 by the new rate, 6, to get 2.  Your answer is 2 boxes away.

Hope this helped!

Two cones have a radius of 2 cm. The height of one cone is 8 cm. The other cone is 14 that height. Which of these statements is NOT true?

Answers

the correct question is 
Two cones have a radius of 2 cm. The height of one cone is 8 cm. The other cone is 1/4 that height. Which of these statements is NOT true?

the statements  in th
e attached figure

we know that 
r=2 cm
h1=8 cm
h2=(1/4)*8=2 cm
[Volume of cone 1]=(π*r²*h)/3--------> (π*2²*8)/3= 33.49 cm³
[Volume of cone 2]=(π*r²*h)/3--------> (π*2²*2)/3---------> 8π/3= 8.37 cm³

Statements A)
The volume of the smaller cone is (1/4)(1/3π • 2 • 2 • 8) cm3---------> is  true

Statements B)
The volume of the smaller cone is (1/3)(4π • 2) cm3.-----------> is  true

Statements C)
The volume of the smaller cone is (8/3)π cm3. -----------> is  true

Statements D)
The volume of the smaller cone cannot be determined because its height is unknown-----------> is not true

the answer is the Statements D)
The volume of the smaller cone cannot be determined because its height is unknown-----------> is not true

A city council consists of six democrats and five republicans. If a committee of seven people is selected, find the probability of selecting four Democrats and three republicans.

Answers

Use hypergeometric distribution where there are two categories of identical objects/persons, each with a know size.
d=number of Democrats selected
D=total number of Democrats = 6
r=number of Republicans
R=total number of Republicans =5
Then 
[tex]P(d,r)=\frac{C(D,d)C(R,r)}{C(D+R,d+r)}[/tex]
where 
[tex]C(n,r)=\frac{n!}{(n!(n-r)!)}[/tex]  = combination of r items selected from n,
D+R=total number of members = 6+5 =11
d+r=number of members selected = 7

[tex]P(d,r)=\frac{C(D,d)C(R,r)}{C(D+R,d+r)}[/tex]
[tex]P(4,3)=\frac{C(6,4)C(5,3)}{C(6+5,4+3)}[/tex]
[tex]=\frac{C(6,4)C(5,3)}{C(11,7)}[/tex]
[tex]=\frac{15*10}{330}[/tex]
[tex]=\frac{5}{11}[/tex]

Answer: the probability of selecting 4 Democrats and 3 Republicans is 5/11

Find the difference (7a-6b+7) - (8a-2)

Answers

Hey there!

Let's set up our expression:

(7a-6b+7)-(8a-2)

In order to simplify, we can use that subtraction sign and distribute it, using the distributive property. We have:

7a-6b+7-8a+2

Notice how it's plus two, because a negative times a negative two is a positive two. Now, it's a matter of finding the like terms and adding or subtracting them. These like terms can either have no variable, or have different coefficients but the same variable. That means our like terms are the 7a and -8a, and the 7 and 2. There's no like term for the 6b. That means we have:

(7a-8a) - 6b + (7+2) =

-a - 6b + 9

Hope this helps!
Other Questions
Which number set has only irrational numbers?A){-7.4, 0, 3.14}B){-56, 78, 2}C){2, 5, }D){8, 9, 10} Use the interactive to find an expression equivalent to 4x 4 2x + 3.2x 16x 12x 72x + 3 Mr kenrick made three deposits to his account to his bank account in this order 460,185, and 240 show how to use a commutative property to find the sum of the deposits mentally Rita ____________________ (perder) su bolsa. A 79 year-old male resident of a long term care facility has contracted clostridium difficile and is experiencing consequent diarrhea. auscultation of the man's abdomen indicates hyperactive bowel sounds. what processes in the man's small intestine is most likely accompanying his current status? Rank the following from smallest current to largest current.A 1200W microwave connected to 110V outlet.I=P/U=1200/110=10.9 A A 1500W water heater connected to 220V outlet.I=P/U=1500/220=6.8 A A 100W light bulb connected to 110V outlet.I=P/U=100/110=0.9 A A 2000W oven connected to a 220V outlet.I=P/U=2000/220=9.1 A A 40W Light bulb connected to a 12V battery.I=P/U=40/12=3.3 A Luis and ted both get racing hearts once in a while. when it happens to ted, he panics and thinks he is going to die. gradually, he has developed panic attacks if he even thinks that his heart is beating strongly. when luis's heart starts beating strongly, he looks to his current activity to understand what is producing the sensations (hard work). ted apparently has a high degree of: ) with the box still on the truck, the truck attains its maximum velocity. as the truck comes to a stop at the next stop light, what is the magnitude of the maximum deceleration the truck can have without the box sliding? 30 POINTSIn 50 words, explain what this quote means and why Lincoln includes it in his Gettysburg Address: "We can not dedicate -- we can not consecrate -- we can not hallow -- this ground. The brave men, living and dead, who struggled here, have consecrated it, far above our poor power to add or detract." Part A: The area of a square is (25x2 10x + 1) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points) Part B: The area of a rectangle is (81x2 9y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points) A(n) ________ occurs when a voter can wait until the day of the primary to choose which party to enroll in to select candidates for the general election. HELP!!! 100 POINTS+ BRAINLIEST for correct answerMary leaves her house to take a walk. The graph shows the distance, d, in feet from her house that Mary is at any given time, t, in minutes. How many minutes has Mary walked when she reaches the farthest point from her house? Which of the following ideas is BEST supported by the information in this paragraph? The map below shows areas of Europe controlled by Charles V (of Spain) at the time he stepped down as king. Use the map below to answer the following question:A map of Europe showing territories held by Charles (I of Spain, V of the Holy Roman Empire) at the time he stepped down as king, shaded in green. In addition to the Iberian Peninsula (aside from Portugal), Sardinia, Sicily, Naples, parts of Eastern Europe including Austria and Bohemia, parts of eastern France, and the Netherlands are shaded. Public DomainWhat does this map show about the boundaries of empires in the 16th century? (5 points)Empires outside of Spain were small and insignificant.Empires were not necessarily one continuous territory.Empires were formed according to strict geographic boundaries.Empires outside of Spain were located in Spanish-speaking regions of Europe. helppppppppppppppppppppppppppppppp there are 238 juniors at a high school. the ratio of girls to boys in the junior class 3:4. how many Juniors are girls? how many are boys? adding and subtracting fractions with unlike denominators Which statement evaluates a text?The text is a novel. The text is understandable. The text has 150 pages. The text was published in English. Consider the net of a triangular prism where each unit on the coordinate plane represents five feet. If a can of spray paint covers 25 square feet, how many cans of spray paint are needed to paint the outside of the prism blue? After reading the speech, describe what roosevelt meant by the only thing we have to fear is fear itself