In Exercises 51−56, the letters a, b, and c represent nonzero constants. Solve the equation for x
ax + b = c

Answer:

x=17

Step-by-step explanation:

These are alternate interior angles and alternate interior angles are equal when the lines are parallel

9x+23= 10x+6

Subtract 9x from each side

9x+23 -9x= 10x-9x+6

23 = x+6

Subtract 6 from each side

23-6 = x+6-6

17 =x

Answer:

-1

Step-by-step explanation:

Vector a=(1,0) if visualized as a line has points (0,0) and (1,0). This means the line is horizontal and has equation y=0.

This means we are looking for a vertical line.

Instead of lambda, I'm going to use u.

So we want a+ub=(1,0)+u(1,1). to vertical. If we visualize this as a line with points (0,0) and (1+u,u). We would need u=-1 so this would be vertical.

So vectors a=(1,0) and a+ub=(1,0)+u(1,1) are perpendicular for u=-1.

So we are saying vectors (1,0) and (0,-1) are perpendicular. If you draw these, you can get a visual confirmation.

The value of λ is -1 and is perpendicular to vector a.

A vector is a number or phenomena with two distinct properties: magnitude and direction. The term can also refer to a quantity's mathematical or geometrical representation. In nature, vectors include velocity, momentum, force, electromagnetic fields, and weight.

We have,

Vector a = (1, 0) and b = (1, 1).

Here the vector is visualized as line is horizontal and has equation y=0.

Now, we have a + λb is perpendicular to vector a.

So, a + λb = (1, 0) + λ(1, 1)

                 = (1 + λ, 1)

Now, to get the vertical component we must have λ= -1.

Then, a(1, 0) and a+λb= (1,0)+ λ(1, ) are perpendicular to λ=-1.

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Answer:

C

Step-by-step explanation:

Using the sine ratio and the exact value sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex]  = [tex]\frac{6}{a}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

a = 6[tex]\sqrt{2}[/tex]

Using the tangent ratio and the exact value tan45° = 1 , then

tan45° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{6}{b}[/tex] = 1 , so

b = 6

Answer:

75

Step-by-step explanation:

Since the two angles are on the same side of the parallelogram, they're supplementary.

x + (2x - 45) = 180

3x - 45 = 180

3x = 225

x = 75

Answer:

plotting the (x,y) coordinates in graph

Answer:

80°

Step-by-step explanation:

m<COB = 80°, it's the central angle for arc CB,

so mCB = 80°

Answer:

C

Step-by-step explanation:

==========================================================

Explanation:

"Use 3 for pi" is something I've never seen a teacher do before. Usually it's "use 3.14 for pi".

Anyway, the diameter of this cylinder is 2 inches, which cuts in half to 1 inch. This is the radius.

The height is 10 inches.

So we have r = 1 and h = 10

V = pi*r^2*h

V = 3*1^2*10

V = 30 cubic inches approximately

Answer:

V = 30

Step-by-step explanation:

1. lets find the radius

r = 1/2 diameter

2/2 = 1

r = 1

2. plug in our info into the equation!!!- using 3 for pi as said in the question

V = (pi) r^2 h

V = (3)*(1)^2*(10)

3. solve

V = 30

Answer:

[tex]\frac{1}{10} * \frac{1}{100} = \frac{1}{1000}[/tex]

1000 times

Step-by-step explanation:

Answer:

0.1% = 1 spin then

100% = ( 100×1) ÷0.1 = 1000

we are using 100% because its a sure bet it will happen but not logically

the answer is 1000

Answer:

4 :45 pm

Step-by-step explanation:

2 : 20 + 17 minutes = 2:37

2:37 + 1hr 1 minute  = 3 : 38

3 : 38 + 1 hr 7 = 4 :45 pm

Step-by-step explanation:

Right, okay, so this is a bit of a weird one. Let's go step by step.

"Today, 6 friends went out for lunch." = The number 6 is gonna be in our equation somewhere.

"Their total bill was $27.60" = so is the number 27.6

"They decided to split the bill equally" = 27.6 "split equally" (aka divided by) 6 friends is 4.6

"each paid with a $10 bill" = This is where it gets a lil weird. So, if they divided the bill among them, none of their amounts are gonna be anywhere near ten dollars. This is one of those questions that wouldn't really happen in real life. People would probably use fives instead, but whatever. So a number we'll be using for something is 10.

"How much money will each person get back?" = So we have to find the amount they all paid (10) minus the amount each one had to pay (4.6).

To put it all into a full equation...

10 - ( 27.6 / 6 )

Divide.

10 - 4.6

Subtract.

5.4

Put back into money form.

$5.40

Answer:

Each person will get back $5.40.

Answer:

if each paid a $10 bill, in total they paid $60 (cuz 10 x 6)

60 - 27.60 = 32.4

32.4/6 = 5.4 (divide the change between 6 people)

Each person will get $5.40 back.

hope it helps :)

Answer:

D.

Step-by-step explanation:

5 times a number is 5n. We need to subtract 6 from that, so we have 5n-6 for any value n.

Answer:

D. 5n - 6

Step-by-step explanation:

6 less means -6

The product of 5 and a number means 5 x n which is the same as 5n

And it wants us to subtract 6 from 5n

so we would write it as...

5n - 6

Answer:

a

Step-by-step explanation:

3x+5=17

3x=17-5

3x=12

x=4

Answer:

m<XUY = 40

Step-by-step explanation:

The central angles theorem states that in a circle, the measure of an angle with its vertex on the center of the circle is equal to the angle measure of the arc surrounding it. As a given fact, the sum of degree measures in a circle is (360) degrees. Thus, one can form the following equation:

(mZUV) + (mVUW) +(mWUX) +(mXUY) + (mYUZ) = 360

Substitute,

(-15x) + (30) + (90) + (x + 47) + (95) = 360

Simplify,

(-15x) + (30) + (90) + (x + 47) + (95) = 360

-14x + 262 = 360

Inverse operations,

-14x + 262 = 360

-14x = 98

x = -7

Substitute back into the equation for the measure of angle (<XUY)

m<XUY = x + 47

= -7 + 47

= 40

Answer:

Infenitely many solutions

Answer:

the answer is 100:60:40 hope it helps

Answer:

31

Step-by-step explanation:

To rationalise 7 + 3[tex]\sqrt{2}[/tex] , multiply by its conjugate

The conjugate of 7 + 3[tex]\sqrt{2}[/tex] is 7 - 3[tex]\sqrt{2}[/tex] , then

(7 + 3[tex]\sqrt{2}[/tex])(7 - 3[tex]\sqrt{2}[/tex]) ← expand using FOIL

= 49 - 21[tex]\sqrt{2}[/tex] - 21[tex]\sqrt{2}[/tex] - (3[tex]\sqrt{2}[/tex])²

= 49 - 18

= 31

[tex]we conclude that option B:[/tex]

[tex]y + 5 = -\frac{1}{2}*(x - 3)^2[/tex]

[tex]Is the graphed function.[/tex]

On the graph we can see a parabola that opens downwards, so it has a negative leading coefficient.

We also can see that the vertex of the parabola is on the point (3, -5)

Then the equation of the parabola is something like:

y + 5 = a*(x - 3)^2

Where a is a negative real number.

The only option of this form is option B, so we conclude that option B:

[tex]y + 5 = -\frac{1}{2}*(x - 3)^2[/tex]

Is the graphed function.

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Answer:

C i think sorry if its wrong

Step-by-step explanation:

Answer:

bottom left one

note the >, < ≤ , ≥

for x > 0 the dot should NOT be solid

Step-by-step explanation:

Answer:

here's the answer to your question

Answer:

(i) 7/10

(ii) 3/10

(iii) 1/5

(iv) Rs 40,000

Step-by-step explanation:

The fraction of the salary spent on food = 1/2

The fraction of the salary spent on rented house fee = 1/5

(i) The fraction spent for both food and rental fee = (1/2) + (1/5) = (5 + 2)/10 = 7/10

(ii) The remainder (rest) of the salary = 1 - 7/10 = 3/10

The fraction of the remainder spent for children's education = 1/3

The fraction of the total salary spent for the children's education = (1/3) × (3/10) = 1/10

(iii) The remaining portion deposited in the bank = 1 - (1/10 + 7/10)) = 2/10 = 1/5

(iv) The amount equal to portion of 1/5 of his salary deposited in the bank is Rs 8000

Let x represent his whole salary, we have;

(1/5) × x = Rs 8,000

x = 5 × Rs 8,000 = Rs 40,000

His whole salary is Rs 40,000.

Answer:

247 = j - 285

Step-by-step explanation:

Anything that is labeled with "is" will be what the entire equation is equal to. (Also because the instructions are asking for an equation which is equal to something). Also, fewer than is the subtraction of two things. In this case it will be 285 and j. In the end the equation will be:

247 = j - 285

Hope this helped.

Answer:

b) y

Step-by-step explanation:

joannes speed = 250/2.5 =100km/h

francois speed = 100-10 = 90km/h

after 5h, francois would have travelled 450

Answer:

x=6, y=4, z=8

I hope this is helpful!

Answer:

200

hope it help

Answer:

160

Step-by-step explanation:

got it right

Answer:

See pic below.

Step-by-step explanation:

Answer:

8.69 per pair

Step-by-step explanation:

Take the total cost and divide by the number of pairs

26.07 /3

8.69 per pair