Evaluate the following expressions if a = 2, b = -3, c = -1, and d = 4. then solve for
2a + C

Answer:

Yes, the bridge will hold 1 ton.

Step-by-step explanation:

The ratio of the scale of the model to the real bridge = 1:4

The test model shows the model can take 8000 ounces

The real bridge will therefore take 8000 x 4 = 32000 ounces

but,

16 ounces = 1 pound

32000 ounces = [tex]x[/tex] pounds

==> [tex]x[/tex] = 32000/16 = 2000 pounds

also,

2000 pounds = 1 ton,

therefore, the bridge will hold 1 ton

Answer:

it would be able to hold 1 ton

Step-by-step explanation:

Answer:  see proof below

Step-by-step explanation:

Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ

Use the Sum/Difference Identities:

sin(α + β) = sinα · cosβ + cosα · sinβ

cos(α - β) = cosα · cosβ + sinα · sinβ

Use the Unit circle to evaluate: sin45 = cos45 = √2/2

Use the Double Angle Identities:   sin2Ф = 2sinФ · cosФ

Use the Pythagorean Identity: cos²Ф + sin²Ф = 1

Proof LHS → RHS

LHS:                                  2sin(45 + 2A) · cos(45 - 2A)

Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)

Unit Circle:    2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]  

Expand:        2[(1/2)cos²2A  + cos2A·sin2A + (1/2)sin²2A]

Distribute:              cos²2A   + 2cos2A·sin2A + sin²2A  

Pythagorean Identity:    1 + 2cos2A·sin2A

Double Angle:                1 + sin4A

LHS = RHS:  1 + sin4A = 1 + sin4A   [tex]\checkmark[/tex]

Answer:

-3x+14≥3-2x

-3x+2x≥-14+3

-x≥-11

x≥11

8[2x/2-1/4]≤14

8[2x-1/4]≤14

16x-8/4≤14

16x-8≤56

16x≤56+8

16x≤64

x≤64/16

x≤4

Answer:

5000 rupees

Step-by-step explanation:

Given the following :

Dimension of room = 5m × 2.5m

Cost of granite = 600 rupees per square meter

Cost of marble = 1000 rupees per square meter

Additional cost of using marble instead of granite :

Area of room = Area of rectangle = Length * width

Area of room = 5m × 2.5m = 12.5m^2

Cost of using granite:

Area of room × cost of granite per square meter

12.5 × 600 = 7500 rupees

Cost of using marble:

Area of room × cost of marble per square meter

12.5 × 1000 = 12,500 rupees

Difference in cost :

(12500 - 7500) rupees = 5000 rupees

Additional cost incurred if marble is used = 5000 rupees

Answer:

P,M,R

Step-by-step explanation:

collinear points are two or more points that form a straight line

Option - B is the correct answer.

We have the following figure given in the question.

We have to determine which three points are collinear.

Three or more points are said to be collinear if they lie on a single straight line.

According to question, we have to check which three points lie on a straight line.

It can be seen that two set of points - (P, M, R) and (N, M, O) lie on the same straight line. Of the options mentioned one is - (P, M, R).

Hence, the correct option is Option - B.

To solve more questions on Collinear points, visit the link below -

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Answer:

The correct option;

136 cubic inches

Step-by-step explanation:

The dimension of the rectangular flour canister are;

Length = 5 1/2 inches (5.5 inches)

Width = 4 inches

Height = 10 inches

The dimensions of the smaller sugar canister

Length = 3 1/2 inches (3.5 inches)

Width = 3 inches

Height = 8 inches

The volume of a cube is given by the relation;

V = Length × Width × Height

Therefore, we have;

The volume of the rectangular flour canister  = 5 1/2 × 4 × 10 = 220 in³

The volume of the rectangular sugar canister  = 3 1/2 × 3 × 8 = 84 in³

The difference in volume between the two canisters = 220 in³ - 84 in³ = 136 in³

The difference in volume between the two canisters = 136 in³

Answer:

Yeah, what they said. Above.

Step-by-step explanation:

Answer:

-8, 5, 6 , |-7|, 8

Step-by-step explanation:

We can solve the absolute functions to make it easier to determine which set is from least to greatest

-8, 8, 6, 7, 5 x

7, -8, 8, 6, 5

-8, 5, 6, 7, 8

5, 6, 8, -8, 7

Therefore the group of order integers from least to greatest is -8, 5, 6 , |-7|, 8

Answer:

D

Step-by-step explanation:

Answer:

[tex]y=-\frac{2}{3}x+12[/tex]

Step-by-step explanation:

Step 1: Rule out answers

The answer cannot be B or D because the y-intercept is at 12(b = 12) and in a linear equation y=mx+b, b is the y intercept.

B has the y intercept at 18

D has the y intercept at 18

Step 2: Find the slope

The slop is the change in y over the change in x.  We can also write this as [tex]\frac{rise}{run}[/tex]

We see it lowers by 2 so we will put -2 as the numerator

We also the x value increase by 3 every time it gets lowered by 2 so the run is 3

Therefore the slope is [tex]-\frac{2}{3}[/tex]

Step 3: Plug in the the variables to get the linear equation

[tex]y=mx+b[/tex]

[tex]y=-\frac{2}{3}x+12[/tex]

Therefore the answer is A. [tex]y=-\frac{2}{3}x+12[/tex]

Answer:

[tex]\Large \boxed{{y=-\frac{2}{3}x +12}}[/tex]

Step-by-step explanation:

y = mx + b (slope-intercept form of a line)

m is slope

b is y-intercept

The y-intercept of the line is (0, 12) or 12.

y = mx + 12

The slope of the line can be found through rise over run.

(0, 12) and (18, 0) are two points on the line.

m = (y2-y1)/(x2-x1)

m = (0-12)/(18-0)

m = -12/18

m = -2/3

The slope of the line is -2/3.

y = -2/3x + 12

Answer:

[tex]P(T_1\ n\ T_2) = \frac{2}{21}[/tex]

Step-by-step explanation:

From the comments in your question; we have

Stars = 4

Triangles = 5

Circles = 3

Squares = 3

Required  

Determine the probability of both shapes being triangles

First, calculate the total

[tex]Total = 4 + 5 + 3 + 3[/tex]

[tex]Total = 15[/tex]

Next, calculate the probability of the first selected shape being a triangle;

P(T₁) = Number of triangles divided by total number of shapes

[tex]P(T_1) = \frac{5}{15}[/tex]

[tex]P(T_1) = \frac{1}{3}[/tex]

Next, calculate the probability of the second selected shape being a triangle;

P(T₂) = Number of triangles divided by total number of shapes

Because it's probability without replacement. the number of triangle left is 4 and the number of shapes left is 14;

So:

[tex]P(T_2) = \frac{4}{14}[/tex]

[tex]P(T_2) = \frac{2}{7}[/tex]

Hence:

[tex]P(T_1\ n\ T_2) = P(T_1) * P(T_2)[/tex]

[tex]P(T_1\ n\ T_2) = \frac{1}{3} * \frac{2}{7}[/tex]

[tex]P(T_1\ n\ T_2) = \frac{2}{21}[/tex]

Hence, the required probability is [tex]\frac{2}{21}[/tex]

Answer:

2/21

Step-by-step explanation:

There are 4 stars, 5 triangles, 3 circles, and 3 squares

For the first drawing there are 5 triangles and a total of 15 shapes.

p(first triangle) = 5/15 = 1/3

Since there is no replacement, for the second drawing, and one triangle has been taken, now there are 4 triangles left and 14 total shapes left.

p(second triangle) = 4/14 = 2/7

p(two triangles) = p(first triangle) * p(second triangle)

p(two triangles) = 1/3 * 2/7

p(two triangles) = 2/21

Answer22:

Step-by-step explanation:

edge2021

The height Abby climb above their original starting position is 20 feet.

Suppose the considered function whose graph is to be made is

f=f(x) f(x)

The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values

f=f(x) f(x)

are plotted on the vertical axis.

They are together plotted on the point

f(x)) (x,y) = (x, f(x))

This is why we usually write the functions as:

f(x) y = f(x)

We are given that;

Time= 12min

Now,

To find how high Abby climbed above their original starting position, we need to look at the graph and find the highest point of Abby’s climb.

We can see that Abby’s climb is represented by the blue line on the graph.

The highest point of Abby’s climb is at (6, 22), which means that after 6 minutes, Abby reached a height of 22 feet.

Since the original starting position is at (0, 2), which means that at the beginning, Abby was at a height of 2 feet, we can subtract 2 from 22 to find how high Abby climbed above their original starting position.

Abby climbed 22 - 2 = 20 feet above their original starting position.

Therefore, by the graph the answer will be 20 feet.

Learn more about graphing functions here:

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Answer:

6

Step-by-step explanation:

3 x 2

Answer:

Definition and Equation

This form of the equation of a line is called the slope-intercept form. The y-intercept of a line (b), is the y-coordinate of the point where the graph of the line crosses the y-axis. As we have seen in the Wild About Cupcakes example, it is the value of y when x = 0.

Hope it helped u if yes mark me BRAINLIEST!

Tysm!

:)

Answer: Hi!

Slope - intercept form is a type of equation (or formula.) It shows you how to graph a line and find the slope and y - intercept of that line.

Slope - intercept form looks like this: y = mx + b

M represents the slope of the line. B represents the y - intercept.

The y - intercept is where the line would intercept the y - axis. The slope is kind of like the angle the line is at (For example: it slopes downward.)

Hope this helps!

Answer:

they switched the terms 24 is term b and 16 is term a

Answer:  Need more points.

Step-by-step explanation:

If George's total point  is 5 less than susan's points then  George needs more points to  make up to susan or pass susan's points.

For example ,

g =  s - 5       where g is George's points and s is susan's point.  

As you can see for G to catch up with s you will need 5 more points.

Answer:

NP= 9

Step-by-step explanation:

MP = 15

MN = 6

Let NP be x

MN+NP=MP

6+x=15

x=15-6

x=9

The value of NP is 9

Answer:

29.4 meters

Step-by-step explanation:

Given the following :

A submarine ascended from 56.8 meters under the sea level to 27.4 meters under the sea level.

distance it moved between two positions. Use the "distance on the number line "formula

Initial Position or distance of submarine before ascension = 56.8 meters

Final position after ascension = 27.4 meters

The distance moved by the submarine between the two positions can be obtained by.

(Initial distance - Final distance)

(56.8 - 27.4) = 29.4 meters

Answer:

B

Explanation:

Line segments do not extend or extract, they come together to form 1 line instead of going in one/two directions forever.

Answer:

[tex] \frac{1}{76543^4} [/tex]

Step-by-step explanation:

We are given base that is raised to a negative power of 4, [tex] 76543^{-4} [/tex].

Another way to rewrite this is as indicated as follows: thus, [tex] a^{-x} = \frac{1}{a^x} [/tex], where, a is the base, and x is the exponent.

Therefore, an equivalent expression of [tex] 76543^{-4} [/tex] = [tex] \frac{1}{76543^4} [/tex]

Answer:

refection in the y axis

(-x,y)

therefore (-8,3)

becomes (8,3)

Answer:

a.three

b.the line containing them lies in the plane.

c.one point

Answer:

Step-by-step explanation:

[tex] \sf{Given}[/tex]

[tex] \sf{hypotenuse = 5}[/tex]

[tex] \sf{base = 2.1}[/tex]

[tex] \sf{perpendicular = x}[/tex]

Now, Let's find the value of x

Using Pythagoras theorem

[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]

Plug the values

⇒[tex] \sf{ {5}^{2} = {x}^{2} + {2.1}^{2} }[/tex]

Evaluate the power

⇒[tex] \sf{25 = {x}^{2} + 4.41}[/tex]

Swap the sides of the equation

⇒[tex] \sf{ {x}^{2} + 4.41 = 25}[/tex]

Move constant to R.H.S and change it's sign

⇒[tex] \sf{ {x}^{2} = 25 - 4.41}[/tex]

Calculate the difference

⇒[tex] \sf{ {x}^{2} = 20.59}[/tex]

Squaring on both sides

⇒[tex] \sf{x = 4.54}[/tex]

Hope I helped!

Best regards!!

Answer:

(x,y) = (2/3 , 26/3)  .. so no I'm guessing

Step-by-step explanation:

{ y = x = 8 , y=7x+4

= x + 8= 7 x = 4

= x=2/3

= y= 2/3+8

= y=26/3

= )x,y) = 2/3, 26,3

Answer:

Amna is the fastest typist.

Step-by-step explanation:

Amna = 710 words/15 minutes = 47.3 words per minute

Sara = 810 words/18 minutes = 45 words per minute

Uzma = 780 words/20 minutes = 39 words per minute

Answer:

7

Step-by-step explanation:

h,n

m,n

n,o

j,k

k,l

k,i

Answer: [tex]x = \frac{\pi}{4} \ \text{radians}, \ \ y = \frac{\sqrt{2}}{2}[/tex]

Note: pi/4 radians is equal to 45 degrees

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

To get this answer, you can use the unit circle to see that at 45 degrees or pi/4 radians, the sine and cosine value are both [tex]\frac{\sqrt{2}}{2}[/tex]

You could also use your calculator to graph y = sin(x)-cos(x) to find the x intercept in the interval [tex]0 < x < \frac{\pi}{2}[/tex] to find the approximate x intercept to be x = 0.70710678

Then note how [tex]\frac{\sqrt{2}}{2} \approx 0.70710678[/tex]

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

Or you could do the following steps

sin(x) = cos(x)

sin^2(x) = cos^2(x)

sin^2(x) = 1 - sin^2(x)

sin^2(x) + sin^2(x) = 1

2sin^2(x) = 1

sin^2(x) = 1/2

sin(x) = sqrt(1/2)

sin(x) = sqrt(2)/2

Again you'll have to turn to the unit circle, or some reference sheet, to determine the x value that makes the last equation above to be true. That x value is x = pi/4 radians.

Answer:

$3 Each

Step-by-step explanation:

27 Spent Toatal.

Soft Drink for 3.

27-3 = 24

He bought eight candy bars, so divide 24 by 8.

24/8 = 3

So each was 3 dollars.

Greetings from Brasil...

Rewriting the problem sets

A = {-7, 4, 2, 14, 21, 34, 42}

B = {...; 2; 4; 6; 8; 10; 12; 14; 16; 18; 20; 22; 24; 26; 28; 30; 32; 34; 36; 38; 40; 42;...}

C = {...; -14; -7; 0; 7; 14; 21; 28; 35; 42; 49; 56; 63; 70; 77;...}

So, according to the statement, it is desired:

A ∩ B ∩ C - the intersection between the 3 sets, that is, which numbers are present simultaneously in the 3 sets....

Looking at the sets we conclude that

Answer:

Student Ticket: $8

Adult $28

Step-by-step explanation:

To find out the price of each ticket create 2 equations, then solve for x & y

x = student tickets

y = adult tickets

25x + 28y = 984

25x + 25y = 900

To do this first put x on one side of the equation

25x = 900 - 25y

x = 36 - y

Now substitute this equation in x for the first equation

25(36 - y) + 28y = 984

Now distribute 25 in 36 - y, 900 - 25y + 28y = 984

After this combine like term, then subtract 900 from each side, 3y = 84

Then divide 3 on each side, y = 28

Lastly substitute 28 for y in any equation to solve for x, x = 8

x & y are the price of each ticket

Answer:

12.

Step-by-step explanation:

2x - 6; x = 9.

2(9) - 6

= 18 - 6

= 12.

Hope this helps!

Answer:

Step-by-step explanation:

Given,

x = 9

Now, let's find the value of x

[tex] \sf{2x - 6}[/tex]

Plug the value of x

⇒[tex] \sf{2 \times 9 - 6}[/tex]

Multiply the numbers

⇒[tex] \sf{18 - 6}[/tex]

Subtract 6 from 18

⇒[tex] \sf{12}[/tex]

Hope I helped!

Best regards!!