ABC is a straight line.




The length AB is five times the length BC .

AC =90 cm.


Work out the length AB .


(3 marks)

Answer:

Step-by-step explanation:

I am assuming the tank starts empty. It means that in 1 hour the tank has half that water, or 3600 gallons. And the good thing of lines passing through 0.0 is that the value at 1 IS the slope we need. ie 3600.

At this point it's easy to find that if in 2 hours it filled 1/10th of the tank, in 20 hours the tank will be full.

Graph done with paint, obviously not to scale.

Answer:

49/4 inches

Step-by-step explanation:

Inches below ground=  3 1/2 inches

Plant's full  height=15 3/4 inches

Height above ground = 15 3/4 inches -3 1/2 inches

63/4 - 7/2

63-14/4

49/4 inches

Answer:

[tex]12^1/_4[/tex] [tex]inches[/tex]

Step-by-step explanation:

We can make this an equation

[tex]-3 ^1/_{2}+15^3/_4[/tex]

We can make them the same denominator by looking for the GCF which we get as 2

Now we have

[tex]-3 ^2/_{4}+15^3/_4[/tex]

Do the equation and we get

[tex]12 ^1/_4[/tex] [tex]inches[/tex] as our answer

Answer:

Step-by-step explanation:

The standard form of an equation for a straight line is y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).

We can calculate the slope from the two given points, A(5,7) and B(9,-1).

Slope is Rise/Run, where Rise is the change in y and Run is the change in x.

From the two given points, starting at (5,7) and going to (9,-1):

Rise = (-1 -7) = -8

Run = (9-5) = 4

Rise/Run (slope) = -8/4 or -2

The equation becomes y = -2x + b

We can find b by entering either of the two given points and solving for b. I'll pick (5,7):

y = -2x + b

7 = (-2)*(5) + b

7 = -10 + b

b = 17

The equation is y = -2x + 17

Check this with a DESMOS graph (attached).

The equation of line AB is y= -2x +17

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

Points A(5, 7) and B(9, -1)

So, slope for the equation is

sloe= (-1 - 7)/ (9- 5)

slope = -8/ 4

slope= -2

Now, using slope- intercept form

y - b = m ( x- a)

y - 7= -2( x - 5)

y- 7 = -2x + 10

y= -2x + 17

Hence, the equation of line AB is y= -2x +17

Learn more about slope here:

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#SPJ2

Answer:

The side ST is 10. If the quadrilateral Q is reflected, and the side is 10, the others should also have 10 as the side for ST.

Answer:

18.06

Step-by-step explanation:

7+6=13

34+38=72

13 IS 18.06 PERCENT OUT OF 72.

Answer:

Percentanges are factors so

41 Women + 44 Men = 85 shoppers

7 Women + 6 Men = 13 Online shoppers

13 out of 85 13/85 = 15% of total people surveyed shop online

Step-by-step explanation:

Hope this helps! BH

Answer:2/3

Step-by-step explanation:

10-4=6

12-8=4

4/6=2/3

Answer:

1.12+8.13-3.5=5.75

2.6×300=780

Answer:

1) 5.75

2) 780

Step-by-step explanation:

1.12+8.13=9.25

9.25-3.5=5.75

Multiple 26x300, then move two decimal places to the right

3 exponent 2 × 5 exponent 1 × 7 exponent 1

Answer:

616

Step-by-step explanation: hope it helps :)

Answer:665,830 my answer

Step-by-step explanation:

so. what have you got so far?

How can a digit have no value?

Answer:

40 miles, 2000seconds or 33minutes and 20 seconds

Step-by-step explanation:

a. multiple time by miles/hour -> 40*60/60=40 so 40 miles

b. 60+12=72 so her new speed is 72mph. next, to find the time we need to divide distance by 1/mph -> 40* 1/(72/60)=40*60/72=100/3 which is 2000seconds or33minutes and 20 seconds

Answer:

  61°

Step-by-step explanation:

We have to take the arcs at P to mean angles RPW and MPW are congruent. That means each is 58°/2 = 29°. Angle PMR is the other acute angle in right triangle PMW, so it will be the complement of 29°.

  ∠PMR = 90° -29° = 61°

Answer:

12a^9b^7

Step-by-step explanation:

Answer

12a^9b^7

Step-by-step explanation:

4x3=12

add the indices

3+6=9

2+5=7

12a^9b^7

The growth amount is given by the growth rate the duration of the growth

and how the rate is applied to each period.

The correct selections are;

Reasons:

First part;

The given formula for the annual growth rate is; [tex]A(t) = \mathbf{P \cdot \left(1 + r)^t}[/tex]

[tex]\displaystyle A(t) = \mathbf{P \cdot \left (1 + \frac{r}{[a]} \right)^{n \cdot t}}[/tex]

Where;

P = The principal

r = The rate per period

n = The number of compounding per period

t = The number of periods

In the above formula, we have that the number of compounding per periods = n

Therefore;

Which gives the fraction of the interest applied to each period as [tex]\displaystyle \frac{r}{n}[/tex]

Which gives;

[tex]\displaystyle A(t) = \mathbf{P \cdot \left (1 + \frac{r}{n} \right)^{n \cdot t}}[/tex]

Second part;

When [tex]x = \displaystyle \frac{n}{r}[/tex], we have; [tex]A(t) = \mathbf{P \cdot \left(1 + [b])^{n \cdot t}}[/tex]

[tex]\displaystyle A(t) = P \cdot \left (1 + \frac{r}{n} \right)^{n \cdot t}[/tex]

Therefore;

[tex]\displaystyle b=\frac{r}{n}[/tex]

[tex]\displaystyle \frac{1}{x} = \frac{1}{\left(\frac{n}{r} \right)} =\frac{r}{n}[/tex]

Which gives;

[tex]\displaystyle b=\frac{r}{n} = \mathbf{\frac{1}{x}}[/tex]

[tex]\displaystyle \underline{ b = \frac{1}{x} }[/tex]

Third part;

Where, n = x·r, and [tex]\displaystyle A(t) = \mathbf{P \cdot \left (1 + \frac{1}{x} \right)^{[c] \cdot t}}[/tex]

We have;

[tex]\displaystyle x= \frac{n}{r}[/tex]

[tex]\displaystyle \frac{1}{x}=\frac{r}{n}[/tex]

[tex]\displaystyle A(t) = P \cdot \left (1 + \frac{1}{x} \right)^{[c] \cdot t} = \mathbf{P \cdot \left (1 + \frac{r}{n} \right)^{[c] \cdot t}}[/tex]

Which gives;

c = n = x·r

Fourth part;

If x is a really large number, we have; [tex]\displaystyle \mathbf{\left(1 + \frac{1}{x} \right)^x}[/tex]

Where x approaches ∞, we have;

[tex]\displaystyle \frac{1}{\infty}=0[/tex]

Which gives;

[tex]\displaystyle \displaystyle \left(1 + \frac{1}{x} \right)^x= \left(1 + \frac{1}{\infty} \right)^\infty = \displaystyle \left(1 + 0\right)^\infty = 1 ^\infty = 1[/tex]

Learn more about growth rate formula here:

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Answer:

D) 16

Step-by-step explanation:

TE=8

TE is half of FE, meaning that FE is equal to double TE.

8x2=16

Hope this helps :)

Answer:

Step-by-step explanation:

42 square inches.

Step-by-step explanation:

A = 1/2 b × h

A = 1/2 x 12 x 7

A = 6 × 7

A = 42

Answer:

270°

Step-by-step explanation:

∠ PQR = 90° ( angle in a semicircle )

PRST is a cyclic quadrilateral

The opposite angles in a cyclic quadrilateral are supplementary, sum to 180°

Then

∠ PRS + ∠ PTS = 180°

∠ PQR + ∠ PRS + ∠ PTS = 90° + 180° = 270°

Answer:

$26.40

Step-by-step explanation:

Answer:

$26.40

Step-by-step explanation:

1 paper flower=$0.55

Therefore,48 paper flowers=?

cross multiplying,we have 0.55×48=$26.40

home within our geographic footprint.

Goals: Increase awareness of key homes for sale in our portfolio and generate traffic to the website for more information.

Step-by-step explanation:

the total is 8+5+7=20

the probabliliy that its gonna be 7/20

this fraction cannot be reduced

Answer: y = -66x + 201

Step-by-step explanation:

Answer:

1 is 13

2 is 13

3 is -7

4 is 7

Step-by-step explanation:

Answer:

54.28 cm²

Step-by-step explanation:

Area rectangle = 10 x 4 = 40 cm²

Area semicircle = 1/2(π(2²)) = 1/2(π(4)) = 2π ≈ 6.28 cm²

Area triangle = 1/2(4 x (10-14)) = 1/2( 4 x 4) = 2 x 4 = 8 cm²

Total Area = 40 cm² + 6.28 cm² + 8 cm² = 54.28 cm²

-Chetan K

Answer:

$114.46

Step-by-step explanation:

40.51+73.95=114.46

Answer is (5,7)

Step-by-step explanation:

In the given image, move two points from P to right and move two points left from Q, in such a way that the gap between the two squares of P and Q are equal.

Then from the middle point of the line, mark down to the X-axis where you will get 5. Likewise, from the middle point, mark left to the Y-axis.

Any doubts, please refer the attached image.

So, you will get the answer as (5,7) .

Answer:

2

Step-by-step explanation:

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

Answer:

Step-by-step explanation:

To multiply a decimal by 100, move the decimal point in the multiplicant by two places to the right. Here we multiplied the number 98.26 by 100 so we move 2 places to the right. 3. To multiply a decimal by 1000, move the decimal point in the multiplicant by three places to the right

Answer:

I'm assuming you know how to solve first degree equations, in particular how to move terms from one side to the other.

Top figure. The two angles measuring 3x and 5x-20 are congruent (they are alternate angles related to the two parallels and the transversal closing the triangle.. Now, if 3x = 5x-20 a simple solution is x=10. Now into the triangle, the sum of the internal angles has to be 180, and we already know how much x measures. 2y+4y+30 =180. Solve for y =25

Middle figure. From the bottom right corner, you can already tell that 2y+106= 180, or y=37. But 2y and x are congruent (corresponding angles), so x= 74. Pick the method you prefer to say that either 4z+6=106 (both angles are congruent to the one in the bottom corner since they're corresponding, thus they have to be equal to each other) OR 4z+6+x = 180 (they're conjugate angles to x, so their sum is 180). To get z=25

Bottom row in both cases, the two angles sum up to 90°

Left one: 4x-20+2x-16 = 90 so x = 21

Right one: 2x-30 +x+15= 90 so x = 35

Answer:

Step-by-step explanation:

Use two given points (-6, -3) and (6, -7) to find equation of the line.

The slope:

The y - intercept is also visible on the graph (0, -5):

The line is:

Answer:

[tex] \huge{ \boxed{y = - \frac{1}{3} x + 1}}[/tex]

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

From the graph to find the equation of the line we must first find the slope

The slope of a line given two points can be found by using the formula

[tex]m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\[/tex]

where

(x1 , y1) and (x2 , y2) are the points

Using the points (-6 , -3) and (6,-7) we have

[tex]m = \frac{ - 7 - - 3}{6 - - 6} = - \frac{4}{12} = - \frac{1}{3} \\ [/tex]

Next we use the slope that has been found and one of the points to find the equation of the line

To find an equation of a line when given the slope and a point we use the formula

y - y1 = m(x - x1)

where

m is the slope

( x1 , y1) is the point

From the question using slope -1/3 and point (-6,3) we have

[tex]y - 3 = - \frac{1}{3} (x - - 6) \\ y - 3 = - \frac{1}{3} (x + 6) \\ y - 3 = - \frac{1}{3} x - 2 \: \: \: \\ y = - \frac{1}{3} x - 2 + 3 \: \: [/tex]

The equation of the line in slope-intercept form is

[tex]y = - \frac{1}{3} x + 1 \\ [/tex]

Hope this helps you

[tex] = \: \: \: c = 0 \\ \\ hope \: it \: \: helps \\ \\ see \: \: the \: \: attachement[/tex]