A rectangle has a long side of 8.5 cm length. Its perimeter is 24cm Work out the length of the shorter sides

None of the ratios is valid implies no angle lies in quadrant 4.

Angles lie in quadrant 4. Without using a calculator, it is to determine which ratio is valid from the following 1) sin =0.789, 2) tan =0.573, 3) sin =-1.083 and 4) tan = 0.841.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Since in 4th quadrat only values of cos are positive other else operators tend to give negative value so,
1 ) sin = 0.789, here ratio is positive so it does not lies in quadrant 4.
2) tan = 0.573, it is also positive so it does not lies in quadrant 4.
3) sin = -1.083 this ratio is not possible because sin lies between (-1 to +1).
4) tan =0.841, it is also positive so it does not lie in quadrant 4.

Thus, None of the ratios is valid implies no angle lies in quadrant 4.

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Answer:

Yes

Step-by-step explanation:

Estimated difference > Actual difference. Hence, 1000 is the approximate answer. 2. We can estimate the product and quotient of numbers by rounding off the numbers to the greatest place.

Answer:

-10

-5

5

Step-by-step explanation:

From the answers given, you probably mean f(x) = x^3 + 10x2 – 25x – 250

The Remainder Theorem is going to take a bit to solve.

You have to try the factors of 250. One way to make your life a lot easier is to graph the equation. That will give you the roots.

The graph appears below. Since the y intercept is -250 the graph goes down quite a bit and if you show the y intercept then it will not be easy to see the roots.

However just to get the roots, the graph shows that

x = -10

x = - 5

x = 5

The last answer is the right one. To use the remainder theorem, you could show none of the answers will give 0s except the last one. For example, the second one will give

f((10) = 10^3 + 10*10^2 - 25*10 - 250

f(10) = 1000 + 1000 - 250 - 250

f(10) = 2000 - 500

f(10) = 1500 which is  not 0.

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

f(1) = (1)^3 + 10*(1)^2 - 25(1) - 250

f(1) = 1 + 10 - 25 - 250

f(1) = -264 which again is not zero

Answer:

yes its true

Step-by-step explanation:

just took the test

Answer:

-x³ - 6x - 2

Step-by-step explanation:

We can either use long division or synthetic division to help us divide this. You could also factor to get your answer.

Answer:

D is the right ans

Step-by-step explanation:

if i write step by step it will take a long time so quick

Answer:

D.

Step-by-step explanation:

Simplify the numerator and denominator separately. Let's do the numerator first. In the numerator, we have: [tex]x^2-8x-9[/tex]. We can factor this.

[tex]x^2-8x-9=(x-9)(x+1)[/tex]

(I did this by picking two numbers that multiply to -9 and add to -8. -9 and 1 are the only possible candidates).

Now, let's simplify the denominator. The denominator is:

[tex]5x^2-45x=5x(x-9)[/tex]

Thus, all together we will have:

[tex]\frac{(x-9)(x+1)}{5x(x-9)}[/tex]

We can cancel the (x-9) term. Thus:

[tex]=\frac{x+1}{5x}[/tex]

Answer:

a) Pop

b) 30

c) 230

Step-by-step explanation:

Answer:

the nth term of the sequence is 3n+5.

now, 5th term=5×3+5=20

6th term = 6×3+5=23

is your answer...

Answer:

its 60198.6

Step-by-step explanation:

use the formula present price=orginal price(1-rate/100)^years

Answer:

(4, -1) is not a solution to the system

Step-by-step explanation:

The first point: (4,-1)  doesn't satisfy the first inequality:

[tex]y>x-5\\(-1) > 4-5\\-1>-1[/tex]

since we get to an absurd, because -1 cannot be strictly smaller than -1!

Step-by-step explanation:

(4x² + 3y) by (3x² - 4y)

(4(1)² + 3(2)) by (3(1)² - 4(2))

(4 + 6) and (3 - 8)

10 x (-5) = -50 or 50 if negatives aren't an option

Answer:

22

Step-by-step explanation:

(4×1²+3×2) × (3×1²-4×2)

(16+6)×(9-8)

22×1=22

Answer:

 I think its D?

         Hope this helped!

Answer: 2.6 for the first one

Step-by-step explanation:

First absolute deviation: 1 6 5 8 3 7 1 4 10 9

Solve using the formula and get 2.6

For the second one I do not understand the digits. Therefore I cannot solve it.

I am very sorry, please forgive me

The mean absolute deviation of the data is M = 2.6

The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.

Mean = Sum of Values / Number of Values

Given data ,

Let the total number of points be n

Now , the value of n = 10

And , the number of points on each data is given by set A

Now , the value of set A = { 1 , 6 , 5 , 8 , 3 , 7 , 1 , 4 , 10 , 9 }

So , the total sum of data = 1 + 6 + 5 + 8 + 3 + 7 + 1 + 4 + 10 + 9

The total sum of data = 54

Now , the mean number of data points = 54 / 10 = 5.4

And , the mean deviation is M

M = 1/10 | [ ( 1 - 5.4 ) + ( 6 - 5.4 ) + ( 5 - 5.4 ) + ( 8 - 5.4 ) + | ( 3 - 5.4 ) | + ( 7 - 5.4 ) + ( 1 - 5.4 ) + ( 4 - 5.4 ) + ( 10 - 5.4 ) + ( 9 - 5.4 ) |

M = ( 1/10 ) [ 4.4 + 0.6 + 0.4 + 2.6 + 2.4 + 1.6 + 4.4 + 1.4 + 4.6 + 3.6 ]

M = ( 1/10 ) [ 26 ]

M = 2.6

Therefore , the value of M is 2.6

Hence , the mean deviation is 2.6

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Answer:

h = 1/2

Step-by-step explanation:

Step 1: Write equation

2.4(5h + 10) - 3 = 27

Step 2: Distribute

12h + 24 - 3 = 27

Step 3: Combine like terms

12h + 21 = 27

Step 4: Subtract 21 on both sides

12h = 6

Step 5: Divide both sides by 12

h = 6/12

Step 6: Simplify

h = 1/2

Answer:

a

Step-by-step explanation:

Answer:

From the attached graph, the x-intercept is (13, 0)

Step-by-step explanation:

The question equation is y = x³ + 11·x² - 312·x

To graph the equation, we find the value of y for a given value of x and we plot the values on a graph as follows;

x,              y

13,            0

14,            532

15,            1170

16,            1920

17,            2788

18,           3780

19,           4902

20,           6160

21,           7560

22,          9108

23,          10810

24,          12672

25,          14700

From the graph, the x-intercept can be found at at x = 13.

The x-intercept can also be obtained by equating the right hand side of the equation to 0 (y = 0 is the x -intercept) as follows;

0 = x³ + 11·x² - 312·x

Therefore, x = 0 is one of the x-intercepts

By dividing by x, we have

x² + 11·x - 312 = 0

By completing the square we have

x² + 11·x + (11/2)² = 312+(11/2)²

(x + 11/2)² = 1369/4

x + 11/2 = ±37/2

x = 37/2 - 11/2 = 13 or x = -37/2 - 11/2 = -24

Which gives the x-intercept as (13, 0).

Answer:

Point B coordinates' are: (3.2, 1.6)

Step-by-step explanation:

Since this is a rhomboid the diagonals AC and OB, must be perpendicular to each other. Then we can find first the equation of the line where segment AC lies, seeing that this line will cross the y axis at the point (0,4), and the x axis at the point (2, 0). The line can then be obtained by calculating the slope of the segment that joins the two points, and then using that the line's y-intercept must be at the point (0, 4):

[tex]slope=\frac{0-4}{2-0} =-2[/tex]

then the equation of the line for segment AC must be:

[tex]y=-2x+4[/tex]

Next, we calculate the equation of a perpendicular line to the previous one, and that passes through the point (0, 0) to determine the equation of the line that contains the segment OB. Recall that the perpendicular line to one of slope m must have a slope given by: -1/m (the opposite of the reciprocal of "m". Then this new perpendicular line passing through (0, 0) must be given by:

[tex]y=\frac{1}{2} x+0\\y=\frac{1}{2} x[/tex]

Now we can find the point at which both lines intersect:

[tex]\frac{1}{2} x=-2x+4\\\frac{1}{2} x+2x=4\\\frac{5}{2} x = 4\\x=\frac{8}{5}[/tex]

and therefore the y value of the intersection point can be calculated via:

[tex]y=\frac{1}{2} x\\y=\frac{1}{2} (\frac{8}{5} )\\y=\frac{4}{5}[/tex]

Then, point point B must be located at an x value that doubles the x value of the intersecting point, and similarly the y value of point B must be at the double of the value of the intersection point we just calculated. That is:

Point B = [tex](2\,*\frac{8}{5} ,\,2\,*\frac{4}{5} )=(\frac{16}{5} ,\frac{8}{5}) =(3.2,1.6)[/tex]

We can see the coordinates of point B and the lines we just generated in the attached image.

Answer:

10 more men

Step-by-step explanation:

1.5 road made per man

Answer: option 4) 15°, 30°, 135°

Step-by-step explanation: because the triangle angle rule says that all the intererior angles of the triangle sum upto 180° always

Answer:

4) 15°,30°,135°

Step-by-step explanation:

The interior angles of a triangle will add up to 180°, so we have to choose an answer choice with angles that all add up to 180.

Answer #4 is correct because 15 + 30 + 135 = 180.

Answer:

  H.  $12.50

Step-by-step explanation:

Misha wants 1 1/4 yards for each of two straps, for a total of 2 1/2 yards. The ribbon costs $5 per yard, so the total cost for the two straps is ...

  (2 1/2 yards)($5 /yard) = $12.50

Answer:

x=6

Step-by-step explanation:

Answer:

x = 6

hope this helps!

Answer:

h = 40°

Step-by-step explanation:

These 2 angles are congruent due to the Corresponding Angles Theorem.

Answer:

40°

Step-by-step explanation:

The lines are parallel. We know this because of the 2 arrows that are on the lines, indicating they are parallel.

Therefore, the 2 angles are congruent by the Corresponding Angle Theorem.

So, we can set the 2 angles equal to each other.

40=h

Therefore, angle h is 40 degrees.

Answer:

1. (7/8) 2. (4/5)

Step-by-step explanation:

https://brainly.com/question/15513807 (1st question)

A torch and a battery cost 2.50 altogether. The torch costs 1.50 more than the battery.

Torch (t) = b+1.50

Torch (t) + Battery (b) = 2.50

t+b=2.50

b+1.50+b=2.50

2b=1

b=.5

Battery costs .50 and torch costs 1.50 more = 2.00

Battery = .50

Torch = 2.00

.50 + 2.00 = 2.50 = true

Total price is 2.50- torch price is 2

200/250- divide both by 50=

200/50  /   250/ 50=

4/5

Answer:

Explained below.

Step-by-step explanation:

A standard abacus is a traditional method used to perform basic mathematical calculations, such as addition, subtraction, multiplication and division.

There are 5 rods on a standard abacus.

The shape of the abacus has a series of vertical rods on which a number of beads are placed.

Each bead on a particular rod is considered as 1 unit, i.e. if there are three beads on a rod, the value of that rod is 3.

The last rod on an abacus is for the unit's place, the second last rod is for the ten's place, the third last rod is for the hundredth's place, the fourth last rod is for the thousandth's place and the fifth rod is for the ten thousandth's place.

Answer:

  x = 20%

Step-by-step explanation:

The area is the product of side lengths. If the original side is "a", then the one increased by 25% is ...

  a + 0.25·a = 1.25a

The one decreased by x is ...

  a -x·a = a(1 -x)

We want the area of the square to be the same as that of the rectangle, so we write an equation that says that, then solve for x.

  square area = rectangle area

  a^2 = (1.25a)(a)(1-x)

  1 = 1.25 -1.25x . . . . divide by a^2, eliminate parentheses

  1.25x = 0.25 . . . . . add 1.25x -1

  x = 0.25/1.25 = 0.20

  x = 20% . . . . . . expressed as a percentage

Answer:A triangle ABC with positive integer side lengths has perimeter 35, centroid G, and incenter I. If ∠GIC=90∘, what is the length of AB¯¯¯¯¯¯¯¯?

We use barycentric coordinates with reference triangle △ABC. Letting k=a+b+c, we have the displacement vectors GI→=(13−ak,13−bk,13−ck) and IC→=(ak,bk,ck−1). EFFT gives us

a2(4b+c3k−13−2bck2)+b2(4a+c3k−13−2ack2)+c2(a+b3k−2abk2)=0

. Multiplying by 3k2, writing k=a+b+c, and expanding out, the equation turns into

a2((a+b+c)(3b−a)−6bc)+b2((a+b+c)(3a−b)−6ac)+c2((a+b)(a+b+c)−6ab)=0.

Expanding further and factoring an a+b+c out, we have

(a+b+c)((a+b)(4ab−a2−b2+c2)−6abc)=0.

Notice that when c=a+b the term (a+b)(4ab−a2−b2+c2)−6abc) vanishes, so we factor further to obtain

(a+b+c)(c−a−b)(a2+b2+c(a+b)−4ab)=0⟹a2+b2+c(a+b)−4ab=0⟹(a+b)2+c(a+b)=6ab⟹35(35−c)=6ab.

From the triangle inequality, we have c≤17 and we also know 6|35−c; it's now easy to find a triple (a,b,c)=(10,14,11) satisfying the equation above, and the answer is 11.

Hope this helps......

Answer:

a = -20/9.

Step-by-step explanation:

We can write it as

f(x) = a(x - 7)(x + 1)

When x = -2 and y = -20   (at the point(-2, -20):

-20 = a(-2 -7)(-2 + 1)

-20 = -9*-1 a

9a = -20

a = -20/9.

Answer:

since 3x^2-7x+4=0 is in the form ax^2+bx+c=0, a=3, b=-7, c=4

Answer:

a) 16.25 centimeters

b) 6.8 centimeters

Step-by-step explanation:

We can set up a proportion for both of these problems.

a) Look at the longest side of each triangle. We can set up a fraction: 7.2/18. We can also set up a fraction for XZ and PR:

6.5/x

x represents the length you're trying to find.

Since the triangles are similar, we have an equation:

7.2/18=6.5/x

Cross multiply

16.25

XZ is 16.25 centimeters long.

b)

We can do same thing:

7.2/18=x/17

Cross multiply

6.8

QR is 6.8 centimeters long.

Hope this helps!

Answer:

QR = 6.8

XZ = 16.25

Step-by-step explanation:

We can use ratios to solve since the triangles are similar

7.2         QR

------- = ------------

18           17

Using cross products

7.2 *17 = QR*18

Divide by 18

7.2 *17/18 = QR*18/18

QR = 6.8

7.2          6.5

------- = ------------

18           XZ

Using cross products

7.2 XZ = 6.5*18

Divide by 7.2

7.2 XZ = 6.5*18/7.2

XZ = 16.25