A rectangular gate has a diagonal bar running across it.The gate is 80cm high and 2m wide.Work out the length of the bar.Give your answer in surd form..

Step-by-step explanation:

To prove :

( 1 - sin x ) ( 1 + sin x ) = sec² x

LHS : -

( 1 - sin x ) ( 1 + sin x )

Formula / Identity : -

( a - b ) ( a + b ) = a² - b²

Here,

a = 1

b = sin x

( 1 - sin x ) ( 1 + sin x )

= 1 - sin² x

Identify : -

sin² θ + cos² θ = 1

cos² θ = 1 - sin² θ

Similarly,

1 - sin² x

= cos² x

= RHS

Hence verified.

Answer:11

Step-by-step explanation:

There are 11 cuts to make 12 pieces on 1ft each

Answer:

Step-by-step explanation:

Given:

The ratio of corresponding sides (consider the order of letters in the name of figures):

Answer:

Solution given:

qrst~nkpm

since the side of similar quadrilateral are proportional so

qt/mn=rs/kp

60/42=?/35

?=60/42×35=50

missing side =50 is your answer

Answer:

The shapes are triangles with same base and height

The area of a triangle is the half of the product of the base and height

A = 1/2bh is same for both shapes, so they have same area

Answer:

-1

Step-by-step explanation:

Answer:

Yes, because Gabriel is the swimming. He was in 2nd or maybe 10th.

Answer:

Step-by-step explanation:

so first you wanna break down the 85 minutes so 1 hour is 60 minues now its 7:45 but we still have 25 minutes left sow now we add the minutes it will be 8:05

8:05 is the answer

Answer:

Step-by-step explanation:

Answer:

Christmas lights are price based shopping products

Step-by-step explanation:

From the question we understand that, Beth bought as many cheapest lights as possible. This means that she places value over quantity than quality.

The above is an illustration of price based shopping products where customers (in this case, Beth) see all products (in this case, Christmas lights) as similar products, irrespective of their different qualities (after all, they all light Christmas trees).

Because of this, the customer will opt for least expensive items, leaving the more expensive items.

Answer:

arc TQ= 69°          (44 + 25)

arc QR = 155°       (180 - 25)

arc TS = 111°         (360 - 44 - 25 - 155 - 25)

arc SQR = 335°    (360 - 25)

arc RQT = 224°    (155 + 25 + 44)

Answer:

1. C(9,4) : n=9, s=4

2. C(10,5) : r=5

3. C(5,5) : n=5

4. C(7,7) : n=6

5. C(18,17) : r=3

Step-by-step explanation:

Answer:

The area of the circle is 27

Step-by-step explanation:

Using the formula given to us, we know that the area of the circle = pi times the radius squared. This gives us an indication of what we need to do. We must first understand that the radius of the circle is 3. Multiply the radius by the 2nd power (multiply 3 by 3), and we get 9. They then ask us to substitute 3 for pi, meaning instead of pi times 9, it's 3 times nine, and 3*9=27. And there is your answer.

Answer: $5,150

Step-by-step explanation:

5000x0.03=150+5000=5,150

Answer:

About 7.84 years before the deer population is 400

Step-by-step explanation:

So first we write our equation

125(1.16)^x = 400

Then we divide all sides by 125

1.16^x=3.2

x log 1.16 = log 3.2

06445798922x=0.50514997832

x= 7.83688700862

7.83688700862 years to go!

Answer: 406 miles

Step-by-step explanation: First you have to figure out how many miles he traveles per hour and to do that you divide 174 by 3 to get 58. Then multiply that by 7 because that is the amount of hours he should be traveling to get 406

Answer:

406 miles

Step-by-step explanation:

First find how far Martin can travel in 1 hour, then multiply by 7(hours):

174 ÷ 3 = 58

58 × 7 = 406

Answer:

5x + 4

Step-by-step explanation:

4 more = +4

5 times a number = 5x

Answer:

B) x = (-5 + √10)/3 and (-5 - √10)/3 is the answer.

Step-by-step explanation:

3x² + 10x + 5 = 0

a = 3

b = 10

c = 5

Finding the Discriminant (D),

D = b² - 4ac

D = 10² - 4 × 3 × 5

D = 100 - 60

D = 40

√D = 2√10

Using quadratic formula,

x = (-b ± √D)/2a

x = (-b + √D)/2a

x = (-10 + 2√10)/2 × 3

Taking out the common factor 2,

x = (-5 + √10)/3

Similarly,

x = (-b - √D)/2a

x = (-10 - 2√10)/2 × 3

x = (-5 - √10)/3

Answer:

[tex]\huge \red {\bigg \{\frac{ - 5 + \sqrt{10}}{3}, \: \: \frac{ - 5 - \sqrt{10}}{3}\bigg \}}[/tex]

Step-by-step explanation:

[tex]3 {x}^{2} = - 10x - 5 \\ 3 {x}^{2} + 10x + 5 = 0 \\ equating \: it \: with \\ a {x}^{2} + bx + c = 0 \\ a = 3 \: \: b = 10 \: \: c = 5 \\ now \: by \: quadratic \: formula \\ x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} \\ plug \: a = 3 \: \: b = 10 \: \: c = 5 \: in \: the \\ above \: formula \\ x = \frac{ - 10 \pm \sqrt{ {(10)}^{2} - 4(3)(5) }}{2 \times 3} \\ x = \frac{ - 10 \pm \sqrt{ {100} - 60}}{6} \\ x = \frac{ - 10 \pm \sqrt{40}}{6} \\ x = \frac{ - 10 \pm2 \sqrt{10}}{6} \\ x = \frac{ 2(- 5 \pm \sqrt{10})}{6} \\ x = \frac{ - 5 \pm \sqrt{10}}{3} \\ x = \purple{ \bold{\bigg \{\frac{ - 5 + \sqrt{10}}{3}, \: \: \frac{ - 5 - \sqrt{10}}{3}\bigg \}}}[/tex]

Answer:

C. To control both unintentional research bias and participant prior beliefs

Step-by-step explanation:

Double blinding is a type of study where neither the participants nor the researchers know the treatment or intervention that the participants receive until the whole study/research is completed. This is very important because it means that the results gotten from the study have a very slim chance of being biased.

Thus,the correct answer is option C as it includes both the researcher and the participants

The original price of the gourmet candy is $44, as per linear equation.

"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, 'x' is a variable, 'A' is a coefficient and 'B' is constant."

Given, the percent of discount at Dave's candy store is 15% = 0.15.

Sale price of a gourmet candy is $37.40.

Let, the original price of the gourmet candy is x.

Therefore, [x - (x × 0.15)] = 37.40

⇒ (x - 0.15x) = 37.40

⇒ 0.85x = 37.40

⇒ x = (37.40/0.85)

⇒ x = 44

Therefore, the original price of the gourmet candy is $44.

Learn more about a linear equation here: brainly.com/question/2984088

#SPJ2

Answer:

40213........................

Answer:

5647+34566=40213 is your answer

Answer:

(364.595 ; 391.405)

Step-by-step explanation:

Given the sample data:

406, 385, 389, 383, 352, 379, 388, 343, 368, 387

Using calculator :

Sample mean, xbar = 378

Standard deviation, s = 18.74

Confidence interval :

Xbar ± Margin of error

Margin of Error = Tcritical * s/√n

TCritical at df = 24 ; 0.05 = 2.262

Margin of Error = 2.262 * 18.74/√10 = 13.405

Lower boundary = (378 - 13.405) = 364.595

Upper boundary = (378 + 13.405) = 391.405

(364.595 ; 391.405)

Answer:

[tex]BE = 4\sqrt2[/tex]

Step-by-step explanation:

Given

The attached square

Required

Find BE

First, we calculate BD (the diagonal) using Pythagoras theorem.

[tex]BD^2 = BA^2 + AD^2[/tex]

Since the shape is a square, then

[tex]BA = AD = 8[/tex]

So:

[tex]BD^2 = 8^2 + 8^2[/tex]

[tex]BD^2 = 2(8^2)[/tex]

Take square roots

[tex]BD = \sqrt{2(8^2)[/tex]

[tex]BD = \sqrt{2} * 8[/tex]

[tex]BD = 8\sqrt{2}[/tex]

BE is half BD.

So:

[tex]BE = \frac{1}{2} * BD[/tex]

[tex]BE = \frac{1}{2} * 8\sqrt2[/tex]

[tex]BE = 4\sqrt2[/tex]

Answer:

3

one

will represent

the student

Answer:

24

Step-by-step explanation:

Sara = x age

Amy = x+2        when Sara  x = 22    Amy is x + 2 = 24

Product of ages = 528 so............

    x(x+2) = 528

    x² + 2x - 528 = 0     solve for x         I did it graphically first to get x = -24, 22

    (x+24) (x-22)  = 0

   (x+24) = 0         (x-22) = 0

           x = -24             x = 22        since you really can't have a negative age

Answer:

17/5

Step-by-step explanation:

If cosθ = 12/13, find (1+cotθ)

As shown in the diagram attached,

Cotθ = 1/tanθ = adjacent/opposite

From the diagram attached,

cotθ = 12/a................... Equation 1

But we can find the value of a by using  pythagoras theorem

13² = 12²+a²

169 = 144+a²

a² = 169-144

a² = 25

a = √25

a = 5.

Substitute the value of a into equation 1

Therefore,

cotθ = 12/5

(1+cotθ) =(12/5)+1 = (5+12)/5

(1+cotθ) = 17/5

Answer:

C. 4x + x < 150

Step-by-step explanation:

x = Joey's points

4x = Liz's Points

together they have fewer than 150 points means the inequality is < 150

So the answer is:  4x + x < 150

Answer:

This may help you I think so

Answer:

seniors: 780

juniors: 1170

sophomores: 975

freshmen: 585

Step-by-step explanation:

4 + 6 + 5 + 3 = 18

3510/18 = 195

195(4) = 780

195(6) = 1170

195(5) = 975

195(3) = 585

It is equal to 1 kilometer

Please mark brainliest