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3 years ago

5

Which of the following statements has the same truth value as the statement "If it is Friday, then Bruce has beans for supper."?

1 answer:

german3 years ago

6 0

<span>If Bruce does not have beans for supper, then it is not Friday.</span>

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Points H and F lie on circle c What is the length of line segment GH?

Nina [5.8K]

Answer:

6 units

Step-by-step explanation:

Given: Points H and F lie on circle with center C. EG = 12, EC = 9 and ∠GEC = 90°.

To find: Length of GH.

Sol: EC = CH = 9 (Radius of the same circle are equal)

Now, GC = GH + CH

GC = GH + 9

Now In ΔEGC, using pythagoras theorem,

$(Hypotenuse)^{2} = (Base)^{2} +(Altitude)^{2}$ ......(ΔEGC is a right triangle)

$(GC)^{2} = (GE)^{2} +(EC)^{2}$

$(GH + 9)^{2} = (9)^{2} +(12)^{2}$

$(GH )^{2} + (9)^{2} + 18GH = 81 + 144$

$(GH )^{2} + 81 + 18GH = 81 + 144$

$(GH )^{2} + 18GH = 144$

Now, Let GH = <em>x</em>

$x^{2} +18x = 144$

On rearranging,

$x^{2} +18 x - 144 = 0$

$x^{2} - 6x +24x + 144 = 0$

$x (x-6) + 24 (x - 6) =0$

$(x - 6) (x + 24) = 0$

So x = 6 and x = - 24

∵ x cannot be - 24 as it will not satisfy the property of right triangle.

Therefore, the length of line segment GH = 6 units. so, Option (D) is the correct answer.

3 0

3 years ago

Read 2 more answers

(FIRST PERSON TO ANSWER GETS BRAINLIEST!!!) A student earned $2500.75 at his summer job making $12.50 per hour. Let h represent

laiz [17]

<u>Answer:</u>

$12.50 \space\ h = 2500.75$

<u>Step-by-step explanation:</u>

We know from the question that the student earned $12.50 <em>per hour</em>.

Using this information, we can say that if the student worked for <em>h </em>hours, they would make a total of 12.50 × <em>h </em>dollars.

We also know that the total money they earned is $2500.75.

∴ Therefore, we can set up the following equation:

$\boxed {12.50 \times h = 2500.75}$

From here, if we want to, we can find the number of hours worked by simply making <em>h</em> the subject of the equation and evaluating:

<em>h </em>=<em> </em> $\frac{2500.75}{12.50}$

= 200.6 hours

5 0

2 years ago

Read 2 more answers

Help!! It's question 14

Leona [35]

Answer:

200/120 = 5/3

5/3 x 3 = 5 oz

<u>you can also do it this way:</u>

3/120 = x/200

x = 600/120 = 5

5 0

3 years ago

the store where henry's family. shops sold 10 3 times as many pounds of corn as henry's family bought. the weight of the corn is

saveliy_v [14]

Times it by 3 and see what u get try see if it work

7 0

3 years ago

Hey guys<br>im new here<br>please solve this for me with steps!<br>ill mark as the best answer

Vinil7 [7]

Answer:

The factors of $2(x+y)^2-9(x+y)-5$ is ((x+y)-5)(2x+2y+1)

Step-by-step explanation:

Given polynomial

=> $2(x+y)^2-9(x+y)-5$

To Find:

The factors of the polynomial =?

Solution:

Lets assume k = (x+y)

Then $2(x+y)^2-9(x+y)-5$ can be written as $2k^2-9k-5$

Now by using quadratic formula

k = $\frac{-b\pm\sqrt{(b^2-4ac}}{2a}$

where

a= 2

b= -9

c= -5

Substituting the values, we get

k = $\frac{-b\pm\sqrt{(b^2-4ac)}}{2a}$

k = $\frac{-(-9) \pm \sqrt{((-9)^2-4(2)(-5)}}{2(2))}$

k = $\frac{-(-9) \pm \sqrt{(81+40)}}{4}$

k = $\frac{-(-9) \pm \sqrt{(121)}}{4}$

k = $\frac{-(-9) \pm 11}}{4}$

k= $\frac{ 9 \pm 11}{4}$

k = $\frac{20}{4}$ k = $\frac{-2}{4}$

$k_1 =5$ $k_2 = -\frac{1}{2}$

$2k^2-9k-5= 2(k-5)(k+\frac{1}{2})$

Solving the RHS we get

$\frac{2}{2}(k-5)(2k+1)$

$(k-5)(2k+1)$

Substituting k = x+y

$((x+y)-5)(2(x+y+1)$

$((x+y)-5)(2x+2y+1)$

5 0

3 years ago