After swimming to a depth of 55 feet below the surface of
the water, a fish swims back up 30 feet. Use a number line
a
to help you create an equation that shows the new location
of the fish in relation to the water's surface.
-80 -70 -60 -50 -40 -30 -20 -10 0
10
Interpret the sum in the context of the problem.
A. The equation is -55 +(-30) = -85. The fish is 85 feet below
the water's surface.
O B. The equation is -55+ 30 = -25. The fish is 25 feet below the
water's surface.
C. The equation is -55+ (-30) = -25. The fish is 25 feet below
the water's surface.
D. The equation is -55+ 30 = -85. The fish is 85 feet below the
water's surface.

Similar triangles may or may not be congruent.

The congruent criterion to use in her proof is (b) SAS theorem

From the question, we understand that she draws an angle bisector from [tex]\mathbf{\angle Q}[/tex] to side PR

This means that, either sides of angle Q are congruent. (this is represented by A i.e. angle)

When [tex]\mathbf{\angle Q}[/tex] is bisected, sides PB and RB become congruent

i.e. [tex]\mathbf{PB \cong RB}[/tex] ... (this is represented by S i.e. side)

Lastly, both triangles share a common side at QB .. (this is also represented by S i.e. side)

So, we have: SAS

Hence, the congruent criterion to use in her proof is (b) SAS theorem

Read more about similar and congruent triangles at:

https://brainly.com/question/19589236

Number of sold cappuccinos will be 60.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

A coffee shop sells lattes for $4 and cappuccinos for $3.

Last Friday, they sold 78 drinks for a total of $252.

Now,

Let number of lattes = x

Number of cappuccinos = y

Since, Last Friday, they sold 78 drinks.

So, we can formulate;

x + y = 78   ... (i)

And, Last Friday, they sold 78 drinks for a total of $252.

So, we can formulate;

4x + 3y = 252 ... (ii)

Solve equation (i) and (ii) we get;

x + y = 78

4x + 3y = 252

Multiply by 4 in equation (i) and subtract from (ii) we get;

4x + 3y - 4x - 4y = 252 - 312

- y = - 60

y = 60

And, x + y = 78

x + 60 = 78

x = 18

Thus, Number of sold cappuccinos will be 60.

Learn more about the linear expression visit:

https://brainly.com/question/28718030

#SPJ2

Part (i)

I'll use H in place of T to represent the heat of the object. That way there isn't a clash of variables lowercase t vs uppercase T.

The equation we're working with is updated to:

H(t) = 22 + a*2^(bt)

Plugging in t = 0 as the initial time value should lead to the temperature being H = 86 degrees Celsius.

So,

H(t) = 22 + a*2^(bt)

86 = 22 + a*2^(b*0)

86 = 22 + a*2^0

86 = 22 + a*1

86 = 22 + a

a+22 = 86

a = 86-22

a = 64

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

Part (ii)

We'll use the value of 'a' we found earlier. Plus we'll use the fact that H = 28 when t = 0.5 (since 30 min = 30/60 = 0.5 hr).

H(t) = 22 + a*2^(bt)

28 = 22 + 64*2^(b*0.5)

28-22 = 64*2^(0.5b)

64*2^(0.5b) = 6

2^6*2^(0.5b) = 6

2^(6+0.5b) = 6

log(  2^(6+0.5b)   ) = log(6)

(6+0.5b)*log(2) = log(6)

6+0.5b = log(6)/log(2)

6+0.5b = 2.5849625

0.5b = 2.5849625-6

0.5b = -3.4150375

b = -3.4150375/(0.5)

b = -6.830075

Answer:

3/2

Step-by-step explanation: I took the test

Answer:

look at the photo..................

Answer:

x = 4.8 , y = 4

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{KJ}{NP}[/tex] = [tex]\frac{KL}{NM}[/tex] , substitute values

[tex]\frac{x}{3}[/tex] = [tex]\frac{8}{5}[/tex] ( cross- multiply )

5x = 24 ( divide both sides by 5 )

x = 4.8

and

[tex]\frac{JL}{PM}[/tex] = [tex]\frac{KL}{NM}[/tex] , that is

[tex]\frac{6.4}{y}[/tex] = [tex]\frac{8}{5}[/tex] ( cross- multiply )

8y = 32 ( divide both sides by 8 )

y = 4

Answer:

You will need 32 ounces

Step-by-step explanation:

2 pounds x 16 = 32 ounces

300 cal / 3 oz = x / 32 oz

(300 * 32) / 3 = 3,200 calories

Step-by-step explanation:

follow the above attachment.

hope this helps you.

All numbers greater or equal to 1

Answer:

-4y(3y + 1) (9y^2 - 3y + 1)

Step-by-step explanation:

-108y^4 - 4y

= -4y(27y^3 + 1)

= -4y(3y + 1) (3^2y^2 - 3y + 1)

= -4y(3y + 1) (9y^2 - 3y + 1)

Answer:

-4y(3y + 1) (9y^2 - 3y + 1)

Answer:

59

Step-by-step explanation:

Given: a = 13, b = 6, and c = 5

(13-6)^2+2 x 5 (=10)

(13-6)^2+10

=59

Answer:

59

Step-by-step explanation:

Given,

a = 13

b = 6

c = 5

To find : ( a - b )^2 + 2c

Answer : -

( a - b )^2 + 2c

= ( 13 - 6 )^2 + 2 ( 5 )

= ( 7 )^2 + 10

= 49 + 10

= 59

Therefore,

the value of ( a - b )^2 + 2c is 59.

Answer:

10

Step-by-step explanation:

Let's call Ahmed's number x,

To solve for x,

You could also work backwards:

If he ×2 then ÷5, you would ×5 then ÷2 (doing the opposite):

Hope this helps!

Answer:

Kznnznxndnnx xkndnx xjx xjxndjxs mxmzmxmx. J xnd dnxndnxjndnx. Jx xis bx 9837ei3xid dus

Step-by-step explanation:

Szjnznz s8sbbsnsjs

Mzmzmznzm

Mzmsmxmx

Mzmxmkx

Z

Km mmx

Zkskms

Kzmz

An advantage of debt consolidation is: B. You will have one monthly payment to manage.

Debt consolidation can be defined as the way in which a person borrow  or collect a loan so as to payoff their old debt or liabilities.

One of the advantage of debt consolidation loan is that you will have one monthly payment to manage or one bill to pay  per  month instead of several bill.

Therefore the correct option is B.

Learn more about debt consolidation here:https://brainly.com/question/11199005

#SPJ1

Answer:

m∠2 = 75°

m∠1 = 105°

Step-by-step explanation:

1. First, we should recognize that the angle that's 75° and ∠2 are alternate interior angles, formed on the interior of the opposite sides of the transversal. Alternate interior angles are congruent, so m∠2 = 75°.

2. Next, ∠2 and ∠1 are a linear pair, meaning their angle measures add up to 180°. Considering that m∠2 is 75 degrees, we just have to subtract 75 from 180, and we get the measure of ∠1.

Therefore, m∠1 = 105°.

Answer:

x = 6

Step-by-step explanation:

All angles of a triangle equal 180

180 - 70 - 60 = 50

8x+2 = 50

x = 6

Answer:

x = 6

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 given angles and equate to 180

70 + 60 + 8x + 2 = 180 , collect like terms

132 + 8x = 180 ( subtract 132 from both sides )

8x = 48 ( divide both sides by 8 )

x = 6

The equation with only one unique solution is 9 − |2x − 1| = 9, with the solution x = 1/2. D.

To determine which equation has only one unique solution, let's analyze each equation:

|3 − x| = 3

In this equation, the absolute value term represents a distance.

By setting up two cases, where the absolute value is positive and negative, we can find the solutions.

Case 1:

3 - x = 3

Solving for x, we have x = 0.

Case 2:

x - 3 = 3

Solving for x, we have x = 6.

Thus, this equation has two solutions.

|x − 2| − 7 = 7

Similar to equation A, the absolute value term represents a distance.

By adding 7 to both sides, we have |x - 2| = 14.

This equation implies that the distance between x and 2 is 14.

There are two possible values for x: x = 2 + 14 = 16 and x = 2 - 14 = -12.

This equation has two solutions.

-4|x| + 1 = -3

To solve this equation, we isolate the absolute value term:

-4|x| = -4

Dividing both sides by -4:

|x| = 1

The absolute value of any number is always positive or zero.

The equation |x| = 1 has two solutions: x = 1 and x = -1.

9 − |2x − 1| = 9

The absolute value term represents a distance.

Subtracting 9 from both sides, we have |2x - 1| = 0.

The only way the absolute value of a real number can be equal to zero is if the number inside the absolute value is zero.

Thus, we set 2x - 1 = 0 and solve for x:

2x - 1 = 0

2x = 1

x = 1/2

Equation D has only one unique solution: x = 1/2.

For similar questions on unique solution

https://brainly.com/question/14282098

#SPJ8

Answer:

B4= 4-6(4-1)

B4= 4-7(3)

B4= 4-18

B4= -14

Answer:

98

Step-by-step explanation:

1. (-4)(-2) equals 14 beacuse when you muiltpy two negatives yiui get a postive.

2. 14(7) equals 98

Answer:

x° = 35°

Step-by-step explanation:

at 125° to get the opposite angle

180° - 125° = 55°

then,

x° + 90° + 55° = 180°

x° = 180° - 145°

x° = 35°

Answer:

the answer is 5...............

Answer:

[tex]5[/tex]

Step-by-step explanation:

[tex]\sf x-7[/tex]

[tex]\sf x=12[/tex]

→ [tex]\sf (12)-7[/tex]

→ [tex]\sf 5[/tex]

Answer:

continuous becasue the arrows point out meaning the go on forever

Step-by-step explanation:

Answer:

-5 divide by 28

Step-by-step explanation:

so the question supposed be " 15-20 divided by 2(4) + 20

15-20 which is also 15 + (-20)= -5

2(4)=8, 8+20=28

so it can simplify into -5 / 28

(hope it helps :)

Answer:

It will take roughly 8 weeks to save the money she needs

Step-by-step explanation:

129.89 ÷ 15.75 = 8.246984126984

Answer: 9 weeks

Explanation:

It would take her 9 weeks for her to save at least $129.89 with a leftover of $11.86.

Answer:

82/9

Step-by-step explanation:

Picture below

Answer:

25,36,49,64,81,100

................................

Answer:

Your answer is 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

Step-by-step explanation:

1 - 4  

+ 3

4 - 9

+ 5

9 - 16

+ 7

+9, +11, +13, +15, +17, +19...

Answer:

The number of protons

Step-by-step explanation:

Its the correct answer