What is the length of the hypotenuse of the triangle below ?

*Translate into an algebraic expression: How much 50% sugar syrup can you make if you have x grams of sugar?

Irina-Kira [14]

Answer:

w = x/50% = x/50/100

Step-by-step explanation:

We would turn the above question into an algebraic expression using variables.

To make a sugar syrup, we need sugar and water to form the solution.

Amount of sugar = x gram

Let amount of water = w gram

Sugar syrup solution = 50%

Sugar syrup solution = (amount of sugar)/(amount of water) × 100

50% = x/w × 100%

50% = x/w

Making w subject formula

w = x/50%

w = x/50/100

5 0

3 years ago

Finley and Cooper are wanting to go to SkyZone. Finley pays $53.75 for 5 hours. How much will Cooper pay for 3 hours?

IrinaK [193]

Answer:

10.75 x 3 = $32.25

Step-by-step explanation:

first, we need to figure out how much the cost is for one hour:

53.75/5 = 10.75

therefore, the cost at skyzone for 1 hour is $10.75 , BUT, we still need to figure out the time for 3 hours.

so, 10.75 x 3 = $32.25

6 0

3 years ago

Read 2 more answers

A. f(x) = l-2xl - 3 Domain: {1, 2, 3} Find the range

gizmo_the_mogwai [7]

Hello there!

We are given the function:

$\displaystyle \large{ f(x) = | - 2x| - 3} \\$

To find the range, we know that domain is the set of all x-values and also called 'input' while range is the set of all y-values and also called 'output'.

Basic Function - you add the input, you get the output. You add x-value in a function, you get y-value. You add domain, you get range.

So, we substitute x = 1,2 and 3 in the function.

x = 1

$\displaystyle \large{ f(1) = | - 2(1)| - 3} \\ \displaystyle \large{ f(1) = | - 2| - 3} \\$

Recall that any numbers in absolute value are always positive.

$\displaystyle \large{ f(1) = 2 - 3} \\ \displaystyle \large{ f(1) = - 1} \\$

x = 2

$\displaystyle \large{ f(2) = | - 2(2)| - 3} \\ \displaystyle \large{ f(2) = | - 4 | - 3} \\ \displaystyle \large{ f(2) = 4 - 3} \\ \displaystyle \large{ f(2) = 1}$

x = 3

$\displaystyle \large{ f(3) = | - 2(3)| - 3} \\ \displaystyle \large{ f(3) = | - 6| - 3} \\ \displaystyle \large{ f(3) = 6 - 3} \\ \displaystyle \large{ f(3) = 3}$

Therefore, Range: {-1,1,3}

Let me know if you have any questions!

Topic: Absolute Value Function / Modulus Function

6 0

3 years ago

Isosceles JAM has convex angle M. JM=35,MA=4n+3, angle J=14w-1, and angle m=98 Find n. Find w. Find the perimeter of JAM

Lena [83]

Answer:

n = 8, w = 3 and perimeter = 122.83 units.

Step-by-step explanation:

Let the angle M is the angle between the equal sides of isosceles JAM.

So, JM = MA

⇒ 35 = 4n + 3

⇒ 4n = 32

⇒ n = 8 (Answer)

Now, if ∠ J = 14w - 1 and ∠ M = 98°, then

2(14w - 1) + 98 = 180

⇒ 2(14w - 1) = 82

⇒ 14w - 1 = 41

⇒ w = 3 (Answer)

Now, draw a perpendicular bisector on JA from vertex M and it meets JA at P say.

So, Δ MPJ will be a right triangle with ∠ J = (14w - 1) = 41° {Since w = 3}

Hence, $\cos 41 = \frac{JP}{JM} = \frac{JP}{35}$

⇒ JP = 35 cos 41 = 26.415

So, JA = 2 × JP = 52.83

So, the perimeter of Δ JAM is = 35 × 2 + 52.83 = 122.83 units (Answer)

4 0

4 years ago

Resuelve el siguiente ejercicio de velocidad. El vector de posición de un móvil es r (t) =2 (t −7) i +12t j, en intervalos de ti

krek1111 [17]

To Find :

Position vector at time $t_1 = 5\ s$ and $t_2 = 8\ s$ .

Solution :

r (t) = 2 (t −7)i + 12t j

Putting t = 5 s and t = 8 s, we get :

r(5) = 2( -2 )i + 60j

r(5) = -4i + 60j

r(8) = 2i + 96j

Now, to find speed differentiating the r(t) w.r.t t :

$v=\dfrac{dr}{dt}= \dfrac{d(2(t-7)i + 12tj)}{dt}\\\\v=\dfrac{dr}{dt}= 2i + 12j$

Hence, this is the required solution.

7 0

3 years ago

Read 2 more answers