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3 years ago

Bills sleight is 48 kilograms. This is 10 more than one half of his father weight. What is his dads weight? Explain the steps

Mathematics

2 answers:

Vinvika [58]3 years ago

6 0

Let the equation be 1/2x=48-10
where x is the dad's weight
1/2x=48-10
1/2x=38
x=76 ( i divided both sides by 1/2)

belka [17]3 years ago

4 0

$x-\ dad's\ weight\\\\
48-10=\frac{1}{2}x\\\\
38=\frac{1}{2}x\ \ \ \ | multiply\ by\ 2\\\\
76=x\\\\
Dad's\ weight\ is\ 76\ kilorams.$

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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.

konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

$BC^2=BD\cdot AB.$

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

$x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.$

Take positive value x. You get

$AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.$

2. According to the previous theorem,

$AC^2=AD\cdot AB.$

Then

$AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

Answer: $AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

$CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D$

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0

4 years ago

Read 2 more answers

Could use some help pls.

Murrr4er [49]

Answer:

9 cans of soup and the 4 frozen dinners were purchased

Step-by-step explanation:

Let x represent the number of cans of soup purchased.

Let y represent the number of frozen dinners purchased.

Lincoln purchased a total of 13 cans of soup and frozen dinners. This means that

x + y = 13

Each can of soup has 250 mg of sodium and each frozen dinner has 550 mg of sodium. The 13 cans of soup and frozen dinners which he purchased collectively contain 4450 mg of sodium. This means that

250x + 550y = 4450 - - - - - - - - -1

Substituting x = 13 - y into equation 1, it becomes

250(13 - y) + 550y = 4450

3250 - 250y + 550y = 4450

- 250y + 550y = 4450 - 3250

300y = 1200

y = 1200/300

y = 4

Substituting y = 4 into x = 13 - y, it becomes

x = 13 - 4 = 9

7 0

3 years ago

The children in my subdivision were bored one summer and decided to hold a competition to see who could run to the end of the st

Ainat [17]

Answer:

6.7% of children who finished the race in under 45 seconds.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 75 seconds

Standard Deviation, σ = 20 seconds

We are given that the distribution of time of completion is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(finished the race in under 45 seconds.)

P(x < 45)

$P( x < 45) = P( z < \displaystyle\frac{45 - 75}{20}) = P(z < -1.5)$

Calculation the value from standard normal z table, we have,

$P(x < 45) = 0.067 = 6.7\%$

6.7% of children who finished the race in under 45 seconds.

4 0

4 years ago

Which equation has a solution of 4? Select all that apply .

8_murik_8 [283]

Answer: C and B

Step-by-step explanation:

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2 years ago

Summer’s here and the ice cream truck is in town. The truck offers 3 flavors of ice cream: vanilla, chocolate, and strawberry. T

taurus [48]

Answer:

12 choices

Step-by-step explanation:

There are 3 possible flavors Zoe can choose from: vanilla, chocolate, and strawberry.

Meanwhile, there are 4 possible toppings Zoe can choose from: walnuts, sprinkles, and chocolate fudge and cookie crumbs.

Each flavor can go with each topping, so we just multiply these two numbers together:

3 * 4 = 12

Zoe has 12 choices.

5 0

3 years ago