Can you solve these two problems please

The length of the side JH in the triangle ΔHIJ is 97.9.

We are given two triangles. The vertices of the first triangle are E, F, and G. The vertices of the second triangle are H, I, and J. The triangles ΔEFG and ΔHIJ are similar to each other. The lengths of the sides FG, GE, and IJ are 12, 25, and 47, respectively. We need to find the length of the side, JH. The figure of the triangles is attached below.

Let the length of the side JH in the triangle ΔHIJ be represented by the variable "x". The side IJ is proportional to the side FG. Let the constant of proportionality be "k".

IJ ∝ FG

IJ = k*FG

k = IJ/FG

k = 47/12

The side JH is proportional to the side GE.

JH = k*GE

x = (47/12)*25

x = 97.9

Hence, the length of the side JH is 97.9 units.

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The probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%

It is a branch of mathematics that deals with the occurrence of a random event.

Given,

Amounts of weight that male college students gain during their freshman year are normally distributed

mean of μ = 1.1 kg and

Standard deviation of o= 4.6 kg.

Z score=x-μ/o

=25-1.1/4.6

=23.9/4.6

=5.196

Z score=x-μ/o

=25-1.1/0

=0

Z score=25-1.1/3

=23.9/3

=7.966

By observing the z table the probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%

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Answer:

t - 10 = 61

Step-by-step explanation:

We are given that the tortoise was 61 years old 10 years ago. Let's suppose that t is the tortoise's current age. We can then write the equation t - 10 = 61

so t = 71.

The missing variables are b, x, x and y are 3.73m, 7.88 units, 41.06 units and 8.94 units respectively

We will use trigonometrical ratios to solve this problem. Below are the definitions of the trigonometrical ratios:

sin = opposite/hypotenuse

cos = adjacent/hypotenuse

tan = opposite/adjacent or tan = sin/cos

The opposite is the side the angle of consideration is facing

The hypotenuse is the side the right angle  is facing

The adjacent is the side left after determining the opposite and hypotenuse

1st triangle

tan 25° = b/8   (tan = opp/adj)

b = 8 tan 25° = 3.73m

2nd triangle

sin 21° = x/22    (sin = opp/hyp)

x = 22 sin 21° = 7.88 units

3rd triangle

cos 47° = 28/x    (cos = adj/hyp)

x =  28/cos 47° = 41.06 units

4th triangle

Use Pythagoras' theorem:

12² = 8² + y²

y² = 12² - 8²

y² = 144 - 64

y² = 80

y = √80 = 8.94 units

Therefore, the missing variables are b = 3.73m, x = 7.88 units, x = 41.06 units and y = 8.94 units

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Answer:

27/8 or 3.375 or 3 3/8

Step-by-step explanation:

The measurement of angles ∠1 is 126° and ∠2 is 154°.

According to the question,

We have the following information:

We have a figure of two triangles and some of the measurements of the angles are given.

We know that the sum of three angles of a triangle is 180°.

So, for the larger triangle, we have the following expression:

96+30+third angle = 180

Third angle = 180-126

Third angle = 54°

We know that sum of angles on a straight line is 180°.

So, we have:

∠1+54 = 180

∠1 = 180-54

∠1 = 126°

Now, finding the sum of angles in smaller triangle:

126+28+third angle = 180

Third angle = 180-154

Third angle = 26°

Now, angle 2 and this angle will make a straight line.

∠2+26 = 180

∠2 = 180-26

∠2 = 154°

Hence, the measurement of angles ∠1 is 126° and ∠2 is 154°.

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Answer:  

48

Step-by-step explanation:

The distance from the top of the cliff that Jose is after 14 minutes is 12.8 feet downward.

An elevation simply means the height above sea level.

In this case, José climbs down from the top of a steep cliff for 4 minutes at a rate of 12.2 feet per minute. The total feet will be:

= 12.2 × 4

= 48.8 feet

He then climbs back up for 10 minutes at a rate of 3.6 feet per minute. This will be:

= 3.6 × 10

= 36 feet.

Therefore, the change in elevation will be:

= Elevation up - Elevation down

= 36 - 48.8

= 12.8 feet.

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Answer:

Step-by-step explanation:

7*5

Answer:

he got 8 apples left and made a profit of 16

Step-by-step explanation:

Answer:

b)  f(x) = -16x² + 8x + 30

Step-by-step explanation:

When a ball is thrown, its path of motion can be modelled as a parabola that opens downwards.

The graph of a quadratic equation f(x) = ax² + bx + c is a parabola.

Therefore,  f(x) = -16x² + 8x + 30  could potentially model the time (in seconds) it takes a ball tossed from a window to touch the ground, as its graph is a parabola that opens downwards.

If this function was used to model the scenario, the height of the window above the ground would be the y-intercept (30 feet), and the time when the ball touched the ground would be the positive x-intercept (approx 1.64 s).

The change in temperature in United States since last night is -6 degree centigrade.

Given the temperature in United States last night is = -9 degree C

Now the temperature is = -3 degree C

So the change in temperature is given by,

= Final Temperature - Initial Temperature

= -9 - (-3)

= -9 + 3

= -6 degree C

Hence the change in temperature in United States since last night is -6 degree centigrade.

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The set of side that could be used to form a right triangle is {√3 , √13 , 4} , the correct option is (d)  .

In the question ,

four set of sides is given ,

we need to find the set of side that forms a right triangle ,

we know that for right triangle , By Pythagoras Theorem , the sum of square of two shorter side is equal to the square of the longest side .

Option(a)

the sides are 4 , 8 , 11.

4 + 8 = 11

16 + 64 = 121

80 = 121

we know that 80 121 ,

So , the sides do not form a right triangle

Option(b)

the sides are 6 , 8 , 13

6 + 8 = 13

36 + 64 = 169

100  169

we know that 100 169 ,

So , the sides do not form a right triangle .

Option(c)

the sides are √3, √5 , 8

√3 + √5 = 8

3 + 5 = 64

8 = 64

we know that 8  64 ,

So , the sides do not form a right triangle .

Option(d)

the sides are √3, √13 , 4

√3 + √13 = 4

3 + 13 = 16

16 = 16

Yes , the sides form a right triangle .

Therefore , The sides {√3 , √13 , 4} forms a right triangle  .

The given question is incomplete , the complete question is

Determine which set of side measurements could be used to form a right triangle ?

(a) 4, 8, 11

(b) 6, 8, 13

(c)√3, √5,8

(d)√3, √13, 4

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The perimeter and area of the polygon is B. Perimeter = 72 feet; Area = 308 square feet.

It is important to note that the perimeter is the addition of all the sides. Therefore, the perimeter will:

= 16 + 15 + 16 + 8 + 17

= 72 feet

The area will be:

= Area of triangle + Area of rectangle

= (1/2 × base × height) + (length × width)

= (1/2 × 8 × 17) + (15 × 16)

= 68 + 240

= 308ft²

Therefore, the correct option is B.

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Answer: 0.051, 0.134, 0.2, 0.46

Step-by-step explanation:

Answer:

Exact Form: 16/3

Decimal Form: 5.3

Mixed Number Form: 5 1/3

Step-by-step explanation:

A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2 + 2 = 4 .

The end behaviour of the graph of f(x) [tex]=[/tex] x⁵ - 8x⁴ [tex]+[/tex] 16x³  is f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞ , the correct option is (a) .

In the question ,

it is given that ,

the function is f(x) [tex]=[/tex] x⁵ - 8x⁴ [tex]+[/tex] 16x³ ,

In the function as x approaches -∞ , x⁵ will also approach -∞ , because negative number raised to the odd power , gives a negative result .

In the function as x approaches ∞ , x⁵ will also approach ∞ , because positive number raised to the odd power , gives a positive result .

that is f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞

let us find the roots of the function ,

f(x) [tex]=[/tex] 0

x⁵ - 8x⁴ [tex]+[/tex] 16x³ = 0

taking x³ common ,

x³(x² - 8x [tex]+[/tex] 16) = 0

x³(x² - 4x - 4x + 16) = 0    .... by using splitting the middle term method

x³(x(x - 4) - 4(x - 4)) = 0

x³(x - 4)(x - 4) = 0

which means x³ [tex]=[/tex] 0   and x-4 = 0  

that is x=0    and x = 4 .

So , the roots of the function f(x) are x=0 and x=4 .

This means that the graph has a repeated root and so it will touch the x-axis but not at the repeated root of x [tex]=[/tex] 4.

Therefore , The end behaviour of the graph of f(x) [tex]=[/tex] x⁵ - 8x⁴ [tex]+[/tex] 16x³  is f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞ , the correct option is (a) .

The given question is incomplete , the complete question is

What is the end behavior of the graph of f(x) = x⁵ - 8x⁴ + 16x³ ?

(a) f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞

(b) f(x)→∞ as x→-∞0; f(x) → +∞ as x→ +∞

(c) f(x)→∞ as x→ -∞; f(x) →-∞ as x→ +∞

(d) f(x)→-∞ as x→∞ ; f(x)→ -∞ as x→∞

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Answer:

3/2 month

Step-by-step explanation:

Write an equation and solve: Sandy has $60 and saves $10 a month. Randy has $45 and saves $20 per month. After how many months will they have the same amount of money?

When x = months:

Sandy: 10x + 60

Randy: 20x + 45

You are looking for x when:

Sandy = Randy

10x + 60 = 20x + 45

subtract 45 from both sides:

10x + 60 - 45 = 20x + 45 - 45

10x + 15 = 20x

subtract 10x from both sides:

10x + 15 - 10x = 20x - 10x

15 = 10x

divide both sides by 10:

15/10 = 10x/10

x = 15/10

reduce:

x = 3/2

It will take 3/2 months of Sandy and Randy to have the same amount of money.

[3/2 month also equals 1.5 months, depending on the format of the answer you need]

Answer:

C. Trust me on this one, it is an easy one.

The true equations are :

2 + 7 = 9

8 × 5 = 4 0

6 ÷ 3 = 2

2 - 1 = 1

We are given a total of ten digits. The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. We are given four equations with blanks. An equation is a mathematical statement that proves the equality of two mathematical expressions. The first equation involves addition. The second equation involves multiplication. The third equation involves division. The fourth equation involves subtraction. We need to use every digit only once.

The first true equation is 2 + 7 = 9.

The second true equation is 8 × 5 = 4 0.

The third true equation is 6 ÷ 3 = 2.

The fourth true equation is 2 - 1 = 1.

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Answer:

[tex]y=-43x-173[/tex]

Step-by-step explanation:

[tex]y+1=-43(x+4) \\ \\ y+1=-43x-172 \\ \\ y=-43x-173[/tex]

By using the graphing method, an ordered pair which represent a solution to the given system of equations is (-6, -6).

A graph simply refers to a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

In order to plot the system of equations on a graph, we would simplify the second equation as follows:

4u = 2v - 12

Dividing both sides of the equation by 4, we have the following:

4u/4 = 2v/4 - 12/4

u = v/2 - 3

Note: The values of v would be plotted on the y-axis of a graph while the values of u would be plotted on the y-axis of a graph.

By critically observing the graph (see attachment) of the given system of equations, we can logically deduce that its solution occur at this point of intersection (-6, -6).

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Answer: put it in a caculator

Step-by-step explanation:

Combine 18x^3 and 5x^3.

Combine x^2 and 6x^2.

Combine 9x and −14x.

Add −3 and 11.

The values of x and y using angle relationships are as follows:

When parallel lines are cut by a transversal, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles.

Therefore, the angle relationship can be used to find the value of x and y in the diagram.

In the diagram, l and m are parallel lines and are cut by a transversal line.

Therefore,

10.

10x - 17 = 8x + 1(alternate exterior angles are congruent)

10x - 8x = 1 + 17

2x = 18

x = 18 / 2

x = 9

8x + 1 + 6y + 29  = 180(sum of angles on a straight line is 180 degrees)

72 + 1 + 29 + 6y = 180

102 + 6y = 180

6y = 180 - 102

6y = 78

y = 78 / 6

y  = 13

11.

7x - 30 = 5x + 14(Corresponding angles)

Corresponding angles are congruent.

7x - 5x = 14 + 30

2x = 44

x = 44 / 2

x = 22

3y + 11 + 7x - 30 =  180(sum of angles on a straight line)

3y + 11 + 7(22) - 30 =  180

3y + 11 + 154 - 30 = 180

3y = 180 - 11 - 154 + 30

3y = 45

y = 45 / 3

y = 15

12.

7y - 23 = 23x - 16 (vertically opposite angles)

7y - 23x = 7

8x - 21 + 23x - 16 = 180 (same interior angles are supplementary)

31x  - 37 = 180

31x = 180 + 37

31x = 217

x = 217 / 31

x = 7

7y - 23(7) = 7

7y = 7 + 161

7y = 168

y = 168 / 7

y = 24

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Answer:

4(13)

Step-by-step explanation:

[tex]28+24=7(4)+6(4)=\boxed{4(13)}[/tex]

Each set of prices should be matched with the correct percentage of increase or decrease as follows:

Mathematically, percentage increase can be calculated by using this formula:

Percentage increase = [original price - new price]/new price × 100

At original price: $63.00 and new price: $56.07, we have:

Percentage decrease = [63.00 - 56.07]/56.07 × 100

Percentage decrease = 6.93/56.07 × 100

Percentage decrease = 0.124 × 100

Percentage decrease = 12.4%.

At original price: $98.00 and new price: $108.78, we have:

Percentage increase = [108.78 - 98.00]/98.00 × 100

Percentage increase = 10.78/98.00 × 100

Percentage increase = 0.11 × 100

Percentage increase = 11%.

At original price: $37.50 and new price: $34.50, we have:

Percentage decrease = [37.50 - 34.50]/34.50 × 100

Percentage decrease = 3/34.50 × 100

Percentage decrease = 0.087 × 100

Percentage decrease = 8.7%.

At original price: $12.25 and new price: $13.23, we have:

Percentage increase = [13.23 - 12.25]/12.25 × 100

Percentage increase = 0.98/12.25 × 100

Percentage increase = 0.08 × 100

Percentage increase = 8%.

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The equation when Nicole charges a flat fee of $3, plus $5 per hour is c = 3 + 5h.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario

Let the number of hours be given as h.

Since Nicole charges a flat fee of $3, plus $5 per hour, this will be:

c = 3 + (5 × h)

c = 3 + 5h

where c = total cost

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Answer:

15%

Step-by-step explanation:

15%*40=46

Answer:

15%

Step-by-step explanation:

[tex]Percent of change =\frac{new -old}{ old} *100\\[/tex]

The boy was 40 inches tall so that means 40 inches is the old value

The boy is currently 46 inches tall now, so 46 is the new value

Plug these values into the equation:

[tex]Percent of change =\frac{46 -40}{ 40} *100\\[/tex]

Simplify:

[tex]Percent of change =\frac{6}{ 40} *100\\[/tex]

[tex]Percent of change =\frac{600}{ 40} \\[/tex]

[tex]Percent of change =15[/tex]

I hope this answers your question :)

The radiation intensity, in Roentgens at a distance of 1 foot is 8.1 R/hr

Radiation intensity is defined as the radiation energy that strikes in one second upon a surface of 1 square unit perpendicular to the direction of the ray

The equation below relates the radiation intensity and distance:

I₁/I₂ = D₂²/D₁²

where:  I₁ = intensity  at distance 1, I₂ = intensity at distance 2, D₁ = distance 1 from source and D₂ = distance 2 from source

Given: D₁ = 9 feet, I₁ = 100 mR/hr and D₂ = 1 foot

Using the formula:

100/I₂ = 1²/9²

100/I₂ = 1/81

I₂ = 100 × 81

I₂ = 8100 mR/hr

I₂ = 8100×10⁻³ R/hr                (1 mR/hr = 1×10⁻³ R/hr)

I₂ = 8.1 R/hr

Therefore, the radiation intensity in Roentgens is 8.1 R/hr

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Answer: Adding will make a perfect square trinomial. It is always positive because it is the square of the number.

When a binomial is squared, the result is the square of the first term added to twice the product of the two terms and the square of the last term. a2+2ab+b2=(a+b)2anda2−2ab+b2=(a−b)2.

Hope this helps.

Step-by-step explanation:

Answer: I think you would earn $8.35 per hour

Step-by-step explanation:

Answer: $880

Step-by-step explanation:

As I understand you are working 20 hours a day for 4 days.

[tex]\frac{11 dollars}{hour} * \frac{20 hours}{day} * 4 days[/tex] = $880