38. Solve the simultaneous equations
3x + 4y = 11, x + 6y = 13.
​

Answer:

The temperature after 10 hours is -9 ºF.

Step-by-step explanation:

This statement can be translated mathematically as follows. The temperature after 10 hours from sunrise is:

[tex]T = -10\,^{\circ}F + \left(1\,\frac{^{\circ}F}{h} \right)\cdot (7\,h)+ \left(-2\,\frac{^{\circ}F}{h} \right)\cdot (3\,h)[/tex]

[tex]T = -9\,^{\circ}F[/tex]

The temperature after 10 hours is -9 ºF.

Answer:

The answer is in the picture

Step-by-step explanation:

Answer:

i)  -240[tex]a^{4}b^{3} c^{3}[/tex]

ii) -15x²y² + 3x³y²

iii)x³y³z³ - x²y³z³ + x³y²z³

iv) pq -7p+6q-42

v)9x²-33x +42

vii)  2x² - 2y² + 7x -13y - 15

Step-by-step explanation:

To find product here means to multiply the algebraic expressions together

i) (–5a²bc)×(6ab)×(8abc² )

multiply like terms together

= -240[tex]a^{4}b^{3} c^{3}[/tex]

ii) (–3x²y) ×(5y – xy)

(–3x²y)×(5y) –  (–3x²y) ×(xy)

multiply like terms together

multiplication of same sign gives +, while that of opposite sign gives -

= -15x²y² + 3x³y²

iii) (x²y²z²) ×(xy – yz + zx)

(x²y²z²)×(xy) – (yz)× (x²y²z²) + (zx)  ×(x²y²z²)

multiply like terms together

multiplication of same sign gives +, while that of opposite sign gives -

= x³y³z³ - x²y³z³ + x³y²z³

iv) (p+6)and (q–7)

p(q–7)  +6(q–7)

multiply like terms together

multiplication of same sign gives +, while that of opposite sign gives -

= pq -7p+6q-42

v) (2x+7)and(x² –5x+6)

multiply like terms together

multiplication of same sign gives +, while that of opposite sign gives -

= 2x² -10x+12x+7x²-35x+42

collect like terms

= 9x²-33x +42

vii) (x + y + 5) and (2x – 2y – 3)

multiply like terms together

multiplication of same sign gives +, while that of opposite sign gives -

= 2x²-2xy-3x+2xy-2y²-3y+10x-10y-15

collect like terms

= 2x² - 2y² + 7x -13y - 15

Answer:

61.6%

Step-by-step explanation:

We know that the tank contains 250 litres and that 96 litres are used. We are trying to find the percentage of the leftover quantity.

First, we need to subtract 250 from 96 litres to get the quantity that is left in the tank in litres. 250-96=154.

Then we need to find the percentage. To find a percentage we need to divide the total minus and the used amount by the total amount and then multiple the whole thing by 100. So in our case, that would be 250-96=154/250*100. Or 154/250*100.

Thus the answer is 61.6%.

Answer:

Step-by-step explanation:

Quantity left in the tank = 250 - 96 = 154 litres

Percentage = [tex]\frac{154}{250}*100\\[/tex]

                   = 0.616 * 100

                   = 61.6 %

Answer:

119.43cm^2

Step-by-step explanation:

The computation of the area of the shaded region is shown below:

As we know that

= Area of the rectangle - Area of the circle

where,

Area of rectangle is

[tex]= length \times breadth[/tex]

[tex]= 11\times 12[/tex]

= 132 cm^2

And, the area of the circle is

[tex]= \pi\times r^2\\\\ = \frac{22}{7} \times 2^2\\\\ = \frac{88}{7} cm^2[/tex]

Now the area of the shaded region is

[tex]= 132 cm^2- \frac{88}{7}cm^2[/tex]

= 119.43cm^2

We simply deduct the area of the circle from the area of the rectangle so that the area of the shaded region.

Answer:

the answer

is 128.86 Step-by-step explanation:

Answer:

x = 1, y = -2

Step-by-step explanation:

- 2x + 10y = -22 _______(1)

-2x - 4y = 6 _______(2)

From (1),

10y + 22 = 2x

x = (10y + 22) / 2

x = 5y + 11 .______(3)

Substitute (3) into (2),

-2 ( 5y + 11) -4y = 6

-10y - 22 - 4y = 6

-14y = 6 + 22

-14y = 28

y = 28/ -14

y =-2

Substitute y = -2 into (3).

x = 5y + 11

x = 5(-2) + 11

x = -10 + 11

x = 1

Therefore, the solution is x = 1, y = -2.

Answer:

student 2

Step-by-step explanation:

35/50 = 70%

51/60 = 85%

Answer:

x^2+11x+30

Step-by-step explanation:

This is a parallelogram.

Area of a parallelogram can be found with:

A=bh

Plug our values in.

A=(x+6)(x+5)

FOIL-

First: x*x=x^2

Outside: x*5=5x

Inside: 6*x=6x

Last: 6*5=30

x^2+5x+6x+30

Combine like terms.

x^2+11x+30

Answer:

it's 22.5

Step-by-step explanation:

You do 25% of 90 =22.5

Answer:

£120

Step-by-step explanation:

A reduction of 25% of the price, means the price of the dress in sale is 75%.

⇒ £90 →75%

    X→100%

⇒ the price before the reduction= X=(90×100)÷75=£120

Answer:

The second choice.

Step-by-step explanation:

Open the compass to the width of the line and draw two arcs.

These arcs should be on the same side of the original line.

You can then draw the parallel line with the straight edge just touching the top of each arc.

Parallel lines can be drawn using compass and straightedge using the concept of corresponding angle.

Two lines are called parallel when they never meet each other if they are increased on the either side of them.

When constructing parallel lines with a compass and straightedge we can follow the below mentioned steps.

1. At first we need to draw a straight line. Then take a random point on it.

2. After that, we need to take a random point above the line that is drawn. Then, we need to connect two points.

3. After that, draw two arcs using the compass. First arc is on the angle formed by two lines drawn. The next arc is on the line that connects two points.

4. Now using the compass, we can copy the angle formed on the first line on the point above the first line.

5. Now, complete the angle on the point above the first line. These two lines are parallel lines.

Learn more about parallel lines here: https://brainly.com/question/1418314

#SPJ2

Step-by-step explanation:

For one course:

6+8+5=

Two courses with appetizers and main meals (* means times)

6*8

Two courses with appetizers and dessert

6*5

Two courses with main meals and dessert

8*5

Answer:

32 years old

Step-by-step explanation:

Please see attached picture for full solution.

Let Sunil's present age be 4x and his wife's present age be 3x.

Answer:

1 hour 26 Minutes

Step-by-step explanation:

Tanya needs 2 hours to do the job.

Pat needs 5 hours to do this same job.

Tanya's rate  [tex]=\frac{1}{2}[/tex]

Pat's rate[tex]=\frac{1}{5}[/tex]

Let the number of hours it will take both of them =x

Rate when two of them work together  [tex]=\frac{1}{x}[/tex]

Therefore:

[tex]\frac{1}{2}+\frac{1}{5}=\frac{1}{x}\\$Taking lowest common multiple$\\\frac{5+2}{10}=\frac{1}{x}\\\\\frac{7}{10}=\frac{1}{x}\\\\$Cross multiply$\\7x=10\\x=1.43$ hours[/tex]

[tex]0.43 X 60 =25.8 \approx 26$ minutes[/tex]

Therefore: 1.43 hour = 1 hour 26 Minutes

It will take both of them approximately 1 hour 26 minutes to  the job.

Answer:

11.67

Step-by-step explanation:

Data given in the question

∠ADC = 42°

∠BAC = 68°

Let us assume that AC be Y

Now

In ΔACD

tan 42° = AC ÷ CD = Y ÷ x ...............................(i)

In ΔACB  

tan 68° = BC ÷ AC = 26 ÷ Y ..........................(ii)

Now take the value of Y from the equation (ii)

Y = 26 ÷ Tan 68° ...................... (iii)

Now place the value of Y in equation (i)

So,

Tan 42° = 26 ÷ tan 68° × X

X = 26 ÷  tan 68° × Tan 42° ......................(iv)

Now placing the values of tan 42° and tan 68° in equation (iv)

So,

X = 26 ÷ 0.900 × 2.475

= 11.67

The tan 42° = 0.900

And, the tan 68° = 2.475

Answer:

50,000,000 centímetros cúbicos.

Step-by-step explanation:

En la pregunta anterior, se nos dan las dimensiones de este cubo en metros como:

Longitud = 5m

Ancho = 4 m

Altura = 2.5 m

Nos dijeron que encontraramos el volumen en centímetros cúbicos

Paso 1

Convierta todas estas dimensiones a centímetros

1m = 100cm

Por lo tanto:

Longitud = 5 m = 5 × 100 cm = 500 cm

Ancho = 4 m = 4 × 100 cm = 400 cm

Altura = 2.5 m = 2.5 × 100cm = 250cm

Paso 2

Fórmula para el volumen de un cubo = Largo × Ancho × Alto

Volumen = 500 cm × 400 cm × 250 cm

Volumen = 50,000,000 centímetros cúbicos.

Por lo tanto, el volumen, en centímetros cúbicos, de la habitación es de 50,000,000 centímetros cúbicos.

Answer:

(2,6)

Step-by-step explanation:

x+2y = 14

y = x+4

Substitute x+4 into the first equation for y

x+2(x+4) = 14

Distribute

x+2x+8 = 14

3x+8 = 14

Subtract 8 from each side

3x+8-8 = 14-8

3x = 6

Divide by 3

3x/3 = 6/3

x = 2

Now solve for y

y = x+4

y =2+4

y =6

(2,6)

Answer:

D. (2, 6)

Step-by-step explanation:

Put y as x+4 in the first equation and solve for x.

x + 2(x + 4) = 14

x + 2x + 8 = 14

3x = 14 - 8

3x = 6

x = 2

Put x as 2 in the second equation and solve for y.

y = 2 + 4

y = 6

Answer:

1) 78.87%

2) 99.7%

Step-by-step explanation:

The z-score for a normal distribution is given by:

[tex]z=\frac{X-\mu}{\sigma}[/tex]

1- The given data is:

σ = 4 years

μ = 50 years

For X = 45 and X =55

[tex]z_1=\frac{45-50}{4}\\z_1=-1.25\\z_2=\frac{55-50}{4}\\z_2=1.25[/tex]

A z-score of -1.25 corresponds to the 10.57th percentile of a normal distribution, while a z-score of 1.25 is equivalent to the 89.44th percentile.

Therefore, the percentage of the alligators are between 45 and 55 years old is:

[tex]P=89.44-10.57=78.87\%[/tex]

78.87% of alligators.

2- The given data is:

σ = 2 minutes

μ = 17 minutes

For X = 11 and X =23

[tex]z_1=\frac{11-17}{2}\\z_1=-3\\z_2=\frac{23-17}{2}\\z_2=3[/tex]

A z-score of -3.0 corresponds to the 0.135th percentile of a normal distribution, while a z-score of 3.0 is equivalent to the 99.865th percentile.

Therefore, the percentage of people that should be seen by the doctor between 11 and 23 minutes is:

[tex]P=99.865-.0135=99.73\%[/tex]

99.7% of people.

Using the normal distribution, it is found that:

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

The proportion between 45 and 55 years old is the p-value of Z when X = 55 subtracted by the p-value of Z when X = 45, then:

X = 55:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{55 - 50}{4}[/tex]

[tex]Z = 1.25[/tex]

[tex]Z = 1.25[/tex] has a p-value of 0.8944.

X = 45:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{55 - 50}{4}[/tex]

[tex]Z = -1.25[/tex]

[tex]Z = -1.25[/tex] has a p-value of 0.1057.

0.8944 - 0.10567= 0.7887.

0.7887 = 78.87% of the alligators are between 45 and 55 years old.

For the second question, by the Empirical Rule, 99.7% of people should be seen by the doctor between 11 and 23 minutes for this to be considered a normal distribution.

To learn more about normal distribution, you can take a look at https://brainly.com/question/24663213

At least 105 children must attend the event

Answer:

D. Infinite number

Step-by-step explanation:

A circular plate can be rotated by a part of a degree and it will look the same (as long as it does not have a design on it)

Assuming this plate does not have a design on it, we can rotate through infinite number of lines of symmetry

Answer:

D. infinite number

Step-by-step explanation:

Hope this helps ^_^

Answer:   (x - 2)² + (y - 3)² = 4

Step-by-step explanation:

The equation of a circle is: (x - h)² + (y - k)² = r²    where

Given:  (h, k) = (2, 3)  and   (x, y) = (2, 1)

Input those values to find r²:

(x - h)² + (y - k)² = r²

(2 - 2)² + (1 - 3)² = r²

  0       +     4     = r²

                   4    = r²

Now input (h, k) = (2, 3) and r² = 4 into the equation of a circle:

(x - h)² + (y - k)² = r²

(x - 2)² + (y - 3)² = 4

Answer:

$105

Step-by-step explanation:

I used a proportion to solve this:

[tex]\frac{63}{3} = \frac{x}5}[/tex]

Cross multiply:

3x = 315

Divide both sides by 3

x = 105

Answer:$105

Step-by-step explanation:

Salary for 3 hrs=$63

Salary for 5hrs= salary for one hour×5 hrs,

Salary for one hour= 63/3=$21

Salary for 5 hours= 21×5: $105

Answer: The length AC equals 10.25 cm (approximately)

Step-by-step explanation: Please refer to the diagram attached for further details.

The triangle has been constructed according to the dimensions provided with the top B going down to the "little square inside the triangle" which is C. This clearly identifies it as a right angled triangle. The point B meets with point C at the right angle and A is the sharp tip of the triangle, which makes point A the third angle. Hence we now have a right angled triangle with side AB measuring 11 cm, side BC measuring 4 cm and side AC is unknown.

We can now apply the Pythagoras' theorem which is stated as follows;

AC² = BC² + AB²

Where AC is the hypotenuse (longest side) and BC and AB are the other two sides. We can now substitute for the appropriate sides in this question as all the sides have been labelled differently. Hence,

BA² = BC² + CA²

11² = 4² + CA²

121 = 16 + CA²

Subtract 16 from both sides of the equation

105 = CA²

Add the square root sign to both sides of the equation

√105 = √CA²

10.2469 = CA

CA ≈ 10.25 cm

The third side AC (or CA) measures approximately 10.25 cm

Answer:

D

Step-by-step explanation:

If we plug in the points to A, not all 3 of them work so A is not the answer. If we repeat this process with the other functions we see that the answer is D.

Answer:

Since the speed can't be negative it was 60 km/h for the first stage and 80 km/h on the second stage, averaging 70 km/h for the whole course.

Step-by-step explanation:

The speed of the truck for the first stage of the route is "x" km/h, while on the second one it raises to "x + 20" km/h. The time it takes to complete each stage is shown below:

[tex]t_{stage 1} = \frac{150}{x}\\t_{stage 2} = \frac{200}{x + 20}[/tex]

The sum of these times must be equal to the total time of the trip, therefore:

[tex]t_{stage1} + t_{stage2} = 5[/tex]

[tex]\frac{150}{x} + \frac{200}{x + 20} = 5\\\frac{150*(x + 20) + 200*x}{x(x + 20)} = 5\\150*x + 3000 + 200*x = 5*x*(x + 20)\\5*x^2 + 100*x - 350*x - 3000 = 0\\5*x^2 - 250*x - 3000 = 0\\x^2 - 50*x - 600 = 0\\x_{1,2} = \frac{-(-50) \pm \sqrt{(-50)^2 - 4*1*(-600)}}{2*1}\\x_{1,2} = \frac{50\pm \sqrt{2500 + 2400}}{2}\\x_{1,2} = \frac{50\pm \sqrt{4900}}{2}\\x_{1,2} = \frac{50 \pm 70}{2}\\x_{1} = 60\\x_{2} = -10[/tex]

Since the speed can't be negative it was 60 km/h for the first stage and 80 km/h on the second stage, averaging 70 km/h for the whole course.

Answer:

86 B

Step-by-step explanation:

32+62=94

180-94=86

The sum of the interior angles of a triangle always add up to 180 degrees.

Answer:

The third angle is 86

Step-by-step explanation:

The sum of the angles of a triangle add to 180

32+62+x = 180

94+x = 180

Subtract 94 from each side

x = 180-94

x =86

Answer:

Step-by-step explanation:

The mode is 24 so we know that at least 2 of the 5 numbers are 24.

The mean is 20 so we know that the 5 numbers add up to 100.

The median is 21 so the third number is 21.

100-(24+24+21)= 31

Now, I am pretty certain that the last 2 numbers can be anything as long as they add up to 31 AND they are not also 21 because 24 then would no longer be the mode.

E.g. 24, 24, 21, 11 & 20

Answer:

see below

Step-by-step explanation:

To find the percent increase, take the new amount and subtract the original amount

25-20 = 5

Divide by the original amount

5/20 = .25

The increase is 25%

100% + 25% = 125%

The new amount is 125% of the old amount

Answer:

yes........ correct

Step-by-step explanation:

Although, the method that i tried to justfy is not the same as yours, I got the same final answer. so, what you wrote is right.

Answer:

B and D

Step-by-step explanation:

=> All of the sides are unequal so it's a scalene triangle.

=> It have a 90 degrees angle, so it is a Right Angled Triangle.

Answer:

B. Scalene

D. Right

Step-by-step explanation:

The triangle is a scalene triangle, because all the three sides have different lengths.

The triangle is a right triangle, because it has an angle of 90 degrees.

The answer is C.) The model is not a good fit.

Answer:

B. 1 out of 5,005

Step-by-step explanation:

Given

Number of Friends = 15

Required

Probability of selecting 6 friends

The first step is to calculate the number of ways 6 friends can be selected

The keyword in the above statement is selection;

This implies combination;

The number of ways is calculated as follows;

[tex]\left[\begin{array}{c}n&r&\end{array}\right] = \frac{n!}{(n-r)!r!}[/tex]

Where n = 15 and r = 6

[tex]\left[\begin{array}{c}n&r&\end{array}\right] = \frac{n!}{(n-r)!r!}[/tex]

becomes

[tex]\left[\begin{array}{c}15&6&\end{array}\right] = \frac{15!}{(15-6)!6!}[/tex]

[tex]\left[\begin{array}{c}15&6&\end{array}\right] = \frac{15!}{9!6!}[/tex]

[tex]\left[\begin{array}{c}15&6&\end{array}\right] = \frac{15 * 14 * 13 * 12 * 11 *10 * 9!}{9! *6 * 5 * 4 * 3 * 2 * 1}[/tex]

[tex]\left[\begin{array}{c}15&6&\end{array}\right] = \frac{15 * 14 * 13 * 12 * 11 *10}{6 * 5 * 4 * 3 * 2 * 1}[/tex]

[tex]\left[\begin{array}{c}15&6&\end{array}\right] = \frac{3603600}{720}[/tex]

[tex]\left[\begin{array}{c}15&6&\end{array}\right] =5005[/tex]

Hence, there are 5005 ways of selecting 6 from 15 friends

Since, there's only one way of selecting the 6 named friends

Then, the probability is 1 out of 5,005

Answer:

The answer is 3x(x - 3)(x + 2)

Step-by-step explanation:

3x³ - 3x² - 18x

Factor out 3x from the expression

We have

3x ( x² - x - 6)

Solve the terms in the bracket

We have

3x ( x² + 2x - 3x - 6)

Factor out x the expression in the bracket

We have

3x ( x ( x + 2) - 3( x + 2) )

Factor out x + 2 from the expression in the bracket

We have the final answer as

Hope this helps you.