b) Describe fully the single transformation that maps triangle B onto triangle C. (2)
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9514 1404 393

Answer:

  a) a straight line

  b) a hyperbola

Step-by-step explanation:

a) When a = v/r is plotted against v as the independent variable, it will be a straight line through the origin with a slope of 1/r.

__

b) When a = v/r is plotted against r as the independent variable, it will be a hyperbola with a "constant of proportionality" of v. Here, a is inversely proportional to r.

Answer:

x=9/5 − 4y/5

x = 7 + y/2

Step-by-step explanation:

Move all terms that don't contain x to the right side and solve.

Answer:

25%

Step-by-step explanation:

U flipped a coin 12 times, it lands on tail 9 times. Now the probability of landing on head = 12-9

= 3

In percentage= 12\3 *100

=25%

Answer:

0.25%

Step-by-step explanation:

Answer:

\( - 3 \leqslant x \leqslant 5\)

Answer:  translation 8 units to the right

Step-by-step explanation:

An even function is a function such that:

h(x) = h(-x)

and the function is odd if:

h(-x) = -h(x)

Now, let's talk about transformations:

A) Reflection over the x-axis:

When we have a point (x,y) and we do a reflection over the x-axis, the reflected point will be:

(x, -y).

Then for the case of a function:

y = h(x).

then the reflection will be:

g(x) = - y = -h(x).

And if h(x) is even, -h(x) is also even, so this is not the correct option.

B) Vertical stretch by a factor of 7.

This is written as:

g(x) = 7*h(x).

then:

g(x) = 7*h(x)

g(-x) = 7*h(-x) = 7*h(x) = g(x)

the transformation is even.

C) Translation of 8 units to the right.

We can write this as:

g(x) = h(x - 8).

Then:

g(-x) = h(-x -8) = h(x + 8)

Then g(-x) is not equal to g(x)

and also g(-x) ≠ -g(x)

So in this case the transformation is neither odd or even.

C)  horizontal compression by a factor of One-half.

This transformation is written as:

g(x) = h( (1/2)*x)

And, similar as the case of the vertical compression, in this case the transformation is also even.

Answer: C

Step-by-step explanation:

Translation 8 units to the right

Answer:

Part A:   -3x^8 + 2x^5 + 4x^3

Part B:   8

Part C:   3

Part D:   -3x^8

Part E:   -3

Step-by-step explanation:

A. Standard polynomial is :

\( - 3 {x}^{8} + 2 {x}^{5} + 4 {x}^{3} \)

B. Degree of the polynomial is : 8

C. Number of terms are : 3

D. Leading term of the polynomial is:

\(-3 {x}^{8} \)

E. Leading co effecient of the polynomial is: -3

Let the first of the two consecutive integers be n. Then the next consecutive integer is n+1.

From the given information, we can form an inequality, which is:2n + (n+1) ≥ 25

The above inequality is formed from the statement "Twice the smaller of two consecutive integers increased by the larger integer is at least 25". Now, let's solve this inequality and find the values of n that satisfy it.2n + (n+1) ≥ 25Simplifying the above inequality, we get:3n + 1 ≥ 25

Subtracting 1 from both sides, we get:3n ≥ 24

Dividing both sides by 3, we get:n ≥ 8

Hence, the first of the two consecutive integers is greater than or equal to 8.

Therefore, the two consecutive integers that satisfy the given information are 8 and 9.

Now, we need to check which of the given values, 7, 8, or 9, satisfy the above inequality. Let's check for

n=7.2n + (n+1) = 2(7) + (7+1) = 15 < 25

Therefore, n=7 is not a solution.

Let's check for n=8.2n + (n+1) = 2(8) + (8+1) = 25 ≥ 25

Therefore, n=8 is a solution. Let's check for n=9.2n + (n+1) = 2(9) + (9+1) = 28 ≥ 25

Therefore, n=9 is also a solution.

Thus, we have found that the solutions to the given problem are n=8 and n=9.

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Answer: 9-11 below

Step-by-step explanation:

9. Well, we're given that the hole drains color(red)(3.5color(white)(l)"L" in color(green)(4color(white)(l)"d", so we can write the rate as

(color(red)(3.5color(white)(l)"L"))/(color(green)(4color(white)(l)"d"))

Now we perform this division, and afterward the denominator will be 1 and thus it will tell us the number of liters drained per day:

(color(red)(3.5color(white)(l)"L"))/(color(green)(4color(white)(l)"d")) = color(blue)(ulbar(|stackrel(" ")(" "(0.875color(white)(l)"L")/(1color(white)(l)"d")" ")|)

Therefore, color(blue)(0.875color(white)(l)"liters" are drained every day on average.

10. $

9.25

decrease per day

Explanation:

We can divide the total price decrease by the number of days it took to reach that decrease to find the average decrease per day:

$

45.75

5

=

$

9.25

decrease per day

11. The average change of altitude per minute would simply be the ratio of distance descended over time. That is:

average change of altitude = distance / time

average change of altitude = 0.44 mile / 0.8 minutes

average change of altitude = 0.55 mile / minute

Answer:

7.70

Step-by-step explanation:

maths

Answer:

y=-x+6

Step-by-step explanation:

make it into y=mx+b form

x+y=6

-x      -x

y=-x+6

Answer:

y=-x+6

Step-by-step explanation:

slope intercept form means y=mx+b

y is y

m is the slope (in this one I don't have a picture, so I didn't put slope)

x turns into -x (because to get x to the other side, you have to subtract x from both sides)

b is the y intercept (in this case 6)

To find the volume of the solid whose base is the region enclosed by x=2 and x=7, we need to integrate the cross-sectional area over the interval from x=2 to x=7. The area of the cross-section at any value of x is given by y^2/2, where y is the distance from the x-axis to the curve.

Therefore, the volume of the solid can be found by the following integral:

V = ∫[2,7] A(x) dx
where A(x) = y^2/2

We can find y in terms of x by solving for y in the equation of the curve. Since no curve is given in the problem, we will assume that the curve is y = f(x).

Thus, the volume of the solid is given by the integral:

V = ∫[2,7] (f(x))^2/2 dx

Note that this integral assumes that the solid is being formed by rotating the region about the x-axis. If the solid is being formed by rotating the region about the y-axis, the formula for A(x) would be x^2/2, and the integral for V would be:

V = ∫[a,b] (f(y))^2/2 dy

where a and b are the y-coordinates of the endpoints of the region.

Overall, the solution for finding the volume of the solid whose base is the region enclosed by x=2 and x=7 can be found using the formula:

V = ∫[2,7] (f(x))^2/2 dx

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Answer:6.56

Step-by-step explanation:

Answer:

Step-by-step explanation:

Length of the third board = Total length - ( sum of other two boards)

                                         = 21.35 - ( 8.2 + 6.42)

                                        = 21.35 - 14.62

                                       =      6.73 m

Answer:

If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

Step-by-step explanation:

If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

Answer:

16 Miles/Hours

Step-by-step explanation:

Average speed is the total distance covered divided by the total time

In that case we have a distance of 4 miles

Time is 15 minutes and in order to convert from minutes to hours we divide by 60 and it becomes 0.25 hours

So 4/0.25 is 16 Miles/Hours

Answer:1.2mph

Step-by-step explanation:

3/5*2=1.2 and 1/2*2=1 so it’s 1.2 mph

Answer: \(3^{\circ}C\)

Step-by-step explanation:

Given

The temperature on Monday was \(-5^{\circ}C\)

By Tuesday, it becomes \(-2^{\circ}C\)

Change in temperature is the difference between the two temperatures.

\(\Rightarrow \Delta T=-2-(-5)\\\Rightarrow \Delta T=-2+5\\\Rightarrow \Delta T=3^{\circ}C\)

Therefore, the change in temperature is \(3^{\circ}C\).

Answer:

The efficiency of the kettle is 75%

Step-by-step explanation:

Given;

total input energy of the kettle, Qi = 1000 J

energy transferred as sound = 100 J

energy transferred as light = 50 J

energy transferred to surrounding =  100 J

Total lost energy = 100 J + 50 J + 100 J

Total lost energy = 250 J

Total output energy = 1000 J - 250 J  = 750 J

Efficiency of the kettle is given by;

\(E_f =\frac{0utput \ energy}{1nput \ energy} *100\%\\\\E_f = \frac{750 \ J}{1000 \ J}*100\\\\ E_f = 75 \%\)

Therefore, the efficiency of the kettle is 75%

The circumference of the circle is 26.38 inches and the area of the circle is 55.39 square inches, both rounded to the nearest hundredth.

The diameter of a circle is the distance across the circle passing through its center. In this problem, the diameter of the circle is given as 8.4 inches. We can use the formula for the circumference and the area of a circle in terms of its diameter to find the solutions.

First, we can find the radius of the circle by dividing the diameter by 2. So, the radius is 8.4/2 = 4.2 inches.

To find the circumference of the circle, we can use the formula:

C = πd

where d is the diameter. Substituting the value of d = 8.4 inches and π = 3.14, we get:

C = 3.14 x 8.4 = 26.376

Therefore, the circumference of the circle is 26.38 inches (rounded to the nearest hundredth).

To find the area of the circle, we can use the formula:

A = πr²

where r is the radius. Substituting the value of r = 4.2 inches and π = 3.14, we get:

A = 3.14 x (4.2)² = 55.3896

Therefore, the area of the circle is 55.39 square inches (rounded to the nearest hundredth).

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Question 9: Choice (A) is the answer  

    \(\frac{1}{5} * x+\frac{1}{3} =\frac{7}{15} \\\\\frac{x}{5}=\frac{7}{15} -\frac{1}{3} = \frac{7}{15} -\frac{1*5}{3*5} =\frac{7-5}{15} \\\\\frac{x}{5} =\frac{2}{15} \\\\15x = 10\\\\x = \frac{10}{15} =\frac{2}{3} ; (A)\)

Question 10: Choice (B) is the answer:

   \(\frac{4}{6}+x=\frac{11}{12} \\\\x= \frac{11}{12} -\frac{4}{6} =\frac{11}{12} -\frac{4*2}{6*2} =\frac{11-8}{12} \\\\x = \frac{3}{12} =\frac{1}{4}; (B)\)

Hope that helped!

Answer:

he already answered it for me and you.

Step-by-step explanation:

Answer:

x=9

Step-by-step explanation:

You would change it to x^2 = 81 which is 9.

We have the next system of equations

First, we need to substitute the value of y of the second equation in the first equation.

Then we simplify the expression

then we sum like terms

then we isolate the x

the value of x is 1.

Then to know the value of y we will substitute the value of x in the second equation

the value of y is 4.

The solution of the system of equations is x=1, y=4 in point notation (1,4) this system only has one solution.

Answer:

∠4 = 64°

Step-by-step explanation:

If ∠3 and ∠4 are congruent, it means that both angles sum up to 180°

Given that, ∠3 = 116°

=> ∠3 + ∠4 = 180°

=> 116° + ∠4 = 180°

=> ∠4 = (180 - 116)°

=> ∠4 = 64°

If my answer helped, kindly mark me as the brainliest!!

Thank You!!

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

The rule for the function g(x) is:

g(x) = 1.15*(x^2 - 3x -16)

First we know that the function f(x) is f(x) = x^2 - 7x

And we know that h(x) is a translation of 6 units down and 2 units to the left of f(x), then:

h(x) = f(x + 2) - 6

Now we know that g(x) is 115% of h(x), then we can write:

g(x) = 1.15*h(x)

Replacing h(x) by the rule above we get:

g(x) = 1.15*(f(x + 2) - 6)

Replacing the actual function there:

g(x) = 1.15*( (x + 2)^2 - 7*(x + 2) - 6)

g(x) = 1.15*( x^2 + 4x + 4 - 7x - 14 - 6)

g(x) = 1.15*(x^2 - 3x -16)

This is the rule for function g(x).

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Answer:

B

Step-by-step explanation:

Answer:

it's C

Step-by-step explanation:

because B is wrong

The half life period is the time in which only half of the given population remains. It can be represented through this equation:

\(f(t)=a\times(1/2)^{\frac{t}{h}}\)

We're given:

For most questions like this, we would have to plug these values into the equation mentioned above. However, this question asks for the time elapsed after 3 half-lives.

This can be calculated simply by multiplying the given half-life by 3:

28 million years x 3

= 84 million years

84 million years

Answer:

A) 250

B) 1250

Step-by-step explanation:

Amount = 125 x no. People

A) amount = 125 x 2 =250g pasta

B) amount = 125 x 10 =1250g pasta.

Hope this helped!

Answer:

0.16 pounds. I am pretty sure you just add up all the numbers. I hope this helps!

Step-by-step explanation:

Answer:

The sum of money received by Ali, Carrie and Bryan is $ 740.

Step-by-step explanation:

At first we translate mathematically each sentence:

(i) Ali, Carrie and Bryan received a sum of money.

\(a\) - Ali's money.

\(b\) - Bryan's money.

\(c\) - Carrie's money.

(ii) Bryan's money was \(\frac{3}{5}\) of  Ali's money.

\(b = \frac{3}{5}\cdot a\) (1)

(iii) The ratio of Ali's money to Carrie's money was 4 : 1.

\(\frac{a}{c} = 4\) (2)

(iv) Ali had $ 160 more than Bryan.

\(a = b + 160\) (3)

After some algebraic handling, we have the following system of linear equations:

\(3\cdot a - 5 \cdot b = 0\) (1b)

\(a - 4\cdot c = 0\) (2b)

\(a - b = 160\) (3b)

The solution of the system is: \(a = 400\), \(b = 240\), \(c = 100\)

The sum of money is:

\(s = a + b + c\)

\(s = 740\)

The sum of money received by Ali, Carrie and Bryan is $ 740.

Step-by-step explanation:

(2*5)*4 = 10*4 = 40

2*(5*4) = 2*20 = 40