Find the missing side

Answer:

4 cm

Step-by-step explanation:

Given 2 similar figures with sides in ratio a : b , then

ratio of areas = a² : b²

let n be the length of the smaller one , then

ratio of sides = n : 10

ratio of areas = n² : 10² = n² : 100

Using proportion

( [tex]\frac{ratio}{area}[/tex] )

[tex]\frac{n^2}{24}[/tex] = [tex]\frac{100}{150}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )

3n² = 48 ( divide both sides by 3 )

n² = 16 ( take the square root of both sides )

n = [tex]\sqrt{16}[/tex] = 4

length of the smaller one is 4 cm

Answer:2 and 6

Step-by-step explanation:

Given

In 4 years Craston's age will be the same as Terrins age is now

Suppose the present of Craston's and Terrins are [tex]x[/tex] and [tex]y[/tex] respectively

According to the question

[tex]\Rightarrow x+4=y\\\Rightarrow y-x=4\quad \ldots(i)[/tex]

In 2 years Terrin will be twice as old  as craston

[tex]\Rightarrow (y+2)=2(x+2)\\\Rightarrow y-2x=4-2\\\Rightarrow y-2x=2\quad \ldots(ii)\\[/tex]

Solving (i) and (ii) we get

[tex]x=2,y=6[/tex]

Thus, the present age of Craston and Terrins are [tex]2[/tex] and [tex]6[/tex]

Answer:

Please find attached, the required graph created on MS Excel

Step-by-step explanation:

The distance between Sandy's house and the school = 200 m

The number of minutes Sandy talked to her friend for = 10 minutes

The time it took Sandy to return home to pick her homework = 5 minutes

Let x represent Sandy's location she stops to talk to her friend 10 minutes, we have;

The slope of the motion on the graph, m₁ = (x - 0)/(t - 0)

The slope of her motion running home to pick the up her homework, m₂ = (x - 0)/(5 - 0)

Given that t > 5, the slope on trip back home, m₁, is larger than are her initial slope, m₂

Therefore, where x = 125, we have;

The rate at which she returned home = m₂ = (125 m - 0)/(5 min - 0) = 25 m/min

Given that the same rate m₂ is what she used in heading back to school, we have;

The time it takes her to get to school = 200 m/(25 m/min) = 8 minutes

Therefore, whereby it took her 10 minutes to reach point x, we have the following coordinate points on the graph in a tabular form;

[tex]\begin{array}{ccc} Time \ (minutes) \ x-axis&&Distance \ (meters) \ y-axis\\0&&0\\10&&25\\15&&0\\23&&200\end{array}[/tex]

The plot of the above point is completed using MS Excel as shown in the attached diagram.

Answer:

2(2)+7=11

2(3)+7=13

2(4)+7=15

2(5)+7=17

2(9)+7=25

Step-by-step explanation:

2(2)+7

4+7=11

2(3)+7

6+7=13

2(4)+7

8+7=15

2(5)+7

10+7=17

2(9)+7

18+7=25

Answer:

a) Degree of 2; non-linear

b) Degree of 1; linear

Step-by-step explanation:

a) The degree is the highest power of the variable in the given equation:

Given  y = x^2 + 2x + 1

From the given equation, we can see that the highest power of x is 2. Hence the degree of the equation is 2.

Any equation with degrees of 2 and above is a non-linear equation. Hence the equation is a non-linear equation

b) For the equation 3x + 3y = 6

Divide through by 3

x + y = 2

From the given equation, we can see that the highest power of x and y is 1. Hence the degree of the equation is 1.

Any equation with a degree of 1 is a linear equation. Hence the equation is a linear equation

Answer:

Since this is a linear (non-exponential) population problem you can just use the standard y=mx+b form of an equation. Where m = (change in population/change in years)

The numbers you were provided state that over the course of 7 years (1998-1991) the population increased by 420 people (4130-3710). So, (420/7) = 60 = m. Assuming that the growth rate for 1990 is the same as 1991. then you would have a starting population of (3710-60) or 3650, that would be your "b" value since at t=0 P(t) = 3650. This yields a final equation of P(t) = 60t +3650. Check the answer at t=1 and you get the population during 1991: 3710.

Step-by-step explanation:

.

Answer:

3.6

Step-by-step explanation:

the ratio of AB to AD is 3/5 so the ratio of BC to DE is also 3/5, therefore BC=3/5 DE= (3/5)6= 3.6

Answer:

.441320612

or

44.132%

Step-by-step explanation:

This is binomial

fewer than 3 is equal to p(0)+p(1)+p(2)

[tex]p(0)={19\choose0}*.15^0*(1-.15)^{19}=.045599448\\p(1)={19\choose1}*.15^1*(1-.15)^{18}=.152892268\\p(2)={19\choose2}*.15^2*(1-.15)^{17}=.242828896\\p(0)+p(1)+p(2)=.441320612[/tex]

Answer:

156

Step-by-step explanation:

f(x)= 4^(2x) -100

Let x =2

f(2)= 4^(2*2) -100

   = 4^4 - 100

   = 256 -100

   = 156

Answer:

40 kg

Step-by-step explanation:

[tex]\frac{5}{83.75} :\frac{y}{670}[/tex]

y · 83.75 = 5 · 670

83.75y = 3350

83.75y ÷ 83.75 = 3350 ÷ 83.75

y = 40

The amount of rice you can buy for ₹670 is given by the equation

A = 40 kilograms

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount of rice for ₹670 be A

Now , the equation will be

The amount for 5 kg of rice = ₹ 83.75

So , the amount for 1 kg of rice = amount for 5 kg of rice / 5

The amount for 1 kg of rice = 83.75 / 5

The amount for 1 kg of rice = ₹ 16.75

So , the amount of rice for ₹ 670 = 670 / amount for 1 kg of rice

The amount of rice for ₹ 670 = 670 / 16.75

The amount of rice for ₹ 670 = 40 kilograms

Therefore , the value of A is 40 kilograms

Hence , the amount of rice is 40 kg

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Answer:

D

Step-by-step explanation:

A function means that each input value (in this case, x) has only one output value (y). The vertical line test states that if a vertical line intersects with the relation more than once, it is not a function. Therefore, as a vertical line at x=0 intersects with the graph twice, the graph fails the vertical line test

Answer:

-8 is less than -1

Step-by-step explanation:

If you look at a number line

-8 -7 -6 -5 -4 -3 -2 -1 0

Which one is closest to 0. -1, therefore it is greater

The set of all numbers shown on the number line 8 < -1.

A number line is a horizontal line that has numbers in equal intervals. The numbers included on the line can be negative or positive taking zero as a reference point at the center called the origin.

The horizontal straight lines in which the integers are placed in equal intervals increase as we go right. The horizontal straight lines in which the integers are placed in equal intervals decreases as we go left.

A number line can be described as an instant line with numbers positioned at identical intervals or segments alongside its period. a variety of lines may be extended infinitely in any route and is commonly represented horizontally.

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Answer:

C.

Step-by-step explanation:

Dis means apart and junc means join so disjunction means the "state of being disconnected".

Answer:

[tex](2x-3)^{3}[/tex]

Step-by-step explanation:

2x * 2x * 2x would get the 8x^3

the -3 * -3 * -3  would get the -27

if you do all the other multiplications -36x^2 and 54 X would result

Answer:

65%

Step-by-step explanation:

120 * x = 78

78/120 = x

.65 = x

Answer:

35%

Step-by-step explanation:

First, set up the equation.

Then solve.

78-120 is -42.

Divide by 120. -0.35.

Multiply by 100. -35.

The negative sign means that it is decreasing, so you can take it away.

I hope this helps!

Answer:

MO, NO, MN

Step-by-step explanation:

First, we can identify this triangle as a right triangle, as given by the square next to the O. Next, we know that a right angle is equal to 90 degrees, and the sum of the angles of a triangle is equal to 180 degrees.

Therefore,

∠M + ∠O + ∠N (the angles of the triangle) = 180

49 + 90 + ∠N = 180

139 + ∠N = 180

subtract both sides by 139 to isolate the variable

∠N = 41

Therefore, ∠N is 41 degrees.

In a triangle, given the angles, we know that the side opposite the smallest angle is the side with the smallest length and so on.

Our angle lengths are

41, 49, and 90 degrees in order.

Therefore, the side opposite the largest angle (90 degrees, or ∠O) is the longest side. This is MN. Similarly, ∠N is the smallest angle, and the side opposite of that (MO) is the shortest side. This leaves NO to be in the middle

Answer:

3x10^17

Step-by-step explanation:

(9.3/3.1) * 10^(34-17) = 3^17

law of indices, x^m/x^n =x^m-n

Answer:

98

Step-by-step explanation:

1) You shulduse the formula x^2-y^2= (x-y)(x+y)

That obvious, that 9.9 is considered as x, and 0.1 as y

2) So  9.9²- 0.1²​= (9.9-0.1) * (9.9+0.1)=9.8*10=98

Answer:

q = 1/4

Step-by-step explanation:

-5/4 - (-1/4) = -1

-1/(q-1/2) = 4

-1 = 4(q-1/2)

-1 = 4q - 2

1 = 4q

q = 1/4

Answer:

Tote bag ; Picture Frame ; Mug

Step-by-step explanation:

Given the following souvenir list :

tote bags: 25 for $49.00

picture frames: 15 for $32.25

water bottles: 12 for $27.60

mugs: 8 for $15.92

T-shirts: 10 for $25.00

To determine the cost per item in the sourvenir :

Divide the cost of sourvenir by the number of items in each sourvenir ;

Tote bag = $49.00 / 25 = $1.96

picture frames = $32.25 / 15 = $2.15

water bottles = $27.60 / 12 = $2.30

mugs = $15.92 / 8 = $1.99

T-shirts = $25.00 / 10 = $2.50

Hence, souvenirs which costs less than 2.25 per item are :

Tote bag ; Picture Frame ; Mug

Answer:

y=-7/4x +10

Step-by-step explanation:

that the graph, you can plug the equation in desmos,

hope it helps! :)

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The usual glide slope for landing is about 3°. The descent rate here of 0.25 km/min corresponds to 15 km/h. For the slope to be 3°, the forward speed of the airplane would need to be 286 km/h, about 154 knots.

This is not unreasonable for an approach speed for a (very) heavy airplane. Usually, the rate would be a little lower, but we wanted something that would fit on the grid provided.

Answer:

4 triangles and 1 square

Step-by-step explanation:

Required

The shapes in two-dimensional net of a square pyramid

To do this, I will attach an attachment of a 2D net of a square pyramid (see attachment)

From the attachment, we can see that:

The 2d shape of the pyramid is made of 4 triangles and 1 square

Answer:

D

Step-by-step explanation:

Answer: A. 25 miles

Step-by-step explanation: I used Pythagorean’s Theorem.

Answer:

S = 35 + 20w

Step-by-step explanation:

Amount Samantha has in her account = $35

Additional savings per week = $20

Let

S =Totai savings in Samantha's account at the end of the week

w = number of weeks

The equation:

Totai savings in Samantha's account at the end of the week = Amount Samantha has in her account + (Additional savings per week * number of weeks)

S = 35 + 20w

Answer:

s=35+20w

Step-by-step explanation:

Answer:

8.8 =x

Step-by-step explanation:

We know x is the median so

(5.5+12.1) /2 = x

17.6/2 =x

8.8 =x

Answer:

x = -8/b

Step-by-step explanation:

2bx – bx = -8

Combine like terms

bx = -8

Divide by b

bx/b = -8/b

x = -8/b

Answer:

22/5

Step-by-step explanation:

3m+18+2m=40

5m=40-18

5m=22

m=22/5

[tex] \bf \large \longrightarrow \: 3m \: + \: 18 \: + \: 2m \: = \: 40[/tex]

[tex] \bf \large \longrightarrow \:5m \: + \: 18 \: = \: 40[/tex]

[tex] \bf \large \longrightarrow \:5m \: = \: 40 \: - \: 18[/tex]

[tex] \bf \large \longrightarrow \:5m \: = \: 22[/tex]

[tex] \bf \large \longrightarrow \:m \: = \: \frac{22}{5} \\ [/tex]

[tex] \bf \large \longrightarrow \:m \: = \: \cancel\frac{22}{5} \: \: ^{4.4} \\ [/tex]

[tex] \bf \large \longrightarrow \:m \: = \: 4.4[/tex]

Answer:

[tex] \sqrt[]{ \frac{0}{0} } [/tex]

Explainion are shown in pictures above

Answer:

D, [tex](90-y)[/tex] degrees

Step-by-step explanation:

Complementary angles are angles that add up to 90 degrees. Since angle A and angle B are complementary, they add up to 90. Since the value of angle A is y degrees, we can substitute y into the equation to get

[tex]y+B=90[/tex]

To get the measure of angle B, we must isolate B.

To isolate B, we have to remove every term from its side.

The only term on the side that B is on other than B is y. To remove y from the left side, we must subtract y from both sides. Doing this will result in the equation:

[tex]B=90-y[/tex]

The only answer option that meets this criteria is D.