The present age of Madison's Mother is 3 time that of Madison. After 6 1/4 years, the sum of their age will be 53 3/4 years. Find their present ages. (Estimate to the nearest whole number)

Write the area A of an equilateral triangle as a function of the length s of its sides. Draw the triangle; label each side "2s". Draw the altitute; it will bisect the base into s and s. ... Therefore, the area is equal to the measure of the bisected side times the measure of the altitude, quantity divided by 2.

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Answer:

Step-by-step explanation:

Part A

Each side including     the base is s.

Part B

Use 1/2 the base to find the height. The height meets the base at 90 degrees which gives you the right to use c^2 = b^2 + a^2

The hypotenuse is s

The base is 1/2s

h^2 = s^2 - (1/2s)^2

h^2 = s^2 - 1/4 s^2

h^2 = 3s^2/4

h = sqrt(3)/2 *s

Area = 1/2 * s * sqrt(3)/2 s

Area = 1/4 * s^2 * sqrt(3)

Answer:

-10k×2+7

= -20k+7

Step-by-step explanation:

is the answer

Answer:

a) X=75°

y= 105°

b) b= 120°

a=45°

d) r=75°

q=37°

p= 37°

e) y=100°

X= 143°

Step-by-step explanation:

soln no. a

here,

X+50+55=180(sum of all angle of triangle)

or, X= 180-105

or, X= 75°

again,

X+y = 180 (straight angle)

or, y= 180-75

or, y= 105°

soln no b

here,

b+60=180(straight angle)

or, b = 180 - 60

or, b = 120°

again,

a+60+75=180(sum of all angle of triangle)

or, a = 180- 135

or, a = 45°

soln no. d

here,

r=70°( alternate angle)

again,

73°+q+r=180( sum of all angle of triangle)

or,q=180-143

or,q=37°

again,

p=q=37(alternate angle)

soln no. e

y+80=180(straight angle)

or,y= 180-80

or, y = 100°

again,

63+80+<RMB=180(sum of all angles of triangle)

or, 143+<RMB=180

or, <RMB=180-143

or,<RMB= 37°

again,

X+ <RMB= 180(straight angle)

or,X= 180°-37°

or, X = 143°

Answer:

The answer is A. [tex]\frac{3(x-21)}{(x+7)(x-7)}[/tex].

Step-by-step explanation:

To find the difference of this problem, start by simplifying the denominator, which will look like [tex]\frac{3}{x+7}-\frac{42}{(x+7)(x-7)}[/tex]. Next, multiply [tex]\frac{3}{x+7}[/tex] by [tex]\frac{x-7}{x-7}[/tex]  to create a fraction with a common denominator in order to subtract from [tex]\frac{42}{(x+7)(x-7)}[/tex]. The problem will now look like [tex]\frac{3}{x+7}*\frac{x-7}{x-7}-\frac{42}{(x+7)(x-7)}[/tex].  

Then, simplify the terms in the problem by first multiplying [tex]\frac{3}{x+7}[/tex] and [tex]\frac{x-7}{x-7}[/tex], which will look like [tex]\frac{3(x-7)}{(x+7)(x-7)}-\frac{42}{(x+7)(x-7)}[/tex]. The next step is to combine the numerators over the common denominator, which will look like [tex]\frac{3(x-7)-42}{(x+7)(x-7)}[/tex].

Next, simplify the numerator, and to simplify the numerator start by factoring 3 out of [tex]3(x-7)-42[/tex], which will look like [tex]\frac{3(x-7-14)}{(x+7)(x-7)}[/tex]. Then, subtract 14 from -7, which will look like [tex]\frac{3(x-21)}{(x+7)(x-7)}[/tex]. The final answer will be [tex]\frac{3(x-21)}{(x+7)(x-7)}[/tex].    

Answer:

60 (E)

Step-by-step explanation:

He plants seeds -> plants grow to 12 times the original weight of the seeds -> he sells 50 tonnes from the harvest -> remainder is used as the next batch of seeds

He harvested 120 tonnes this year which means the original weight of the seeds planted was 120÷12 = 10 tonnes. This means that last years harvest would be the 10 tonnes used as seeds plus the 50 tonnes that would have been sold immediately, 10+50 = 60 tonnes

Answer:

B

Step-by-step explanation:

Open circle means the number is not included.

Hope this helps <3

Answer:

530in²

Step-by-step explanation:

Area of triangle(a)=1/2bh=1/2*40*26.5=530

Answer: A): 15.90 ounces to 16.4 ounces.

Step-by-step explanation:

Considering the standard deviation is 0.25 ounces. The mean of the juice is 16.15 ounces. Additionally, 68% is one standard deviation away from the mean.

With that being said, you would do the following calculations:

[tex]16.15-0.25=15.90\\\\16.15+0.25=16.40[/tex]

This question relates to The Empirical Rule and understanding how it works. A brief summary is that within one standard deviation of the mean, that is where 68% of the data lies. Two standards deviations is 95%. And three standard deviations is 99.5%.

The formula: [tex]u\frac{+}{-} o[/tex]

the mean PLUS OR MINUS the standard deviation.

Answer:

A

Step-by-step explanation:

Answer:

1. h

2. b

3. a

4. d

5. c

Step-by-step explanation:

all answers are straight forward. only the last (5) is phrased a bit strangely. I would have said "reflect across a horizontal line".

Given a function g(x), its derivative, if it exists, is equal to the limit

[tex]g'(x) = \displaystyle\lim_{h\to0}\frac{g(x+h)-g(x)}h[/tex]

The limit is some expression that is itself a function of x. Then the derivative of g(x) at x = 1 is obtained by just plugging x = 1. In other words, find g'(x) - and this can be done with or without taking a limit - then evaluate g' (1).

Alternatively, you can directly find the derivative at a point by computing the limit

[tex]g'(1) = \displaystyle\lim_{h\to0}\frac{g(1+h)-g(1)}h[/tex]

But this is essentially the same as the first method, we're just replacing x with 1.

Yet another way is to compute the limit

[tex]g'(1) = \displaystyle\lim_{x\to1}\frac{g(x)-g(1)}{x-1}[/tex]

but this is really the same limit with h = x - 1.

You do not compute g (1) first, because as you say, that's just a constant, so its derivative is zero. But you're not concerned with the derivative of some number, you care about the derivative of a function that depends on a variable.

Answer:

Step-by-step explanation:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Answer:  D) 8

Work Shown:

32/24 = 2x/12

32*12 = 24*2x

384 = 48x

48x = 384

x = 384/48

x = 8

The correct option is Option D: the value of x is 8

The triangles whose corresponding angles are equal and the corresponding sides are in equal proportiion are called similar triangles.

If two triangles are similar

then a₁/a₂=b₁/b₂=c₁/c₂

where a₁, b₁, and c₁ are the sides of one triangle

a₂, b₂, and c₂ are the sides of another triangle

Here it is given that

triangles ΔJLK and ΔRJS are similar.

so by the property of similar triangles,

JR/JL = JS/JK = RS/KL

Given that JR=24

JL=32

JS=12

JK=2x

By using the property

JR/JL = JS/JK

⇒ 24/32 = 12/2x

⇒2x= 12*32/24

⇒2x=16

⇒x=16/2

⇒x=8

Therefore the value of x is 8.

Learn more about similar triangles

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Answer:

y ≥ 0

Step-by-step explanation:

The range of the function is the output values.

The y value goes from 0 to infinity

y ≥ 0

Answer:

d. -4x² + 8x - 6

Step-by-step explanation:

(3x² + 2x - 4) + (-7x² + 6x - 2)

3x² + 2x - 4 - 7x² + 6x - 2

3x² - 7x² + 2x + 6x - 4 - 2

-4x² + 8x - 6

Answer:

rational

Step-by-step explanation:

it can be written as a fraction

Answer:

Hello,

a=0.5

Step-by-step explanation:

[tex]\left \{ \begin{array}{ccc}ax+2y&=&12\\8x+32y&=&144\\\end{array}\right.\\\\\\\Longleftrightarrow\ \left \{ \begin{array}{ccc}ax+2y&=&12\\x+4y&=&18\\\end{array}\right.\\\\\\\Longleftrightarrow\ \left \{ \begin{array}{ccc}(1-2a)x&=&-6\\x+4y&=&18\\\end{array}\right.\\\\if\ 1-2a\neq 0\ (or\ a\neq \dfrac{1}{2} )\ then\\\left \{ \begin{array}{ccc}x&=&\dfrac{6}{2a-1}\\\\y&=&\dfrac{18-\dfrac{6}{2a-1}}{4} \\\end{array}\right.\\\\[/tex]

[tex]\Longleftrightarrow\ \left \{ \begin{array}{ccc}x&=&\dfrac{6}{2a-1}\\\\y&=&\dfrac{ 3(3a-2)}{2a-1} \\\end{array}\right.\\\\[/tex]

else\

[tex]a=\dfrac{1}{2} \\\Longleftrightarrow\ \left \{ \begin{array}{ccc}\dfrac{1}{2} x+2y&=&12\\\\x+4y&=&18 \\\end{array}\right.\\\\\\\Longleftrightarrow\ \left \{ \begin{array}{ccc}x+4y&=&24\\\\x+4y&=&18 \\\end{array}\right.\\\\\\\Longleftrightarrow\ \left \{ \begin{array}{ccc}0=6\ !!!!!\\\end{array}\right.\\\\Syetem\ has\ no\ solution\\[/tex]

Answer:

[tex]\boxed{x=13.89\:km}[/tex]

Step-by-step explanation:

Pythagorean theorem

[tex]x^2=(12^2)+(7^2)[/tex]

[tex]x^2=144+49[/tex]

[tex]x^2=193[/tex]

[tex]x=\sqrt{193}[/tex]

[tex]\boxed{x=13.89\:km}[/tex]

Answer:

Organize into a table for good gatherings.

Answer:

8

Step-by-step explanation:

-2 xy

Let x = -4 and y = 1

-2 (-4)*(1)

8(1)

8

Answer:

1/36

Step-by-step explanation:

it is the exact same as if both your dice had the numbers {1,2,3,4,5,6}

you said the SUM of the dice that is indicates the answer of the addition of two (or for that matter more) numbers,... the only numbers that would sum 2 is 1+1,... and because you only have two ones (one per die) the answer is the same as if they where die with normal numbers,...

The probability of rolling a sum of 2 with these dice is 1/36.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that;

Pair of dice have= {1,2,2,3,3,4}

Now,

The probability of rolling a sum of 2 with two dice is the same as the probability of rolling snake eyes, since the only way to get a sum of 2 is if both dice show a 11. The probability of rolling a 1 on a single die is 1/6, so the probability of rolling a 1 on both dice is (1/6) × (1/6) = 1/3612.

However, in this case, the dice are not standard six-sided dice, but have different numbers on their faces. The first die has {1,2,2,3,3,4} and the second die has {1,3,4,5,6,8}. The probability of rolling a 1 on the first die is still 1/6, but the probability of rolling a 1 on the second die is also 1/6. Therefore, the probability of rolling a sum of 2 with these dice is still (1/6) × (1/6) = 1/36.

This probability cannot be reduced any further, since 1 and 36 have no common factors other than 1.

Therefore, the probability will be 1/36.

Learn more about probability here;

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Answer:

(f+g)(x)=5x+2x²-7x+4+3x-7 = 2x²+x-3

Step-by-step explanation:

Answer:

=6x^3-20x^2+26x-28

Step-by-step explanation:

Answer:

r=8

Step-by-step explanation:

45=6r-3

48=6r

r=8

Answer:

the volume is 1000 cm^3

Step-by-step explanation:

first we need to find where is the base, and height, for this case, the trian is the base, not the rectangle, so it maybe eas if you draw a upright angle os the shape, with the triangle facing down.

As show you need to have bare and height for the volume of the prism, which we already know the height is 25 (h=25) so now we need to find the base.

for the base, since it’s a triangle, which has the area formal of 1/2(bh), so now just plot the number in, 1/2x10x8= 40 cm^2

now using the volume of prism formal; V = bh = 40 x 25 = 1000 cm^3

Answer:

A={x| x>7} = 8,9

B= {5,6}

1,

2,{5,6,8,9}

3,{}

4{}

Answer:

Diana sold 25 tickets and Dulce sold 30 tickets

Step-by-step explanation:

Let us assume that Diana sold x number of tickets, dulce sold 20% more x or 1.2x. ATQ, x+1.2x=55. x=25. So Diana sold 25 tickets and Dulce sold 30 tickets

Answer:

3 ft per minute

Step-by-step explanation:

Take the distance and divide by the time

3/4 ft ÷ 1/4 minute

Copy dot flip

3/4 * 4/1

Rewriting

3/1 * 4/4

3/1 *1

3 ft per minute

Answer:

Definition of Congruent angles.

Step-by-step explanation:

Given

See attachment

Required

Complete the proof at step 8

At step 8, we have:

[tex]\angle ABC \cong \angle ABD[/tex]

When the sign [tex]\cong[/tex] is used, it means congruence

In other words;

ABC and ABD are congruent

Hence, the missing statement at step 8 is: Definition of Congruent angles.

Answer:

ABC and ABD are congruent

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

Kristian : Stephanie

3                 2

Kristian receives 72

72/3 = 24

Multiply each side by 24

Kristian : Stephanie

3*24                 2*24

72                        48