The altitude (i.e., height) of a triangle is increasing at a rate of 2 cm/minute while the area of the triangle is increasing at a rate of 1.5 square cm/minute. At what rate is the base of the triangle changing when the altitude is 12 centimeters and the area is 99 square centimeters

Answer:  D: x = (-9, 0) U (0, 4) U (4, 8)

Step-by-step explanation:

Line 1:      y = -2               where      -9 < x < 0

Line 2:     y = 2)x + 1        where       0 < x < 4

Line 3:    y = -(1/2)x + 6    where       4 < x < 8

Domain represents the x-values.  Since all of them are open dots, the intervals are strictly less than (<).

-9 < x < 0   and   0 < x < 4   and   4 < x < 8 is the union of these intervals

-9 < x < 0   U   0 < x < 4   U   4 < x < 8

Interval Notation: D: x = (-9, 0) U (0, 4) U (4, 8)

Answer:

1st piece:  

✔ –10 < x < 0

2nd piece:  

✔ 0 < x < 4

3rd piece:  

✔ 4 < x < 8

Step-by-step explanation:

Step-by-step explanation:

Hi there!

From above question;

A cuboid has a length of 25cm, a width of 5cm and height of (x-2)cm.

Length (l) = 25cm

width (b) = 5cm

height (h) = (x-2)cm.

a).

Volume= l*b*h

V = 25*5*(x-2)

V = 125(x-2)

V = 125x - 250 → Answer

b).

(i)

V = 750cm³

V = 125x - 250

750 = 125x - 250..........(i)

(ii)

The equation (i) is: 750 = 125x - 250

or, 125x = 750+250

or, 125x = 1000

or, X = 1000/125

Therefore, X= 8cm.

(iii)

Height (h) = x-2

= 8-2

= 6

Therefore, height is 6cm.

Hope it helps!

Answer:

Step-by-step explanation:

That's an awful lot of points. You don't have to give that many. 10 or 15 points would be more than enough.

The graph touches the x axis at 1 point. That means its basic formula is y = (x - a)^2

Since it  upside down, the formula is y = -(x - a)^2. A couple of other things are true.

a = 1 because that's where the graph touches the x axis. y = - x^2 has shifted 1 unit to the right.

Finally the y intercept is -4 which means that the final equation is y = -4(x-1)^2

That's all preliminary. The actual question is, what does the discriminate look like?

y = -4(x^2 - 2x + 1)

y = -4x^2 + 8x - 4

a = - 4

b = 8

c = - 4

sqrt(b^2 - 4ac)

sqrt(8^2 - 4(-4)(-4) )

sqrt(64 - 64) = 0

The answer is the third one. The answer will always be 0 when the graph touches the x axis and does not go through it.

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-intercept.

If we know that the line passes through two points, (x₁, y₁) and (x₂, y₂), then we can write the slope as:

a = (y₂ - y₁)/(x₂ - x₁).

Also, for a given line:

y = m*x + s

A perpendicular line to that one must have a slope:

a = -(1/m)

And the intersection between two perpendicular lines forms four 90° angles.

So first, we need to find the slope of the line that passes through A and B.

A = (-3, 3)

B = (-1, -1)

Then the slope of the line is:

a = (-1 - 3)/(-1 - (-3)) = -4/2 = -2

a = -2

The slope of a perpendicular line should be:

slope = -(1/a) = -(1/-2) = 1/2

Then the perpendicular line will be something like:

y = (1/2)*x + b

To find the value of b, we can use the other restriction.

This line needs to pass through point C.

And we can see that point C is:

C = (1, 2)

This means that when x is equal to 1, y must be equal to 2.

Then replacing these in the above equation we get:

2 = (1/2)*1 + b

2 = 1/2 + b

2 - 1/2 = 4/2 - 1/2 = 3/2 = b

Then our equation is:

y = (1/2)*x+ 3/2

The graph of this line can be seen in the image below, the green line is the line that we found.

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Answer:

Step-by-step explanation:

Answer:

x = 6       la cantidad de estantes

y = 65    cantidad de libros

Step-by-step explanation:

LLamemos "x" la cantidad de estantes que tiene Marta, y llamaremos "y" la cantidad de libros.

La primera condición que se debe cumplir es que cuando Marta coloca 12 libros en cada estante entonces le faltan 7, esto lo expresamos así:

y  +  7  = 12*x        (1)

La segunda condición establece que si Marta coloca los libros en número de 10 por estante le quedan 5 sin colocar, luego esto en lenguaje matemático se expresa así:

y  -   5   = 10*x     (2)

Ahora hemos obtenido un sistema de dos ecuaciones con dos incógnitas que se resuelve por cualquiera de los métodos conocidos, usaremos el método de sustitución.

Despejamos   y en la primera ecuación y lo sustituimos en la segunda, de esa forma obtendremos el valor de x

y  =  12*x  - 7

(12*x - 7 ) - 5  = 10*x

2*x  -12 = 0

2*x = 12

x = 6       la cantidad de estantes, y

y  =  12*x -7

y  =  72  -  7

y =  65    cantidad de libros

answer:

-1

here's the explanation below :))

Answer: D is my guess.

Step-by-step explanation:

If you multiply those two number and subtract it by tanisha that probably is your answer if I'm  incorrect I'm sorry hopefully this helped

Answer:

Does the answer help you?

Answer:

vertex(-3,27)

Step-by-step explanation:

f(x)= x^2+ 6x + 36 ( a=1,b=6,c=36)

V(h,k)

h=-b/2a=-6/2=-3

k=f(-3)=3²+6(-3)+36

f(-3)=9-18+36=27

vertex(-3,27)

Answer:

[tex]\boxed{x=60}[/tex]

Step-by-step explanation:

The exterior angle theorem states that the exterior angle of a triangle is equal to the sum of the two opposite interior angles of the triangle.

[tex]130=70+x[/tex]

Subtract 70 from both sides.

[tex]130-70=70+x-70[/tex]

[tex]60=x[/tex]

Answer:

x = 60°

Step-by-step explanation:

Exterior angle is equal to the  sum of opposite interior angles

x + 70 = 130

Subtract 70 from both sides

x = 130 - 70

x = 60°

Hi there! :)

Answer:

[tex]\huge\boxed{y = 4x - 2}[/tex]

Given line with an equation of y = 4x + 3

Parallel lines contain equivalent slopes, so a parallel line to the given equation would contain a slope of m = 4.

Plug in the coordinates of the point given, along with the slope into the equation y = mx + b where:

m = slope

y = y-coordinate of point

x = x-coordinate of point

Solve for the 'b' value, or y-intercept:

y = mx + b

6 = 4(2) + b

6 = 8 + b

b = -2

Rewrite the equation as slope-intercept form:

y = 4x - 2

Answer:

When you see the word "parallel", you know the new line will have the same slope.

parallel to y = 4x + 3

So, the new line will have a slope of 4

"Indicate the region where y≥ 4x + 3

Plot y= 4x + 3 by finding the points that make it true. For example, (y = 0, x = 3/4), (y = 2, x = 2) and so on.

y = 4x + b

b is the y intercept ( point y when x = 0)

Insert new coefficients:

+2 = 4(0) + b

b = +2

[tex] \: [/tex]

[tex](2n+1)^2=4n^2+4n+1[/tex] therefore, the first blank is 1.

[tex]4n^2+4n+1=2(2n^2+2n)+1[/tex] therefore, the two other blanks are both 2.

The number in the proof ''The square of the sum of two consecutive integers is odd'' is 2 and 2.

To prove that, The square of the sum of two consecutive integers is odd.

The expression to prove is,

Let us assume that two consecutive integers are n and (n + 1).

Hence, the expression is written as,

[n + (n + 1)]² = (2n + 1)²

= (2n)² + 2 × 2n × 1 + 1²

= 4n² + 4n + 1

= 2 (2n² + 2n) + 1

= odd

Therefore, the number in the blanks are 2 and 2.

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Answer:

28 4/9

Step-by-step explanation:

5 1/3 times 5 1/3

Answer:

Part A:

Two types of translation are;

1) Horizontal translation left T(0, 8),

2) Vertical translation T(16, 0)

Part B:

For the horizontal translation transformation, k = 8

For the vertical translation transformation, k = 16

Part C:

For the horizontal translation transformation, the equation is f(x + 8) = g(x)

For the vertical translation transformation, the equation is f(x) + 16 = g(x)

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

Part A

We can shift f(x) up to g(x)

or we can shift f(x) to the left into g(x)

Part B

y = f(x) + k  k > 0 moves it up

f(x) goes from -1 to 17 for a distance of 18 units

We are moving up 18 units

k = 18

y = f(x + k) k> 0 moves it left

We are moving to the left from 0 to -6 units for a distance of 6 units

k = 6

Part C

Up:

g(x) = f(x) +18

Left:

g(x) = f(x+6)

A Gallup poll asked 1200 randomly chosen adults what they think the ideal number of children for a family is. Of this sample, 53% stated that they thought 2 children is the ideal number. Construct and interpret a 95% confidence interval for the proportion of all US adults that think 2 children is the ideal number.

Answer:

at 95% Confidence interval level: 0.501776   < p < 0.558224

Step-by-step explanation:

sample size n = 1200

population proportion [tex]\hat p[/tex]= 53% - 0.53

At 95% confidence interval level;

level of significance ∝ = 1 - 0.95

level of significance ∝ = 0.05

The critical value for [tex]z_{\alpha/2} = z _{0.05/2}[/tex]

the critical value [tex]z _{0.025}= 1.96[/tex] from the standard normal z tables

The standard error S.E for the population proportion can be computed as follows:

[tex]S,E = \sqrt{\dfrac{\hat p \times (1-\hat p)}{n}}[/tex]

[tex]S,E = \sqrt{\dfrac{0.53 \times (1-0.53)}{1200}}[/tex]

[tex]S,E = \sqrt{\dfrac{0.53 \times (0.47)}{1200}}[/tex]

[tex]S,E = \sqrt{\dfrac{0.2491}{1200}}[/tex]

[tex]S,E = 0.0144[/tex]

Margin of Error E= [tex]z_{\alpha/2} \times S.E[/tex]

Margin of Error E= 1.96 × 0.0144

Margin of Error E= 0.028224

Given that the confidence interval for the proportion  is  95%

The lower and the upper limit for this study is as follows:

Lower limit: [tex]\hat p - E[/tex]

Lower limit: 0.53 - 0.028224

Lower limit: 0.501776

Upper limit: [tex]\hat p + E[/tex]

Upper limit: 0.53 + 0.028224

Upper limit: 0.558224

Therefore at 95% Confidence interval level: 0.501776   < p < 0.558224

Answer:

x=-7/2, x=4/3

Step-by-step explanation:

[tex]6x^2+13x-28=0[/tex]

Multiply 6 and -28 to get -168

Find 2 numbers that multiply to 168 but add to 13

They are 21 & -8

Rewrite the equation into:

[tex]6x^2+21x-8x-28=0[/tex]

Factor

[tex]3x(2x+7)-4(2x+7)=0[/tex]

(3x-4)(2x+7)=0

3x=4

x=4/3

2x=-7

x=-7/2

Answer:

10

Step-by-step explanation:

it is Pythagoras theorem

6*6=36

8*8=64

64+36=100

square root of 100 is 10

Answer:

The vertex form is f(x) = (x + 5)² + 12

The minimum value of f(x) is point (-5, 12)

Step-by-step explanation:

1) The vertex form of a quadratic equation f(x) = x² + 10·x + 37,  which is the form f(x) = a·(x - h)² + k is found as follows;

For the general form of the quadratic equation, f(x) = a·x² + b·x + c

h = -b/(2·a) and k = f(h)

Therefore, for f(x) = x² + 10·x + 37,

a = 1, b = 10

∴ h = -10/2 = -5

k = f(-5) = (-5)² + 10×(-5) + 37 = 12

The vertex form is f(x) = a·(x - h)² + k gives;

f(x) = 1·(x - (-5))² + 12 = (x + 5)² + 12

The vertex form is f(x) = (x + 5)² + 12

2) The minimum value of x is found when d(f(x))/dx = 0

d(f(x))/dx = d(x² + 10·x + 37)/dx = 2·x + 10

d(f(x))/dx = 0 = 2·x + 10

x = -10/2 = -5

We check that it is the minimum by f''(x) being positive;

f''(x) = d(2·x + 10)/dx = 2 which is positive and x = -5 is the x-coordinate of the minimum value of f(x)

The x-coordinate of the minimum value of f(x) minimum value is f(-5) = (-5)² + 10×(-5) + 37 = 12

Therefore, we have;

The minimum value of f(x) = (-5, 12)

Answer:

The vertex is (-5,f(-5)=12), The minimum value of f(x) is 12.

Answer:

around 17 mistakes

Step-by-step explanation:

We can write a ratio to solve

54 words             300 words

------------------ = -------------------

3 mistakes             x mistakes

Using cross products

54x = 3*300

54x = 900

Divide by 54

54x/54 = 900/54

x =50/3

x = 16.66666666(repeating)

around 17 mistakes

X = mistakes in 300 words

54/3 = 300/X

54X = 3 x 300

X = 900/ 54

X = about 17 words, since 16 and 2/3 rounded to the nearest tenth is 17

Answer:

D

Step-by-step explanation:

vertical is basically the x axis, so the y axis has to be 0. using elimination, (0,8) and (0,7) are the only ones left.

Answer:

(a) 1:12

(b) 12:1

(c) 1:100

(d) 100:1

Answer:

7.50

Step-by-step explanation:

Take the total cost and divide by the number of pizzas

22.50/ 3 pizzas

7.50 per pizza

[tex] \rm \longrightarrow \:Cost \: \: of \: \: 1 \: \: pizzas \: = \frac{Cost \: \: of \: \: 3 \: \: pizzas }{Total \: \: pizzas }[/tex]

[tex]\rm \longrightarrow \:Cost \: \: of \: \: 1 \: \: pizzas \: = \frac{22.50 }{3 } \\ [/tex]

[tex]\rm \longrightarrow \:Cost \: \: of \: \: 1 \: \: pizzas \: = \cancel\frac{22.50 }{3 } \: \: ^{7.5} \\ [/tex]

[tex]\rm \longrightarrow \:Cost \: \: of \: \: 1 \: \: pizzas \: = \: 7.5 [/tex]

Hence, the cost of 1 pizza is $7.5

Answer:

I think its C because if I remember correctly zero of the function is just the x intercept

Answer:

Value of F(2) = 12

Step-by-step explanation:

Given:

F(x) = 7x - 2

Find:

Value of F(2)

Computation:

F(x) = 7x - 2

putting x = 2

f(2) = 7(2) -2

f(2) = 14 - 2

f(2) = 12

So, Value of F(2) = 12

Answer:

the answer is $27.90

Step-by-step explanation:

if you do 15 times 2.79 you will get $41.85

then do 25 times 2.79 and you will get $69.75

then subtract 69.75 from 41.85 and your answer will be $27.90

i hope this helps this is the only way i could find the answer!

$29.4864 money will you save by driving your friend's car.

Given that, your car gets 15 miles per gallon and your friend's car averages 25 mpg.

You decide to go on a road trip to St. George Island, which is 361 miles away.

A unit of volume for measuring liquids. 1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces. 1 US gallon = 231 cubic inches = 3.785411784 liters exactly.

Gallons needed for your car =361/15=24.06 gallons

Cost of 24.06 gallons of gas=24.06×2.79=$69.774

Gallons needed for friends car =361/25=14.44 gallons

Cost of 4.44 gallons of gas=14.44×2.79=$40.2876

Hence, while driving a friend's car you will save 69.774-40.2876=$29.4864

Therefore, $29.4864 money will you save by driving your friend's car.

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Answer:

0.069

Step-by-step explanation:

0.3*0.23=0.069

Step-by-step explanation:

x be an irrational number between 9.5 and 9.7.

So, we consider that  x = 9.562536941412578914...

Rounding to the nearest hundredth

x = 9.56.

9.56763865854637984..... (rounded 9.57)

irrational because it has no pattern

Answer:  [tex]\large \sqrt{91}[/tex]

Step-by-step explanation:

An irrational number is a square root in its simplest form.

We want an irrational number between 9.5 and 9.7

                               [tex]\huge 9.5<\sqrt x <9.7[/tex]

square all sides     90.25 < x < 94.09

Answer: The square root of any number between 90.25 and 94.09 will work so there are an infinite number of possible answers. [tex]\sqrt{91}, \sqrt{92}, \sqrt{93}, \sqrt{94}[/tex]

Answer: Choose randomly from the pile on the left.

Step-by-step explanation: The ratio of brown to black sticks on the left pile is 16:28 and on the right pile is 44:12. Therefore, jack should choose from the left side because there is a higher chance in picking a black stick.