Which figure is not a trapezoid?

Answer:

She needs 4 more gallons of blue paint than red paint

Step-by-step explanation:

Since the ratio is 3 to 2, 3 + 2 = 5.

The artist needs 20 gallons of purple paint, so 20/5 = 4

The amount of blue and red paint needed is 4x3 to 4x2, or 12 to 8.

She needs 12 gallons of blue paint and 8 gallons of red paint.

12 - 8 = 4

She needs 4 more gallons of blue paint than red paint.

Answer:

ok!

Step-by-step explanation:

blue = 8 gallons

red = 12 gallons

Answer:

0.2312

Step-by-step explanation:

Using the formula given,

[tex]P(x) = p(1-p)^{x-1}[/tex],

we use 0.34 for p and 2 for x:

[tex]P(2) = 0.34(1-0.34)^{2-1}\\\\P(2) = 0.34(0.68)^1\\\\P(2) = 0.34(0.68) = 0.2312[/tex]

Answer:

C

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h. k) are the coordinates of the centre and r is the radius

here (h, k) = (- 1, 10) and r = 2, thus

(x - (- 1))² + (y - 10)² = 2², that is

(x + 1)² + (y - 10)² = 4 → C

Answer:

3/32 of a cup of food

Step-by-step explanation:

Sammy's dog eats 3/4 cup of food at each meal. His cat eats 1/8 of that.

This comes out to (1/8)th of (3/4 cup), or:

 1        3

----- · ----- cup  =  3/32 cup

  8      4

The cat eats 3/32 of a cup of food.

Final answer:

Sammy's cat eats 3/32 cup of food per meal, which is calculated by multiplying the dog's portion, 3/4 cup, by 1/8.

Explanation:

Solving the question involves a basic understanding of fractional multiplication. Since Sammy's cat eats 1/8 of what the dog eats, we calculate the cat's portion by multiplying the dog's portion by 1/8.

Sammy's dog eats 3/4 cup of food at each meal. To find out what fraction of a cup Sammy's cat eats, we multiply 3/4 by 1/8.

Here's the calculation: 3/4 × 1/8 = 3/32

Therefore, Sammy's cat eats 3/32 cup of food at each meal.

Answer:

d 7(8 + 3)

Step-by-step explanation:

Answer:

x + y = z

y=5

z=10

x = z - y =10-5 =5

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

To answer this question we must evaluate

y = 0° on both sides of the equation.

For the left side we have:

[tex]sin(0\°) tan(0\°)[/tex]

We know that [tex]tan(0\°) =\frac{sin(0\°)}{cos(0\°)}[/tex]

We know that [tex]cos(0\°) = 1[/tex] and [tex]sin(0\°) = 0[/tex].

Therefore [tex]tan(0\°) = 0[/tex].

Then the left-hand side of the equals is equal to zero.

On the right side we have:

[tex]cos(y)[/tex]

When evaluating [tex]cos(y)[/tex] at [tex]y = 0[/tex]

We have to [tex]cos(0\°) = 1[/tex].

0 ≠ 1

The equation is not satisfied. Therefore y = 0 ° is a counterexample to the equation

Answer:true

Step-by-step explanation:

edge

Answer:

Final answer is approx x=1.27.

Step-by-step explanation:

Given equation is [tex]8^{-x+7}=3^{7x+2}[/tex].

Now we need to solve equation [tex]8^{-x+7}=3^{7x+2}[/tex] and round to the nearest hundredth.

[tex]8^{-x+7}=3^{7x+2}[/tex]

[tex]\log(8^{-x+7})=\log(3^{7x+2})[/tex]

[tex]\left(-x+7\right)\cdot\log\left(8\right)=\left(7x+2\right)\cdot\log\left(3\right)[/tex]

[tex]-x\cdot\log\left(8\right)+7\cdot\log\left(8\right)=7x\cdot\log\left(3\right)+2\cdot\log\left(3\right)[/tex]

[tex]-x\cdot\log\left(8\right)-7x\cdot\log\left(3\right)=2\cdot\log\left(3\right)-7\cdot\log\left(8\right)[/tex]

[tex]x\left(-\log\left(8\right)-7\cdot\log\left(3\right)\right)=\left(2\cdot\log\left(3\right)-7\cdot\log\left(8\right)\right)[/tex]

[tex]x=\frac{\left(2\cdot\log\left(3\right)-7\cdot\log\left(8\right)\right)}{\left(-\log\left(8\right)-7\cdot\log\left(3\right)\right)}[/tex]

Now use calculator to calculate log values, we get:

[tex]x=1.26501646392[/tex]

Round to the nearest hundredth.

Hence final answer is approx x=1.27.

Answer:

  5

Step-by-step explanation:

The horizontal distance between the points is 3 units; the vertical distance is 4 units. The straight-line distance is the length of the hypotenuse of a right triangle with those side lengths. So, the distance between the two points is ...

  √(3² +4²) = √(9+16) = √25 = 5 . . . . units

_____

Comment on this triangle

The numbers 3, 4, 5 are the smallest set of integers that satisfy the relation of the Pythagorean theorem. They are also the only set of sequential numbers or numbers in arithmetic sequence that satisfy the Pythagorean theorem. As a consequence, they show up often in geometry and algebra problems. The "3-4-5 triangle" is worth remembering. So, anytime you see numbers that have these ratios, such as 9, 12, 15, for example, you know they can be the sides of a right triangle.

Answer:

A

Step-by-step explanation:

cos(x)=2/3 in Q 4

sin(x/2)=+√(1-cos(x))/2

√(1-cos(x))/2=√(1-[2/3]/2=√(1/3)/2=-√(1/6) because sin is negative in Q 4

Answer:

See below.

Step-by-step explanation:

Because cos x = 2/3 the adjacent side = 2 and hypotenuse = 3 so the length of the opposite side =  

√(3^2 - 2^2) =  -√5 (its negative because we are in Quadrant 4).

So sin x =  -√5/3.

(a) sin (x /2) =  - √ [ (1 - cos x)/2 ]

= -√(1 - 2/3)/ 2)

= -√(1/6).  or -0.4082.

(b)  cos (x/2)  = √ [ (1 + cos x)/2]

=  √ 5/6 or 0.9129.

(c)   tan (x /2) =   ( 1 - cos x) / sin x.

=  ( 1 - 2/3) /   -√5/3

= -0.4472.

Answer:

wut is it

Step-by-step explanation:

[tex]f(x)=\ln(x^2+2x+4)\implies f'(x)=\dfrac{2x+2}{x^2+2x+4}[/tex]

The numerator determines where the derivative vanishes (the denominator has a minimum value of 3, since [tex]x^2+2x+4=(x+1)^2+3\ge3[/tex]).

[tex]2x+2=0\implies x=-1[/tex]

At this critical point, we have

[tex]f(-1)=\ln((-1)^2+2(-1)+4)=\ln3\approx1.099[/tex]

At the endpoints, we have

[tex]f(-2)=\ln4\approx1.386[/tex]

[tex]f(2)=\ln12\approx2.485[/tex]

so [tex]f[/tex] attains a maximum value of [tex]\ln12[/tex] and a minimum value of [tex]\ln3[/tex].

The absolute minimum of the function f(x) = ln(x2 + 2x + 4) is at x=-2 where the value is ln(4) and the absolute maximum is at x=2 where the value is ln(8). There are no critical numbers within the selected interval.

The given function is

f(x) = ln(x

2

+ 2x + 4)

, for which we need to find the absolute maximum and minimum in the interval [-2, 2]. Firstly, we find the derivative of the function:

f '(x) = (2x + 2) / (x

2

+ 2x + 4)

. To find the critical points, we set the derivative equal to zero and solve for x, finding no real solutions, indicating there are no critical numbers within the given interval. Thus, the extrema must occur at the endpoints. So, we find f(-2) = ln(4) and f(2) = ln(8).

The absolute minimum is ln(4) at x = -2 and the absolute maximum is ln(8) at x = 2

.

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Answer:

 112 candles

Step-by-step explanation:

We can simply add up the 5 numbers of candles, or we can take advantage of the invention of multiplication to replace repeated addition. The number of candles altogether is the sum of the numbers of candles in each of the 5 boxes.

  16 + 4×24 = 16 +96 = 112

The total number of candles is 112.

Square B Area = 144cm²

Square B = X

The dimensions of Square A are three times The dimensions of Square B

Square A = 3 * Square B

Square A = 3X

The area of Square A is 1,296 cm2.

Square A Area = (3X)² = 1296

Square B Area = X²

Solve to find X.

(3X)² = 1296

3X = 36

X = 36/3 = 12

Square B Area = 12² = 144

Square B Area = 144cm²

Final answer:

The area of Square B is 144 cm², calculated by dividing the area of Square A (1,296 cm²) by 9, because the area of a square scales with the square of its linear dimensions.

Explanation:

The area of Square A is given as 1,296 cm². Since the dimensions of Square A are three times the dimensions of Square B, we can find the area of Square B by understanding that area scales in proportion to the square of the linear dimensions. This means that if one dimension is three times another, the area will be nine times (3² = 9) larger.

To find the area of Square B, we simply divide the area of Square A by 9:

Area of Square B = Area of Square A / 9

Area of Square B = 1,296 cm² / 9

Area of Square B = 144 cm².

Therefore, the area of Square B is 144 cm².

Answer:

Step-by-step explanation:

It would help you if you drew charts of what is happening. The red tank is loosing volume. It's chart is on the left.

The blue tank is gaining water (the same amount as the red is loosing)

The red graph is the red tank.

The blue graph is the blue tank.

All  you really have to understand is the the slopes (3 and - 3) and the same numerically and the rates are the same numerically. So the negative slope means loose. and the positive slope (blue) gains.

The graphs have to start somewhere. You can't make a graph like one without a starting point.

The blue container starts at 0,0. I think that's easy enough to understand. At the beginning of your experiment, the blue container is empty.

The red container starts (arbitrarily) at 3 (the y intercept).  It is just a number. It means that the red container starts with 3 gallons.

Neither graph should go into a negative region. I don't know how to make desmos not go into a negative region. Just block them out in your mind. Everything should take place in quadrant 1 bound by the +x and + y axis.

The answer is 150 to this question

Answer:

Step-by-step explanation:

#1.

228 ÷ 6 = 38 in

#2.

186 ÷ 3 = 62 ft

#3.

360 ÷ 8 = 45 yd

#4.

119 ÷ 7 = 17 ft

I hope I helped you.

Answer:

Perimeter is the total outside dimension.

To find the length of one side, divide the total perimeter by the number of sides.

1. 228 / 6 = 38 inches.

2. 186 / 3 = 62 feet.

3. 360 / 8 = 45 yards

4. 119 / 7 = 17 feet.

We can use the fact that, for [tex]|x|<1[/tex],

[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]

Notice that

[tex]\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1{1-x}\right]=\dfrac1{(1-x)^2}[/tex]

so that

[tex]f(x)=\displaystyle\frac5{(1-x)^2}=5\frac{\mathrm d}{\mathrm dx}\left[\sum_{n=0}^\infty x^n\right][/tex]

[tex]f(x)=\displaystyle5\sum_{n=0}^\infty nx^{n-1}[/tex]

[tex]f(x)=\displaystyle5\sum_{n=1}^\infty nx^{n-1}[/tex]

[tex]f(x)=\displaystyle5\sum_{n=0}^\infty(n+1)x^n[/tex]

By the ratio test, this series converges if

[tex]\displaystyle\lim_{n\to\infty}\left|\frac{(n+2)x^{n+1}}{(n+1)x^n}\right|=|x|\lim_{n\to\infty}\frac{n+2}{n+1}=|x|<1[/tex]

so the series has radius of convergence [tex]R=1[/tex].

The Maclaurin series for the function 5(1 − x)⁻² is obtained by applying the binomial series theorem, resulting in the series: 5*(1 + 2x - 2 + 3x² - 3x + 4x³ - 4x² + ...). The radius of convergence for the series is 1.

The function given is f(x) = 5(1 − x)−2. The Maclaurin series of a function f is the expression of that function as an infinite sum of terms calculated from the values of its derivatives at a single point. Here, we can use the binomial theorem as a starting point. It states that (1+x)ⁿ = 1 + nx + (n(n-1)/2!)x² + ..., where n is a real number and -1

Now, f(x) is similar to the binomial series: if we let n=-2, and x become -(x-1), we have f(x) = 5(1 – x)⁻² = 5*(1 + 2(x-1) + 3*(x-1)² + 4*(x-1)³ + ...)

So the Maclaurin series for the function is: 5*(1 + 2x - 2 + 3x² - 3x + 4x³ - 4x² + ...). The next step is to find the radius of convergence. The series has a radius of convergence R such that for all x in the interval -R

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3x+4=5x-50

54=2x

27=x

Answer:

x = 27

Step-by-step explanation:

The diagonals of a rectangle are congruent, hence

BD = AC ← substitute values

5x - 50 = 3x + 4 (subtract 3x from both sides )

2x - 50 = 4 ( add 50 to both sides )

2x = 54 ( divide both sides by 2 )

x = 27

Answer:150

Step-by-step explanation:75 on 100 multiply by 400 u will get 300.then 50 on 100 multiply 300 .your answer is 150.check???

Answer:

150.

Step-by-step explanation:

Answer:

The function has no undefined points nor domain constraints, therefore the Domain is (-∞ < x < ∞). Since your answers don't match the real results, the interval notation is (-∞,∞)

Step-by-step explanation:

Answer:

Where is the red object?

Step-by-step explanation:

I CANT SEE THE RED OBJECT U DIDNT PUT ITTT

Answer:

y = 3x^2 + 1/3

Step-by-step explanation:

The first step is the easiest. Find the value of c. That means that all you are left with is c and y because x and a disappear when x = 0.

y = ax^2 + c

Givens

Solution

1/3 = a(0)^2 + c

1/3 = 0 + c

c = 1/3

Second Given

Second Solution

82/3 = a*(-3)^2 + 1/3            Subtract 1/3 from both sides

82/3 - 1/3 = a*(9) + 1/3 - 1/3

81/3 = 9a                              Reduce the left

27 = 9a                                Divide by 9

27/9 = a

3 = a

Answer

y = 3x^2 + 1/3

Answer: 8

Step-by-step explanation:

 The triangle shown in the image attached is a right triangle.

Therefore, to calculate the missing lenght of the triangle you can apply the Pythagorean Theorem, which is shown below:

[tex]a^2=b^2+c^2[/tex]

Where a is the hypotenuse and b and c are the legs.

The problem gives you the value of the hypotenuse and the value of one leg. Therefore, you must solve for the other leg from [tex]a^2=b^2+c^2[/tex], as following:

[tex]17^2=15^2+c^2\\c=\sqrt{17^2-15^2}\\c=8[/tex]

Therefore, the lenght of the missing side is: 8

Answer:

The value of third side= 8 units

Step-by-step explanation:

It is given a right angled triangle with base = 15 and hypotenuse = 17

We have to find the height of given triangle.

Points to remember

By Pythagorean theorem

Base² + Height² = Hypotenuse²

To find the third side

Here base = 15 and hypotenuse = 17

We have,

Base² + Height² = Hypotenuse²

Height² = Hypotenuse² - Base² = 17² - 15² = 64

Height = √64 = 8 units

Therefore the value of third side = 8 units

Answer:

Step-by-step explanation:

If N is midpoint between Q and R, then use the formula of a midpoint:

[tex]\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]

We have the points Q(0, 2b) and R(2c, 0). Substitute:

[tex]x=\dfrac{0+2c}{2}=\dfrac{2c}{2}=c\\\\y=\dfrac{2b+0}{2}=\dfrac{2b}{2}=b[/tex]

Answer:

a) A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers; b) A series is divergent if it is not convergent. A series is convergent if the sequence of partial sums is a convergent sequence.

Step-by-step explanation:

A sequence is a pattern.  It is an ordered list of objects, such as numbers, letters, colors, etc.

A series is a sum of a sequence.

A divergent series is one that is not convergent.

A convergent series is one in which the sequence of partial sums approaches a limit; this means the partial sums form a convergent sequence.