The ratio of Melanie's allowance to Jacob's allowance is 4.1 to20.5.If Jacob gets 5.00 dollars, how much allowance does Melanie get

Congruent means they are the same. Match the letter with the corresponding dimension on the other cone.

A = 6.2/2 = 3.1 units

B = 4.2 units

C = 5.2 units

D = 42 units^3

The unknown measures of the cones are A = 3.1, B = 4.2, C = 5.22 and D = 42 units³

Two figures are said to be congruent if they have the same shape and the their corresponding sides are the same.

Given that both cones are congruent. Hence:

A = 6.2 / 2 = 3.1

B = 4.2

Using Pythagoras:

C² = A² + B²

C² = 3.1² + 4.2²

C = 5.22

D = 42 units³

The unknown measures of the cones are A = 3.1, B = 4.2, C = 5.22 and D = 42 units³

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There are no numbers here

Answer:

Step-by-step explanation:

From what I understand about parabolic motion in the English system, the equation for flight is

[tex]s(t)=-16t^2+v_{0}t+h_{0}[/tex]

where [tex]v_{0}t[/tex] is the initial upwards velocity and

[tex]h_{0}[/tex] is the initial height from which the object was launched.  Filling in that equation with those values gives you

[tex]s(t)=-16t^2+64t+3[/tex].  That's a.

In order to determine how long it will take the ball (or rocket...the problem is mixing up the 2) to reach its max height you need to put the equation into vertex form, since the vertex of a parabola is the absolute max (or min depending upon the parabola) of the function.  The absolute max is the heighest that the ball will go.  Completing the square is the way to solve this.  Begin by setting the equation equal to 0, the moving the 3 over by subtraction:

[tex]-16t^2+64t=-3[/tex]

Now factor out the -16 since the leading coefficient HAS to be a positive 1:

[tex]-16(t^2-4t)=-3[/tex]

Now take half the linear term (half of 4t which is 2), square it (4) and add it into the parenthesis:

[tex]-16(t^2-4t+4)=-3[/tex]

BUT since you added in a 4*-16 on the left you have to add it in on the right:

[tex]-16t^2(t^2-4t+4)=-3-64[/tex]

which simplifies to

[tex]-16(t-2)^2=-67[/tex]

Now bring the 67 over by addition and you have your vertex:

[tex]s(t)=-16(t-2)^2+67[/tex].

The vertex is (2, 67).  The 2 stands for time, so 2 seconds, and the 67 stands for feet, so at 2 seconds the max height is 67 feet.

How long it will be in the air is found by factoring to find the zeros.  These can be found by plugging the quadratic into the quadratic formula and getting that the zeros are -0.046 and 4.046

So the quadratic starts a tiny tiny bit to the left of the origin, but for all intents and purposes we can say it starts at the origin (x = 0) and ends at

x = 4.05 seconds.  Which makes sense if you know anything about parabolic motion and physics.  The vertex indicates not only the time and the max height at that time, it also is indicative of the halfway mark.  Meaning that if it takes 2 seconds to reach its max height, it will hit the ground at 4 seconds.  And 4.05 is close enought to 4 (but since you were told to round to the nearest hundredth, that .05 matters).  Sorry it's so long, but it's not a question that can be answered with just a few sentences.

Answer:

Final answer is E. 10

Step-by-step explanation:

Apply Pythagorean theorem to the given right triangle.

[tex]\left(Hypotenuse\right)^2=\left(Leg_1\right)^2+\left(Leg_2\right)^2[/tex]

[tex]\left(h\right)^2=\left(5\sqrt{2}\right)^2+\left(5\sqrt{2}\right)^2[/tex]

[tex]\left(h\right)^2=50+50[/tex]

[tex]\left(h\right)^2=100[/tex]

take square root of both sides

[tex]h=10[/tex]

Hence final answer is E. 10

ANSWER

E. 10

EXPLANATION

Using Pythagoras Theorem, which says the hypotenuse squared is equal to the sum of squares of the two shorter legs.

[tex] {h}^{2} = {(5 \sqrt{2} )}^{2} + {(5 \sqrt{2} )}^{2} [/tex]

Evaluate the squares on the RHS.

[tex] {h}^{2} = 25 \times 2 + 25 \times 2[/tex]

[tex] {h}^{2} = 50 + 50[/tex]

Simplify:

[tex] {h}^{2} = 100[/tex]

Take positive square root.

[tex]h = \sqrt{100} [/tex]

[tex]h = 10[/tex]

The hypotenuse is 10 units.

The correct answer is E

Answer:

  [4, 8]

Step-by-step explanation:

You want to find t such that ...

  T ≥ 69

  24t − 2t^2 + 5 ≥ 69

  t^2 -12t +32 ≤ 0 . . . . . subtract the left side, divide by 2

  (t -4)(t -8) ≤ 0 . . . . . . . factor

The factors will have different signs, so their product will be negative, for values of t between 4 and 8. Of course, the equality holds at t=4 and t=8, so the solution interval is ...

  t ∈ [4, 8]

Answer:

$6.48

Step-by-step explanation:

Answer:

$2950

Step-by-step explanation:

Add together the following three items:

Materials:  $2000 plus 15%, or 1.15($2000), or $2300

Labor:  $500

Equipment Rental:  $150

Total:  $2300 + $500 + $150 = $2950

Final answer:

The slope of a line perpendicular to a line with slope 3/4 is -4/3. This follows from the principle that slopes of perpendicular lines are negative reciprocals of each other.

Explanation:

The question pertains to finding the slope of a line that is perpendicular to another line with a given slope. Given that the slope (m) of line l is 3/4, let's find the slope of line m which is perpendicular to l. In algebra, the slope of perpendicular lines are negative reciprocals of each other. This means that to find the slope of m, you take the negative reciprocal of 3/4, which is -4/3.

Thus, the correct answer is C. - 4 over 3.

Answer:

[tex](x+3)^2 + y^2 =25[/tex]

Step-by-step explanation:

The general equation of a circle has the form:

[tex](x-h)^2 + (y-k)^2 =r^2[/tex]

Where the point (h, k) is the center of the circle and r is the radius

In this case the center is (-3, 0) and the radius is [tex]r=5[/tex]

So [tex]h=-3\\k=0[/tex]

Finally the equation of the circle is:

[tex](x-(-3))^2 + (y-0)^2 =5^2[/tex]

[tex](x+3)^2 + y^2 =25[/tex]

(X+3)^2 +y^2 =25

This is the correct answer

Check on Desmos

A prism is rectangular shaped,. a pyramid is triangular shaped.

The ratio would be  1 to 3

The formula for the pyramid is V = 1/3Bh

It seems that the boundary of [tex]M[/tex] is the circle [tex]x^2+y^2=49[/tex] in the plane [tex]z=0[/tex]. By Stokes' theorem,

[tex]\displaystyle\iint_M(\nabla\times\vec f)\cdot\mathrm d\vec S=\int_{\partial M}\vec f\cdot\mathrm d\vec r[/tex]

Parameterize [tex]\partial M[/tex] by

[tex]\vec r(t)=(7\cos t,7\sin t,0)[/tex]

with [tex]0\le t\le2\pi[/tex]. Then the line integral is

[tex]\displaystyle\int_{\partial M}\vec f(x(t),y(t),z(t))\cdot\mathrm d\vec r=\int_0^{2\pi}(56\sin t,35\cos t,0)\cdot(-7\sin t,7\cos t,0)\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^{2\pi}(245\cos^2t-392\sin^2t)\,\mathrm dt=\boxed{-147\pi}[/tex]

The question involves computing the double surface integral of the curl of the given vector field over a specified surface. The curl of the vector field is found first using a determinantal formula, and the surface integral is then evaluated over the capped cylindrical surface. These concepts are fundamental in vector calculus and have applications in fields such as physics and engineering.

This question requires the application of vector calculus concepts, specifically surface integrals and the divergence theorem. Given the vector field f=(zx+z²y+8y, z³yx+5x, z⁴x²), your task is to compute the double surface integral of the curl of f over a capped cylindrical surface m, which is a union of a cylinder and a hemispherical cap.

To solve it, you will start by finding the curl of the vector field using the determinant of a special kind of 3x3 matrix, called the curl matrix, containing the unit vectors i, j, k, the coefficients of the derivatives in the Cartesian coordinate system, and the components of the vector field. Once you get an expression for the curl of f, you will set up and evaluate a double surface integral over the given region m to find the desired quantity.

The concept of surface integrals is prevalent in many fields including physics and engineering where it is used to calculate quantities like flux. The divergence theorem, also known as Gauss's theorem, connects the flux of a vector field through a closed surface to the divergence of this field in the volume enclosed by the surface.

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Answer:

(10 yd) ............=x.....

Answer:

The measure of angle JKL is m∠JKL=35°

Step-by-step explanation:

step 1

Find the measure of the arc KL

we know that

arc KL+arc KN+arc NL=360° ----> by complete circle

arc KL+150°+140°=360°

arc KL=360°-290°=70°

step 2

Find the measure of angle JKL

we know that

The inscribed angle is half that of the arc it comprises.

so

m∠JKL=(1/2)[arc KL]

substitute

m∠JKL=(1/2)[70°]=35°

Answer:

The solution is (-3, 10.8)

Step-by-step explanation:

While it's rather obvious that you want to solve this system of linear equations, you should share that instruction when you post the problem.

To solve this system using elimination by addition and subtraction, combine the two equations as shown below (to eliminate y):

-0.18x + y = -6.54

-2.8x - y = -2.4

--------------------------

-2.98x = -8.94

Dividing both sides by -2.98, to isolate x, yields:  x = -8.94 / (-2.98) = -3.

Then x = 3.  Find y from -2.8x - y = -2.4:  -2.8x + 2.4 = y, and here,

y = -2.8(-3) + 2.4 = 8.4 + 2.4 = 10.8

Then the solution is (-3, 10.8)

By the inscribed angle theorem,

[tex]12y-1=9y+11[/tex]

[tex]3y=12[/tex]

[tex]y=4[/tex]

So the angles have measure

[tex](12\cdot4-1)^\circ=\boxed{47^\circ}[/tex]

The measure of the angle is 47 degrees. Thus, the correct option is B.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

The angles at the periphery made by the same chord will be equal.

The equation is given as,

12y - 1 = 9y + 11

Simplify the equation, then we have

12y - 1 = 9y + 11

12y - 9y = 11 + 1

3y = 12

y = 4

Then the measure of the angle is given as,

Angle = 12 x 4 - 1

Angle = 48 - 1

Angle = 47

Thus, the correct option is B.

More about the circle link is given below.

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Answer: (3b + 5)(3b - 5)

Because both terms, 9b² and 25, are perfect squares, you can factor by taking the square roots of both terms.

The square root of 9b² is 3b (3b × 3b = 9b²).

The square root of 25 is 5 (5 × 5 = 25).

9b² - 25 has a negative, so the factored expression would be

(3b + 5)(3b - 5). The signs (+ and -) alternate in this case because the  expression, 9b² - 25, has no middle term.

You can check your work by using FOIL. See the attachment below.

F irst

O utside

I nside

L ast

Answer:

(3b + 5)(3b - 5)

Step-by-step explanation:

(3b + 5)(3b - 5)

Answer:

  True

Step-by-step explanation:

The first power of the variable is what makes it a linear term.

In converting to spherical coordinates, we use

[tex]x=\rho\cos\theta\sin\varphi[/tex]

[tex]y=\rho\sin\theta\sin\varphi[/tex]

[tex]z=\rho\cos\varphi[/tex]

so that

[tex]\mathrm dV=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi[/tex]

Then the integral is

[tex]\displaystyle\iiint_Ey^2\,\mathrm dV=\int_0^\pi\int_0^\pi\int_0^3\rho^4\sin^2\theta\sin^3\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta=\boxed{\frac{162\pi}5}[/tex]

To evaluate the expression using spherical coordinates, express the given solid hemisphere in spherical coordinates by replacing x, y, and z with r, θ, and φ. Substitute the volume element in spherical coordinates, and integrate over the limits specified by the solid hemisphere. Finally, evaluate the expression numerically.

To evaluate the expression ∫ey2dv using spherical coordinates, we first need to express the solid hemisphere in spherical coordinates. The given condition for the solid hemisphere is x2 + y2 + z2 ≤ 9 and y ≥ 0. In spherical coordinates, the equation for the solid hemisphere becomes r ≤ 3 and 0 ≤ θ ≤ π/2.

The volume element dv in spherical coordinates is dV = r2sinθdrdθdφ. Substituting this into the original expression, we have ∫ey2dv = ∫e(r*sinθcosφ)2r2sinθdrdθdφ. Since we are integrating over the solid hemisphere, the limits of integration for r, θ, and φ are r = 0 to r = 3, θ = 0 to θ = π/2, and φ = 0 to φ = 2π.

After substituting the expressions for y and dv in terms of spherical coordinates and integrating over the given limits, we can find the numerical value of the given expression.

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the answer is 3 I bet the oven is hot tbh

Title: The Infallible Logic of 1 + 1 = 2

Introduction:

The seemingly simple equation, 1 + 1 = 2, holds a profound and fundamental place in mathematics and logic. Its truth is evident, self-evident, and indisputable, serving as a cornerstone for mathematical reasoning and human understanding. In this essay, we explore the underlying principles and irrefutable logic behind the statement that 1 + 1 equals 2.

Body:

Basic Arithmetic Principles:

At its core, mathematics is a system of rules and principles that govern the manipulation of numbers and quantities. The equation 1 + 1 = 2 is a fundamental expression of these principles. It demonstrates the addition of two individual units (1) to form a collective sum (2). This is a foundational concept in arithmetic.

Axiomatic Truth:

In the realm of mathematics, certain statements are considered axioms—self-evident truths that do not require proof. 1 + 1 = 2 is one of these axioms. It is a statement that is true by definition and serves as a building block for more complex mathematical operations.

Logical Proof:

One way to understand why 1 + 1 equals 2 is through logical proof. We can start with the premise that we have one unit (1) and add another unit (1) to it. The result, by definition, is two units (2). This logical progression is simple and irrefutable.

Set Theory:

In set theory, a branch of mathematics that deals with sets and their relationships, the equation 1 + 1 = 2 is rigorously defined. In set theory, 1 represents a set containing a single element, and adding another set with one element results in a set with two elements. This is a formalized representation of why 1 + 1 equals 2.

Real-World Application:

The equation 1 + 1 = 2 has practical applications in various fields, including science, engineering, economics, and everyday life. It reflects the way we count and aggregate objects, making it essential for quantitative analysis and problem-solving.

Conclusion:

The equation 1 + 1 = 2 is not merely a mathematical expression; it is a reflection of the logical and axiomatic foundation upon which mathematics and much of human reasoning are built. Its undeniable truth serves as a testament to the precision and consistency of mathematics. The simple act of adding one to one resulting in two exemplifies the elegance and power of mathematical logic, making it an enduring principle in our understanding of the world. In a universe governed by mathematical laws, 1 + 1 will always equal 2, and this irrefutable truth is a testament to the beauty and reliability of mathematics.

Answer:

(D)[tex]x=104^{\circ}[/tex]

Step-by-step explanation:

Given: It is given that circle O is circumscribed about quadrilateral ABCD such that ∠ABC=91° and ∠ADC=x-15°.

To find: the value of x.

Solution: It is given that circle O is circumscribed about quadrilateral ABCD such that ∠ABC=91° and ∠ADC=x-15°.

We know that the sum of opposite angles of the cyclic quadrilateral is 180°, therefore

[tex]{\angle}ABC+{\angle}ADC=180^{\circ}[/tex]

Substituting the given values, we have

[tex]91^{\circ}+x-15^{\circ}=180^{\circ}[/tex]

[tex]x+76^{\circ}=180^{\circ}[/tex]

[tex]x=104^{\circ}[/tex]

thus, the value of x is [tex]104^{\circ}[/tex].

Hence, option D is correct.

Answer:

the answer is 104 i just took quiz 6.11.3

Step-by-step explanation:

Final answer:

This question pertains to calculating the volume of a triangular pyramid using given measurements of the base edge, base height, and volume.

Explanation:

The subject of this question involves calculating the volume of a triangular pyramid and understanding its geometric properties. Given the volume (56 cubic centimeters), base edge (8 centimeters), and base height (7 centimeters), one can determine various other properties of the pyramid. In geometry, the formula to calculate the volume of a pyramid is V = (1/3)*Base Area*Height, where the Base Area for a triangular pyramid is ½ times the base length times the base height. The challenge here would involve determining the height of the pyramid based on the given volume and base dimensions.

Answer:

Associative property of multiplication

Explanation:

The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis.

ANSWER

4.1 units to the nearest tenth.

EXPLANATION

The graph of the two functions are shown in the attachment.

The coordinates of point A is (1.6,4.1).

The coordinates of point B is (7.1,6.1)

The x-axis represents the ground level.

The distance of point A from the ground level is how far the y-coordinate of this point is from the x-axis.

Which is |4.1-0|=4.1

5 5/8= 45/8

1 1/2= 3/2

45/8 divided by 3/2

Or

45/8 times 2/3

15/4 or 3 3/4

Answer:

A

Step-by-step explanation:

Answer:

answer is A

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

A negative exponent turns into positive when it is put into fraction form.

5^-2 = 1/5^2

5^-2 = 1/25

Answer:

Step-by-step explanation:

It's true. A minus power means that you put the denominator in the numerator and the numerator in the denominator. For example

(5/3)^(-2) = (3/5)^2 = 9/25

Answer: B) 0.40 mi

Step-by-step explanation:

Using the Pythagorean Theorem.

A squared + B squared = C squared.

A = leg B = leg C = hypotenuse

A = 0.3 B = ? C = 0.7

0.3 squared x ? squared = 0.7 squared

Answer:

on usatestprep its 0.63

Step-by-step explanation:

Answer:

It is B because this triangle Q and R are congruent

Step-by-step explanation:

Answer:

B. 68

Step-by-step explanation:

Because the side lengths PQ and PR both equal 5 and are congruent, the angles opposite them (angle Q and angle R) are also congruent to each other.

Angle Q is 68, so angle R is also 68.

The expression 6(x − 5) means the product of 6 and the difference of x minus 5. If x = 7, the value of the expression is 12.

We can see that the number 6 to the left of the expression 6(x - 5), this means 6 times (x - 5), The reason we write it that way is because the multiplication symbol, ×, can be confused with the variable x, follow by (x - 5) which is the difference of x minus 5. All together is the product of 6 and the difference of x minus 5.

If x = 7, then:

6(7 - 5) = 6(2) = 12

Following are the solution to the given expression:

Given:

[tex]6(x-5) \\\\ x=7 [/tex]

To find:

value=?

Solution:

[tex]\to 6(x-5)\\\\ [/tex]

putting the x value into the above expression:

[tex]\to 6(7-5)\\\\ \to 6(2)\\\\ \to 12[/tex]

Therefore the final answer is "12".

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