In a​ triangle, the measure of the first angle is three times the measure of the second angle. The measure of the third angle is 70 degrees more than the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is 180 degrees to find the measure of each angle.

The measure of the first angle is _____

Answer:

option D

Step-by-step explanation:

So we know that [tex]\sqrt{a} \sqrt{b} = \sqrt{ab}[/tex]

Applying this to our function, we have that:

[tex]\sqrt{(x-5)} \sqrt{(x+2)} = \sqrt{(x+2)(x-5)}[/tex]

We know that the argument of a square root should always BE POSITIVE.

So we need to evaluate in which points the expression (x+2)(x-5) is positive.

So we know that (x+2) is possitive when x>-2 and negative when x<-2.

Also we know that (x-5) is possitive when x>5, if x<5 then x is negative.

Then we have:

if x<-2, then:

(x-5) is negative

(x+2) is negative

Then (x+2)(x-5) is positive.

If x>5 then:

(x-5) is positive

(x+2) is positive.

Then (x+2)(x-5) is positive.

If -2<x<5 then:

(x-5) is negative

(x+2) is positive

Then (x+2)(x-5) is negative, so it's undefined.

So the function is defined for x>5 and x<-2

So the correct option is option D.

Answer:

Note: the last sentence in the problem statement text should read, "Therefore, the volume of the sphere is 4/3πr³ by Cavalieri's principle.

Step-by-step explanation:

I believe it can help a lot if you have seen and understand this derivation of the volume of a sphere. Here is the basic idea.

Shown in the attachment is a cross section of half the volume under consideration. Basically, it is showing one cone and the (red) top hemisphere in a (green) cylinder of radius R and height R. (The problem text refers to a sphere and two cones in a cylinder of height 2R. This is the top half of that geometry.) Actually, only the left edge of the cone is represented here, in order to avoid cluttering the diagram.

We can use this figure to think about a horizontal cross section (cut plane) of this geometry at height h from the center of the sphere. We want to consider the annulus of inner radius C between the cylinder of radius R and the cone, and we want to consider the circle of radius S where the cut plane intersects the hemisphere.

Because the cone has a height of R and a radius of R, the radius C of the cross section will be the same as the height h. That is, in our figure, h = C. We know from the Pythagorean theorem that ...

  h² + S² = R²

  S² = R² - C² . . . . . . subtract h² and substitute C for h

The area of the circular cross section of the hemisphere is πS², and the area of the annulus between the cylinder and cone is π(R² - C²). The above equation tells us these areas are the same.

By Cavalieri's principle, since the cross sections have the same area at every height, the volume of the space between the cylinder and cone is the same as the volume of the hemisphere. Using the formulas for the volumes of cylinder and cone, we find the difference to be ...

  difference volume = hemisphere volume = πr²·r - 1/3πr²·r = 2/3πr³

__

Once this approach to the sphere volume formula derivation is understood, filling in the blanks in your problem statement may become much simpler.

Answer:

  360 minutes

Step-by-step explanation:

(1.5 h/wk)·(4 wk)·(60 min/h) = 1.5·4·60 min = 360 min

Multiply reading time per week by the number of weeks to get reading time. Multiply the number of hours by the number of minutes in an hour to get minutes.

Answer:

8x^2 - 14xy + 3y^2

Step-by-step explanation:

You need to find the product of (2x - 3y )(4x - y ). To solve this, we're going to be using the distributive distribution as follows:

(2x - 3y )(4x - y ) = 8x^2 - 2xy - 12xy + 3y^2

Combining like-terms:

(2x - 3y )(4x - y ) = 8x^2 - 14xy + 3y^2

Therefore, the result is: 8x^2 - 14xy + 3y^2

Answer:

8x^2 - 14xy - 3y^2

the other explains it, it just forgets to factor in a negitive

Answer:

Part A) The height of the cylinder is [tex]7.8\ in[/tex]

Part B) The volume of one tennis ball is [tex]9.2\ in^{3}[/tex]

Part C) The volume of the cylinder is [tex]41.4\ in^{3}[/tex]

Part D) The volume of space in the cylinder not taken by the tennis balls is [tex]13.8\ in^{3}[/tex]

Step-by-step explanation:

Part A) Each tennis ball has a diameter of 2.6 inches

What is the height of the cylinder?

we know that

The height of the cylinder is equal to the diameter of one ball of tennis multiplied by 3

so

[tex]h=2.6*3=7.8\ in[/tex]

Part B)  Find the volume of one tennis ball

The volume of the sphere (one tennis ball) is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=2.6/2=1.3\ in[/tex] ----> the radius is half the diameter

[tex]\pi=3.14[/tex]

substitute

[tex]V=\frac{4}{3}(3.14)(1.3)^{3}[/tex]

[tex]V=9.2\ in^{3}[/tex]

Part C) Find the volume of the cylinder

The volume of the cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=2.6/2=1.3\ in[/tex] ----> the radius is half the diameter

[tex]\pi=3.14[/tex]

[tex]h=2.6*3=7.8\ in[/tex]

substitute

[tex]V=(3.14)(1.3)^{2} (7.8)[/tex]

[tex]V=41.4\ in^{3}[/tex]

Part D) What is the volume of space in the cylinder not taken by the tennis balls?

we know that

The volume of space in the cylinder not taken by the tennis balls, is equal to the difference from the volume of the cylinder and the volume of three ball of tennis

[tex]V=41.4-(3)*(9.2)=13.8\ in^{3}[/tex]

Answer:

Part A) The height of the cylinder is

Part B) The volume of one tennis ball is

Part C) The volume of the cylinder is

Part D) The volume of space in the cylinder not taken by the tennis balls is

Step-by-step explanation:

Part A) Each tennis ball has a diameter of 2.6 inches

What is the height of the cylinder?

we know that

The height of the cylinder is equal to the diameter of one ball of tennis multiplied by 3

so

Part B)  Find the volume of one tennis ball

The volume of the sphere (one tennis ball) is equal to

we have

----> the radius is half the diameter

substitute

Part C) Find the volume of the cylinder

The volume of the cylinder is equal to

we have

----> the radius is half the diameter

substitute

Part D) What is the volume of space in the cylinder not taken by the tennis balls?

we know that

The volume of space in the cylinder not taken by the tennis balls, is equal to the difference from the volume of the cylinder and the volume of three ball of tennis

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

I usually use a z-score table, but you can do this with a calculator.

If we go to a z-score table, we first look up the first two digits (in this case, 2.8) in the far left column.  Then we find the hundredths digit in the top row (0.07).  Where they intersect is P(z < 2.87).

P(z < 2.87) = 0.9979

Answer D.

Using the normal distribution, it is found that the correct option regarding P(z < 2.87) is given by:

D. 0.9979

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Hence, P(z < 2.87) is the p-value of Z = 2.87, which is of 0.9979, hence option D is correct.

More can be learned about the normal distribution at https://brainly.com/question/24663213

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Answer: First option

[tex]g(x) = \frac{1}{8}x^2[/tex]

Step-by-step explanation:

Step-by-step explanation:

If the graph of the function [tex]y=cf(x)[/tex]  represents the transformations made to the graph of [tex]y= f(x)[/tex]  then, by definition:

If  [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor c.

If  [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor c

If [tex]c <0[/tex]  then the graph is reflected on the x axis.

In this problem we have the function [tex]f(x)=x^2[/tex] If this function is vertically compressed by a factor of 8 then  [tex]0 <c <1[/tex]  and [tex]c=\frac{1}{8}[/tex]

Therefore the graph of g(x) is  [tex]g(x)=\frac{1}{8}f(x)[/tex]

[tex]g(x) = \frac{1}{8}x^2[/tex]

The answer is the first option

Answer: Option D

D. [tex]880 = 45d + 70[/tex]; [tex]18\ days[/tex]

Step-by-step explanation:

We know that the cost of preschool is $ 45 per day plus a monthly fee of $ 70.

We also know that a total of $ 880 was paid last month

To write an equation that represents this situation, let us call "d" the number of days that Barry attends school

So the cost was:

[tex]45d + 70 = 880[/tex]

Now we solve the equation for the variable d

[tex]45d= 880-70[/tex]

[tex]d= \frac{810}{45}[/tex]

[tex]d= 18\ days[/tex]

Therefore answer is the option D

Final answer:

The recursive rule for the given sequence is [tex]a_n = a_{n-1} - 13.8[/tex],

where a₁ = -7.4 and n > 1.

Explanation:

You are looking for the recursive rule for the sequence -7.4, -21.2, -35, -48.8, -62.6, and so on. To find this, we observe how the sequence progresses from one term to the next. The pattern here is that each term decreases by the same amount when compared to the previous term. By calculating the difference between successive terms, we can identify the common difference.

For instance, the second term (-21.2) minus the first term (-7.4) equals the third term (-35) minus the second term (-21.2), and this difference equals -13.8. Hence, each term is -13.8 less than the term before it.

To express this as a recursive formula, we start by stipulating the first term:

Then, we provide the recursive rule that relates each term to the one before it:

Using this recursive formula, given any term in the sequence, we can find the next term by subtracting 13.8 from the given term.

[tex]175 - 14[/tex]

I think that will help you I'm not sure you just have to try to resolve if you get ranked if you get it wrong just send me a message cuz I am a fifth grade teacher

Step-by-step explanation:

A, B, and C have the same area.  So P(A) = 1/3 and P(B) = 1/3, which means P(A or B) = 2/3.

P(success) = 2/3 and P(failure) = 1/3.

The probability of 2 failures is:

P = (1/3)² = 1/9

The probability of 2 successes is:

P = (2/3)²= 4/9

The probability of 1 success and 1 failure can be found either with binomial probability, or simply by subtracting the probabilities we found earlier from 1.

P = 1 - 1/9 - 4/9

P = 4/9

So the answer is the one in the bottom left corner.

Answer: C

X              P

0             1/9

1              4/9

2             4/9

Step-by-step explanation:

Screenshot provided

Do 15 divided by 3 equals 5

Final answer:

To determine Alyssa's age, we set up the equation 15 = 3A, based on the assumption that Eric being '3 times older' than Alyssa means he is 3 times her age. We divide both sides by 3 to get Alyssa's age, which is 5 years old.

Explanation:

To find Alyssa's age, we need to write an equation based on the information provided: Eric is 3 times older than his sister Alyssa, and we know that Eric is 15 years old. The phrase '3 times older' would technically mean 3 times Alyssa's age plus her age again (Alyssa's age times 4). However, this phrase can sometimes be used colloquially to mean '3 times Alyssa's age,' which is more common. So, we need clarification on the intended meaning. If we assume the latter, more common interpretation, the equation based on the information provided would be:

Let A be Alyssa's age. Since Eric is 15 years old and 3 times Alyssa's age, we have: E = 3A, where E is Eric's age.

Substituting Eric's age into the equation, we get: 15 = 3A

To find Alyssa's age, we then divide both sides by 3: 15 / 3 = A

Alyssa's age A would then be 5 years old. So, the equation to find Alyssa's age is: 15 = 3A

Answer:

Approach: Difference of Squares Pattern

[tex]4 {x}^{2} - 25 = (2x - 5)(2x + 5)[/tex]

Step-by-step explanation:

The given binomial is:

[tex]4 {x}^{2} - 25[/tex]

We can rewrite to obtain:

[tex] {(2x)}^{2} - {5}^{2} [/tex]

This is a difference of two squares, so we will factor using difference of squares pattern.

Recall that:

[tex] {a}^{2} - {b}^{2} = (a + b)(a - )[/tex]

If we let

[tex]a = 2x[/tex]

and

[tex]b = 5[/tex]

Then we can factor the given binomial to obtain:

[tex] {2x}^2 - {5}^{2} = (2x - 5)(2x + 5)[/tex]

[tex] \therefore4 {x}^{2} - 25 = (2x - 5)(2x + 5)[/tex]

Answer:

  an = 5·2^(n-1)

Step-by-step explanation:

The explicit formula for a geometric sequence with first term a1 and common ratio r is ...

  an = a1·r^(n-1)

Your sequence has a1=5 and r=2, so the explicit formula is ...

  an = 5·2^(n-1)

Final answer:

The explicit formula for the geometric sequence 5, 10, 20, 40, 80, 160,... is ,[tex]a_{n}=5(2^{n-1} )[/tex], where 'aₙ' represents the nth term in the sequence.

Explanation:

The student is asking for the explicit formula for a given geometric sequence. In mathematics, a geometric sequence is one where any term after the first is found by multiplying the previous term by a fixed, non-zero number known as the common ratio. Looking at the sequence provided (5, 10, 20, 40, 80, 160,...), we can observe that each term is twice the previous term, thus the common ratio is 2.

To find the explicit formula of a geometric sequence, we use the formula ,[tex]a_{n}=a_{1} (r^{n-1} )[/tex], where an is the nth term, a₁ is the first term in the sequence, r is the common ratio, and n is the term number. For this sequence, a₁ is 5, and r is 2.

The explicit formula for the given geometric sequence is therefore [tex]a_{n}=5(2^{n-1} )[/tex].

Answer:

The price of one gallon of milk is $3.5

Step-by-step explanation:

Let

x----> the price of one loaves of bread

y----> the price of one gallon of milk

we know that

4x+y=12.50 ----> equation A

2x+2y=11.50 ----> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (2.25,3.5)

see the attached figure

therefore

The price of one loaves of bread is $2.25

The price of one gallon of milk is $3.5

Answer:

B. [tex]r_{x-axis}(x,y) \circ R_0,90\degree)[/tex]

Step-by-step explanation:

The vertices of triangle ABC have coordinates A(5,2) B(2,4) and C(2,1).

The mapping for reflection in the x-axis is

[tex](x,y)\to (x,-y)[/tex]

When we reflect triangle ABC in the x-axis, we obtain

A1(5,-2) B1(2,-4) and C1(2,-1).

The mapping for 90 degrees clockwise rotation about the origin is

[tex](x,y)\to (y,-x)[/tex]

When we rotate the resulting triangle through 90 degrees clockwise above the origin, we obtain;

A2(-2,-5) B2(-4,-2) and C2(-1,-2).

The vertices of triangle A''B''C'' also have coordinates A''(-2,-5) B''(-4,-2) and C''(-1,-2).

Hence the rule that describes the composition of transformation that maps ABC to A''B''C'' is

[tex]R_0,90\degree \circ r_{x-axis}(x,y)[/tex]

The correct choice is B.

Answer:

Option C is correct

Step-by-step explanation:

First we will convert the mixed fractions into fraction form.

5/4, 5/8, 3/4, 1/2, 3/2, 7/4

Now, to find the range the formula used is:

Range= Maximum Value - Minimum Value

To find the maximum value and minimum value in fractions, we need to make the denominator of each fraction same. Since the highest value of denominator is 8, so other fractions denominator should be 8.

10/8, 5/8, 6/8,4/8,12/8,14/8

Maximum Value = 14/8 (having highest numerator)

Minimum value = 4/8 (having lowest numerator)

Range of data set = Maximum Value - Minimum value

                             = 14/8 - 4/8

                             = 10/8 = 5/4

                             = 1 1/4

so, option C is correct.

Answer:

The answer is C. 1 1/4

Step-by-step explanation:

To get the range of a set of data, all you need to do is get the difference between the highest value and the lowest value. Since you have different fractions, you first need to determine which is the highest and the lowest.

Since your given are not similar fractions (they do not have the same denominator), you need to make them similar first.

What I did first is make all mixed fractions into improper to make it easier for me to make them similar.

[tex]1\dfrac{1}{4},\dfrac{5}{8},\dfrac{3}{4},\dfrac{1}{2},1\dfrac{1}{2},1\dfrac{3}{4}\\\\\\\dfrac{5}{4},\dfrac{5}{8},\dfrac{3}{4},\dfrac{1}{2},\dfrac{3}{2},\dfrac{7}{4}[/tex]

The LCD of all fractions is 8 so I will need to get the proper proportion that will make all of them have 8 as the denominator.

[tex]\dfrac{5}{4}\times\dfrac{2}{2}[/tex] , [tex]\dfrac{5}{8}\times\dfrac{1}{1}[/tex] , [tex]\dfrac{3}{4}\times\dfrac{2}{2}[/tex] , [tex]\dfrac{1}{2}\times\dfrac{4}{4}[/tex] , [tex]\dfrac{3}{2}\times\dfrac{4}{4}[/tex] , [tex]\dfrac{7}{4}\times\dfrac{2}{2}[/tex]

So now we have the new set of fractions to compare:

[tex]\dfrac{10}{8}, \dfrac{5}{8},\dfrac{6}{8}, \dfrac{4}{8}, \dfrac{12}{8},\dfrac{14}{8}[/tex]

Looking at the set, all you have to do is get the fraction with the highest numerator (which will be our highest value) and get the fraction with the lowest numerator (which is the lowest value), then get the difference.

[tex]\dfrac{14}{8}-\dfrac{4}{8} = \dfrac{10}{8}[/tex] or [tex]1\dfrac{2}{8}[/tex]

Simplify it and you will get:

[tex]1\dfrac{1}{4}[/tex]

Answer:

12 in²

Step-by-step explanation:

Since the figures are similar

linear ratio = a : b , then

area ratio = a² : b²

linear ratio of sides = 8 : 12 = 2 : 3

ratio of areas = 2² : 3² = 4 : 9

let the area of smaller figure be x then

[tex]\frac{4}{x}[/tex] = [tex]\frac{9}{27}[/tex] ( cross- multiply )

9x = 108 ( divide both sides by 9 )

x = 12

Area of smaller figure is 12 in²

Answer:

176 cubic feet

Step-by-step explanation:

volume of each box is given by area of base * height.

Volume of Box 1 = 16 * 3 = 48

Volume of Box 2 = 16 * 3 = 48

Volume of Box 3 = 16 * 5 = 80

Total Volume = 48 + 48 + 80 = 176 ft^3

To calculate the total volume of the three boxes, we sum the individual volumes of two boxes at 48 cubic feet each and one box at 80 cubic feet, resulting in a total of 176 cubic feet.

To find the total volume of the three boxes shipped on a truck, we need to calculate the volume of each box and then sum the volumes. The volume of a rectangular prism (which is the shape of the boxes) is calculated by the formula Volume = length × width × height. In this case, the boxes have a common base of 16 square feet.

The two boxes with a height of 3 feet each have a volume of 16 square feet × 3 feet = 48 cubic feet per box. For both, this gives us a total of 48 cubic feet × 2 = 96 cubic feet.

The third box with a height of 5 feet has a volume of 16 square feet × 5 feet = 80 cubic feet.

Adding the volumes of all three boxes together, the total volume is 96 cubic feet + 80 cubic feet = 176 cubic feet. This is the total volume of the three boxes combined.

60.0 is the area of the triangle

Answer:

limaçon (no inner loop)

Step-by-step explanation:

The equation of a limaçon is written generically as ...

r = b + a·cos(θ)

For b=2 and a=1, this would put the flat side on the left. Rotating it 180° can be accomplished by adding or subtracting π from θ. Then the equation can be ...

r = 2 + cos(θ-π) . . . . or ...

r = 2 - cos(θ)

The 10 cm string is 7 times smaller than the 70 cm string

Answer:

Step-by-step explanation:

since the order of choosing out students to hand out papers doesnt matter because the paper handed is just the same and that the purpose or task of each student is just the same, combination should be used. Otherwise, when the order is based on ranking of students for example, permutation is used. answer is true

Answer:

b.120in3

Step-by-step explanation:

you just take the high width and length and times together

4*5*6=120

Answer:

B. {(4,6), (8,8), (–3,6)}

Step-by-step explanation:

The given inequality is

[tex]y\ge\frac{1}{4}x+5[/tex]

The set of points that satisfy the inequality are solutions.

We can verify that,all the points in the set  {(4,6), (8,8), (–3,6)} satisfy the given inequality.

[tex]6\ge\frac{1}{4}(4)+5[/tex]  ;[tex]\implies 6\ge6[/tex]: True

[tex]8\ge\frac{1}{4}(8)+5[/tex]  ;[tex]\implies 8\ge7[/tex]: True

[tex]6\ge\frac{1}{4}(-3)+5[/tex]  ;[tex]\implies 6\ge4.25[/tex]: True

Therefore, the correct answer is B.

The equation of the tangent plane to the surface x=h(y,z) at the point (3,0,3) given that ∂h/∂y=−5 and ∂h/∂z=−3 is x = -5y -3z + 12.

In Mathematics, the equation for the tangent plane to a surface x = h(y,z) at a point can be determined by the following formula: x - x0 = ∂h/∂y(y - y0) + ∂h/∂z(z - z0). In your expression ∂h/∂y (derivatives of h with respect to y) is given as -5 and ∂h/∂z (derivatives of h with respect to z) is given as -3. By plugging the value of these derivatives and the point (3,0,3) into the formula, the equation of the tangent plane would be: x - 3 = -5(y - 0) - 3(z - 3).

After simplifying this, we'll get x = -5y -3z + 12. It's worth noting that derivation of the equation for a tangent plane to a parametrized surface relies heavily on partial derivatives and the study of multi-variable calculus.

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Answer:

A

Step-by-step explanation:

The volume (V) of a pyramid is calculated using the formula

V = [tex]\frac{1}{3}[/tex] × area of base × height

note the height = 48 × 10 = 480 ( 48 storeys at 10 feet )

V = [tex]\frac{1}{3 }[/tex] × 571,536 × 480

  = 91,445,760 ft³

[ 1 yd³ = 27 ft³ ], hence

V = [tex]\frac{91445760}{27}[/tex] = 3, 386, 880 yd³ → A

Answer:

c

Step-by-step explanation:

Answer:

the correct solution is letter A.

Step-by-step explanation:

We have the following expression:

6sqrt(7) - 5x*sqrt(7) - x*sqrt(7)

Grouping the expression, we have:

=sqrt(7)*[6 - 5x - x]

=sqrt(7)*[6 - 6x]

=  6*sqrt(7)- 6x*sqrt(7)

So the correct solution is letter A.

Answer:

To quickly solve this problem, we can use a graphing tool or a calculator to plot each equation.

Please see the attached image below, to find more information about the graph

s

The equations are:

1) y = tan (x)

2) y = cot (x)

3) y = -tan (x)

4) y = -cot (x)

Looking at the graphs, we can see which corresponds to each equation

1) y = tan (x)

Graph C

2) y = cot (x)

Graph A

3) y = -tan (x)

Graph B

4) y = -cot (x)

Graph D

Answer:

A) 1C, 2A, 3B, 4D

Step-by-step explanation:

We can graph each of the functions in your preferred grapher, the we compare each graph with the corresponding example. (attached images)

By doing this we can see that graph C is tanx, graph A is cotx, graph B is -tanx, graph D is -cotx