What equation can be used to solve for c?c = (5)cos(35o) c = 5/cos(350), c = (5)sin(35o) c =

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y-4=(4/3)(x-2)[/tex]

This is the equation of a line into point slope form

The point is (2.4)

The slope is m=4/3

To plot the line find the intercepts

The y-intercept is the value of y when the value of x is equal to zero

For x=0

y-4=(4/3)(0-2)

y=(-8/3)+4

y=4/3

The x-intercept is the value of x when the value of y is equal to zero

0-4=(4/3)(x-2)

-4=(4/3)x-(8/3)

Multiply by 3 both sides

-12=4x-8

4x=8-12

x=-1

we have the points

(2,4), (0,4/3),(-1,0)

Plot the line

Note With only two points it was necessary to draw the line. The third point was calculated for didactic purposes.

see the attached figure

Answer:

D. [tex]g(x)=\frac{1}{5}x^2[/tex]

Step-by-step explanation:

Answer:

Yes

Every straight line can be represented by an equation: y = mx + b.

m=slope

b=y-intercept

(www.math.com/school/subject2/lessons/S2U4L2GL.html)

Answer:

3.6 fl oz

Step- by-step explanation:

Well if one gallon equal 2.4 fl oz that would mean that half of a gallon would be half of that amount. Half of that amount would be 1.2 fl oz. we have now found how much a full gallon needs and how much half a gallon need. Now we add these 2 numbers. 2.4 fl oz + 1.2 fl oz = 3.6 fl oz.

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Final answer:

To get the correct oil mix for 1.5 gallons of gasoline at a ratio of 2.4 fl oz of oil per gallon, you should add 3.6 fl oz of oil.

Explanation:

To calculate the amount of oil needed for 1.5 gallons of gasoline with a mix ratio of 2.4 fl oz of oil per gallon, you follow these steps:

Determine the amount of oil needed for one gallon of gas, which is 2.4 fl oz.

Multiply this amount by the total gallons of gas. In this case, 2.4 fl oz x 1.5 gallons.

The calculation will be 2.4 fl oz/gallon x 1.5 gallons = 3.6 fl oz of oil.

Therefore, you should add 3.6 fl oz of oil to 1.5 gallons of gasoline to achieve the correct mix ratio.

For this case we have by definition, that the area of a rectangular prism is given by:

[tex]V = A_ {b} * h[/tex]

Where:

[tex]A_ {b}:[/tex] is the area of the base

h: It's the height

Before finding[tex]A_ {b}[/tex]we convert the mixed numbers to fractions:

length: [tex]2 \frac {1} {4} = \frac {4 * 2 + 1} {4} = \frac {9} {4}[/tex]

width: 6

Height:[tex]3 \frac {1} {2} = \frac {2 * 3 + 1} {2} = \frac {7} {2}[/tex]

So, we have to:[tex]A_ {b} = \frac {9} {4} * 6 = \frac {54} {4} = 13.5[/tex]

Finally, the volume is given by:

[tex]V = 13.5 * \frac {7} {2} =47.25\ ft ^ 3[/tex]

Answer:

[tex]47.25 \ ft ^ 3[/tex]

ANSWER

[tex]Volume = 47\frac{1}{4} {ft}^{3} [/tex]

EXPLANATION

The formula for calculating the volume of a rectangular prism is

[tex]Volume = l \times b \times h[/tex]

Where

[tex]l = 2 \frac{1}{4} ft[/tex]

is the length of the rectangular box,

[tex]w = 6ft[/tex]

is the width and

[tex]h = 3 \frac{1}{2} ft[/tex]

is the height of the rectangular prism.

We plug in the given dimensions into the formula to get:

[tex]Volume = 2 \frac{1}{4} \times 6 \times 3 \frac{1}{2} [/tex]

Convert the mixed numbers to improper fraction to get:

[tex]Volume = \frac{9}{4} \times 6 \times \frac{7}{2} [/tex]

Multiply out to get

[tex]Volume = \frac{189}{4} {ft}^{3} [/tex]

Or

[tex]Volume = 47\frac{1}{4} {ft}^{3} [/tex]

Answer:

C.

Step-by-step explanation:

Add up the number of minutes Evan played.  you can ignore the number of minutes Josh played, the number of players in the team and the number of times Evan was substituted.

Answer:

The number of minutes Evan played.

Step-by-step explanation:

The most important variable is :  The number of minutes Evan played.

As at the end we have to find out how long did Evan play. And to get the answer, we have to consider Evan's play time in each quarter.

By adding all those numbers, we will get the answer.

Hence, option C is correct.

Answer:

a(n) = -3(-1/5)^(n - 1)

Step-by-step explanation:

From the first term, -3, we get the second term, 3/5, by multiplying -3 by -1/5.

Thus, the common ratio is -1/5.

The general formula in this case is a(n)=(first term)(common ratio)^(n - 1), or

a(n) = -3(-1/5)^(n - 1)

Answer:

A) Obtuse

Step-by-step explanation:

It is Obtuse due to the angle 115° being in the Triangle. This rules out Acute since the middle angle is not less than 90°. It is not Equiangular since all three angles are not equal. Furthermore it is not a right triangle either since there is no 90° angles. Making it Obtuse.

To classify a triangle based on angle measures, we need to know the specific angles. Triangles can be obtuse, acute, right, or equiangular, and each type has its own unique properties used in various applications across different fields.

To classify the following triangle based on its angle measures, we must first understand the definitions of different types of triangles. A triangle can be classified as:

Considering these definitions, the seeking student must provide the angle measures of their specific triangle to accurately classify it.

Making distinctions between different types of triangles is crucial because each classification has unique properties that are important in various fields such as mathematics, engineering, architecture, and physics. These properties assist in solving problems and understanding the world around us.

For instance, an obtuse triangle may be used in special construction scenarios, while right triangles are essential in trigonometry and geometry, appearing frequently in real-life applications like building and navigation.

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Answer: C)46 ft

Step-by-step explanation:

We know that the circumference of a circle can be calculated with this formula:

[tex]C=2\pi r[/tex]

Where "r" is the radius of the circle.

Since John is putting a fence around his garden that is shaped like a half circle and a rectangle, then we can find how much fencing he needs by making this addition:

[tex]Fencing=\frac{2\pi r}{2}+2l+w[/tex]

Where "l" is the lenght of the rectangle and "w" is the width of the rectangle.

Since we know that the radius of the circle is half its diameter, we can find "r". This is:

[tex]r=\frac{7ft}{2}=3.5ft[/tex]

Then, substituting values (and using [tex]\pi=\frac{22}{7}[/tex]), we get:

[tex]Fencing=\frac{2(\frac{22}{7})(3.5ft)}{2}+2(14ft)+7ft=46ft[/tex]

The answer is C) 46ft

Answer:

congrats

Step-by-step explanation:

Answer:

g(x)=4

Step-by-step explanation:

5.23(0)+4=4

Hope this helps!

ANSWER

[tex]y = 4x - 2[/tex]

EXPLANATION

The equation of a straight line can be found using the formula

[tex]y =mx + b[/tex]

We have that,the y-value increases by 4 for every x that increases by 1.

This implies that, the slope is

[tex]m = \frac{4}{1} = 4[/tex]

The line also crosses the y-axis at –2.

Hence the y-intercept is b=-2.

Therefore the equation is

[tex]y = 4x - 2[/tex]

The correct answer is A

The graph of the equation y = x + 3 is a straight line with a slope of 1 and a y-intercept of 3. This means that for every increase of 1 in x, y increases by 1 and the line crosses the y-axis at y = 3.

The student is asking for the graph of the function g(x)=[x+3]. Please note, the symbol '[' and ']' is usually used to denote the greatest integer function or floor function, but since the context is not very clear, I'll assume that this is a simple linear function y = x + 3.

In such case, the graph of y = x + 3 is a **straight line** with a **slope** of 1 and a y-**intercept** of 3. Remember, the ^ slope is the change in y for every increase of 1 in x, and in this equation, for every increase of 1 in x, y increases by 1 . The intercept is simply where the line crosses the y-axis, and in this case it's at y = 3.

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Answer:

A, B, and D are the correct statements.

Answer:

The turning point is (-2,10)

Step-by-step explanation:

we have

[tex]y=6-4x-x^{2}[/tex]

This is a quadratic equation (vertical parabola) open downward

we know that

The turning point of a quadratic equation is the vertex

so

Convert the quadratic equation into vertex form

[tex]y-6=-4x-x^{2}[/tex]

[tex]y-6=-(x^{2}+4x)[/tex]

[tex]y-6-4=-(x^{2}+4x+4)[/tex]

[tex]y-10=-(x^{2}+4x+4)[/tex]

[tex]y-10=-(x+2)^{2}[/tex]

[tex]y=-(x+2)^{2}+10[/tex] ----> equation in vertex form

The vertex is the point (-2,10)

therefore

The turning point is (-2,10)

The turning point of the parabola described by the equation y=6-4x-x^2 is at the point (-2, 10), which is a maximum since the parabola opens downwards.

To find the turning point of the curve given by the equation y=6-4x-x^2, we first need to rewrite the equation in the form of the vertex of a parabola, which is given by y=a(x-h)^2+k, where (h,k) is the coordinate of the turning point or vertex. Noting that there is a mistake in the information provided since the second derivative would actually be y" = -2, and not 6x - 12, indicating that we have a concave down parabola with a maximum point, not a point of inflection. We can complete the square to rewrite the function in vertex form.

Start by completing the square: y = -x^2 - 4x + 6 can be rewritten as y = -(x^2 + 4x) + 6. Adding and subtracting 4 inside the parenthesis (which is the square of half the coefficient of x), we get y = -(x^2 + 4x + 4 - 4) + 6, which simplifies to y = -(x + 2)^2 + 10. Thus, the vertex or turning point is at (-2, 10).

This shows the turning point of the parabola is at the point (-2, 10), which is a maximum since the parabola opens downwards as reflected by the negative coefficient of the x^2 term. This can be visualized on the graph of the function as the highest point on the curve. Remember that a quadratic equation represents a parabola in a Cartesian coordinate system.

Answer: There are no solutions to the system because the equations represent parallel lines.

The value 0 = -12 indicates an inconsistent system with no solution.

0 = -12 means that the system of equations is inconsistent, and there is no solution. In this case, the equations represent parallel lines that never intersect, hence no common solution exists.

Answer:

Step-by-step explanation:

Givens

Height = h = 4cm

b = ?

Area = 40 cm^2

Formula

Area = 1/2 * h * b

Solution

40 cm^2 = 1/2 * 4 * b      Combine the right

40 cm^2 = 2 * b              Divide by 2

40 cm^2 /2 = 2b/2         Do the division

20 cm = b

Answer D

Answer:

90

Step-by-step explanation:

Write the ratio this way

Pip: Sara: Total

5    : 4 :      9

We multiply each by 10 to get Pip to 50  (5*10 = 50)

5*10: 4*10: 9*10

50  : 40 :  90

Answer:

$90

Step-by-step explanation:

Given that the ratio of Pip: Sara is 5:4

This means :

Pip gets 5 parts

Sara gets 4 parts

Together they have 5 + 4 parts = 9 parts

Also given that Pip's 5 parts is equivalent to $50

Hence each 1 part is $50/5 = $10

if 1 part = $10

The total 9 parts = 9 x $10 = $90

The geometric mean of two numbers is the square root of their product.

sqrt{4 • 12}

sqrt{48}

sqrt{16} •sqrt{3}

4•sqrt{3}.

The geometric mean of 4 and 12 is

4•sqrt{3}.

To determine the first five terms of the given recursive sequence, we begin with the first term, a1 = -10, and use the provided recurrence relation to calculate each subsequent term. The first five terms of the sequence are -10, -33, -125, -493, and -1965.

The student has presented a recursive sequence with the first term stated as – 10 and a recursive formula to find any subsequent term, an, defined as an = 4an-1 + 7 for n ≥ 2.

To find the first five terms of the sequence, we'll apply the formula starting with a1 and proceed to each next term.

First term, a1: – 10

Second term, a2: 4(– 10) + 7 = – 40 + 7 = – 33

Third term, a3: 4(– 33) + 7 = – 132 + 7 = – 125

Fourth term, a4: 4(– 125) + 7 = – 500 + 7 = – 493

Fifth term, a5: 4(– 493) + 7 = – 1972 + 7 = – 1965

Therefore, the first five terms of the sequence are – 10, – 33, – 125, – 493, and – 1965.

Answer:

12 sqrt(2)

Step-by-step explanation:

Givens

a = 12 cm

b = 12 cm

c = ??

The triangle is isosceles with 1 right angle and 2 45 degree angles.

Formula

c^2 = a^2 + b^2

c^2 = 12^2 + 12^2

c^2 = 144 + 144

c^2 = 288

c^2 = 144 * 2

c = sqrt(144) * sqrt(2)

c = 12 * sqrt(2)

The answer isn't there. 12*sqrt(2) is the correct answer, 12sqrt(3).

Was this just a typo of some kind.

Answer:

Step-by-step explanation:

U-4.5=6.46

   +4.5   +4.5

U=10.96

Answer:

[tex]\frac{4x^3-3x^2+5x+6}{x+6}=4x^2-27x+167-\frac{996}{x+6}[/tex]

Step-by-step explanation:

The division problem given to us is [tex](4x^3-3x^2+5x+6)\div (x+6)[/tex].

To perform the synthetic division, we write out the coefficient of the polynomial. We set the linear factor to zero and solve for x, this becomes our divisor. That is [tex]x+6=0\implies x=-6[/tex].

We carry out the synthetic division as shown in the attachment.

The result of the synthetic division is 4   -27   167   -996

The first three terms are the coefficients of the quotient and the last term is the remainder.

Therefore the quotient is [tex]q(x)=4x^2-27x+167[/tex] and the remainder is [tex]r(x)=-996[/tex].

The dividend, the quotient and the divisor are written as

[tex]\frac{4x^3-3x^2+5x+6}{x+6}=4x^2-27x+167-\frac{996}{x+6}[/tex]

The correct answer is A

Answer:

x = - 1, x = [tex]\frac{1}{8}[/tex]

Step-by-step explanation:

Given

8x² + 7x - 1 = 0 ← in standard form

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term

product = 8 × - 1 = - 8 and sum = + 7

The factors are + 8 and - 1

Use these factors to split the x- term

8x² + 8x - x - 1 = 0 ( factor the first/second and third/fourth terms )

8x(x + 1) - 1(x + 1) = 0 ← factor out (x + 1) from each term

(x + 1)(8x - 1) = 0

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

8x - 1 = 0 ⇒ 8x = 1 ⇒ x = [tex]\frac{1}{8}[/tex]

Answer:

x

=

1

8

,

−

1

x=1/8,-1 I solved using  the quadratic formula

Step-by-step explanation:

Suppose [tex]x=3.1\overline6[/tex]. Then [tex]10x=31.\overline6[/tex], and [tex]100x=316.\overline6[/tex].

Now,

[tex]100x-10x=316.\overline6-31.\overline6=316-31[/tex]

[tex]\implies90x=285[/tex]

[tex]\implies x=\dfrac{285}{90}=\boxed{\dfrac{19}6}[/tex]

Answer: B is the answer

Step-by-step explanation:

Just subtract 1/6 from 11/18 to get the answer!

Answer:

m < b = 70, m < c = 110 and m < d = 70 degrees.

Step-by-step explanation:

The opposite angle a ( angle c) = a = 110 degrees  (Property of a parallelogram).

The angle on the same line as a ( that is angle b) = 180 - 110 = 70 degrees.

(Property of a parallelogram).

Finally angle d which is opposite angle b = 70 degrees.

Final answer:

In parallelogram ABCD with angle A being 110 degrees, angle C is also 110 degrees as opposite angles are equal. Angles B and D are 70 degrees each since consecutive angles in a parallelogram are supplementary and add up to 180 degrees.

Explanation:

To find the measures of the angles B, C, and D in the parallelogram ABCD with angle A being 110 degrees, we can use the properties of parallelograms. Specifically, opposite angles in a parallelogram are equal, and consecutive angles are supplementary (add up to 180 degrees).

Since angle A is 110 degrees, angle C, being opposite to angle A, also measures 110 degrees. Now, to find the measures of angles B and D we know that:

Angle A and angle B are consecutive, so they add up to 180 degrees. Therefore, angle B equals 180 degrees - 110 degrees which is 70 degrees.

Similarly, angle C and angle D are consecutive, so angle D also measures 180 degrees - 110 degrees, giving us 70 degrees for angle D as well.

Thus, the measures of angles B, C, and D in parallelogram ABCD are 70 degrees, 110 degrees, and 70 degrees, respectively.

Answer:

x = 3.133

Step-by-step explanation:

I'm going to take a chance and assume that you meant "ln 11," not "in11."

If I'm right, then we have:

3x-5 = ln 11 + 2.

Adding 5 to both sides yields

3x = ln 11 + 2 + 5, or ln 11 + 7.  Since ln 11 = 2.398,

3x = 2.398 + 7, or    3x = 9.398, and so

x = 3.133.

If this is not what you expected, please ensure that you have copied down the original problem accurately.  Thank you.

For this case we must find an expression equivalent to:

[tex]\sqrt [5] {13 ^ 3}[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

Then, rewriting the expression:

[tex]13 ^ {\frac {3} {5}}[/tex]

Answer:

Option D

[tex]13 ^ {\frac {3} {5}}[/tex]

Answer:

Option 4 (3)

Step-by-step explanation:

The first step involved in calculating the median it to list the observations in the ascending order. This gives:

12 15 33 45 46 51 52 57.

The second step is to identify the middle number (in case the observations are in odd numbers) or numbers (in case the observations are in even numbers) after the ascending order step has been done. It can be observed that the middle numbers in this data set are 45 and 46. Since there are two numbers, so their average will be the median of this data set. Therefore, the median is 45.5.

It can be observed that that there are 2 outliers in the data set: 12 and 15. Once removed, the data set will be:

33 45 46 51 52 57.

The middle numbers are 46 and 51 and the mean of the two middle numbers is 48.5.

Therefore, the difference between the median of the data, including the possible outliers and excluding the possible outliers is given by 48.5 - 45.5 = 3. Therefore, Option 4 is the correct answer!!!