Two sides of a triangle have lengths 20 km and 35 km. Describe the possible lengths of the third side.

Final answer:

Julian needs to practice at least 8 and 1/6 hours on each of the last two days of the week.

Explanation:

To determine the minimum number of hours Julian needs to practice on each of the last two days of the week, we can use an inequality. Julian needs to spend at least seven hours each week practicing the drums, and he has already practiced five and one-third hours this week. Let's represent the minimum number of hours he needs to practice on each of the remaining two days as 'x'. The inequality can be written as:

5 1/3 + 2x ≥ 7

Now let's solve the inequality:

So, the minimum number of hours Julian needs to practice on each of the last two days of the week is 8 and 1/6 hours (or approximately 8.17 hours).

Answer:

  12 friends

Step-by-step explanation:

Fill in the given number and solve for x.

  855 = 5x +795 . . . . . the total fee was 855

  60 = 5x . . . . . . . . . . . subtract 795

  12 = x . . . . . . . . . . . . . divide by 5

The number of friends you brought was 12.

Answer:

It's B.

Step-by-step explanation:

That is B because there are no duplicate x-values in the ordered pairs.

D is a set of numbers, not a function.

Answer:

Step-by-step explanation:

Let's start with a function first.  The domain of a function is all the x values that are covered by the graph of the function; the range is all the y values that are covered by the graph of the function.

In order to graphically find the inverse of a function, you literally switch the x and y variables and replot them.  For example if a point on your function is

(3, -1), then the point on its inverse is (-1, 3).  Because of this, you interchange the domains and the ranges.  Therefore, the domain of a function is the range of its inverse, and the range of a function is the domain of its inverse.

The domain of the inverse function f⁻¹(x) will be (c, d) and the range of the inverse function f⁻¹(x) will be (a, b).

The domain means all the possible values of x and the range means all the possible values of y.

Let the function be f(x).

Let the domain of the function f(x) is (a, b) and the range of the function f(x) is (c, d).

The inverse function of f(x) will be f⁻¹(x).

Then the domain of the inverse function f⁻¹(x) will be (c, d) and the range of the inverse function f⁻¹(x) will be (a, b).

More about the domain and range link is given below.

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Answer:

= (100)^3(1/4)^3

= 15,625  i think im not that good at math but i passed

Step-by-step explanation:

Hi there! My name is Zalgo and I am here to help you out on this gracious day. If n=3, a=100 and b=1/4, the equation should look like "100^3 * 1/4^3". The answer would be 15625.

I hope that this helps! :D

"Stay Brainly and stay proud!" - Zalgo

To find the total cost of the ribbon, multiply the length needed (20.5 feet) by the cost per foot ($0.45), which equals $9.225. Round this to the nearest cent to get $9.23.

To calculate the cost of the ribbon needed for a sewing project, you multiply the length of the ribbon required by the cost per foot. In this case, the project calls for 20.5 feet of ribbon and the ribbon costs $0.45 per foot. The formula to use is: Total Cost = Length in Feet x Cost Per Foot. Now, let's do the math:

Total Cost = 20.5 feet x $0.45/foot = $9.225.

To round to the nearest cent, the total cost would be $9.23.

Answer:

[tex]\boxed{\text{B. 13}}[/tex]

Step-by-step explanation:

1. Find the equation of the parabola

The vertex is at (0, 0), so the axis of symmetry is the y-axis.

The graph passes through (7, 7), so it must also pass through (-7,7).

The vertex form of the equation for a parabola is

y = a(x - h)² + k

where (h, k) is the vertex of the parabola.

If the vertex is at (0, 0),  

h = 0 and k = 0

The equation is

y = ax²

2. Find the value of a

Insert the point (7,7).

7 = a(7)²

1 = 7a

a = ⅐

The equation in vertex form is

y = ⅐x²

3. Calculate the length of the segment when y = 6

[tex]\begin{array}{rcl}6 & = & \dfrac1{7}x^{2\\\\42 & = & x^{2\\x & = & \pm \sqrt{42}\\\end{array}[/tex]

The distance between the two points is the length (l) of line AB.

A is at (√42, 6); B is at (-√42, 6).

l = x₂ - x₁ = √42 – (-√42) = √42 + √42 = 2√42 ≈ 2 × 6.481 ≈ 13.0

[tex]\text{The length of the segment joining the points of intersection is }\boxed{\mathbf{13.0}}[/tex]

Answer:

$13

Step-by-step explanation:

Depost of 650.00 into a bank account paying 2% simple interest per year. You left the money in for 1 year. Find the interest earned and the amount earned in 1 year.

The interest is $13, and the amount is 663.00.

Answer:

13

Step-by-step explanation:

Answer: Option C

"The sides opposite and adjacent to theta are the same length."

Step-by-step explanation:

By definition the tangent of an angle [tex]\theta[/tex] is written as:

[tex]tan(\theta) = \frac{opposite}{adjacent}[/tex]

Where:

"opposite" is the side opposite the [tex]\theta[/tex] angle

"adjacent" is the side that contains the angle [tex]\theta[/tex] and the angle of 90 °.

In this case we know that

[tex]tan(\theta) = \frac{opposite}{adjacent} = 1[/tex]

If [tex]\frac{opposite}{adjacent} = 1[/tex] then [tex]opposite = adjacent[/tex]

Finally the answer is the option C

"The sides opposite and adjacent to theta are the same length."

Answer:

C. The sides opposite and adjacent to theta are the same length.

Step-by-step explanation:

Given :  tanθ = 1

recall tanθ = [tex]\frac{opposite}{adjacent}[/tex]

the only way for [tex]\frac{opposite}{adjacent}[/tex] to equal 1, is that the numerator is the same value as the denominator,

hence  the answer is

C. The sides opposite and adjacent to theta are the same length.

Answer:

  A)  0.2x +1 = x . . . . x is the volume of liquid in the bottle (liters)

  B)  0.25 liters of milk are in the bottle

Step-by-step explanation:

It is often convenient to define a variable as the answer to the question. Here, the question says "find the total number of liters of milk and water in the bottle", so that is the definition of our variable, x.

A) The problem statement tells us that 20% of the liquid is milk, so that amount is 0.2x (as the hint says). Then the sum of milk volume and water volume is the total volume:

  0.2x + 1 = x . . . . . . . an equation in one variable that can find total volume

We can solve this equation by subtracting 0.2x, then dividing by the coefficient of x.

  1 = 0.8x

  1/0.8 = x = 1.25 . . . the total number of liters of milk and water is 1.25

__

B) The number of liters of milk is 0.2x, so is 0.2·1.25 = 0.25

  There are 0.25 liters of milk in the bottle.

Answer:

Slope = 4

Step-by-step explanation:

The x-axis values to represent the number of correct answers.

The y-axis values to represent the number of points earned.

The points on the graph are: (17,68) , (20,80) and (24,96)

The slope(m) of the graph = change in y ÷ change in x

i.e [tex]\frac{80 - 68}{20 - 17}[/tex] = [tex]\frac{96 - 80}{24 - 20}[/tex] = 4

The equation of the straight line graph is;

y=4x

The slope of the graph, representing points earned per correct answer on the quiz, is 4. This is found by dividing the change in points earned by the change in correct answers between any two points on the graph.

The slope of a graph in the coordinate plane is the ratio of the change in y (the vertical difference) to the change in x (the horizontal difference) between any two points on the line. In this case, the difference in y (points earned) for the pairs given by Ms. Walker, for example between (20, 80) and (24, 96), is 16. The difference in x (number of correct answers) in the same pairs is 4. Therefore, the slope of the graph, which represents the points per question, is 16 divided by 4: 4 points per question. This means that for each correct answer (each increase in 1 on the x-axis), the number of points earned (y) increases by 4.

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ANSWER

B. 310°

EXPLANATION

The sum of angles in a circle is 360°

From the diagram, the measure of arc SY is 50°

The measure of arc STY plus the measure of arc SY is 360°

To find the measure of arc STY, we subtract 50° from 360° to get:

Measure of arc STY

[tex] = 360 \degree - 50 \degree[/tex]

This simplifies to

[tex]310 \degree[/tex]The correct answer is B 310°

Answer:

The correct answer is option B.  310°

Step-by-step explanation:

From the figure we can see that, a circle with center o.

And an arc SY with central angle 50°

To find the measure of arc STY

From the figure we can write,

arc SY + arc STY = 360

measure of arc STY = 360 - measure of arc SY

 = 360 - 50 - 310°

Therefore the  correct answer is option B.  310°

Answer:

  (1/8)(cos(4x) -4cos(2x) +3)

Step-by-step explanation:

Your answer is correct as far as it goes. You now need to use a power-reducing identity on the cos(2x)² term in your answer. The appropriate one is ...

  cos(x)² = (1/2)(1 +cos(2x))

In the context of this problem, using this formula gives you ...

  sin(x)⁴ = (1/4)(1 -2cos(2x) +(1/2)(1 +cos(4x))

  sin(x)⁴ = (1/8)(cos(4x) -4cos(2x) +3)

Answer:

  A)  CUB

Step-by-step explanation:

Of the suggested planes, only CUB contains both points C and T.

___

Comments on the other answer choices

BED contains point T, but not C

ACE contains point C, but not T

ABE contains neither C nor T

Answer:

A) CUB

Step-by-step explanation:

Answer:

CosA/CosB =1

CosA = Adjacent side/Hypotenuse

=AC/AB = 3/4.24

Cos B =  Adjacent side/Hypotenuse  

= BC/AB = 3/4.24

CosA/CosB = (3/4.24)/(3/4.24) = 1

The value of CosA/CosB = 1

Answer:

1

Step-by-step explanation:

trust lol

Answer:

[tex]f(3)=1.9[/tex]

Step-by-step explanation:

we have

[tex]f(x)=\frac{14}{7+2e^{-0.6x}}[/tex]

we know that

f(3) is the value of the function for the value of x equal to 3

so

substitute the value of x=3 in the function

[tex]f(3)=\frac{14}{7+2e^{-0.6(3)}}=1.9[/tex]

Answer:

1.9

Step-by-step explanation:

fX)=14/7=2e^-0.6x = 1.9

Answer:

1225

Step-by-step explanation:

hihi. So the equation for MoE is (z*) * SE. The z* for a 95% Confidence is one you should have memorized but for repeatability sake you can always just do an inverse Norm to find the z* for these types of applications. To do so, you can always type this command into your calculator: invNorm(conf + (1-conf)/2, 0, 1).

(When I say conf here I am referring to the confidence level as a decimal).

All that's left is the Standard Error or SE to be short. Since you gave a p* estimate then we can use the equation for SE when dealing with proportions/percents which is sqrt(p(1-p) / n) where p is the proportion and n is the sample size, which we are solving for. Once you have this established it's a basic multi-step solve for n which comes out to be 1225 after rounding.

A side note, the included picture is a bit messy due to my refusal to round when doing these kinds of problems. Rounding errors are more common than you think

The sample size would be 1225 needed to construct a margin of error of 2% with 95% confidence and this can be determined by using the formula of margin of error.

Given :

The following calculation can be used to determine the sample size needed to construct a margin of error of 2% with 95% confidence.

[tex]\rm MOE = z \times \sqrt{\dfrac{p(1-p)}{n}}[/tex]

[tex]0.02=1.96\times \sqrt{\dfrac{0.15\times 0.85}{n}}[/tex]

[tex]\left(\dfrac{0.02}{1.96}\right)^2= \dfrac{0.15\times 0.85}{n}[/tex]

[tex]n = \dfrac{(1.96)^2\times 0.15 \times 0.85}{(0.02)^2}[/tex]

[tex]n = 1224.51[/tex]

n = 1225  (round off)

The sample size would be 1225 needed to construct a margin of error of 2% with 95% confidence.

For more information, refer to the link given below:

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[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ Q(\stackrel{x_1}{0.3}~,~\stackrel{y_1}{1.8})\qquad R(\stackrel{x_2}{2.7}~,~\stackrel{y_2}{3.9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{2.7+0.3}{2}~~,~~\cfrac{3.9+1.8}{2} \right)\implies \left(\cfrac{3}{2}~,~\cfrac{5.7}{2} \right)\implies (1.5~,~2.85)[/tex]

Final answer:

The coordinates of the midpoint are (1.35, 2.85).

Explanation:

The coordinates of the midpoint of a segment can be found by averaging the x-coordinates of the endpoints and averaging the y-coordinates of the endpoints. In this case, the x-coordinate of the midpoint is (0 + 2.7) / 2 = 1.35, and the y-coordinate of the midpoint is (1.8 + 3.9) / 2 = 2.85. Therefore, the midpoint of the segment with endpoints Q(0.3, 1.8) and R(2.7, 3.9) is (1.35, 2.85).

Answer:

  96 squares

Step-by-step explanation:

The number of squares is ...

  (wall area)/(square area) = (24 ft²)/(1/4 ft²) = 24×4 = 96 . . . . squares

Answer:

96 squares

Step-by-step explanation:

Answer:

The answer to this question is p-125, because P is the cost of the bike, and reduce = subtract. YW :)

If p is the mountain bike's initial price in dollars, the (P- $ 125 is an algebraic equation indicates the lowered price.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

If p is the initial price of the mountain bike in dollars, the algebraic equation (P- $ 125) reflects the reduced price.

Hence, (P- $ 125) is the correct expression.

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Answer:

  15x + 50 = 10x + 75

Step-by-step explanation:

The cost at Black Diamond for ski rental and x hours of skiing is ...

  50 +15x

The cost at Bunny Hill for ski rental and x hours of skiing is ...

  75 +10x

These costs will be equal when ...

  15x + 50 = 10x + 75

Answer:

C: 15x + 50 = 10x + 75

Step-by-step explanation:

Answer:

ITS 100% A

Step-by-step explanation:

Answer:

Option 2.

Step-by-step explanation:

Let as consider x be the  air conditioning unit's actual capacity and y is the maximum variance in British thermal units (Btu).

It is given that an air conditioning unit promises to have a cooling capacity of 6,000 British thermal units (Btu).

We need to find the graph that could be used to determine the variance levels that would cause a unit to be rejected because of its cooling capacity.

It means the maximum variance is less than or equal to absolute difference of actual capacity and 6,000.

[tex]y\leq |x-6000|[/tex]

The related equation of this inequality is

[tex]y=|x-6000|[/tex]

It is a V-shaped curve with vertex (6000,0) and y-intercept (0,6000).

The related curve is a solid V-shaped curve because the points on curve included in the solution set.

The shaded region lie below the curve because the sign of inequality is ≤.

Therefore the correct option is 2.

Answer:

[tex]f^{-1}(x)=6(x+7)^{3}[/tex]

Step-by-step explanation:

we have

[tex]f(x)=\sqrt[3]{\frac{x}{6}}-7[/tex]

Let

[tex]y=f(x)\\ y=\sqrt[3]{\frac{x}{6}}-7[/tex]

Exchanges the variable x for y and y for x

[tex]x=\sqrt[3]{\frac{y}{6}}-7[/tex]

Isolate the variable y

[tex]x+7=\sqrt[3]{\frac{y}{6}}[/tex]

elevates to the cube both members

[tex](x+7)^{3}=\frac{y}{6} \\ \\y=6(x+7)^{3}[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=6(x+7)^{3}[/tex] ------> inverse function

Answer:

A=Pe^rt

P= princible (1300)

e= (2.71828)- function on a graphing calculator

r = interest rate (.05 or 5%)

t = time (10 years)  

A = 1300e^.05(10)

A = 1300e^.5

A = 2143.337652

A = 2143

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1300\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases}[/tex]

[tex]\bf A=1300\left(1+\frac{0.05}{1}\right)^{1\cdot 10}\implies A=1300(1.05)^{10}\implies \stackrel{\textit{rounded up}}{A=2118}[/tex]

Answer:

  C, B, A

Step-by-step explanation:

From smallest to largest, the side lengths are ...

The shortest side is opposite the smallest angle, so the angles, smallest to largest, are C, B, A.

___

Comment on side naming

Side c is opposite vertex (and angle) C, so is between vertices A and B. Thus the names AB and c are both names for the side of the triangle opposite angle C.

Answer:

C, B, A

Step-by-step explanation:

Answer:

TM = (3,-9,-9)

The magnitude of TM = 3√19

Step-by-step explanation:

Given T=(-5,8,3) and M = (-2,-1,-6)

TM is the difference between the vector M and the vector T

So,

TM = M - T = (-2,-1,-6) - (-5,8,3) = (-2+5 , -1-8 , -6-3) = (3,-9,-9)

The magnitude of TM = The distance of TM = [tex]\sqrt{3^2+(-9)^2+(-9)^2}=\sqrt{9+81+81}=\sqrt{171} = \sqrt{9*19} =3\sqrt{19}[/tex]

So, TM = (3,-9,-9) and |TM| = 3√19

1. How much more iced tea did Pablo have than Rosa?

Pablo has 1 1/36 quarts of ice tea more than Rosa.

2.  Pablo gave Rosa 15% of his iced tea today. How much iced tea do each of them have now? Write your answer in fraction form.

      Iced tea given

      Pablo iced tea

      Rosa iced tea

Pablo has 3 7/9 quarts of iced tea and Rosa has 4 1/12 quarts.

[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in feet} \\\\ h(t) = -16t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{64}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{0\qquad \textit{from the ground}}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf h(t)=-16t^2+64t+0\implies h(t)=-16t^2+64t\implies \stackrel{\textit{hits the ground}~\hfill }{0=-16t^2+64t} \\\\\\ 0=-16t(t-4)\implies t= \begin{cases} 0\\ \boxed{4} \end{cases}[/tex]

Check the picture below, it hits the ground at 0 feet, where it came from, the ground, and when it came back down.

Answer:

69.09 yd^2

Step-by-step explanation:

14.1*9.8=138.18

138.18*0.5=69.09

Answer:

69.09 square yd.

Step-by-step explanation:

Area of a triangle is

[tex]A=\dfrac{1}{2}\times base\times height[/tex]

From the given figure it is clear that height of the triangle is 9.8 yd and base of the triangle is 14.1 yd.

Substitute the given values in he above formula, to find the area of triangle.

[tex]A=\dfrac{1}{2}\times 14.1\times 9.8[/tex]

[tex]A=69.09[/tex]

Hence, the area of triangle is 69.09 square yd.