Translate and simplify: the difference of -5 and -30

The approximate difference in the maximum height achieved by the two projectiles is 5.4 ft. (Option C).

How to calculate the difference between two maximum heights?

The approximate difference in the maximum height achieved by the two projectiles is calculated as follows;

The given function of one of the projectile;

f(x) = -16x² + 42x + 12

The function of the second projectile shown in the table, shows that the maximum of the function, g is 33

g(1) = 33 ft (maximum height)

The maximum height attained by the projectile with f(x) function occurs at x = 1

f(1) = -16(1)² + 42(1) + 12

f(1) = 38 ft

The difference between two maximum heights;

Δh = f(1) - g(1)

Δh = 38 ft - 33 ft

Δh = 5 ft

The option that is approximately 5 ft is option C (5.4 ft).

Answer:

B. 75 Degrees

Step-by-step explanation:

A triangle is up to 180 degrees. Since you're given two angles already, you can add both of those together and subtract it from 180.

75 + 35 = 105

180 - 105 = 75

75 + 75 + 35 = 180

See the attached picture.

The negative sign in front of the 2 makes the graph an upside down U shape.

We know that the general equation of a parabola in vertex form is given by:

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

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

and if a>0 then the parabola is open upward and if a<0 then the parabola is open downward.

a)

[tex]f(x)=-2(x+3)^2-1[/tex]

Since, the leading coefficient is negative.

Hence, the graph of the function is a parabola which is downward open.

The vertex of the function is at (-3,-1)

b)

[tex]f(x)=-2(x+3)^2+1[/tex]

Again the leading coefficient is negative.

Hence, graph is open downward.

The vertex of the function is at (-3,1)

c)

[tex]f(x)=2(x+3)^2+1[/tex]

The leading coefficient is positive.

Hence, graph is open upward.

The vertex of the function is at (-3,1)

d)

[tex]f(x)=2(x-3)^2+1[/tex]

The leading coefficient is positive.

Hence, graph is open upward.

The vertex of the function is at (3,1)

Answer:

I guess c I just plain out guessed

1. Let [tex]a,b,c[/tex] be the three points of intersection, i.e. the solutions to [tex]f(x)=g(x)[/tex]. They are approximately

[tex]a\approx-3.638[/tex]

[tex]b\approx-1.862[/tex]

[tex]c\approx0.889[/tex]

Then the area [tex]R+S[/tex] is

[tex]\displaystyle\int_a^c|f(x)-g(x)|\,\mathrm dx=\int_a^b(g(x)-f(x))\,\mathrm dx+\int_b^c(f(x)-g(x))\,\mathrm dx[/tex]

since over the interval [tex][a,b][/tex] we have [tex]g(x)\ge f(x)[/tex], and over the interval [tex][b,c][/tex] we have [tex]g(x)\le f(x)[/tex].

[tex]\displaystyle\int_a^b\left(\dfrac{x+1}3-\cos x\right)\,\mathrm dx+\int_b^c\left(\cos x-\dfrac{x+1}3\right)\,\mathrm dx\approx\boxed{1.662}[/tex]

2. Using the washer method, we generate washers with inner radius [tex]r_{\rm in}(x)=2-\max\{f(x),g(x)\}[/tex] and outer radius [tex]r_{\rm out}(x)=2-\min\{f(x),g(x)\}[/tex]. Each washer has volume [tex]\pi({r_{\rm out}(x)}^2-{r_{\rm in}(x)}^2)[/tex], so that the volume is given by the integral

[tex]\displaystyle\pi\int_a^b\left((2-\cos x)^2-\left(2-\frac{x+1}3\right)^2\right)\,\mathrm dx+\pi\int_b^c\left(\left(2-\frac{x+1}3\right)^2-(2-\cos x)^2\right)\,\mathrm dx\approx\boxed{18.900}[/tex]

3. Each semicircular cross section has diameter [tex]g(x)-f(x)[/tex]. The area of a semicircle with diameter [tex]d[/tex] is [tex]\dfrac{\pi d^2}8[/tex], so the volume is

[tex]\displaystyle\frac\pi8\int_a^b\left(\frac{x+1}3-\cos x\right)^2\,\mathrm dx\approx\boxed{0.043}[/tex]

4. [tex]f(x)=\cos x[/tex] is continuous and differentiable everywhere, so the the mean value theorem applies. We have

[tex]f'(x)=-\sin x[/tex]

and by the MVT there is at least one [tex]c\in(0,\pi)[/tex] such that

[tex]-\sin c=\dfrac{\cos\pi-\cos0}{\pi-0}[/tex]

[tex]\implies\sin c=\dfrac2\pi[/tex]

[tex]\implies c=\sin^{-1}\dfrac2\pi+2n\pi[/tex]

for integers [tex]n[/tex], but only one solution falls in the interval [tex][0,\pi][/tex] when [tex]n=0[/tex], giving [tex]c=\sin^{-1}\dfrac2\pi\approx\boxed{0.690}[/tex]

5. Take the derivative of the velocity function:

[tex]v'(t)=2t-9[/tex]

We have [tex]v'(t)=0[/tex] when [tex]t=\dfrac92=4.5[/tex]. For [tex]0\le t<4.5[/tex], we see that [tex]v'(t)<0[/tex], while for [tex]4.5<t\le8[/tex], we see that [tex]v'(t)>0[/tex]. So the particle is speeding up on the interval [tex]\boxed{\dfrac92<t\le8}[/tex] and slowing down on the interval [tex]\boxed{0\le t<\dfrac92}[/tex].

Answer:

9 + 15 = 3(3 + 5)

Step-by-step explanation:

The greatest common factor of 9 and 15 is 3.

Factor 3 out of both 9 and 15.

9 + 15 = 3(3 + 5)

Answer:

[tex]\dfrac{\sqrt[12]{55296}}{2}[/tex]

Step-by-step explanation:

Rationalize the denominator, then use a common root for the numerator.

[tex]\dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}=\dfrac{(2\cdot 3)^{\frac{1}{4}}}{2^{\frac{1}{3}}}\\\\=\dfrac{(2\cdot 3)^{\frac{1}{4}}}{2^{\frac{1}{3}}}\cdot\dfrac{2^{\frac{2}{3}}}{2^{\frac{2}{3}}}=\dfrac{2^{\frac{1}{4}+\frac{2}{3}}3^{\frac{1}{4}}}{2}\\\\=\dfrac{2^{\frac{11}{12}}3^{\frac{3}{12}}}{2}=\dfrac{\sqrt[12]{2^{11}3^{3}}}{2}\\\\=\dfrac{\sqrt[12]{55296}}{2}[/tex]

Answer:

1) given

3)being alternate angleS

5)ASA condition

6)corresponding sides of congruent triangle are equal

7)Pt=Rt and ST =QT

Answer:

Step-by-step explanation:

By definition, Volume of Sphere = [tex]\frac{4}{3}[/tex]πr³

If r = 4 in,

then Volume = [tex]\frac{4}{3}[/tex]π(4)³ = 268.08 in³

Answer:

267.95

Step-by-step explanation:

4/3 * pi * 4^3

4/3 * pi *64

256/3* pi = 267.95

Answer:

A) It takes Brian longer to bike home because his work is farther away.

Step-by-step explanation:

Out of the four statements, A makes the most sense. B and C are implausible based on the given information. D makes no sense seeing that it isn't given that they work in/at the same place, making it something that can't be proven.

The tangent half angle formula, one of several, is

[tex]\tan \dfrac a 2 = \dfrac{1 - \cos a}{\sin a}[/tex]

We have θ is opposite 4 in the 3/4/5 right triangle so

[tex]\cos \theta = \dfrac{3}{5}[/tex]

[tex]\sin \theta = \dfrac{4}{5}[/tex]

[tex]\tan \dfrac{\theta}{2} = \dfrac{1 - 3/5}{4/5} = \dfrac{5-3}{4}=\dfrac{1}{2}[/tex]

Answer: 1/2

This is actually pretty deep.  It says half the big acute angle in the 3/4/5 triangle is the small diagonal angle of the 1x2 rectangle.   Similarly, the small acute angle in 3/4/5 triangle is twice the small diagonal angle of the 1x3 rectangle.

To find the value of tan(1/2)θ, we calculate θ using the fact that tan(θ) = opposite/adjacent = 4/3, then apply the half-angle formula from trigonometry. We cannot complete the calculation as we don't have the exact cosine value of θ.

The question asks to find the value of tan(1/2)θ where θ is an angle in standard position, and its terminal side passes through the point (3, 4). In this case, first, we need to find the value of θ. This can be found using the formula tan(θ)=opposite/adjacent. Given the point (3, 4), let's consider the coordinates as (x,y). Here, 3 is the x-coordinate, which acts as the adjacent side, and 4 is the y-coordinate, which acts as the opposite side. Therefore, θ=tan^-1(4/3).

To find the value of tan(1/2)θ, we can use the half-angle formula from trigonometry: tan(1/2)θ = √((1-cos(θ))/(1+cos(θ)))

However, this question does not provide enough information to determine which option is the solution, as the cosine of θ is needed for completing the calculation.

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Answer:

x-2y = -12

Step-by-step explanation:

Standard form of a line is in the form Ax + By = C   where A is a positive integer

y − 3 = 1/2(x + 6)

Multiply each side by 2 to eliminate the fractions

2(y-3)= 1/2*2 (x+6)

Distribute

2y -6 = x+6

Subtract x from each side

-x +2y -6 = x-x +6

-x+2y -6 = 6

Add 6 to each side

-x+ 2y -6+6 = 6+6

-x +2y = 12

Multiply each side by -1 to make A a positive integer

x-2y = -12

Answer:

[tex]900\ cm^2[/tex]

Step-by-step explanation:

We can notice that the the prism provided is a rectangular prism.

By definition, The lateral  area of a rectangular prism can be calculated by multiplying the  perimeter of its base by its height.

The height is:

[tex]height=15\ cm[/tex]

Then, the perimeter of the base is:

[tex]Perimeter=17\ cm+17\ cm+13\ cm+13\ cm=60\ cm[/tex]

Then the lateral area is:

[tex]LA=60\ cm*15\ cm\\\\LA=900\ cm^2[/tex]

Probability of  randomly picking a yellow marble is [tex]\frac{2}{9}[/tex].

Probability of not picking a yellow marble is [tex]\frac{7}{9}[/tex].

Probability denotes the possibility of the outcome of any random event. The meaning of this term is to check the extent to which any event is likely to happen.

According to the question

A bag contains 4 red marbles, 3 green marbles, and 2 yellow marbles.

Probability of  randomly picking a yellow marble is

Number of favorable outcomes = 2

Total number of favorable outcomes = 4 + 3 + 2 = 9

Probability of  randomly picking a yellow marble is [tex]\frac{2}{9}[/tex].

Probability of not picking a yellow marble

= 1 - Probability of  randomly picking a yellow marble

= 1 - [tex]\frac{2}{9}[/tex]

= [tex]\frac{9-2}{9}[/tex]

= [tex]\frac{7}{9}[/tex]

Probability of not picking a yellow marble is [tex]\frac{7}{9}[/tex].

Hence,

Probability of  randomly picking a yellow marble is [tex]\frac{2}{9}[/tex].

Probability of not picking a yellow marble is [tex]\frac{7}{9}[/tex].

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The probability of not picking a yellow marble from a bag with 9 marbles total, where only 2 are yellow, is 7/9 or approximately 77.78%.

The question is related to calculating the probability of an event not occurring—in this case, not picking a yellow marble from a bag that contains different colored marbles. The total number of marbles is 4 red marbles + 3 green marbles + 2 yellow marbles = 9 marbles. To find the probability of not picking a yellow marble, we consider the total marbles that are not yellow, which are 4 red + 3 green = 7 marbles. The probability is then the number of non-yellow marbles divided by the total number of marbles, so it's 7/9. To calculate this, we divide the 7 non-yellow marbles by the total of 9 marbles, resulting in a probability of 7/9, or about 77.78%.

Answer:

  see below

Step-by-step explanation:

The image is reflected across the origin and enlarged by a factor of 3.

___

The first choice shows some funny combination of translation, rotation, and dilation. The last choice has point N invariant, which means that is the center of the (horizontal only) dilation. Neither of these matches the problem description.

Answer:

[tex]g(x)= \frac{1}{9} \times x^2[/tex]

Step-by-step explanation:

Here we can see that the parent function is [tex]f(x)=x^2[/tex] and the translated function is g(x). f(x) is a parabola.

Rule says that any factor if multiplied by f(x) is going to contract the graph towards the y axis and vice versa.

Similarly any factor if  f(x) is divided by some factor it is going to be stretch the graph away from the y axis and vice versa.

Here we can see that the translated graph g(x) is stretched away from the y axis with reference to the parent function f(x). Hence as per he rule discussed above, we get a preliminary information that the parent function f(x) is being divided by some factor.

now we are given that

[tex]f(x) = x^2[/tex]

[tex]f(3) = 3^2 = 9[/tex]

Where as

[tex]g(3) = 1[/tex]  {as given in the graph}

Hence

at x=3 , f(x) = 9 and g(x) = 1 , and also we have discussed above that f(x) is divided by some factor. Hence [tex]g(x)= \frac{1}{9}f(x)[/tex]

[tex]g(x)= \frac{1}{9} \times x^2[/tex]

Answer:

889

Step-by-step explanation:

The required proof that the measure of the angle A is  60° is below in the solution part.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.

By the triangle sum theorem, the sum of angles in a triangle is equal to 180°.

Therefore,  m∠A + m∠B + m∠C = 180  using the Substitution property (3x)° + 90° + (x+10)° = 180°

To solve for x, first combine like terms to get 4x + 100 = 180,

using the subtraction property of equality, 4x = 80

using the Division property of equality,  x = 20.

To find the measure of the angle A, use the substitution property to get m∠A = 3(20)°.

Finally, simplify the expression gets m∠A = 60°

Learn more about the triangles here:

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The missing figure has been attached below.

bearing in mind that the variable with the positive sign is the "y", meaning the hyperbola  is opening vertically, and thus its vertices/foci will be along the center's y-coordinate.

[tex]\bf \textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf 4y^2-25x^2=100\implies \cfrac{4y^2-25x^2}{100}=1\implies \cfrac{4y^2}{100}-\cfrac{25x^2}{100}=1 \\\\\\ \cfrac{y^2}{25}-\cfrac{x^2}{4}=1\implies \cfrac{(y-0)^2}{5^2}-\cfrac{(x-0)^2}{2^2}=1\qquad \begin{cases} h=0\\ k=0\\ a=5\\ b=2 \end{cases} \\\\\\ \stackrel{\textit{vertices}}{(0, 0\pm 5)}\implies \begin{cases} (0,5)\\ (0,-5) \end{cases}[/tex]

This question is not complete because his height and age was not indicated in the above question.

Complete Question:

Rick is a healthy 19-year-old college student who is 70 inches tall and weighs 205 pounds. He has decided to "get a six-pack" over the summer with a diet and exercise program. As part of his new plan, he has stopped drinking soda and is eating more salads in addition to his usual diet. Besides of these changes, he is unclear on how to proceed to reach his fitness goal. Rick's mother wants to make sure his approach will not interfere with his normal growth and development, and has asked him to seek reliable information to help him make a reasonable plan.

If Rick wishes to reduce his BMI to 27, he needs to eat fewer kcalories than he expends. For an adolescent who carries excess fat, the recommended maximal weight loss is one pound per week. Since there are 3500 kcalories in a pound of body fat, a deficit of 3500 kcalories for the week or 500 kcalories per day would be required. Calculate the maximum number of kcalories Rick can consume per day to achieve a weight loss of one pound per week. Assume that his weight is 205 pounds and that his physical activity factor is "low active."

Answer:

2696 kilocalories

Step-by-step explanation:

STEP 1

First we need to calculate Rick's Basal Metabolic Rate( BMR)

Weight in pounds = 205 pounds

Age = 19 years

Height in inches = 70 inches

The formula for calculating Basal Metabolic Rate for men =

BMR = 66.47 + ( 6.24 × weight in pounds ) + ( 12.7 × height in inches ) − ( 6.755 × age in years )

BMR = 66.47 + ( 6.24 × 205 ) + ( 12.7 × 70 ) − ( 6.755 × 19)

= 2247

STEP 2:

The next step is to calculate the maximum amount kilocalories per day Rick should consume

Formula is given as :

For a person with physical activity factor of a ' low Active'

Maximum amount of kilocalories to consume per day = Basal Metabolic rate × 1.2

= 2247 × 1.2

= 2696 Kilocalories (kcalories) per day

Answer:

Measure 8 is 135°

Step-by-step explanation:

Measure 1 and Measure 8 are alternate exterior angles.

Answer:

B) 135°

Step-by-step explanation:

<1 = <4 vertical angles

<4 = <5 alternate interior angles

<5 = <8 vertical angles

Therefore <1 = <8

Since <1 = 135, we know <8 = 135

Answer:

2) 64°

Step-by-step explanation:

If A and B are complementary, that means that they add up to 90.  Therefore, A + 26 = 90 and A = 64.

Answer:

2.) 64 degrees

Step-by-step explanation: 90-26 = 64

Reminder: Complementary are 90 degrees angle

Supplementary are 180 degrees angle

Answer:

B

Step-by-step explanation:

Conditional probability is:

P(A given B) = P(A and B) / P(B)

Here, P(A and B) = 0.052 and P(B) = 0.17:

P(A given B) = 0.052 / 0.17

P(A given B) = 0.306

D. [tex]x[/tex] represents the number of level 1 tickets; [tex]y[/tex] represents the number of level 2 tickets

The costs of the tickets are represented as constants ([tex]50[/tex] and [tex]150[/tex]), and so they are not variables.

We know [tex]x[/tex] is level 1 tickets and [tex]y[/tex] is level 2 tickets because the price of a level 1 ticket is $50 and the second equation contains [tex]50x[/tex].  Similarly, the cost of a level 2 ticket is $150 and the equation contains [tex]150y[/tex].

Answer:

(D) X represents the number of level 1 tickets.

Answer:

0 is the answer

Step-by-step explanation:

Answer:

  $32,500

Step-by-step explanation:

Sarah's gross income is the income amount before taxes and other deductions. It is $32,500.

Answer:

[tex]\large\boxed{a.\ 23}[/tex]

Step-by-step explanation:

[tex]\dfrac{y-8}{5}=3\qquad\text{multiply both sides by 5}\\\\5\!\!\!\!\diagup^1\cdot\dfrac{y-8}{5\!\!\!\!\diagup_1}=5\cdot3\\\\y-8=15\qquad\text{add 8 to both sides}\\\\y-8+8=15+8\\\\y=23[/tex]

Answer:

-7x(x + 4)

Step-by-step explanation:

Not sure exactly what you're doing with this, but I know you're not solving it for x because there's no " = " there so I am assuming you're simplifying it as much as possible.  I'm going with that.

First thing is to distribute through the parenthesis by multiplying 4x by 3x and then 4x by -7 to get:

[tex]12x^2-28x-19x^2[/tex]

Now combine like terms to get

[tex]-7x^2-28x[/tex]

The last thing you could do now is pull out what's common between each of those terms which is -7x.  When you do that, you're left with

-7x(x + 4)

Answer:

  C)  a positive correlation

Step-by-step explanation:

More people ⇒ Longer time is a positive correlation between those variables. However, longer time is not the desired outcome.

Rather, shorter time is the desired outcome. The correlation between more people and shorter time is negative. In order to compute that correlation numerically, one would have to define a function that would give a numerical value for "shorter time" that would model the goodness of outcome as time gets shorter.

Answer: The temperature is -1 degrees

Step-by-step explanation: Trust me!

Answer:

  (a) see below for a graph

  (b) the vertex is (months, sales) = (12, 15); sales is $15M at 12 months

  (c) .375 million per month increasing and decreasing

Step-by-step explanation:

(a) You can read the vertex from the equation of the function. The equation is of an absolute value function translated so its vertex is at (12, 15), and vertically scaled by a factor of -0.375. The negative scale factor means the graph will open downward.

__

(b) Since graph is of sales in millions versus months, the meaning of the vertex at (12, 15) is that sales is $15 millions 12 months after the phone comes on the market.

__

(c) If the function were written as a piecewise function, the coefficient of x would be +0.375 for x < 12 and -0.375 for x > 12. The "rate of change" is 0.375 millions per month both going up and coming down.

_____

Translation of a point on the graph of f(x) by "h" horizontal units and "k" vertical units changes the function to f(x -h) +k. That is, if you can identify the function f(x), you can read the translation from the expression f(x -h) +k. For the absolute value function |x|, the vertex is normally (0, 0). Translating it to (h, k) makes the expression be |x -h|+k, the form you see in this problem. It's not a mystery. It's just pattern matching.