Which of the following parabolas opens down?

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

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.

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:

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:

  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:

  $32,500

Step-by-step explanation:

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

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:

I guess c I just plain out guessed

Answer:

true

The wording does not quite mean anything,

but what I think was meant to ask is

"if we use some parts of two triangles to prove they are congruent,

can we then use that to prove that

a pair of corresponding parts not used before are congruent?"

The answer is

Yes, of course,

Corresponding Parts of Congruent Triangles are Congruent,

which teachers usually abbreviate as CPCTC.

For example, if we find that

side AB is congruent with side DE,

side BC is congruent with side EF, and

angle ABC is congruent with angle DEF,

we can prove that triangles ABC and DEF are congruent

by Side-Angle-Side (SAS) congruence.

We then, by CPCTC, can conclude that other pairs of corresponding parts are congruent:

side AB is congruent with side DE,

angle BCA is congruent with angle EFD, and

angle CAB is congruent with angle FDE.

It was possible (by CPCTC) to prove those last 3 congruence statements,

after proving the triangles congruent.

The expected answer is FALSE.

Step-by-step explanation:

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:

Third choice

Step-by-step explanation:

The standard form of a circle is

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

where h and k are coordinates of the center and r is the radius squared.  We have h = 2, k = 7, and r = 4 (we will have to square it to fit it into the equation properly).  Filling in accordingly:

[tex](x-2)^2+(y-7)^2=16[/tex]

The third choice is the one you want.

Answer:

0 is the answer

Step-by-step explanation:

Answer:

  t ≈ 1.118 . . . seconds

Step-by-step explanation:

Set h=0 and solve for t.

  0 = -16t^2 +20

  0 = t^2 -20/16 . . . . . . . . . . . . . . . divide by the coefficient of t^2

  t = √(5/4) = (1/2)√5 ≈ 1.118 . . . . . add 5/4 and take the square root

The pinecone hits the ground about 1.12 seconds after it drops.

For the mathematical model h = -16t² + 20, corresponding to a pinecone dropping from a tree, the pinecone would hit the ground after approximately 1.118 seconds.

In order to know when a pinecone hits the ground, we would need to solve the equation provided for the variable t when h equals zero, as that would represent the pinecone being on the ground. The equation given is quadratic in nature: h = -16t² + 20. In this equation, h represents the height of the pinecone, and t represents time in seconds.

To find when the pinecone hits the ground (h=0), we set h to zero and solve for t:

0 = -16t² + 20
Therefore, 16t² = 20
So, t² = 20/16 = 1.25
Then, t = sqrt(1.25) = 1.118 (remember we exclude negative root as it doesn't go with time).

The pinecone hits the ground approximately at t = 1.118 seconds.

https://brainly.com/question/35505962

#SPJ11

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

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.

https://brainly.com/question/34719941

#SPJ2

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].

Find out more information about probability here

https://brainly.com/question/11234923

#SPJ2

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:

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]\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: The temperature is -1 degrees

Step-by-step explanation: Trust me!

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

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:

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:

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:

https://brainly.com/question/17997149

#SPJ7

The missing figure has been attached below.

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]

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.

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)

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.

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]

The statement that explains why the squares are similar is

Option C. Translations and dilations preserve betweenness of points; therefore, the corresponding sides of squares T and T″ are proportional.

There are several types of transformations:

Let us now tackle the problem!

[tex]\texttt{ }[/tex]

This problem is about Translation and Dilation.

Properties of Translation of the images compared to pre-images:

[tex]\texttt{ }[/tex]

Properties of Dilation of the images compared to pre-images:

[tex]\texttt{ }[/tex]

From the information above, we can conclude that:

Option A is not true because Dilations do not preserve side length.

Option B is not true because Dilations do not preserve orientation.

Option C is true because Translations and Dilations preserve betweenness of points.

Option D is not true. Although Translation and Dilations preserve collinearity but it cannot be related to the corresponding angles are congruent.

[tex]\texttt{ }[/tex]

Grade: High School

Subject: Mathematics

Chapter: Transformation

Keywords: Function , Trigonometric , Linear , Quadratic , Translation , Reflection , Rotation , Dilation , Graph , Vertex , Vertices , Triangle