Figure A is a scale image of Figure B. What is the value of x?

By "slope" I assume you mean slope of the tangent line to the parabola.

For any given value of x, the slope of the tangent to the parabola is equal to the derivative of y :

[tex]y=ax^2+bx+c\implies y'=2ax+b[/tex]

The slope at x = 1 is 5:

[tex]2a+b=5[/tex]

The slope at x = -1 is -11:

[tex]-2a+b=-11[/tex]

We can already solve for a and b :

[tex]\begin{cases}2a+b=5\\-2a+b=-11\end{cases}\implies 2b=-6\implies b=-3[/tex]

[tex]2a-3=5\implies 2a=8\implies a=4[/tex]

Finally, the parabola passes through the point (2, 18); that is, the quadratic takes on a value of 18 when x = 2:

[tex]4a+2b+c=18\implies2(2a+b)+c=10+c=18\implies c=8[/tex]

So the parabola has equation

[tex]\boxed{y=4x^2-3x+8}[/tex]

Using function concepts, it is found that the parabola is: [tex]y = 4x^2 - 3x + 14[/tex]

----------------------------

The parabola is given by:

[tex]y = ax^2 + bx + c[/tex]

----------------------------

Slope 5 at x = 1 means that [tex]y^{\prime}(1) = 5[/tex], thus:

[tex]y^{\prime}(x) = 2ax + b[/tex]

[tex]y^{\prime}(1) = 2a + b[/tex]

[tex]2a + b = 5[/tex]

----------------------------

Slope -11 at x = -1 means that [tex]y^{\prime}(-1) = -11[/tex], thus:

[tex]-2a + b = -11[/tex]

Adding the two equations:

[tex]2a - 2a + b + b = 5 - 11[/tex]

[tex]2b = -6[/tex]

[tex]b = -\frac{6}{2}[/tex]

[tex]b = -3[/tex]

And

[tex]2a - 3 = 5[/tex]

[tex]2a = 8[/tex]

[tex]a = \frac{8}{2}[/tex]

[tex]a = 4[/tex]

Thus, the parabola is:

[tex]y = 4x^2 - 3x + c[/tex]

----------------------------

It passes through the point (2, 18), which meas that when [tex]x = 2, y = 18[/tex], and we use it to find c.

[tex]y = 4x^2 - 3x + c[/tex]

[tex]18 = 4(2)^2 - 3(4) + c[/tex]

[tex]c + 4 = 18[/tex]

[tex]c = 14[/tex]

Thus:

[tex]y = 4x^2 - 3x + 14[/tex]

A similar problem is given at https://brainly.com/question/22426360

Answer:

B

Step-by-step explanation:

the slope of parallel lines are equal

The closest we get is the addition property, which was used in step 2. This is a fairly similar idea because subtraction is effectively adding on a negative number. Example: 5-7 = 5+(-7). Though because your teacher is making a distinction between addition property of equality and subtraction property of equality, it's safe to say that the subtraction property is not used.

Answer:

  A(8, 10)

Step-by-step explanation:

Vertex A is on the vertical line x=8, so we can find the y-coordinate by solving the boundary equation ...

  5x +8y = 120

  5(8) +8y = 120 . . . use the x-value of the vertical line

  5 + y = 15 . . . . . . . divide by 8

  y = 10 . . . . . . . . . . subtract 5

Point A is (8, 10).

Answer:

[tex]log_35=x[/tex]

Step-by-step explanation:

I am going to assume you meant [tex]5=3^x[/tex]

When converting exponential equations into logarithmic form, remember this: [tex]y = log_bx[/tex] is equivalent to [tex]x = b^y[/tex]

Answer:

Step-by-step explanation:

Mean & median of 6 packages:

15, 17, 19, 31, 33 , 35

Median =  [tex]\frac{19+31}{2}[/tex]

            = [tex]\frac{50}{2}[/tex]

           = 25

[tex]Mean = \frac{15+17+19+31+33+35}{6}\\\\=\frac{150}{6}\\=25[/tex]

Mean & median of 7 packages:

15,17,19,31,33,35,39

Median = 31

[tex]Mean=\frac{19+15+35+17+33+31+39}{7}\\\\=\frac{189}{7}\\\\=27[/tex]

After including 39 ounce package, Median will increase more

Answer:

False

Step-by-step explanation:

No esta verdad.

8716/4 = 2179 (divisible por 4)

Answer:

96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

A reminder is that the standard deviation is the square root of the variance.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

[tex]\mu = 3639, \sigma = \sqrt{145161} = 381, n = 41, s = \frac{381}{\sqrt{41}} = 59.5[/tex]

Probability that the mean of the sample would differ from the population mean by less than 126 miles

This is the pvalue of Z when X = 3639 + 126 = 3765 subtracted by the pvalue of Z when X = 3639 - 126 = 3513. So

X = 3765

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

By the Central Limit Theorem

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

[tex]Z = \frac{3765 - 3639}{59.5}[/tex]

[tex]Z = 2.12[/tex]

[tex]Z = 2.12[/tex] has a pvalue of 0.983

X = 3513

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

[tex]Z = \frac{3513 - 3639}{59.5}[/tex]

[tex]Z = -2.12[/tex]

[tex]Z = -2.12[/tex] has a pvalue of 0.017

0.983 - 0.017 = 0.966

96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles

Answer:

No solution.

Step-by-step explanation:

Because the equations are combined but the final answers are not equal, the equations have no solution. This is because "no matter what value is plugged in for the variable, you will ALWAYS get a contradiction".

Hope this helps!

Answer:

Sister

Step-by-step explanation:

Let the sister’s age be x.

Let the brother’s age be y.

2 + x = 2x - 2

3 + y = 3y - 3

Solve the first equation.

x - 2x = - 2 - 2

-x = -4

x = 4

Solve the second equation.

y - 3y = -3 - 3

-2y = -6

y = 3

The sister is 4 years old.

The brother is 3 years old.

The sister is older than the brother.

Answer:

x = 64.1 degrees

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj/ hypotenuse

cos x = 7/16

Take the inverse cos of each side

cos ^-1 cos x = cos ^-1 ( 7/16)

x = cos ^-1 ( 7/16)

x =64.05552023

To the nearest tenth

x = 64.1 degrees

Answer: 49/200, numerador= 49

Step-by-step explanation:

Answer:

9 hours, 20 minutes

Step-by-step explanation:

When two ferries work together, they transport a day's cargo in 7 hours

The speed proportion or ratio of larger ferry to smaller ferry is given as 3 : 1

The sum of the ratio = 4 (3 + 1)

This means that it will take the smaller ferry = 7 x 4 hours to work alone = 28 hours, since the larger ferry is faster by 3.

Therefore, when larger ferry works alone, it will take it (7 x 4)/3 = 9.33 hours.

9.33 hours = 9 hours, 20 minutes.

Answer:

first one 5/[tex]\sqrt{39}[/tex]

Step-by-step explanation:

We must calculate cosθ first :

cos²θ+sin²θ =1⇒ cos²θ= 1-sin²θ=1-(25/8)= 39/64⇒cosθ= √39/8

Answer:

The farmer should expect to LOSE 10 pounds of soybeans per acre per year

Step-by-step explanation:

f(x)=-x^2 + 20x + 100

just find how many soybeans his land will yield (per acre) after 10 and 20 years:

After 10: 200 pounds of soybeans/acre

After 20: 100 pounds of soybeans/acre

Because 10 years have passed and they lost 100 pounds of soybean production per acre, the farmer should expect to lose 10 pounds of soybeans per acre per year (-10 pounds of soybeans per acre/year)

Answer:

Step-by-step explanation:

confidence level for the proportion of all American youngsters who are seriously overweight is (0.137, 0.163)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue

Read

Answer:

b) 10

Step-by-step explanation:

In this case the frequency would be equal to the quotient between the sample that creative artists tell us (that is to say 120 people) and the amount of sastrological signs that there are (that is to say 12 signs), therefore it would be:

F = 120/12 = 10

Which means that the expected frequency for each category equal to 10.

So the answer is b) 10

Answer:

a) 4 cm

b) 5 cm

c) 10 cm

Step-by-step explanation:

The side lengths of the reflected square are equal to the original, and the distance from the axis(2) also remains the same.  From there, it is just addition.

Hope it helps <3

Answer:

A) 4

B) 5

C) 10

Step-by-step explanation:

edge2020

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Logarithms,

so we get as,

t = 2

Answer:

f(n + 1) = f(n) + 0.75

Step-by-step explanation:

Answer:

(C) 25,35 and 175,35

Answer:

  6 mL

Step-by-step explanation:

It is a matter of units conversion.

  volume = (mass) × (dose/mass) ÷ (dose/volume)

  (132 lb)/(2.2 kg/lb) × (0.05 mg/kg) / (0.05 mg/0.1 mL) = 6 mL

1). Draw a perpendicular from point A to side BC. Let AD = h

2). sin A = h/c and sin C = h/a

3). h = c Sin A, h = a sin C

4). c Sin A =a sin C

5). Divide both side by Sin A * Sin C

6). c Sin A/(Sin A * Sin C) =a sin C/(Sin A * Sin C)

7). c/sin C = a/Sin A

8). Similarly prove that,  c/sin C = b/Sin B

9).  c/sin C =  b/Sin B = a/Sin A

correct on plato

Answer:

The answer is option 1.

Step-by-step explanation:

Given that the volume of pyramid formula is:

[tex]v = \frac{1}{3} \times base \: area \times height[/tex]

The base area for this pyramid:

[tex]base \: area = area \: of \: rectangle[/tex]

[tex]base \: area = 10 \times 6[/tex]

Then you have to substitute the following values into the formula:

[tex]let \: base \: area = 10 \times 6 \\ let \: height = 12[/tex]

[tex]v = \frac{1}{3} \times 10 \times 6 \times 12[/tex]

Answer:

A. V = 1/3 (10)(6)(12)

Step-by-step explanation:

Just took the test and got it right

Answer:

[tex]F=\frac{s^2_2}{s^2_1}=\frac{5.5}{2.5}=2.2[/tex]

Now we can calculate the p value but first we need to calculate the degrees of freedom for the statistic. For the numerator we have [tex]n_2 -1 =16-1=15[/tex] and for the denominator we have [tex]n_1 -1 =16-1=15[/tex] and the F statistic have 15 degrees of freedom for the numerator and 15 for the denominator. And the P value is given by:

[tex]p_v =2*P(F_{15,15}>2.2)=0.138[/tex]

For this case the p value is highert than the significance level so we haev enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviations are not significantly different

Step-by-step explanation:

Information given

[tex]n_1 = 16 [/tex] represent the sampe size 1

[tex]n_2 =16[/tex] represent the sample 2

[tex]s^2_1 = 2.5[/tex] represent the sample deviation for 1

[tex]s^2_2 = 5.5[/tex] represent the sample variance for 2

[tex]\alpha=0.10[/tex] represent the significance level provided

The statistic is given by:

[tex]F=\frac{s^2_2}{s^2_1}[/tex]

Hypothesis to test

We want to test if the variations in terms of the variance are equal, so the system of hypothesis are:

H0: [tex] \sigma^2_1 = \sigma^2_2[/tex]

H1: [tex] \sigma^2_1 \neq \sigma^2_2[/tex]

The statistic is given by:

[tex]F=\frac{s^2_2}{s^2_1}=\frac{5.5}{2.5}=2.2[/tex]

Now we can calculate the p value but first we need to calculate the degrees of freedom for the statistic. For the numerator we have [tex]n_2 -1 =16-1=15[/tex] and for the denominator we have [tex]n_1 -1 =16-1=15[/tex] and the F statistic have 15 degrees of freedom for the numerator and 15 for the denominator. And the P value is given by:

[tex]p_v =2*P(F_{15,15}>2.2)=0.138[/tex]

For this case the p value is highert than the significance level so we haev enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviations are not significantly different

Answer:

Number of unique treatment combinations  = 8

Step-by-step explanation:

Given:

Number of brands = 3

Number of power settings = 2

Number of microwave times = 3

Find:

Number of unique treatment combinations.

Computation:

Number of unique treatment combinations = Number of brands + Number of power settings + Number of microwave times

Number of unique treatment combinations = 3 + 2 + 3

Number of unique treatment combinations = 8

Answer:

5i² - 25ij +ji-5j²

Step-by-step explanation:

Use distributive property

Answer:

Step-by-step explanation:

A = (5i+j)

B = (i-5j)

A × B is

( 5i + j) ( i - 5j)

Expand

We have

5i² - 25ij + ij - 5j²

The final answer is

5i² - 24ij - 5j²

Hope this helps you.

Answer:

174 square cm

Step-by-step explanation:

2(9×4) + 2(6×4)+ 9×6

2(36) + 2(24) + 54

72 + 48 + 54

120 + 54

174

Step-by-step explanation:

If the scale factor of two similar solids is a: b:. then

(1) the ratio of corresponding perimeters is a:b

(2) the ratio of the base areas, of the lateral areas, and of the total areas is [tex]a^2: b^2[/tex]

(3) the ratio of the volumes is [tex]a^3:b^3[/tex]