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Answer:

gradient = 9

Step-by-step explanation:

Note that [tex]\frac{dy}{dx}[/tex] is a measure of the gradient.

Differentiate y using the power rule

[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex]) = na[tex]x^{n-1}[/tex]

Given

y = x² + 5x - 3, then

[tex]\frac{dy}{dx}[/tex] = 2x + 5

x = 2 : [tex]\frac{dy}{dx}[/tex] = 2(2) + 5 = 4 + 5 = 9 ← gradient

Answer & Step-by-step explanation:

3x²

This term represents a monomial expression. Mono- means one. This term is by itself. It has no other term added or subtracted to it.

The coefficient of this term is 3 because it is the number that the variable is connected to.

There are no constants because this is a monomial expression.

Answer:

(a) [tex]x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}[/tex]

(b) [tex]x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}[/tex]

Step-by-step explanation:

It is given that [tex]0\leq x\leq 2\pi[/tex].

(a)

[tex]\sqrt{2}\sin 2x=1[/tex]

[tex]\sin 2x=\dfrac{1}{\sqrt{2}}[/tex]

[tex]\sin 2x=\dfrac{\pi}{4}[/tex]

[tex]2x=\dfrac{\pi}{4},\dfrac{3\pi}{4},\dfrac{9\pi}{4},\dfrac{11\pi}{4}[/tex]     [tex][\because \sin x=\sin y\Rightarrow x=n\pi+(-1)^ny][/tex]

[tex]x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}[/tex]

(b)

[tex]\csc^2 x-\csc x-2=0[/tex]

[tex]\csc^2 x-2\csc x+\csc x-2=0[/tex]

[tex]\csc x(\csc x-2)+1(\csc x-2)=0[/tex]

[tex](\csc x+1)(\csc x-2)=0[/tex]

[tex]\csc x=-1\text{ or }\csc x=2[/tex]

[tex]\sin x=-1\text{ or }\sin x=\dfrac{1}{2}[/tex]         [tex][\because \sin x=\dfrac{1}{\csc x}][/tex]

[tex]x=\dfrac{3\pi}{2}\text{ or }x=\dfrac{\pi}{6},\dfrac{5\pi}{6}[/tex]

Therefore, [tex]x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}[/tex].

Answer:

C and E

Step-by-step explanation:

Midpoint, as the word suggests, means the point which lies in the middle of something. The statements that are correct are 1, 3, and 5.

Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.

The statements which are correct about the given figure are:

Hence, the statements that are correct are 1, 3, and 5.

Learn more about Midpoint:

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Answer:

Step-by-step explanation:

We khow that the radius of our circle is 6

Let A be the area of our cercle :

A= 6^2*Pi = 36 Pi = 113.09 sq.units

We khow that the mesure of our angle ABC is Pi over 2 wich is 90 degree

So this triangle ABC is a right one .

So I think that we must khow the area of this triangle to be able to khow the area of the sector .

We have a hint : ABC is 90 degree so it is the quarter of our cercle

We need to divide the area of the circle by 4

113.09 ÷4 = 28.27

Answer:

113

28

22

Step-by-step explanation:

Answer:

1, 4, 5, 7, 8

Step-by-step explanation:

once you plot the points you will see that these coordinates are inside the star

Answer:

he proportion of people over 55 who dream in black and white is greater than the proportion of those under.

The proportion of people over 55 who dream in black and white lies in the range (0.112, 0.226).

Step-by-step explanation:

In this case we need to determine if the proportion of people over 55 who dream in black and white is greater than the proportion of those under.

The hypothesis can be defined as follows:  

H₀: The proportion of people over 55 who dream in black and white is not greater than the proportion of those under, i.e. p₁ - p₂ ≤ 0.  

Hₐ: The proportion of people over 55 who dream in black and white is greater than the proportion of those under, i.e. p₁ - p₂ > 0.  

The information provided is:

n₁ = 290

n₂ = 288

X₁ = 68

X₂ = 19

Compute the sample proportions and total proportions as follows:

 [tex]\hat p_{1}=\frac{X_{1}}{n_{1}}=\frac{68}{290}=0.235\\\\\hat p_{2}=\frac{X_{2}}{n_{1}}=\frac{19}{288}=0.066\\\\\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{68+19}{290+288}=0.151[/tex]

Compute the test statistic value as follows:

 [tex]z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)[\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}[/tex]

    [tex]=\frac{0.235-0.066}{\sqrt{0.151(1-0.151)[\frac{1}{290}+\frac{1}{288}]}}\\\\=5.67[/tex]

The test statistic value is 5.67.

The decision rule is:

The null hypothesis will be rejected if the p-value of the test is less than the significance level.

Compute the p-value as follows:

 [tex]p-value=P(Z>5.67)\\=1-P(Z<5.67)\\=1-\approx1\\=0[/tex]

The p-value of the test is quite small.

The null hypothesis will be rejected at 5% significance level.

Thus, the proportion of people over 55 who dream in black and white is greater than the proportion of those under.

The significance level of the test is 5%.

Then the confidence level will be:

Confidence level = 100% - Significance level

                             = 100% - 5%

                             = 95%

Compute the 95% confidence interval for the difference between proportions as follows:

[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p{2})}{n_{2}}}[/tex]

The critical value of z for 95% confidence level is z = 1.96.

[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p{2})}{n_{2}}}[/tex]

      [tex]=(0.235-0.066)\pm1.96\cdot\sqrt{\frac{0.235(1-0.235)}{290}+\frac{0.066(1-0.066)}{288}}\\\\=0.169\pm 0.057\\\\=(0.112, 0.226)[/tex]

The null hypothesis would be rejected if the null value, i.e. (p₁ - p₂) ≤ 0 is not contained in the interval.

The 95% confidence interval consist of values greater than 0.

Thus, the null hypothesis will be rejected.

Concluding that the proportion of people over 55 who dream in black and white lies in the range (0.112, 0.226).

Answer:

35%

Step-by-step explanation:

He pays 525 out of 1500 dollars.

525/1500 = 7/20

= 0.35

Marlon pays in rent 35% of his earnings.

Answer:

2½ h  

Step-by-step explanation:

Assume the graph is like the one below.

The graph shows how Erin's distance varies with time.

To find out how long it takes Erin to cover 25 mi, find 25 mi on the vertical axis.

From there, draw a horizontal line until it hits the graph.

Then drop a vertical line to the horizontal axis.

It hits half-way between 2 and 3.

It takes Erin 2½ h to run 25 mi.

Answer:

2½ h

Step-by-step explanation:

Answer: PQT and TUV

Step-by-step explanation:

Answer: 9/15, 16/25, 3/4 and 5/6.

Step-by-step explanation:

From the question, we have been given four fractions which are 3/4, 5/6, 16/25 and 9/15. We are told to write them in order starting from the smallest. For this to be done, we will have to change the fractions to percentages. This will be:

3/4 = 3/4 × 100 = 75%

5/6 = 5/6 × 100 = 83.3%

16/25 = 16/25 × 100 = 64%

9/15 = 9/15 × 100 = 60%

From the above percentages, arranging the fractions from the smallest will be:

9/15, 16/25, 3/4 and 5/6.

Answer:

y = 2x + 7

Step-by-step explanation:

Step 1: Find slope

m = (9 - 3)/(1 + 2)

m = 2

y = 2x + b

Step 2: Find b

9 = 2(1) + b

9 = 2 + b

7 = b

Step 3: Rewrite equation

y = 2x + 7

Answer:

B) y - 9 = 2(x - 1)

Step-by-step explanation:

(-2, 3) ;(1,9)

[tex]Slope =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{9-3}{1-[-2]}\\\\=\frac{6}{1+2}\\\\=\frac{6}{3}\\\\=2[/tex]

(1, 9 ) ;  m = 2

Equation: [tex]y - y_{1}=m(x - x_{1})\\\\[/tex]

y - 9 = 2(x - 1)

y - 9 = 2x -2

      y = 2x - 2 + 9

      y = 2x + 7

Answer:

y = 4/3x + 5

Step-by-step explanation:

if the slope is -3/4 then the perpendicular slope is 4/3

y = mx + b

9 = 4/3(3) + b

9 = 4 + b

5 = b

y = 4/3x + 5

Answer:

Simply by using a protractor.

Step-by-step explanation:

Place the center of the protractor on the origin of the angle. The distance between the two lines is the angle in degrees. Read it on the protractor. You can also do basic arithmetics if other angles are given. For instance 180 degrees- 30 degrees = 150 degrees.

Hope it helped pls mark as brainliest.

Answer:

88

Step-by-step explanation:

First you must find the circumference of the entire circle and to do this you use 2πr. The radius in this case is PX=15. This means that the circumference is 30π. Now to find the arc length, we know that the measure of arc XY is 23 degrees, and since there are 360 total degrees in a circle, we must subtract 23 from 360 to get 337° as the measure of arc XQY. Now we have to find what portion of the circumference of the circle is in this arc, and to do this you divide the arc length (337°) by 360° and multiply by the circumference of the circle. Doing this would get you [tex]\frac{337}{360} *30\pi[/tex] which equals ~28. Finally, you have to multiply this by the value of pi and get approximately 88, which is your answer.

Answer:

5/2 or 2.5

Step-by-step explanation:

6/5=3/d

6*d=3*5

d=3*5/6

d= 5/2 or 2.5

Answer:

Solution,

[tex] \frac{6}{5} = \frac{3}{d} \\ or \: 6 \times d = 5 \times 3(cross \: multiplication) \\ or \: 6d = 15 \\ or \: d = \frac{15}{6} \\ d = 2.5[/tex]

hope this helps...

Good luck..

Answer:

Step-by-step explanation:

Exponential Growth:

1). The value of a home in a growing community every year.

2). The amount of money in a saving account that earns interest annually.

Exponential decay:

1). The monthly sale of albums of a band whose popularity is declining.

2). The amount of radioactive element remaining in a sample every decade.

3). The temperature of a hot cup of coffee left on the counter every minute.

Answer:

First find line DE using Pythagoras theorem

That's

DE² = 7² + 24²

DE = √ 49 + 576

DE = 25

The correct trigonometric ratio for triangle DEF is

Cos(E) = 24/25

Hope this helps

Answer:

Cos(E) = 24/25

Step-by-step explanation:

Answer:

The Area of the required figure is  [tex]315\:cm^2[/tex]

Step-by-step explanation:

[tex]Area = (21\times 7)+(14\times 7) + (7\times 10)\\\\=147+98+70\\\\=315[/tex]

Best Regards!

Step-by-step explanation:

No of people likes tea = 4000

No of people like coffee = 4500

Total = 8500

No of people don't like tea and coffee = 2500

No of people like tea and coffee = 8500 - 2500 = 6000

Answer:

500

Step-by-step explanation:

n(t)=4000

n(c)=4500

n(tea only )= 4000-x

n(coffee only )= 4500-x

n(coffee and tea )= x

note...using Venn diagram ..all together must add up to 9000

(4000-x)+(4500-x) +x = 9000

..............

...........collect like terms

9500-9000 = x

x = 500

Answer:

a(4,3).  b( 2,3). c(4,-1). d(-2,-1/2).  e(5/2, 0).

Step-by-step explanation:

Hello , I can help you with that

the mid point is given by

Let

Point 1

[tex](x_{1},y_{1})[/tex]

Point 2

[tex](x_{2},y_{2})[/tex]

the midpoint is(m)

[tex]m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )[/tex]

all you have to do is to put those values into the equation

Step 1

P1(3,4)  and P2(5,2)

[tex]m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )\\m=(\frac{3+5}{2},\frac{4+2}{2} )\\m=(\frac{8}{2},\frac{6}{2} )\\m=(4,3)[/tex]

Step 2

P1(0,6) and P2(4,0)

[tex]m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )\\m=(\frac{0+4}{2},\frac{6+0}{2} )\\m=(\frac{4}{2},\frac{6}{2} )\\m=(2,3)[/tex]

Step 3

P1(4,2) and P2(4,-4)

[tex]m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )\\m=(\frac{4+4}{2},\frac{2-4}{2} )\\m=(\frac{8}{2},\frac{-2}{2} )\\m=(4,-1)[/tex]

Step 4

P1(-1,-5) and P2(-3,4)

[tex]m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )\\m=(\frac{-1-3}{2},\frac{-5+4}{2} )\\m=(\frac{-4}{2},\frac{-1}{2} )\\m=(-2,\frac{-1}{2} )[/tex]

Step 5

P1(-3,2) and P2(8,-2)

[tex]m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )\\m=(\frac{-3+8}{2},\frac{2-2}{2} )\\m=(\frac{5}{2},\frac{0}{2} )\\m=(\frac{5}{2} ,0)[/tex]

I really hope it helps you, have a nice day

Answer:

This is approximately [tex]37.7 ft^{2}[/tex] to the nearest hundredth

Step-by-step explanation:

First of all, we will need to understand that to find the lateral surface area of the cylinder, we simply need to multiply the circumference of the circular base by the height of the cylinder.

In this case, the circumference of the circular base can be obtained by the formula

[tex]2 \pi r[/tex]

Hence we will have the circumference as [tex]2 \times \pi \times \frac{2.5}{2}=7.85 feet[/tex]

Tp get the Lateral area, we will simply have to multiply this value (7.85 feet )

by the height (4.8 feet)

7.85 X 4.8 =[tex]37.68 feet ^{2}[/tex]

This is approximately [tex]37.7 ft^{2}[/tex] to the nearest hundredth

Answer:

a). x = 135°

b). y = 45°

c). z = 67.5°

Step-by-step explanation:

Since sum of interior angles of a regular polygon is represented by,

Sum of interior angles = (n - 2) × 180°

Here n = number of sides

For a regular octagon, n = 8

Sum of interior angles = (8 - 2) × 180° = 1080°

And measure of one interior angles = [tex]\frac{\text{Sum of interior angles}}{n}[/tex]

                                                         x = [tex]\frac{1080}{8}[/tex]

                                                         x = 135°

From the figure attached,

Angle C has been divided in 6 equal parts,

Therefor, m∠ECD = [tex]\frac{135}{6}[/tex] = 22.5°

Since ∠ECD ≅ ∠CED,

m∠CED = 22.5°

Since m∠E = 135°

m∠FEC = 135 - 22.5 = 112.5°

In ΔFEC,

m∠FEC + m∠ECF + m∠CFE = 180°

112.5 + 22.5 + z = 180

z = 180 - 135

z = 45°

Similarly, in ΔCGF,

m∠CGF + m∠CFG + m∠GCF = 180°

(135 - y)° + (135 - z)° + 22.5° = 180°

270 - (y + z) + 22.5 = 180

292.5 - (y + 45) = 180

247.5 - y = 180

y = 247.5 - 180

y = 67.5°

Answer:

Step-by-step explanation:

f(-5) = -5 + 8 = 3

g(3) = 3^3 = 27

Answer:

1:3

Step-by-step explanation:

both divide by 60 so do 60 divided by 60 which is one

then 180 divided by 60 which is three

this gives you the answer

Answer:

1:3

Step-by-step explanation:

a ratio is basically the same as a fraction just in a different form. so it would be 60/180 simplified. both 60 and 180 can be divided by 60. so you would divide both numbers by 60 to get 1/3. this cannot be simplified any further. then to put it as a ratio it would just be 1:3

Answer:

b. 8

Step-by-step explanation:

To solve, we need to plug in the x and y values since we already have the values given to us

1/2(4)(2^2)

We should do the exponents first, 2^2 is 4

Now we are left with 1/2(4)(4)

4 times 4 is 16

16 times 1/2 is the same as 16/2

16/2=8

b. 8

Answer:

[tex]\boxed{\sf \ \ \ x=\dfrac{3}{4} \ \ \ }[/tex]

Step-by-step explanation:

hello,

f(x)=x-1

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

so

[tex]fog(x)=f(g(x))=f(2x^2+3)=2x^2+3-1=2x^2+2 \ and \\gof(x)=g(f(x))=g(x-1)=2(x-1)^2+3=2x^2-4x+2+3=2x^2-4x+5 \ \ So\\\fog(x)=gof(x) <=>2x^2+2=2x^2-4x+5\\<=>4x=5-2=3\\<=>x=\dfrac{3}{4}[/tex]

hope this helps

[tex]\frac{3}{4}[/tex]

The composition of a function is a process in which two functions [tex]f,g[/tex], are combined to produce a new function, [tex]h[/tex], with the formula [tex]h(x)=g(f(x))[/tex]. It means that the [tex]g[/tex] function is being applied to the [tex]x[/tex] function.

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

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

            [tex]=2x^2+3-1\\=2x^2+2[/tex]

[tex]g(f(x))=g(x-1)[/tex]

           [tex]=2(x-1)^2+3\\=2x^2+2-4x+3\\=2x^2-4x+5[/tex]

[tex]f(g(x))=g(f(x))[/tex]

[tex]2x^2+2=2x^2-4x+5[/tex]

       [tex]4x=3[/tex]

        [tex]x=\frac{3}{4}[/tex]

For more information:

https://brainly.com/question/12431044?referrer=searchResults

Answer:

All compositions are affected by the order in which they are performed

Step-by-step explanation:

We have the following transformations:

-translation

-reflection

-rotation

Each of them are affected by the order in which they are performed, for example:

If we rotate we have:

(x, y) -> (y, -x).

After the reflection:

(y, -x) -> (-y, -x).

If we translated by <2, 5> and reflected through the y-axis:

After the translation, (x, y) -> (x + 2, y + 5)

In other words, all compositions are affected by the order in which they are performed

Answer:

Population: all men in the country

Sample: the 1,002 men selected

Step-by-step explanation:

The population describes the people/group of people involved.

The sample describes a portion taken out of the population.

Thus, in this case study, the population is all men in the country

The sample is the 1,002 men selected.

Answer: C) $33

Step-by-step explanation:

1973 tax rate :

2% on the first $1000 income

3% on next $2000 or any part thereof ;

Brown's total income of $1800

2% of $1000

0.02 × $1000 = $20

3% of $800

0.03 × 800 = $24

Total tax = $(20 + 24) = $44

1/4 tax deduction:

(1/4) of total tax

(1/4) × $44

0.25 × $44

= $11

Total tax - tax deduction

$44 - $11 = $33

Tax amount = $33