What is the area of a cross section that is parallel to face BFGC?

Answer:

a = 4

b = -2

Step-by-step explanation:

If the given function is continuous at x = 1

[tex]\lim_{x \to 1^{-}} f(x)=(x+1)[/tex]

                     [tex]=2[/tex]

[tex]\lim_{x \to 1^{+}} f(x)=ax+b[/tex]

                     [tex]=a+b[/tex]

[tex]\lim_{x \to 1} f(x)=ax+b[/tex]

                   [tex]=a+b[/tex]

And for the continuity of the function at x = 1,

[tex]\lim_{x \to 1^{-}} f(x)=\lim_{x \to 1^{+}} f(x)=\lim_{x \to 1} f(x)[/tex]

Therefore, (a + b) = 2 -------(1)

If the function 'f' is continuous at x = 2,

[tex]\lim_{x \to 2^{-}} f(x)=ax+b[/tex]

                     [tex]=2a+b[/tex]

[tex]\lim_{x \to 2^{+}} f(x)=3x[/tex]

                     [tex]=6[/tex]

[tex]\lim_{x \to 2} f(x)=3x[/tex]

                   [tex]=6[/tex]

Therefore, [tex]\lim_{x \to 2^{-}} f(x)=\lim_{x \to 2^{+}} f(x)=\lim_{x \to 2} f(x)[/tex]

2a + b = 6 -----(2)

Subtract equation (1) from (2),

(2a + b) - (a + b) = 6 - 2

a = 4

From equation (1),

4 + b = 2

b = -2

Answer:

0.287671233 or 42/146

Step-by-step explanation:

It's not a clear photo, but I tried my best. Probablilty is just what they're looking for over the total amount.

So the amount of people traveling over 4km is 42 based on the graph.

And the total number of people is 146.

(I don't know if the last bar in the graph represents 10 or 20 people)

So 42/146 = 0.287671233

Forgive me if I'm wrong, but I couldn't see the image clearly.

Good luck!

Answer:

Step-by-step explanation:

Given:

Geometric mean of two digit = √ab

Answer 1;

Geometric mean of [8,18] = √(8)(18)

Geometric mean of [8,18] = √144

Geometric mean of [8,18] = 12

Answer 2;

Geometric mean of [3,7] = √(3)(7)

Geometric mean of [3,7] = √21

Geometric mean of [3,7] = 4.58

Answer 3;

Geometric mean of [5,8] = √(5)(8)

Geometric mean of [5,8] = √40

Geometric mean of [5,8] = 6.32

Answer 4;

Geometric mean of [8,4] = √(8)(4)

Geometric mean of [8,4] = √32

Geometric mean of [8,4] = 5.65

Answer 5;

Geometric mean of [6,3] = √(3)(6)

Geometric mean of [6,3] = √18

Geometric mean of [6,3] = 4.24

Answer 6;

Geometric mean of [2,8] = √(2)(8)

Geometric mean of [2,8] = √16

Geometric mean of [2,8] = 4

Answer:

20

Step-by-step explanation:

the perimeter of the square and the triangle are the same

4×(x + 10) = 3×4x

4x + 40 = 12x

40 = 8x

x = 5

=>

a triangle side is 4x = 4×5 = 20

Answer:

mean value of female = 10.000

standard deviation of female = 1.604

mean value of male = 10.000

standard deviation of male = 2.449

Step-by-step explanation:

Given:

n=8 females

n=8 males

The objective is to find the mean and deviation and also based on the mean and the standard deviation have to describe the differences in intelligence scores for males and females

Solution:

The mean and the standard deviation are found by using MINITAB

The MINITAB procedure is explained as follows,

Step 1

choosing start > Basic statistics > Display Descriptive Statistics

Step 2

In variables supposed to enter the columns Female and Male

Step 3

Here choosing option statistics and select Mean and standard deviation

Step 4

Finally clicking OK

MINITAB output is as follows,

variable Mean standard deviation

Female 10.000 1.604

Male 10.000 2.449

b)

From the MINITAB output the mean are same for females and males.

Here the standard deviation of females is less than the standard deviation of males. That is the male scores are more variable when compared to female scores.

the sum of interior angle is 180:

[tex]x + 160 = 180 \\ x = 180 - 160 \\ x = 20[/tex]

Answer:

27 cm²

Step-by-step explanation:

The surface area is the area of the square plus the area of the 4 congruent triangles.

area of square = 3² = 9 cm²

area of 1 triangle = [tex]\frac{1}{2}[/tex] × 3 × 3 = 4.5 cm²

area of 4 triangles = 4 × 4.5 = 18 cm²

Total surface area = 9 + 18 = 27 cm²

Step-by-step explanation:

SA of a pyramid

=L(2h+L)

=3(2(3)+3)

=3(9)

=27cm^2

Answer:

True

Step-by-step explanation:

The definition of the function is a relation with exactly one x for each y. x is the domain, and y is the range, so all functions have a domain and a range.

Answer:

[tex]\displaystyle x=-\frac{2}{3}[/tex]

Step-by-step explanation:

We want to solve the equation:

[tex]\displaystyle \sqrt{x^2-4x+8}+x=2-x[/tex]

We can isolate the square root. Subtract x from both sides:

[tex]\sqrt{x^2-4x+8}=2-2x[/tex]

And square both sides:

[tex](\sqrt{x^2-4x+8})^2=(2-2x)^2[/tex]

Expand:

[tex]x^2-4x+8=4-8x+4x^2[/tex]

Isolate the equation:

[tex]3x^2-4x-4=0[/tex]

Factor:

[tex]\displaystyle (3x+2)(x-2)=0[/tex]

Zero Product Property:

[tex]3x+2=0\text{ or } x-2=0[/tex]

Solve for each case. Hence:

[tex]\displaystyle x=-\frac{2}{3}\text{ or } x=2[/tex]

Now, we need to check for extraneous solutions. To do so, we can substitute each value back into the original equation and check whether or not the resulting statement is true.

Testing x = -2/3:

[tex]\displaystyle \begin{aligned} \sqrt{\left(-\frac{2}{3}\right)^2-4\left(-\frac{2}{3}\right)+8}+\left(-\frac{2}{3}\right)&\stackrel{?}{=}2-\left(-\frac{2}{3}\right)\\ \\ \sqrt{\frac{4}{9}+\frac{8}{3}+8}-\frac{2}{3}&\stackrel{?}{=}2+\frac{2}{3} \\ \\ \sqrt{\frac{100}{9}}-\frac{2}{3}& \stackrel{?}{=} \frac{8}{3}\\ \\ \frac{10}{3}-\frac{2}{3} =\frac{8}{3}& \stackrel{\checkmark}{=}\frac{8}{3}\end{aligned}[/tex]

Since the resulting statement is true, x = -2/3 is indeed a solution.

Testing x = 2:

[tex]\displaystyle \begin{aligned}\sqrt{(2)^2-4(2)+8}+(2) &\stackrel{?}{=}2-(2) \\ \\ \sqrt{4-8+8}+2&\stackrel{?}{=}0 \\ \\ \sqrt{4}+2&\stackrel{?}{=}0 \\ \\ 2+2=4&\neq 0\end{aligned}[/tex]

Since the resulting statement is not true, x = 2 is not a solution.

Therefore, our only solution to the equation is x = -2/3.  

Step-by-step explanation:

Hey there!

Given;

[tex] \sqrt{ {x}^{2} - 4x + 8} + x = 2 - x[/tex]

Take "X" in right side.

[tex] \sqrt{ {x - 4 + 8}^{2} } = 2 - 2x[/tex]

Squaring on both sides;

[tex] {( \sqrt{ {x}^{2} - 4x + 8 } )}^{2} = {(2 - 2x)}^{2} [/tex]

Simplify;

[tex] {x}^{2} - 4x + 8 = {(2)}^{2} - 2.2.2x + {(2x)}^{2} [/tex]

[tex] {x }^{2} - 4x + 8 = 4 - 8x + 4 {x}^{2} [/tex]

[tex]3 {x}^{2} - 4x - 4 = 0[/tex]

[tex]3 {x}^{2} - (6 - 2)x - 4 = 0[/tex]

[tex] 3 {x}^{2} - 6x + 2x - 4 = 0[/tex]

[tex]3x(x - 2) + 2(x - 2) = 0[/tex]

[tex](3x + 2)(x - 2) = 0[/tex]

Either;

3x+2 = 0

x= -2/3

Or;

x-2 = 0

x= 2

Check:

Keeping X= -2/3,

√(x²-4x+8 ) +X = 2-x

√{(-2/3)²-4*-2/3+8}+(-2/3) = 2+2/3

8/3 = 8/3 (True)

Now; Keeping X= 2

√{(2)²-4*2+8}+2 = 2-2

8 ≠0 (False)

Therefore, the value of X is -2/3.

Hope it helps!

Answer:

22 people were born in the uk  (66 ÷ 360) × 120=22

Step-by-step explanation:

Using the pie chart, the fraction of people born in the UK, is: 7/30.

A pie chart is a graphical representation used to describe the composition of a data using degrees or percentages.

84° is given as the number of people that were born in the UK.

That's about: 84/360 × 120 = 28 people.

28 out of 120 people would give us a fraction of: 28/120 = 7/30.

Learn more about pie chart on:

https://brainly.com/question/26851221

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Answer:

10.

Step-by-step explanation:

Answer:

The number is 10.

Step-by-step explanation:

x/5 = 2

Multiply both sides by 5.

5 * x/5 = 5 * 2

x = 10

Answer: The number is 10.

Answer:

your answer is (2,3) i think so .......am i right...or wrong..

Answer:

(a - b)²

Step-by-step explanation:

(a + b)² - 4ab

= a² + 2ab + b² - 4ab

= a² - 2ab + b²

= (a - b)²

Answer:

Step-by-step explanation:

H

Answer:

Inside

Step-by-step explanation:

Given equation of the Circle is ,

[tex]\sf\implies x^2 + y^2 = 25 [/tex]

And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,

[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]

Here we can say that ,

• Radius = 5 units

• Centre = (0,0)

Finding distance between the two points :-

[tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]

Here we can see that the distance of poiñt from centre is less than the radius.

Hence the point lies within the circle

Answer:

120 miles

Step-by-step explanation:

30 miles per hour * 4 hours

120 miles

Answer:

She travels 120 miles in 4 hours.

Step-by-step explanation:

She travels 120 miles in 4 hours

Answer:

4.15, or 1.32pi

Step-by-step explanation:

arclength is circumference(34/360)

so pi x d (34/360)

3.14 x 14 x (34/360) = 4.15, or 1.32pi

The arc length PR is 4.151 cm.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Moreover, every angle has rotational symmetry around the centre.A section of a line that runs from a circle's centre to any point on the circle itself. "R" or "r" stand for the circle's radius.

As per the given data:

The diameter of circle Q = 14 cm

From the given diagram:

∠PQR = 34°

For finding out the arc length PR:

arc length = angle in radian × radius

radius = diameter / 2 = 14 / 2 = 7 cm

angle in radian = 34° × (π / 180°) = 0.593 radians

arc length PR = 0.593 × 7 = 4.151 cm

Hence, the arc length PR is 4.151 cm.

To learn more about circle, click:

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Answer:

Tara has to pay £324 for 4 nights

Step-by-step explanation:

Regular price of a room per night

= £90

Regular price of a room for 4 nights

= 90*4

= £360

Price of a room for 4 nights after discount

= 75% (360)

= 75/100 * 360 = 75 * 3.6

= £270

Price of the room after charging VAT

= 270 + 20%(270)

= 270 + 20/100 * 270

= 270 + 2 * 27

= 270 + 54

= £324

Answer:

tan 72°=58/19

Step-by-step explanation:

i think this is the right answer

Answer:

Step-by-step explanation:

I can tell you what it represents, but not what it means. Or maybe the units.

V(5/7) means that wherever you see an r on the right hand side, you put in 5/7 where the R is.

V = 4/3 * pi * r^3

V(5/7) = 4/3 * 3.14 * (5/7)^3

V(5/7) = 4/3 * 3.14 * 125 / 343

V(5/7) = 4/3 * 3.14 * 0.3644

V(5/7) = 1.526 cubic units (of whatever the units of 5/7 were to begin with)

solution :-

here,

We know that interior opposite angles are equal.

So,

110° = 50° + x (being interior opposite angles)

110° - 50° = x

60° = x

the value of x =60°

hope it is helpful to you ☺️

Answer:

option c

Step-by-step explanation:

Quadratic function f(x) = ax² + bx  +c

Here the the co-efficient of x,  that is a tells if the graph is wider or narrower.

1) a < 1  that is if a is decimal less than 1, then the graph is wider.

2) a > 1, then the graph is narrow.

Answer:

The correct answer is not shown in your picture. You must get a = 60.

Step-by-step explanation:

(1/2)a + (2/3)b = 50

b = 30

(1/2)a + (2/3)(30) = 50

(1/2)a + 20 = 50

(1/2)a + 20 - 20 = 50 - 20

(1/2)a = 30

2 * (1/2)a = 2 * 30

a = 60

The correct answer is not shown in your picture. You must get a = 60.

Answer:

[tex] \rm Numbers = 4 \ and \ -3.[/tex]

Step-by-step explanation:

Given :-

The sum of two numbers is 1 .

The product of the nos . is 12 .

And we need to find out the numbers. So let us take ,

First number be x

Second number be 1-x .

According to first condition :-

[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]

Hence the numbers are 4 and -3

Let integers be x and x-1

ATQ

[tex]\\ \sf\longmapsto 2x-1=1[/tex]

[tex]\\ \sf\longmapsto 2x=1+1[/tex]

[tex]\\ \sf\longmapsto 2x+2[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{2}{2}[/tex]

[tex]\\ \sf\longmapsto x=1[/tex]

Now

[tex]\\ \sf\longmapsto x-1=1-1=0[/tex]

But

Integers can be x and 1-x as their sum is 1

[tex]\\ \sf\longmapsto x(1-x)=-12[/tex]

[tex]\\ \sf\longmapsto x- x^2=-12[/tex]

[tex]\\ \sf\longmapsto x^2-x-12=0[/tex]

[tex]\\ \sf\longmapsto x^2-4x+3x-12=0[/tex]

[tex]\\ \sf\longmapsto x(x-4)+3(x-4)=0[/tex]

[tex]\\ \sf\longmapsto (x-4)(x+3)=0[/tex]

[tex]\\ \sf\longmapsto x=4,-3[/tex]

Answer:

x - 2y + 8 = 0

Step-by-step explanation:

that is the procedure above

Answer:

[tex](a)\ r = 1in : 9ft[/tex]

[tex](b)\ r = 1 in: 15ft[/tex]

[tex](c)\ r = 1 in: 16ft[/tex]

[tex](d)\ r = 1in:4ft[/tex]

Step-by-step explanation:

Given

See comment for complete question

Required

The scale of each area

The scale ratio (r) is calculated as:

[tex]r = scale:actual[/tex]

So, we have:

(a)  scale : 13 square inches  and actual : 117 square feet

[tex]r = 13in : 117ft[/tex]

Divide by 13

[tex]r = 1in: 9ft[/tex]

(b) scale : 5 square inches  and actual : 125 square feet

[tex]r = 5in : 125ft[/tex]

Divide by 5

[tex]r = 1in : 25ft[/tex]

(c) scale : 8 square inches  and actual : 128 square feet

[tex]r = 8in : 128ft[/tex]

Divide by 8

[tex]r = 1in : 16ft[/tex]

(d) scale : 12 square inches  and actual : 48 square feet

[tex]r = 12in : 48ft[/tex]

Divide by 12

[tex]r = 1in:4ft[/tex]

Answer:

Step-by-step explanation:

Take two points on the line and find the slope.

(1 , 2)  ; (4 , 4)

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\[/tex]

          [tex]=\frac{4-2}{4-1}\\\\=\frac{2}{3}[/tex]

m = 2/3  & (1 , 2)

Slope point form : y - y1 = m(x-x1)

[tex]y - 2 = \frac{2}{3}*(x - 1)\\\\y - 2 =\frac{2}{3}x - \frac{2}{3}\\\\y =\frac{2}{3}x-\frac{2}{3}+2\\\\y = \frac{2}{3}x-\frac{2}{3}+\frac{2*3}{1*3}\\\\y=\frac{2}{3}x-\frac{2}{3}+\frac{6}{3}\\\\y=\frac{2}{3}x+\frac{4}{3}\\\\Multiply \ equation \ by \ 3\\\\3y = 2x + 4\\\\2x - 3y + 4 = 0[/tex]

Answer:

19

Step-by-step explanation:

(3-2)(3^2+3x2+2^2)

(1)(9+6+4)

(1)(19)

[tex]\displaystyle\bf \underbrace{ (x-y)(x^2+xy+y^2)}}_{x^3-y^3}=3^3-2^3=19\\\\Answer: b)19[/tex]

Answer:

x = 27.5.

Step-by-step explanation:

There are given numbers on each side. If the figures are similar, then they have a set ratio for each value.

So, 55:8 and x:4. If you want to, you can flip it, so that it is 8:55 and 4:x.

With that in mind, it is easy to see what the ratio is. Because 4 is half of 8, x is half of 55. 55 divided by 2 is 27.5.

Therefore, x = 27.5.