The formula for the surface area of a
sphere that has a radius 7 is shown in
the box below.
SA = 4tr-2
A sphere and one of its dimensions are
shown in the diagram below.
5 in.
What is the surface area, in square
inches, of the sphere?

Answer:

A) There are two complex solutions.

Step-by-step explanation:

To know how many solutions a quadratic equation has, calculate the discriminant of the equation.

discriminant = b² - 4ac              

    where a = coefficient of x²

                b = coefficient of x

                c = constant of equation

if b² - 4ac > 0 , then equation has 2 real roots

if b² - 4ac = 0 , then equation has 1 real, repeated root

if b² - 4ac < 0 , then equation has 2 complex roots

In this case, discriminant = 9² - 4(-2)(-12)

                                          = -15

As -15 < 0, equation has 2 complex roots.

Answer:

  (c)  x = 2 and x = -8

Step-by-step explanation:

The rules of logarithms let you rewrite this as a quadratic equation. That equation will have two (2) potential solutions. We know from the domain of the log function that any negative value of x will be an extraneous solution.

__

The rules of logarithms that apply are ...

  [tex]\log(a)+\log(b)=\log(ab)\qquad\text{all logarithms to the same base}\\\\\log_b(a)=c\ \Longleftrightarrow\ b^c=a\\\\[/tex]

__

We can rewrite the equation so that only one logarithm is involved. Then we can take antilogs.

  [tex]\log_4(x)+\log_4(x+6)=2\\\\\log_4(x(x+6))=2\qquad\text{using the first rule}\\\\4^2=x(x+6)\qquad\text{using the second rule}[/tex]

__

Adding (6/2)² = 9 to both sides will "complete the square."

  16 +9 = x² +6x +9 . . . . . . . add 9

  25 = (x +3)²

  ±√25 = x +3 = ±5 . . . . . take the square root(s)

  x = -3 ±5 = {-8, +2}

The two potential solutions are x = 2 and x = -8.

[tex]\\ \rm\Rrightarrow log_4x+log_4(x+6)=2[/tex]

[tex]\\ \rm\Rrightarrow log_4(x(x+6))=2[/tex]

[tex]\\ \rm\Rrightarrow x(x+6)=4^2[/tex]

[tex]\\ \rm\Rrightarrow x^2+6x=16[/tex]

[tex]\\ \rm\Rrightarrow x^2+6x-16=0[/tex]

[tex]\\ \rm\Rrightarrow x^2-2x+8x-16=0[/tex]

[tex]\\ \rm\Rrightarrow x(x-2)+8(x-2)=0[/tex]

[tex]\\ \rm\Rrightarrow (x+8)(x-2)=0[/tex]

[tex]\\ \rm\Rrightarrow x=-8\:and\:x=2[/tex]

Answer:

।बवछॅनछॅठै रटटृ रटटृरटॅलठट

Answer:

A.

Step-by-step explanation:

As shown in the question we can interpret the following:

[tex]x_{1} = -2\\y_{1} = 1\\x_{2} = 5\\y_{2} = -4[/tex]

Now all we have to do is plug these values into the equation, and so we find that A. is the correct answer.

Answer:

Option C: 41

Step-by-step explanation:

<ABD+<CBD=90

<ABD=8x+1

<CBD=6x+5

(8x+1)+(6x+5)=90

Combine like terms

(8x+6x)+(1+5)=90

14x+6=90

14x=90-6

14x=84

divide both sides by 14

x=6

Now we plug that value into <DBC = 6x+5

6(6)+5=

36+5

41

Let's take this problem step by step:

∠ABC is 90 degrees

 ⇒ made up of two angles ⇒ ∠ABD and ∠DBC

     ⇒ in mathematical equation form:

            [tex]ABD + DBC= ABC[/tex]

Since ∠ABD = 8x + 1 and ∠DBC = 6x+5

    [tex]8x + 1+6x + 5=90\\14x+6=90\\14x=84\\x=6[/tex]

Let's plug it into ∠DBC = 6x+5

  ∠DBC = 6x+5 = 6(6)+5=41

Answer: ∠DBC = 41

Hope that helps!

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Answer:

Step-by-step explanation:

Answer:

[tex]c=4 \sqrt{2}[/tex]

Step-by-step explanation:

Pythagoras Theorem

    [tex]a^2+b^2=c^2[/tex]

where:

Given values:

Substitute the given values into Pythagoras Theorem formula and solve for c:

[tex]\begin{aligned}a^2+b^2 & = c^2 \\\implies 4^2+4^2 & =c^2\\16+16 & =c^2\\32 & =c^2\\ \sqrt{c^2}& =\sqrt{32}\\ c & =\sqrt{16 \cdot 2}\\& = \sqrt{16}\sqrt{2}\\& =4\sqrt{2}\end{aligned}[/tex]

Therefore, the measure of the third side of the given right triangle is [tex]4 \sqrt{2}[/tex]

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Answer:

1991.759

Step-by-step explanation:

1810.69×%10=181.069

1810.69+181.069=1991.759

Answer:

It's rounded to the whole, which is 6.

Step-by-step explanation:

Answer:

x = 37

Step-by-step explanation:

A straight angle is 180 degrees. That means ∠DFG & ∠EFG have to add together to be 180.

2x + 6 + 3x - 11 = 180     Combine like terms

5x - 5 = 180                   Add 5 to both sides

5x = 185                         Divide by 5

x = 37

∠DFG = 80°

∠EFG = 100°

Answer:

C. -6

Step-by-step explanation:

-3(2)²+4(2)-2

-3(4) + 8 - 2

-12+8-2

-14+8

-6

Angle DAB will be equal to angle CAB

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

AC is a straight line and forms one of the sides of the triangle ABC. If point D is placed on line AC, angle DAB would remain equal to angle CAB since they are on the same line the angle formed with line AB remains the same.

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Answer:

x=9

y=?

36= 1/2(x*y)

36 *2 = 2* 1/2 (9*y)

72 = 9*y

72/9= 9*y/9

8=y

The other number is 8.

The height of the base will be 15 cm. The candy bar has a 2400 cubic centimeter box with a triangular prism form to it.

Join the edges of three rectangles. Now, from both ends, seal their triangle mouths. A triangular prism is a name for the form.

The complete question is;

"A candy bar is in the shape of a triangular prism the volume of the box is 2400 cubic centimeters.  It is shown with a base of the triangle labeled 16 cm, the sides of triangles labeled 17 cm, and the length of the box equal to 20 cm. what is the height of the base triangular prism"

The volume of the triangular prism;

[tex]\rm V = \frac{1}{2}\times b \times h\times l\\\\ 2400 \ cm^3 = \frac{1}{2}\times 16 \ cm \times h\times 20 \ cm \\\\ h = 15 \ cm[/tex]

Hence, the height of the base will be 15 cm.

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Using the binomial distribution, it is found that there is a 0.9815 = 98.15% probability that at least one of them has been vaccinated.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem, the values of the parameters are:

n = 5, p = 0.55

The probability that at least one of them has been vaccinated is given by:

[tex]P(X \leq 1) = 1 - P(X = 0)[/tex]

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.55)^{0}.(0,45)^{5} = 0.0185[/tex]

Then:

[tex]P(X \leq 1) = 1 - P(X = 0) = 1 - 0.0185 = 0.9815[/tex]

0.9815 = 98.15% probability that at least one of them has been vaccinated.

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Answer:

18

Step-by-step explanation:

closest whole numberd are 5, 8 and 5. 5 + 5 = 10 + 8

= 18.

Answer:

[tex]-\dfrac{69}{14}[/tex]

Step-by-step explanation:

Substitute the given values of the variables into the given expression:

[tex]\implies \dfrac{60 \left(\dfrac{1}{3}\right)\left(-\dfrac{1}{5}\right)\left(\dfrac{1}{4}\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}[/tex]

When multiplying fractions, simply multiply the numerators and the denominators:

[tex]\implies \dfrac{60 \left(\dfrac{1 \cdot -1 \cdot 1}{3\cdot 5 \cdot 4}\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}[/tex]

[tex]\implies \dfrac{60 \left(-\dfrac{1}{60}\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}[/tex]

[tex]\implies \dfrac{\left(-1\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}[/tex]

When adding or subtracting fractions, make the denominators the same:

[tex]\implies \dfrac{\left(-1\right)\left(\dfrac{20}{60}-\dfrac{12}{60}+\dfrac{15}{60}\right)}{\left(\dfrac{5}{15}-\dfrac{3}{15}\right)\left(\dfrac{4}{12}+\dfrac{3}{12}\right)}[/tex]

Now add the numerators and put that over the denominator:

[tex]\implies \dfrac{\left(-1\right)\left(\dfrac{20-12+15}{60}\right)}{\left(\dfrac{5-3}{15}\right)\left(\dfrac{4+3}{12}\right)}[/tex]

[tex]\implies \dfrac{\left(-1\right)\left(\dfrac{23}{60}\right)}{\left(\dfrac{2}{15}\right)\left(\dfrac{7}{12}\right)}[/tex]

Again, multiply the fractions:

[tex]\implies \dfrac{\left(-1 \cdot \dfrac{23}{60}\right)}{\left(\dfrac{2 \cdot 7}{15 \cdot 12}\right)}[/tex]

[tex]\implies \dfrac{-\dfrac{23}{60}}{\dfrac{14}{180}}[/tex]

To divide the fractions, turn the second fraction upside down, then multiply it by the first fraction:

[tex]\implies -\dfrac{23}{60} \cdot \dfrac{180}{14}[/tex]

[tex]\implies -\dfrac{4140}{840}[/tex]

Finally, simplify:

[tex]\implies -\dfrac{4140 \div 60}{840 \div 60}[/tex]

[tex]\implies -\dfrac{69}{14}[/tex]

The height of a vertical brace placed 8 ft from the low end of the roof is 6 feet.

An equation is an expression that shows the relationship between two or more variables and numbers.

Slope of roof = ratio of rise to run = rise / run = 9/12 = 3/4

If the brace is placed 8 ft from the low end of the roof, hence:

height of brace = slope * 8 = 3/4 * 8 = 6 ft

The height of a vertical brace placed 8 ft from the low end of the roof is 6 feet.

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Hey there!

ASSUMING:

p = 2l + 2w

IF SO:

• We already have our perimeter (p) & our width (w), now you have to find our length (l)

160 = 2l + 2(34)

CONVERT TO:

2l + 2(34) = 160

SIMPLIFY IT:

2l + 68 = 160

SUBTRACT 68 to BOTH SIDES:

2l + 68 - 68 = 160 - 68

SIMPLIFY IT:

2l = 160 - 68

2l = 92

DIVIDE 2 to BOTH SIDES:

2l/2 = 92/2

SIMPLIFY IT:

l = 92/2

l = 46

Therefore, your answer should be:

l = 46

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

ΔDGC is right because Line E G is perpendicular-to CC', Option D is the correct answer.

Reflection along a line is plotting a new object as a mirror image of the original object .

It is given that the there are two Triangles , ABC and A'B'C' as an image.

The figure is attached with the answer.

D is the mid point of the line joining BB'

As the line of reflection is always perpendicular to the object and the image.

And as it is given that C G F is a right angle.

Therefore triangle DGC is right angled triangle , (the option given in the question is incorrect ) ,  Line E G is perpendicular-to CC'.

Option D is the correct answer.

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Answer:

D

Step-by-step explanation:

The value of g(1) is 4 because  (x, y) satisfy the function f(x) then (y, x) will satify the function g(x) option (D) 4 is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

As we know if the f(x) has inverse function g(x)

Let (x, y) satisfy the function f(x) then (y, x) must satify the function g(x)

f(x) has ordered pair = (4, 1)

Then g(x) has (1, 4)

g(1) = 4

Thus, the value of g(1) is 4 because  (x, y) satisfy the function f(x) then (y, x) will satify the function g(x) option (D) 4 is correct.

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Answer: Answer below.

Step-by-step explanation: If x is pi, and y is 1/pi, then multiplying x by y is 1; yes. So, for y, 1 is being divided by pi. The opposite of division is multiplication. If you multiply 1/pi by pi, the pi in the denominator cancels. Just how if it is 5x = 10, dividing by 5 cancels it on the left side, and gets you x = 2.

This is general for everything. If you multiply 2 by 1/2, you get 1. This is because dividing is also like multiplying by its reciprocal. 1/2's reciprocal is 2/1, and multiplying leaves you with 1. Go and use a calculator, it's correct. Actually, any problem a/b × b/a = 1.

Answers + Step-by-step explanation :

a) the equation should be:
7(n + 5) = 91 since you first add 5 to n and then multiply it by 7. The answer is 91 so that is on the other side of the equal sign

b) we can solve our equation to find for n, the number jim thought of

7(n + 5) = 91
I will use the distributive property.

7n + 35 = 91

Subtract 35 on both sides

7n = 56

Now divide 7 on both sides to find n

n = 8

The number Jim was thinking of was 8! this should be correct, hope this helps!

Answer: This represents a linear function.

Step-by-step explanation:

I used Desmos to plot them on a graph. You can see that this is linear because each point is in a line. I hope this helps!!

Inequalities help us to compare two unequal expressions. The correct option is B.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The given inequality -6 ≤y + 2x < 15 can be broken into two small inequality, as shown below.

Now, if we plot the inequality as shown below, then the area in which both the shaded region overlap is the area of the this inequality.

Hence, the correct option is B.

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The equation of the given sine graph is gotten as; y = 4 sin [(0.4(x + 2.5)] - 1

We know that the  general formula for equation of a sine graph is;

y = A sin [(B(x - D)] + C

where;

A is Amplitude

Period = 2π/B.

Phase Shift = -C/B.

Vertical Shift = D.

From the graph;

A = 4

B = 2π/5π = 2/5

C = -1

D = -5/2

Thus;

y = 4 sin [(0.4(x + 2.5)] - 1

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