Solve for
5(x + 1) = 4x + 8)

Answer:

[tex]\large\boxed{36x^3a+45xa=9xa(4x^2+5)}[/tex]

Step-by-step explanation:

[tex]36x^3a=(9xa)(4x^2)\\\\45xa=(9xa)(5)\\\\36x^3a+45xa=(9xa)(4x^2)+(9xa)(5)=9xa(4x^2+5)[/tex]

Answer:

see explanation

Step-by-step explanation:

Given

6a² - a - 5 = 0

Consider the factors of the product of the a² term and the constant term which sum to give the coefficient of the a- term.

product = 6 × - 5 = - 30 and sum = - 1

The factors are - 6 and + 5

Use these factors to split the a- term

6a² - 6a + 5a - 5 = 0 ( factor the first/second and third/fourth terms )

6a(a - 1) + 5(a - 1) = 0 ← factor out (a - 1) from each term

(a - 1)(6a + 5) = 0

Equate each factor to zero and solve for a

a - 1 = 0 ⇒ a = 1

6a + 5 = 0 ⇒ 6a = - 5 ⇒ a = - [tex]\frac{5}{6}[/tex]

Solution set = { 1, - [tex]\frac{5}{6}[/tex] }

Answer:  The solution set of the given quadratic equation is  [tex]\{1,-\dfrac{5}{6}\}.[/tex]

Step-by-step explanation:  We are given to find the solution set of the following quadratic equation :

[tex]6a^2-a-5=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We will be solving the given quadratic equation by the method of FACTORIZATION.

To factorize the expression on the L.H.S. of equation (i), we need two integers with sum -1 and product -30. Those two integers are -6 and 5.

The solution of equation (i) is as follows :

[tex]6a^2-a-5=0\\\\\Rightarrow 6a^2-6a+5a-5=0\\\\\Rightarrow 6a(a-1)+5(a-1)=0\\\\\Rightarrow (a-1)(6a+5)=0\\\\\Rightarrow a-1=0,~~~~~~6a+5=0\\\\\Rightarrow a=1,~-\dfrac{5}{6}.[/tex]

Thus, the solution set of the given quadratic equation is  [tex]\{1,-\dfrac{5}{6}\}.[/tex]

Answer:

P (over 6 feet tall or good aim) = 5/9

Step-by-step explanation:

We are given that there are a total of 27 players who are trying out for the school basketball team.

8 of them are more than 6 feet tall while 7 of them have good aim.

We are to find the probability that the coach would randomly pick a player over 6 feet tall or a player with a good aim, considering that no players over 6 feet tall have good aim.

P (more than 6 feet tall) = [tex]\frac{8}{27}[/tex]

P (good aim) = [tex]\frac{7}{27}[/tex]

P (over 6 feet tall or good aim) = [tex]\frac{8}{27} + [/tex] [tex]\frac{7}{27}[/tex] = 5/9

Answer:

5/9

Step-by-step explanation:

just did test

Answer:

Approximately 1130 cubic feet.

Step-by-step explanation:

The volume of a cylinder is the area of its base times its height.

The height of this cylinder is given to be 10 feet. What's the area of its base?

The base of a cylinder is a circle. The area of a circle with radius [tex]r[/tex] is equal to [tex]\pi \cdot r^{2}[/tex]. For the base of this cylinder, [tex]r = 6[/tex] feet. The question also dictates that [tex]\pi = 3.14[/tex]. The area of each circular base will thus be:

[tex]\text{Base} = \pi\cdot r^{2} = 3.14 \times 6^{2} = 113.04[/tex] square feet.

The volume of this cylinder will be

[tex]\text{Volume} = \text{Base}\times \text{Height} = 113.04\times 10 \approx 1130[/tex] cubic feet.

ANSWER

-2 shift the graph of the basic function down by 2 units.

EXPLANATION

The given cosine function is:

[tex]y = - 2 - 3 \cos(x + \pi) [/tex]

This equation can be rewritten as:

[tex]y = - 3 \cos(x + \pi) + - 2[/tex]

We compare this to

[tex]y = a \cos(bx + c) + d[/tex]

The effect d has on the graph is that, it shifts the graph up by d units.

If d is negative the graph shifts down by d units.

Since d=-2, the graph will shift down by 2 units.

Answer:

Vertical Shift Down 2 Units

Step-by-step explanation:

Answer:

16:9

Step-by-step explanation:

If the linear ratio is 4:3, the area ratio will be the square of that.

(4/3)² = 16/9

Answer:

16/9

Step-by-step explanation:

we know that R1/R2= 4/3 and L1/L2= 4/3. where R1 and L1 are cone dimensions 1 and R2 and L2 are cone dimensions 2.

We also know that the cone sourface is S=pi x R x L .

So that S1/S2= (pi R1 L1)/(pi R2 L2)

replacing and operating mathematically

S1/S2=R1 L1/R2 L2 = R1/R2 L1/L2=4/3 4/3=  16/9

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = [tex]\frac{2}{5}[/tex], hence

y = [tex]\frac{2}{5}[/tex] x + c ← is the partial equation

To find c substitute (- 3, - 1) into the partial equation

- 1 = - [tex]\frac{6}{5}[/tex] + c ⇒ c = - 1 + [tex]\frac{6}{5}[/tex] = [tex]\frac{1}{5}[/tex]

y = [tex]\frac{2}{5}[/tex] x + [tex]\frac{1}{5}[/tex] ← in slope- intercept form

Answer:

-80, -110

Step-by-step explanation:

Step-by-step explanation:

12. BAE+DAE=90 (angle in a right angle) BAE=48

90=48+DAE

DAE=90-48=42

14. CE=5X+8 BD=13-2

AC=2*CE

=2*(5X+8)

=10X+16

13. BE=22

AE=22(ISSOCELES TRIANGLE)

Answer:

Reflection across the x-axis, followed by reflection across y-axis and Reflection across the x-axis, followed by translation 10 units rights

Answer:

Reflection across the x-axis, followed by translation 10 units right.

Step-by-step explanation:

I'm sorry, I know the question asks for two transformations, but let's look a the math before tackling the figure (see attachment).

When you are asked to do a reflection on the x-axis, they are asking you to invert the sign on the y coordinate of every point, and when you are asked to do a reflection on the y-axis, just invert the sign of the x coordinate, always following the convention of (x, y).

Translation to the right means to add the amount of units given to all the x coordinates, to the left means to subtract said number of units.

Translation down is to subtract those units to the y coordinate and translation up, is to add to that y coordinate.

So in this exercise:

Fig 1 coordinates are:

(-5, 2)  (-3, 4)  (-4, 7)  (-6, 5)

Fig 2 coordinates are:

(5, -2)  (7, -4)  (6, -7)  (4, -5)

So let's test the options given:

a. Reflection across the y-axis, followed by reflection across x-axis

Reflection across the y-axis:

Fig 1.1: (5, 2)  (3, 4)  (4, 7)  (6, 5) <- Every x coordinate with inverted sign

Then reflection across x-axis:

Fig 1.2: (5, -2)  (3, -4)  (4, -7)  (6, -5) <- Every y coordinate with inverted sign

if we compare this new Fig 1.2 with Fig 2:

(5, -2)  (3, -4)  (4, -7)  (6, -5)  ≠  (5, -2)  (7, -4)  (6, -7)  (4, -5)   Wrong

b. Reflection across the x-axis, followed by reflection across y-axis

Reflection across the x-axis:

Fig 1.1: (-5, -2)  (-3, -4)  (-4, -7)  (-6, -5) <- Every y coordinate with inverted sign

Then reflection across y-axis:

Fig 1.2: (5, -2)  (3, -4)  (4, -7)  (6, -5) <- Every x coordinate with inverted sign

if we compare this new Fig 1.2 with Fig 2:

(5, -2)  (3, -4)  (4, -7)  (6, -5)  ≠  (5, -2)  (7, -4)  (6, -7)  (4, -5)   Wrong

c. Reflection across the x-axis, followed by translation 10 units right

Reflection across the x-axis:

Fig 1.1: (-5, -2)  (-3, -4)  (-4, -7)  (-6, -5) <- Every y coordinate with inverted sign

Then translation 10 units right:

Fig 1.2: (5, -2)  (7, -4)  (6, -7)  (4, -5) <- Every x coordinate +10

if we compare this new Fig 1.2 with Fig 2:

(5, -2)  (7, -4)  (6, -7)  (4, -5)  =  (5, -2)  (7, -4)  (6, -7)  (4, -5)   Correct!

d. Reflection across the y-axis, followed by translation 5 units down

Reflection across the y-axis:

Fig 1.1: (5, 2)  (3, 4)  (4, 7)  (6, 5) <- Every x coordinate with inverted sign

Then translation 5 units down:

Fig 1.2: (5, -3)  (3, -1)  (4, 2)  (6, 0) <- Every y coordinate -5

if we compare this new Fig 1.2 with Fig 2:

(5, -3)  (3, -1)  (4, 2)  (6, 0)  ≠  (5, -2)  (7, -4)  (6, -7)  (4, -5)     Wrong

So from all options only c. works

Answer:

The volume is 113.04 cubic inches

Step-by-step explanation:

We are given:

Radius = r = 3 inches

As we know the formula for finding the volume of sphere is:

[tex]V=\frac{4}{3} \pi r^{3} \\Putting\ values\ of\ \pi \ and\ r\\V = \frac{4}{3} * 3.14 * (3)^3\\= \frac{12.56}{3} * 27\\= \frac{339.12}{3}\\ =113.04\ cubic\ inches[/tex]

The volume is 113.04 cubic inches ..

Answer:

3/4

Step-by-step explanation:

Line up points

(3  , 7)

(-1,   4)

subtract vertically

4      3

2nd diff/1st diff=3/4

Answer:

The diagonal of this rectangle is 41 units.

Step-by-step explanation:

The relationship between the length and width of a rectangle and the diagonal is given by the Pythagorean identity:

[tex]d=\sqrt{l^2+w^2}[/tex]

From, the given question, the rectangle has a width of 9 units and a length of 40 units.

We substitute the width and length of the rectangle into the equation to get:

[tex]d=\sqrt{40^2+9^2}[/tex]

[tex]d=\sqrt{1600+81}[/tex]

[tex]d=\sqrt{1681}[/tex]

[tex]d=41[/tex] units.

Answer:

41

Step-by-step explanation:

Answer:

16.7%.

Step-by-step explanation:

There are initially [tex]24 + 15 + 8 = 47[/tex] pencils in the bag.

Take a pencil out of this bag of 47 pencils. 15 out of the 47 pencils blue. Let [tex]A[/tex] represent the event of getting a blue pencil on the first pick. The probability of getting a blue pencil is:

[tex]\displaystyle P(A) = \frac{15}{47}[/tex].

There are now [tex]47 - 1 = 46[/tex] pencils left in the bag. However, given that the first pencil removed from the bag is blue, the number of red pencils in the bag will still be 24. Take another pencil out of this bag of 46 pencils. Let [tex]B[/tex] represent the event of getting a red pencil on the second pick. The possibility that the second pencil is red given that the first pencil is blue will be:

[tex]\displaystyle P(B|A) = \frac{24}{46}[/tex].

The question is asking for the possibility that the first pencil is blue and the second pencil is red. That is:

[tex]\displaystyle P(A\cap B) = P(A) \cdot P(B|A) = \frac{15}{47}\times \frac{24}{46} = 0.166512 \approx 16.7\%[/tex].

Answer:

Part A: X=0

Part B: x=0

Step-by-step explanation:

Part A

(6^2)^X = 1

Applying the exponent rule: [tex](a^b)^c = a^{bc}[/tex]

So, our equation will become:

[tex]6^{2X} = 1[/tex]

We know if f(x) = g(x) then ln(f(x))= ln(g(x))

SO, taking natural logarithm ln on both sides and solving.

[tex]ln(6^{2X}) =ln(1)[/tex]

We know,[tex]log(a^b) = b.loga[/tex] Applying the rule,

[tex]2Xln6 =ln(1)\\We\,\,know\,\,ln(1)=0\\2Xln6 =0\\Solving:\\X=0[/tex]

Part B

(6^9)^x = 1

Applying the exponent rule: [tex](a^b)^c = a^{bc}[/tex]

So, our equation will become:

[tex]6^{9x} = 1[/tex]

We know if f(x) = g(x) then ln(f(x))= ln(g(x))

SO, taking natural logarithm ln on both sides and solving.

[tex]ln(6^{9x}) =ln(1)[/tex]

We know,[tex]ln(a^b) = b.lna[/tex] Applying the rule,

[tex]9xln6 =ln(1)\\We\,\,know\,\,ln(1)=0\\9xln6 =0\\Solving:\\x=0[/tex]

Answer:

The answer is 7/17

Step-by-step explanation:

Answer:

x = 7/2 ± 3/2*(i√3)

Step-by-step explanation:

The equation is

(x - 5)^2 + 3(x - 5) + 9 =0

Let A = (x-5)

The equation becomes now

(A)^2 + 3(A) + 9 =0

We then apply the quadratic formula

A = [-(3) ± √((3)^2-4(1)(9)) ]/ (2(1))

A = -3/2 ± 3/2*(i√3)

Now, we revert the substitution

(x-5) = -3/2 ± 3/2*(i√3)

x = 7/2 ± 3/2*(i√3)

Answer: D. 61.2 cm

Step-by-step explanation:

The formula to calculate the circumference of a circle is given by :-

[tex]\text{Circumference}=\pi d[/tex], where d is the diameter of the circle.

In the given picture.,  we have the diameter of circle = 19.5 cm

Then , the circumference of the circle is given by :-

[tex]C=(3.14) (19.5)=61.23\approx61.2\ cm[/tex]

Hence, the circumference of the circle = 61.2 cm

Answer:

61.2

Step-by-step explanation:

Answer:

[tex]\frac{1}{12y}[/tex]

Step-by-step explanation:

This is a multiplication problem.

We want to multiply [tex]\frac{9z^3}{16xy}\cdot \frac{4x}{27z^3}[/tex]

We factor to get:

[tex]\frac{9z^3}{4\times 4xy}\cdot \frac{4x}{9\times 3z^3}[/tex]

We now cancel out the common factors to get:

[tex]\frac{1}{4\times y}\cdot \frac{1}{1\times 3}[/tex]

We now multiply the numerators and the denominators separately to get.

This simplifies to [tex]\frac{1}{12y}[/tex]

Therefore the simplified expression is [tex]\frac{1}{12y}[/tex]

Answer:

see explanation

Step-by-step explanation:

Since the denominators of both fractions are common

Add the numerators leaving the denominator

= [tex]\frac{8g^2+8-4g^2-2}{h^2-3}[/tex]

= [tex]\frac{4g^2+6}{h^2-3}[/tex]

Answer:

A survey shows that the probability that an employee gets placed in a suitable job is 0.65.

So, the probability he is in the wrong job is 0.35.

The test has an accuracy rate of 70%.

So, the probability that the test is inaccurate is 0.3. 

Thus, the probability that someone is in the right job and the test predicts it wrong is [tex]0.65\times0.3=0.195[/tex]

The probability that someone is in the wrong job and the test is right is [tex]0.35\times0.7=0.245[/tex]

Answer:

.105

Step-by-step explanation:

The probability that he is in the right job is 0.65, so the probability he is in the wrong job is 0.35, and similarly, the probability that the test is inaccurate is 0.3.  Thus, the probability that someone is in the right job and the test is then wrong is 0.65*0.3=.195, and the probability that someone is in the wrong job and the test is wrong is 0.35*.3=.105.

Answer:

The tower is approximately 381 feet high.

Step-by-step explanation:

Refer to the sketch attached. The height of the tower can be found in two parts:

Each part can be seen as a leg of a right triangle. The other leg is the distance between the building and the tower and is 300-feet long. The angle opposite to the leg is given.

The height of the tower is the sum of the two parts:

[tex]300\cdot \sin{42^{\circ}} + 300\cdot \sin{37^{\circ}} = 300(\sin{42^{\circ}}+\sin{37^{\circ}}) = 381[/tex] feet.

To calculate the height the radio tower, trigonometry is used. The 'tangent' function is employed twice, once each for the angle of elevation and the angle of depression, to find out the distances to the top and bottom of the tower respectively, which are added together to get the total height.

There are two triangles formed in this problem, one from the observer's line of sight upwards to the top of the radio tower and one downwards to the bottom of the tower. The radio tower is the side that the two triangles share.

We can find the distance to the top and to the bottom of the tower separately using trigonometry, which is based on understanding of angle of elevation and angle of depression.

The height to the top of the tower can be found using the tangent of the angle of elevation (42°), which is the opposite side (height of the tower) divided by the adjacent side (distance from the tower):
height_to_top = tan(42°) * 300 feet.

The height to the bottom of the tower can be found using the tangent of the angle of depression (37°):
height_to_bottom = tan(37°) * 300 feet.

So, the overall height of the radio tower is the sum of these two heights.

https://brainly.com/question/31896723

#SPJ3

Answer:

120

Step-by-step explanation:

Slope = rise / run

1/20 = 6 / run

run = 120

Answer:

y = -3 + 6ˣ

Step-by-step explanation:

-3 is the lowest it goes, and the more you increase the base, the more it its stretch will become. Now, although it passes through -2, we are not dealing with y-intercept here because this is NOT a linear function. This is called a horizontal asymptote. This is an exponential function, from the parent function of y = abˣ, if I can recall correctly. Anyway, you understand?

Answer:

171 tons of plastic and 835 tons of aluminium was recycled

Step-by-step explanation:

So with the amount they recycle, it is a ratio of 5:1

Add those two together gives the number in which you divide 1026. 5 + 1 = 6

Now divide 1026 by 6.

1026 : 6 = 171

As there is five time more aluminium recycled than plastic, times 171 by 5. 171 * 5 = 835

Aluminium is easy. 171 tons of it.

Answer:

171 tons of plastic and 835 tons of aluminium was recycled

Step-by-step explanation:

Answer:

she is wrong, LMN is not a right triangle.

Answer:

lydias assertion is not correct

Step-by-step explanation:

Points to remember

Distance formula

Length of a line segment with end points (x1, y1) and (x2, y2) is given by,

Distance = √[(x2 - x1)² + (y2 - y1)²]

It is given that,  triangle LMN at the coordinates L (0, 0), M(2, 2) and N(2, -1).

To find the side lengths of triangle LMN

By using distance formula,

LM = √[(2 - 0)² + (2 - 0)²]

 =√[4 + 4]

 = √8

MN = √[(2 - 2)² + (-1 - 2)²]

 =√[0 + 9]

 = √9 = 3

LN = √[(2 - 0)² + (-1 - 0)²]

 =√[4 + 1]

 = √5

To check ΔLMN is right triangle

LN < LM <MN

LN² + LM² = (√5)² + (√8)² = 13

MN² = 3² = 9

Therefore LN² + LM²  ≠ MN²

lydias assertion is not correct

Step-by-step explanation:

Answer is B but what kind of question is this? You don't even have to find the equation just find which one is different from the others.

A) y+2 = 4x-4

y = 4x-6

B)y-2 = 4x+4

y= 4x+6

C)y = 4x-6 (same with A )

D)y-6 = 4x-12

y= 4x-6 (Same with A and C)

So b is the different one.

Answer:

t = [tex]\frac{d}{r}[/tex]

Step-by-step explanation:

Given

d = rt , or

rt = d ( solve for t by dividing both sides by r )

t = [tex]\frac{d}{r}[/tex]

Answer:

Can confirm that the correct answer is t=d/r

Step-by-step explanation:

hope u have a nice day

Answer:

Option A

Step-by-step explanation:

Given

[tex]x^2-x[/tex]

We know that the formula is:

[tex]a^2-2ab-b^2[/tex]

The middle term is:

x which should be equal to 2ab. So,

[tex]x = 2ab\\x = 2*x*b\\x/2x = b\\1/2 = b[/tex]

So we know now that we will add (1/2)^2 = 1/4 in the given expression to complete the square as the last term is square in the formula.

The expression will become:

[tex]x^2-x+1/4[/tex]

Option A is correct ..

Answer:

A. (3x^2 + 1)(x + 3)

Step-by-step explanation:

3x3 + 9x2 + x + 3

I will factor by grouping

Factor out a 3x^2 from the first two terms

3x^2 (x+3) + (x+3)

Then factor out an x+3

(x+3)(3x^2+1)

Answer:

a or d

Step-by-step explanation: