If m∠APW = 20°, then the measure of ∠WPZ is

20

70

90

160

To solve for x in 5x² - 34x = -24, set the equation to equal 0, factor the equation, and find the possible values for x. In this case, the solutions are x = 6/5 and x = 4.

This is a problem in algebra, more specifically quadratic equations. To solve for x in the equation 5x² - 34x = -24, you first need to set the equation to equal zero: 5x² – 34x + 24 = 0.

Next you can factor the equation to find the possible values for x. In this case, the factored form is 5x² - 20x - 14x + 24 = 0 which further simplifies to 5x(x - 4) - 6(x - 4) = 0, and then (5x - 6)(x - 4) = 0.

When you set each factor equal to zero, you find the possible solutions for x. From 5x - 6 = 0, x = 6/5; and from x - 4 = 0, x = 4. Therefore the solutions are x = 6/5 and x = 4.

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Answer:

x=3

Step-by-step explanation:

volume = l x w x h

1568 /8 = 196

sqrt(196) = 14

 each side is 14 feet

Answer with Step-by-step explanation:

A fish tank is in the shape of cuboid.

It's height is 8 feet

and volume=1568 cubic feet

we know that volume of cuboid=lbh

where l is the length, b is the width and h is the height

The base of the tank is square

i.e. l=b

Volume=l²h

⇒ 1568=l²×8

⇒ l²=196

⇒ l=14

Hence, The length of base of tank=14 feet

width of tank=14 feet

and height=8 feet

The ratio of men to class is 0.41.

We have a class of 10 men and 14 women.

We have to find out what is the ratio of men to the class.

Yes, a : b is same as [tex]\frac{a}{b}[/tex]. Here, ' a ' is called Antecedent and ' b ' is called Consequent.

In the question given -

Total number of men in the class , n(m) = 10

Total number of students in class, n(c) = 24

Ratio of men to class = [tex]\frac{n(m)}{n(c)}[/tex] = [tex]\frac{10}{24}[/tex] = 0.41

Hence, the ratio of men to class is 0.41.

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Final answer:

The ratio of men to the entire class of 10 men and 14 women is 5:12, simplified by dividing the numbers of men and total students by the greatest common divisor.

Explanation:

The question asks to find the ratio of men to the entire class. The class has a total of 10 men and 14 women, which means the class size is 10 (men) + 14 (women) = 24 students.

To calculate the ratio of men to the entire class, divide the number of men by the total number of students: Ratio = 10 (men) / 24 (students). This can be simplified by dividing both numbers by the greatest common divisor, which is 2, giving us a simplified ratio of 5 (men) to 12 (students).

The ratio of men to the class is therefore 5:12.

The length of AM is:

                                21 units.

Point M is the midpoint of AB.

AM= 3x+3, and AB=8x−6

Since, the midpoint divides the line segment into two equal parts i.e. it bisects the line segment.

Hence, we have:

                         AM+MB=AB

Also, AM=MB

Hence, we have:

     [tex]3x+3+3x+3=8x-6[/tex]

on combining the like terms in the left hand side of the equation we have:

[tex]3x+3x+3+3=8x-6\\\\6x+6=8x-6[/tex]

Now, on subtracting both side of the equation by 6x we have:

[tex]6=8x-6-6x\\\\6=8x-6x-6\\\\6=2x-6[/tex]

on adding 6 on both side of the equation we have:

[tex]6+6=2x\\\\12=2x\\\\2x=12\\\\x=\dfrac{12}{2}\\\\x=6[/tex]

Hence, we have:

[tex]AM=3\times 6+3\\\\AM=21\ \text{units}[/tex]

Answer:

Factor of [tex]64-x^{15}[/tex] is [tex](4-x^{5})(16+4x^{5}+x^{10})[/tex]

Step-by-step explanation:

We need to factor the expression [tex]64-x^{15}[/tex]

Re-write the given expression  [tex]64-x^{15}[/tex] as;

[tex]4^{3}-(x^{5})^{3}[/tex]

Since, [tex]a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})[/tex]

so, here [tex]a = 4[/tex] and [tex]b = x^{5}[/tex]

[tex](4-x^{5})(4^{2}+4x^{5}+(x^{5})^{2})[/tex]

[tex](4-x^{5})(16+4x^{5}+x^{10})[/tex]

Hence, factor of  [tex]64-x^{15}[/tex] is

[tex](4-x^{5})(16+4x^{5}+x^{10})[/tex]

The value of factor of expression 64 - x¹⁵ is,

⇒ (4 - x⁵) (16 + 4x⁵ + x¹⁰)

We have to given that;

To factor the expression,

⇒ 64 - x¹⁵

Now, We can simplify as;

⇒ 64 - x¹⁵

⇒ 4³ - (x⁵)³

⇒ (4 - x⁵) (4² + 4x⁵ + (x⁵)²)

⇒ (4 - x⁵) (16 + 4x⁵ + x¹⁰)

Therefore, The value of factor of expression 64 - x¹⁵ is,

⇒ (4 - x⁵) (16 + 4x⁵ + x¹⁰)

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Charli,

First find what 1/4 of 2/3 is.

1/4 of 2/3 = 1/6

(That is 1/4 times 2/3 = 1/6)

So, the bottle was 2/3 full, it is now ...

2/3 - 1/6

=4/6 - 1/6

= 3/6 or 1/2 full.

We know that the bottle of soft drink has a remaining volume which is 2 / 3 of the original.

Since Jack drank 1 / 4 of the remaining volume, hence only 3 / 4 now finally remains, the total is:

(2 / 3) * (3 / 4) = 6 / 12 = 1 / 2

Hence the bottle is now one half full

Answer:

[tex]2.99x+12.99y=43.92[/tex]

Step-by-step explanation:

Hanna shops for socks that cost $2.99 for each pair.

And blouses that cost $12.99 each.

Let x represent the number of pairs of socks purchased.

Let y represent the number of blouses purchased.

So, the cost for x socks will be [tex]2.99x[/tex]

And cost of y blouses will be [tex]12.99y[/tex]

Total amount spent by Hanna = $43.92

So, the equation that will model this situation will be:

[tex]2.99x+12.99y=43.92[/tex]

The option that represents cos M is MN / MO

Using trigonometric ratios, we can find the ratio of sides of a right angle triangle.

Therefore,

cos M = adjacent / hypotenuse

cos M = MN / 0M

Therefore, cos M = MN / MO

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Answer:

About 7 hours per person

Step-by-step explanation:

412 divided by 60 because there are 60 minutes in an hour.

6.8667 which is about 7 hours.

The each member will take 7 hours.

The formula of the unitary method is to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value

Given:

total member = 6 member

Each flower take = 412 minutes

we know

1 hour= 60 minutes

So, each member will have

=412/60

=6.866

=7 hours

Hence, each member will work for 7 hours

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we will proceed to resolve each case to determine the solution

we have

[tex]2x+y>-4[/tex]

[tex]y>-2x-4[/tex]

we know that

If an ordered pair is the solution of the inequality, then it must satisfy the inequality.

case a) [tex](5,-12)[/tex]

Substitute the value of x and y in the inequality

[tex]-12>-2*5-4[/tex]

[tex]-12>-14[/tex] ------> is True

therefore

the ordered pair [tex](5,-12)[/tex] is a solution of the inequality

case b) [tex](-3,0)[/tex]

Substitute the value of x and y in the inequality

[tex]0>-2*-3-4[/tex]

[tex]0>2[/tex] ------> is False

therefore

the ordered pair [tex](-3,0)[/tex] is not a solution of the inequality

case c) [tex](-1,-1)[/tex]

Substitute the value of x and y in the inequality

[tex]-1>-2*-1-4[/tex]

[tex]-1>-2[/tex] ------> is True

therefore

the ordered pair[tex](-1,-1)[/tex] is a solution of the inequality

case d) [tex](0,1)[/tex]

Substitute the value of x and y in the inequality

[tex]1>-2*0-4[/tex]

[tex]1>-4[/tex] ------> is True

therefore

the ordered pair [tex](0,1)[/tex] is a solution of the inequality

case e) [tex](4,-12)[/tex]

Substitute the value of x and y in the inequality

[tex]-12>-2*4-4[/tex]

[tex]-12>-12[/tex] ------> is False

therefore

the ordered pair [tex](4,-12)[/tex] is not a solution of the inequality

Verify

using a graphing tool

see the attached figure

the solution is the shaded  area above the line

The points A,C, and D lies on the shaded area, therefore the ordered pairs A,C, and D are solution of the inequality

Answer:

The value of the index at the end of the day is $45392.6.

Step-by-step explanation:

Given : A simple index of three stocks opens the day with these values:

[name]  [number of shares] [price per share]

stock x      5000 shares            $4.10

stock Y      2000 shares           $4.50

stock z      4000 shares            $3.60

The index rises 3.4% over the course of the day.

To find : What is the value of the index at the end of the day? Round your answer to the nearest hundred ?

Solution :

Stock values of x,y and z is given by,

Stock x,

[tex]5000\times 4.10=\$20500[/tex]

Stock y,

[tex]2000\times 4.50=\$9000[/tex]

Stock z,

[tex]4000\times 3.60=\$14400[/tex]

The total amount will be

[tex]A=20500+9000+14400[/tex]

[tex]A=\$43900[/tex]

The index rises 3.4% over the course of the day.

The value of the index at the end of the day is

[tex]V=43900 \times (1+3.4\%)\\V=43900 \times (1+0.034)\\V=43900 \times 1.034\\V= 45392.6[/tex]

Therefore, the value of the index at the end of the day is $45392.6.

As per the slope of a line, the value of 'b' is 4.

The slope of a line(m) passing through two points (x₁, y₁) and (x₂, y₂)can be represented as:

m = (y₂ - y₁)/(x₂ - x₁)

Given, the slope of the line is (m) = 0.

Here the given points are  (–2, 4) and (3, b).

Therefore, substituting the values, we get:

0 = (b - 4)/[(3 - (- 2)]

⇒  (b - 4)/5 = 0

⇒ b - 4 = 0

⇒ b = 4

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Answer:  The co-ordinates of the image H' are (-7, 6).

Step-by-step explanation:  Given that the rectangle EFGH is translated according to the following rule :

[tex]T_{-5,9}(x,y).[/tex]

We are to find the co-ordinates of the image H' if the co-ordinates of the pre-image H are (-2, -3).

We know that

[tex]T_{h,k}(x,y)=(x+h,y+k).[/tex]

For the given information, we have

(h, k) = (-5, 9)      ⇒ h = -5  and  k = 9.

Therefore, we get

[tex]T_{-5,9}(-2,-3)=(-2-5,-3+9)=(-7,6).[/tex]

Thus, the co-ordinates of the image H' are (-7, 6).

To find the answer the question first write it out. 3*x-5=40. move the five over next to the 40 and cancel out -5. so the new equation looks like this. Then add 40+5 which is 45.Lastly you have the number 3 and the variable x. now you have to divide 3 by 45 to get your final answer 15. so x=15.

                                                                            3*x=40+5

                                                                            3*x=45

Hope this helps!!

Answer:

Option A is correct

The value of (h ∘ g)(−5) is, 104

Step-by-step explanation:

Given the functions:

g(x) = 2x

[tex]h(x) = x^2 + 4[/tex]

We have to find (h ∘ g)(−5).

[tex](h o g)(-5) = h(g(-5))[/tex]          ....[1]

At x = -5

g(-5) = 2(-5) = -10

then

Substitute the g(-5) in [1] we have;

[tex](h o g)(-5) = h(-10)[/tex]

⇒[tex](h o g)(-5) = (-10)^2+4 = 100+4 = 104[/tex]

⇒[tex](h o g)(-5) = 104[/tex]

therefore, the value of (h ∘ g)(−5) is, 104

multiply 300.5 feet by -0.2 mph

300.5 * -0.2 = -60.1 change

→A = (-5,1)

A' = (4,3)

 so x moved from -5 to 4 which is an increase of 9

so x+9

 y moved from 1 to 3 which is an increase of 2

 so y+2

so answer should be:

(x,y) → (x+9,y+2)

Answer:

The given triangle is possible.

Step-by-step explanation:

Given, the measurement of triangle ABC are,

∠ B = 153°, c = 10, b = 14,

By the law of sine,

[tex]\frac{sin C}{c}=\frac{sin B}{b}[/tex]

By cross multiplication,

[tex]sin C = \frac{c\times sin B}{b}[/tex]  

By substituting the values,

[tex]sin C=\frac{10\times sin 153^{\circ}}{14}[/tex]

[tex]sin C=0.324278928386[/tex]

[tex]\implies \angle C=18.9218948147\approx 18.922^{\circ}[/tex]

Since, with help of sin law we found the measurement of the unknown angle of the triangle.

Hence, the given triangle is possible.

Answer:

C = 18.9°, A = 8.1°, a ≈ 4.3