Mathematics College

4z - 7 in terms of z

Answers

Answer 1
The expression is already in terms of z. Nothing need be done.

Related Questions

What is the equation for the vertical asymptote of f(x)= (x+2)/(4x+4)

Answers

Try this option:
if   [tex]f(x)= \frac{x+2}{4x+4} [/tex]
then according to 
[tex] \lim_{x \to (-1-0)} ( \frac{x+2}{4x+4})=+ \infty[/tex]
and [tex]\lim_{x \to (-1+0)} ( \frac{x+2}{4x+4})=- \infty[/tex]
an equation for vertical asymptote is x=-1.
The graph of this function is in the attached picture.

The sum of the reciprocals of two consecutive even integers is 7/24. Write an equation that can be used to find the two integers. Find the two integers.

Answers

Assume the first even integer is x.
The next even integer will be 2 digits after this digit. So the next even integer will be x+2.

The reciprocals of these two even integers can be written as [tex] \frac{1}{x} [/tex] and [tex] \frac{1}{x+2} [/tex] respectively.

The sum of their reciprocals is 7/24. So we can set up the equation as:

[tex] \frac{1}{x}+ \frac{1}{x+2}= \frac{7}{24} [/tex]

Taking LCM on left hand side:

[tex] \frac{x+2+x}{x(x+2)}= \frac{7}{24} \\ \\ \frac{2x+2}{ x^{2} +2x}= \frac{7}{24} [/tex]

Cross Multiplying the denominators:

[tex]24(2x+2)=7({ x^{2} +2x}) \\ \\ 48x+48=7 x^{2} +14x \\ \\ 7 x^{2} +14x-48x-48=0 \\ \\ 7 x^{2} -34x-48=0 \\ \\ [/tex]

Using the quadratic formula to solve the above equation:
[tex]7 x^{2} -34x-48=0 \\ \\ x= \frac{34+- \sqrt{1156+1344} }{14} \\ \\ x= \frac{34+- \sqrt{2500} }{14} \\ \\ x=\frac{34+-50 }{14} \\ \\ x=6 \\ x=- \frac{8}{7} [/tex]

Since, the value of x can only be an integer, we discard the fractional value and keep x=6

So the first even integer is 6 and the next even integer is 8. The sum of reciprocals of 6 and 8 is 7/24

If an object is projected upward with an initial velocity of 125 125 ft per​ sec, its height h after t seconds is h equals negative 16 t squared plus 125 t h=−16t2+125t. Find the height of the object after 5 5 seconds.

Answers

for this problem all we need to do is ignore everything except the equation and the input (5.5)

so the steps for this problem are below
we need to plug in 5.5 into our equation as it's our input of time to get our output of height
[tex]t(5.5) = - 16(5.5) {}^{2} + 125(5.5)[/tex]
after simplifying you get

remember to square the 5.5 first (order of operations)

[tex]t(5.5) = - 16(30.25) + 687.5[/tex]

simplify just a tad more and we get this as the final answer
[tex]t(5.5) = - 484 + 687.5 = 203.5[/tex]
[tex]203.5 \: ft[/tex]

244 ft I’m pretty sure

Algebra Functions and Data Analysis

Answers

Hello there!


The correct answer is option C (-∞,10)

Best of luck with your study!

There are 1,505 fruits for sale at at farmer’s market. 39% of them are apples, 28% are oranges, 13% are honeydrew melons, and the rest are watermelons. How many watermelons are there ?

Answers

100% - (39% + 28% + 13%) = 100% - 80% = 20%
so 20% are watermelons.

20% of 1505...
0.20(1505) = 301

so 301 are watermelons

Answer:

13

Step-by-step explanation:

Does 3pi/5 have a supplementary angle?

Answers

If two angles are supplementary, then their measures add to 180 deg.
Since 180 deg = pi rad, then supplementary angles are two angles whose measures add to pi rad.

Since 3pi/5 is less than 1 rad, then there is an angle that is supplementary to an angle measuring 3pi/5. The measure of the supplement is 2pi/5.

For which set of lines is it reasonable to state that The two lines are ALMOST perpendicular to each other? A) y = 2.1x + 3, y = 2.1x + 5 B) y = 0.9x + 5, y = -1.26x + 8 C) y = 5x + 1.25, y = -5x + 1.25 D) y = 3 4 x + 0.28, y = 4 3 x + 0.29

Answers

Selection B is the best.

The product of the slopes of the lines is closest to -1 for that pair of lines.

if y = 6x - 3 which of the following see represents possible inputs and outputs of the function represented as ordered pairs

Answers

If it’s giving you a chart you’ll have to use the inputs which are the x and then simplify each number and it will give you the answer of your outout
y = 6x - 3
 For this case, the first thing we can do is write a table with the input and output values of the function.
 Take an example in the interval from x = 0 to x = 5.
 We have then:
 x    y
 0   -3
 1    3
 2    9
 3    15
 4    21
 5    27

 We now represent the inputs and outputs as ordered pairs:
 (0, -3)
 (1,3)
 (2,9)
 (3,15)
 (4,21)
 (5,27)
 Answer:
 the following is represented possible inputs and outputs of the function represented as ordered pairs

 (0, -3)
 (1,3)
 (2,9)
 (3,15)
 (4,21)
 (5,27)

×
[tex] \frac{x}{4} = \frac{6}{12} [/tex] solve the proportions

Answers

To solve a problem like this, you can use a method called cross-multiplying. This is when you multiply the denominator of the first fraction by the numerator of the other and then multiply the two remaining numbers.

[tex] \frac{x}{4} = \frac{6}{12} [/tex]  To make this easier on yourself, simplify first!
[tex] \frac{x}{4} = \frac{1}{2} [/tex]   Multiply x by 2 and multiply 4 by 1.
2x = 4   Divide both sides by 2.
x = 2

You can check this by comparing the fractions with 2 in the place of x.

[tex] \frac{2}{4} = \frac{6}{12} [/tex]   Simplify!
[tex] \frac{1}{2} = \frac{1}{2} [/tex]

The fractions are equal, so x = 2 .

How do you solve 7.2>0.9(n+8.6)

Answers

7.2>0.9(n+8.6)
multiply 0.9 by all in parentheses

7.2> (0.9*n) + (0.9*8.6)
7.2> 0.9n + 7.74

subtract 7.74 from both sides
-0.54> 0.9n

divide both sides by 0.9
-0.6> n

ANSWER: -0.6> n

Hope this helps! :)

After solving the given equation, the value obtained for n will be equal to n < -0.6.

What is an equation?

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the equation given in the question,

7.2 > 0.9(n + 8.6)

Solve the equation for n,

7.2 > 0.9n + 7.74

7.2 - 7.74 > 0.9n

-0.54/0.9 > n

-0.6 > n or,

n < -0.6

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Solve for x: x^4 = 3^x

Answers

There are no algebraic methods for finding solutions to a general mix of exponential and polynomial terms. A graphing calculator can be helpful.

This equation has 3 real solutions, approximately ...
  x ∈ {-0.802246431546, 1.51677641228, 7.17475582739}

_____
In the folder "iteration for solutions" is an equation for Newton's method iteration, essentially, ...
  g(x) = x -f(x)/f'(x)
where f(x) is defined as shown in the picture.

Many graphing calculators can compute a numerical derivative, so you can essentially write the formula in this form without having to do the derivative-taking yourself. This calculator is nicely interactive, so the iteration result is produced at the same time the argument for g(x) is entered. Essentially, you write the answer by copying the answer using the 4-digit zero-crossing values shown on the graph as the iteration starting point.

What is decomposing fractions

Answers

Explanation:

"Decomposing fractions" means breaking them into a sum of fractions, often unit fractions (fractions with a numerator of 1). Here are a few examples:

  3/8 = 1/8 + 1/8 + 1/8

  5/6 = 1/2 + 1/3

  3/4 = 1/2 + 1/4

what fraction would you add to 29/6 to make 4

Answers

keeping in mind that 29/6 is greater than 4, is actually 4 and 5/6, so the amount we'll "add" will be a negative one.

[tex]\bf \cfrac{29}{6}+x=4\implies x=4-\cfrac{29}{6}\implies x=\cfrac{4}{1}-\cfrac{29}{6}\implies x=\cfrac{(6)4-(1)29}{6} \\\\\\ x=\cfrac{24-29}{6}\implies x=\cfrac{-5}{6}\\\\ -------------------------------\\\\ \cfrac{29}{6}+\left( -\cfrac{5}{6} \right)=4[/tex]

Two ships leave the same port in different directions, forming a 120° angle between them. One ship travels 70 mi. and the other 52 mi. before they each drop their anchors. What is the distance between the ships to the nearest mile?

Answers

Answer : Distance between the ships to the nearest miles = 106.03 ≈ 106 mi.

Explanation :

Since we have shown in the figure below :

a=70 mi.

b=52 mi.

c=x mi.

[tex]\text{Since two ships leaves the same port in different directions forming a }120\textdegree\text{angle between them.}[/tex]

So, we use the cosine rule , which states that

 [tex]c^2=a^2+b^2-2ab.cosC\\\\x^2=70^2+52^2-2\times 70\times 52\times cos(120\textdegree)\\\\x^2=4900+2704-7280\times (-0.5)\\\\x^2=7604+3640\\\\x^2=11244\\\\x=\sqrt{11244}\\\\x=106.03[/tex]

So, c = x= 106.03 mi.

Hence, distance between the ships to the nearest miles = 106.03 ≈ 106 mi.


10 Points Here come get them

Answers

The answer is option D. (15°)

Two angles are said to be supplementary when both angles together make a straight line. Since the measure of a straight line is 180°, it then follows that the sum of two supplementary angle is 180°

Let the unknown angle = x
x is supplementary to 165°
⇒ x + 165° = 180°
x = 180° - 165°
x = 15°
The answer to this is d. 15. 

Supplementary angles are two angles that equal to 180. So you take the known angle (165) and subtract it from 180 to find the other angle measure.

180-165=15

15 is your answer. 

Which term is the perfect square of 3x4 ?

Answers

A perfect square is the product when a number is multiplied to itself. Hence,the square of (3x4) is (3 x 4 x 3 x 4). We can rearrange this and have (3 x 3) x (4 x 4) which gives you 9 x 16. We now have the perfect square of (3x4) re-written as (9 x 16). Thus, the answer is: 9 x 16.

Hope it helps m8!

Answer:

just took the test answer is D

Step-by-step explanation:

152.5225 to two decimal places

Answers

152.52 is your Answer
If you want 152.5225 2 decimal places to the left:
1.525225
If you want 152.5225 2 decimal places to the right:
15252.25

Hope this helps..... ;)

What does x equal (x/4)+12=38

Answers

[tex] \frac{x}{4} +12=38\\\\ \frac{x}{4}=26\\\\x=104[/tex]
x/4 = 26
X = 104
I think that’s it....

Twenty, which is 4 more than half, of the students in Bryan’s homeroom have tickets to attend the school’s musical. Choose Yes or No to tell whether each of the following equations can be used to find the number of students in Bryan’s homeroom.

Answers

One possible equation would be 20 = 1/2x + 4.

Let x be the number of students in his homeroom.  1/2x is half of the students in his homeroom.  Four more than 1/2 would be 1/2x + 4.  This is, or equals, the 20 students that have tickets.

The equations that can be used to find students with tickets is given as m/2 + 4 = 20. The correct options are (B) and (D).

How to write a linear equation?

A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.

Suppose the number of students in homeroom be m.

Then, as per the question the equation can be written as,

m/2 + 4 = 20

It can also be written as,

4 = 20 - m/2

Hence, the required equation for the given case is m/2 + 4 = 20.

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The complete question with all the options is attached here.

Can I have help with this please?

Answers

Try this:

2. 2.5/5=16/32; 2/4=16/34.

3. one - 6;6;6; two - 6;8;10; three - 5;10;12.

NAME_____________________________________DATE_________________PER._______
TRAPEZOIDS
RSTV is an isosceles trapezoid. Decide whether each statement is TRUE or FALSE.
Justify your answer.

1. TRUE or FALSE
Why?
TR ⊥ SV

2. TRUE or FALSE
Why?
∠RVT ≅ ∠STV

3. TRUE or FALSE
Why?
∠SRV & ∠TVR are
supplementary.

WXYZ is an isosceles trapezoid with bases WZ and XY and median MN. Use the given
information to solve each problem.
4. MN = ____________ Find MN if WZ = 11 and XY = 3.

5. m∠XMN = ____________ Find m∠XMN if m∠WZN = 78°.

6. XY = ____________ If MN = 10 and WZ = 14, find XY.

7. x = ____________ What is the value of ‘x’ if m∠MWZ = (15x –5)° and m∠WZN = (90 – 4x)°?

8. x = ____________ If m∠XWZ = (2x – 7)° and m∠XYZ = 117°, find
the value of ‘x’.

9. x = ____________ If MN = 60, XY = 4x – 1, and WZ = 6x + 11, find
the value of ‘x’.

10. x = ____________ If MN = 10x + 3, WZ = 11, and XY = 8x + 19,
find the value of ‘x’.

11. x = ____________ If MN = 2x + 1, XY = 8, and WZ = 3x – 3, find
the value of ‘x’.

Can someone do this for me? im having a hard time and I have a 42 in math rn and I just need these done cause they are late.. if anyone likes geometry then here you go

Answers

1. False
2. True
3. True
4. I believe the answer is 7

Answer:NAME:     Nzube Erobu        DATE: 02/ 06 / 2020

Step-by-step explanation: With reference to the attached document, below:

1) False, the lines linking between TR and SV are diagonals

2) True,  ∠RVT = ∠ STV because they have the same right angled triangles.

3) True, because they separate triangles that have all angles in each triangle summing up to 180°  

4) (11 + 3)/2 = 14/2= 7

7) (15x - 5)° + (90 - 4x)° = 180°

(15x - 4x + 90 - 5)° = 180°

( x + 85)° = 180°

∴ x = 180° - 85° = 95°

8) (2x - 7)° + 117° = 180°

2x° +117° - 7° = 180°

2x° + 110° = 180°

2x = 180° - 110°

∴ x = 70°/2 = 35°

9) 4x - 1 + 6x + 11 = 60

4x + 6x + 11 -1 = 60

10x + 10 = 60

10x = 60 - 10 = 50

∴ x = 50/10 = 5

10) 18x + 19 - (10x + 3)  = 11

       18x - 10x + 19 - 3 = 11

8x + 16 = 11

8x = 11 - 16 = - 5

∴ x = - 5/8

11) 2x + 1 + 3x - 3 = 8

2x + 3x  - 3 + 1 = 8

5x - 2 = 8

5x = 8 + 2= 10

∴ x = 10/5 = 2

Your cousin has a goat in his backyard, tied with a 4 foot rope. The goat can move in a circular motion the length of the rope. What is the area of the backyard where his goat can eat the grass? Hint: The 4 foot rope represents the radius of the circle.
1. What equation can be used to calculate the area of the yard that his goat can eat the grass?
2. What is the area of this circle in your cousin’s backyard?
3. What would the new area be if he decides to use a 5 foot rope?

Answers

The stake the rope is tied to is the center of the circle. If the goat pulls the rope as far as it can go and walks around like this he makes a circle and he can eat the grass anywhere within this circle.

(a) Since the area of a circle is given by [tex]A= \pi r^{2} [/tex] this is the formula we can use to find the area of the yard where the goat can roam/eat/reach.

(b) Since the rope is 4 feet the radius r = 4 and the area is given by [tex] 4^{2} \pi =16 \pi ^{2} [/tex] square feet. That's the exact area. For an approximation you could substitute 3.14 for pi and get 50.24 square feet.

(c)Since the rope is 5 feet the radius r = 4 and the area is given by [tex]5^{2} \pi =25 \pi ^{2}[/tex] square feet. That's the exact area. For an approximation you could substitute 3.14 for pi and get 78.5 square feet.

Which of the following is equivalent to the expression below?

(8x + 10) + (13 - 8x)

A.
3
B.
8x + 23
C.
16x + 23
D.
23

Answers

= x(8 -8) +(10 +13)
= 0 +23
= 23

Selection D is appropriate.

What is the value of the leading coefficient a if the polynomial function P(x) = a(x + b)2(x − c) has multiplicity of 2 at the point (−3, 0) and also passes through the points (2, 0) and (0, 36)?
answers:
−2−3336

Answers

The polynomial is of the form:

[tex]P(x)=a (x+b)^{2}(x-c) [/tex]

We are provided with the two zeros in the question statement. The zero with multiplicity 2 is -3, and zero with multiplicity 1 is 2. So using these values, the polynomial becomes:

[tex]P(x)=a (x+3)^{2}(x-2) [/tex]

The polynomial also passes from the point (0,36). This mean if we substitute x=0, the answer should be 36.

[tex]P(0)=36=a (0+3)^{2}(0-2) \\ \\ 36=a(9)(-2) \\ \\ 36=-18a \\ \\ a=-2 [/tex]

Thus the value of a for given polynomial will be -2. The complete equation of polynomial will be:

[tex]P(x)=-2 (x+3)^{2}(x-2)[/tex]

Two mechanics can assemble 10 bicycles in 8 hours. How many bicycles could one mechanic assemble in 8 hours?

Answers

Answer:

5 bicycles

Step-by-step explanation:

In the same time period (8 hours), half as many mechanics can assemble half as many bicyles: 10/2 = 5.

How to find the x intercepts of f(x)=-2x^2+x+5

Answers

Completing the square, you have
.. -2(x^2 -x/2) +5 = 0
.. -2(x^2 -x/2 +1/16) = -5 -1/8 . . . . . add -2*(1/16)
.. (x -1/4)^2 = 2 9/16 . . . . . . . . . . . . divide by -2
.. x = (1 ±√41)/4 . . . . . . . . . . . . . . . .take the square root, add 1/4
.. x ∈ {-1.35078, 1.85072}

PLEASEEEEE HEEEEEELPPPPPPPPPPPPPPP

Suppose ABCD is a rhombus such that the angle bisector of ∠ABD meets AD at point K. Prove that m∠AKB = 3m∠ABK.

Answers

1. Let m∠ABK=x°. Since line BK bisects ∠ABD, then

m∠ABK=m∠KBD=x°.

Also m∠ABD=m∠ABK+m∠KBD=2x°.

2. The diagonal BD of rhombus ABCD bisects ∠ABC, then

m∠ABD=m∠DBC=2x°.

This gives you that

m∠ABC=4x°.

3. Angles A and B are supplementary, so

m∠A+m∠B=180°,

m∠A=180°-4x°.

4. Consider triangle ABK. The sum of the measures of interior angles in triangle is always 180°, thus

m∠A+m∠ABK+m∠AKB=180°,

m∠AKB=180°-x°-(180°-4x°),

m∠AKB=3x°=3m∠ABK.

Answer:

Given information: ABCD is a rhombus, angle bisector of ∠ABD meets AD at point K.

[tex]\angle ABK\cong \angle DBK[/tex]         (Definition of angle bisector)

[tex]m\angle ABK=m\angle DBK[/tex]          (Definition of concurrency)

Let as assume the measure of angle ABK is x.

[tex]m\angle ABK=x[/tex]

[tex]m\angle ABD=m\angle ABK+m\angle DBK[/tex]

[tex]m\angle ABD=x+x[/tex]

[tex]m\angle ABD=2x[/tex]

All sides of a rhombus are same.

Since AB=AD, therefore ABD is an isosceles triangle and two angles of an isosceles triangle are congruent.

[tex]m\angle ADB=m\angle ABD[/tex]

[tex]m\angle ADB=2x[/tex]

According to exterior angle theorem, sum of two interior angles of a triangle is equal to third exterior angle.

Using exterior angle theorem, we get

[tex]m\angle AKB=m\angle ADB+m\angle DBK[/tex]

[tex]m\angle AKB=2x+x[/tex]

[tex]m\angle AKB=3x[/tex]

[tex]m\angle AKB=3(m\angle ABK)[/tex]

Hence proved.

f(x)=x^2-2x-1  and   g(x)=5x-1/7x-3

find f(x+7) and g(x/2)

Answers

f(x + 7)
(x + 7)² - 2(x + 7) - 1
x² + 14x + 49 - 2x - 14 - 1
x² + 12x + 49 - 15
x² + 12x + 34
f(x + 7) = x² + 12x + 34

g(x/2)
5(x/2)² - 1/7(x/2) - 3
5(x²/4) - x/14 - 3
5x²/4 - x/14 - 3
g(x/2) = 5x²/4 - x/14 - 3

A total of
276

tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold?

Answers

Final answer:

The number of adult tickets sold for the school play was 92, found by setting up an equation where the number of adult tickets plus twice the number of adult tickets equals the total of 276 tickets sold.

Explanation:

Calculating the Number of Adult Tickets Sold

The student is asked to find out how many adult tickets were sold for the school play, given that a total of 276 tickets were sold and the number of student tickets was two times the number of adult tickets sold. Let's denote the number of adult tickets as x and the number of student tickets as 2x. The total number of tickets is the sum of adult and student tickets which can be represented as:

x + 2x = 276

Combining like terms, we get:

3x = 276

To find the value of x, we divide both sides by 3:

x = 276 / 3

x = 92

Therefore, the number of adult tickets sold was 92.

What value is equivalent to ∣ −14 ∣?

Answers

It is positive 14
The absolute value of any negative number becomes positive.
Your answer is 14

The two lines on each sides mean the number is an absolute value. The absolute value of a number is always positive, even if the number is positive itself!

Hope this helps!
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