=======================================================
If a < 7, then |a-7| = -(a-7) = -a+7 based on how absolute value functions are constructed. We're using the idea that
[tex]|x-k| = \begin{cases}x-k \ \text{ if } \ x \ge k\\ -(x-k) \ \text{ if } \ x < k\end{cases}[/tex]
Also, if a < 7, then |a-9| = -(a-9) = -a+9. This is true whenever 'a' is less than 9 for similar reasoning as above.
---------
So we have,
|a-7| - |a-9| = -a+7 - (-a+9) = -a+7+a-9 = -2
As long as a < 7, the result of |a-7| - |a-9| will always be -2.
---------
As an example, let's say a = 0
|a-7| - |a-9| = |0-7| - |0-9|
|a-7| - |a-9| = |-7| - |-9|
|a-7| - |a-9| = 7 - 9
|a-7| - |a-9| = -2
I recommend you try out other values of 'a' to see if you get -2 or not. Of course only pick values that are smaller than 7.
EMERGENCY HELP! A steady stream of water flows into a partially-filled rectangular tank. After 6 minutes, there are 87 gallons of water in the tank. After 21 minutes, there are 222 gallons. Write an equation to represent the volume of water in the tank y after x minutes. How much water was in the tank to begin?
Answer:
[tex]y=9x+33[/tex]
33 gallons of water to begin with.
Step-by-step explanation:
So, we are essentially given two coordinates: (6,87) and (21,222). To find an equation, we will need to find the slope and y-intercept. We know it's a linear equation because it's a steady stream, meaning a constant slope.
Using the slope formula, the slope is:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}=\frac{222-87}{21-6}=135/15=9[/tex]
So, the rate at which the stream flows is 9 gallons per minute.
Now, let's find the initial amount of water. To do this, we can use point-slope form. Pick either of the two points. I'm going to use (6,87).
Point-slope form is given by:
[tex]y-y_1=m(x-x_1)[/tex]
Substitute:
[tex]y-(87)=9(x-(6))[/tex]
Distribute:
[tex]y-87=9x-54[/tex]
Therefore:
[tex]y=9x+33[/tex]
So, there were 33 gallons of water in the tank to begin with.
what happens to 5/x + 5 as x decreases from a large positive number to a small positive number? does it increase, decrease, or stay the same?
Answer:
Increases
Step-by-step explanation:
It increases because, the greater the value of x the smaller the fraction is. If x was 25 the fraction would be 5/25 this makes the value of the equation 5.2. Now if x was a smaller positive number like 5. Then the fraction would be 5/5 which would cause the equation to be equal to 6.
Please answer it now in two minutes
Answer:
∠ T ≈ 23.6°
Step-by-step explanation:
Using the sine ratio in the right triangle
sin T = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{SU}{ST}[/tex] = [tex]\frac{4}{10}[/tex] , thus
∠ T = [tex]sin^{-1}[/tex] ([tex]\frac{4}{10}[/tex] ) ≈ 23.6° ( to the nearest tenth )
What is slope and how is it determined from a graph? How do you determine the intercepts from an equation or graph? How can linear equations and functions be written and graphed?
Hey there! I'm happy to help!
The slope is the steepness or incline of a line. From a graph, it is known as the rise over the run between two integer values. If you have a point at (1,1) and a point at (2,2), the rise (vertical difference) between them in 1 unit, and the run (horizontal difference) is 1 unit. 1/1 is 1, so the slope of a line that passes through these points is 1. This means that for every one unit to the right it goes, it goes one unit up.
The intercepts are where the line hits the x and y axes. By looking at a graph, you can find the y-intercept by seeing on what y-value the line intersects with the y-axis, and for the x-intercept you do so with the x-axis.
The slope-intercept equation is y=mx+b. This b is the y-intercept. To find the x-intercept, you plug in the value 0 for y and solve for x. This is because the x-axis is the line y=0, so you will see where the x is if y is equal to 0.
Linear equations and functions can be written in slope intercept form (y=mx+b), standard form (Ax+By=C), and point slope form [tex]y-y_{1} =m(x-x_{1} )[/tex].
They can be graphed by finding the y and x intercepts from the equation and then connecting the points to draw the line!
Have a wonderful day! :D
A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 higher than in the first. The tax in the first city was 4.5%, and the tax in the second city was 3.5% . The total hotel tax paid for the two cities was $317.50. How much was the hotel charge in each city before tax? First city: Second city:
Answer:
$3750 and $4250
Step-by-step explanation:
x + 500 = y
.045x + .035y = 317.50
.045x + .035(x + 500) = 317.50
.045x + .035x + 17.5 = 317.50
.08x = 300.00
x = 3750
y = 4250
An item is selling for $7,000. This item gets a discount and it is now $4,900. What percentage was the discount?
Answer:
30%Step-by-step explanation:
Discount =$7000-$4900
Discount% =
[tex] \frac{2100}{7000} \times 100 \\ = \frac{210000}{7000 } \\ = \frac{210}{7} = 30[/tex]
the product of (x+2) (x-3) is
Answer:
x[tex] {}^{2} [/tex] - x - 6Step-by-step explanation:
[tex](x + 2)(x - 3)[/tex]
Multiply each term in the first parentheses by each term in the second parentheses ( FOIL)
[tex]x(x - 3) + 2(x - 3)[/tex]
Calculate the product
[tex] {x}^{2} - 3x + 2x - 6[/tex]
Collect like terms
[tex] {x}^{2} - x - 6[/tex]
Hope this helps..
Best regards!
Answer:
Step-by-step explanation:
Given, (x+2) (x-3)
Multiply every term
(x)(x) + (2)(x) + (-3)(x) + (-3)(2)
x^2 + 2x - 3x -6
x^2 - x -6
HOPE IT HELPS :)
GOOD LUCK WITH YOUR ASSIGNMENT!
What is the solution to the system of equations graphed below?
Answer:
( 3 , -2 )Option B is the correct option.
Step-by-step explanation:
[tex]y = - 2x + 4...........(i)[/tex]
[tex]y = x - 5..........(ii)[/tex]
Equate ( i ) and ( ii ),
[tex] - 2x + 4 = x - 5[/tex]
Move variable to L.H.S and change its sign
Similarly, Move constant to R.H.S and change its sign
[tex] - 2x - x = - 5 - 4[/tex]
Calculate
[tex] - 3x = - 9[/tex]
Divide both sides of the equation by -3
[tex] \frac{ - 3x}{ - 3} = \frac{ - 9}{ - 3} [/tex]
Any expression divided by itself equals 1
[tex]x = \frac{ - 9}{ - 3} [/tex]
Dividing two negatives equals a positive [tex]( - ) \div ( - ) = ( + )[/tex]
[tex]x = \frac{9}{3} [/tex]
calculate the quotient
[tex]x = 3[/tex]
Value of X is 3
Now, put the value of X in equation ( i ) in order to find the value of y
[tex]y = x - 5[/tex]
plug the value of X
[tex] = 3 - 5[/tex]
Calculate
[tex] = - 2[/tex]
Value of y is -2
So, ( 3 , -2 ) is the solution of the given equation.
Hope this helps ....
Best regards!!
Instructions: Find the missing length indicated.
Answer:
? = 3
Step-by-step explanation:
The parallel segments shown divide the sides in the ratio
[tex]\frac{6}{4}[/tex] = [tex]\frac{?}{2}[/tex] ( cross- multiply )
4? = 12 ( divide both sides by 4 )
? = 3
HELP!!! A plumber charges a fee of $25 plus $30 per hour on the job. Make a table of values for the total charge depending on the number of hours the plumber works. Determine if this can be defined by a linear or an exponential function. What is the function? Linear: t=25+30h Linear:T=30+25h Exponential:T=30(25)^h Exponential: T=25(30)^h HELP I HAVE 10 MINS LEFT
Answer:
Yes, this function can be defined by linear model.
Step-by-step explanation:
[tex]\mathrm{Total\:=\:Fixed\:Fee\:+\:Hourly\:Rate\:\times Number\:of\:hours}[/tex]
[tex]\mathrm{Linear:}\:\:T=\:$25+30h[/tex]
Best Regards!
what is the simplified form of the expression (6-4)-9/6
Answer: 1/2
Step-by-step explanation:
solving bracket first we get
2 - 9/6
multiplying and dividing 2 by 6 we get
12/6 - 9/6
=3/6 = 1/2
Answer:
1/2
Step-by-step explanation:
(6-4)-9/6
= (2)-9/6
= 12/6-9/6
= 3/6
= 1/2
Please help me! I am really struggling with this...
Answer:
44°
Step-by-step explanation:
The secant- secant angle y is half the difference of the measure of its intercepted arcs, that is
[tex]\frac{1}{2}[/tex](BHF - CGJ ) = y , that is
[tex]\frac{1}{2}[/tex](156 - CGH) = 56° ( multiply both sides by 2 )
156 - CGH = 112° , thus
CGH = 156° - 112° = 44°
Which phrase matches the expression 2v? A. v divided by 2 B. 2 more than v C. 2 decreased by v D. twice v
Answer:
D. twice v
Step-by-step explanation:
2v
This is 2 times v or twice v
Determine whether the given lengths can be sides of a right triangle. Which of the following are true statements? The lengths 14, 24 and 26 cannot be sides of a right triangle. The lengths 30, 72, and 78 can be sides of a right triangle. The lengths 14, 24 and 26 can be sides of a right triangle. The lengths 30, 72, and 78 cannot be sides of a right triangle. The lengths 14, 24 and 26 can be sides of a right triangle. The lengths 30, 72, and 78 can be sides of a right triangle. The lengths 14, 24 and 26 cannot be sides of a right triangle. The lengths 30, 72, and 78 cannot be sides of a right triangle.
Answer:
The lengths 14, 24, and 26 cannot be the sides of a right triangle. The lengths 30, 72, 78 can be the sides of a right triangle.
Step-by-step explanation:
To prove that the lengths 14, 24, and 26 cannot be the sides of a right triangle:
a=14, b=24, c=26
Pythagoreon theorem: a^2+b^2=c^2
substitute values in: 14^2+24^2=26^2
simplify: 196+576=676
simplify again: 772=676, which is not true
This proves that the lengths 14, 24, and 26 cannot be the sides of a right triangle.
To prove that the lengths 30, 72, and 78 can be the sides of a right triangle:
a=30, b=72, c=78
Pythagoreon theorem: a^2+b^2=c^2
substitute values in: 30^2+72^2=78^2
simplify: 900+5184=6084
simplify again: 6084=6084, which is true
This proves that the lengths 30, 72, and 78 can be the sides of a right triangle.
Answer:
true, true, false,false, false,true,true,false
See explanations below
Step-by-step explanation:
If three sides can make a RIGHT triangle, then the sum of squares of the two shorter sides EQUALS the square of the third side, using the Pythatorean theorem.
Determine whether the given lengths can be sides of a right triangle. Which of the following are true statements?
The lengths 14, 24 and 26 cannot be sides of a right triangle.
TRUE, A^2+B^2-C^2=4sqrt(6)
The lengths 30, 72, and 78 can be sides of a right triangle.
TRUE, A^2+B^2-C^2= 0
The lengths 14, 24 and 26 can be sides of a right triangle.
FALSE, A^2+B^2-C^2=4sqrt(6)
The lengths 30, 72, and 78 cannot be sides of a right triangle.
FALSE, A^2+B^2-C^2= 0
The lengths 14, 24 and 26 can be sides of a right triangle.
FALSE, A^2+B^2-C^2=4sqrt(6)
The lengths 30, 72, and 78 can be sides of a right triangle.
TRUE, A^2+B^2-C^2= 0
The lengths 14, 24 and 26 cannot be sides of a right triangle.
TRUE, A^2+B^2-C^2=4sqrt(6)
The lengths 30, 72, and 78 cannot be sides of a right triangle.
FALSE, A^2+B^2-C^2= 0
Please helpppppppppppp
Answer:
96
Step-by-step explanation:
3*6=18*2=36
6*10=60*2=120
10*3=30*2=60
36+60+120=
216
Answer: 216 m
Step-by-step explanation:
2(10 x 6) = 120
2(6 x 3) = 36
2(10 x 3) = 60
120 + 36 + 60 = 216
Determine whether the underlined number is a statistic or a parameter. Upper A sample of professors is selected and it is found that Modifying 35 % with underline own a television. Choose the correct statement below. Parameter because the value is a numerical measurement describing a characteristic of a population. Statistic because the value is a numerical measurement describing a characteristic of a population. Parameter because the value is a numerical measurement describing a characteristic of a sample. Statistic because the value is a numerical measurement describing a characteristic of a sample
Answer:
Option : Statistic because the value is a numerical measurement describing a characteristic of a sample.
Step-by-step explanation:
A sample of professors is selected and it is found that Modifying 35 % with underline own a television.
The 35% is the value that summarizes the characteristic of the sample taken from the population. Thus, the value 35% is a statistic.
While a parameter gives a value describing the characteristic of the population itself
Given: Sample proportion is (P)=[tex]35%[/tex]%.
Statistics are the constants that are computed from sample observations alone. This is a simple definition of statistics.
Answer: The correct statement is Statistic because the value is a numerical measurement describing a characteristic of a population.
Explanation: That is, statistic because the value is a numerical measurement describing the characteristic of a sample.
The remaining statements are incorrect.
As parameters are the constants of the population. They describe only the population not the sample.
Learn more: https://brainly.com/question/10211620
3. In the diagram, PRST and PQWV are rectangles. Q, V
and U are midpoints of PR, PU and PT respectively.
Find the area of the shaded region.
======================================================
Work Shown:
A = area of trapezoid RSTU
A = height*(base1+base2)/2
A = ST*(UT+RS)/2
A = 14*(5+10)/2
A = 105 square cm
-----------------------
B = area of rectangle PQWV
B = length*width
B = WV*PV
B = 7*2.5
B = 17.5 square cm
If you're curious how I got PV = 2.5, you basically cut PT = 10 in half twice. So you go from 10 to 5, then from 5 to 2.5; which works because we have a bunch of midpoints.
-----------------------
C = total shaded area
C = A + B
C = 105 + 17.5
C = 122.5
It is never possible to solve an inequality that has a number on each side. True or False?
Answer:
true
Step-by-step explanation:
because a number is always greater than, equal to, or less than another number
Which of the following lines the parallel to the line y-9=7(x+5)
A.) y-9=3x+4
B.) y=-9x-5
C.) y+5=7(x-9)
D.) y-9=5(x+4)
Answer:
C.) y + 5 = 7(x - 9)Step-by-step explanation:
Parallel lines have the same slope.
The slope-intercept form of an equation of a line:
y = mx + b
m - slope
b - y-intercept
The point-slope form of an equation of a line:
y - y₁ = m(x - x₁)
(x₁, y₁) - point on a line
m - slope
We have the line y - 9 = 7(x + 5). The slope m = 7.
A) y - 9 = 3x + 4 → m = 3
B) y = -9x - 5 → m = -9
C) y + 5 = 7(x - 9) → m = 7
D) y - 9 = 5(x + 4) → m = 5
The line C) y + 5 = 7(x - 9) has the same slope.
Please answer it now in two minutes
Answer:
[tex]2\sqrt{33}[/tex].
Step-by-step explanation:
This triangle is a 30-60-90 triangle. That means that the hypotenuse is double the length of the smaller side.
Since the smaller side measures [tex]\sqrt{33}[/tex], the hypotenuse is [tex]2\sqrt{33}[/tex].
Hope this helps!
WILL MARK BRAINLIEST!!! 40 POINTS!! ACTUAL ANSWERS, PLZZZ
Answer:
Step-by-step explanation:
PART A: 2x^5 + 3x^2-3
It is a fifth degree polynomial because, the highest degree is 5 and it is in the standard form since, the polynomial is written in descending order i.e, from highest degree to the least
part B:
Closure property is applicable to the subtraction of polynomials.
for example 2x^4+2x^2-5 is a polynomial and 2x^3+2x+2 is also a polynomial.
if we subtract these two polynomials, the outcome
2x^4-2x^3+2x^2-2x-7 is also a polynomial
Step-by-step explanation:
Part AThe fifth degree polynomial
x^5 + x^4 +3x²+4x+9
the three terms 3x², 4x and 9 are forming a second degree polynomial written in standard form
since it has this form : ax²+bx+c
a=3b=4c=9Part BThe closure property for real numbers means that the sum oe the substraction of two real numbers
The substraction of two polynomials is a polynom using the closure property
The nature remains the sameHere is an example :
3x²+5x+8 and x²+x+1calculate the substraction
3x²+5x+8-(x²+x+1)3x²+5x+8-x²-x-12x²+4x+7The result is a polynomial
Please answer this now in two minutes
Answer:
x = 6.6
Step-by-step explanation:
Data obtained from the question include the following:
Angle X = 15°
Angle Y° = 23°
Side y = 10
Side x =..?
The value of side x can be obtained by using the sine rule as shown below:
x/Sine X = y/Sine Y
x/Sine 15 = 10/Sine 23
Cross multiply
x × Sine 23 = 10 × Sine 15
Divide both side by Sine 23
x = (10 × Sine 15) / Sine 23
x = 6.6
Therefore, the value of x is 6.6.
Please help if you are correct you get brainlyest
Answer:
did you already try A???
Answer:
Probability : [tex]\frac{5}{33}[/tex]
Step-by-step explanation:
The probability of drawing an orange on the first attempt would be 5 / 12, considering that in this first attempt their are 5 oranges present out of a total of 12 fruits. Now after that fruit is chosen their are 4 out of 11 oranges present, such that the probability of drawing an orange on the second attempt would be 4 / 11.
Probability of choosing an orange on the first try : [tex]5 / 12[/tex]
Probability of choosing an orange on the second try : [tex]4 / 11[/tex]
Probability of selecting two oranges in a row ( blindfolded ) : [tex]5 / 12 * 4 / 11[/tex]
[tex]\frac{5}{12}\cdot \frac{4}{11}[/tex] ( cross cancel common factor 4 )
[tex]\frac{5}{3}\cdot \frac{1}{11}[/tex] ( multiply fractions )
[tex]\frac{5\cdot \:1}{3\cdot \:11}[/tex] = [tex]\frac{5}{3\cdot \:11}[/tex] = [tex]\frac{5}{33}[/tex] - the probability of selecting two oranges in a row blindfolded, is [tex]\frac{5}{33}[/tex].
How to do this question plz answer me step by step plzz plz
In general and here, when we have an object with a constant cross section of area A, the volume V = A L, where L is the length.
L = V / A = 330 / 55 = 6 cm
Answer: 6 cm
If today is Sunday, then Theodore is either playing soccer or watching television. If Theodore is playing soccer (regardless of the day of the week), it means that he hasn't finished his homework or taken out the trash. If the trash is taken out, and Theodore is watching television, then he has finished his homework. Today is Sunday and the trash is taken out. Then it has to be true that:
A) His homework is finished
B) His homework isn't finished
C) This situation is impossible
D) There isn't one right answer
Answer:
His homework isn't finished.
Step-by-step explanation:
As in this sentence: "If the trash is taken out, and Theodore is watching television, then he has finished his homework.". It says that if trash is taken out, then Theodore has not finished his homework He has just taken out the trash.
Answer:b his homework isnt finished
Step-by-step explanation:
Latesha’s mother puts $85 in Latesha’s lunch account at school. Each day Latesha uses $3 from her account for lunch. The table below represents this situation. Latesha’s Lunch Account Day Amount Left in Account ($) 0 $85 1 2 3 4 5 How much is left in Latesha’s lunch account after she has had lunch for 5 days? $15 $67 $70 $82
Answer: it 70
Step-by-step explanation:
Latesha’s mother puts $85 in Latesha’s lunch account at school. Each day Latesha uses $3 from her account for lunch. The table below represents this situation.
How much is left in Latesha’s lunch account after she has had lunch for 5 days?
$15
$67
$70 is correct$82
you tube guests are for hire
Please help me, I'm so confused
Answer:
C
Step-by-step explanation:
x+4> 8
Subtract 4 from each side
x+4-4>8-4
x > 4
Open circle at 4, line going to the right
━━━━━━━☆☆━━━━━━━
▹ Answer
[tex]Solved - x > 4\\Graphed - C[/tex]
▹ Step-by-Step Explanation
x + 4 > 8
x > 8 -4
x > 4
When graphing inequalities, you have less than, greater than, less than or equal to, and greater than or equal too. When graphing an inequality with less than or greater than, you use an open circle. When graphing an inequality with less than or equal too or greater than or equal too, you used a closed circle.
Since the numbers are positive, we are going to move up the number line therefore leaving us with the answer of C.
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Assume that the random variable X is normally distributed, with mean p = 100 and standard deviation o = 15. Compute the
probability P(X > 112).
Answer:
P(X > 112) = 0.21186.
Step-by-step explanation:
We are given that the random variable X is normally distributed, with mean [tex]\mu[/tex] = 100 and standard deviation [tex]\sigma[/tex] = 15.
Let X = a random variable
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 100
[tex]\sigma[/tex] = standard deviaton = 15
Now, the probability that the random variable X is greater than 112 is given by = P(X > 112)
P(X > 112) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{112-100}{15}[/tex] ) = P(Z > 0.80) = 1- P(Z [tex]\leq[/tex] 0.80)
= 1 - 0.78814 = 0.21186
The above probability is calculated by looking at the value of x = 0.80 in the z table which has an area of 0.78814.
Find the value of sin(θ) for an angle theta in standard position with a terminal ray that passes through the point (4,-3)
Answer:
[tex]\dfrac{-3}{5}[/tex]
Step-by-step explanation:
It is given that a terminal ray that passes through the point (4,-3).
x = 4
y = -3
Using Pythagoras theorem, the value of hypotenuse is
[tex]r=\sqrt{x^2+y^2}[/tex]
[tex]r=\sqrt{(-3)^2+(4)^2}[/tex]
[tex]r=\sqrt{9+16}[/tex]
[tex]r=\sqrt{25}[/tex]
[tex]r=5[/tex]
We, know that
[tex]\sin \theta = \dfrac{y}{r}[/tex]
[tex]\sin \theta = \dfrac{-3}{5}[/tex]
Therefore, the value of [tex]\sin \theta[/tex] is [tex]\dfrac{-3}{5}[/tex].
Answer:
Step-by-step explanation:
Give the greatest common divisor of $6^3$ and $3^6$.
Answer:
27
Step-by-step explanation:
Since 3^6 is only divisible by 3 and powers of 3(including 1) the gcd of 3^6 and 6^3 mus be a power of 3 hence we need to find the highest powers of 3 that divide 6^3 and that divide 3^6, which are respectively 3^3 and 3^6, hence, taking the smaller one (since we want it to divide both), our answer is 3^3=27.
Answer:
Step-by-step explanation:
Greatest common divisor is the largest positive integer that divides each integer in the given problem
6³ = (2* 3)³ = 2³ * 3³
3⁶ = 3³ * 3³
Greatest common divisor = 3³ = 3* 3* 3 = 27