[tex]15 \leq X \leq 25[/tex] is the equation represents the drivers allotted time (x) to receive a bonus.
What us the absolute value of inequality?An absolute value inequality is an expression with absolute functions as well as inequality signs.
According to the question:
Mathematically absolute value inequality is represented as :
|X -20|≤ 5
Solving the equation using
|z| ≤ a→ -a ≤ z ≤ a :
here, z = X- 20 and a = 5:
[tex]| X-20| \leq 5\\\\ - 5\leq X-20 \leq 5[/tex]
By Solving X adding 20 on the three sides of the inequality
[tex]-5 + 20 \leq X -20 +20 \leq 5 + 20[/tex]
By simplifying it:
[tex]15 \leq X \leq 25[/tex]
Therefore the equation or inequality which represents the drivers allotted time (x) to receive a bonus [tex]15 \leq X \leq 25[/tex]
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Using p as the variable for the problem below, solve for p. Submit your answer
as an inequality, using "<=" for < or ">" for ≥ if necessary. Round to two
decimal places.
Hosting a dinner party for 38 people, you plan to serve peach pie for dessert.
Each pie has 8 slices. How many pies must you buy to ensure each guest
gets 1 slice?
Answer:
Step-by-step explanation:
As host, we want to insure each guest has at least one slice of pie. We can say (1 Slice/Guest) and use this as a conversion factor. We also know each pie has 8 slices: (8 Slices/1 Pie). Since this is a conversion factor, we can invert it to (1 Pie/8 Slices). We expect 38 people and want to convert that number of people to the number of pies, p, we need.
p (pies) [tex]\geq[/tex] (38 Guests)*(1 Slice/Guest)*(1 Pie/8 Slices)
We use the [tex]\geq[/tex] sign to note that we need a minimum of pies to be sure everyone is served.
p (pies) [tex]\geq[/tex] (38 )*(1 /)*(1 Pie/8 )
Note how the units cancel:
Guests and Slices both cancel and we are left with pies as the only remaining unit, as we hoped we'd see.
p [tex]\geq[/tex] (38/8) pies
p = 4 +(6/8) pies
Since we cannot purchase 6/8 of a pie, we need to round up to 5 pies.
5 pies, at 8 slices per pie, will provide 40 servings, enough for the 38 guests.
(2x²+3)(3x-2)-3x(x²-4)
Answer:
3x^3-4x^2+12x-6
Step-by-step explanation:
i hope this is right<3
HELP PLEASE! (will be marking brainliest) What is the measure of FJG?
A. 95
B. 100
C. 105
D. 115
Answer:
105
Step-by-step explanation:
Angles HJG and HJG form a straight line so they add to 180
< HJG + < FJG = 180
75 + <FJG = 180
<FJG = 180-75
<FJG = 105
Answer:
C) 105
Step-by-step explanation:
HJG and KJF are vertical angles so they both equal 75 degrees.
A line is 180 degrees so 180-75=105 so 105 = is FJG
Jada is comparing membership costs for two gyms. What is the difference in membership costs after m months if she joins Be strong instead of Zippy Health Club?
Write an expression for each membership cost for m months and subtract them.
Answer: Difference in membership costs after m months = -($24.96m + $34.94)
Step-by-step explanation:
Cost of Zippy health club = $49.95 + $19.95 per month
Cost of Be strong = $24.99 per month and $10 off the first month
Total cost after m months of Zippy health club = $49.95 + $19.95m
Total cost after m months of Be strong = $24.99 (m - 1) + $ 10
Difference in membership costs after m months ={ $24.99m - $24.99 + $10 ]-[$49.95m + $19.95}
=$(24.99 - 49.95) m -$14.99 - $19.95
= -$24.96m - $34.94
=-($24.96m + $34.94)
So Difference in membership costs after m months =-($24.96m + $34.94)
therefore jada have to pay more if she joins Be strong.
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If+you+invest+$100+at+an+interest+rate+of+15%,+how+much+will+you+have+at+the+end+of+eight+years?
Answer:
$305.9022863 or $305.90 (rounded to 2 decimal places)
Step-by-step explanation:
It is a compound interest, meaning an interest accumulates on an initial amount every period. The formula
A= P(1+R)^n
A= the total amount P=Initial amount R= rate n=time period
P=$100 R=15% or 0.15(decimal) n=8 (years)
A= 100 (1.15)^8
A= 100(3.059022863)
A=305.9022863
The amount you will have after 8 years is $220
Calculating simple interestThe formula for calculating simple interest is expressed as:
SI =PRT
P is the principal = $100
T is the time = 8 years
R is the rate. = 15%
SI = 100 * 8 * 0.15
SI = $120
Amount after 8years = $100 + $120
Amount after 8years = $220
Hence the amount you will have after 8 years is $220
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This question was confusing 15 for whoever answers
Answer:
Refer to the attached image. I'm not clear on one point. Yes, it is confusing.
Step-by-step explanation:
See attached image.
5|2x+6|=26...can someone answer this please
Answer:
x = -2/5 or x = -28/5
Step-by-step explanation:
Let's solve your equation step-by-step.
5(|2x+6|)=26
Step 1: Divide both sides by 5.
5(|2x+6|)/5 = 26/5
|2x+6|=26/5
Step 2: Solve Absolute Value.
|2x+6|=26/5
We know either2x+6= 26/5 r2x+6=−26/5
2x + 6 = 26/5(Possibility 1)
2x+6−6= 26/5 - 6 (Subtract 6 from both sides)
2x = -4/5
2x/2 = -4/5/2 (Divide both sides by 2)
x = -2/5
2x + 6=-26/5 (Possibility 2)
2x+6= -26/5 (Simplify both sides of the equation)
2x + 6 - 6 = -26/5 - 6 (Subtract 6 from both sides)
2x = -56/5
2x/2 = -56/5/2(Divide both sides by 2)
x = -28/5
Answer:
x = -2/5 or x = -28/5
In △ABC, ∠C = 2∠B and ∠A = 540, find the measure of ∠B.
Answer:
B = 42°
Step-by-step explanation:
All of the internal angles of a triangle sum to 180°
x + 2x + 54 = 180
3x = 180 - 54
x = 42 ° which is angle B
Mike mixes paint at a hardware store. A certain shade of orange paint is made by
mixing white, red, and yellow paint in a ratio of 4 to 3 to 2. If Mike wants to make 3
gallons of paint that is this shade of orange, how many gallons of red paint will he
need?
Answer: 1 gallon
Step-by-step explanation:
white: red: yellow
4 : 3 : 2
total units: 9 units
total amount: 3 gallons
one unit: 3/9
= 1/3
no of units of red: 3 units
amount of paint needed: 1/3 x 3
= 1 gallon
Which of the following is equivalent to
Answer:
The first one
Step-by-step explanation:
[tex]n^{2} - 6n + 9 = (n-3)^{2}\\\\[/tex]
The expression removes the first 9 terms of the summation so the summation goes from 10 to 19
If 1 < a ⩽ x , then the minimum value of [tex] \rm log_{a}(x) + log_{x}(x) [/tex] is ?
PLEASE HELP!!!!
The minimum value of the expression log_a(x)+log_x(x) is 2 because the minimum value of each term is 1.
What is a logarithm?It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.
[tex]\rm a^b = c\\log_ac =b[/tex]
We have:
1 < a ≤ x
We have an expression:
[tex]\rm log_a(x)+log_x(x)[/tex]
We know,
[tex]\rm log_aa = 1[/tex]
[tex]\rm log_a(x)+1[/tex]
If a = x
Then, [tex]\rm log_a(x)=1[/tex]
We cannot find the function value less than 1 because it goes infinitely in a negative direction.
So the minimum value of the expression:
= 1 + 1
= 2
Thus, the minimum value of the expression log_a(x)+log_x(x) is 2 because the minimum value of each term is 1.
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If f(x) = √2x, then f'(8) =
Answer:
√2
Step-by-step explanation:
Comment
You have differentiated the given equation. When you do that the x becomes 1. F'(x) is going to be √2 no matter what x is.
Drag each expression to the correct location on the table.
Simplify each exponential expression using the properties of exponents and match it to the correct answer.
The solution to the exponential expression is as follows:
[tex]\mathbf{\dfrac{(2\times 3^{-2})^3(5\times 3^2)^2}{(3^{-2})(5\times 2)^2} = 2}[/tex][tex]\mathbf{=(3^3)(4^0)^2(3\times 2)^{-3}(2^2)=\dfrac{1}{2}}[/tex][tex]\mathbf{\dfrac{(3^7\times 4^7)(2 \times 5)^{-3}(5^2)}{12^7\times 5^{-1}\times 2^{-4}} = 2}[/tex][tex]\mathbf{\dfrac{(2\times 3)^{-1}\times 2^0}{(2\times 3)^{-1}}= 1}[/tex]What are exponential expressions?Exponential expressions are convenient ways to express the mathematical power of a number in short forms.
Simplifying the following expressions given:
1.
[tex]\mathbf{\dfrac{(2\times 3^{-2})^3(5\times 3^2)^2}{(3^{-2})(5\times 2)^2} }[/tex]
Applying the exponent rule: [tex]\mathbf{(a\times b)^n = a^n b^n}[/tex]
[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 5^2\times 81}{3^{-2}\times 5^2\times2^2} }[/tex]
cancel out the common factor, we have:
[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 81}{3^{-2}\times2^2} }[/tex]
[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 3^4}{3^{-2}\times2^2} }[/tex]
[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 3^6}{2^2} }[/tex]
[tex]\mathbf{\implies \dfrac{2^3 \times \dfrac{1}{729} \times 3^6}{2^2} }[/tex]
[tex]\mathbf{\implies \dfrac{2^3 \times \dfrac{1}{729} \times729}{2^2} }[/tex]
[tex]\mathbf{\implies \dfrac{2^3 }{2^2} = 2}[/tex]
2.
[tex]\mathbf{=(3^3)(4^0)^2(3\times 2)^{-3}(2^2)}[/tex]
= [tex]\mathbf{\dfrac{1}{2}}[/tex]
3.
[tex]\mathbf{\dfrac{(3^7\times 4^7)(2 \times 5)^{-3}(5^2)}{12^7\times 5^{-1}\times 2^{-4}} = 2}[/tex]
4.
[tex]\mathbf{\dfrac{(2\times 3)^{-1}\times 2^0}{(2\times 3)^{-1}}= 1}[/tex]
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What is the midpoint of the segment (-6.-9)(16.5)
Answer:
M=(11,−2)
Step-by-step explanation:
Find the midpoint for [tex]P = \left(6, -9\right)P=(6,-9) \text{and} Q = \left(16, 5\right)Q=(16,5).[/tex]
The midpoint for two points P and Q is a point M whose coordinates is the half-sum of the corresponding coordinates of the two points.
Thus, [tex]M = \left(\frac{6 + 16}{2}, \frac{-9 + 5}{2}\right) = \left(11, -2\right)[/tex]
M=(11,−2)
In your notebook, set up the following subtraction in a vertical format and select the correct answer.
Find 2p 2 + 3p - 4 less - 2p 2 - 3p + 4.
1. 4p2 + 6p + 8
2. 4p2 - 6p - 8
3. 4p2 + 6p - 8
4. 0
The answer is 4p² + 6p - 8 which is subtraction of one equation from the other in vertical format.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have two polynomial:
2p² + 3p - 4 and -2p² - 3p + 4
Subtraction in a vertical format:
2p² + 3p - 4
- -2p² - 3p + 4
-------------------------
Changin sign of the expression -2p² - 3p + 4:
2p² + 3p - 4
+ 2p² + 3p - 4
-------------------------
Now adding like terms.
2p² + 3p - 4
+ 2p² + 3p - 4
-------------------------
4p² + 6p - 8
Thus, the answer is 4p² + 6p - 8 which is the subtraction of one equation from the other in vertical format.
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Gerald is constructing a line parallel to line l through point P. He begins by drawing line m through points P and Q. He then draws a circle centered at Q, which intersects line l at point N and line m at point S. Keeping the compass measure, he draws a congruent circle centered at point P, which intersects line m at point T.
Which next step will create point R, such that when a line is drawn through points P and R, the line will be parallel to line l?
Lines m and n intersect at point Q. A circle is drawn around point Q and forms point S on line m and forms point N on line l. Point P is also on line m. A circle is drawn around point P and forms point T on line m.
Use the compass to construct a circle centered at Q through point P.
Using the compass measure between points S and N, draw an arc to the right of line m, centered at T, intersecting the edge of circle P.
Using the compass measure between points S and N, draw an arc above line l, centered at N, intersecting the edge of circle Q.
Use the compass to construct a circle centered at P through point Q.
Mark this and return
Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope. The correct option is C.
How are parallel straight lines related?Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.
Since the given parallel line has equation y = 2x + 2 , thus its slope is 2 and thus, the slope of the needed line is 2 too.
The next step that Gerald should take is Using the compass measure between points S and N, draw an arc to the right of line m, centered at T, intersecting the edge of circle P.
Hence, the correct option is C.
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Rosa has $12.29 and spends $4.85. To the nearest dollar, about how much does she have left?
A $3
B $5
C $7
D $9
A recent order for 15,000 items of building supplies was composed of bolts and nails. Nails cost 5 cents each. The entire order arrived at an expense of 1500 dollars. If there were 2500 bolts, what is the cost of each bolt?
The cost of each bolt according to the task content is; 35c.
What is the cost each bolt?Since, there were 2500 bolts, it follows that there were 12500 nails.
The total cost of nail is therefore; 12500 × 5c. = 62500c = 625$.
Hence, the total cost of bolts is; 1500$ -625$ = $875 = 87,500c.
Consequently, the cost of each bolt is; 87,500c/2500 = 35c.
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Find the measure of angle 1.
5)
AB is a straight line.
A
152⁰
B
Let that angle be x
Linear pairs are supplementary
So
152+x=180x=180-152x=28°What is the value of p?
Answer:
p =43
Step-by-step explanation:
Finding the angle in a triangle
The angle next to 133, angle a, is 180-133 = 47 because the angles form a straight line
The angle next to 90, angle b, is 180-90 = 90, because the angles form a straight line
We have a triangle. The angles in a triangle equal 180 degrees
a+b+ p =180
47+90+p = 180
137 + p = 180
p = 180-137
p =43
The population of a small town was 3,150 last year. After a new factory opened close by, the population increased by 8%. What
is the new population of the town?
State the value of 'x' in this equation, and explain why you know this to be true without doing any calculations. 5X=59
The value of x in the equation is 59/5
How to solve for x?The equation is given as:
5x = 59
Divide both sides by 5
x = 59/5
This means that the value of x in the equation is 59/5
To know if the value is accurate, we simply multiply 5 by 59/5 and we get 59 as in 5x = 59
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A 1/25 scale model sports car is 5.5 in long. What was the length of the actual car to the nearest in?
Answer: 137.5 in
Step-by-step explanation: All we have to do is multiply 25 to 5.5 to get the original result. Since the scaling is 1/25, it means it is 25 times smaller. Thus, just multiply 25 to 5.5 and you get 137.5 in, the original result.
A cube has edges measuring 8 centimeters.
Find its surface area.
(please)
The depreciation method that does not initially use the residual value in depreciation calculations is the.
An asset loses value over time as a result of use, damage, or obsolescence.
What is depreciation?An asset loses value over time as a result of use, damage, or obsolescence. Depreciation is the measurement for this decline.
The depreciation method that does not initially use the residual value in depreciation calculations is the depreciating balance.
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I NEED HELP !!! Right now!!!
Answer:
Step-by-step explanation:
22.
(05.07 MC)
The table shows the values of y for different values of x:
x 7 8 9 10 11 12 13
y 13 10 7 6 5 3 0
The correlation coefficient for the data is −0.9847. Which statement is true about the data in the table? (1 point)
There is no relationship between x and y.
There is a weak negative relationship between x and y.
There is a strong positive relationship between x and y.
There 22.
(05.07 MC)
The table shows the values of y for different values of x:
x 7 8 9 10 11 12 13
y 13 10 7 6 5 3 0
The correlation coefficient for the data is −0.9847. Which statement is true about the data in the table? (1 point)
There is no relationship between x and y.
There is a weak negative relationship between x and y.
There is a strong positive relationship between x and y.
There is a strong negative relationship between x and y.
The option fourth "There is a strong negative relationship between x and y" is correct.
What is correlation?It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.
[tex]\rm r = \dfrac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{{[n\sum x^2- (\sum x)^2]}}\sqrt{[n\sum y^2- (\sum y)^2]}}[/tex]
The options are:
There is no relationship between x and y.There is a weak negative relationship between x and y.There is a strong positive relationship between x and y.There is a strong negative relationship between x and y.We have data:
x 7 8 9 10 11 12 13
y 13 10 7 6 5 3 0
The value of correlation r = -0.9847
As we know the value of r between -1 to +1
If r = 1 (perfect and positive correlation)
if r = -1 (perfect and negative correlation)
We have r = -0.9847
The value is near to -1 which means there is a strong negative relationship between x and y.
Thus, the option fourth "There is a strong negative relationship between x and y" is correct.
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x + 4y = -10
2x - y = 7
Answer:
(2, - 3 )
Step-by-step explanation:
x + 4y = - 10 → (1)
2x - y = 7 → (2)
multiplying (2) by 4 and adding to (1) will eliminate y
8x - 4y = 28 → (3)
add (1) and (3) term by term to eliminate y
9x + 0 = 18
9x = 18 ( divide both sides by 9 )
x = 2
substitute x = 2 into either of the 2 equations and solve for y
substituting into (1)
2 + 4y = - 10 ( subtract 2 from both sides )
4y = - 12 ( divide both sides by 4 )
y = - 3
solution is (2, - 3 )
Evaluate the function: g(x) = -x +4 Find: g(b-3)
Answer:
g(b-3) = -b + 7
Step-by-step explanation:
Plug in the value (b-3) as x into the equation
g(b-3) = -(b-3) + 4
distribute the negative sign
g(b-3) = -b + 3 + 4
combine like terms
g(b-3) = -b + 7
sec(pi/2 -x) =csc x true or false
Answer:
true
Step-by-step explanation:
if you rewrite [tex]sec\left(\frac{\pi }{2}\:-x\right)[/tex] with trigonometric identities:
[tex]sec\left(\frac{\pi }{2}\:-x\right)[/tex] [tex]=\frac{1}{\sin \left(x\right)}[/tex]
[tex]\frac{1}{\sin \left(x\right)}[/tex] [tex]=\csc \left(x\right)[/tex]
so, yes, [tex]sec\left(\frac{\pi }{2}\:-x\right)[/tex] [tex]=\csc \left(x\right)[/tex]
hope this helps!!
