The value of the expression |-10+6|-|3²-5| = 0
The expression given is |-10+6|-|3²-5|.
This contains absolute value which needs to be evaluated.
We will go through the definition of absolute value.
Absolute value for x = x, when x is a positive integer.
i.e., |x| = x, when x >0
Absolute value of (-x) = x, when -x is a negative integer.
So absolute value always gives the positive value of the number inside it.
Now |-10+6|-|3²-5| = |-4| - |9-5|
= 4 - |4| [Since |-4| = 4]
= 4 - 4 [Since |4| = 4]
= 0.
So the value of the expression |-10+6|-|3²-5| = 0
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There are 3 consecutive integers with a sum of 45. What are the integers?
The three consecutive integers are 14, 15, and 16.
Assume the three consecutive integers to be x-1, x, and x+1.
Sum of all three = 45.
x-1 + x + x+1 = 45
3x = 45 (-1 and +1 get cancelled)
x = 45/3
x = 15
the first integer is x-1 = 15 - 1 = 14
the second integer is x = 15
the third integer is x+1 = 15 + 1 = 16
So, the three consecutive integers are 14, 15, and 16.
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THERE IS 5 QUESTIONS I NEED TO GET DONE IN TOTAL, BUT IT WONT LET ME PUT MANY PICS IN ONE QUESTION SO PLS GO TO MY ACC AND VIEW THE OTHER ONES !!I NEED THIS BY **TODAY**
Answer:
[tex]y=\frac{1}{2}x-3[/tex]
Step-by-step explanation:
The equation of a line is y=mx+c, where m is the slope and c is the y-intercept (where the line crosses the y-axis).
Looking at the graph, we can see that the line crosses the y-axis at y=-3, so we know c= -3.
The slope of a line can be found by taking two points on the line, [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex], and subbing them into the formula [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]. Let's take the two points (2,-2) and (4:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{(-1)-(-2)}{4-2}=\frac{1}{2}[/tex]
Therefore, since the equation of a line is y=mx+c, our answer is [tex]y=\frac{1}{2}x-3[/tex]
Answer:
y=1/2x-3
Step-by-step explanation: given: (0,-3) (2,-2)
y=mx+b
-3=(m*0)+b
-3=b
-2= (m*2)-3
1=2m
m=1/2
y=mx+b
y=1/2x-3
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1. (a)The vertex of the function [tex]y=x^{2} +5x-7[/tex] is [tex](-\frac{5}{2} ,-\frac{53}{4} )[/tex]
How is the vertex calculated?
In function [tex]y=x^{2} +5x-7[/tex],
a= 1 ,b= 5, c= -7
For a function [tex]y=ax^{2} +bx+c[/tex] , where (a≠0),
The vertex is [tex](-\frac{b}{2a} ,\frac{4ac-b^{2} }{4a} )[/tex]
[tex]x_v=-\frac{b}{2a}\\\\ =-\frac{5}{2*1} \\\\=-\frac{5}{2} \\\\\\y_v=\frac{4ac-b^{2} }{4a} \\\\=\frac{4*1*(-7)-(5^{2} )}{4*1}\\\\ =-\frac{53}{4}[/tex]
So, vertex [tex](-\frac{5}{2} ,-\frac{53}{4} )[/tex] is minimum because a>0
(b)The solutions are [tex](\frac{\sqrt{53} -5}{2},0) (\frac{-5-\sqrt{53} }{2},0)[/tex]
How is the solution calculated?
When a function [tex]y=ax^{2} +bx+c =0[/tex] where (a≠0),
[tex]x=\frac{-b\pm\sqrt{b^{2} -4ac} }{2a} \\\\x=\frac{-5\pm\sqrt{5^{2} -4(1)(-7)} }{2(1)} \\\\x=\frac{-5\pm\sqrt{53} }{2} \\\\x=\frac{\sqrt{53} -5}{2} , x=\frac{-5-\sqrt{53} }{2} \\\\\text{The solutions are } (\frac{\sqrt{53} -5}{2},0) (\frac{-5-\sqrt{53} }{2},0)[/tex]
2. (a)The vertex of the function [tex]y=-x^{2} +3x+8[/tex] is [tex](\frac{3}{2} ,\frac{41}{4} )[/tex]
How is the vertex calculated?
In function [tex]y=-x^{2} +3x +8[/tex]
a= -1 ,b= 3, c= 8
For a function [tex]y=ax^{2} +bx+c[/tex] , where (a≠0),
The vertex is [tex](-\frac{b}{2a} ,\frac{4ac-b^{2} }{4a} )[/tex]
[tex]x_v=-\frac{b}{2a}\\\\ =-\frac{3}{2*(-1)} \\\\=\frac{3}{2} \\\\\\y_v=\frac{4ac-b^{2} }{4a} \\\\=\frac{4*(-1)*(8)-(3^{2} )}{4*(-1)}\\\\ =\frac{41}{4}[/tex]
So, vertex [tex](\frac{3}{2} ,\frac{41}{4} )[/tex] is maximum because a<0
(b)The solutions are [tex](\frac{3+\sqrt{41} }{2},0) (\frac{3-\sqrt{41} }{2},0)[/tex]
How is the solution calculated?
When a function [tex]y=ax^{2} +bx+c =0[/tex] where (a≠0),
[tex]x=\frac{-b\pm\sqrt{b^{2} -4ac} }{2a} \\\\x=\frac{-3\pm\sqrt{3^{2} -4(-1)(8)} }{2(-1)} \\\\x=\frac{-3\pm\sqrt{41} }{-2} \\\\x=\frac{3\pm\sqrt{41} }{2}\\\\x=\frac{3-\sqrt{41}}{2} , x=\frac{3+\sqrt{41} }{2} \\\\\text{The solutions are } (\frac{3+\sqrt{41} }{2},0) (\frac{3-\sqrt{41} }{2},0)[/tex]
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a textbook store sold 324 a combined total of chemistry and biology textbooks in a week. the number of chemistry textbooks sold was three times the number of biology textbooks sold. how many textbooks of each type were sold?
Total number of Chemistry textbooks sold is 81 and total number of Biology textbooks sold is 243
How is the number of each textbooks sold, calculated?Let there are x biology textbooks sold.
No of chemistry textbooks sold = 3 the number of biology textbooks sold
ATQ,
A textbook store sold a combined total of 324 biology and chemistry textbooks in a week.
x + 3x = 324
4x = 324
x = 81
It means there are 81 biology textbooks sold and 3x = 3(81) = 243 chemistry textbooks sold.
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n/−3 +5>4 Solve for this
Answer:
N<3
Step-by-step explanation:
y > x-2 3 4 y> -x + 1 Which point is a solution set to the inequalities? b (0,1) (1.0) (-3, 2) (2.-3) d
Replace each point in both inequalities and see if the inequality remains:
(0,1) = (x,y)
1 ≥ 1/3(0)-2
1≥-2
y>4/3x+1
1>4/3(0)+1
1>1 NOT TRUE.
Point b.
(1,0) = (x,y)
0 ≥ 1/3(1)-2
0≥ 1/3-2
0≥-5/3
0>4/3(1)+1
0>7/3 NOT TRUE
Pint c. (-3,2)
2≥1/3(-3)-2
2≥ -1-2
2≥-3
2>(4/3)-3+1
2>-4+1
2>-3 TRUE
(-3,2) is a solution point to the set of inequalities. (option c)
Which number is the smallest?
pls answer fast
Responses
A 4.68 x 10−44.68 x , 10 -4
B 5.48 x 10−85.48 x , 10 -8
C 2.85 x 10−62.85 x , 10 -6,
D 3.24 x 10−53.24 x , 10 -5,
E 1.28 x 10−4
The smallest number from the given options is
[tex]5.48 × {10}^{ - 8} [/tex]
The correct answer option is option d
How to find the smallest number?A.
[tex]1.28 × {10}^{ - 4} [/tex]
= 1.28 × 0.0001
= 0.000128
B.
[tex]2.85 × {10}^{ - 6} [/tex]
= 2.85 × 0.000001
= 0.00000285
C.
[tex]3.24 × {10}^{ - 5} [/tex]
= 3.24 × 0.00001
= 0.0000324
D.
[tex]5.48 × {10}^{ - 8} [/tex]
= 5 48 × 0.00000001
= 0.0000000548
Therefore, the smallest number is
[tex]5.48 × {10}^{ - 8} [/tex]
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Determine which integer will make the inequality 5x + 12 > 2x + 6 false.
S:{−3}
S:{3}
S:{−1}
S:{1}
Out of the given integer(s), {−3} is the integer which will make the inequality 5x + 12 > 2x + 6 false.
As per the question statement, we are supposed to determine which integer will make the inequality 5x + 12 > 2x + 6 false
Let's solve the inequality for range of x first,
5x + 12 > 2x + 6
5x - 2x > 6 - 12
3x > -6
x > -2
So for all values of x > -2, the inequality 5x + 12 > 2x + 6 is true and for all values of x < -2, the inequality 5x + 12 > 2x + 6 false.
And out of the given options only x = -3 < -2
Hence, we accept {−3} as our required integer.
Inequality: An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.To learn more about inequality and its properties, click on the link given below:
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Answer:
S:{−3}
Step-by-step explanation:
Got it right on a test.
A total of 77 tornadoes have been documented in tuscaloosa county in the period beginning on january 1, 1950 and ending on december 31, 2020. What is the recurrence interval for tornadoes in tuscaloosa county?.
The Recurrence interval for tornadoes in tuscaloosa county is 0.909
What is recurrence interval ?
The time period in which a new occurrence of something that happened or appeared before : a repeated occurrence or The time frame in which a previously occurring event or appearance first occurs: a recurring occurrence
Given that,
Total number of tornadoes is 77
Total time for Recurrence is 70 years
Using these data,
Recurrence = Total time for recurrence / Total number of tornadoes
Substituting we get,
Recurrence interval = 70/77
= (70/77)
= (0.909)
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The employees at a baseball bat factory need to make 350,000 bats in 6 months. They make 2,750 bats each day and work 127 days in the 6 months. Do the employees make enough bats?
Answer:
75 boxes
Step-by-step explanation:
If you divide 24000 bats by 50 boxes, you get 480. Then, if you divide the 36000 by 480, you will get 75
i need 2 more please help me
The remainder when the expression x^3+6x^2+x+c is divided by x-2 is twice the remainder when the expression is divided by x-1.
show that c=24
Answer:
c = 18
Step-by-step explanation:
According to the remainder theorem, the remainder when f(x) is divided by (x - n) is f(n).
As per question we are given:
f(2) = 2f(1)Substitute and solve for c:
2³ + 6*2² + 2 + c = 2(1³ + 6*1² + 1 + c)8 + 24 + 2 + c = 2(1 + 6 + 1 + c)34 + c = 2(8 + c)34 + c = 16 + 2c2c - c = 34 - 16c = 18Note: I got a different value of c. This may be a result of a typo in the given expression. I provided a guide to solve such problems. Let me know is anything is unclear.
An eighteen-acre building lot is five times as long as it is wide. What are its dimensions? [Note: 1 acre = 43,560 ft2.]
The dimensions of building lot are 396 feet width and 1980 feet length.
Let the width of building lot be x. So, the length of the same building lot will be 5x. According to the formula, the area will be length × width.
18 acre = x×5x
Keep the value of acre in the above mentioned relation
18 × 43,560 = 5x²
Performing multiplication on Left Hand Side of the equation
784,080 = 5x²
Performing division by 5
x² = 156,816
Now taking square root to find the value of x
x = ✓156,816
x = 396 ft
Thus, the width of building lot is 396 feet
The length of building lot = 5×396
Performing multiplication
The length of building lot = 1980 feet
Therefore, the length and width of building lot is 1980 feet and 396 feet respectively.
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please try to answer quickly my brainly app is crashing
The formula to calculate the lateral area of a cone is given by
[tex]LA=pi*r*l[/tex]where
LA=10.5pi in2
r=2.1 in
l=? slant height
substitute given values
[tex]\begin{gathered} 10.5pi=pi*2.1*l \\ solve\text{ for l} \\ l=\frac{10.5pi}{pi*2.1} \\ \\ l=5\text{ in} \end{gathered}[/tex]The answer is 5 inchesSimplify 5(−4−8w)−3w.
Answer:
-20-43w
Step-by-step explanation:
5(-4-8w)-3w
-20-40w-3w
-20-43w
The figure below shows a triangle with vertices A and B on a circle and vertex C outside it. Side AC is tangent to the circle. Side BC is a secant intersecting the circle at point X.What is the measure of angle ACB? (6 points)O 29°O 8°O 16°O 21°
The Solution.
Considering triangle ABC, we have
[tex]\begin{gathered} angle\text{ACB}=180-(90+40+42) \\ =180-172=8^o \end{gathered}[/tex]Hence, the correct answer is 8 degrees (option B)
under what circumstances can a very small treatment effect still be significant? group of answer choices if the standard error of m (s m) is very large if the sample size (n) is very large all of the other factors are likely to produce a significant result. if the sample standard deviation (s) is very large
A minor treatment effect may nonetheless be significant under certain circumstances if the sample size is large and the sample variance is low.
What is the standard error, and sample size?The standard error calculates the discrepancy between a sample's estimate and the actual value for the population. Therefore, the standard error should be smaller the better. In fact, a standard error of zero or extremely close to it would indicate that the projected value and the actual value are identical.Sample size determination is the process of deciding how many observations or replicates to include in a statistical sample. The sample size is an important consideration in any empirical study that aims to infer information about a population from a sample.Therefore, a minor treatment effect may nonetheless be significant under certain circumstances if the sample size is large and the sample variance is low.
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how many of these figures have atleast one vertex
3(5y-7)-2(9y-11)=4(8y-13)-17
Answer:[tex]3(5y - 7) - 2(9y - 11) = 4(8y - 13) - 17 \\➪ 15y - 21 - 18y + 22 = 32y - 52 - 17 \\ ➪15y - 18y - 32y = - 52 - 17 + 21 - 22\\➪-35y = - 70 \\➪35y = 70 \\ \: (cancel \: \: out \: "-" \: from \: both \: sides) \\ ➪y = \frac{ 70}{35} = 2 \\ \\ [/tex]
Tʜᴀɴᴋs| (• ◡•)|Hᴏᴘᴇ ɪᴛ ʜᴇʟᴘsI REALLY NEED HELP PLEASE THIS WORK IS FOR MONDAY.can y’all please help me:(
The statement that best describes the total cost of the Screened Loam, Round stone, and Crushed stone is; D: The total cost is greater than $325
How to solve Algebra Word Problems?We are given the amount of each material required for the Landscaping Project as;
Screened Loam = 3.25 cubic yards
Round stone = 1.5 cubic yards
Crushed stone = 2.5 cubic yards
Likewise we are given the cost of each of these materials per cubic yard as;
Cost of Screened Loam = $26 per cubic yards
Cost of Round stone = $112.5 per cubic yards
Cost of Crushed stone = $37.5 cubic yards
Thus;
Total Cost = (26 * 3.25) + (112.5 * 1.5) + (37.5 * 2.5)
Total Cost = 84.5 + 168.75 + 93.75
Total Cost = $347
Looking at the given options, the most appropriate is option D
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i'm still confused. helpppppppppppppppppppppppppppppppppppppppppppppppppppppp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
I believe you forgot to add the attachment
Step-by-step explanation:
There is no math problem I can see to help you
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The inequality for the temperature in the house measured by thermostat is; 24° ≤ t ≤ 26°. The highest temperature is 26° C.
What is defined as the term inequality?In mathematics, an inequality is a relationship representations or values that aren't equal to each other. When two numbers are equal, we use the symbol '=', and if they are not equal, we use the symbol ≠.For the given question.
The thermostat at the house is set at 25° C.
Now, there is a deviation of the temperature of 1° C.
Thus,
The lowest temperature measured = 25° C - 1° C = 24° C.
The highest temperature measured = 25° C + 1° C = 26° C.
Let 't' be the temperature of the house.
The inequality will be;
24° ≤ t ≤ 26°
Thus, the maximum value of the temperature will be 26° C.
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the measure of the angle of a triangle are shown in the figure below. solve for x (8x-18)° 110° 40°
Answer:
x = 6
Step-by-step explanation:
180 = (8x - 18) + 110 + 40
180 = 8x + 132
48 = 8x
6 = x
If the measure of the angle is needed:
8(6) - 18 = 30
Mrs. Smith made 4 pizzas .with 11 oz of cheese How much cheese is
each pizza made with ?
Answer:
2.75
divide 11/4
what’s the answer ???
Answer:
a=29. b=32 c=30. d=30
Step-by-step explanation:
look at the arrow and get the answer if am wrong let me know
9(w + 1) = 99
w =
if you tell me the answer then ur a W
w = 10.
Step-by-step explanation:
9(w+1) = 99
9w+9 = 99
9w = 99-9
9w = 90
w = 90/9
w = 10.
[tex]{ \boxed{ \red{ \sf{w = 10}}}}[/tex]
Step-by-step explanation:
[tex]{ \purple{ \sf{9(w + 1) = 99}}}[/tex]
[tex]{ \purple{ \sf{9w + 9 = 99}}}[/tex]
[tex]{ \purple{ \sf{9w = 99 - 9}}}[/tex]
[tex]{ \purple{ \sf{9w = 90}}}[/tex]
Divide both the sides by 9 then
[tex]{ \purple{ \sf{ \frac{9w}{9} = \frac{90}{9} }}}[/tex]
[tex]{ \pink{ \boxed{ \blue{ \sf{w = 10}}}}}[/tex]
Which of the contexts below could not be modeled by an exponential function?
A certain population of 16 aggressive zombies quintuples every day.
A taxi charges a flat fee of $2.00 for pick-up, then an additional fee of 4.75 per mile.
A coin collection appreciates at a rate of 5.2% per year.
A car depreciates at a rate of 4.9% per year.
The answer choice which could not be modelled by an exponential function among the given answer choices is; A taxi charges a flat fee of $2.00 for pick-up, then an additional fee of 4.75 per mile.
Which context could not be modelled by an exponential function?It follows from the task content that the expression which could not be modelled by an exponential expression be identified among the answer choices.
An exponential function is one in which case the change factor is expressed as an exponent of the independent variable.
However, the function described as; A taxi charges a flat fee of $2.00 for pick-up, then an additional fee of 4.75 per mile is termed a linear model in which case;
The rate of change is constant and is equal to; $4.75 per mile.
Hence the required answer choice which cannot be modelled by an exponential function is; A taxi charges a flat fee of $2.00 for pick-up, then an additional fee of 4.75 per mile.
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PLS HELP!!
Answers: 8,20,35,12
Answer:
the answer is 8.
Step-by-step explanation:
Use the Pythagoras Theorem since it is a triangle.
[tex]a^{2}+b^{2}= c^{2}\\\\a^{2}+15^{2}= 17^{2}\\ a^{2}+225=289\\ a^{2}=289-225\\ a^{2}= 64\\ \sqrt{a}= \sqrt{64}\\ a=8[/tex]
Since you have the hypotenuse and base, just put those into the equation and find the missing side.
suppose you give 10 people a taste test where they each try samples of two different brands of soda. after drinking both samples they tell you which soda they liked best. what is a/the confounding variable in this experiment?
Confounding variables are any other variable that also has an effect on your dependent variable.
What is a confounding variable?
A confounding variable, also called a confounder or confounding factor, is a third variable in a study examining a potential cause-and-effect relationship.
A confounding variable is related to both the supposed cause and the supposed effect of the study. It can be difficult to separate the true effect of the independent variable from the effect of the confounding variable.
In your research design, it's important to identify potential confounding variables and plan how you will reduce their impact.
For example, if you are researching whether drinking both sample lead to taste test, then drinking both sample is your independent variable and taste test is your dependent variable. Confounding variables are any other variable that also has an effect on your dependent variable.
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Function: g(x) = 2x2 – 8
For x ≥ 0, the inverse function is f(x)= √
1
2
x + 4
For x ≤ 0, the inverse function is d(x)= – √
1
2
x + 4
A 3-column table has 3 rows. The first column is labeled x with entries negative 8, 0, 10. The second column is labeled f (x) with entries 0, r, s. The third column is labeled d (x) with entries q, negative 2, t.q =
r =
s =
t =
The inverse function of g(x) = 2x² - 8 for each case is given as follows:
x ≥ 0: y = √(0.5x + 4).x < 0: y = -√(0.5x + 4).Inverse functionTo find the inverse function, we exchange the variables x and y in the original function, and then isolate the variable y.
The original function in this problem is given as follows:
g(x) = 2x² - 8.
The function is not one-to-one, hence the inverse is different for x ≥ 0 and for x < 0.
Exchanging the variables, we have that:
x = 2y² - 8.
Isolating the variable y, we have that:
2y² = x + 8
y² = 0.5x + 4 (the entire equation was divided by 2 to isolate y)
y = ± sqrt(0.5x + 4).
For non-negative values, the inverse function is:
y = sqrt(0.5x + 4) = √(0.5x + 4).
For negative values, the inverse function is:
y = -sqrt(0.5x + 4) = -√(0.5x + 4).
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Answer: 0,2,3,-3
Step-by-step explanation: