The numeric value of the expression 16 + 4(3q + p) when q = 6 and p = 2 is given by: 96.
How to find the numeric value of a function or of an expression?To find the numeric value of a function, we replace each instance of the variable in the function by the desired value. This also works for multi-variable functions or expressions, as each instance of each variable will be replaced by their attributed values.
For this problem, the expression is given by:
16 + 4(3q + p)
The attributed values are given by:
q = 6, p = 2.
Hence the numeric value of the expression is found as follows:
16 + 4(3 x 6 + 2) = 16 + 4(18 + 2) = 16 + 4 x 20 = 16 + 80 = 96.
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Solve for the value of x in the given rational inequalities.
Answer:
see explanation
Step-by-step explanation:
1
1 + [tex]\frac{x-5}{2}[/tex] - [tex]\frac{x+3}{5}[/tex] ≤ 0
multiply through by 10 ( the LCM of 2 and 5 ) to clear the fractions
10 + 5(x - 5) - 2(x + 3) ≤ 0 ← distribute parenthesis on left side and simplify
10 + 5x - 25 - 2x - 6 ≤ 0
3x - 21 ≤ 0 ( add 21 to both sides )
3x ≤ 21 ( divide both sides by 3 )
x ≤ 7
2
[tex]\frac{6x}{5}[/tex] - [tex]\frac{2}{3}[/tex] ≥ 4
multiply through by 15 ( the LCM of 5 and 3 ) to clear the fractions
18x - 10 ≥ 60 ( add 10 to both sides )
18x ≥ 70 ( divide both sides by 18 )
x ≥ [tex]\frac{70}{18}[/tex] , that is
x ≥ [tex]\frac{35}{9}[/tex]
3
[tex]\frac{x}{10}[/tex] - [tex]\frac{2}{8}[/tex] ≥ 1
multiply through by 40 ( the LCM of 10 and 8 ) to clear the fractions
4x - 10 ≥ 40 ( add 10 to both sides )
4x ≥ 50 ( divide both sides by 4 )
x ≥ [tex]\frac{50}{4}[/tex] , that is
x ≥ [tex]\frac{25}{2}[/tex]
Answer:
[tex]\textsf{1.} \quad x \leq 7[/tex]
[tex]\textsf{2.} \quad x \geq \dfrac{35}{9}[/tex]
[tex]\textsf{3.} \quad x \geq \dfrac{25}{2}[/tex]
Step-by-step explanation:
Question 1Given inequality:
[tex]1+\dfrac{x-5}{2}-\dfrac{x+3}{5} \leq 0[/tex]
[tex]\textsf{Add \; $\dfrac{x+3}{5}$ \; to both sides}:[/tex]
[tex]\implies 1+\dfrac{x-5}{2}-\dfrac{x+3}{5} +\dfrac{x+3}{5}\leq 0+\dfrac{x+3}{5}[/tex]
[tex]\implies 1+\dfrac{x-5}{2}\leq \dfrac{x+3}{5}[/tex]
[tex]\textsf{Rewrite $1$ as $\dfrac{2}{2}$}:[/tex]
[tex]\implies \dfrac{2}{2}+\dfrac{x-5}{2}\leq \dfrac{x+3}{5}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]
[tex]\implies \dfrac{2+x-5}{2}\leq \dfrac{x+3}{5}[/tex]
[tex]\implies \dfrac{x-3}{2}\leq \dfrac{x+3}{5}[/tex]
Cross multiply:
[tex]\implies 5(x-3)\leq 2(x+3)[/tex]
[tex]\implies 5x-15\leq 2x+6[/tex]
Subtract 2x from both sides:
[tex]\implies 5x-15-2x\leq 2x+6-2x[/tex]
[tex]\implies 3x-15\leq 6[/tex]
Add 15 to both sides:
[tex]\implies 3x-15+15\leq 6+15[/tex]
[tex]\implies 3x\leq 21[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3x}{3}\leq \dfrac{21}{3}[/tex]
[tex]\implies x \leq 7[/tex]
---------------------------------------------------------------------------------------
Question 2Given inequality:
[tex]\dfrac{6x}{5}-\dfrac{2}{3} \geq 4[/tex]
[tex]\textsf{Add \; $\dfrac{2}{3}$ \; to both sides}:[/tex]
[tex]\implies \dfrac{6x}{5}-\dfrac{2}{3} +\dfrac{2}{3}\geq 4+\dfrac{2}{3}[/tex]
[tex]\implies \dfrac{6x}{5}\geq \dfrac{12}{3}+\dfrac{2}{3}[/tex]
[tex]\implies \dfrac{6x}{5}\geq \dfrac{12+2}{3}[/tex]
[tex]\implies \dfrac{6x}{5}\geq \dfrac{14}{3}[/tex]
Cross multiply:
[tex]\implies 3(6x) \geq 14(5)[/tex]
[tex]\implies 18x \geq 70[/tex]
Divide both sides by 18:
[tex]\implies \dfrac{18x}{18} \geq \dfrac{70}{18}[/tex]
[tex]\implies x \geq \dfrac{70}{18}[/tex]
Reduce the fraction by dividing the numerator and the denominator by 2:
[tex]\implies x \geq \dfrac{70 \div 2}{18 \div 2}[/tex]
[tex]\implies x \geq \dfrac{35}{9}[/tex]
---------------------------------------------------------------------------------------
Question 3Given inequality:
[tex]\dfrac{x}{10}-\dfrac{2}{8} \geq 1[/tex]
[tex]\textsf{Add \; $\dfrac{2}{8}$ \; to both sides}:[/tex]
[tex]\implies \dfrac{x}{10}-\dfrac{2}{8} +\dfrac{2}{8}\geq 1+\dfrac{2}{8}[/tex]
[tex]\implies \dfrac{x}{10}\geq \dfrac{8}{8}+\dfrac{2}{8}[/tex]
[tex]\implies \dfrac{x}{10}\geq \dfrac{8+2}{8}[/tex]
[tex]\implies \dfrac{x}{10}\geq \dfrac{10}{8}[/tex]
Cross multiply:
[tex]\implies 8(x) \geq 10(10)[/tex]
[tex]\implies 8x \geq 100[/tex]
Divide both sides by 8:
[tex]\implies \dfrac{8x}{8} \geq \dfrac{100}{8}[/tex]
[tex]\implies x \geq \dfrac{100}{8}[/tex]
Reduce the fraction by dividing the numerator and the denominator by 4:
[tex]\implies x \geq \dfrac{100 \div 4}{8 \div 4}[/tex]
[tex]\implies x \geq \dfrac{25}{2}[/tex]
What is the area of trapezoid ABCD? Enter your answer as a decimal or whole number in the box. Do not round at any steps.
The area of the trapezoid is given as 100. See the explanation for the same below.
What is a Trapezoid?A trapezoid is a quadrilateral with at least one set of parallel sides in American and Canadian English. A trapezoid is known as a trapezium in British and other varieties of English.
To find the length of each side of the trapezoid, you need to use the distance formula.
AB = (-1,5) and (3,2)
BC = (3,2) and (0,-2)
CD = (0,-2) and (-13, -11)
AD or DA = (-1,5) and(-13, -11)
Now, just use the distance formula for each line.
The Distance Formula is given as: d=√((x2 – x1)² + (y2 – y1)²).
Distance AB = √((3 – (-1))² + (2 – 5)²).
= √(4)² + (-3)²
= √(16+9)
= √25
AB = 5
lets us repeat this for the other section we will get:
Doing so gives us for all the points:
AB = 5
BC = 5
CD = 15.811388300842
DA or AD = 20
Note that:
The height is AD, the first base is AB and the second base is BC. We can plug the values for these sides into the trapezoid area formula, which is:
A = (base 1 + base 2) / 2 x height.
A = (5+5)/2 x 20
A = 5 x 20
A = 100.
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Evaluate u + xy, if u = 18, x = 10, and y = 8
The value of u + xy, if u = 18, x = 10, and y = 8 is 98
What are algebraic expressions?
Algebraic expressions are defined as mathematical expressions that are made up of constants, variables, coefficients, terms and factors.
These algebraic expressions are also composed of arithmetic operations, such as;
SubtractionAdditionDivisionMultiplicationParenthesesBracket, etcGiven the expression;
u + xy
Where;
u = 18x = 10y = 8Now, substitute the values into the expression;
18 + 10(8)
expand the bracket
18 + 80
Add the values
98
Hence, the value is 98
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14.2 to 1 decimal place
A comet is about 6.64 × 107 miles from Earth. Write this number in standard form.
Answer:710.48 miles
Step-by-step explanation:
look it up
two members of the math competition team solve 13 problems in 1 hour. If all team members solve problems at the same rate how many tema members are needed to solve 39 problems in 1 hour
In a case whereby two members of the math competition team solve at the rate 13 problems in 1 hour, the members that are needed to solve 39 problems in 1 hour is 6 member of the team.
How can the rate be calculated?Since two members solve 13 problems in 1 hour, which implies that
2 members= 13 problem/ hr
Then if we want to calculate the number of the team that will be able to solve the problem at the rate of 39 problems in 1 hour, we can represent the number required as X.
Then X = 39 problems/hr.
2 members= 13 problem/ hr
Then in this case we can cross multiply as follows:
13 problem/ hr * X = 39 problems/hr * 2
Then we can make X the subject of the formular as X =( 78 /13)
= 6 member of the team.
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Help me: Brainliest +lots of points
The line segment joining points (2,6) and (6,2) forms a diagonal of a square. Which of the following could be the coordinates of another vertex of that square?
Answer:
(2,2) and (6,6) would be the other two points to the square.
Step-by-step explanation:
Answer:
(2,2) or (6,6)
Step-by-step explanation:
looking at the graph you can see the diagonal of a square and I just followed the points if that make sense please tell me if you need more
at the end of the season, a team’s ratio of wins to losses was 3:5. if there were no ties, what percentage of its games did the team win? (show work)
A.) 33 1/3%
B.) 37 1/2%
C.) 40%
D.) 62 1/2%
E.) 75%
As per given data of end of the season , ratio of teams win to losses is 3:5 and no ties, then percentage of game win by team is equal 37 1/2%.
As given in the question,
For the given dat of end of season,
Ratio of teams win to losses is equal to 3:5
Let x be the percentage of game
As per given ratio we have,
3x+ 5x =100%
⇒ 8x = 100
⇒x =100/ 8
⇒ x= 12.5
Percentage of winning the game by team = 3x
= 3(12.5)
= 37.5%
= 37 1/2%
Therefore, for given data of end of the season , ratio of teams win to losses is 3:5 and no ties, then percentage of game win by team is equal 37 1/2%.
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URGENT!!!!!
math assignment(not to be confused with assessment) that I need help with
Answer: DF
Step-by-step explanation:
What is 2x-8=34?
please answer quickly
Answer: x=21
Step-by-step explanation:
2x-8=34 (change the -8 into a positive since it doesn't have a variable)
34+8=42 (divide 34 by 2)
42/2=21
Check your answer
2 x 21 = 42
42-8=34
x=21
What is the y-intercept of the online given by the equation below
y= -10x+14
Answer:
y - intercept = 14
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 10x + 14 ← is in slope- intercept form
with y- intercept c = 14
7) G is the midpoint of FH. If FG-70 what is the mFH?
A. 35 B. 140
C. 105
D. 100
Answer:
A
Step-by-step explanation:
A submarine to study changes in the sea level of the Pacific Ocean
descends 420 feet below sea level. 3 hours later, it makes an ascent
of 170 feet. What is the submarine's new position?
What is the answer???
Answer:
f = 90 + 32
= 122° (exterior angle)
At which ordered pair will the function f(x) = Vx - 4 + 7
The ordered pair at which the function f(x) = √(x - 4) + 7 would begin on the coordinate plane is (4, 7).
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
What is an ordered pair?An ordered pair can be defined as a pair of two elements that are typically written in a fixed order within parentheses as (x, y), which represents the x-axis (abscissa) and the y-axis (ordinate) on a coordinate plane.
By critically observing the graph of this function (see attachment), the ordered pair would begin at (4, 7) on the cartesian coordinate.
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Complete Question:
At which ordered pair will the function f(x) = √(x - 4) + 7 begin on the
coordinate plane?
pls help will give brainliest
The given point were reflected about the line y = x and the coordinates the reflected point (-5 , 3) is (3, - 5)
According to the question, given that
point reflected line y =x,
Reflected point coordinates of (-5, 3), then find the coordinates of the point after in the line of symmetry :
(-5, 3) → (3, - 5)
A reflection is referred to as a twist in geometry. A reflection is the mirror image of shape . A line, called the line of reflection, will agree an image to reflect without change it. When all of the points in a figure are evenly spaced apart from one another, the two figures are said to reflect each other. The reflected picture should have the same size and shape as the original, but it faces the opposite way. Changes in position during contemplation may also result in translation. Pre-image and image are terms used to refer to the same thing in this context. ABC and A'B'C are used to represent the pre-image and image, respectively.
A reflection point is similar to staring at a flipped mirror picture of yourself.
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tony uses 12 4 1 and 7 to make a new number
Answer:
ishbekshbrishdhtjekdhhfjeid
30 points please help asap!!
Which statement describes a reflection?
A.
A reflection occurs when a point and its image are equidistant from a line on the opposite sides of the line and the line segment joining the two points is perpendicular to the line.
B.
A reflection moves points a specified distance along a line perpendicular to a specified line.
C.
A reflection moves points a specified distance along a line parallel to a specified line.
D.
A reflection occurs when an object moves in a circular arc around a point.
Answer:
A. A reflection occurs when a point and its image are equidistant from a line on the opposite sides of the line and the line segment joining the two points is perpendicular to the line.
Hope this helps! :)
I'm stuck in this word problem pls help me ty
Answer:
GREAT question i have no idea
Step-by-step explanation:
phythegorean theorem
Answer: 6.782
Step-by-step explanation:
Which of the following is
equivalent to the complex number
I27?
The equivalent to the complex number i²⁷ is -i.
what is complex numbers?Every complex number may be represented in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element labeled I sometimes known as the imaginary unit, and satisfying the equation
i² = 1.
Given that,
i²⁷ is a complex number
i²⁷ = i²⁴⁺³
i²⁷ = i²⁴ ₓ i³
i²⁷ = i⁴⁽⁶⁾ ₓ i²⁺¹
i²⁷ = (i⁴)⁶ . i².i
Here, we know that i² = -1
so, i⁴ = (i²)²
i⁴ = 1
Hence, 1⁶(-1)(i) = -i
Therefore, the equivalent to the complex number i²⁷ is -i.
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Select the correct answer.
What is the solution to |x - 6| ≥ 5?
A. 1 ≤ x ≤ 11
B. -11 ≤ x ≤ 1
C. x ≥ 11 or x ≤ 1
D. x ≥ 1 or x ≤ -11
Answer:
C. x ≥ 11 or x ≤ 1
Step-by-step explanation:
x - 6 + 6 ≥ 5 + 6
x ≥ 11
x - 6 ≤ -5
x - 6 + 6 ≤ -5 + 6
x ≤ 1
Hope this helps! :)
Which of the following is equivalent to (2x² − y)²?
what is the answer???????
Answer: Where P is.
Step-by-step explanation
1.50 x 10 ^5 / 5.0 x 10^1 in scientific notation
Simplify to create an equivalent expression.
\qquad{5(10k+1)+2(2+8k)}5(10k+1)+2(2+8k)5, left parenthesis, 10, k, plus, 1, right parenthesis, plus, 2, left parenthesis, 2, plus, 8, k, right parenthesis
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
66k+966k+966, k, plus, 9
(Choice B)
B
64k+964k+964, k, plus, 9
(Choice C)
C
66k+5466k+5466, k, plus, 54
(Choice D)
D
64k-964k−964, k, minus, 9
why is the answer that tho
Answer:
question tho??
URGENT!!!!
answer options:
cannot be determined
closer to point A
closer to point B
the same distance from both point a and b
Point M has the same distance from point A and point B (option d).
Given,
Line segment CD is the perpendicular bisector of line segment AB
AB ⊥ CD
Assume the conjecture that the set of points equidistant from A
and B is the perpendicular bisector of AB is true
Here, line segment CD intersect line segment AB at M
Then, M is the mid-point of line segment AB
So, the length of line AM = the length of line MB
That is, Point M has the same distance from both point A and point B.
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15 times 3 plus 12 time 2 using a t chart
Answer:
69
Step-by-step explanation:
15*3=45
12*2=24
45+24= 69
Answer: 114
Step-by-step explanation:
15×3+12×2
15×3=45
45+12=57
57×2=114
Help needed for trigonometry !!!
Answer:
k = 53.13°
Step-by-step explanation:
[tex]{ tan (k) = \dfrac{\text{side opposite k}}{\text{side adjacent k}}}[/tex]
[tex]= \dfrac{35}{JK}\\\\\textrm{Since JK is a right triangle, by the Pythagorean theorem }\\JK = \sqrt{IK^2 - IJ^2}}\\\\= \sqrt{35^2 - 28^2}\\\\\\ =\sqrt{1225 - 784}\\\\= \sqrt{441}\\\\= 21[/tex]
[tex]\tan(k) = \dfrac{28}{21} = 1.333\\\\k = \tan^{-1}(1.333)\\\\= 53.13^\circ[/tex]