The table is a function and the relation f(x) = 5x + 14 has a greater value when x = 9
Is the table a function?The table of values is given as:
Input (x) 2 5 9 12
Output (y) 20 15 12 8
In the above table of values, each x value have a unique y value.
This means that the table is a one-to-one relation
A one-to-one relation is a function
Hence, the table is a function.
The greater relation at x = 9The function is given as:
f(x) = 5x + 14
This gives
f(9) = 5 * 9 + 14
Evaluate
f(9) = 59
From the table, we have:
y = 12 when x = 9
Hence, the relation f(x) = 5x + 14 has a greater value when x = 9
The value of x if f(x) = 64We have
f(x) = 5x + 14
This gives
5x + 14 = 64
Subtract 14 from both sides
5x = 50
Divide by 5
x = 10
Hence, the value of x when f(x) = 64 is 10
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Which quadratic equation is equivalent to (x-4)2-(x-4) - 6 = 0?
Answer:
x=4
Step-by-step explanation:
2x-8-x+4-6=0
or,2x-x-8+4=0
or,x-4=0
or,x=0+4
•°•x=4
ans
Answer:
x = 2 or 7
Step-by-step explanation:
(x-4)² - (x-4) - 6 = 0
x²-8x+16-x+4 -6 = 0
x²-9x+14 = 0
(x-2)(x-7) = 0
∴x = 2 or 7
Price of an article is marked 40% above the cost price and sold with 15% discount including 10% VAT at Rs. 26,894. Find the cost price, marked price and profit percentage.
Step-by-step explanation:
here is your answer. where are you from
The cost price is Rs22600, the marked price is Rs31640 and the Profit percentage is 19%.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
For example, if you say 678, we must also know the whole number, but if you say 80%, it becomes evident. The percentage is the same as the amount of that value but ranges from 1 to 100.
Let's say
Cost of article = c
Given,
Marked 40% above the cost price and sold with 15% discount including 10% VAT at Rs. 26,894
1.4c - 0.15×(1.4c) = 26894
c = Rs 22600
So,
Marked price = 1.40c = Rs 31640
Profit percentage = ( 26894 - 22600)22600 = 19%.
Hence cost price is Rs22600, the marked price is Rs31640 and the Profit percentage is 19%.
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Glass bottles are redeemed for 50 cents each. Plastic bottles are redeemed for 25 cents each and aluminum cans are .75 cents each. At the end of the event the collected a total of 35 glass bottles 50 plastic bottles and 22 aluminum cans. If there goal was $50 did they make enough money to save the condors
Answer:
no they did not make enough money
Step-by-step explanation:
Glass: 35 ×0.50 = 17.5
plastic: 50 × 0.25 = 12.5
aluminum: 22 × 0.75 = 16.5
17.5 + 12.5 + 16.5 = $46.5
Find the value of y in the equation attached to this question
Answer:
y = 4
Step-by-step explanation:
1) Simplify [tex]3^5[/tex] to 243.
[tex]{9}^{y}=\frac{243\times {9}^{6}}{{27}^{3}}[/tex]
2) Simplify [tex]{9}^{6}[/tex] to 531441.
[tex]{9}^{y}=\frac{243\times 531441}{{27}^{3}}[/tex]
3) Simplify [tex]243\times 531441[/tex] to 129140163.
[tex]{9}^{y}=\frac{129140163}{{27}^{3}}[/tex]
4) Simplify [tex]{27}^{3}[/tex] to 19683.
[tex]{9}^{y}=\frac{129140163}{19683}[/tex]
5) Simplify [tex]\frac{129140163}{19683}[/tex] to 6561.
[tex]{9}^{y}=6561[/tex]
6) Convert both sides to the same base.
[tex]9^y=9^4[/tex]
7) Cancel the base of 9 on both sides.
[tex]y=4[/tex]
Cheers,
ROR
Answer:
y = 4
Step-by-step explanation:
Decompose in base 3
[tex]9^{y} =\frac{3^{5} (3^{2})^{6} }{(3^{3})^{3} } =\frac{3^{5}3^{12} }{3^{9} } =\frac{3^{17} }{3^{9} } =3^{17-9} =3^{8}[/tex]
if
[tex]3^{8} =(3^{2} )^{4} =9^{4}[/tex]
then
[tex]9^{y} =9^{4}[/tex]
[tex]y=4[/tex]
Hope this helps
Given that the sum to infinity of a G.P. is 10. If the first term of the series is given as 5, determine the 3rd term.
Answer:
a₃ = 1.25
Step-by-step explanation:
the sum to infinity is calculated as
S ∞ = [tex]\frac{a_{1} }{1-r}[/tex]
a₁ is the first term and r the common ratio
given a₁ = 5 and S∞ = 10 , then
10 = [tex]\frac{5}{1-r}[/tex] ( multiply both sides by (1 - r)
10(1 - r) = 5
10 - 10r = 5 ( subtract 10 from both sides )
- 10r = - 5 ( divide both sides by - 10 )
r = 0.5
then
a₂ = a₁ × r = 5 × 0.5 = 2.5
a₃ = a₂ × r = 2.5 × 0.5 = 1.25
What is the slope in f(x)=6x+7
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{Slope = 6}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{f(x) = 6x + 7}[/tex]
Find: [tex]\textsf{The slope of the equation}[/tex]
Solution: Looking at the equation it is in standard form which is y = mx + b where m is the slope and b is the y-intercept. Looking at our expression we can see that m is equal to 6 which is our slope.
Therefore, the slope of our expression is equal to 6.
Simplify the expression below using the order of operations. 10+(6-3) 22-4-1 Simplify the expression below using the order of operations . 10+ ( 6-3 ) 22-4-1
The expression is 17.
What is expression?An expression is a sentence with a minimum of two numbers or variables and at least one math operation.
Given:
10+(6-3) 22-4-1
Using the BODMAS rule,
First solve the bracket term
10+ 3 * 22 -4-1
Now, perform multiplication
10+66-4-1
Now, subtraction
10+66-5
=10+61
And lastly addition
=71.
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Answer:
17
Step-by-step explanation:
the answer is 17 :)
Carl is making a garden that is twice as long as it is wide. he wants to cover 271
square feet with the garden. which equation best represents the situation if x
represents the length of the garden?
The equation which best represents the scenario is, x²/2=271
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
Perimeter is a length of the boundary surrounding the area
Area of rectangle=length x Breadth
Perimeter=2(length+breadth)
length=x
breadth=x/2
Area=271ft²
Area=length x breadth
So, using the given value we can write
271=x²/2
⇒x=√542
=23.28ft
Therefore, the equation which best represents the scenario is, x²/2=271
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Joanne has a pile of nickels and a pile of dimes. She counts her money and discovers that she has 30 nickels and 10 dimes. Let x represent the number of nickels and y represent the number of dimes. (HINT: Use the values of the coins.) How much money does Joanne have in total?
Total Amount: $_____
$2.50
Step-by-step explanation:
10 dimes are 100 aka 1 dollar, and 30 nickels make 250
What quadrant is the point (2, -5) in?
Answer:
quadrant 4
Step-by-step explanation:
(2,-5) would be in the 4th quadrant
James can hike f(n) miles after building up n days of stamina subject to a maximum of 10 days. Identify the domain that makes sense in this context.
The domain that makes sense in this context will be (0, 10].
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
James can hike f(n) miles after building up n days of stamina, subject to a maximum of 10 days.
Then the domain that makes sense in this context will be (0, 10].
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You spin the spinner twice.
What is the probability of landing on a 7 and then landing on a number less than 9?
Write your answer as a fraction or whole number.
Answer:
1/3
Step-by-step explanation:
the answer is 1/3 because the probability of landing on a 7 is 1/3 and the probability of landing on any number less than 9 is 2/3. Then, you multiply the probabilities: 1/3 * 2/3 = 2/9 = 1/3
What is the smallest prime factor of 11^7 +7^5?
Answer:
3 is the smallest prime factor.
Step-by-step explanation:
ionk how to explain it but trust me its right.
In the figure below, j || m. Find the values of x and y.
X and 73 are same-side interior angles, which are supplementary (they add up to 180).
x + 73 = 180
x = 107
X and (6y - 79) are vertical angles, which are congruent (have the same measure/value.
x = 6y - 79
107 = 6y - 79
6y = 186
y = 31
Hope this helps!
Write the ratio of corresponding sides for the similar triangles and reduce the ratio to lowest terms.
2 similar triangles. Triangle 1 has side lengths 14, 21, blank. Triangle 2 has side lengths 18, 27, blank.
a.
StartFraction 14 Over 27 EndFraction = StartFraction 21 Over 28 EndFraction = StartFraction 14 Over 27 EndFraction
b.
StartFraction 14 Over 18 EndFraction = StartFraction 21 Over 27 EndFraction = StartFraction 7 Over 9 EndFraction
c.
StartFraction 14 Over 21 EndFraction = StartFraction 18 Over 27 EndFraction = StartFraction 2 Over 3 EndFraction
d.
StartFraction 27 Over 14 EndFraction = StartFraction 28 Over 21 EndFraction = StartFraction 27 Over 14 EndFraction
The ratio of the sides of the given similar triangles is: C. 4/12 = 5/15 = 1/3.
How do the Sides of Similar Triangles Relate?The corresponding sides of similar triangles have ratios that are equal to each other.
The corresponding sides and their ratios are:
4/12 = 1/3
5/15 = 1/3
Therefore, the ratio of their sides in its lowest term is:
C. 4/12 = 5/15 = 1/3
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The Rotation maps all 60° about O the center of the regular hexagon. State the image of B for the following rotation. R^3=
F
E
B
B will be at the place of E after all three rotations. So the correct option is B.
What is Rotation?Moving in a circular plane with respect to the fixed point is called as the rotation of the object.
If rotation maps to The three rotations for B will be
The given B after one rotation will shift in place of C
After the second rotation will shift in place of D
After the third rotation will shift in place of E
B will be at the place of E after all three rotations. So the correct option is B.
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G E Which of the following segments is tangent to the circle ? 1) overline HL 2 ) overline DE 3 overline FG 4 ) overline AC
Answer:
DE
Step-by-step explanation:
........................
Please find x! These are probably simple! ASAP pls! 2 problems!
1) 3 + x + (-7) ; x = 6
2) x + (-5) + 5; x = -3
17 points:)
The numeric values of the given expressions are given as follows:
1) 2.
2) -3.
How to find the numeric value of an expression?We find the numeric value of an expression replacing all instances of x by the number.
The expression 1 is:
3 + x + (-7) = 3 + x - 7 = x - 4.
When x = 6, the value is:
x - 4 = 6 - 4 = 2.
The expression 2 is:
x + (-5) + 5 = x - 5 + 5 = x.
Hence, when x = -3, the value is:
x = -3.
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Which function is the result of vertically stretching f(x) = x ^ 2 - 7 by a factor of 2 and translating downward 5 units?
The function that is the result of vertically stretching f(x) = x²-7 by a factor of 2 and translating downward 5 units is 2x² - 19.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift:
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k × f(x)Horizontal stretch by a factor k: y = f(x/k)The given function f(x) is needed to be stretched vertically by a factor of 2, therefore, the function can be written as,
g(x) = 2(x² - 7) = 2x² - 14
Now, the function is needed to be translated by 5 units in the downward direction, therefore,
p(x) = g(x)-5 = 2x² - 14 -5
p(x) = 2x² - 19
Hence, the function that is the result of vertically stretching f(x) = x²-7 by a factor of 2 and translating downward 5 units is 2x² - 19.
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The figure below shows a large rectangle with a small rectangle cut out of it.
What is the area?
Answer:
40 square units
Step-by-step explanation:
The question gives that both the large shape and the small missing shape are rectangles. The formula for the area of a rectangle is [tex]A=bh[/tex] where "A" is the "Area", "b" is the "base" (bottom edge), and "h" is the height (side edge).
For rectangles, opposite sides (example: top & bottom) have the same length, so the top of the missing rectangle must also be 3.
To find the area of the figure, we must find the difference (subtraction) between the large rectangle (without a hole out of it) and the rectangular hole.
[tex]A_{\text{figure}}=A_{\text{large rectangle without hole}}-A_{\text{hole}}\\A_{\text{figure}}=(7)(7)-(3)(3)\\A_{\text{figure}}=49-9\\A_{\text{figure}}=40[/tex]
So, the area of the figure is 40 square units.
Answer:
40
Step-by-step explanation:
We can make a big square by making a line at the top open edge (as shown in the image attached below). We will first solve for [tex]A_{2}[/tex] and then [tex]A_{1}[/tex], and then finally solving for out answer by subtracting [tex]A_{1}[/tex] from [tex]A_{2}[/tex] .
[tex]A_{2}[/tex] is a square with side lengths of 7, so the area is 7 * 7 = 49.
[tex]A_{1}[/tex] is a smaller square with side lengths of 3, so the area is 3 * 3 = 9.
[tex]A_{2} - A_{1} = 49 - 9 = 40[/tex]
∴ Our final answer is 40
During its descent, the pair of sunglasses passed by a climber in the canyon 6 seconds after stefano dropped them. To the nearest meter, what is difference in elevation between stefano and the climber?.
Answer:
20 can be the answer of it
Select the correct answer.
The cost of renting a community center is $100, with an additional cost of $10 per guest.
Which graph has the most appropriate scales and units for this situation?
О А.
B.
Total Rental Cost ($)
tal Cost ($)
500
400
300
200
100
50
40
30
0
10 20 30 40 50
Number of Guests
The cost of renting a community center for x guest is given as y = 10x + 100
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The standard linear equation is in the form:
y = mx + b
Where m is the rate of change and b is the y intercept.
Let y represent the cost of renting a community center for x guest. Hence:
y = 10x + 100
The cost of renting a community center for x guest is given as y = 10x + 100
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Please help!!!!
Write the equation of the circle in general form. Show all your work
Let's first gather all the information we have:
[tex]\rm\hookrightarrow Center: (-3, 2)\\\rm \hookrightarrow Radius: 5[/tex]
Let's put that into standard form [tex](x-h)^2+(y-k)^2 =r^2[/tex]
(h, k): center's coordinater: radius[tex]\rm \hookrightarrow Equation: (x+3)^2+(y-2)^2 = 5^2[/tex]
To put that equation into general form:
⇒ expand all the quadratics on one side and move the radius squared
to the same side as the quadratics
[tex](x+3)^2+(y-2)^2 = 25\\x^2+6x+9+y^2-4y+4=25\\x^2+y^2+6x-4y-12=0[/tex]
Answer: x² + y² + 6x - 4y - 12 = 0
Hope that helps!
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Solve the inequality and express your answer in interval notation.
The correct answer is option B which is (-4-√11) and (-4+√11).
What is inequality?
Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
The inequality is given as x² + 8x + 5 < 0 for we will draw a graph of the inequality and find the range of x which ranges from ( -7.31,- 0.68) So these points in the options will be equal to (-4-√11) and (-4+√11).
(-4 - √11) = -4 -3.31 =-7.31
(-4 + √11) = -4 +3.31 = -0.68
Therefore the correct answer is option B which is (-4-√11) and (-4+√11).
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What is the chance of landing on $500 and then Lose A Turn?
Answer:
B = an event that in the second turn it will land on Lose a Turn. Based from the given wheel, there are 24 equal parts with three $500 and one Lose a Turn. Thus, the probability of landing on $500 then lose a turn is 1921 .
this is possible IF thewheele consists of 24 parts
The chance of landing on $500 and then Lose A Turn will be 1/192. Then the correct option is C.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
The diagram is given below.
The total number of the events will be
Total events = 24
Then the chance of landing on $500 will be
The number of favorable events will be
Favorable events = 3
⇒ 3/24
⇒ 1/8
Then the chance of the Lose A Turn will be
Favorable event = 1
⇒ 1/24
The chance of landing on $500 and then Lose A Turn will be
P = (1/24)(1/8)
P = 1/192
The chance of landing on $500 and then Lose A Turn will be 1/192.
Then the correct option is C.
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A=(3+[tex]\frac{a+\sqrt{a} }{\sqrt{a}+1 }[/tex])(3-[tex]\frac{a-5\sqrt{a} }{\sqrt{5}-5 }[/tex])
The simplification of the given algebra we see is; 9 + 3((a√a + a - a + √a)/(a - 1)) - ³/₂₀((√5 - 5)(a - 5√a)) - (a² - 4a√a - 5a)/((√a + 1)*√5 + 5))
How to Simplify Algebra?We are given the algebra expression;
A = [3 + ((a + √a)/(√a + 1))][3 - ((a - 5√a)/(√5 + 5))]
When we multiply out, we will get;
9 + 3((a + √a)/(√a + 1)) - 3((a - 5√a)/(√5 + 5)) - [((a + √a)/(√a + 1)) * ((a - 5√a)/(√5 + 5))]
⇒ 9 + 3((a√a + a - a + √a)/(a - 1)) - ³/₂₀((√5 - 5)(a - 5√a)) - (a² - 4a√a - 5a)/((√a + 1)*√5 + 5))
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If f(x) = −3x 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true. x =
The value of x for the equation to the true is 2/3
Solution to equationGiven the following functions
f f(x) = −3x + 4 and;
g(x) = 2
If the functions are equal, then;
-3x + 4 = 2
Subtract 4 from both sides
-3x = 2 - 4
-3x = -2
x = 2/3
Hence the value of x for the equation to the true is 2/3
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Which linear inequality is represented by the graph?
Answer:
The equation of the line is y ≥ 1/3(x)-1
Step-by-step explanation:
Given
The line intersects y-axis at (0,-1). Therefore, the y-intercept is -1
The line passes through the points (0,-1) and (3,0)
The slope can be obtained as follows,
m = 0-(-1)
3-0
= 1/3
The linear equation with slope and intercept is given as follows.
y = mx + c
Substitute 1/3 for m, 3 for x and 0 for y in equation to obtain the value of
c .
0 = 1/3 *3 + c
c= -1
To check whether the equation includes origin substitute 0 for x and 0 for y in equation
Therefore, y≥ mx+c
= 1/3*x-1
Hence, Linear inequality represented is y ≥ 1/3(x) -1
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A person paid by the hour works 22 hours a week and makes $359. How much would they make if they work
37 hours?
Round your answer to 2 decimal places.
Answer:
$ 603.77
Step-by-step explanation:
Find unit rate of dollars per hour : 359/22
now multiply by hours : 359/22 * 37 = 603.77
Answer:
$603.77
Step-by-step explanation:
if they work 22 hours a week
and once a week they make $359
therefore divide to get the hourly rate
359/22 = 16.3181818182
they make 16.3181818182 per hour
then we have to multiply the hourly by the hours worked
16.3181818182 * 37 = 603.772727273
since this is in dollars ($) we round to the second decimal place (hundredths)
meaning we cut off the numbers after it
603.77║2727273
then, determine if the thousandths place is equal to or greater than five or less than five
since it is a 2 then the 7 stays the same
if it were a 5 or greater we would round up, making the 7 in the hundredth place turn into an 8.
therefore your answer is $603.77
hope this helps:)
What is the sum of (4x² + 2x - 3) and (3x² + 6)?
A 7x² + 2x + 3
B. 7x² + 3
C. c. 7x² + 2x - 3
D. 7x² - 2x + 3
Answer:
A
Step-by-step explanation:
(4x² + 2x - 3) + (3x² + 6)
= 4x² + 3x² + 2x - 3 + 6
= 7x² + 2x + 3