The smallest possible prime number x is 17.
What is Fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.
given, Two-thirds of a number x is at least 10.
So,
2/3 x ≥ 10
x ≥ 15
First prime number that is bigger than 15 is 17.
therefore, The smallest possible prime number x is 17.
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The graph of the function f(x) = (x - 3)(x + 1) is shown.
Ty
-10-8-6
10
8
6
-6
8
-10-
6
10
X
Which describes all of the values for which the graph is
positive and decreasing?
O all real values of x where x < -1
O all real values of x where x < 1
O all real values of x where 1
O all real values of x where x > 3
Answer:
all real values of x where x < -1
The correct statement is all real values of x where x < -1.
Option A is the correct answer.
We have,
To determine the values for which the graph of the function
f(x) = (x - 3)(x + 1) is positive and decreasing, we need to analyze the behavior of the function.
Let's consider the factors individually:
(x - 3): This factor is positive for x > 3 and negative for x < 3.
(x + 1): This factor is positive for x > -1 and negative for x < -1.
To determine the overall sign of the function, we need to consider the signs of both factors together.
When both factors are positive or both factors are negative, the function is positive.
When the factors have opposite signs, the function is negative.
From the above analysis, we can conclude the following:
When x > 3, both factors are positive, so the function is positive.
When -1 < x < 3, the factor (x - 3) is negative, while the factor (x + 1) is positive. Therefore, the function is negative.
When x < -1, both factors are negative, so the function is positive again.
Since we are looking for values where the function is positive and decreasing, we can eliminate the options that include positive and increasing regions (such as x > 3).
Thus,
The correct statement is all real values of x where x < -1.
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“The length of a rectangle is two feet greater than twice it’s width. If the perimeter is 25 feet, find the width.” Which of the following translations is correct
The width of the rectangle is 3.5 feet
Solving for the missing sides of a rectangle
The width of the rectangle = w
The length of the rectangle = l
The perimeter = p
Length of the rectangle is two feet greater than twice it’s width
l = 2w + 2
p = 2(l + w)
p = 2(2w + 2 + w)
p = 2(3w + 2)
p = 6w + 4
The perimeter of the rectangle is 25 ft
25 = 6w + 4
This can be rewritten as:
6w + 4 = 25
6w = 25 - 4
6w = 21
w = 21/6
w = 3.5
Therefore, the width of the rectangle is 3.5 feet
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Hey can someone tell me the steps to solving a system of equations with graphing
Answer:
Let's go through the following example to show how to solve a system of equations by graphing. I won't solve this system, I will just show how to.
[tex]8x-3y = 17\\4x+y=21[/tex]
If you can use an online graphing calculator...
If you have an online grapher (like Desmos) at your disposal, then you can put each equation in it as it is.
Lines intersect -> Put your cursor over the point of intersection to get the solution.Lines never intersect -> The lines are parallel and there is no solutionLines perfectly fall on each other -> The lines are the same and have infinite solutionsIf you have a physical graphing calculator (like TI-84)
1. Get both equations in the form [tex]y=mx+b[/tex] by solving for y.
[tex]8x-3y=17\\-3y=-8x+17\\y=\frac{8}{3}x-\frac{17}{3}[/tex] [tex]4x+y=21\\y=-4x+21[/tex]
2. Put both equations in the graphing calculator
Lines intersect -> Find the intersection point using your graphing calculator's mechanics (each one is a little different)Lines never intersect -> The lines are parallel and there is no solutionLines perfectly fall on each other -> The lines have the same equation and have infinite solutionsIf you just have graphing paper...
1. Get both equations into the form [tex]y=mx+b[/tex] by solving for y.
[tex]8x-3y=17\\-3y=-8x+17\\y=\frac{8}{3}x-\frac{17}{3}[/tex] [tex]4x+y=21\\y=-4x+21[/tex]
2. Plug in a few different points for x and calculate their y-values.
3. Plot those points on the graph paper
Lines intersect -> Find the intersection point's coordinates to get the solution for x and y.Lines never intersect -> The lines are parallel and there is no solutionLines perfectly fall on each other -> The lines have the same equation and have infinite solutions.The perimeter of a right angled triangle, with hypotenuse c=101cm and one side b=20cm, is:
Answer:
220
Step-by-step explanation:
We need to find the 3rd side length
We already know the hypotenuse and one side, so we can use the Pythagorean formula.
101^2 = a^2 + 20^2. A is the third side, and solving for it, we find that it equals 99.
Side 1 = 101
Side 2 = 99
Side 3 = 20
101 + 99 + 20 = 220
If x^y = z is there any way to find y if you know x and z?
We make use of [tex]y = \log_x(z)[/tex] to solve for y, when you know x and z
How to solve for y?The expression is given as:
x^y = z
The above expression is an exponential expression.
Start by taking the logarithm of both sides
y log(x) = log(z)
Divide both sides by log(x)
[tex]y = \log_x(z)[/tex]
Hence, we make use of [tex]y = \log_x(z)[/tex] to solve for y, when you know x and z
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please help me i included the images of the questions, ill give brainliest
Answer:
1: r^5, 2: st^2, 3: qr, 4: 1, 5: m, 6: x, 7: 1/z, 8: a, 9: d^4f^2 10: 1, 11: cd^2, 12: b, 13: 1, 14: st^2, 15: 1/mn.
Step-by-step explanation:
1 explanation: Cancel the common factor of r^6 and r.
2 explanation: Simplify the expression.
3 explanation: simplify the expression.
4 explanation: Simplify the expression.
5 explanation: simplify the expression.
6 explanation: Cancel the common factor of x^2 and x.
7 explanation: Cancel the common factor of z^4 and z^5.
8 explanation: Cancel the common factor of a^2 and a.
9 explanation: simplify the expression.
10 explanation: simplify the expression.
11 explanation: simplify the expression.
12 explanation: simplify the expression.
13 explanation: simplify the expression.
14 explanation: simplify the expression.
15: simplify the expression.
What is most likely the line of best fit for this scatter plot?
2234H205642
18
16
14
12
10
0123456789 10 12 14
O Line A
Line B
O Line C
O Line D
The most likely the line of best fit for this scatter plot is line C.
What is scatterplot?It should be noted that a scatterplot simply means a graph that shows the relationship between the variables in the data set.
In this case, the most likely the line of best fit for this scatter plot is line C. The dependent variable is illustrated in the x axis and the dependent variable is illustrated on the y axis.
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una persona compra un terreno a crédito pagadero en 5 año. El primer año paga 5000$. Si cada año paga 10% más que el anterior; calcula cuanto pagará en el quinto año y cual es el importe del terreno
El pago en el quinto año sera de $7,320.50, y el importe total es de $30,525.50
¿Cual es el importe en el quinto año?Sabemos que el importe inicial es $5,000, cada año paga 10% más que el anterior.
Entonces se hacen 5 pagos, y el pago que se hace en cada año esta dado por la ecuación exponencial:
[tex]P(x) = \$5000*(1.10)^{x - 1}[/tex]
Donde x es el número del año.
Entonces en el año número 5, el pago será:
[tex]P(5) = \$5000*(1.10)^{5 - 1} = \$7,320.50[/tex]
¿Cuanto es el importe total?
Está dado por:
[tex]T = P(1) + P(2) + P(3) + P(4) + P(5)\\\\T = \$5000*( 1 + (1.10)^1 + (1.10)^2 + (1.10)^3+ (1.10)^4) = \$30,525.50[/tex]
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Based on the figure below, what is the value of x?
(5x + 15)
01
09
0 11
15
20°
Answer:
undefined
Step-by-step explanation:
because
the figure does not appear
Using the table, what is the average daily balance of the credit card for the July 1 - July 31 billing period? Round your answer to the nearest cent. Do not include a dollar sign or comma in your answer. For example, $5,678.00 should be entered as 5678.00.
Day 1112126 Activity − Payment Purchase Payment Adjustment −−500+750−700 Closing Balance 2500200027502050
To solve, multiply each closing balance by the number of days at that balance, add all of these together and then divide by the total number of days in the billing period.
($2500×10)+($2000×10)+($2750×5)+($2050×6)31≈$2291.94
The average daily balance of the credit card is 2291.94
What is the average daily balance?
The average daily balance can be determined by dividing the total daily balance of month by numbers of days in month.
We can find average daily balance as shown below:
Average daily balance = total balance of the month/total number of days in the month
Total balance = (2500*10) +(2000*10) +(2750*5) +(2050*6)
= 25000+20000+13750+12300
= 71,050
Number of days = 31
Average daily balance = 71,050/31
= 2291.9354
Round to the nearest cent
= 2291.94
Hence, the average daily balance of the credit card is 2291.94
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Determine the function f(x)= kx+m if f(x-1)-f(x)=2 and f(-2)=1-m
[tex]f(x) = kx + m \\ f(x - 1) = k(x - 1) + m[/tex]
[tex]f(x - 1) - f(x) = 2 \\ k(x - 1) + m - kx - m = 2 \\ kx - k + m - kx - m = 2 \\ - k = 2 \\ k = 2[/tex]
[tex]f( - 2) = k( - 2) + m = 1 - m \\ k( - 2) + m = 1 - m \\ ( - 2)( - 2) + m = 1 - m \\ 4 + m = 1 - m \\ 2m = - 3 \\ m = \frac{ - 3}{2} [/tex]
[tex]f(x) = - 2x - \frac{3}{2} [/tex]
in the diagram , what is the value of x
The value of x from the given diagram is 100 degrees
Sum of interior angleFrom the given diagram, we will use the theorem "angle at the vertex is half that at the centre.
<50 = 1/2 x
Cross multiply
50 * 2 = x
x = 50 * 2
x = 100 degrees
Hence the value of x from the given diagram is 100 degrees
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Follow the steps to find the
area of the shaded region.
Now use the formula below
to find the area of the
triangle.
Triangle Area = bh
h = 6.2172 cm
Triangle Area = [?] cm²
Round to four decimal places.
129
8 cm
The area of the triangle will be 14.9835cm².
How fo you find the area of a triangle?Your information is incomplete and the complete question wasn't found. An overview will be given.
The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle.
Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h. Hence, to find the area of a tri-sided polygon, we have to know the base (b) and height (h) of it.
In this case, let the assumed base be 4.82cm and the height is given as 6.2172cm.
The area will be:
= 1/2 × 4.82 × 6.2172
= 14.9835cm²
In conclusion, the area is 14.9835cm².
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A client is instructed to drink 20 ounces of water with 1 hour. The client has only been able to drink 12 ounces. What portion of water remains? (express your answer as a fraction reduced to lowest terms)
Answer:
2/5
Step-by-step explanation:
20 ounces in all - 12 ounces drank = 8 ounces left
8 ounces left/20 ounces in all = 4/10 = 2/5 = 0.4
The portion of water remaining is 2/5 if the client is instructed to drink 20 ounces of water for 1 hour.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
A client is instructed to drink 20 ounces of water for 1 hour. The client has only been able to drink 12 ounces.
The remaining portion = 20 ounces - 12 ounces drank
The remaining portion = 8 ounces left
As we know, the arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
The fraction:
= 8 ounces left/20 ounces in all = 4/10 = 2/5 = 0.4
= 8/20
= 2/5
Thus, the portion of water remaining is 2/5 if the client is instructed to drink 20 ounces of water for 1 hour.
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Tom has 7 hamsters. If each hamster weighs 11 pounds, how much weight is there in total?
Answer:
7
Step-by-step explanation:
7x11=77
evaluate the expression 27 (36)
The value of the expression is 972
How to evaluate the expression?The expression is given as:
27(36)
Express 36 as 18 + 18
27(18+ 18)
Expand
486+ 486
Evaluate the sum
972
Hence, the value of the expression is 972
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Multiply –8m(–6m – 7).
–14m2 – 15m
48m2 + 56m
–14m – 15
48m + 56
Answer: 48m2 + 56m
Step-by-step explanation:
Answer:
Answer B
Step-by-step explanation:
Match each number on the left with the correct description of the number on the right.
Answer:
im not sure the answer tho- just trying
Interior and exterior triangle angles
Answer:
Step-by-step explanation:
Need help with defining this question.
Answer: 19
Step-by-step explanation:
[tex]F(5)=5^2 - 2(5)+4=19[/tex]
Number graph ranging from negative one to seven on the x axis and negative four to four on the y axis. Two lines that are perpendicular to each other intersect at (two, one). The line with a positive slope is labeled a and the line with a negative slope is labeled b. Use the graph to state the solution for the system. x + 2y = 4 (line a) 3x – 2y = 4 (line b) (2, –1) (2, –1) (2, 1) (2, 1) (–2, 1)
The solution for the system of lines is defined as follows,
x-Intercept for line a: (4,0)
y-Intercept for line a: (0,2)
x-Intercept for line b: (1.5, -0)
y-Intercept for line b: (0,-2)
Line a and b intersect at (2,1)
Solving the System of Lines:
Line a: x + 2y = 4
Line b: 3x – 2y = 4
From the graph,
Line a intersect x-axis at (4,0) and y-axis at (0,2)
Line b intersect x-axis at (-1.5,0) and y-axis at (0,-2)
x + 2y = 4
x = 4-2y
Since point P lies on bot the lines A and B, it will satisfy the equations of both a and b.
Thus, substituting x = 4-2y in the equation of line b, we get,
3(4-2y) - 2y = 4
12 - 6y - 2y = 4
8y = 8
y = 1
Putting y=1 in the equation of line a, x = 4-2y, we get,
x = 4-2(1)
x = 4-2
x = 2
Hence, point P≡(2,1).
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Find the interquartile of the data set that consists of 8,18,4,2,3,7,11,13,5,1 answers 11,8,6,3
Answer:
I.Q.R = 11 - 3
I.Q.R = 9
the interquartile range = 9
Can you please help me with this urgently need help?
It is grade 12 advance function question
Answer: The spin of the wheel by the contestant is an illustration of a sine function whose equation is y = -1.25sin(0.8x + 0.25)
The equation that represents the function will be; y = -1.25sin(0.8x) + 0.25
How does sine function works?Suppose that we've got
[tex]f(x) = a\sin(bx + c) + d[/tex]
Amplitude or maximum height from average motion horizontal axis
= a + d
Thus, the minimum low from horizontal axis is –a + d (sin ranges from -1 to 1, and multiplying a to it make it range from -a to a).
A sine function is represented as:
y = Asin(B(x+C)) + D
Now, Substitute the calculated values,
y = -1.25sin(0.8(x+C)) + 0.25
The horizontal shift (C) is 0.
So, the function will be;
y = -1.25sin(0.8x) + 0.25
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Question 3
Show work and solve 3 = 5*+1 using change of base formula.
Answer: [tex]x=\frac{\log (3/5)}{\log 5}[/tex]
Step-by-step explanation:
[tex]3=5^{x+1}\\\\\log_{5} 3=x+1\\\\x=\log_{5} 3-1\\\\x=\log_{5} 3-\log_{5} 5\\\\x=\log_{5} \left(\frac{3}{5} \right)\\\\x=\frac{\log (3/5)}{\log 5}[/tex]
Construct a right angled traiangle ,choosing whole numbers of centimeters for the lengths of the two shorter sides, such that the hypotenuse will be √65 long.Check the accuracy of your drawing by measuring the hypotrnuse and by calculating √65.
Please give me a correct answer.
Answer:
1. Shorter Side: 4
2. Longer Side: 7
3. Hypotenuse: [tex]\sqrt{65}[/tex]
Step-by-step explanation:
[tex]4^{2} +7^{2} =65[/tex]
that any pair of congruent triangles is similar True or false.
Answer:
yes it's true no problem sir
-275+156-(-293)-157 = 17
ME PUEDEN DAR EL PROCEDIMIENTO
PLIS
The procedure for solving -275+156-(-293)-157 = 17 is to follow bodmas operation
Evaluation-275+156-(-293)-157 = 17
Using BODMAS
b - bracketo - offd - divisionm - multiplicationa - additions - subtraction-275+156-(-293)-157 = 17
= -275 + 156 + 293 - 157
= 17
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For each of the following equivalence relations, describe the corre-
sponding partition. Your description of each partition should have no redundancy,
and should not refer to the name of the relation.
The description of the corresponding partition is given as follows:
The infinite classes can be defined as:
At equal distance of x from point [1,2]
Where x can vary from o to infinity.
What is a corresponding partition?The analogous partition, commonly known as "the set of equivalence classes," is the set A/R, the elements of which are the subsets of A satisfying the following:
For every a∈A there is some B∈A/R such that a∈B.
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Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 400 minus quantity y minus 110 end quantity squared over 2304 equals 1 comma where the measurements are in meters. What is the width of the cooling tower at the base of the structure? Round your answer to the nearest whole number.
100 meters
50 meters
48 meters
40 meters
The width of the cooling tower at the base of the structure is 40 meters.
Width of the cooling towerGiven equation
x²/400 -(y-90)²/1600=1
Solving for the width
Cooling tower width =2√400
Cooling tower width=2×20
Cooling tower width=40 meters
Therefore the correct option is D. 40 meters.
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Answer:
40
Step-by-step explanation:
find HM if HG=18, FM=5, and EM=9
Answer:
HM = 3 or HM = 15
Step-by-step explanation:
The product of segment lengths is the same for both chords.
SetupFM·EM = GM·HM
GM +HM = 18
Substituting for GM, we have ...
FM·EM = (18 -HM)·HM
5·9 = (18 -HM)·HM
SolutionEffectively, we want two factors of 45 that have a total of 18. Looking at the factors of 45, we have ...
45 = 1·45 = 3·15 = 5·9
The totals of these pairs are 46, 18, 14. The factor pair we're looking for is 3·15.
Either of these factors could be HM. The other will be GM.
There is nothing in the problem description that suggests the length of HM relative to other lengths on the diagram. (We know the diagram is not to scale.) So, there are two possible solutions:
HM = 3 or HM = 15