Given that 2x − 1∶ − 4 = 16x + 1 ∶ 2x − 1 find the possible values of
The possible values of x are 5 and -1/12
Complete questionGiven that 2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1 find the possible values of x
How to determine the possible values of x?The ratio is given as:
2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1
Express as fraction
[tex]\frac{2x - 1}{x-4} = \frac{16x + 1}{2x -1}[/tex]
Cross multiply
4x^2 -4x + 1 = 16x^2 + x -64x - 4
Collect like terms
-16x^2 + 4x^2 + 64x - x - 4x + 1 + 4 = 0
Evaluate the like terms
-12x^2 + 59x + 5 = 0
Divide through by -1
12x^2 - 59x - 5 = 0
Expand
12x^2 + x - 60x - 5 = 0
Factorize
x(12x + 1) - 5(12x + 1) = 0
Factor out 12x + 1
(x - 5)(12x + 1) = 0
Expand
x - 5 = 0 or 12x + 1 = 0
Solve for x
x = 5 or x = -1/12
Hence, the possible values of x are 5 and -1/12
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three interior angles of a quadrilateral measure 55 , 117 , and 120. what is the measure of the fourth interior angle?
The measure of the fourth interior angle of the quadrilateral will be 68°.
What is the interior angle of a quadrilateral?Angles in a quadrilateral are the four angles that occur at each vertex within a four-sided shape, these angles are called interior angles of a quadrilateral. The measure of interior angles of a quadrilateral always sums up to 360°.
Let the measure of the fourth interior angle be x.
x + 55° + 117° + 120° = 360°
x + 292° = 360°
x = 68°
Hence, the fourth interior angle will be 68°.
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Answer:68
Step-by-step explanation:
I got it right on e2020
$50 item discounted 30%
what is 349,001 + 209, 499?
Answer:
558, 500
Step-by-step explanation:
round 349,001 to 349,000 subtracted 1
round 209, 499 to 209, 500 added 1
349,000 + 209, 500 = 558, 500
Now, the added and subtract 1 cancel out so that is the final answer
Four parallel lines are drawn in a rectangular sign. The sign is painted using two colors in an alternating pattern, as shown.
A rectangle is shown. 4 parallel lines are drawn diagonally from one side of the rectangle to the opposite side. The shapes formed by the parallel lines are colored in an alternating pattern.
Which statements must be true about the two congruent, shaded figures? Select two options.
The figures are rectangles because they are formed inside a rectangle.
The figures are rhombi because they are formed by four congruent line segments.
The figures are trapezoids because each has exactly one pair of parallel sides.
The figures are parallelograms because their opposite sides are parallel.
The figures are quadrilaterals because each has four sides.
Answer:
D & E
Step-by-step explanation:
The figures are parallelograms because their opposite sides are parallel
The figures are quadrilaterals because each had four sides
The two statements that must be true about the two congruent, shaded figures are:
The figures are parallelograms because their opposite sides are parallel.
The figures are rhombi because they are formed by four congruent line segments.
What is parallelogram?A special form of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.
The fact that the figures are formed inside a rectangle does not necessarily mean that they are rectangles themselves.
Similarly, the fact that each figure has one pair of parallel sides does not necessarily make them trapezoids, as trapezoids have only one pair of parallel sides.
Finally, the fact that each figure has four sides does not necessarily make them quadrilaterals, as any closed shape with four sides can be considered a quadrilateral.
The two statements that must be true about the two congruent, shaded figures are:
The figures are parallelograms because their opposite sides are parallel.
The figures are rhombi because they are formed by four congruent line segments.
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HELPPPPP I NEED HELP ITS URGENT !
Answer:
-5=m
Step-by-step explanation:
-3/4m-1/2=2+1/4m
-2/4m-1/2=2
-2/4m=2 1/2
m=-5
The table above shows some values of the linear function F. Which of the following defines F? A) f(n) = n-3 B) f(n) = 2n-4 C) f(n) = 3n-5 D) f(n) = 4n-6
Answer:
3n - 5
Step-by-step explanation:
f(n) = 3n - 5. Works for all of them
the perimeter of a right angle triangle is 24 cm and its area is 24 cm square if the hypotenuse is 13 cm find the remaining sides
Answer:
let the remaining sides be X and Y
perimeter = X + Y + 13
24 = X + Y + 13
11 = X + Y ---(1).
Area = 1/2 * base * height
24 = 1/2 * X * Y
XY = 48.-----(2)
solving eq 1 and 2
X + Y = 11
XY = 48
Xy + y² = 11y
Xy = 48
y²= 11y - 48
y² -11y + 48 = 0
no real solution of this equation.
Answer:
Step-by-step explanation:
the triangle is NOT a 3–4–5 or multiple,
so it is not a right triangle or your data is wrong.
Problem 4
(a) three friends are packing sweets into gift boxes. they agree that
each box should contain the same number of sweets, but they are
each working in separate locations with their own pile of sweets so
cannot share boxes. gwen has 286 sweets, bill has 390 sweets and
zeta has 468 sweets. if they put the largest number of sweets into
each box that they can and they use up all their sweets, how many
boxes of sweets will they pack?
(b) use the euclidean algorithm to find the highest common factor of
8008 and 24255 (you need to show all working).
Answer:
286+390+468÷3= answer
Question 9 of 10
If f(x)= (3 + x) over (x-3)
what is f(a + 2)?
A. 3+ f(a+2) over f(a)-1
B. (5+ a) over (a-1)
c. (3+a) +2
(a-3)
Answer:
[tex]\huge\boxed{\sf f(a+2)=\frac{5+a}{a-1}}[/tex]
Step-by-step explanation:
Given function:[tex]\displaystyle f(x)=\frac{3+x}{x-3}[/tex]
Put x = a + 2
[tex]\displaystyle f(a+2)=\frac{3+a+2}{a+2-3} \\\\f(a+2)=\frac{5+a}{a-1} \\\\\rule[225]{225}{2}[/tex]
any
ete the equivalent ratio table.
D
B
(Equivalent Ratio
21
35
20 50
27
70
12:13
17:5
23
S
9
11
2
18
22
Answer:
????????????????????????????????????????/
Step-by-step explanation:
Write a system of equations that could be used to solve the situation described below.
You find 12 coins under the couch. Every coin is either a nickel or a penny, and they add up to a total of 32 cents. How many of each type of coin do you have? Let x represent the number of pennies and y represent the number of nickels.
Please select the best answer from the choices provided
A. x+y=12
0.05x+0.01y=0.32
B. x+y=0.32
0.01x+0.05y=12
C. x+y=12
0.01x+0.05y=0.32
D. not enough information
If there are 12 coins under the couch and every coin is either a nickel or a penny and together they are forming 32 cents then the equations which represent the problem will be x+y=12, 0.01x+0.05y=0.32. The correct option is B which is x+y=12, 0.01x+0.05y=0.32.
Given There are 12 coins and total money is 32 cents.
Let the number of pennies be x and the number of nickels be y.
According to question there are 12 coins so the first equation becomes:
x+y=12.
Then we have been told that together they amount to 32 cents.
We know that 1 penny is 1 cent coin and 1 nickel is 5 cent coin so the equation becomes :
1*x+5*x=32
x+5y=32
converting into dollar
0.01x+0.05y=0.32.
Hence the right equations showing the problem of nickel and pennies are x+y=12, 0.01x+0.05y=0.32.
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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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Given f of x is equal to the quantity 8x plus 1 end quantity divided by the quantity 2x minus 9 end quantity, what is the end behavior of the function? As x → -∞, f(x) → 9 ; as x → ∞, f(x) → 9. As x → -∞, f(x) → -9; as x → ∞, f(x) → -9. As x → -∞, f(x) → -4; as x → ∞, f(x) → -4. As x → -∞, f(x) → 4; as x → ∞, f(x) → 4.
Using limits, it is found that the end behavior of the function is given as follows:
As x → -∞, f(x) → 4; as x → ∞, f(x) → 4.
How to find the end behavior of a function f(x)?The end behavior of a function f(x) is given by the limit of f(x) as x goes to infinity.
In this problem, the function is:
[tex]f(x) = \frac{8x - 1}{2x - 9}[/tex]
Considering that x goes to infinity, for the limits, we consider only the terms with the highest exponents in the numerator and denominator, hence:
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} \frac{8x}{2x} = \lim_{x \rightarrow -\infty} 4 = 4[/tex].[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{8x}{2x} = \lim_{x \rightarrow \infty} 4 = 4[/tex].Hence the correct statement is:
As x → -∞, f(x) → 4; as x → ∞, f(x) → 4.
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Answer:
D
Step-by-step explanation:
PLEASE PLEASE HELP ME WITH THSI MATH PROBLEM!!!
Answer:
23
Step-by-step explanation:
area of a trapezoid = 1/2 × (a + b) × h
so, we have
96 = 1/2 × ((4x - 1) + (x + 3)) × 6 = (5x + 2) × 3
32 = 5x + 2
30 = 5x
x = 6
a = 4x - 1 = 4×6 - 1 = 24 - 1 = 23
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
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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Kojo is twice as old as Esi who in turn is 5 years older than kwaku .if their total age is 47 . How old is each of them?
The age of Kwaku is 8 years old , Esi is 13 years old and Kojo is 26 years old.
What is an Equation ?An equation is a statement that contains algebraic expressions equated by an equal sign with constants or other variables.
Let the age of Kwaku is x
Let the age of Esi is y
From the given data
The age of Kojo is 2y
y = x +5
Sum of their age = 47
2y = 2x +10
therefore the equation formed is
x + y +2y = 47
x + x+5 + 2x +10 = 47
4x +15 = 47
4x = 32
x = 8
y = 13
2y = 26
Therefore Kwaku is 8 years old , Esi is 13 years old and Kojo is 26 years old.
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Can someone please help me with this
Answer:
The last figure.
Answer:
Figure 1, 3 and 6
Point symmetry is when two figures or (equal) parts of a figure lies at a same distance but in opposite direction from a certain point.
The proportional relationship between two variables, y and z, is represented by y = 11/2z. What is the constant of proportionality from z to y?
Answer:
Step-by-step explanation:
Comment
The constant you want is just the reciprocal of the constant you have been given. You can show it this way
y = 11/2 z Multiply both sides by 2
2y = 11z Divide both sides by 11
Answer
2/11 y = z
A study of all 33,043 infants with a heart rhythm abnormality in Italy was conducted to find a link between heart rhythm abnormality and sudden infant death syndrome. (Source: New England Journal of Medicine)
What is known about the 33,043 infants?
They are the population.
They are the variance.
They are a sample.
They are the stratified random sample.
Using sampling concepts, it is found that the 33,043 infants represent the sample.
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.
In this problem, all infants represent the population, while 33,043 infants represent the sample.
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a woman bought some oranges and 30% of them were bad if there were 60 bad oranges how many oranges did she buy
Answer:
if 60 is 30%, then add up to 100%
60+60+60= 180
but we still have 10% left so divide 30% by 3 to get 10% then add
30% (or 60) /3 is 20
add 20 to 180
boom you get 200 she bought 200 oranges i wonder how shes gonna fit them in her car that's a lot of oranges
Answer:
200
Step-by-step explanation:
To calculate 30 percent of a number, we multiply the number by 30 and then divide by 100. Therefore, we can make the following function:
30 ∗ x÷100
= 60
To solve for x, we first multiply both sides by 100 and then divide both sides by 30 to get the x = 200. Therefore, the answer to 60 is 30 percent of what number? is:
200
Graphs of tinear Relationships: Mastery Test
Select the correct answer from each drop-down menu.
The graphs below show the average temperature of a city, y, in "F, for the first 8 months of last year. Both graphs show the same information.
Change in Temperature
Change in Temperature
Y
60
40
20
2
Month
Graph A
Month
Graph B
Bejaron is preparing a report and wants to emphasize that the temperature increased greatly over the first 3 months
Complete the forowing sentences
To me the
should
crease in temperature, it would be best for Benjamin to usa
us this graph for his presentation because the temperature
Temperature (°F)
150
120
BO
Temperature ("F)
To me, Benjamin should use graph A to show the decrease in temperature. It would be best for Benjamin to use this graph for his presentation because the temperature decrease in this graph
How to determine the appropriate graph?The graphs that complete the question are added as an attachment
From the attached graph, we have the following highlights:
The data points on the y-axis of graph A are in an arithmetic sequence i.e. 30, 60, 90, 120....The data points on the y-axis of graph B are not in an arithmetic sequence i.e. 60, 20, 40, 80....The above means that graph B is a misleading graph
Hence, Benjamin should use graph A for his report
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Given two terms in a geometric sequence find the first five terms.
6) a5 = -162 and a2=-6
Help please!!!
The first five terms of the geometric series is : -2, -6, -18, -54, -162.
To solve the given problem :Given : [tex]a_{5} = -162[/tex]
[tex]a_{2} = -6[/tex]
We know G.P. series always increases in the form [tex]a.r^{n-1}[/tex]
Similarly, [tex]a_{5} = a.r^{5-1} = a.r^{4} = -162[/tex]
[tex]a_{2} = a.r^{2-1} = a.r = -6[/tex]
Now, [tex]\frac{a_{5} }{a_{2} } = \frac{a.r^{4} }{a.r^{1} } = r^{4-1}[/tex]
[tex]r^{3} = \frac{-162}{-6} = 27[/tex]
[tex]r = \sqrt[3]{27} = 3[/tex]
Now,
[tex]a_{2} = a.r = -6\\a.(3) = -6\\a = -2[/tex]
The first 5 terms are : [tex]a, a.r, a.r^{2} , a.r^{3} , a.r^{4}[/tex]
[tex]-2 , (-2).3 , (-2).3^{2} , (-2).3^{3} , (-2).3^{4}[/tex]
Therefore, The first 5 terms are : -2, -6, -18, -54, -162.
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18% Commission on a $500 couch
Step-by-step explanation:
please mark me as brainlest
Answer:
$90
Step-by-step explanation:
Rate of commission = 18%Amount = $500Commission = 18% 0f 500 = 0.18*500 =$90Which of the following are solutions to the equation below?
Check all that apply.
(3x - 5)² = 19
☐A. X=
14
B. X= -√19+5
□ C. x= -√19 +5
3
□ D. X = √19 +5
3
DEX=√14
OF X= √19+
Answer:
[tex]\sf x = \dfrac{\sqrt{19}+5}{3} \ ; \ x = \dfrac{-\sqrt{19}+5}{3}[/tex]
Step-by-step explanation:
(3x - 5)² = 19
To find the solution for the equation, take square root on both sides.
[tex]\sf 3x - 5 = \± \sqrt{19}\\\\ Add \ 5 \ to \ both \ sides \\\\ 3x = \±\sqrt{19} + 5\\\\ Divide \ both \sides \ by 3\\\\ x = \dfrac{\±\sqrt{19}+5}{3}\\\\x = \dfrac{\sqrt{19}+5}{3} \ ; \ x = \dfrac{-\sqrt{19}+5}{3}[/tex]
Describe the
translation.
y = (x - 5)² +5 →
y = (x −0)² +0
A.T<5,-5>
OB.T<-5,-5>
OC.T<-5,5>
OD. T<5,5>
The translation of the parabola from y = (x – 5)² + 5 to y = (x − 0)² + 0 will be (-5, -5). Then the correct option is B.
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
The equation of a quadratic function, of vertex (h, k), is given by:
y = a(x – h)² + k
where a is the leading coefficient.
The translation of the parabola is given below.
y = (x – 5)² + 5 → y = (x − 0)² + 0
Then the translation will be (-5, -5).
Then the correct option is B.
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Simplify The Following - c^5xc
if a + b is equal to 2 find the value of a cube plus b cube + 6ab
Write a quadratic equation, in factored form solution are 0,and 6
Answer: [tex]x(x-6)=0[/tex]
A recent order for 15,000 items of building supplies was composed of bolts and nails. Nails cost 5 cents each. The entire order arrived at an expense of 1500 dollars. If there were 2500 bolts, what is the cost of each bolt?
The cost of each bolt according to the task content is; 35c.
What is the cost each bolt?Since, there were 2500 bolts, it follows that there were 12500 nails.
The total cost of nail is therefore; 12500 × 5c. = 62500c = 625$.
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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