The value of x is -101/4 or the simplified form of the expression can be given as -1/2x = 101/8
This question relates to equation in mathematics and all we need to do is solve for x. But this requires some step by step process which are
open the bracketcollect like termsdivide through by the coefficient of xThe given equation is
[tex]2(\frac{x}{2} - 5) - \frac{3}{2} (x+\frac{7}{4} )\\[/tex]
Open Bracket[tex]2(\frac{x}{2} - 5) - \frac{3}{2} (x+\frac{7}{4} )\\\\(\frac{2}{2}x-10)-(\frac{3}{2}x-\frac{21}{8}) \\x- 10 -\frac{3}{2}x-\frac{21}{8}\\[/tex]
Collect like terms[tex]x-\frac{3}{2}x-10-\frac{21}{8}=0\\-\frac{1}{2}x =10+\frac{21}{8}\\-\frac{1}{2}x=101/8\\[/tex]
Divide ThroughWe have to divide through by coefficient of x
[tex]-\frac{1}{2}x =\frac{101}{8}\\(-1/2x)/(-1/2)=(101/8)/(-1/2)\\x=\frac{-101}{4} \\[/tex]
from the above calculation, the value of x is -101/4. The simplified form of the expression is -1/2x = 101/8
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given f(x)=4x-18
solve for the following f(-3) and f(x)=-46
write the two as an ordered pair
PLEASE HELP
f(x) = 4x - 18
f(-3) - put x = -3 to the equation of the function
f(-3) = 4(-3) - 18 = -12 - 18 = -30
Answer: (-3, -30).f(x) = -46
We have the equation:
4x - 18 = -46 add 18 to both sides
4x = -28 divide both sides by 4
x = -7
Answer: (-7, -46)Since Beth was born, the population of her town has increased at a rate of 850 people per year. Beth's 9h birthday, the total population was nearly 307,650. Write and solve a linear equation to find the population on Beth's 16th birthday.
[tex]\frac{y-307,650}{x-9} = 850\\\\y-307,650 =850(x-9)\\\\multiply\\\\y =307,650 +850(x -9)\\\\y =307,650+850(16-9)\\\\y= 313,600[/tex]
The linear equation can be formed as P = P0 + rt. Replacing each variable with the values from the problem, we find that the population of Beth's town on her 16th birthday will be approximately 319,600.
Explanation:The question refers to a situation of linear growth. It states that the population of Beth's town grows at a constant rate of 850 people per year. If on Beth's 9th birthday the population was 307,650, we can create a linear equation to find the population when she turns 16. This linear equation can be represented as follows: P = P0 + rt, where P is the future population, P0 is the initial population, r is the rate of growth, and t is the time elapsed.
In Beth's situation, we will let her 9th birthday be the starting point (time zero). So, P0 is 307,650, r is 850, and t is 7 (the years from her 9th birthday to her 16th birthday). Plugging these values into our equation gives us P = 307,650 + 850 * 7. Solving the equation gives us P = 313,650 + 5,950 = 319,600. Therefore, the estimated population of Beth's town on her 16th birthday is 319,600.
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Carmen is currently 28 years old and her daughter is 3 years old. How old will Carmen be when she is twice her daughter's age?
Answer:
50
Step-by-step explanation:
if x years past she is twice her daughter's age,
so we get:
28+x=2(3+x)
x=22, 22+28=50
Answer:
Step-by-step explanation:
Thank you that helped me with mine
eg:
L is 26, C is 4, how many years until L is 2 times as old as C?
26+x=2(4+x)
26+x=8+2X
-8 -8
18+x=2x
-x -x
18=1x
in 18 years L will be 2 times as old as C
What does the fundamental theorem of algebra illustrate?
Answer:
see below
Step-by-step explanation:
The "fundamental theorem of algebra" tells you the number of roots of a polynomial is equal to its degree. This includes real and complex roots and counts repeated roots the number of times they are repeated. (Real numbers are a subset of Complex numbers, so the choice of "complex" for this problem is appropriate.)
_____
The given quadratic can be solved using the quadratic formula:
for ax²+bx+c=0, the solutions are
... x = (-b±√(b²-4ac))/(2a)
Here, a=2, b=-4, c=-1, so ...
... x = (4 ±√(16 -4·2·(-1)))/(2·2)
... x = (2±√6)/2
Answer:
1. complex 2. 2+6 3. 2-6
Step-by-step explanation:
i took the test :)
The value of a car depreciates by 24% per year. Work out the current value of a car brought 3 years ago for ?20000.
Answer:
$8779.52
Step-by-step explanation:
24% = 0.24.
Each year the value of the car = 1 - 0.24 = 0.76 of the previous year.
Value after 3 years = 20,000 * (0.76)^3
= $8779.52
ΔDEF ≅ ΔD'E'F'. Use the picture to answer the question below.
Describe a sequence of rigid motions that would prove a congruence between ΔDEF and ΔD'E'F'
Answer:
1) Translation
2) Rotation
3) Reflection
Step-by-step explanation:
To make ΔDEF ≅ ΔD'E'F' , we will carry on the following steps:
Step 1: Translate ΔD'E'F' in upward direction, the figure will remain same but it will shift a little in upwards direction.
Step 2 : Rotate ΔD'E'F' about 180°. The figure obtained will be reflection of the original image ΔDEF.
Step 3 : Reflect ΔD'E'F'.
This implies that ΔDEF≅ΔD'E'F'.
Suppose there are 20 questions on a multiple choice test. Is 25% of the answers are choice B, how many of the answers are not choice B?
To find the number of answers that are not choice B, subtract the number of answers that are choice B from the total number of questions.
Explanation:To find the number of answers that are not choice B, we first need to calculate the number of answers that are choice B. Since 25% of the answers are choice B, we can multiply the total number of questions (20) by 0.25 to find that there are 5 answers that are choice B. To find the number of answers that are not choice B, we subtract the number of answers that are choice B from the total number of questions. So, the number of answers that are not choice B is 20 - 5 = 15.
The fourth grade students at Riverside School are going on a field trip. There are 68 students from each of the four buses. How many students are going on the field trip?
Answer:
There are 272 students going on the field trip.
Step-by-step explanation:
68 students on each bus. 4 busses. 68 x 4 = 272
Answer:
The answer is 272 students.
Step-by-step explanation:
1. First, I looked at how many students and buses are there.
2. I looked at the question, "How many students are going on the field trip?"
3. Next, I will multiply the number of students on each bus by the number of buses on there.
4. 68
x 4
272
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Hope this helped! Your answer is 272 students. ❤️
The sum of the measures of angle 5 and angle 6 is equal to 180° and the sum of the measures of angle 2 and angle 3 is equal to 180° because angles on a _____ _____ measure 180°.
Fill in the blanks
Final answer:
The blanks are filled with 'straight line' as angles on a straight line sum to 180°, which is a key concept in geometry related to the properties of angles and triangles.
Explanation:
The sum of the measures of angle 5 and angle 6 is equal to 180° and the sum of the measures of angle 2 and angle 3 is equal to 180° because angles on a straight line measure 180°. This concept is related to the geometric property that when two angles lie on the same line and add up to form a straight angle, their measures sum up to 180°.
In geometry, specifically the study of polygons and angles, we learn that a triangle is a three-sided figure lying on a plane with three angles adding up to 180°. This is called the Triangle Sum Theorem, which is fundamental to understanding the properties of triangles and other polygons.
Given:
RSTU is a parallelogram.
SX =
RX
ST
UX
SX is equal to UX
Step-by-step explanation:US and Rt are the lines which make the center of the parallelogram. Hence the center of both lines is X so both the lines must be present at the same distance from the mid point. US is divided in two equal parts on point X and we know that center point is always equidistant from the end points. X must be equidistant from both UX and SX so we can say that SX = UX.
Miguel the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday there were 5 clients who did Plan A and 2 who did Plan B. On Tuesday there were 3 clients who did Plan A and 8 who did Plan B. Miguel trained his Monday clients for a total of 6 hours and his Tuesday clients for a total of 7 hours. How long does each of the workout plans last?
length of each plan A work out: ___ hours
length of plan B work out:__ hours
Answer:
length of each plan A work out: 1 hour
length of plan B work out: [tex]\frac{1}{2}[/tex] hours
Step-by-step explanation:
Let x represents the time taken to do plan A
y represents the time taken to do plan B
On Monday there were 5 clients who did Plan A and 2 who did Plan B.
Miguel trained his Monday clients for a total of 6 hours
5x + 2y = 6 -----------> equation 1
On Tuesday there were 3 clients who did Plan A and 8 who did Plan B. .He trained his Tuesday clients for a total of 7 hours
3x + 8y = 7 -------------------> equation 2
Now we solve for x and y
Let multiply the first equation by -4 to eliminate y
-20x -8y = -24
3x + 8y = 7
------------------------ (add both equations)
-17x = -17
Divide both sides by -17
So x= 1
Plug in 1 for x in first equation and solve for y
5x + 2y = 6
5(1) + 2y = 6
5 + 2y =6
Subtract 5 on both sides
2y = 1
y = 1/2
length of each plan A work out: 1 hour
length of plan B work out: [tex]\frac{1}{2}[/tex] hours
Given the linear function g(x) = 3x, describe the effect h(x) = 3x – 1 has on the original graph.
Answer:
x) =g(x) -1 shifts the graph g(x) down 1 unit
Step-by-step explanation:
g(x) = 3x
When we add to g(x) and make it g(x) +c, we shift the graph vertically,
+c shifts the graph up
-c shifts the graph down
h(x) =g(x) -1 shifts the graph g(x) down 1 unit
Which equation represents this situation?
Five less than a number is equal to three times the sum of the number and two?
A.) 5 - x = 3x + 2
B.) x - 5 = 2x + 3
C.) x - 5 = 3(x + 2)
D.) 5 - x = 3(2x)
Answer:
I would say...
C.)x - 5 = 3 (x + 2)
Really really sorry if I'm wrong...
One thing I can say is that when it says 5 less than a #, that means the # is being subtracted from another #...
The correct equation for the situation 'Five less than a number is equal to three times the sum of the number and two' is x - 5 = 3(x + 2).
Explanation:The correct equation for this situation is C.) x - 5 = 3(x + 2).
Here's how you can decipher the sentence: 'Five less than a number' translates to 'x - 5' in mathematical terms where 'x' stands for the number. 'Is equal to' signifies the equality sign '='. Finally, 'three times the sum of the number and two' corresponds to '3(x + 2)', where 'x' is the number, '2' is the two and '3' the three times mentioned in the equation. So, putting it all together gives you
x - 5 = 3(x + 2).
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A theater group charges $12.50 per ticket for its opening play of the season. Production costs for the play are $150. Which function could be used to determine the profit the theater group earns from selling x tickets?
Answer:
[tex]P(x)=12.50x-150.[/tex]
Step-by-step explanation:
Let x be the number of tickets sold. If a theater group charges $12.50 per ticket for its opening play of the season, then x tickets cost $12.50x. Production costs for the play are $150. Then the profit the theater group earns from selling x tickets is
[tex]P(x)=12.50x-150.[/tex]
He vertices of ?ABC are A(2, 8), B(16, 2), and C(6, 2). The perimeter of ?ABC is units, and its area is square units.
Answer:
Perimeter = 32.44 unit
Area of triangle = 30 unit²
Step-by-step explanation:
By distance formula distance between (a,b) and (c,d) is [tex]\sqrt{(c-a)^2+(d-b)^2}[/tex]
So, we have
[tex]AB=\sqrt{(16-2)^2+(2-8)^2}=15.23\\\\BC=\sqrt{(16-6)^2+(2-2)^2}=10\\\\AC=\sqrt{(2-6)^2+(8-2)^2}=7.21[/tex]
Perimeter = 15.23 + 10 + 7.21 = 32.44 unit
We have [tex]s=\frac{15.23+10+7.21}{2}=16.22[/tex]
Area of triangle[tex]=\sqrt{s(s-AB)(s-BC)(s-AC)}=\sqrt{16.22(16.22-15.23)(16.22-10)(16.22-7.21)}=30[/tex]
Area of triangle = 30 unit²
Jar one has 133 pennies. Jar 2 has 127 times jar one. How many pennies does jar 2 have?
The ratio of green pepper plants to red pepper plants in joes garden is 2 to 7 if joe has 20 more red peppers plants than green pepper how many of each does he have
Joe has 8 green pepper plants and 28 red pepper plants in his garden.
Explanation:Let's denote the number of green pepper plants as G and the number of red pepper plants as R.
According to the given information, the ratio of green pepper plants to red pepper plants is 2 to 7.
This can be written as G:R = 2:7.
It is also mentioned that there are 20 more red pepper plants than green pepper plants. This can be written as R = G + 20.
Now, we can substitute the value of R from the second equation into the first equation:
G:G+20 = 2:7
By cross-multiplying, we have 7G = 2(G+20).
Simplifying the equation, we get 7G = 2G + 40.
Subtracting 2G from both sides, we have 5G = 40.
Dividing both sides by 5, we get G = 8.
Therefore, there are 8 green pepper plants and 8 + 20 = 28 red pepper plants in Joe's garden.
Calculate s50 for the arithmetic sequence defined by
Answer:
617.5
Step-by-step explanation:
If you expand the series by putting in [tex]n=1,n=2,n=3...[/tex] values, you will see:
Put 1 in [tex]n[/tex], [tex]71-2.3(1)=68.7[/tex]Put 2 in [tex]n[/tex], [tex]71-2.3(2)=66.4[/tex]Put 3 in [tex]n[/tex], [tex]71-2.3(3)=64.1[/tex]68.7, 66.4, 64.1, ....
To find common difference (d) (difference in a term and its previous term) we take any term and subtract from it the term before it:
[tex]66.4-68.7=-2.3[/tex]
The sum of arithmetic series formula is:
[tex]S_{n}=\frac{n}{2}[2a+(n-1)d][/tex]
Where,
[tex]S_{n}[/tex] is the sum of nth terma is the first term (in our case it is 68.7)n is the term number (in our case we want to find 50th sum, so n = 50)d is the common difference (in our case it is -2.3)Substituting these values, we get:
[tex]S_{50}=\frac{50}{2}[2(68.7)+(50-1)(-2.3)]\\S_{50}=25[137.4+(49)(-2.3)]\\S_{50}=25[24.7]\\S_{50}=617.5[/tex]
Last answer choice is right.
Answer: D. 617.5 hope that helps !
Please help me!!!!!!!!!!!!!
The total number of observations is
2+9+16+12+8+6+4+2+1=60
The first five counts refer to 0 to four cars:
2+9+16+12+8=47
The probability is the fraction less than five,
p= 47/60 = 0.783333...
Answer: 78%
Answer:
59%
Step-by-step explanation:
First let us work out the total number of cars waiting in the given period.
= 0 *2 + 1*9 + 2*16 + 3*12 + 4*8 + 5*6 + 6*4+7*2+8*1
= 185
Now the number when there are less than 5 cars in line ( that is when there are 0 - 4 cars in line) =
0*2 + 1*9 + 2*16 +3*12+4*8
= 109
Thus the required probability = 109/185
= 0.589
= 59% (answer)
The gift shop at manatee mall was having a clearance sale everything marked down 30%. The original price of a manatee hat was 18$. What was the clearance price ?
Answer:
$12.60
Step-by-step explanation:
To find this, you need to remember this equation:
Starting amount x [tex]\frac{100 - percent}{100}[/tex]
Plug these values in:
18 x [tex]\frac{70}{100}[/tex] = 12.6
So the clearance price was $12.60!
Geometry problem below
Answer:
A quadrilateral has 4 right angles
Step-by-step explanation:
In a conditional statement
If hypothesis, then conclusion
OR
Conclusion, if hypothesis.
The hypothesis goes with the if part.
At lunch 3 1/4 small pizzas were equally divided amping students. If each student ate 1/4 of a pizza, how many students were fed?
Final answer:
By converting the total amount of pizza into an improper fraction and dividing it by the portion each student ate, it's determined that 13 students were fed.
Explanation:
To find out how many students were fed, we first need to convert the total amount of pizza available into a form that can be easily divided by the portion each student eats. The total pizza available is 3 1/4 small pizzas. Since each student ate 1/4 of a pizza, we can see how many times 1/4 fits into 3 1/4 to determine the number of students.
We convert 3 1/4 into an improper fraction to make the calculation easier. 3 1/4 is equivalent to 13/4. Now, we divide 13/4 by 1/4 to find out how many students were fed. This is equivalent to multiplying 13/4 by the reciprocal of 1/4, which is 4/1.
13/4 × 4/1 = 13, meaning that 13 students were fed.
Point A of the vector from the origin represents a complex number plotted on the complex plane. Which point represents the product of the complex number and -1?
Multiplying a complex number by -1 flips it across the origin on the complex plane, changing its direction by 180 degrees but not its magnitude, resulting in a point directly opposite to the initial position.
Explanation:The question asks about the effect of multiplying a complex number by -1 in the complex plane. Multiplying a complex number by -1 essentially flips the point representing the complex number across the origin. If Point A represents a complex number on the complex plane, multiplying that complex number by -1 will result in a point that lies exactly opposite of Point A with respect to the origin. This operation does not change the magnitude of the complex number but changes its direction by 180 degrees. This is because the complex plane is analogous to a two-dimensional Cartesian coordinate system where complex numbers are represented as vectors. The multiplication by -1 is a reflection across the origin in such a plane.
For example, if a complex number z is represented by the point (a, b) where a is the real part and b is the imaginary part, then multiplying z by -1 gives us the point (-a, -b). This operation is similar to rotating the vector z 180 degrees around the origin or mirroring it across both the x and y axes.
Which graph represents f(x)=4*2x?
[tex]f(x)=4\cdot2^x\\\\y-intercept\ for\ x=0:\\\\f(0)=4\cdot2^0=4\cdot1=4[/tex]
Answer: Third option (bottom left)
Step-by-step explanation: We want to find which one of the graphs is the graph of the function f(x) = 4*2^x
Let's analyze some interesting points.
f(0) = 4*2^0 = 4*1 = 4
So we need to find the graph that passes through the point (0,4) (this means that intercepts the y-axis in the 4)
The graph that passes through the point (0,4) is the third option (bottom left one)
1 .) 3 5/8 divided by 1/2
2.) 3 2/6 divided by 2/3
3. ) 4 1/2 divided by 3/4
4. ) 3 1/2 divided by 3/4
5. ) 3 2/9 divided by 3
Thank youu.
Answer:
1. 29/4
2. 5
3. 6
4. 14/3
5. 29/27
Step-by-step explanation:
Answer: You the answer
Step-by-step explanation: cause your fine
A watermelon at the grocery store weighs 4.5 kg. How much does the watermelon weigh in pounds and ounces?
Answer: 4.5kg = 9.9208lbs
4.5kg = 158.733oz
The watermelon weighs approximately 4.5 kg, which can be converted to pounds and ounces by using the conversion factors. It is approximately 9 pounds and 15 ounces after conversion.
Explanation:A watermelon at the grocery store weighs 4.5 kg. To convert this weight into pounds and ounces, we can use the fact that 1 kg is equivalent to 2.205 pounds (lb) and 1 pound equals 16 ounces.
First, let's find out how much the watermelon weighs in pounds:
Multiply the weight of the watermelon in kilograms (4.5 kg) by the conversion factor (2.205).4.5 kg × 2.205 lb/kg = 9.9225 pounds.Since we want the weight in pounds and ounces, we'll convert the decimal part of the pounds to ounces:
The whole number part is the pounds, so we have 9 pounds.To find the ounces, take the decimal part (0.9225) and multiply it by 16 ounces per pound (0.9225 × 16 oz).0.9225 × 16 oz = 14.76 ounces.Therefore, the watermelon weighs approximately 9 pounds and 15 ounces (rounding 14.76 ounces to the nearest whole number).
Ryan is 14. Her brothers age is three more than half her age. How old is your brother?
Answer: 10
Step-by-step explanation:
Lina took out a 4-year loan for $14,000 to buy a new car. She has to pay 4% simple interest on the loan. How much will Lina have paid in all after the four years?
HELP I HAVE TO GO IN A MINUTE Which function has a y-value of 12, if the x-value is 3?
y = x - 6
y = 4x
y = x + 8
y = 3x
7. Which of the following is false? A none, since all of the other answer choices are true B the cost to mail an envelope and the weight of the envelope is a positive correlation C a child's age and a child's shoe size is a positive correlation D the graduation rate in a city and the rate of unemployment in a city is a positive correlation
Answer:
Both A and D are false
Step-by-step explanation:
We expect lower academic performance when unemployment is high, so a lower graduation rate. Dropouts—those who don't graduate—tend to have a higher unemployment rate, so there is cause/effect working in both directions. Thus graduation rate and unemployment would be negatively correlated. (One study showed the correlation coefficient to be about -0.11.)
Because D is false, A is also false.