An inequality that represents Alicia’s possible age is x < 8.
For given question,
let x represent Alicia's age.
Amy is eight years older than twice her cousin Alicia’s age.
So, Amy's age would be 2x + 8
The sum of their ages is less than 32.
We write above statement in mathematical expression.
sum of their ages = (2x + 8) + x
= 3x + 8
The sum of their ages is less than 32.
We use the symbol < for 'less than'
So, the mathematical expression form of given statement would be,
(3x + 8) < 32
So, we get an inequality 3x + 8 < 32
⇒ 3x < 32 - 8
⇒ 3x < 24
⇒ x < 24/3
⇒ x < 8
Therefore, an inequality that represents Alicia’s possible age is x < 8.
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If point P (-1, 4) is translated to the right 4 units and up 2 units, what are the new coordinates.
Answer:
The correct answer should be P(1, 7)
helllllp asap pls!!!!!
6. The measure of each angle is m∠ E = 46°, m∠ D = 46°.
Angle of elevation from point A to B (∠ E ) is the angle between the horizontal line from A to B.
And, Angle of depression from B to A ( ∠D ) is the angle from the horizontally downward line from B to A.
As we can see that all the horizontal lines are in parallel to each other,
Alternative Interior Angle : When two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent.
With the help of above theorem,
Angle of elevation from point A to B = Angle of depression from point B to A,
∠E and ∠D are interior opposite angles.
Then, m ∠ E = m ∠ D
3x + 1 = 2(x + 8) ( Given )
3x + 1 = 2x + 16
x = 15,
So, m∠ E = 3x + 1 = 45 + 1 = 46°
Hence, m∠D = 46°
7. The measure of each angle is m∠ E = 20°, m∠ D = 20°.
By following same method as given above we will solve this question.
So, As we know that
Angle of elevation from point A to B = Angle of depression from point B to A,
∠E and ∠D are interior opposite angles.
Then, m ∠ E = m ∠ D
5(x - 2) = (x + 14)
5x - 10 = x + 14
5x -x = 14 + 10
4x = 24
x = 24/4 = 6
So, m∠ D = (x + 14) = 6 + 14 = 20°
Hence, m ∠ E = 20°
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Please Help! Best answer gets Brainliest.
Find P on NM that is the given fractional distance from N to M. Please explain.
Equation:
1/5; N (-3, -2), M (1, 1)
The coordinates of the point P that partitions the Line N, into the ratio 1:5 is; P(x, y) = (-14/6), (-9/6)
How to partition line segment?We are told that the point P partitions the Line N, into the ratio 1:5.
Now, the coordinates of N and M are;
N(-3, -2), M(1, 1)
The formula to find the coordinates that partition a line is;
P(x, y) = (bx1 + ax2)/(a + b), (by1 + ay2)/(a + b)
where the ratio is a:b. Thus;
Thus, the coordinates of point P here are calculated as;
P(x, y) = (5*-3 + 1*1)/(1 + 5), (5*-2 + 1*1)/(1 + 5)
P(x, y) = (-14/6), (-9/6)
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Find the coordinates of the missing endpoint if b is the midpoint of AC. A(-4,2),B(6,-1)
Answer:
Step-by-step explanation:
Answer:(3,2)
Step-by-step explanation:
find the quotient 4 4/5 divided by 4/5
Answer:
Step-by-step explanation:
6
What is the value of x? enter your answer in the box. x = two lines slightly inclined with vertical intersect at the midpoint. the left and right angles made by these lines are obtuse. the right obtuse angle is labeled left square bracket 5 left parenthesis x minus 4 right parenthesis right square bracket degrees. the left obtuse angle is labeled left parenthesis 4 x plus 7 right parenthesis degrees.
The value of 'x' in the given question is 27°.
Obtuse Angle may be defined as an angle that is greater than 90° and less than 180°. It may be also defined as an angle between a right angle and a straight-line angle.
From the question we can conclude that the given angles are vertically opposite to each other, and vertically opposite angles are always equal to each other.
Vertically opposite angles are formed when two lines are intersecting each other and the angles formed on each side of the intersection point are called vertically opposite angles.
Now according to the question:
[5(x-4)]°=(4x+7)°
Rearranging the terms:
(5x-20)°=(4x+7)°
=>x=27°
Therefore, the value of x is 27°.
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A​ 150-pound person uses 5.9 calories per minute when walking at a speed of 4 mph. how long must a person walk at this speed to use at least 250 ​calories?
The time taken when the person wants to burn 250 calories will be 42.37 minutes.
How to illustrate the information?From the information, the 150-pound person uses 5.9 calories per minute when walking at a speed of 4 mph.
Therefore, the time taken when the person wants to burn 250 calories will be:
= Number of calories / 5.9
= 250 / 5.9
= 42.37 minutes.
Therefore, the time taken when the person wants to burn 250 calories will be 42.37 minutes.
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Can you pls help me tink u <3
the sum of 17 and 3 times x *
The sum of 17 and 3 times x is given by the algebraic expression "17+3x" .
A mathematical construct called an algebraic expression is made up of integer constants, variables, and algebraic operations (addition, subtraction, multiplication, division, and exponentiation by a rational exponent).
Let us take an expression 4x³+6xy+9 is an algebraic expression. Where
x,y are variables 4 and 6 are co-efficients and 9 is the constant .
In the above statement it is given that the sum of 17 and times x. Here x is a variable.
3 times x equates to 3x and when 17 is added we get the expression 17+3x.
Hence the required algebraic expression is 17+3x
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CHECK MY ANSWERS
1. How would you write the name of a segment differently than the name of a line. What symbols would you use?
Answer: A line and a line segment may sound quite similar however they are very different. A line, in short, is a line that never ends so it's infinite. It's the same for a line segment except at its end it is indicated by dots rather than arrows
2. How is constructing a perpendicular bisector similar to constructing an angle bisector? How is it different
Answer: A perpendicular bisector and an angle bisector are similar because they both require the need to find where two arcs meet. They are different because angle bisectors split into congruent angles meanwhile a perpendicular bisector splits into congruent segments.
3. Describe a process you would use to create the perpendicular bisector to a segment AB using only an unmarked straightedge and an unmarked compass.
Answer: The first step I will do will be to open the compass and stretch it to a width that will be greater than the length of AB. Then I would place one point of the compass onto the line's segments A, then I would move the compass and draw the arcs above and below the AB line. Next step I would do would be to remove the compass from point A and place it onto point B, then repeat the second step (drawing arcs above and below the line). Then lastly, I will use my straightedge and draw a line that will go vertically through where they connect.
1. A line segment can be written with just naming it by its end points and a bar above it while the name of a line requires an double-headed arrow mark above its name.
2. For constructing both a perpendicular and an angle bisector, we need to construct two arcs using a compass and their intersection point. A perpendicular bisector divided a line segment into two equal parts whereas an angle bisector divides an angle into two equal parts.
3. A perpendicular bisector can be drawn by drawing two arcs each above and below the line segment and joining using an straight edge.
1. A line and a line segment may sound quite similar however they are very different. A line, in short, is a line that never ends so it's infinite. It's the same for a line segment except at its end it is indicated by dots rather than arrows.
This difference can be seen in naming them too. A line segment is named using the initial and terminal points of the segment. Sometimes we put a 'bar' mark above its name. For example, [tex]\bar{AB}[/tex]
For a line of infinite length, it is named simply as 'line A' or 'line B' or sometimes put a double-headed arrow mark above its name.
2. A perpendicular bisector and an angle bisector are similar because they both require the need to find where two arcs meet. They are different because angle bisectors split into congruent angles meanwhile a perpendicular bisector splits into congruent segments.
Constructing a perpendicular bisector is similar in the sense that both are drawn using straight edge and compass and need to find the intersection point of the arcs. But they are different in their use as perpendicular bisector equally divides a line segment and an angle bisector equally divides an angle.
3. We have an unmarked straightedge and a compass. First put the compass at one end point A of the line. Then stretch the compass to a length more than half of the line segment AB to be bisected. In the next step, draw an arc above and one below the line. Next put the compass on the other end B of the line. Then repeat drawing two arcs, each above and below the line and also intersecting with the previous arcs. Finally join the two points got with a line cutting the line segment AB. This will be the perpendicular bisector of the line AB.
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Find the area of a circle with radius 6 in. Use the value 3.14 for π, and do not round your answer.
Step-by-step explanation:
Área of a circle is given as
[tex]\pi \times {r}^{2} [/tex]
Therefore you can substitute the values as follows:
[tex]3.14 \times {6}^{2} = 113.09733552923[/tex]
Answer not rounded to any decimal place and used of 3.14 as said in the instruction
The area is:
113.04 in²Explanation:
To find the circle's area, use the formula [tex]\sf{A=\pi r^2}[/tex].
where:
A = area;
π = 3.14 (pi);
r = radius
Diagram:
[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 6\ in}\end{picture}[/tex]
Plug in the data:
[tex]\sf{A=3.14\times6^2}[/tex]
[tex]\sf{A=3.14\times36}[/tex]
[tex]\sf{A=113.04\:in^2}[/tex]
290951.867863 rounded to the nearest hundred
The shaded area of the square is:
14 12 34
Answer:
5902
Step-by-step explanation:
that's what it tells with my calculations
suppose a jar contains 9 red marbles and 14 blue marbles. if you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red. answer should be in fractional form.
The probability that both are red should be 0.1423.
The possibility of picking up x number of balls among n number of balls is ⁿCₓ.
jar contains 9 red marbles and 14 blue marbles. Total number of marbles are 23.
favorable cases of picking two red marbles among 9 red marbles is ⁹C₂
And the total possible cases of picking two marbles among 23 marbles is ²³C₂
Therefore, the probability of picking both red marbles are = ( no. Of favorable cases/no. Of possible cases) = ( ⁹C₂ )/( ²³C₂ ) = 36/253 = 0.1423.
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Temperature Suppose there is a 1.6°F drop in temperature for every thousand feet that an airplane climbs into the sky. If the temperature on the ground is 46.2°F, what
will be the temperature when the plane reaches an altitude of 10,000 ft?
The temperature will be
PF. (Type an integer or a decimal.)
The temperature at 10,000 feet altitude will be 30.2 ° F.
We are given that:
As the airplane moves 1000 feet above the ground, the temperature drops by 1.6 ° F.
Now, the temperature on the ground is given as
Temperature on ground = 46.2 ° F
Now, the plane is at the altitude of 10,00 feet.
We need to tell the temperature at that altitude.
At 1000 feet, temperature drops by = 1.6 ° F.
At 10000 feet, the temperature will drop by = 1.6 ° F. × 10,000 / 1000
= 16 ° F.
So, the temperature will be = 46.2 ° F - 16 ° F
Temperature = 30.2 ° F
Therefore, the temperature at 10,000 feet altitude will be 30.2 ° F.
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HELP !!!
Point (2,6) is 2/3 of the way from A to B. If A has coordinates (-8, 6), what are the coordinates of B?
The coordinates of the point B are (-5, 6)
How to determine the coordinates of the point B?The given parameters are
A = (-8, 6)
Point = (2, 6)
Proportion = 2/3
Because the y coordinates are the same, we can make use of only the x coordinate
So, we have
Point = Proportion * (B - A)
This gives
2 = 2/3 * (B + 8)
Multiply through by 3/2
So, we have
3 = B + 8
Subtract 8 from both sides
B = -5
Hence, the coordinates of the point B are (-5, 6)
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What percentage of those who were married were obese?
a. 25.6%(331/1293)
b. 44.4% (147/331)
c. 32.8%(424/1293)
d. 34.7% (147/424)
The percentage of those who were married were also obese is: 34.7% (147/424; Option B)
What are percentages?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. A % is a number without dimensions and without a standard measurement.Now,
The percentage of number of married participants who were obese is calculated by: dividing the former (147) by the total number of married participants(424)
=> Percentage of married participants who were obese = 147/424.
Hence, The percentage of those who were married were also obese is: 34.7% (147/424; Option B)
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(COMPLETE QUESTION:
A 2009 study analyzed data from the National Longitudinal Study of Adolescent Health. Participants were followed into adulthood. Each study participant was categorized as to whether they were obese (BMI >30) or not and whether they were dating, cohabiting, or married. The table below summarizes the results.
Dating Cohabiting Married Total
Obese 81 103 147 331
Not Obese 359 326 277 962
Total 440 429 424 1293
What percentage of those who were married were obese? (Round your answer to 1 decimal place.)
A. 32.8% (424/1293)
B. 34.7% (147/424)
C. 25.6% (331/1293)
D. 44.4% (147/331))
"One subtracted
from the
product of 4 and
a number is Il”
The number will be 3.
How to calculate the value?Let the number be represented by x.
Therefore based on the information, the equation will be:
(x × 4) - 1 = 1
4x - 1 = 11
Collect like terms
4x = 11 + 1
4x = 12
Divide
x = 12/4
x = 3
The number is 3.
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math wizard! help me out
Answer: 27 days 60 miles
Step-by-step explanation: 162/6=27
6x17=102 162-102=60
Step-by-step explanation:
no wizardry is needed, as the function is already there. we only need to use it.
(a)
find d, so that 162 - 6d = 0 (0 miles are left)
162 - 6d = 0
162 = 6d
d = 162/6 = 27
it will take them 27 days.
(b)
L(17) = 162 - 6×17 = 162 - 102 = 60 miles
after 17 days they still have to lay 60 miles.
Some sales positions pay a commission only if sales exceed a sales
quota. The salesperson is rewarded only for having sales beyond an
expected amount. Joyce Doyle is a sales trainee. She is paid $1,550 per
month plus a commission of 7.5% on all sales of more than a $20,000
monthly quota. What is Joyce's total pay for a month in which her sales
totaled $22,650?
The sales on which Joyce earns commission is the sale beyond $20,000 which is $2,650. So the total pay for a month for Joyce in which her sales is $22,650 is $1748.75.
Joyce is paid $1,550 per month plus a commission of 7.5% on all sales of more than a $20,000 monthly quota. For the given month her sales is $22,650.
Percentage means a number or a ratio represented in the form of fractions of 100. It is represented using the percentage sign ‘%’. The abbreviations used to represent the percentage are ‘pct’ or ‘pc’. In other words, the percentage is defined as how much of one quantity is made by another quantity and it is evaluated in terms of 100.
Total pay of Joyce = Her pay per month + Commission that she gets
Commission she gets is on the sales beyond $20,000.
Here, commission is on $22,650 - $20,000 = $2,650
She gets 7.5% commission. So, her commission is 7.5% * $2,650
=> 75/1000 * $2,650 = $198.75
So, the total pay of Joyce is $1,550 + $198.75
=> $1748.75 for the month.
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Draw a scaled copy of polygon with the scaled factor of 2
A scaled copy of polygon with the scaled factor of 2 is Scale factor is defined as
It is a growing organism that falls between (0, infinity). According to the scale factor, an original figure might be either raised or decreased.
Consider two circles that appear to be the same. The word "identical" does not guarantee that both circles are of similar size. They could have various radii. One figure would be the other figure scaled down.
The ideas of ratio and proportion are intimately related to scale considerations. A given amount is multiplied or divided in ratio and proportions to create a new quantity.
A Scaled copy involves multiplying the lengths in the original figure by scale factor.
Here scale factor = 2,
Since the scale factor > 1, so there is an enlargement.
So, the scale copy's sides are 2 times of the sides of figure A.
Take the reference of grid:
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-1/4 divided by (-7/9)
Answer:
9/28
Step-by-step explanation:
when you divide a fraction by fraction you need to multiply the left fraction by the opposite of right fraction so -7/9 becomes -9/7 and then you multiply -1/4 by -9/7. When you multiply negative with negative you get a positive value.
it's better to display fractions vertically like this to understand better
1
_
4
Answer:9/28
Step-by-step explanation:
Which of the following expressions have the same value as the mixed number
Answer:
-29/4-7 - 1/4- (7 + 1/4)Step-by-step explanation:
your welcome <3
In the segment below, QV = 23. QT = 8. TR = RS = SV.
Answer:
RS = 5
QS = 18
TS = 10
TV = 15
Step-by-step explanation:
Given QV = 23 and QT = 8 and TR = RS = SV
now, we subtract the length of QT from the whole line, QV
23 - 8 = 15 then we divide this by 3 because TR = RS = SV so there must be 3 equal pieces
15 ÷ 3 = 5
RS = 5
QS = QT + TR + RS so
QS = 8 + 5 + 5
QS = 18
TS = TR + RS so
TS = 5 + 5 and
TV = TR + RS + SV
TV = 15
What do you need to add to -6 to get 10? i need helppp
Answer:
16
Step-by-step explanation:
x+(-6)=10 Take (-6) to the other side it becomes (+6).
x= 10 + 6
x=16
help help help help help help help help help help help help help help help
Step-by-step explanation:
11. Is a real numer
12. Is integer
13. Is rational
14. Is whole number
Define a variable and write an inequality to model the given situation. The restaurant can seat at most 154 people. *** If p is the restaurant's capacity, which of the following inequalities models the given situation?
A. p≥ 154
B. p≤ 154
C. p< 154
D. p>154
Answer:
B. p ≤ 154
Hope that helps :)
Step-by-step explanation:
The restaurant can hold 154 people or less than that.
The length of a bacterial cell is about 4 x 10 to the negative power of 6 m, and the length of an amoeba cell is about 2.5 x 10 to the power of 4 m. How many times smaller is the bacterial cell than the amoeba
cell? Write the final answer in scientific notation with the correct number of significant digits.
A. 06.25 x 10²
B. 2x10²
C. 6x 10¹
D. 16 x 10¹
The number of times the bacterial cell is smaller than the amoeba cell is 1.6 * 10^-10
How many times smaller is the bacterial cell than the amoeba cell?The given parameters are:
Bacteria cell = 4 x 10^-6 m
Amoeba cell = 2.5 x 10^4 m
The number of times (n) is calculated as
n = Amoeba cell/Bacteria cell
This gives
n = (4 x 10^-6 m)/(2.5 x 10^4 m)
This gives
n = 1.6 * 10^-10
Hence, the number of times the bacterial cell is smaller than the amoeba cell is 1.6 * 10^-10
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A dress has a retail price of $195, but the store is running a sale and is giving 15% off of the retail price on all dresses. The store is located in Los Angeles, CA, which has a sales tax rate of 8%. Note: The 15% discount is applied prior to the item being taxed. You have $180 to spend. Can you afford to buy the dress? How much will it cost you?
Answer:
$179.01
Step-by-step explanation:
(First Step) $195 - 15% = $165.75
(Second Step) $165.75 + 8% = $179.01
with show work please. a and b.
Step-by-step explanation:
(a)
the sum of all internal angles in a polygon with n sides is
(n - 2)×180.
since in a regular polygon all angles are equally large, we get for one internal angle :
(n - 2)×180/n
for our hexagon this means the internal angle is
(6 - 2)×180/6 = 4×30 = 120°
(b)
the area of the hexagon is (as the graphic so nicely suggests) the sum of the areas of all 6 inner triangles.
the area of a triangle is
baseline × height / 2
baseline = 10 cm
the height (from the tip of the triangle down to the baseline in a right angle) is half of 17.3 cm, because these 17.3 cm are the sum of the 2 heights of 2 triangles placed tip to tip.
so, height = 17.3/2 = 8.65 cm
the area of one of the triangles is therefore
10 × 8.65 / 2 = 5 × 8.65 = 43.25 cm²
the total area of the hexagon is then
6 × 43.25 = 259.5 cm²