The value of x in the figure is 4
How to determine the value of x in the figure?From the attached figure, we have the following parameters:
DE = x + 1
BC = 4x - 6
The triangles ADX and ABC are similar triangles
Based on the representation of the sides, we have:
BC = 2 * DE
So, we have
2 * (x + 1) = 4x - 6
Expand
2x + 2 = 4x - 6
Evaluate the like terms
2x = 8
Divide by 2
x = 4
Hence, the value of x in the figure is 4
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Which value of b results in infinitely many solutions for the system?
9x+6y=b
3x+2y=1
6
1
5
3
Answer: 3
Step-by-step explanation:
I just finished the test and this was the answer I put and it was right.
9x+6y=b
6y=b-9x
y=b/6 -9/6x
y=b/6-3x/2
y= -3x/2 +b/6
3x + 2y = 1
2y = 1 - 3x
y = 1/2 -3/2x
y = -3/2x + 1/2
b/6=1/2
b=3
Answer:
Step-by-step explanation:
Analyze the diagram below and complete the instructions that follow.
K
B
A
гс
F
E
Given that ZCFE ZCFA, mZCFB = 68°, and mZEFD= 62°, find the measure of ZAFD.
The measure of ZAFD is 50 degrees.
Based on the given information:
ZCFE is congruent to ZCFA.
mZCFB = 68°.
mZEFD = 62°.
To find the measure of ZAFD, we can use the fact that angles in the same segment of a circle are equal.
Since ZCFE and ZCFA are congruent, angle ZCFE is equal to angle ZCFA.
Therefore, mZCFA = mZCFE.
Now, let's find the measure of angle ZCFE:
mZCFE = mZCFB + mZEFD (Angle Addition Postulate)
mZCFE = 68° + 62°
mZCFE = 130°
Since ZCFA is congruent to ZCFE, we can conclude that mZCFA is also equal to 130°.
Now, to find the measure of ZAFD, we need to consider the angles in the quadrilateral ZAFD.
The sum of the angles in a quadrilateral is always 360°.
mZAFD + mZAFB + mZBFD + mZBFA = 360°
We know that mZAFB and mZBFD are equal to 90° because they are right angles (angle AFB and angle BFD are right angles in the diagram).
Therefore, we can rewrite the equation as:
mZAFD + 90° + 90° + mZBFA = 360°
Simplifying:
mZAFD + 180° + mZBFA = 360°
Rearranging the equation:
mZAFD + mZBFA = 360° - 180°
mZAFD + mZBFA = 180°
We know that mZBFA is equal to mZCFA, which is 130°.
Substituting the known values into the equation:
mZAFD + 130° = 180°
Subtracting 130° from both sides:
mZAFD = 180° - 130°
mZAFD = 50°
Therefore, the measure of ZAFD is 50 degrees.
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Please help! Easy question, answer pls, 15 pts.
Answer:
360 in
Step-by-step explanation:
To figure out how many inches the dressmaker has in 10, 3 ft rolls, we can multiply by the conversion ratio:
\(\dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies (10 \cdot 3 \text{ ft}) \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30 \text{ ft} \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30\cdot 12 \text{ in} \\ \\ \text{} \ \ \implies \boxed{360 \text{ in}}\)
So, the dressmaker has 360 in of ribbon.
through (-6,4), slope:2
Answer:
y - 4 = 2(x + 6)
Step-by-step explanation:
Use the point-slope formula y - k = m(x - h):
y - 4 = 2(x + 6)
Tell which value of the variable is the solution of the equation. 128÷n=16; n=5, 6, 7, 8
Answer:
8
Step-by-step explanation:
128/n * n = 16 * n
128 = 16n
128/16 = 16/16 n
n = 8
A grasshopper makes jumps that are either 17 or 19 cm in length, in either direction (forwards or backwards). Is it possible for the grasshopper to cover a distance of 101 cm in 100 jumps?
Answer: No. The grasshopper cannot cover exactly 101 cm in exactly 100 jumps.
Step-by-step explanation:
If the grasshopper makes 50 forward jumps of 19 cm and 50 backward jumps of 17 cm (in any order) the jumps total 950-850 for a net result of 100.
Changing to any other amount just gets farther away from the goal.
A system of equations yields no solution of integers.
x + y ==100
19x - 17y =101
You can try it, but the result has a decimal. This grasshopper cannot make partial jumps!
the scalar product between two vectors involves which function of the angle between the lines of action of the two vectors
The scalar product between two vectors involves the cosine function of the angle between the lines of action of the two vectors.
What is the scalar product?The dot product, also known as the scalar product, is an algebraic operation that takes two sequences of numbers of equal length (often coordinate vectors) and outputs a single number. The dot product of two vectors' Cartesian coordinates is frequently used in Euclidean geometry. Although other inner products can be defined in Euclidean space, it is frequently referred to as the inner product (or, less frequently, projection product) of Euclidean space (see Inner product space for more). The sum of the products of the matching entries of the two number sequences is the dot product, according to algebra. Geometrically, it is the result of adding the cosine of the angle between the two vectors and the Euclidean magnitudes of the two vectors.
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Mr. Alexander was traveling home from a business
trip. A taxi driver took him from his hotel room to a
bus station that was 18 miles away. The taxi traveled at an average rate of 60 miles an hour.
Mr. Alexander waited 15 minutes at the bus station
before leaving on a 178-mile bus ride.
Mr. Alexander's trip took a total of 5 hours from the time he left the hotel to the time the bus arrived at its destination. At
what average rate did the bus travel? Explain or show calculations to support the answer.
Using the relation between velocity, distance and time, it is found that the bus traveled at a rate of 40 miles per hour.
What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
\(v = \frac{d}{t}\)
The taxi took 18 minutes(60 miles per hour = 1 mile per minute), while he waited for 15 minutes at the station. Thus, the 178-mile bus trip took 4 hours and 27 minutes, so t is given by:
\(t = 4 + \frac{27}{60} = 4.45\)
Hence, the velocity is given by:
\(v = \frac{d}{t} = \frac{178}{4.45} = 40\)
The bus traveled at a rate of 40 miles per hour.
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round 467 to the nearest ten
Answer:
470 is it right if is you welcome
Need help with -9x - x + 3 + 5
Answer:
8x+8
Step-by-step explanation:
-9x-x+3+5
-9x-1x+3+5
9x-1x+3+5
8x+3+5
8x+8
HAVE A GREAT DAY!! HOPE THIS HELPS!! :))
chewbacca has 20 pieces of cherry gum and 30 pieces of grape gum. some of the pieces are in complete packs, while others are loose. each complete pack has exactly x pieces of gum. if chewbacca loses one pack of cherry gum, then the ratio of the number of pieces of cherry gum he has to the number of pieces of grape gum will be exactly the same as if he instead finds 5 packs of grape gum. find x.
Let's assume the number of complete packs of cherry gum is c1 and the number of complete packs of grape gum is c2. The number of loose pieces of cherry gum is l1, and the number of loose pieces of grape gum is l2.
According to the given information, we have the following equations:
c1 * x + l1 = 20 (equation 1)
c2 * x + l2 = 30 (equation 2)
If Chewbacca loses one pack of cherry gum, the new ratio of the number of pieces of cherry gum to the number of pieces of grape gum will be the same as if he instead finds 5 packs of grape gum.
This can be represented as:
[(c1 - 1) * x + l1] / (c2 * x + l2 + 5 * x) = (c1 * x + l1) / (c2 * x + l2)
Simplifying the equation, we have:
[(c1 - 1) * x + l1] = (c1 * x + l1) * (c2 * x + l2 + 5 * x) / (c2 * x + l2)
Expanding and simplifying further:
(c1 - 1) * x + l1 = (c1 * x + l1) * (c2 + 6) / c2
Let's now substitute the values for c1, l1, and c2:
From equation 1: c1 * x + l1 = 20
From equation 2: c2 * x + l2 = 30
Substituting these values, we get:
(20 - 1) * x + l1 = (20 * x + l1) * (c2 + 6) / c2
Simplifying:
19x + l1 = (20x + l1) * (c2 + 6) / c2
Since we are looking for the value of x, we need another equation to solve for it. Unfortunately, we do not have enough information or constraints in the given problem to determine the exact value of x. Additional information or equations are required to solve for x.
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Dan has a piece of wood that is 3 feet long. He needs a piece that is 2 feet 5 inches long for a science project. How many inches of wood will be left after Dan cuts off the piece he needs for his project?
Answer: 7 Inches left
Step-by-step explanation:
1 foot is 12 inches
12 inches minus 5 = 7
subtract the 2 feet from 3
7 inches left
A conical candle is to be made from 250 cm3 of wax. If the candle's height is three times its diameter, what radius and height should it have, to the nearest tenth?
Answer:
The radius and height of the cone are 3.41 cm and 20.46 cm respectively.
Step-by-step explanation:
Given that,
The volume of a conical candle is 250 cm³.
The height of candle is 3 times of its diameter.
h = 3d (d = 2r, radius)
So,
h = 6r
The formula of volume of a cone is given by :
\(V=\dfrac{1}{3}\pi r^2h\\\\250=\dfrac{1}{3}\pi \times r^2\times 6r\\\\250=2\pi r^3\\\\r=(\dfrac{250}{2\pi })^{1/3}\\\\r=3.41\ cm\)
Height, h = 6r = 6(3.41) = 20.46 cm
Hence, the radius and height of the cone are 3.41 cm and 20.46 cm respectively.
possible answer
5
-5
2.8
-2.8
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A(n) ___________ solution satisfies all the constraint expressions simultaneously.
a.feasible
b.objective
c.infeasible
d.extreme
A problem is said to be infeasible if no solution exists which satisfies all the constraints.
Objective function: the expression that defines the quantity to be maximized or minimized in a linear programming model. Constraints: restrictions that limit the settings of the decision variables.
When it comes to linear programming, the solution which would be effective in satisfying all constraints in the given program in a simultaneous matter is called that of feasible programming. This is due to the fact that the program can satisfy all requirements at the same time.
Linear programming, also known as linear optimization, is a method for achieving the best result in a mathematical model with requirements represented by linear relationships. Linear programming is a special case of mathematical programming.
In linear programming, a solution that does not simultaneously satisfy all constraints is called an infeasible solution.
Therefore,
A problem is said to be infeasible if no solution exists which satisfies all the constraints.
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Jay works two jobs, at a daycare center and at a grocery store. The number of hours he works at the grocery store is twice the number of hours he works at the daycare. Jay works a total of 42 hours per week. Which equation can be used to find the number of hours that Jay works at the daycare?
Answer:
3x=42
Step-by-step explanation:
assume Jay works x hours in daycare, which means he works 2x hours in the grocery store, he totally works 42 hours per week equal to x hours in daycare plus 2x in the grocery store.
write the symbolic expression for each of the following descriptions, then get rid of the radical and make them exponential expressions in fractional form. 11. the eighth root of fifty seven to the sixth degree
The final exponential expression in fractional form for "the eighth root of fifty-seven to the sixth degree" is 57^(3/4).
To express the given description as a symbolic expression and then convert it into an exponential expression in fractional form, we'll follow these steps:
Step 1: Symbolic Expression
The description states "the eighth root of fifty-seven to the sixth degree." Let's denote this as √[57]^(1/8)^6.
Step 2: Removing Radical
To eliminate the radical (√), we can rewrite it as a fractional exponent. The numerator of the fractional exponent corresponds to the power (6) applied to the base, and the denominator corresponds to the index of the root (8).
So, the expression becomes (57^(1/8))^6.
Step 3: Simplifying Exponents
To simplify the exponent, we multiply the powers:
(57^((1/8)*6))
Simplifying further:
(57^(6/8))
Step 4: Fractional Form
The exponent 6/8 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2:
(57^(3/4))
Therefore, the final exponential expression in fractional form for "the eighth root of fifty-seven to the sixth degree" is 57^(3/4).
This means that we raise 57 to the power of 3/4 to represent the original description. The fraction 3/4 indicates taking the eighth root of 57 and then raising it to the sixth power.
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the graph of line g is shown below. which equation describes a line parallel to the line g and passes through the point (-1, 3)?
Answer:
Write the equation of a line passing through point (8, -3 ) and is perpendicular to
−
2
x
+
y
=
9
Step-by-step explanation:
Graph the system of equations {y=−12x+4y=−12x−2
Answer:
Step-by-step explanation: i hope this help if not let me know so i can fix it
1. Mike's family went out for dinner. The meals including tax cost
$69.57. If they leave a 15% tip...
a. How much is the tip?
b. How much money did they spend on dinner?
(Round to the nearest cent)
Answer:
Tip: \($10.44\)
Total: \(80.01\)
Step-by-step explanation:
\(\frac{x}{69.57} =\frac{15}{100} \)
\(\frac{100x}{100} =\frac{1043.55}{100} \\ x=10.4355\)
\(69.57+10.44=80.01\)
x = y -16
solve for y
Answer:
x+16=y
Step-by-step explanation:
\(x=y-16\\x+16=y\)
rewite 3/2:1/4 as a unit rate
An 8-sided fair die is rolled twice and the product of the two numbers obtained when the die is rolled two times is calculated.(a) Draw the possibility diagram of the product of the two numbers appearing on the die in each throw (b) Use the possibility diagram to calculate the probability that the product of the two numbers is I) A prime number ii) Not a perfect square iii) A multiple of 5 iv) Less than or equal to 21 v) Divisible by 4 or 6
Answer:
(a) Shown below.
(b) Explained below.
Step-by-step explanation:
(a)
The sample space of rolling an 8-sided die twice is as follows:
S = {(1 , 1) , ( 1 , 2) , ( 1, 3) , ( 1, 4 ) , ( 1, 5) , ( 1 , 6 ) , ( 1, 7 ) , ( 1, 8) ,
(2 , 1) , (2 , 2) , ( 2, 3) , ( 2, 4 ) , ( 2, 5) , (2 , 6 ) , ( 2, 7 ) , ( 2, 8) ,
(3 , 1) , ( 3, 2) , ( 3, 3) , ( 3, 4 ) , ( 3, 5) , ( 3 , 6 ) , (3, 7 ) , ( 3, 8) ,
(4, 1) , ( 4 , 2) , ( 4, 3) , ( 4, 4 ) , ( 4, 5) , (4 , 6 ) , (4, 7 ) , (4, 8) ,
(5, 1) , ( 5 , 2) , ( 5, 3) , (5, 4 ) , ( 5 ,5) , (5, 6 ) , ( 5, 7 ) , ( 5, 8) ,
(6 , 1) , ( 6 , 2) , ( 6, 3) , (6, 4 ) , ( 6, 5) , (6 , 6 ) , ( 6, 7 ) , ( 6, 8) ,
(7 , 1) , ( 7 , 2) , ( 7, 3) , ( 7, 4 ) , ( 7 , 5) , ( 7, 6 ) , ( 7, 7 ) , (7, 8) ,
(8 , 1) , ( 8 , 2) , (8, 3) , ( 8, 4 ) , ( 8, 5) , ( 8 , 6 ) , ( 8, 7 ) , ( 8, 8)}
There are a total of N = 64 elements.
(b)
(i)
The product of the two numbers is a prime number:
Product is a prime number samples:
2 = ( 1, 2) , ( 2, 1)
3 = ( 1 , 3) , ( 3 , 1)
5 = ( 1, 5) , ( 5 , 1)
7 = ( 1, 7) , ( 7 , 1)
Number of samples, n = 8
P (Product is a prime number) = 8/64 = 1/8 = 0.125.
(ii)
The product of the two numbers is not a perfect square :
Product is not a perfect square samples:
2 = ( 1, 2) , ( 2, 1)
3 = ( 1 , 3) , ( 3 , 1)
5 = ( 1, 5) , ( 5 , 1)
6 = ( 1, 6) , ( 2, 3) , ( 3, 2) , ( 6 , 1)
7 = ( 1, 7) , ( 7 , 1)
8 = ( 1 , 8) , ( 2, 4) , ( 4 , 2) , ( 8 , 1)
10 = ( 2, 5) , ( 5, 2)
12 = (2 , 6) , ( 3 , 4) , ( 4 3) , ( 6 , 2)
14 = ( 2, 7) , ( 7 , 2)
15 = (3 , 5) , ( 5 , 3)
18 = ( 3, 6) , ( 6 , 3)
20 = ( 4, 5) , ( 5, 4)
21 = ( 3 , 7) , ( 7 , 3)
24 = ( 3 , 8) , ( 4 , 6 ) , ( 6 , 4) , ( 8 , 3)
28 = ( 4 , 7) , ( 7 , 4)
30 = ( 5 , 6) , ( 6 ,5 )
32 = ( 4 , 8) , ( 8 , 4)
35 = ( 5 , 7) , ( 7 , 5)
40 = ( 5 , 8) , ( 8 , 5)
42 = ( 6 , 7) , ( 7 , 6)
48 = ( 6 , 8) , ( 8 , 6)
56 = ( 7 , 8) , ( 8 , 8)
Number of samples, n = 52
P (Product is not a perfect square) = 52/64 = 0.8125
(iii)
The product of the two numbers is a multiple of 5:
Product is a multiple of 5 samples:
5 = ( 1, 5) , ( 5 , 1)
10 = ( 2, 5) , ( 5, 2)
15 = (3 , 5) , ( 5 , 3)
20 = ( 4, 5) , ( 5, 4)
25 = ( 5 , 5)
30 = ( 5 , 6) , ( 6 ,5 )
35 = ( 5 , 7) , ( 7 , 5)
40 = ( 5 , 8) , ( 8 , 5)
Number of samples, n = 15
P (Product is a multiple of 5 ) = 15/64 = 0.2344.
(iv)
The product of the two numbers is less than or equal to 21:
Product is less than or equal to 21 samples:
1 = ( 1, 1)
2 = ( 1, 2) , ( 2, 1)
3 = ( 1 , 3) , ( 3 , 1)
4 = (1 , 4) , ( 2, 2) , ( 4, 1)
5 = ( 1, 5) , ( 5 , 1)
6 = ( 1, 6) , ( 2, 3) , ( 3, 2) , ( 6 , 1)
7 = ( 1, 7) , ( 7 , 1)
8 = ( 1 , 8) , ( 2, 4) , ( 4 , 2) , ( 8 , 1)
9 = ( 3, 3)
10 = ( 2, 5) , ( 5, 2)
12 = (2 , 6) , ( 3 , 4) , ( 4 3) , ( 6 , 2)
14 = ( 2, 7) , ( 7 , 2)
15 = (3 , 5) , ( 5 , 3)
16 = (2 , 8) , ( 4 , 4) , ( 8 , 2)
18 = ( 3, 6) , ( 6 , 3)
20 = ( 4, 5) , ( 5, 4)
21 = ( 3 , 7) , ( 7 , 3)
Number of samples, n = 40
P (Product is less than or equal to 21) = 40/64 = 0.625.
(v)
The product of the two numbers is divisible by 4 or 6:
Product is divisible by 4 or 6 samples:
4 = (1 , 4) , ( 2, 2) , ( 4, 1)
6 = ( 1, 6) , ( 2, 3) , ( 3, 2) , ( 6 , 1)
8 = ( 1 , 8) , ( 2, 4) , ( 4 , 2) , ( 8 , 1)
12 = (2 , 6) , ( 3 , 4) , ( 4 3) , ( 6 , 2)
16 = (2 , 8) , ( 4 , 4) , ( 8 , 2)
18 = ( 3, 6) , ( 6 , 3)
20 = ( 4, 5) , ( 5, 4)
24 = ( 3 , 8) , ( 4 , 6 ) , ( 6 , 4) , ( 8 , 3)
28 = ( 4 , 7) , ( 7 , 4)
30 = ( 5 , 6) , ( 6 ,5 )
32 = ( 4 , 8) , ( 8 , 4)
36 = (6 , 6)
40 = ( 5 , 8) , ( 8 , 5)
42 = ( 6 , 7) , ( 7 , 6)
48 = ( 6 , 8) , ( 8 , 6)
56 = ( 7 , 8) , ( 8 , 8)
64 = ( 8 , 8)
Number of samples, n = 42
P (Product is less than or equal to 21) = 42/64 = 0.6563.
I’ll give you 20 points if you help me
Answer:
f(g(x)) = 2x +(-5)
Step-by-step explanation:
Put the argument value into the function and simplify the result.
f(g(x)) = f(x -3) = 2(x- 3) +1 = 2x -6 +1
f(g(x)) = 2x +(-5)
The circumference of a circle is 137 in. What is the area, in square inches?
Express your answer in terms of pi.
Answer:
\(A= \frac{18769}{4 \pi}\)
Step-by-step explanation:
The formula for the circumference of a circle is \(C=2\pi r\), where C is the circumference and r is the radius. The formula for the area of a circle is \(A=\pi r^2\), where A is the area and r is the radius. To find the area, we need to find the radius.
Since we know the circumference but not the radius, we set up the circumference formula with r as the unknown: \(137=2\pi x\). We divide \(2 \pi\\\) into both sides to get the radius: \(x=\frac{137}{2 \pi}\). (We leave pi, as it is asking in terms of pi).
Now, we plug the radius into the formula for area: \(A= \pi (\frac{137}{2 \pi})^2\). First, we double the radius: \(A= \pi \frac{18769}{4 \pi ^2}\) and then we simplify the right side of the equation again by multiplying: \(A= \frac{18769 \pi }{4 \pi ^2}\). Then, we cancel out pi on both sides to finally get the area: \(A= \frac{18769}{4 \pi}\).
an italian sausage is 8 inches long. into how many pieces can the sausage be cut if each piece is to be two-thirds of an inch?
12 pieces can the sausage be cut if each piece is to be two-thirds of an inch.
Define division.Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.
8 inches long. into how many pieces can the sausage be cut if each piece is to be two-thirds of an inch.
Divide 8 by 2/3
8÷ 2/3
8× 3/2
12
12 pieces can the sausage be cut if each piece is to be two-thirds of an inch.
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The primary limitation of linear programming's applicability is the requirement that all decision variables be nonnegative. true false
False. The primary limitation of linear programming's applicability is the requirement that all decision variables be nonnegative.
Linear programming does have some limitations beyond the requirement that decision variables be nonnegative. The primary limitation is indeed the assumption of linearity. Linear programming assumes that the relationships between variables and constraints can be represented by linear equations or inequalities. However, in many real-world scenarios, relationships are not strictly linear and may exhibit nonlinearity or complex dynamics.
For example, in production processes, there might be diminishing returns or economies of scale, which introduce nonlinearities. Additionally, in optimization problems involving resource allocation or scheduling, there can be constraints with nonlinearity or discrete decision variables.
Another limitation is the scalability of linear programming. As the number of variables or constraints increases, solving the linear programming problem can become computationally expensive and time-consuming. This is particularly true for large-scale problems with thousands or millions of variables.
In some cases, the assumptions and limitations of linear programming can be overcome by using more advanced optimization techniques such as nonlinear programming or integer programming, which allow for nonlinearity and discrete decision variables. These techniques can handle a wider range of problems but may come with their own computational challenges.
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Which of the lists of letters all have rotational symmetry?
1, (C, H, N, X)
2, (N, O, S, Z)
3, (H, J, N, S)
4, (F, H, X, Z)
(No explanation is needed but it would be helpful)
Answer:
The alphabets Z, H, S, N and O have rotational symmetry.
What is the ratio of new books to used books?
15 books 7 of these books are new . The rest of them are used
Answer:
7 to 8
Step-by-step explanation:
7-15=8
Multiply.
(-3.2) • 1.7
A. -5.44
B. -1.5
C. 1.5
D. 5.44
Answer: A
Step-by-step explanation: