The equation (in slope-intercept form) of the line as described whose slope is; 0 and passes through the point given is; y = -8.
What is the equation of the line whose slope is; 0 and passes through the point given;It follows from the task content that the equation of the line whose slope is; 0 and passes through the point; (-3, -8) is to be determined.
Hence, from the slope formula;
slope, m = ∆y/∆x
Therefore; 0 = ∆y/∆x
By cross-multiplication; we have;
∆y = 0
Recall, ∆y = y - y1 = y - (-8)
y - (-8) = 0
y + 8 = 0
y = -8.
Therefore, it follows that the equation of the line described is; y = -8.
Consequently, the line in discuss is a horizontal line.
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A security keypad uses five digits (0 to 9) in a specific order. How many different
keypad patterns are possible if the first three digits must be even and the last digit
cannot be zero?
The different keypad patterns that are possible if the first three digits must be even and the last digit cannot be zero is 17500 ways.
How to calculate the value?It should be noted that the security keypad uses five digits (0 to 9) in a specific order. On this case, the numbers from 0 to 9 make up 10 numbers.
In this case, there are 5 even numbers.
The total number of possible codes will be:
= 5 × 5 × 10 × 10 × 7
= 17500
There are 17500 ways.
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What is the standard form for yt and factored form
Given:
The leading coefficient of a polynomial is 3.
And the roots of the polynomial is -1, 1, and 2.
Required:
To write g(t) in factored form and standard form.
Explanation:
From the given data, the factored form is given by
[tex]\begin{gathered} g(t)=3(x-(-1))(x-1)(x-2) \\ =3(x+1)(x-1)(x-2) \end{gathered}[/tex]The standard form is,
[tex]\begin{gathered} g(t)=3(x+1)(x^2-2x-x+2) \\ =3(x+1)(x^2-3x+2) \\ =3(x^3-3x^2+2x+x^2-3x+2) \\ =3(x^3-2x^2-x+2) \\ =3x^3-6x^2-3x+6 \end{gathered}[/tex]Final Answer:
The factored form:
[tex]g(t)=3(x+1)(x-1)(x-2)[/tex]The standard form:
[tex]g(t)=3x^3-6x^2-3x+6[/tex]Shona is bundling magazines to recycle he notices at 6 magazines weigh 5/8 pound in all and that the magazines all weigh the same amount. What is the unit rate for pounds per magazine?I don't understand this at all
Given data:
The given weight of 6 magazines is 5/8 pound.
The given expression is,
6M=5/8 pounds
6M=0.625 pounds
1M=0.1041667 pounds
The weight of one magzine is 0.104167 pounds.
harry and marie despoit $800.00 into a savings account which earns 9% interest compounded monthly they want to use the money in the account to go on a trip in 3 years how much will they be able to spend
harry and marie despoit $800.00 into a savings account which earns 9% interest compounded monthly they want to use the money in the account to go on a trip in 2 years how much will they be able to spend
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
P=$800
r=9%=9/100=0.09
n=12
t=2 years
substitute in the expression above
[tex]\begin{gathered} A=800(1+\frac{0.09}{12})^{12\cdot2} \\ \\ A=800(\frac{12.09}{12})^{(24)} \\ A=\$957.13 \end{gathered}[/tex]the answer is $957.13please help me brainliest?
Answer:
See below.
Step-by-step explanation:
Given multiplication:
[tex]3 \dfrac{1}{5} \times 2 \dfrac{5}{8}[/tex]
Convert the mixed numbers into improper fractions by multiplying the whole number by the denominator of the fraction, adding this to the numerator of the fraction, and placing the answer over the denominator:
[tex]\implies \dfrac{3 \times 5+1}{5} \times \dfrac{2 \times 8+5}{8}[/tex]
[tex]\implies \dfrac{15+1}{5} \times \dfrac{16+5}{8}[/tex]
[tex]\implies \dfrac{16}{5} \times \dfrac{21}{8}[/tex]
[tex]\textsf{Apply\;the\;fraction\;rule} \quad \dfrac{a}{b} \times \dfrac{c}{d}=\dfrac{ac}{bd}:[/tex]
[tex]\implies \dfrac{16 \times 21}{5 \times 8}[/tex]
[tex]\implies \dfrac{336}{40}[/tex]
Reduce the fraction by dividing the numerator and denominator by the common factor of 8:
[tex]\implies \dfrac{336 \div 8}{40 \div 8}[/tex]
[tex]\implies \dfrac{42}{5}[/tex]
Divide the numerator by the denominator:
[tex]\implies 42 \div 5=8\;\textsf{remainder}\;2[/tex]
The mixed number answer is the whole number and the remainder divided by the denominator:
[tex]\implies 8 \dfrac{2}{5}[/tex]
Step-by-step explanation:
when you want to start solving it you will do 16 over 5 * 21/8equals 8 whole number 2/5
it will give you 336 all over 40 if you divide by 8 you will get 42/5 which is 8 whole number 2/5
Can you do the graph please I left some notes on the yellow sticky notes
The equation is a linear one, therefore its graph will be a line on the plane.
To completely define a line we need two points.
We can use the information about the y-intercept and use it as one of the points we need. (0, -3)
As for the second point, we can get the x-intercept by setting y=0 and evaluating the function for x:
[tex]\begin{gathered} y=0 \\ \Rightarrow\frac{1}{2}x-3=0 \\ \Rightarrow\frac{1}{2}x=3 \\ \Rightarrow x=6 \\ \Rightarrow(6,0) \end{gathered}[/tex]Then, we have the points we need: (0, -3) and (6,0).
Now, we only need to mark those points on the plane and draw a line through both of them.
Since the plane in the image only reaches the point (5,0), we need to calculate another point to specifically draw the graph on that grid.
Let set y=-1, then:
[tex]\begin{gathered} y=-1 \\ \Rightarrow\frac{1}{2}x-3=-1 \\ \Rightarrow\frac{1}{2}x=2 \\ \Rightarrow x=4 \\ \Rightarrow(4,-1) \end{gathered}[/tex]Now, we will use the points (0,-3) and (4,-1)
4505 x 219 standard algorithm
After throughfall calculating the multiplication 4505 x 219 in standard algorithm, we have come to find that product is 986595
What is standard algorithm?In elementary math, a standard algorithm or method is a particular computation technique that is typically taught for resolving particular mathematical issues. In general, these techniques include exchanging, regrouping, long division, long multiplication using a standard notation, and standard formulas for average, area, and volume.
These techniques can vary somewhat by country and time, but they typically include these techniques. Similar techniques are also available for more complex functions like square roots, but they are no longer taught in general mathematics classes because calculators are more convenient.
4505 x 219 in standard algorithm is as follows:
⇒ 4 5 0 5
× 2 1 9
4 0 5 4 5
+ 4 5 0 5
+ 9 0 1 0
9 8 6 5 9 5
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the volume of a cube is 125 cubic centimeters. How many centimeters long is each edge of the cube?
Answer:
Each edge of the cube is 5 cm
Explanation:
The volume of a cube can be calculated using the formula;
[tex]V=l^3[/tex]Where;
V = volume of the cube
l = length of each side (since all the sides are equal)
Making length l the subject of formula by cube rooting both sides of the formula;
[tex]\begin{gathered} \sqrt[3]{V}=\sqrt[3]{l^3} \\ \sqrt[3]{V}=l \\ l=\sqrt[3]{V} \end{gathered}[/tex]Next, let's substitute the value of volume given;
V = 125 cubic centimeters
[tex]\begin{gathered} l=\sqrt[3]{V} \\ l=\sqrt[3]{125} \\ l=5\text{ cm} \end{gathered}[/tex]Each edge of the cube is 5 cm
The list price of a DVD player is $129. Sam found the player on sale for $90.30. What was the percent discount?
A percent discount of 30%
Explanation:
Since $129 represent 100% of the price, then the new price $90.30 represent 70 %
129 * 100 / 90.30 = 70 %
Since from the 100% of the price, it went to 70% of it, there was a discount of 30%
100 - 70 = 30%
What is the slope of the line that contains these points? 9 X 17 13 21 -24 -21 -18 Y - -15 slope:
We have to use the slope formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's replace the points (9,-24) and (13,-21). Where
[tex]\begin{gathered} x_1=9 \\ x_2=13 \\ y_1=-24 \\ y_2=-21 \end{gathered}[/tex][tex]m=\frac{-21-(-24)}{13-9}=\frac{-21+24}{4}=\frac{3}{4}[/tex]Hence, the slope is 3/4.Find the average rate of change of
refer to the image please
The average rate of change of the function f(x) = -2x² - 2 from x = 2 to x = 6 is -16
How to solve an equationAn equation shows the relationship between two or more numbers and variables.
The average rate of change of a function f(x) over the interval x = a to x = b is given by:
A(x) = [f(b) - f(a)]/[b - a]
Given that function f(x) = -2x² - 2 from x = 2 to x = 6, hence:
f(2) = -2(2)² - 2 = -10
f(6) = -2(6)² - 2 = -74
The average rate of change is:
A = [f(b) - f(a)]/[b - a]
Substituting:
A = [-74 - (-10)] / [6 - 2] = -16
The average rate of change is -16
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Instructions: Solve the system. Enter your answer as an ordered pair.
Given the system:
[tex]\begin{gathered} 3x-9y=12\text{ Eq. 1} \\ 3x+4y=-1\text{ Eq. 2} \end{gathered}[/tex]First, we solve for 3x on both equations, as follows:
[tex]\begin{gathered} 3x=12+9y \\ 3x=-1-4y \end{gathered}[/tex]Equating both equations:
[tex]\begin{gathered} 12+9y=-1-4y \\ 13=-4-9y \\ 13=-13y \\ y=-1 \end{gathered}[/tex]Substituting y on equation 2:
[tex]\begin{gathered} 3x+4y=-1\text{ Eq. 2.} \\ 3x+4\times(-1)=-1 \\ 3x=-1+4 \\ 3x=3 \\ x=1 \end{gathered}[/tex]ANSWER
(1, -1)
Given the function: f(x) = (x − 3)(x + 7)(x − 1)its f-intercept is:its x-intercepts are:
Given: Given the function: f(x) = (x − 3)(x + 7)(x − 1)
Required: its f-intercept and its x-intercepts.
Explanation:
[tex]f(x)=(x-3)(x+7)(x-1)[/tex]For f-intercept, put x = 0
[tex]\begin{gathered} f(0)=(0-3)(0+7)(0-1) \\ f(0)=21 \end{gathered}[/tex]So the f-intercept is (0,21).
For x-intercepts, put f(x) = 0
[tex]\begin{gathered} 0=(x-3)(x+7)(x-1) \\ x=3,-7,1 \end{gathered}[/tex]So x-intercepts are (3,0),(-7,0) and (1,0).
Final Answer:
f-intercept: (0,21)
x-intercept: (3,0),(-7,0),(1,0).
Two bicyclists, 44 miles apart, begin riding toward each other on a long straight avenue. One cyclist
travels 16 miles per hour and the other 17 miles per hour. At the same time, Spot (a greyhound), starting
at one cyclist, runs back and forth between the two cyclists as they approach each other. If Spot runs 39
miles per hour and turns around instantly at each cyclist, how far has he run when the cyclists meet?
The Greyhound has run to a distance equal to 50.7 miles.
This question can be solved using the distance, speed and time relation. The Distance, Speed and time are related to each other by the relation
Speed = Distance/Time, Let the time travelled be equal to t.
Distance travelled by first bicyclist is equal to 16t and Distance travelled by second bicyclist is equal to 17t. The total distance is equal to 44 miles. So, we get
44 = 17t + 16t
44 = 33t
=> t = 44/33
=> t = 1.3 hours
At this time a greyhound starts running back and forth around each cyclist. The speed of Greyhound is equal to 39 miles per hour. Distance will be given by
Distance = Speed × Time
Distance = 39 × 1.3
Distance = 50.7 miles
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A local farm raises horses and goats. • Let x represent the number of horses on the farm. • The number of goats is 3 times the number of horses. • The total number of horses and goats on the farm is 96. What is x, the number of horses on the farm?
The number of horses on the harm will be 24.
What is an expression?
Expression in math is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
A local farm raises horses and goats.
The total number of horses and goats on the farm is 96.
Let number of horses = x
Since, The number of goats is 3 times the number of horses.
Then, Number of goats = 3x
The total number of horses and goats on the farm is 96.
Hence, we can formulate;
x + 3x = 96
4x = 96
x = 24
Thus, The number of horses on the harm will be 24.
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Graph the equation using the slope and the y-interceptY=-8/5x-4
We got the linear equation:
[tex]y=\frac{-8}{5}x-4[/tex]The slope of this line will be -8/5 and the y-intercept will be -4.
To graph it, first find the intercept with x - axis.
We can find it if we equal the equation to zero.
[tex]\begin{gathered} \frac{-8}{5}x-4=0 \\ \\ -\frac{8}{5}x=4 \\ \\ x=-\frac{20}{8}=-\frac{10}{4}=-\frac{5}{2} \end{gathered}[/tex]Now, we got two points:
[tex](-\frac{5}{2},0),(0,-4)[/tex]To graph the function, we only join these points:
So that's the graph for the function.
What is the polynomial function of lowest degree with rational real coefficients and roots 2 and squared root 5?
The polynomial having the above quantities is expressed as x³ - 2x² - 5x + 10 = 0
The above situations will form a Cubic polynomial. A Cubic polynomial function may be defined as an expression which can be written in the form of ax³ + bx² + cx + d = 0 where a, b, c and d are coefficients and x is the independent variable. Since, the polynomial should have real coefficients so its multiplicity will be equal to 1. Now, the roots of the polynomial are given as 2 and √5. Since, square roots always occur in pair so the polynomial will have -√5 as its root. Now, the polynomial formed will be
(x - 2) (x - √5) (x + √5) = 0
(x - 2) (x² - 5) = 0
x³ - 5x - 2x² + 10 = 0
=> x³ - 2x² - 5x + 10 = 0 which is the required polynomial.
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Poland Spring Hotel is a 500-room property that offers only rooms, no F&B service. You are in the process of evaluating the business as an investment. Calculate the breakeven sales and rooms using the information below
Answer: GAS
Step-by-step explanation:
use reference angle to find the exact value of the expression, do not use a calculator sin 2(pi)/3
Given the expression below:
[tex]\sin (\frac{2\pi}{3})[/tex]To find the exact value of the expression, let us determine the quadrant of the expression. It should be noted that the value of angles compare with the quadrants is as shown below
[tex]\begin{gathered} First\text{ quadrant, the measure of reference angle in radian is } \\ 0-\frac{\pi}{2} \end{gathered}[/tex][tex]\begin{gathered} \text{second quadrant, the measure of reference angle in radian is} \\ \frac{\pi}{2}-\pi \end{gathered}[/tex][tex]\begin{gathered} \text{third quadrant, the measure of reference angle in radian is} \\ \pi-\frac{3\pi}{2} \end{gathered}[/tex][tex]\begin{gathered} \text{fourth quadrant, the measure of reference angle in radian is} \\ \frac{3\pi}{2}-2\pi \end{gathered}[/tex]It can be observed that the expression given in the question is a fraction of (pi), greater than half of (pi) but less than (pi). This means that it lies in the second quadrant.
It should be noted that sine is positive in the second quadrant
The equivalent of the expression in the first quadrant is as shown below:
[tex]\begin{gathered} \sin (\frac{2\pi}{3})=\sin (\pi-\frac{2\pi}{3}) \\ =\sin (\frac{3\pi-2\pi}{3}) \\ =\sin (\frac{\pi}{3}) \end{gathered}[/tex][tex]\begin{gathered} \text{Therefore,} \\ \sin (\frac{2\pi}{3}),in\text{ second quadrant is the same } \\ \sin (\frac{\pi}{3}),in\text{ first quadrant.} \\ \sin (\frac{\pi}{3})=\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]Hence, the exact value of the expression is √3/2
how the absolute value is never negative
Answer:
absolute value is a distance from 0; distance cannot be negative
Step-by-step explanation:
the def of absolute value is a numbers distance from 0
distances cannot be negative no matter what you are talking about
Answer: The point of absolute value is to find the distance from a number to 0, which can never be less than 0.
Step-by-step explanation:
The point of absolute value is to find the distance from a number to 0.
For example, if a number line has a -3 point on it, how far away will it be to 0.
<=====o=======o======>
-3 0
The answer is 3! Just like the absolute value
|-3| = ?
3 = ?
Cuál es la cantidad de divisores en 2121?
Answer:
2121 tiene 8 divisores respuesta B
Maya has 846 beads. She is making bracelets with 18 beads on each. How many bracelets is she able to make?
Answer:
maya is able to make 47 bracelets
Step-by-step explanation:
If the formular-(X-X|Y-Xwere used to find the r-value of the5x буfollowing data, what would be the value of x?XY8496101811912|13A. 8B. 10C. 6D. 4
The value of x⁻, is the mean of the x values of the table.
The mean of x is obtained by adding all values of x, and divided the result by the total number of data, which is 5.
Then, you have:
[tex]\bar{x}=\frac{8+9+10+11+12}{5}=\frac{50}{5}=10[/tex]Hence, the mean of x, which is used in the formula to calculate the r-value, is 10
The standard height from the floor to the bull's-eye at which a standard dartboard is hung is 5 feet 8 inches. A standard dartboard is 18 inches in diameter.
Suppose a standard dartboard is hung at standard height so that the bull's-eye is 12 feet from a wall to its left.
Brian throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5 feet above the floor.
Does Brian's dart land on the dartboard?
The equation of the circle that represents the dartboard is (x - 12)² + (y - 17/3)² = 9/16, where the origin is the lower left corner of the room and the unit of the radius is feet.
The position of Brian's dart is represented by the coordinates (11.5, 5). Brian's dart does land on the dartboard.
What is the equation of a circle?Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center.r represents the radius of a circle.From the question, we have the following information:
The height of this standard dartboard, k = 5 feet, 8 inches.
The diameter of this standard dartboard = 18 inches.
The bull's eye, h = 12 feet.
Next, we would convert the all of the units in inches to feet as follows:
Height, k = 5 + 8/12
Height, k = 5 + 2/3
Height, k = 17/3 feet.
For the diameter, we have:
Diameter = 18/12
Diameter = 3/2 feet.
Also, we would determine the radius as follows:
Radius, r = diameter/2
Radius, r = (3/2)/2
Radius, r = 3/4 feet.
Substituting the parameters into the standard equation, we have;
(x - 12)² + (y - 17/3)² = (3/4)²
(x - 12)² + (y - 17/3)² = 9/16
Next, we would determine whether Brian's dart land on the dartboard:
(x - 12)² + (y - 17/3)² < 9/16
(x - 12)² + (y - 17/3)² < 9/16
(11.5 - 12)² + (5.5 - 5.67)² < 0.5625
0.25 + 0.0289 < 0.5625
0.2789 < 0.5625 (Yes, it does land because it's within the circumference of this standard dartboard).
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Compute the horizontal force P required to prevent the block from sliding down the plane for the 100 lb block shown. Assume the coefficient of static friction to be 0.65.
canThe first First step we need to do is to make the decomposition of the vectors W and P.
Both will have a component perpendicular and parallel to the plane. The perpendicular will be used to calculate the maximum static friction force, and the horizontal will be used to find the P required to prevent the block from sliding.
From the sketch, we are able to define both, parallel and perpendicular components of P, as it follows:
[tex]\begin{gathered} P_{\text{//}}=P\cos (30\degree)=\frac{P\sqrt[]{3}}{2} \\ P_{perp}=P\sin (30\degree)=\frac{P}{2} \end{gathered}[/tex]Now, we can do the same for W.
And for W we also can provide the two components as follows:
[tex]\begin{gathered} W_{//}=W\sin (30\degree)=\frac{W}{2} \\ W_{\text{perp}}=W\cos (30\degree)=\frac{W\sqrt[]{3}}{2} \end{gathered}[/tex]Now, we can elaborate on both equations: one for the perpendicular direction and the other for parallel. In the perpendicular direction, we have a component of W, one component of P, and the normal force N. Because the block is going to move, or change its movement along this direction, the sum of the forces pointing upwards must be equal to the sum of the forces pointing downwards. From this, we can write the following:
[tex]\begin{gathered} N=P_{\text{perp}}+W_{\text{perp}} \\ N=\frac{P}{2}+\frac{W\sqrt[]{3}}{2}=\frac{P+W\sqrt[]{3}}{2} \end{gathered}[/tex]Now, for the horizontal, we have the P component to the right and the W component to the left. If we imagine the block is almost sliding. We can write the following equation, from the premise the forces will cancel each other just like the perpendicular case:
[tex]\begin{gathered} P_{//}+F_{\mu}=W_{//} \\ \frac{P\sqrt[]{3}}{2}+N\times\mu_{static}=\frac{W}{2} \end{gathered}[/tex]Here it is used the fact that the friction force is equal to the multiplication of the coefficient of static friction by the normal force. Here we assumed also that the friction is maximum because the block is on the verge of motion downwards, and for this reason, the Friction is upwards, with the P component.
Now, substituting N and the coefficient, we find:
[tex]\begin{gathered} \frac{P\sqrt[]{3}}{2}+\frac{P+100\sqrt[]{3}}{2}0.65=\frac{100}{2}=50 \\ \frac{P(\sqrt[]{3}+0.65)+65\sqrt[]{3}}{2}=50 \\ P(\sqrt[]{3}+0.65)+65\sqrt[]{3}=100 \\ P(\sqrt[]{3}+0.65)=100-65\sqrt[]{3} \\ P=\frac{100-65\sqrt[]{3}}{\sqrt[]{3}+0.65}\cong\frac{100-65\times1.732}{1.732+0.65}=\frac{100-112.58}{2.382} \\ P=-\frac{12.58}{2.382}\cong-5.275\text{lbf} \end{gathered}[/tex]From this, we can see that the force P made to the left with an intensity equal to -5.275 lbf will bring the block on the verge of motion downwards. If we consider that P is strong enough to make it almost move upwards, it is, the Normal Force will be downwards, we can remake the calculation as it follows:
[tex]\begin{gathered} P_{//}=W_{//}+F_{\mu} \\ \frac{P\sqrt[]{3}}{2}=\frac{W}{2}+N\times\mu_{static} \end{gathered}[/tex]And substituting values, we have:
[tex]\begin{gathered} \frac{P\sqrt[]{3}}{2}=50+\frac{P+100\sqrt[]{3}}{2}0.65 \\ \frac{P(\sqrt[]{3}-0.65)}{2}=50+50\sqrt[]{3}\times0.65 \\ P=\frac{2}{\sqrt[]{3}-0.65}\times50(1+\sqrt[]{3}\times0.65)\cong196.46 \end{gathered}[/tex]From this, we know that the max value for P, where the block will not slide is going to be 196.46 lbf to the right.
Express your answer in scientific notation.
5.4x10^5 + 6.7x10^4
Answer:
Step-by-step explanation:
5.4*10*10*10*10*10+6.7* 10*10*10*10
540,000+6.7*10,000
540,000+60,000
114,000=1.14*10^5
How much solute is in each Percent Solution below
How many grams of KOH are in a 25% w/w solution?
25% w/w solution has 25 grams of solute.
The expression w/w stands for weight by weight. This expression indicates the amount of solute present in solution. Concerning this, 25 gram of KOH or potassium hydroxide is present in 100 gram of solution.
Further elaborating, the amount of solvent will be calculated by the formula -
Amount of solution = amount of solute + amount of solvent
Amount of solvent = 100 - 25
Performing subtraction to find the amount of solvent
Amount of solvent = 75 grams
Thus, the 100 gram of solution has 25 grams solute and 75 grams of solvent.
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12Solve using the Quadratic Formula for 2x2 + 5x – 3 = 0x = -5, 7b. X = -12,2X = -3,42
2x² + 5x - 3 = 0
Multiply the coeeficient of x² and the constant (-3)
That is 2 ( - 3) = -6
Find the numbers whose sum is 5 and whose product is -6
The number is 6 and -1
Replace 5x by the numbers
2x² + 6x - x - 3 = 0
2x( x + 3) - 1 ( x + 3) = 0
(2x - 1 ) ( x + 3) = 0
Either 2x -1 = 0 or x + 3 = 0
2x = 1
x = 1/2 or x = -3
Choose all equivalent expression ( s). (4) ^ (3z ^ 2); (4) ^ (- 3x ^ 2); (1/4) ^ (3z ^ 2); (pi/4) ^ (3x)
Answer:
B, C
Step-by-step explanation:
You want to find the equivalent expressions among ...
4^(3x^2)4^(-3x^2)(1/4)^(3x^2)(x/4)^(3x)Rules of exponentsThe relevant rule of exponents is ...
a^b = (1/a)^-b
Equivalent expressionsExpressions with the same base and different exponents will not be equivalent. (A≠B).
Expressions with different bases and the same exponent will not be equivalent. (A≠C).
A variable in the base cannot replace a variable in the exponent. (A≠D).
The rule of exponents tells us replacing the base by its reciprocal and negating the exponent will result in an equivalent expression. (B=C).
The equivalent expressions are 4^(-3x^2) and (1/4)^(3x^2).
7/8 × 9/8 , but the answer as a fraction
We are given the following multiplication problem.
[tex]\frac{7}{8}\times\frac{9}{8}[/tex]To perform the fractional multiplication, simply multiply the numerators and the denominators
[tex]\frac{7}{8}\times\frac{9}{8}=\frac{7\times9}{8\times8}=\frac{63}{64}[/tex]Therefore, the result of the multiplication is 63/64