If [tex]\rm \: x = log_{a}(bc)[/tex], [tex]\rm \: y = log_{b}(ca)[/tex], [tex]\rm \: z = log_{c}(ab)[/tex] , the xyz is equal to :
(a) x + y + z
(b) x + y + z + 1
(c) x + y + z + 2
(d) x + y + z + 3
![If[tex]\rm \: X = Log_{a}(bc)[/tex],[tex]\rm \: Y = Log_{b}(ca)[/tex],[tex]\rm \: Z = Log_{c}(ab)[/tex],](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/gegwJ1lm67qnq8UOj4gRuI3SiKikU3JZ.jpeg)
Answers
Use the change-of-basis identity,
[tex]\log_x(y) = \dfrac{\ln(y)}{\ln(x)}[/tex]
to write
[tex]xyz = \log_a(bc) \log_b(ac) \log_c(ab) = \dfrac{\ln(bc) \ln(ac) \ln(ab)}{\ln(a) \ln(b) \ln(c)}[/tex]
Use the product-to-sum identity,
[tex]\log_x(yz) = \log_x(y) + \log_x(z)[/tex]
to write
[tex]xyz = \dfrac{(\ln(b) + \ln(c)) (\ln(a) + \ln(c)) (\ln(a) + \ln(b))}{\ln(a) \ln(b) \ln(c)}[/tex]
Redistribute the factors on the left side as
[tex]xyz = \dfrac{\ln(b) + \ln(c)}{\ln(b)} \times \dfrac{\ln(a) + \ln(c)}{\ln(c)} \times \dfrac{\ln(a) + \ln(b)}{\ln(a)}[/tex]
and simplify to
[tex]xyz = \left(1 + \dfrac{\ln(c)}{\ln(b)}\right) \left(1 + \dfrac{\ln(a)}{\ln(c)}\right) \left(1 + \dfrac{\ln(b)}{\ln(a)}\right)[/tex]
Now expand the right side:
[tex]xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} \\\\ ~~~~~~~~~~~~+ \dfrac{\ln(c)\ln(a)}{\ln(b)\ln(c)} + \dfrac{\ln(c)\ln(b)}{\ln(b)\ln(a)} + \dfrac{\ln(a)\ln(b)}{\ln(c)\ln(a)} \\\\ ~~~~~~~~~~~~ + \dfrac{\ln(c)\ln(a)\ln(b)}{\ln(b)\ln(c)\ln(a)}[/tex]
Simplify and rewrite using the logarithm properties mentioned earlier.
[tex]xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} + \dfrac{\ln(a)}{\ln(b)} + \dfrac{\ln(c)}{\ln(a)} + \dfrac{\ln(b)}{\ln(c)} + 1[/tex]
[tex]xyz = 2 + \dfrac{\ln(c)+\ln(a)}{\ln(b)} + \dfrac{\ln(a)+\ln(b)}{\ln(c)} + \dfrac{\ln(b)+\ln(c)}{\ln(a)}[/tex]
[tex]xyz = 2 + \dfrac{\ln(ac)}{\ln(b)} + \dfrac{\ln(ab)}{\ln(c)} + \dfrac{\ln(bc)}{\ln(a)}[/tex]
[tex]xyz = 2 + \log_b(ac) + \log_c(ab) + \log_a(bc)[/tex]
[tex]\implies \boxed{xyz = x + y + z + 2}[/tex]
(C)
Related Questions
I require assistance.
Answers
Answer:
its 3.348 - crown pls
Step-by-step explanation:
easiest way of doing this is multiplying the total by the known number then put that number on top. After that divide and check if its right
PLEASEEE HELPPPP IM BEGGIN U
[tex]Y=x^4-x^3-28x^2-20x+48[/tex]
a. How many possible negative real zeros, positive real zeros, and non-real zeros does this equation have? Explain how you determined this.
b. Graph the equation in your calculator or in a graphing app. What is the general shape of the graph and how does the graph’s shape relate to the function? What are the zeros of the graph?
c. Create a table* of synthetic substitution for various values of x.
d. Using synthetic division, show* the way to divide this equation by one of its factors.
I already finished A and B but I am stuck on the synthetic division part of the question. Thanks!
Answers
Answer:
a) positive real zeros: 2 or 0; negative real zeros: 2 or 0; complex zeros: 0, 2, or 4. (rule of signs)
b) ∪-shaped, as for an even-degree polynomial with positive leading coefficient. See attached.
c, d) See attached
Step-by-step explanation:
Descarte's rule of signs gives bounds on the number of positive and negative real roots. The numbers it gives may be reduced by multiples of 2, as complex roots will come in conjugate pairs. The total number of roots of all kinds will match the degree of the polynomial.
Synthetic division is essentially polynomial long division with some modifications:
the variables are omitted ("place value" is used instead)the constant in the divisor is negated so its product with the partial quotient can be added to obtain the new dividendthe divisor binomial is assumed to have a leading coefficient of 1.__
a)The signs of the terms of the given polynomial are + - - - +. There are two sign changes, so 2 possible positive real roots.
When the signs of the odd-degree terms are changed, the signs become + + - + +. There are still two sign changes, so 2 possible negative real roots.
Either or both of these numbers can be reduced by 2 if the roots include a conjugate pair. That is, there may also be 0 possible positive real roots, and 0 possible negative real roots.
The number of non-real (complex) zeros may be any multiple of 2 up to the degree of the polynomial. The may be 0, 2, or 4 possible non-real zeros.
__
b)The graph is the first attachment. It shows 4 real zeros: x = -4, -2, 1, 6.
Since the polynomial is of even degree (4) and has a positive leading coefficient (+1), we expect the general shape to be ∪-shaped. It is.
__
c)The second attachment shows synthetic division using x = -4. (The binomial divisor is (x+4).) The remainder (lower right value in the tableau) is the value of y when x=-4. The third attachment shows synthetic division using the value x=3. (y is -210 when x=3.)
Maybe this is the table you want:
[tex]\begin{array}{|c|c|c|}\cline{1-3}x&-4&3\\\cline{1-3}y&0&-210\\\cline{1-3}\end{array}[/tex]
__
d)The second attachment shows synthetic division by the factor (x+4).
_____
Additional comment
The synthetic division attachments show instructions for carrying out the synthetic division and interpreting the results. As we said above, "the entry on the left" is the opposite of the constant in the binomial divisor. It is the actual value of x you want to use to evaluate the function.
The equations shown are merely for the purpose of indicating the operations that are used. An actual synthetic division tableau is simply a 3-row table of numbers, with the bottom row being the quotient coefficients and remainder.
f(x)=3x^4-5x^2 this function is because
Answers
This is a polynomial of degree 4, for each value of x, we get only one value of y, so we conclude that this is a function.
Is this a function?
A function is a relation that maps inputs (usually written as x) into outputs (usually written as y). Such that each input is mapped into only one output.
For example, if we had:
y = ±√x
Notice that for the same input x = 1, we would have two outputs:
y = 1 and y = -1.
So that is not a function.
Now, for the given one:
[tex]y = f(x) = 3x^4 - 5x^2[/tex]
This is a polynomial of degree 4, for each value of x, we get only one value of y, so we conclude that this is a function.
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Copy and complete the workings to find the value of each expression when m=2 and p=-4
Answers
Answer:
- 24
Step-by-step explanation:
4(m + 2p) ← substitute m = 2 and p = - 4 into the expression
= 4(2 + 2(- 4) )
= 4(2 - 8)
= 4(- 6)
= - 24
The graph of y =[tex]\sqrt[]{x}[/tex]nis transformed as shown in the graph below. Which equation represents the transformed function?
Answers
Answer:
[tex]\textsf{A)}\quad y=-\sqrt{x}+2[/tex]
Step-by-step explanation:
Parent function:
[tex]y = \sqrt{x}[/tex]
The properties of the parent function are:
Starts at the origin, so y-intercept is at (0, 0)Domain: x ≥ 0Range: y ≥ 0As x increases, y increasesFrom inspection of the graph, as the x-values increase, the y-values decrease. Therefore there has been a reflection in the x-axis.
The y-intercept is now at (0, 2), therefore the function has been translated 2 units up.
Translations
For a > 0
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
Therefore:
Reflected in the x-axis: [tex]-f(x)=-\sqrt{x}[/tex]
Then translated 2 units up: [tex]-f(x)+2=-\sqrt{x}+2[/tex]
So the equation that represents the transformed function is:
[tex]y=-\sqrt{x}+2[/tex]
What is the approximate horizontal distance between Amelia and Brendon? Explain your reasoning
Answers
Answer:
60 ft
Step-by-step explanation:
using the sine ratio in the right triangle and the exact value
sin30° = [tex]\frac{1}{2}[/tex] , then
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{CD}{AD}[/tex] = [tex]\frac{30}{AD}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
AD = 60 ft
Write an equation for the linear function f with the given values
Question number 8
Answers
Answer:
5. y = 2/3x + 1
8. y = 4/7x - 4
Step-by-step explanation:
5. (-6, -3) and (6, 5)
You can use the slope formula which is (y2-y1)/(x2-x1) to find the slope and plug it back into the slope-intercept form to find the y-intercept
(5-(-3)) / (6-(-6)) = 8 / 12 = 2/3
slope-intercept form: y=mx+b where m is the slope and b is the y-intercept
to find b you can plug in one of the coordinates and the slope
5 = 6(2/3) + b
5 = 4 + b
1 = b
y = 2/3x + 1
8. (-7, -8), (21, 8)
m = (8 - (-8)) / (21 - (-7)) = 16 / 28 = 4/7
plug in one of the coordinates and the slope to find b or the y-intercept
8 = 21(4/7) + b
8 = 12 + b
-4 = b
y = 4/7x - 4
180 is equivalent to π/2 radians
true
false
Answers
Answer:
[tex]\fbox {False}[/tex]
Step-by-step explanation:
To convert a degree measure to radian measure, multiply with π/180.
⇒ 180 × π/180
⇒ π radians
false is the answers
please mark me as brainlest
A rectangular prism has a square base with a width of 6 and a volume of 360 cm3. If a square pyramid has a base with the same width and height, what is the volume of the pyramid? Round to the nearest tenth.
Answers
The volume of the square pyramid is the one-third of the square prism with same height and base area. Then the volume of the pyramid will be 120 cubic cm.
What is the volume of the pyramid?Suppose the base of the pyramid has length = L units, width = W units, slant height = K units, and the height of the pyramid is of H units.
Then the volume of the pyramid will be
V = (L × B × H) / 3
The volume of the square prism will be
V = (L × B × H)
Then the volume of the square pyramid is the one-third of the square prism with same height and base area.
[tex]\rm V_{pyramid} = \dfrac{V_{prism} }{3}[/tex]
A rectangular prism has a square base with a width of 6 and a volume of 360 cm³.
If a square pyramid has a base with the same width and height.
Then the volume of the pyramid will be
V = 360 / 3
V = 120 cubic cm
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Evaluate:
lim h->0 (√(x+h) - √x) / h
Answers
Rationalizing the numerator, it is found the result of the limit is given as follows:
[tex]\lim_{h \rightarrow 0} \frac{(\sqrt{x + h} - \sqrt{x})}{h} = \frac{1}{2\sqrt{x}}[/tex]
What is a limit?A limit is given by the value of function f(x) as x tends to a value.
The first step to find the limit is replace the variable by the value, hence:
[tex]\lim_{h \rightarrow 0} \frac{(\sqrt{x + h} - \sqrt{x})}{h} = \frac{0}{0}[/tex]
Undefined limit, hence we have to find another way. The numerator includes square roots, hence it should be rationalized using the subtraction of perfect squares, as follows:
[tex]\lim_{h \rightarrow 0} \frac{(\sqrt{x + h} - \sqrt{x})}{h} \times \frac{(\sqrt{x + h} + \sqrt{x})}{(\sqrt{x + h} + \sqrt{x})} = \lim_{h \rightarrow 0} \frac{(\sqrt{x + h})^2 - (\sqrt{x})^2}{h(\sqrt{x + h} + \sqrt{x})} = \lim_{h \rightarrow 0} \frac{x + h - x}{h(\sqrt{x + h} + \sqrt{x})} = \lim_{h \rightarrow 0} \frac{h}{h(\sqrt{x + h} + \sqrt{x})}[/tex]
Then we simplify the h, so:
[tex]\lim_{h \rightarrow 0} \frac{1}{\sqrt{x + h} + \sqrt{x}} = \frac{1}{2\sqrt{x}}[/tex]
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The sum of the ages of 5 children is 20 years, after how many years will the sum of their ages be 40 years. a) 4 b) 5 c) 10 d) 20
Answers
Answer:
20
Step-by-step explanation:
each year each child will get additional age
example 5 children average of the age 20 years old.
after 20 years all of them.will be 20+20=40 years old.
the group of the children not changing but average of the groups will be increase in 20 years.
[tex]f(x) = \sqrt{9 - {x}^{2} } [/tex]
I have a doubt. I know that the domain will be [-3, 3] because this is a real function. But what will be the range. Everywhere it is given as [0, 3]. But shouldn't it be [-3, 3].
For example let x = 0, then f(x) = √9, and it can be either -3 or 3. Why are we considering just the positive value?
Please explain.
Answers
Answer:
range of f is [0,3]
Step-by-step explanation:
The "square root" symbol, [tex]\sqrt{\text{ \quad }}[/tex], is a function. As a result, it only has a single output because functions must only have a single output for each input.
Thinking about it graphically, if the square root function did give both a positive and a negative result, the function "f" would not pass the vertical line test and it would not be a function.
When solving an equation like [tex]x^2=25[/tex], to solve, we must apply the square root property. The square root property says that to find both solutions, one must look at both the positive and the negative of the square root. So, to solve:
[tex]x^2=25[/tex]
Apply square root property...
[tex]\sqrt{x^2} = \pm \sqrt{25}[/tex]
[tex]x=\sqrt{25}[/tex] or [tex]x=-\sqrt{25}[/tex]
[tex]x=5[/tex] or [tex]x=-5[/tex]
In this case, because the square root function itself only outputs non-negative results (so, including zero, as you already identified), the range will only be [0,3].
Suppose you know the slope of a linear relationship and one of the points that it’s graph passes through how can you determine if the relationship is proportional or not?
Answers
Answer:
I exactly don't have or know the answer
Use the graph and the given point to determine the second point. Connect the two points by a straight line. If the graph passes through the origin, the relationship is proportional and if the graph does not pass through the origin, the relationship is non-proportional.
What is 850,000,000,000,000,000 divided by 860,000,000,000,000,000,000,000
Answers
the answer would be 9.88372093e-7
1 )Simplify.
[tex]\frac{850000000000000000}{8.6E}[/tex]+23
2 )Answer
9.88372093e-7
Does the taxable capital gains added to the banker’s income move them to a higher tax rate?
Answers
The taxable capital gains added to the banker’s income move them to a higher tax rate. the statement is true.
What is income tax?Income tax is a tax applied on individuals or entities concerning income or profit earned by them.
Qualified plans provide two tax benefits that are not available in other types of investments.
Tax rates will be higher in the future with the increment of time, but the benefits of the tax-deferred savings plan will overcome higher tax rates over time.
The taxable capital gains added to the banker’s income move them to a higher tax rate. the statement is true.
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The measure of central angle QRS is 8pi/9 radians. What is the area of the shaded sector?
Answers
The area of the shaded sector must be 144π units².
What is the area of the circle?The area of the circle is defined as the product of the pie and the square of the radius.
The area of the circle = [tex]\pi r^{2}[/tex]
We know that the angle measurement of central angle QRS is less than π radians.
for r = 18 units
The area of the circle = π18² = 324π units²
The area of the half of a circle = 324π /2 = 162π units²
The area of a quarter of a circle = 324π /4 = 81π units²
so
The area of the shaded sector < 162π units²
and
The area of the shaded sector > 81π units²
Hence the answer must be 144π units²
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pls help me with this question
Answers
Answer:
D, C
Step-by-step explanation:
for part a, there is a negative slope with the graph shifted two units upwards
for part b, if you plug in C, you get an answer that works
What is the solution to this equation log(2x-100)=3
Answers
For more explanation, please see the attachment
An experiment consists of rolling a standard six-sided die once. Event A is "rolling a 5{}^{\prime\prime} and event B is "rolling an odd number." Are the events dependent or independent? Why? Select the option that correctly answers both questions.
O Events A and B are independent, because P(B) = P(B|A) = 1/2.
O Events A and B are independent, because P(A) = P(B|A) = 1/12.
O Events A and B are dependent, because P(A) =/ P(B|A).
O Events A and B are dependent, because P(B) =/ P(B|A).
Answers
Based on the given probability events, we can calculate that Events A and B are independent, because P(B) = P(B|A) = 1/2.
Is event B independent of event A?Events are independent if P(B) = P(B|A)
The probability of event B is:
= 3 odd numbers / 6 numbers
= 1 / 2
The probability of A is:
= 3 prime numers / 6
= 1/2
P(B|A) = ((1 / 2) x (1 / 2)) / (1 / 2)
= 1/2
So P(B) = P(B|A) = 1/2.
The events are independent.
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Two students were asked to graph a rational number -7.1. Amy states that The number is between -8 and -7, but Laura states that the point is between -7 and -6 how can you determine which student is correct?
Answers
Amy is correct, -7.1 is between -7 and -8.
What is the number pattern?A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.
Two students were asked to graph a rational number -7.1.
Amy states that The number is between -8 and -7, but Laura states that the point is between -7 and -6.
In order to be in between -6 and -7, the number would have to be a decimal with a whole number of 6.
But -7.1 has a whole number of 7 then it is in between -7 and -8.
Thus, Amy is correct, -7.1 is between -7 and -8.
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3/4=6/x x =
!!!!PLEASE HELP I WILL MARK BRAINLIEST!!!!
Answers
Answer:
x=8
Step-by-step explanation:
You cross multiply, 6 times 4 is 24, so what times 3 is 24. 8 times 3 is 24.
Answer:
x = 8
Step-by-step explanation:
There are several ways you can solve a proportion like this. Most of the algebraic solutions involve what amounts to multiplying both sides by (4x/3). There are also graphical solutions and solutions that rely on relations that make fractions be equal.
__
cross multiplicationThe method of solution usually recommended is to "clear fractions" and then solve the resulting one-step linear equation. To "clear fractions," multiply both sides of the equation by the least common denominator: 4x.
[tex](4x)\dfrac{3}{4}=(4x)\dfrac{6}{x}\\\\3\cdot x=4\cdot6\qquad\text{looks like "cross multiplication"}[/tex]
We describe this as "cross-multiplication" because it looks like each numerator has been multiplied by the opposite denominator.
This "one-step" linear equation is solved by dividing by the coefficient of x, which is 3:
[tex]\dfrac{3x}{3}=\dfrac{4\cdot6}{3}\\\\\boxed{x=8}\qquad\text{simplify}[/tex]
Note that we could have done these operations in one step. The two steps, multiply by 4x and divide by 3, are identical to the one step, multiply by (4x/3).
[tex]\left(\dfrac{4x}{3}\right)\cdot\dfrac{3}{4}=\left(\dfrac{4x}{3}\right)\cdot\dfrac{6}{x}\\\\\boxed{x=8}\qquad\text{simplify}[/tex]
__
compare fractionsWe can see the solution almost immediately if we rewrite the fractions so they have the same numerator.
[tex]\dfrac{3}{4}=\dfrac{6}{x}\\\\\dfrac{3\cdot2}{4\cdot2}=\dfrac{6}{x}\\\\\dfrac{6}{8}=\dfrac{6}{x}\ \Longrightarrow\ \boxed{x=8}[/tex]
The same thing happens if we multiply the equation by the inverse of either side.
[tex]\dfrac{3}{4}=\dfrac{6}{x}\ \Longrightarrow\ \left(\dfrac{4}{3}\right)\dfrac{3}{4}=\left(\dfrac{4}{3}\right)\dfrac{6}{x}\ \Longrightarrow\ 1=\dfrac{8}{x}\ \Longrightarrow\ \boxed{x=8}\\\\\textsf{ or ...}\\\\\dfrac{3}{4}=\dfrac{6}{x}\ \Longrightarrow\ \left(\dfrac{x}{6}\right)\dfrac{3}{4}=\left(\dfrac{x}{6}\right)\dfrac{6}{x}\ \Longrightarrow\ \dfrac{x}{8}=1\ \Longrightarrow\ \boxed{x=8}[/tex]
__
graphical solutionIf the equation is rewritten to a form that has a value of 0 at the solution, then the x-intercept of the graph will be the solution to the equation.
3/4 = 6/x . . . . . . . . original equation
6/x -3/4 = 0 ⇒ f(x) = 0
f(x) = 6/x -3/4
The graph shows the solution to f(x) = 0 is x=8.
9) Find ST
geometry
Answers
ST and RU are equal,
24x = 23x + 1
Subtract 23x from both sides:
x = 1
Now replace x to solve for ST
24x = 24(1) = 24
ST = 24
Which is the graph of y = 3√x+1-2?
Answers
Answer:
I'm not sure how to interpret "y = 3√x+1-2."
I'll assume y = 3[tex]\sqrt{x+1}[/tex] - 2
Step-by-step explanation:
Use the free online app DESMOS. Either enter the equation, or make a table of individual points and plot them as ordered pairs.
GRAPH: See attached image
PLOT: Calculate a few points, mark them on the graph and then connect the dots. I selected a few values of x and calculated y from the equation. Each calculation provides a (x,y) ordered pair which can be marked on the graph and the dots are then connected. Note that x values less than -1 result in a value of y that includes i, an imaginary number. So the graph ends abruptly at that point.
Please explain how it is simplified. Thank you. No random or inexperienced mathematicians please
Answers
Answer:
[tex]\fbox {Work is attached below.} \downarrow[/tex]
Step-by-step explanation:
Consider the following graph.
Which statement best describes Cheryl's commute?
A. Cheryl accelerated to 65 mph, made a stop for 5.5 minutes, and then decelerated to 45 mph.
B. Cheryl accelerated to 65 mph, drove at a constant speed for 5.5 minutes, and the decelerated to 45 mph.
C. Cheryl drove at a speed of 65 mph for 1 minute, drove at a constant speed for 5.5 minutes, and then drove at a speed of 45 mph for 2.5 minutes.
D. Cheryl drove at a speed of 65 mph for 1 minute, made a stop for 5.5 minutes, and then drove at a speed of 45 mph for 2.5 minutes
Answers
Cheryl drove at a speed of 65 mph for 1 minute, drove at a constant speed for 5.5 minutes, and then drove at a speed of 45 mph for 2.5 minutes.Option C is correct.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
Cheryl traveled at a steady pace for 5.5 minutes, then 45 mph for 2.5 minutes after traveling at 65 mph for a minute.
Statement C best describes Cheryl's commute.
Hence option C is correct.
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A ferris wheel with a diameter of 214 feet was built in a city. The top of the wheel stands 223 feet above the ground. Find h if θ = 150°, 240°, and 315°. Round your answers to the nearest whole number.
The diagram in the attached image is a model of the wheel.
Answers
The height at 150°, 240°, and 315° will be 208.66 feet, 169.5 feet, and 40.34 feet, respectively.
What is a vector?The quantity which has magnitude, direction and follows the law of vector addition is called a vector.
A Ferris wheel with a diameter of 214 feet was built in a city.
The top of the wheel stands 223 feet above the ground.
Then the radius will be
r = 214 / 2
r = 107 feet
The distance between the ground and bottom of the Ferris wheel will be
d = 223 – 214
d = 9 feet
Then the height will be given as
h = r(1 – cos θ) + h
h = 107(1 – cos θ) + 9
At θ = 150°, then the height will be
h = 107(1 – cos 150°) + 9
h = 208.66 feet
At θ = 240°, then the height will be
h = 107(1 – cos 240°) + 9
h = 169.5 feet
At θ = 315°, then the height will be
h = 107(1 – cos 315°) + 9
h = 40.34 feet
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The sum of 16 and a number is less than 24. Which of the following inequalities
expresses the solution?
Answers
Inequalities help us to compare two unequal expressions. The correct option is A.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The complete question is:
The sum of 16 and a number is less than 24. Which of the following inequalities expresses the solution?
x<8
x>8
x=8
x<-8
Given the sum of 16 and a number is less than 24. Let the number be represented by x, therefore,
16 + x < 24
x < 24 - 16
x < 8
Hence, the correct option is A.
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MATH!!! find the surface area of the prism
Answers
(9x2) + (21x2) + (21x2)
=102cm^2
What are the coordinates of R', the image of R(-4, 3) after a reflection in the line
y = x
Answers
The coordinate for the R' is (3, -4) if the R(-4, 3) is reflected in the line y = x option (D) is correct.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
We have:
Image of R(-4, 3) after a reflection in the line y = x
The rule for the reflection over y = x is:
(x, y) = (y, x)
(-4, 3) = (3, -4)
Thus, the coordinate for the R' is (3, -4) if the R(-4, 3) is reflected in the line y = x option (D) is correct.
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If triangles ABC and DEF are congruent, then find the measure of DE.
Answers
Answer:
DE = 3 UnitsReason -
In the question it is given that triangle ABC is congruent to triangle DEF
if a triangle is congruent to other triangle than the corresponding parts of it (.ie sides and angles) are equal to that of other