Answer:
[tex]15a^2b^2-20a^2b+6ab^2-4ab+7[/tex]
Step-by-step explanation:
The sum of two polynomials is
[tex]10a^2b^2-8a^2b+6ab^2-4ab+2[/tex]
First addend is
[tex]-5a^2b^2+12a^2b-5[/tex]
Second addend x.
Hence,
[tex]x+(-5a^2b^2+12a^2b-5)=10a^2b^2-8a^2b+6ab^2-4ab+2\\ \\x=10a^2b^2-8a^2b+6ab^2-4ab+2-(-5a^2b^2+12a^2b-5)=\\ \\=10a^2b^2-8a^2b+6ab^2-4ab+2+5a^2b^2-12a^2b+5=\\ \\=(10a^2b^2+5a^2b^2)+(-8a^2b-12a^2b)+6ab^2-4ab+(2+5)=\\ \\=15a^2b^2-20a^2b+6ab^2-4ab+7[/tex]
Answer: The correct option is (A) [tex]15a^2b^2-20a^2b+6ab^2-4ab+7.[/tex]
Step-by-step explanation: Given that the sum of two polynomials is [tex](10a^2b^2-8a^2b+6ab^2-4ab+2)[/tex] and one addend is [tex](-5a^2b^2+12a^2b-5).[/tex]
We are to find the other addend.
Let P(x) be the other addend.
Then, according to the given information, we must have
[tex]-5a^2b^2+12a^2b-5+P(x)=10a^2b^2-8a^2b+6ab^2-4ab+2\\\\\Rightarrow P(x)=(10a^2b^2-8a^2b+6ab^2-4ab+2)-(-5a^2b^2+12a^2b-5)\\\\\Rightarrow P(x)=10a^2b^2-8a^2b+6ab^2-4ab+2+5a^2b^2-12a^2b+5\\\\\Rightarrow P(x)=15a^2b^2-20a^2b+6ab^2-4ab+7.[/tex]
Thus, the other addend is [tex]15a^2b^2-20a^2b+6ab^2-4ab+7.[/tex]
Option (A) is CORRECT.
A student simplifies (6b + 4r) – (2b + r) and says that the result is 4b + 5r. Explain the error and describe the correct steps to simplify the expression.
Answer: 4b + 3r
Step-by-step explanation: The student correctly subtracted the 2b, but accidentally added the r instead of subtracting it, she likely misunderstood the parentheses.
The correct answer would be 4b + 3r
Answer:
Third option ✔ 4b + 3r
Step-by-step explanation:
E D G E N U I T Y
How can I round decimals
Answer:
Find the place value you want (the "rounding digit") and look at the digit just to the right of it.
If that digit is less than 5, do not change the rounding digit but drop all digits to the right of it.
If that digit is greater than or equal to five, add one to the rounding digit and drop all digits to the right of it.
Step-by-step explanation:
Step-by-step explanation: To round a decimal, you first need to know the indicated place value position you want to round to. This means that you want to first find the digit in the rounding place which will usually be underlined.
Once you locate the digit in the rounding place, look to the left of that digit. Now, the rules of rounding tell us that if a number is less than 4, we round down but if a number is greater than or equal to 5, we round up.
I'll show an example.
Round the following decimal to the indicated place value.
0.8005
To round 0.8005 to the indicated place value position, first find the digit in the rounding place which in this case is the 0 in the thousandths place.
Next, find the digit to the right of the rounding place which in this case is 5. Since 5 is greater than or equal to 5, we round up.
This means we add 1 to the digit in the rounding place so 0 becomes 1. So we have 0.801. Now, we change all digits to the right of the rounding place to 0 so 5 changes to 0.
Finally, we can drop of any zeroes to the right of our decimal as long as they're also to the right of the rounding position.
So we can write 0.8010 as 0.801.
Image provided.
I need help with this problem.
Answer:
42 degrees
Step-by-step explanation:
So we are given that m<BOC+m<AOB=90
So we have (6x-6)+(5x+8)=90
11x+2=90
11x=88
x=8
We are asked to find m<BOC
m<BOC=6x-6=6(8)-6=48-6=42
Scenario:
A rectangular plot of ground is 5 meters longer than it is wide. Its area is 20,000 square meters.
Question:
What equation will help you find the dimensions?
Note: Let W represent the width.
Options:
w(w+5)=20,000
w^2=20,000+5
(w(w+5))/2=20,000
w+2(w+5)=20,000
To find the area you multiply the length by the width.
W = the width, and you are told the length is 5 meters longer, so the length would be (W +5)
Now multiply those together to equal 20,000 square meters:
w(w+5) = 20,000
A tourist boat is used for sightseeing in a nearby river. The boat travels 2.4 miles downstream and in the same amount of time, it travels 1.8 miles upstream. If the boat travels at an average speed of 21 miles per hour in the still water, find the current of the river. (SHOW WORK)
Answer:
3 miles per hour
Step-by-step explanation:
Let x miles per hour be the current of the river.
1. The boat travels 2.4 miles downstream with the speed of (21+x) miles per hour. It takes him
[tex]\dfrac{2.4}{21+x}\ hours.[/tex]
2. The boat travels 1.8 miles upstream with the speed of (21-x) miles per hour. It takes him
[tex]\dfrac{1.8}{21-x}\ hours.[/tex]
3. The time is the same, so
[tex]\dfrac{2.4}{21+x}=\dfrac{1.8}{21-x}[/tex]
Cross multiply:
[tex]2.4(21-x)=1.8(21+x)[/tex]
Multiply it by 10:
[tex]24(21-x)=18(21+x)[/tex]
Divide it by 6:
[tex]4(21-x)=3(21+x)\\ \\84-4x=63+3x\\ \\84-63=3x+4x\\ \\7x=21\\ \\x=3\ mph[/tex]
if f(x) = -3x+4 and g(x) =2, solve for the value of x for which f(x) = g(x) is true
Answer: 0.67 (to 3 s.f)
Step-by-step explanation:
f(x)=g(x)
-3x + 4 = 2
-3x = -2
x = 2/3
x = 0.67
Hope it helped
Which answer is right please help
Answer:
A
Step-by-step explanation:
Linear functions go into a straight line in order
Y in set b goes from 2 to 1250 so it is traveling much faster than set A
Solve the equation 1/t-2=t/8
Answer:
Two solutions were found :
t =(16-√288)/-2=8+6√ 2 = 0.485
t =(16+√288)/-2=8-6√ 2 = -16.48
Step-by-step explanation:
Answer:
-IF THE EQUATION IS [tex]\frac{1}{t-2}=\frac{t}{8}[/tex], THEN:
[tex]t_1=4\\t_2=-2[/tex]
-IF THE EQUATION IS [tex]\frac{1}{t}-2=\frac{t}{8}[/tex], THEN:
[tex]t_1=-16.485\\t_2=0.485[/tex]
Step-by-step explanation:
-IF THE EQUATION IS [tex]\frac{1}{t-2}=\frac{t}{8}[/tex] THE PROCEDURE IS:
Multiply both sides of the equation by [tex]t-2[/tex] and by 8:
[tex](8)(t-2)(\frac{1}{t-2})=(\frac{t}{8})(8)(t-2)\\\\(8)(1)=(t)(t-2)\\\\8=t^2-2t[/tex]
Subtract 8 from both sides of the equation:
[tex]8-8=t^2-2t-8\\\\0=t^2-2t-8[/tex]
Factor the equation. Find two numbers whose sum be -2 and whose product be -8. These are -4 and 2:
[tex]0=(t-4)(t+2)[/tex]
Then:
[tex]t_1=4\\t_2=-2[/tex]
-IF THE EQUATION IS [tex]\frac{1}{t}-2=\frac{t}{8}[/tex] THE PROCEDURE IS:
Subtract [tex]\frac{1}{t}[/tex] and [tex]2[/tex]:
[tex]\frac{1}{t}-2=\frac{t}{8}\\\\\frac{1-2t}{t}=\frac{t}{8}[/tex]
Multiply both sides of the equation by [tex]t[/tex]:
[tex](t)(\frac{1-2t}{t})=(\frac{t}{8})(t)\\\\1-2t=\frac{t^2}{8}[/tex]
Multiply both sides of the equation by 8:
[tex](8)(1-2t)=(\frac{t^2}{8})(8)\\\\8-16t=t^2[/tex]
Move the [tex]16t[/tex] and 8 to the other side of the equation and apply the Quadratic formula. Then:
[tex]t^2+16t-8=0[/tex]
[tex]t=\frac{-b\±\sqrt{b^2-4ac}}{2a}\\\\t=\frac{-16\±\sqrt{16^2-4(1)(-8)}}{2(1)}\\\\t_1=-16.485\\t_2=0.485[/tex]
the sum and express it in simplest
(-6b3 - 362.6) + (2b3 - 362)
Enter the correct answer.
Answer:
[tex]\large\boxed{(-6b^3-362.6)+(2b^3-362)=-4b^3-724.5}[/tex]
Step-by-step explanation:
[tex](-6b^3-362.6)+(2b^3-362)\\\\=-6b^3-362.6+2b^3-362\qquad\text{combine like terms}\\\\=(-6b^3+2b^3)+(-362.5-362)\\\\=-4b^3-724.5[/tex]
Consider that lines B and C are parallel. What is the value of x? What is the measure of the smaller angle?
Answer:
the awncer would be x=0
Step-by-step explanation:
.
If sin θ=24/25 and 0 less than or equal to θ less than or equal to π/2, find the exact value of tan 2θ.
Answers;
A) -527/336
B) -336/527
C)7/24
D) 24/7
Answer:
Option B. [tex]tan(2\theta)= -\frac{336}{527}[/tex]
Step-by-step explanation:
we know that
[tex]tan(2\theta)= \frac{sin(2\theta)}{cos(2\theta)}[/tex]
[tex]sin(2\theta)=2(sin(\theta))(cos(\theta))[/tex]
[tex]cos(2\theta)=cos^{2}(\theta)-sin^{2}(\theta)[/tex]
[tex]cos^{2}(\theta)+sin^{2}(\theta)=1[/tex]
we have
[tex]sin(\theta)=\frac{24}{25}[/tex]
step 1
Find the value of cosine of angle theta
[tex]cos^{2}(\theta)+sin^{2}(\theta)=1[/tex]
[tex]cos^{2}(\theta)+(\frac{24}{25})^=1[/tex]
[tex]cos^{2}(\theta)=1-\frac{576}{625}[/tex]
[tex]cos^{2}(\theta)=\frac{49}{625}[/tex]
[tex]cos(\theta)=\frac{7}{25}[/tex]
The value of cosine of angle theta is positive, because angle theta lie on the I Quadrant
step 2
Find [tex]sin(2\theta)[/tex]
[tex]sin(2\theta)=2(sin(\theta))(cos(\theta))[/tex]
we have
[tex]sin(\theta)=\frac{24}{25}[/tex]
[tex]cos(\theta)=\frac{7}{25}[/tex]
substitute
[tex]sin(2\theta)=2(\frac{24}{25})(\frac{7}{25})[/tex]
[tex]sin(2\theta)=\frac{336}{625}[/tex]
step 3
Find [tex]cos(2\theta)[/tex]
[tex]cos(2\theta)=cos^{2}(\theta)-sin^{2}(\theta)[/tex]
we have
[tex]sin(\theta)=\frac{24}{25}[/tex]
[tex]cos(\theta)=\frac{7}{25}[/tex]
substitute
[tex]cos(2\theta)=(\frac{7}{25})^{2}-(\frac{24}{25})^{2}[/tex]
[tex]cos(2\theta)=(\frac{49}{625})-(\frac{576}{625})[/tex]
[tex]cos(2\theta)=-\frac{527}{625}[/tex]
step 4
Find the value of [tex]tan(2\theta)[/tex]
[tex]tan(2\theta)= \frac{sin(2\theta)}{cos(2\theta)}[/tex]
we have
[tex]sin(2\theta)=\frac{336}{625}[/tex]
[tex]cos(2\theta)=-\frac{527}{625}[/tex]
substitute
[tex]tan(2\theta)= -\frac{336}{527}[/tex]
By using the Pythagorean identity and the double angle identity for tangent, it is found that the value of tan 2θ when sin θ =24/25 and 0 ≤ θ ≤ π/2 is -527/336.
Explanation:In the field of Mathematics, particularly in trigonometric equations, the problem given is asking for the value of tan 2θ, given that sin θ=24/25 and 0 ≤ θ ≤ π/2.
Firstly, we can find cos θ by using the Pythagorean identity sin²θ + cos²θ = 1. This gives us cos θ = sqrt (1 - sin²θ) = sqrt (1 - (24/25)²) = 7/25.
Then, knowing that tan θ = sin θ/cos θ, we can plug in these values to get tan θ = (24/25) / (7/25) = 24/7. Finally, using the double angle identity for tan (tan 2θ = 2 tan θ / (1 - tan²θ)), we can find that tan 2θ = 2(24/7) / (1 - (24/7)²) = -527/336.
So, the exact value of tan 2θ when sin θ =24/25 and 0 ≤ θ ≤ π/2 is -527/336, which is answer option A.
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do you know the answer plz help me and thank you if you know the answer
Answer: 8 remainder 2
Step-by-step explanation:
3 • 8 = 24
26 - 24 = 2
Your answer is 8 with a remainder of 2
Answer:
8 r2
Step-by-step explanation:
x+16=24hvvcgcfcycdfdxfxxdgfv
To do solve this you must isolate x. First subtract 16 to both sides (what you do on one side you must do to the other). Since 16 is being added to x, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.
x + (16 - 16) = 24 - 16
x = 8
Check:
8 + 16 = 24
24 = 24
Hope this helped!
~Just a girl in love with Shawn Mendes
if you subtract 16 from both sides you would get x=8
A combination lock like the one shown below has three
dials. Each of the dials has numbers ranging from 1 to 25. If
repeated numbers are allowed, how many different
combinations are possible with the lock?
Answer:
15625
Step-by-step explanation:
Let us consider each dial individually.
We have 25 choices for the first dial.
We then have 25 choices for the second dial.
We then have 25 choices for the third dial.
Let us consider any particular combination, the probability that combination is right is (probability the first number is right) * (probability the second number is right) * (probability the third number is right) = 1/25 * 1/25 * 1/25 = 1/15625
Therefore there are 15625 combinations
What is the value of –2|6x – y| when x = –3 and y = 4?
Answer:
-44
Step-by-step explanation:
We have the expression
[tex]-2|6x - y|[/tex]
We need to find the value of the expression when x = -3 and y = 4
Then we must replace the variable with the number -3 and the variable y with the number 4
This is:
[tex]-2|6(-3) - (4)|[/tex]
[tex]-2|-18 - 4|[/tex]
[tex]-2|-22|[/tex]
Remember that the absolute value always results in a positive number.
So
[tex]-2|-22| = -2(22)=-44[/tex]
the answer is -44
Answer:
The correct answer is -44
Step-by-step explanation:
Points to remember
|x| = x
|-x| = x
To find the value of –2|6x – y|
We have –2|6x – y| When x = -3 and y = 4
Substitute the value of x and y
–2|6x – y| = –2|(6 * -3) – 4|
= -2|-18 - 4|
= -2|-22|
= -2 * 22
= -44
Therefore the value of –2|6x – y| when x = -3 and y = 4
–2|6x – y|
What is the true solution to the logarithmic equation below?
Answer:
x = 4/9
C
Step-by-step explanation:
log_2(6x/) - log_2(x^(1/2) = 2 Given
log_2(6x/x^1/2) = 2 Subtracting logs means division
log_2(6 x^(1 - 1/2)) = 2 Subtract powers on the x s
log_2(6 x^(1/2) ) = 2 Take the anti log of both sides
6 x^1/2 = 2^2 Combine the right
6 x^1/2 = 4 Divide by 6
x^1/2 = 4/6 = 2/3 which gives 2/3 now square both sides
x = (2/3)^2
x = 4/9
Answer:
Option c
Step-by-step explanation:
The given logarithmic equation is
[tex]log_{2} (6x)-log_{2}(\sqrt{x})=2[/tex]
[tex]log_{2}[\frac{(6x)}{\sqrt{x}}]=2[/tex] [since log[tex](\frac{a}{b})[/tex]= log a - log b]
[tex]log_{2}[\frac{(6\sqrt{x})\times\sqrt{x}}{\sqrt{x}}]=2[/tex] [since x = [tex](\sqrt{x})(\sqrt{x})[/tex]]
[tex]log_{2}(6\sqrt{x} )=2[/tex]
[tex]6\sqrt{x} =2^2[/tex] [logₐ b = c then [tex]a^{c}=b[/tex]
[tex]6\sqrt{x} =4[/tex]
[tex]\sqrt{x} =\frac{4}{6}[/tex]
[tex]\sqrt{x} =\frac{2}{3}[/tex]
[tex]x=(\frac{2}{3})^2[/tex]
= [tex]\frac{4}{9}[/tex]
Option c is the answer.
What are the solutions of the equation?
0 = x2 + 3x - 10
Ox=5.2
Ox=-5,-2
x = -5,2
x=5-2
Answer:
Step-by-step explanation:
0 = x2 + 3x - 10
10 = 2x+3x
10 = 5x
x = 2
0x = 5.2
0x = 10
x = 10.2 = 20
x = 20
0x = -5.-2
0x = -10
x = -10.2 = -20
x = -20
x = -5.2
x = -10
x = 5-2
x = 3
GOOD LUCK ! ;)
For the given functions f and g, find the requested function and state its domain.
f(x) = 8x - 3; g(x) = 4x - 9
Find f - g.
Answer:
4x+6
Step-by-step explanation:
f(x)=8x-3
g(x)=4x-9
f(x)-g(x) = 8x-3-(4x-9)=8x-3-4x+9=4x+6
The value of f(x) - g(x) is 4x+6 and The domain is all real value of x.
What is a function ?A function can be defined as a mathematical expression which establishes relation between a dependent variable and an independent variable.
It always comes with a defined range and domain.
It is given in the question
functions f and g
f(x) = 8x - 3; g(x) = 4x - 9
f- g = ?
The value of f(x) - g(x) = 8x -3 - (4x -9)
f(x) - g(x) = 8x -3 - 4x +9
f(x) - g(x) = 4x +6
h(x) = 4x+6
The domain is all real value of x.
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The hypotenuse of a 45°-45°-90° triangle measures 128 cm. What is the length of one leg of the triangle? 64 cm cm 128 cm cm
Answer:
Answer 64*sqrt(2)
Step-by-step explanation:
Givens
c = 128 cm
a = b = ??
formula
a^2 + b^2 = c^2 combine the two equal legs.
2a^2 = c^2 Substitute 128 for c
2a^2 = 128^2 Square
2a^2 = 16384 Divide by 2
a^2 = 16384/2
a^2 = 8192 Factor (8192)
8192 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 count the 2s
8192 = 2^13 Break 13 into 2 equal values with 1 left over
sqrt(8192) = sqrt(2^6 * 2^6 * 2^1)
sqrt(8192) = 2^6 * sqrt(2)
The length of one leg is 64*sqrt(2)
Answer:
Length of one leg of the given triangle will be 64√2 cm.
Step-by-step explanation:
Length of the hypotenuse of a 45°- 45°- 90° triangle has been given as 128 cm.
Since two angles other than 90° are of same measure so other two sides of the triangle will be same in measure.
Therefore, by Pythagoras theorem,
Hypotenuse² = Leg(1)² + Leg(2)²
Let the measure of both the legs is x cm
(128)² = 2x²
16384 = 2x²
x² = [tex]\frac{16384}{2}[/tex]
x² = 8192
x = √8192
= 64√2 cm
Therefore, length of one leg of the given triangle will be 64√2 cm.
what is the equation of the circle with Center (-6, 7) that passes through the point (4, -2)
we know the center of the circle, and we also know a point on the circle, well, the distance from the center to a point is just the radius.
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[4-(-6)]^2+[-2-7]^2}\implies r=\sqrt{(4+6)^2+(-2-7)^2} \\\\\\ r=\sqrt{10^2+(-9)^2}\implies r=\sqrt{100+81}\implies r=\sqrt{181} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-6}{ h},\stackrel{7}{ k})\qquad \qquad radius=\stackrel{\sqrt{181}}{ r}\\[2em] [x-(-6)]^2+[y-7]^2=(\sqrt{181})^2\implies (x+6)^2+(y-7)^2=181[/tex]
needdd hellpppppssssssss
Answer:
Choice number one:
[tex]\displaystyle \frac{5}{10}\cdot \frac{4}{9}[/tex].
Step-by-step explanation:
Let [tex]A[/tex] be the event that the number on the first card is even.Let [tex]B[/tex] be the event that the number on the second card is even.The question is asking for the possibility that event [tex]A[/tex] and [tex]B[/tex] happen at the same time. However, whether [tex]A[/tex] occurs or not will influence the probability of [tex]B[/tex]. In other words, [tex]A[/tex] and [tex]B[/tex] are not independent. The probability that both [tex]A[/tex] and [tex]B[/tex] occur needs to be found as the product of
the probability that event [tex]A[/tex] occurs, andthe probability that event [tex]B[/tex] occurs given that event [tex]A[/tex] occurs.5 out of the ten numbers are even. The probability that event [tex]A[/tex] occurs is:
[tex]\displaystyle P(A) = \frac{5}{10}[/tex].
In case A occurs, there will only be four cards with even numbers out of the nine cards that are still in the bag. The conditional probability of getting a second card with an even number on it, given that the first card is even, will be:
[tex]\displaystyle P(B|A) = \frac{4}{9}[/tex].
The probability that both [tex]A[/tex] and [tex]B[/tex] occurs will be:
[tex]\displaystyle P(A \cap B) = P(B\cap A) = P(A) \cdot P(B|A) = \frac{5}{10}\cdot \frac{4}{9}[/tex].
18. What is the y-intercept of the graph of the function y = 3x + 2x - 13?
[tex]y=3\cdot0 + 2\cdot0 - 13=-13[/tex]
The y-intercept is [tex](0,-13)[/tex]
Please help !!!!!urgent !!!!!Which statement is true according to the diagram ??
Answer:
the second one
Suppose a triangle has two sides of length 2 and 3 and hat angle between these two sides is 60. what is the length of the third side of he triangle?
A boy purchased (bought) a party-length sandwich 54 in. long. He wants to cut it into three pieces so that the middle piece is 6 in. longer than the shortest piece and the shortest piece is 9 in. shorter than the longest piece. How long should the three pieces be?
Answer:
length of shortest piece = 13 in
length of middle piece = 19 in
length of longest piece = 22 in
Step-by-step explanation:
Total length of sandwich = 54 inch
Let shortest piece = x
Middle piece = x+6
Longest piece = x+9
Add this pieces will make complete sandwich
x+(x+6)+(x+9) = 54
Solving
x+x+6+x+9 = 54
Combining like terms
x+x+x+6+9 = 54
3x + 15 = 54
3x = 54 -15
3x = 39
x = 13
So, length of shortest piece = x = 13 in
length of middle piece = x+6 = 13+6 = 19 in
length of longest piece = x+9 = 13+9 = 22 in
Answer:
The three pieces should be 13 , 19 , 22 inches
Step-by-step explanation:
* Lets study the information to solve the problem
- The length of the sandwich is 54 in
- The sandwich will cut into three pieces
- The middle piece is 6 inches longer than the shortest piece
- The shortest piece is 9 inches shorter than the longest piece
* Lets change the above statements to equations
∵ The shortest piece is common in the two statements
∴ Let the length of the shortest piece is x ⇒ (1)
∵ The middle piece is 6 inches longer than the shortest piece
∴ The length of the middle piece = x + 6 ⇒ (2)
∵ The shortest piece is 9 inches shorter than the longest piece
∴ The longest piece is 9 inches longer than the shortest piece
∴ The longest piece = x + 9 ⇒ (3)
∵ the length of the three pieces = 54 inches
- Add the length of the three pieces and equate them by 54
∴ Add (1) , (2) , (3)
∴ x + (x + 6) + (x + 9) = 54 ⇒ add the like terms
∴ 3x + 15 = 54 ⇒ subtract 15 from both sides
∴ 3x = 39 ⇒ divide both sides by 3
∴ x = 13
* The length of the shortest piece is 13 inches
∵ The length of the middle piece = x + 6
∴ The length of the middle piece = 13 + 6 = 19 inches
* The length of the middle piece is 19 inches
∵ The length of the longest piece = x + 9
∴ The length of the longest piece = 13 + 9 = 22 inches
* The length of the longest piece is 22 inches
* The lengths of the three pieces are 13 , 19 , 22 inches
A home improvement store advertises 60 square feet of flooring for $253.00, plus an additional $80.00 installation fee. What is the cost per square foot for the flooring?
A. $4.95
B. $5.25
C. $5.55
D. $6.06
Answer:
your answer is C.$5.55
Step-by-step explanation:
cost of square feet flooring is $253.00cost of additional installation fee $80.00NOW TAKE THE TOTAL OF BOTH,THEN WE GET
$253+$80=333NOW DO THE DIVIDE OF 333 BY 60, THEN WE GET
333/60=$5.55What are the zeros of this function?
Answer:
x =0 and x = 4
Step-by-step explanation:
It is a quadratic function and hence will have two roots. It cuts graph at 2 points( x - axis ). Hence has two roots.
what is 1/6 as a percent
Answer:16.66
Step-by-step explanation:
To convert 1/6 into a percent, multiply by 100 to get approximately 16.67 percent.
To convert a fraction to a percent, you can follow a standard way of expressing the fraction such that the denominator equals 100. For 1/6, you want to find what number over 100 is equivalent to it. To do so, you can set up a proportion where 1/6 equals x/100. Solving for x, you would cross-multiply and divide to get:
1 * 100 = 6 * x
[tex]\( x = \frac{100}{6} \)[/tex]
x ≈ 16.67
Therefore, 1/6 as a percent is approximately 16.67 percent.
consider each table of values
of the three functions,
f & h
none
f & g
g & h
all three
represent linear relationships
Answer:
g and h
Step-by-step explanation:
both g and h have constant relationships while f's f(x) values aren't constant so it doesn't have a linear relationship
Answer:
Of the three functions g and h represent linear relationship.
Step-by-step explanation:
If a function has constant rate of change for all points, then the function is called a linear function.
If a lines passes through two points, then the slope of the line is
[tex]m=\frac{x_2-x_1}{y_2-y_1}[/tex]
The slope of function f(x) on [1,2] is
[tex]m_1=\frac{11-5}{2-1}=6[/tex]
The slope of function f(x) on [2,3] is
[tex]m_2=\frac{29-11}{3-2}=18\neq m_1[/tex]
Since f(x) has different slopes on different intervals, therefore f(x) does not represents a linear relationship.
From the given table of g(x) it is clear that the value of g(x) is increased by 8 units for every 2 units. So, the function g(x) has constant rate of change, i.e.,
[tex]m=\frac{8}{2}=4[/tex]
From the given table of h(x) it is clear that the value of h(x) is increased by 6.8 units for every 2 units. So, the function h(x) has constant rate of change, i.e.,
[tex]m=\frac{6.8}{2}=3.4[/tex]
Since the function g and h have constant rate of change, therefore g and h represent linear relationship.
Round $499.76 to the nearest dollar
This is your answer:
if then number is $499.49 that would mean it rounds down to $499.00
but in your case $499.76 rounds to $500.00
(Remember .50 and up goes up!)
Therefor your answer is $500.00
Answer:
$499.76 rounded to the nearest dollar is $500 !!
Step-by-step explanation:
Why?
A dollar ($1) would be in the ones column and it's asking for the nearest dollar! So you would round it by the number on the right of the dollar, the tenths.