When does the value of f(x) = (1/2)x equal the value of g(x) =2x+8 ?
Answer:
[tex]\huge\boxed{f=g(x)\ \text{for}\ x=-\dfrac{16}{3}=-5\dfrac{1}{3}}[/tex]
Step-by-step explanation:
When does the value of f(x) = (1/2)x equal the value of g(x) =2x+8?
[tex]f(x)=g(x)\iff\dfrac{1}{2}x=2x+8\qquad|\text{subtract}\ 2x\ \text{from bpoth sides}\\\\\dfrac{1}{2}x-2x=2x-2x+8\\\\-1\dfrac{1}{2}x=8\qquad|\text{convert the mixed number to the improper fraction}\\\\-\dfrac{2\cdot1+1}{2}x=8\\\\-\dfrac{3}{2}x=8\qquad\text{multiply both sides by}\ -\dfrac{2}{3}\\\\\left(-\dfrac{2\!\!\!\!\diagup}{3\!\!\!\!\diagup}\right)\left(-\dfrac{3\!\!\!\!\diagup}{2\!\!\!\!\diagup}x\right)=\left(-\dfrac{2}{3}\right)\cdot8\\\\x=-\dfrac{2\cdot8}{3}\\\\x=-\dfrac{16}{3}[/tex]
what is 8455 divided by 89?
Answer:
95
Step-by-step explanation:
Answer:
95
Step-by-step explanation:
8455 divided by 89
If the sum of three consecutive numbers is 1998, what is the first one?
Answer: 665
Step-by-step explanation: X + X + 1 + X + 2 = 1998
3X + 3 = 1998
3X + 3 - 3 = 1998 - 3
3X = 1995
3X/3 = 1995/3
X = 665
ASAP!! PLEASE I NEED HELP!!
A farmer needs to fence a rectangular plot of land with the area of 3000 square yards. He considers several possible length of the plot: 50 yards, 40 yards, 48 yards, and 36 yards. What will be the width of the plot in each case? Do the length and the width of the rectangular plot vary directly or inversely when the same area is needed? Explain why.
Answer:
If the length is 50 yd, the width is
yd.
If the length is 40 yd, the width is
yd.
If the length is 48 yd, the width is
yd.
If the length is 36 yd, the width is
yd.
The length and the width vary .
Answer:
If the length is 50 yd, the width is 60 yd.
If the length is 40 yd, the width is 75 yd.
If the length is 48 yd, the width is 62.5 yd.
If the length is 36 yd, the width is 83.33 yd.
The length and the width vary inversely because when the length decreased the width increased
Step-by-step explanation:
The area of any rectangle A = L × W, where
L is its lengthW is its widthThe relation is direct proportion if the quotient of two quantity equals constant (y/x = k, when y and x increased) and inverse if the product of the two quantity equals constant (yx = k, when x increased y decreased and vice versa)
∵ The area of the rectangular plot of land = 3000 yards²
∴ A = 3000
∵ Its length = 50 yards
∴ L = 50
→ Substitute them in the rule above to find W
∵ 3000 = 50 × W
→ Divide both sides by 50 to find W
∴ 60 = W
∴ The width of the plot is 60 yards
∵ Its length = 40 yards
∴ L = 40
→ Substitute them in the rule above to find W
∵ 3000 = 40 × W
→ Divide both sides by 40 to find W
∴ 75 = W
∴ The width of the plot is 75 yards
∵ Its length = 48 yards
∴ L = 48
→ Substitute them in the rule above to find W
∵ 3000 = 48 × W
→ Divide both sides by 48 to find W
∴ 62.5 = W
∴ The width of the plot is 62.5 yards
∵ Its length = 36 yards
∴ L = 36
→ Substitute them in the rule above to find W
∵ 3000 = 36 × W
→ Divide both sides by 36 to find W
∴ 83. 33 = W
∴ The width of the plot is 83.33 yards
∵ The area is a constant value
∵ A = LW
→ The product of L and W equals the constant value, can you discover
that from the values of L and W
∴ The length and the width of the rectangular plot vary inversely
The length and the width of the rectangular plot vary inversely when the same area is needed.
Area of Rectangle:Area of rectangular plot [tex]=length *width[/tex]
Given that, Area of plot is 3000 square yards.
If the length is 50 yards. Then,[tex]width=\frac{3000}{50} =60yd[/tex]
If the length is 40 yards. Then,[tex]width=\frac{3000}{40}=75yd[/tex]
If the length is 48 yards. Then,[tex]width=\frac{3000}{48}=62.5yd[/tex]
If the length is 36 yards. Then,[tex]width=\frac{3000}{36}=83.34yd[/tex]
Learn more about the area of rectangle here:
https://brainly.com/question/25292087
y=12x^2-9x+4 does this have one two or no solution
So what s the meaning for X and Y
The first x is the horizontal coodinate (abscisa) and second is the vertical coordinate (ordenate). Both are coordinates. (x,y) has the meaning of a complex number: x is the real part and y is the imaginary part: x+yi. (x,y) has the meaning of a plane's vector from origin of coordinates.
PLEASE help thank you
Solve for x. Enter the solution from least to greatest (x-4)(-5x+1)=0
Answer:
hee ya go (x-4)(-5x+1)=0. (x−4)(−5x+1)=0 ( x - 4 ) ( - 5 x + 1 ) = 0.
Step-by-step explanation:
If any individual factor on the left side of the equation is equal to
0.
Answer:
x=4
Step-by-step explanation:
If you do 4-4 in the first one you get 0. Then the problem would look like this.
(0)(-5x+1)=0
It wouldn't matter what the next one looks like because you would multiply it by 0 which would give you 0.
(0)(-19)
0 x (-19) = 0
how many inconsiderate people take up space in this world?
Answer:
Too many :(
Step-by-step explanation:
Its life u know
can i pls have brainliest
Answer:
that number is probably too high to count, don't ya think
Evaluate:
-77 + (-46)
-77 + (-46 )
- 77 - 46 (+ × - = - )
-123
Answer:
-123
Step-by-step explanation:
This is the answer because:
1) First, multiply the negative sign with the positive sign.
Negative x Positive = Negative
Equation: -77 - 46
2) Now, multiply the negative sign with the negative sign.
Negative x Negative = Positive
Equation: 77 + 46 = 123
3) Finally, add the greater number's sign (-77) in front of the number.
-123
Hope this helps! :D
drag numbers to write an equation for the line in slope intercept form number is may be used once more than once or not at all
Answer:
y = -4x + 5
Step-by-step explanation:
The equation for the line, in slope-intercept form will take the following equation format which is y = mx + b.
Where,
b = y-intercept = 5 (this is where the line intercepts the y-axis, and also, x = 0 here)
m = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Use any two points on the line. Using (0, 5) and (1, 1), calculate m as follows:
m = [tex] \frac{1 - 5}{1 - 0} = \frac{-4}{1} = -4 [/tex]
Substitute m = -4, and b = 5 into y = mx + b.
y = -4x + 5
Answer:
Y=-4x+5
Step-by-step explanation:
I need help with rounding
Answer:
ok so say the number is 23 you would look at the 3 and ask yourself is the 3 greater or smaller than 5 if its 4 and under you keep the number the same and just add a zero which would make it 20 and if its 5 and over you would add 1 to the first number and put a 0 at the end making it 30. HOPE THIS HELPS!
he average 30- to 39-year old man is 69.5 inches tall, with a standard deviation of 2.7 inches, while the average 30- to 39-year old woman is 64.2 inches tall, with a standard deviation of 3.2 inches. Who is relatively taller based on their comparison to their gender, LeBron James at 81 inches or Candace Parker at 76 inches
Answer:
2. LeBron is relatively taller because he has a larger z-score.
Step-by-step explanation:
Given that ,
mean =[tex]\mu[/tex] = 69.5
standard deviation [tex]=\sigma[/tex] = 2.7
x = 81
Now use the formula of z-score
[tex]z = x - \frac{\mu}{\sigma}[/tex]
z =[tex]81 - \frac{69.5}{2.7}[/tex]
z = 4.26 LeBron
mean = [tex]\mu[/tex] = 64.2
standard deviation =[tex]\sigma[/tex] = 3.2
x = 76
Now use the formula of z-score
[tex]z = x - \frac{\mu}{\sigma}[/tex]
[tex]z = 76 - \frac{64.2}{3.2}[/tex]
z = 3.69 Candace
As it can be seen that the lebron is taller as he has more z-score as compared to the Candace
what is the rule that describes this pattern of numbers -10,000; -1,000; -100; -10; -1; -0.1; -0.01; -0.001
Each number is one-tenth the number to its left.
Each number is 10 more than the number to its left.
Each number is 10 times the number to its left.
Each number is one-tenth the number to its right.
Answer:
Each number is one-tenth the number to its left.
Step-by-step explanation: -1,000 is one tenth of -10,000 for example
The solution for x^2+2x+8<0_ is
Answer:
Step-by-step explanation:
x
2
−2x−8=0
x
2
−4x+2x−8=0
x(x−4)+2(x−4)=0
(x+2)(x−4)=0
⟹x=−2,4
Which table represents a function?
Answer:
B
Step-by-step explanation:
What is the reciprocal of 3
Answer:
1/3
Step-by-step explanation:
3/1 backwards is 1/3
that's why its reciprocal is 1/3
hope this helps:)
The length of a new rectangular playing field is 2 yards longer then double the width. If the perimeter of the rectangular playing field is 322 yards, what are its dimensions?
Answer:
Step-by-step explanation:
First, we want to take the information we have and turn it into an equation, where x is our unknown dimension. For this problem, it would be better if x was equal to the width.
Let's write out the equation:
X is the width, 2x + 2 is the length, and we are multiplying both by two since there are two sides of the field. It will all equal to 322, because that is the perimeter.
2*x + 2(2x +2) = 322
Now, let's solve:
2*x + 2(2x + 2) = 322
2x + 4x + 4 = 322
6x + 4 = 322
6x = 318
x = 318 ÷ 6
x = 53
The width is 53 yards. To find the length, we multiply 53 by two and add two.
53 * 2 + 2 = 106 + 2 = 108 yards, as the length
I will give you branilest!
When you mix two colors of paint in equivalent ratios, the resulting color is always the same. Complete the table as you answer the questions.
cups of blue paint cups of yellow paint
2 10
1 5
3 15
3. What is the proportional relationship represented by this table?
The amount of (blue paint or red paint?) is (proportional or related?)to the amount of [yellow paint or green paint? ] .
Answer:
When simplified they all are 1/5
So yes they are proportional
6x4x8x5=
that is the
Can you help me find abcd please
Answer:
A.2 B.4 C.3 D.4 E.6
Step-by-step explanation:
1/2 ÷ 3/4 = 1/2 x 4/3 (flip 3/4 and keep 1/2)
If you multiply 1/2 x 4/3 you will get 4/6.
Which equation represents the model below
A) 2x - 2 = -6
B) 4x = 6
C) 2x + 2 = -6
D) 4x = -6
The greatest comen factor of 21, 30,49
6) What is the mystery number?
The mystery number has ...
• 9 in the Ones place.
8 in the Millions place.
4 in the Hundred Thousands place.
3 in the Hundreds place.
3 in the Thousands place.
3 in the Tens place.
O in the Ten Thousands place.
Answer:
8,403,339
Step-by-step explanation:
What is the pattern in the numbers 1,8,27,64
Answer:
3
Step-by-step explanation:
he pattern is continued by adding 3 to the last number each time, like this: 1, 8, 27, 64, 125, 216, 343, 512, 729
A study was designed to compare the attitudes of two groups of nursing students towards computers. Group 1 had previously taken a statistical methods course that involved significant computer interaction. Group 2 had taken a statistic methods course that did not use computers. The students' attitudes were measured by administering the Computer Anxiety Rating Scale (CARS). A random sample of 12 nursing students from Group 1 resulted in a mean score of 59.7 with a standard deviation of 2.8. A random sample of 15 nursing students from Group 2 resulted in a mean score of 64.7 with a standard deviation of 8.3. Can you conclude that the mean score for Group 1 is significantly lower than the mean score for Group 2? Let µ1 represent the mean score for Group 1 and µ2 represent the mean score for Group 2. Use a significance level of α = 0.1 for the test. Assume that the population variances are equal and that the two populations are normally distributed.Step 1: State the null and alternative hypotheses for the test.Step 2: Compute the value of the t test statistic. Round your answer to three decimal placesStep 3: Determine the decision rule for rejecting the null hypothesis H0. Round your answer to three decimal places. Reject or fail to reject your hypothesis?
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Group 1:
μ1 = 59.7
s1 = 2.8
n1 = sample size = 12
Group 2:
μ2 = 64.7
s2 = 8.3
n2 = sample size = 15
α = 0.1
Assume normal distribution and equ sample variance
A.)
Null and alternative hypothesis
Null : μ1 = μ2
Alternative : μ1 < μ2
B.)
USing the t test
Test statistic :
t = (m1 - m2) / S(√1/n1 + 1/n2)
S = √(((n1 - 1)s²1 + (n2 - 1)s²2) / (n1 + n2 - 2))
S = √(((12 - 1)2.8^2 + (15 - 1)8.3^2) / (12 + 15 - 2))
S = 6.4829005
t = (59.7 - 64.7) / 6.4829005(√1/12 + 1/15)
t = - 5 / 2.5108165
tstat = −1.991384
Decision rule :
If tstat < - tα, (n1+n2-2) ; reject the Null
tstat < t0.1,25
From t table :
-t0.1, 25 = - 1.3163
tstat = - 1.9913
-1.9913 < - 1.3163 ; Hence reject the Null
help help thanks and PLEASE
Answer:
ion know if imma be right or wrong but im guessing that #1 is C & #4 is either 6 or 7
Step-by-step explanation:
Bc both of the top part of the trapezoids look equal to each other but i could be wrong hopefully this helps
Find the exact value using a half angle identity. Cos(-pi/8)
9514 1404 393
Answer:
cos(-π/8) = (√(2+√2))/2
Step-by-step explanation:
The half-angle formula is ...
[tex]\cos{\dfrac{\theta}{2}}=\pm\sqrt{\dfrac{1+\cos{\theta}}{2}}[/tex]
Since cosine is an even function, cos(-π/8) = cos(π/8).
For θ/2 = π/8, θ = π/4 and cos(θ) = (√2)/2. Filling in the formula, we have ...
[tex]\cos{(-\dfrac{\pi}{8})}=\cos{\dfrac{\pi}{8}}=\sqrt{\dfrac{1+\cos{\dfrac{\pi}{4}}}{2}}=\sqrt{\dfrac{1+\dfrac{\sqrt{2}}{2}}{2}}\\\\=\sqrt{\dfrac{2+\sqrt{2}}{4}}=\boxed{\dfrac{\sqrt{2+\sqrt{2}}}{2}}[/tex]
the product of m and the sum of m and 82. Tranlate into a variable expression
Step-by-step explanation:
This expression will be;
m(m + 82).
Geometry: Write and solve an equation to find the value of x so that the figures have the same area.
Answer:
e
Step-by-step explanation:
e