create and solve a linear equation that represents the model, where circles and a square are shown evenly balanced on a balance beam.
A. + 7 = 12; x = 5
B. x = 5 + 7; x = 12
C. x + 5 = 7; x = 2
D. x + 7 = 5; x = -2
Answers
Answer:
C
Step-by-step explanation:
We can notice that the balance beam has in one side 7 balls and in the other one 5 balls and a square
The balance beam is balenced
Let x be the square mass
x+5 = 7 substract five from each side x+5-5 = 7-5 x = 2The solution is 2
C fits perfectly what we prooved
Answer:
C: x + 5 = 7; x = 2
Step-by-step explanation:
Refer to the given model. On the left-hand side of the balance beam, there are five circles and one square. On the right-hand side of the balance beam, there are seven circles. The balance beam is evenly distributed, so the value on the left-hand side of the balance beam must be the same as the value on the right-hand side of the balance beam.
The square stands for an unknown quantity. In algebra, variables are used to represent unknown quantities, so x will represent the value of the square.
The model shows that the value of x plus five circles is the same as seven circles. Replacing the word "plus" with a plus sign and replacing "is the same as" with an equal sign gives the equation x + 5 = 7.
To solve the equation, subtract 5 from both sides of the equation to isolate x.
Thus, the solution to the equation is x = 2.
Related Questions
Boris is selling pirate hats. If he sells the hats for $50 he will sell 135 hats.
For each increase in price of $2 he will sell 3 fewer hats.
Determine the possible prices he could charge to earn $6486 or more.
Answers
Answer:
Current price $50eax135hats= $6750
Step-by-step explanation:
If he sells the hats at $52 he sells 3 less hats so $52x132=$6864
if he sells the hats at $54 he has 6 less hats= 54x129=6966 etc
$56 x 126=$7056
Help please!!!!!! Thank you
Answers
Answer:
1/4
Step-by-step explanation:
Well see how far each points are from each other.
Start at the red triangle and go up 1, go to the right 4.
Thus,
the rise/run is 1/4.
Hope this helps :)
Answer:
1/4
Step-by-step explanation:
To find the rise/run, you first need to pick two points from the line. You can pick whichever points you want, and you will get the right answer. I will pick (-8, -3) and (8, 1).
Divide the difference of the y's by the difference of the x's.
-3 - 1 = -4
-8 - 8 = -16
-4/-16 = 1/4
The rise/run is 1/4.
The population of a certain type of seahorse grew by 13% from year to year.
Should the be modeled linear function or Exponential function ?
Answers
Answer: Exponential function
Step-by-step explanation:
A linear function is the form[tex]f(x)=mx+c[/tex] , where m is the constant rate of change of y with respect to x and c is the y-intercept.
An exponential growth function is in the form [tex]f(x)=A(1+r)^x[/tex], where r is the rate of growth (generally in percent) and A is initial value.
If the population of a certain type of seahorse grew by 13% from year to year, then the rate of growth is 13% .
Hence it is an exponential equation.
What is the answer to 85% of 62
Answers
Answer:
52.7
Step-by-step explanation:
Of means multiply
85% * 62
.85 * 62
52.7
Turn the percentage into a decimal.
85% = 0.85
Multiply.
62 * 0.85 = 52.7
So, 52.7 is 85% of 62.
Best of Luck!
Which of the following is an arithmetic sequence?
Answers
Answer:
B: 3,0,-3,-6
Step-by-step explanation:
An arithmetic sequence has constant adding or subtracting. In this case, 3 is being subtracted as a constant.
Using the order of operations, what should be done first to evaluate 6 squared + 10 divided by (negative 5) (3) minus 5?
A.Subtract 5 from 3.
B.Divide 10 by –5.
C.Add 6 and 10.
D.Evaluate 6 squared.
Answers
Answer:
apply the BODMAS concept
brackets, off, division, multiplication, addition, subtraction
Step-by-step explanation:
(6²+10)÷(-5×3)-5
in this case the answer is D
The amount that two groups of students spent on snacks in one day is shown in the dot plots below. Which statements about the measures of center are true? Select three choices. The mean for Group A is less than the mean for Group B. The median for Group A is less than the median for Group B. The mode for Group A is less than the mode for Group B. The median for Group A is 2. The median for Group B is 3.
Answers
Answer:
The mean for Group A is less than the mean for Group B. The median for Group A is less than the median for Group B.The mode for Group A is less than the mode for Group B.Step-by-step explanation:
First, we can find the measures of center for each group.
Group A
Mode: 1
Median: (1 + 2) / 2 = 3 / 2 = 1.5
Mean: (1 * 5 + 2 * 4 + 3) / 10 = (5 + 8 + 3) / 10 = 16 / 10 = 1.6
Group B
Mode: 3
Median: 92 + 3) / 2 = 5 / 2 = 2.5
Mean: (1 * 3 + 2 * 2 + 3 * 4 + 5) / 10 = (3 + 4 + 12 + 5) / 10 = 24 / 10 = 2.4
From here, we can see that...
The mean for Group A is less than the mean for Group B. The median for Group A is less than the median for Group B.The mode for Group A is less than the mode for Group B.Hope this helps!
Answer:
ABC
Step-by-step explanation:
Sophie is riding her bike home when she runs over a nail. It gets stuck to the tire of her bike but does not pop the tire. As she continues to cycle home the nail hits the ground every 2 seconds and reaches a maximum height of 48cm. a) Write a sinusoidal equation that models the nails height off the ground in cm, h, in terms of time,t. Sketch one full revolution of the nail, assuming that sophie first runs over the nail at 0seconds . b) Algebraically determine the height of the nail above the ground at 0.8 seconds. Round your answer to the nearest tenth of a cm
Answers
Answer:
a) The sinusoidal equation is;
The function is h = -24·cos[π(t )] + 24
The sketch of one full revolution is attached
b) The height of the nail at 0.8 seconds is 43.42 cm
Step-by-step explanation:
The sinusoidal equation that models the nails height can be given as follows;
y = A·cos[B(x - C)]+D
A = The amplitude = Half maximum height = 48/2 = 24 cm
The period = 2·π/B = Time to complete one oscillation = 2 seconds
∴ B = 2·π/2 = π
x = t = Time
C = The horizontal shift
D = the vertical shift = 24 cm
y = The height of the nail = h
We have;
h = -24·cos[π(t - C)] + 24
At t = 0, h = 0, therefore, we have;
0 = -24·cos[π(0 - C)] + 24
24·cos[π(0 - C)] = 24
∴ cos[π(0 - C)] = 24/24 = 1
π(0 - C) = 0
C = 0
The function is h = -24·cos[π(t )] + 24
b) The height of the nail at 0.8 seconds is given as follows;
h = -24×cos[π(0.8)] + 24 =
h = 19.42 + 24 = 43.42 cm.
Clarise evaluated this expression.
(66.3 – 14.62) ÷ 0.6 – 0.22
(51.68) ÷ 0.6 – 0.22
(51.68) ÷ 0.42
51.68 ÷ 0.16
32.3
Which errors did Clarise make?
Answers
Answer:
(66.3-14.62)/0.6-0.22
(51.68)/0.6-0.22
(51.68/0.6)-0.22
(86.14667)-0.22
85.92667
the figure is cut into 8 equal pieces shade 3/4 of the figure
Answers
Answer:
You have to shade 6 pieces.
Step-by-step explanation:
Hope it helps!
Two fair dices, X and Y , are tossed separately. Let A, B and C represent the following three events. A: You got an odd number from die X. B: You got an even number from die Y . C: The sum of two dice is an odd number. Whether A, B, C are independent
Answers
Answer:
Events A and B are independent but Event C is dependent on both Event A and Event B.
Step-by-step explanation:
Find whether events A, B and C are independent.
- Events A and B are independent of each other, because the appearance of an odd number on die X does not effect or influence the appearance of an even number on die Y.
- Event C, on the other hand, is dependent on both event A and event B. How?
For Event C to take place, one die will have to show an odd number while the other shows an even number.
NOTE: The odd number must not show up on die X and the even number show up on die Y. Both number types can appear on any die.
The key is just that one number must be odd and the other even; in order for their sum to be an odd number.
Pls help (probability)
The table below provides the drinking and smoking habits of 1200 college students surveyed. What is the
probability that someone in this group drinks, if you already know that that
person smokes?
Answers
Answer:
315/1200 = 63/240 = 21/80 = 0.2625 = 26.25%
Step-by-step explanation:
Which list is in order from least to greatest
Answers
The correct answer to this question is A. 9.4 x [tex]10^{-8}[/tex], 9.25 x [tex]10^{-6}[/tex], 2.5 x [tex]10^{3}[/tex], 7 x
Explanation:
These numbers are written in scientific notation. In this system, the exponent shows the number of spaces the period has been moved to make the number shorter. Additionally, a positive exponent shows the number has a certain number of digits to the right, while a negative exponent shows the number has digits to the left. In this way, the numbers presented can be converted as:
9.4 x [tex]10^{-8}[/tex] = 0.000000094 (Exponent indicates eight spaces to the left)
9.25 x [tex]10^{-6}[/tex] = 0.00000925 (Exponent indicates six spaces to the left)
2.5 x [tex]10^{3}[/tex] = 2500 (Exponent indicates three spaces to the right)
7 x [tex]10^{3}[/tex] = 7000 (Exponent indicates three spaces to the right)
Solve using the quadratic formula.
2x2=8x-7
Answers
Answer:
[tex]\boxed{x=\frac{4\pm\sqrt{2}}{2}}[/tex]
Step-by-step explanation:
Part 1: Rewriting equation to match ax² + bx + c = 0 (quadratic function)
The given equation is not written in quadratic form. To rewrite the equation:
All values need to be on the left side of the equation and set equal to zero.To overcome this difficulty, follow these mathematical steps:
[tex]2x^2=8x-7\\2x^2-8x=-7\\2x^2-8x+7=0[/tex]
Subtract 8x from both sides of the equation to rearrange it to the left side. Then, add 7 to rearrange it as well. Finally, set the three values on the left of the equation equal to zero.
Part 2: Using the quadratic formula
The quadratic formula is defined as [tex]\boxed{x=\frac{-b\pm\sqrt{b^2-4ac} }{2a} }[/tex].
Using the parent quadratic function, the values are easy to find in the given equation. [tex]\boxed{a=2, b=-8, c=7}[/tex]
Substitute these values into the quadratic formula and solve for x.
[tex]x=\frac{8\pm\sqrt{(-8)^2-4(2)(7)}}{2(2)} \\\\x=\frac{8\pm\sqrt{64-4(14)}}{4}\\\\x=\frac{8\pm\sqrt{64-56}}{4} \\\\x=\frac{8\pm\sqrt{8}}{4}\\\\x= 2\pm\frac{\sqrt{8}}{4}\\ \\x=2\pm\frac{\sqrt{2}}{2}[/tex]
Part 3: Solving for x with the values from the quadratic formula
Now that x is set equal to the simplified version of the equation, the operations have to be followed through with.
This equation will have two zeros/roots to solve for by setting x equal to zero.
Operation 1: Addition
[tex]x=2+\frac{\sqrt{2} }{2}\\\\x=\frac{4+\sqrt{2}}{2}[/tex]
Operation 2: Subtraction
[tex]x=2-\frac{\sqrt{2}}{2}\\ \\x=\frac{4-\sqrt{2}}{2}[/tex]
Because both values are the exact same (minus the operations), the roots can be simplified even further to one value:
[tex]\boxed{x=\frac{4\pm\sqrt{2}}{2}}[/tex]
Michael is on page 28 of a 315-page book. He must finish the book within the next 14 days. He solved the inequality 28+ 14p = 315 He did not use the correct value as the coefficient of p and should have solved 14 + 28p <= 315
Answers
Answer:
yes you're right it is 14 + 28p = 315
Answer:
C
Step-by-step explanation:
I had this question edge 2021
What is the solution to the equation ? 5{n-1 over 10}= 1 over 2
Answers
Answer:
n = 2
Step-by-step explanation:
Given
5( [tex]\frac{n-1}{10}[/tex] ) = [tex]\frac{1}{2}[/tex] ← distribute parenthesis on left side
[tex]\frac{n-1}{2}[/tex] = [tex]\frac{1}{2}[/tex]
Since denominators are both 2 then equate numerators
n - 1 = 1 ( add 1 to both sides )
n = 2
The area of circle Z is 64 ft^2.
What is the value of r?
Or= 4 ft
O r= 8 ft
O r= 16 ft
O = 32 ft
Answers
Answer:
The answer is
r =4 ftStep-by-step explanation:
Area of a circle is given by πr²
Where r is the radius
From the question
Area = 64 ft²
So the radius is
64 = πr²
Divide both sides by π
[tex] {r}^{2} = \frac{64}{\pi} [/tex]
Find the square root of both sides
[tex]r = \sqrt{ \frac{64}{\pi} } [/tex]
r = 4 ft
Hope this helps you
The answer is 8 not 4.5 or 4!!!!!!!!
Step-by-step explanation: It's not just "64" its 64pi. when you posted the question your device could not put the pi symbol so people were thinking that it was just 64.
Please Help! A pair of equations is shown below. x + y = 2 y = one halfx + 5 If the two equations are graphed, at what point do the lines representing the two equations intersect? (4, −2) (−2, 4) (2, 5) (5, −2)
Answers
Answer:
(-2,4)
Step-by-step explanation:
First, put x+y=2 into slope-intercept form: y=-x+2
Second, set the to equations equal to each other: -x+2=1/2x+5
Then, add x to both sides: -x+x+2=1/2x+x+5 to get: 2=3/2x+5
Next, subtract 5 from both sides: 2-5=3/2x+5-5, to get -3=3/2x
Finally, to get the x-value, divide both sides by 3/2: -3(2/3)=3/2x(2/3), to get x=-2
Lastly, substitute -2 for x into one of the equations to find y:
x+y=2
-2+y=2
add 2 to both sides: -2+2+y=2+2, to get y=4
The solution is (-2,4)
Answer:
(- 2, 4 )
Step-by-step explanation:
Given the 2 equations
x + y = 2 → (1)
y = [tex]\frac{1}{2}[/tex] x + 5 → (2)
Substitute y = [tex]\frac{1}{2}[/tex] x + 5 into (1)
x + [tex]\frac{1}{2}[/tex] x + 5 = 2 ( multiply through by 2 to clear the fraction )
2x + x + 10 = 4
3x + 10 = 4 ( subtract 10 from both sides )
3x = - 6 ( divide both sides by 3 )
x = - 2
Substitute x = - 2 into (1) and evaluate for y
- 2 + y = 2 ( add 2 to both sides )
y = 4
Solution is (- 2, 4 )
How would 7/2 be written as a complex number
Answers
Answer:
We could rewrite 7/2 as 7a + 2
Step-by-step explanation:
Complex numbers is when real numbers [i.e: 1, 1/2, 200, 5/7, etc..) and an imaginary numbers [numbers that give a negative result when squared] are combine together.
Opal is collecting data on water levels in different parts of town. She notices that her sample data has a low-value outlier. Which statement must be true?
A. Removing the outlier will not change the spread of the graph of the data set.
B. Removing the outlier will not change the variance of the data set.
C. Removing the outlier will increase the variance of the data set.
D. Removing the outlier will decrease the spread of the graph of the data set.
Answers
Answer:
D.
Step-by-step explanation:
if you remove the low value outlier, the variation from the mean will decrease therefore decreasing the varianc.
Answer:
D. Removing the outlier will decrease the spread of the graph of the data set.
Step-by-step explanation:
Outliers increase the spread of the data set.
So removing an outlier will generally decrease the spread or variance or standard deviation of a data set.
The answer is
D. Removing the outlier will decrease the spread of the graph of the data set.
Together, two apples have 1/5 gram of fat. How many apples have a total of 4 grams of a
apples
Answers
Answer:
40 apples
Step-by-step explanation:
2 apples= [tex]\frac{1}{5}[/tex] grams
x apples= 4 grams
8/[tex]\frac{1}{5}[/tex] = 8 x 5/1=40
Answer:
40
Step-by-step explanation:
edu instruction correct
Evaluate ƒ(x) = –x2 + 1 for x = –3. a) 4 b) –4 C) –9 D) –8
Answers
[tex]f(x)=-x^2+1[/tex]
Plug in the value [tex]x=-3[/tex] into this function
[tex]f(-3)=-(-3)^2+1[/tex]
[tex]=-(9)+1[/tex]
[tex]=-8[/tex]
Thus, your answer will be D) -8. Let me know if you need any clarifications, thanks!
Answer:
D. -8
Step-by-step explanation:
We are given
f(x)= -x^2+1
and asked to evaluate f(x) for x= -3. Therefore, we must substitute -3 for x in the function.
f(x)= -x^2+1 for x= -3
f(-3)= -(-3^2)+1
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
First, evaluate the exponent: -3^2
-3^2= -3*-3= 9
f(-3)= -(9)+1
f(-3)=-9+1
Next, add -9 and 1
f(-3)= -8
When f(x)= -x^2+1 is evaluated for x= -3, the result is -8. Therefore, the correct answer is D. -8
The ratio of George's money and Tia's
money was 9 : 4. After George spent
$24 and Tia collected $11, the amounts
money they had are the same. How
much
money
did Tia have at first?
Answers
===================================================
Explanation:
G = amount of money George starts with
T = amount of money Tia starts with
Initially the ratio of their money is 9:4 so G/T = 9/4. Solve for G to get G = (9/4)T.
--------
After George spends 24 dollars he's left with (G-24) dollars. Tia gains 11 dollars so she has (T+11) dollars. They have the same amount of money after these two events occur, so G-24 = T+11.
Plug in G = (9/4)T and solve for T
G-24 = T+11
(9/4)T-24 = T+11 ... replace G with (9/4)T
4*[ (9/4)T-24 ] = 4*[ T+11 ] ... multiply both sides by 4 to clear out fraction
9T - 96 = 4T + 44 ... distribute
9T - 4T = 44 + 96
5T = 140
T = 140/5
T = 28
Tia started off with 28 dollars. We could stop here because your teacher is only asking about Tia's initial amount.
----------
If you want to find how much George started with, then plug T = 28 into G = (9/4)T to get...
G = (9/4)T
G = (9/4)*28
G = 2.25*28
G = 63
George started off with 63 dollars
The ratio of 63:28 reduces to 9:4 after dividing both parts by the GCF 7. This confirms the first fact we're given.
Notice how 63 drops to 63-24 = 39 after George spends $24. At the same time, Tia's amount increases to 28+11 = 39, which is the same as George's updated amount. Both facts match the description, so we have confirmed the answer.
Answer:
$28
Step-by-step explanation:
rotate the triangle below: A(5,3) B(8,10) C(11,3) angle of rotation is 180 centre origin direction is anti- clock wise
Answers
Answer:
see explanation
Step-by-step explanation:
Under a rotation ( clockwise or anticlockwise ) about the origin of 180°
a point (x, y ) → (- y, - x ), thus
A(5, 3 ) → A'(- 3, - 5 )
B(8, 10 ) → B'(- 10, - 8 )
C(11, 3 ) → C'(- 3, - 11 )
please help :) Which of these numbers is the greatest? A. 1.9 x 10 to the 5 power B. 9.1 x 10 to the 2 power C. 7.9 x 10 to the 4 power D. 89,900
Answers
Answer: The answer is A.
Step-by-step explanation:
1.9x10^5= 190000
9.1x10^2= 910
7.9x10^4 =79000
X²+Y²=250 and XY=117
What are the values of X and Y?
Answers
Answer:
x = -9, y = -13 or x = 13, y = 9 or x = -13, y = -9 or x = 9, y = 13Step-by-step explanation:
[tex]x^2+y^2=250\\\\x^2-2xy+y^2+2xy=250\\\\(x-y)^2=250-2xy\\\\(x-y)^2=250-2\cdot117\\\\ (x-y)^2=16\\\\x-y=4\qquad\qquad\vee\qquad \qquad x-y=-4\\\\x=4+y \qquad\qquad \vee\qquad\qquad x=-4+y\\\\(y+4)y=117\qquad\vee\qquad\quad (y-4)y=117\\\\y^2+4y-117=0\qquad\vee\qquad y^2-4y-117=0\\\\y=\dfrac{-4\pm\sqrt{4^2-4(-117)}}{2\cdot1}\qquad\vee\qquad y=\dfrac{4\pm\sqrt{4^2-4(-117)}}{2\cdot1}\\\\y=\dfrac{-4\pm\sqrt{16+468}}{2}\qquad\ \ \vee\qquad y=\dfrac{4\pm\sqrt{16+468}}{2}[/tex]
[tex]y_1=\dfrac{-4-22}{2}\ ,\quad y_2=\dfrac{-4+22}{2}\ ,\quad y_3=\dfrac{4-22}{2}\ ,\quad y_4=\dfrac{4+22}{2}\\\\y_1=-13\ ,\qquad y_2=9\ ,\qquad\quad\qquad\ y_3=-9\ ,\qquad y_4=13\\\\x_{1,2}=4+y_{1,2}\qquad\qquad\qquad\qquad\qquad x_{3,4}=-4+y_{3,4}\\\\x_1=-9\ ,\qquad x_2=13\ ,\qquad\quad\qquad x_3=-13\ ,\qquad x_4=9[/tex]
write the expression in radical form. (88c)^2/3
Answers
Answer:
[tex]\sqrt[3]{88c^{2} }[/tex]
Step-by-step explanation:
If we have a term to a fractional power, that’s the same as finding the denominator root of the number - if the numerator of the fraction isn’t 1, then the term itself inside the root sign becomes the term to the numerator power.
So - since the denominator of this fraction is 3, we find the cube root of 88c. Since the numerator is 2, we square 88c.
[tex]\sqrt[3]{88c^{2} }[/tex].
Hope this helped! (By the way, this was my 100th answer!)
i need help with this equation 20 points help quick
Answers
Answer:
[tex]\boxed{y=|\frac{1}{2}x - \frac{3}{2}|+3}[/tex]
Step-by-step explanation:
The translation is a horizontal translation.
The graph is translated 1 unit to the left. So the value of x is added by 1.
[tex]f(x+1)[/tex]
[tex]y=|\frac{1}{2} (x+1)-2|+3[/tex]
[tex]y=|\frac{1}{2}x + \frac{1}{2} -2|+3[/tex]
[tex]y=|\frac{1}{2}x + - \frac{3}{2}|+3[/tex]
Sandra y Roberto, cada uno de ellos con una copia del libro, deciden que ellos pueden ganar tiempo "leyendo en equipo" la novela. En este esquema, Sandra leerá desde la página 1 hasta una cierta página y Roberto leerá desde la página siguiente hasta la pagina 760. Cuando ellos hayan terminado cada uno contará la parte que leyó al otro. ¿Cuál es la última página que Sandra debería leer de tal manera que ella y Roberto pasen la misma cantidad de tiempo leyendo la novela?
Answers
Answer:
La última página que Sandra deberá leer es la página 380.
Step-by-step explanation:
Sandra y Roberto tienen un libro de 760 páginas y se lo dividen, la pregunta es ¿Cuál es la última página que debería leer Sandra de tal manera que ella y Roberto pasen la misma cantidad de tiempo leyendo la novela?
Para que ambos pasen la misma cantidad de tiempo leyendo la novela, tendrían que dividirse el libro a la mitad, por lo que cada uno debería leer 760 ÷ 2 = 380 páginas.
Por lo que Sandra deberá leer de la página 1 a la 380 y Roberto leerá de la 381 a la 760.
Por lo tanto, la última página que Sandra deberá leer es la página 380.
What is the product?
(negative 3 s + 2 t)(4 s minus t)
negative 12 s squared minus 2 t squared
negative 12 s squared + 2 t squared
negative 12 s squared + 8 s t minus 2 t squared
negative 12 s squared + 11 s t minus 2 t squared
Mark
Answers
Answer:
The answer is
negative 12 s squared + 11 s t minus 2 t squared
Step-by-step explanation:
( - 3s + 2t)( 4s - t)
Expand the terms
We have
- 12s² + 3st + 8st - 2t²
Simplify
We have the final answer as
- 12s² + 11st - 2t²Hope this helps you
Answer:
D. -12s^2+11st-2t^2