Answer:
Step-by-step explanation:
Given the equation solved by Morgan, Dakota and Taylor expressed as 7x+5x+1=73, to get the value of x, the valid steps are as shown;
7x+5x+1=73
take the sum of 7x and 5x
12x+ 1 = 73
subtract 1 from both sides
12x+1-1 = 73-1
12x = 72
Divide both sides by 12
12x/12 = 72/12
x = 6
Based on the calculation above, the students with invalid first step is Dakota.
Dakota added 5x with 1 to get 6x which is an invalid step because 1 is not attached to a variable x. A function cannot be added to a constant hence making his first step invalid.
Answer:
As you can see, Taylor failed to add 1 to her equation. This ruins the whole first step. She also used 72 instead of 73 for the answer. Taylor is incorrect.
Write 9.1 as a mixed number and as an improper fraction.
Do not try to simplify your answers.
Answer: 9 1/10 91/10
Step-by-step explanation:
Answer:
9 1/10 and 91/10
Step-by-step explanation:
hope it helps :)
brainliest pls? have a good day/night
write an equation of the line that passes through each pair of points (0,1),(5,3)
find the value of n and w if w is between x and y.
wx = 6n -10, xy = 17, and wy = 3n
answer:
n=3
Step-by-step explanation:
6n-10+3n=17
6n+3n=27
9n=27
n=3
Please help me to prove this!
Answer: see proof below
Step-by-step explanation:
Given: A + B + C = π → A + B = π - C
→ B + C = π - A
→ C + A = π - B
→ C = π - (B + C)
Use Sum to Product Identity: cos A + cos B = 2 cos [(A + B)/2] · cos [(A - B)/2]
Use the Sum/Difference Identity: cos (A - B) = cos A · cos B + sin A · sin B
Use the Double Angle Identity: sin 2A = 2 sin A · cos A
Use the Cofunction Identity: cos (π/2 - A) = sin A
Proof LHS → Middle:
[tex]\text{LHS:}\qquad \qquad \cos \bigg(\dfrac{A}{2}\bigg)+\cos \bigg(\dfrac{B}{2}\bigg)+\cos \bigg(\dfrac{C}{2}\bigg)[/tex]
[tex]\text{Sum to Product:}\qquad 2\cos \bigg(\dfrac{\frac{A}{2}+\frac{B}{2}}{2}\bigg)\cdot \cos \bigg(\dfrac{\frac{A}{2}-\frac{B}{2}}{2}\bigg)+\cos \bigg(\dfrac{C}{2}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{A-B}{4}\bigg)+\cos \bigg(\dfrac{C}{2}\bigg)[/tex]
[tex]\text{Given:}\qquad \quad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{A-B}{4}\bigg)+\cos \bigg(\dfrac{\pi -(A+B)}{2}\bigg)[/tex]
[tex]\text{Sum/Difference:}\quad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{A-B}{4}\bigg)+\sin \bigg(\dfrac{A+B}{2}\bigg)[/tex]
[tex]\text{Double Angle:}\quad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{A-B}{4}\bigg)+\sin \bigg(\dfrac{2(A+B)}{2(2)}\bigg)\\\\\\.\qquad \qquad \qquad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{A-B}{4}\bigg)+2\sin \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{A+B}{4}\bigg)[/tex]
[tex]\text{Factor:}\quad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\bigg[ \cos \bigg(\dfrac{A-B}{4}\bigg)+\sin \bigg(\dfrac{A+B}{4}\bigg)\bigg][/tex]
[tex]\text{Cofunction:}\quad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\bigg[ \cos \bigg(\dfrac{A-B}{4}\bigg)+\cos \bigg(\dfrac{\pi}{2}-\dfrac{A+B}{4}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{A-B}{4}\bigg)+\cos \bigg(\dfrac{2\pi-(A+B)}{4}\bigg)\bigg][/tex]
[tex]\text{Sum to Product:}\ 2\cos \bigg(\dfrac{A+B}{4}\bigg)\bigg[2 \cos \bigg(\dfrac{2\pi-2B}{2\cdot 4}\bigg)\cdot \cos \bigg(\dfrac{2A-2\pi}{2\cdot 4}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =4\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi-B}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi -A}{4}\bigg)[/tex]
[tex]\text{Given:}\qquad \qquad 4\cos \bigg(\dfrac{\pi -C}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi-B}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi -A}{4}\bigg)\\\\\\.\qquad \qquad \qquad =4\cos \bigg(\dfrac{\pi -A}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi-B}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi -C}{4}\bigg)[/tex]
LHS = Middle [tex]\checkmark[/tex]
Proof Middle → RHS:
[tex]\text{Middle:}\qquad 4\cos \bigg(\dfrac{\pi -A}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi-B}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi -C}{4}\bigg)\\\\\\\text{Given:}\qquad \qquad 4\cos \bigg(\dfrac{B+C}{4}\bigg)\cdot \cos \bigg(\dfrac{C+A}{4}\bigg)\cdot \cos \bigg(\dfrac{A+B}{4}\bigg)\\\\\\.\qquad \qquad \qquad =4\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{B+C}{4}\bigg)\cdot \cos \bigg(\dfrac{C+A}{4}\bigg)[/tex]
Middle = RHS [tex]\checkmark[/tex]
What is the answer??
Answer:
x = -2±i
Step-by-step explanation:
what is the mathematical expression for the problem withdrawing $10 every week from an outstanding $400?
Answer:
40
Step-by-step explanation:
because if you do 400 divided by 10, it gives you 40
What is the square root of 169
Answer:13
Step-by-step explanation:
13^2
To amend a country's constitution, 5/6 of the 44 states in that country must approve the amendment.If 35 states approve an amendment, will the constitution be amended?
Find the measure of angle XAZ in the figure below.
Answer:
m∠XAZ = 40°
Step-by-step explanation:
Since ∠YAU, ∠YAZ and ∠XAZ are the angles based at a point on a straight line, and the sum of the all angles on a line is 180°.
Therefore, m∠YAU + m∠YAZ + m∠XAZ = 180°
50° + 90° + m∠XAZ = 180°
m∠XAZ = 180° - 140°
= 40°
Therefore, measure of angle XAZ is 40°.
do two lines meet in more than one point
Answer:
It depends.
Step-by-step explanation:
If it is two straight lines, then no, there is no way for the lines to intersect in more than one place. If the line is a parabola, then the lines would intersect in 2 places. It depends on what type of line you have.
Lcm of 4 , 8 , 12???
Answer:
It is 4
Step-by-step explanation:
4
4 8
4 8 12
as you can tell 4 is your answer.
8. What is the solution to 0,3(12x16)=0.4(12-3x)?
Answer: False
Step-by-step explanation: First, you are going to multiply the numbers in the first set of parenthesis, getting 72. Now, have 72 take the place of 12x6 in the equation. Your new equation looks like this: 0.3 x 72 = 0.4(12-3).
Going off of step one, you will be doing the same thing with the second set, but you will be subtracting instead. You will get 9, and plug it place of the parenthesis. Your equation now looks like o.3 x 72 = 0.4 x 9.
Next, you will multiply the set of numbers on the left side of the equal sign, getting 21.6. You now have an equation of 21.6 = 0.4 x 9.
Going off of step 3, you are going to do the exact same thing we did in step 3. Multiply 0.4 and 9, and you will get 3.6. The equation now looks like 21.6 = 3.6.
Now, the inequality is false because the left-hand side and right-hand side are two completely different numbers. A bigger number cannot be equal to a smaller number.
Hope this helps!
Which ratios are equivalent to 8 : 12? Select all that apply. A 4 : 6 B 12 : 8 C 16 : 20 D 24 : 36 E 56 : 84
Answer:
A, D, E
Step-by-step explanation:
like with division if you multiply the same thing on both sides it is still equal
The ratios are equivalent to 8 : 12 are A 4 : 6 , D 24 : 36 and E 56 : 84.
Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
What is the ratio of two quantities?Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b
We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).
Suppose that we've got a = 8, and b= 12,
[tex]a:b = 8 : 12\\\\ = \dfrac{8}{12} = \dfrac{2 \times 4}{2 \times 6} \\= \dfrac{2}{3} \\\\a : b = 2 : 3[/tex]
So, the ratios are equivalent to 8 : 12
A 4 : 6
D 24 : 36
E 56 : 84
Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.
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I need help to make it positive
Answer:
-8c^4/m^3
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)^c = a^(bc)
a^-b = 1/a^b
__
[tex](-2)^3\cdot(c^{-2})^{-2}\cdot m^{-6}=-8\cdot c^{(-2)(-2)}\cdot m^{-3}\\\\=\boxed{\dfrac{-8c^4}{m^3}}[/tex]
The temperature at 3:00 pm is 27 degrees. The temperature drops 4 degrees every hour for 8 hours. What is the temperature at 11:00 pm?
On a coordinate plane the vertices of a triangle are A(-1, 4), B(-3,2), and C(0, -1). Find the coordinates of the
midpoint of side AB.
A)
(3,-2)
B)
(-2,3)
(2, -3)
D)
(2, 1)
Answer:
B) (-2,3)
Step-by-step explanation:
Graph all your points. No count the distance from point A to B. divide in half .
I didn't understand how C wasn't a correct answer to this problem alongside A, as the only correct answer is A/
Answer: It is A
Step-by-step explanation:
In the given figure D) DC/BC has the same ratio as AB/BC.
What is the interior angle bisector theorem?The interior angle bisector theorem states that in a triangle the angle bisector of an angle divides the opposite side to the angle in the ratio of the remaining two sides.
In ΔABC m∠A = 28° and the ratio is taken for the sides which is opposite to the given angle BC and the side which not base AB.
Given the ratio AB/BC.
∴ In ΔBCD in which m∠B is also 28° we have to take the same sides opposite side is DC and the side which is not the base BC.
So, in the triangles ABC and ABD The ratio which has the same value as AB/BC is BC/DC.
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Solve the following equations, show all work. Leave your answers in reduced improper fraction form .
X+7/6=2x-7/6
[tex] \huge \purple {\tt {x + \frac{7}{6} = 2x - \frac{7}{6}}} [/tex]
To Find:[tex] \large {\tt {The \: answer \: in \: reduced}} [/tex]
[tex] \large {\tt { improper \: fraction \: form.}} [/tex]
Solution:[tex] \huge \pink {\tt {x + \frac{7}{6} = 2x - \frac{7}{6}}} [/tex]
[tex] \huge \blue {\tt {or, \: x - 2x = - \frac{7}{6} - \frac{7}{6}}} [/tex]
[tex] \huge \red {\tt {or, \: - x = \frac{ - 14}{6} = \frac{ - 7}{3}}} [/tex]
[tex] \huge \green {\tt {or, \: x = \frac{7}{3}}} [/tex]
Answer:[tex] \huge \orange {\tt {x = \frac{7}{3}}} [/tex]
Plz help I’ve been doing this for 6 days
Hi there! :)
t ≥ -22t + 8 ≥ -4(t + 1)
Distribute the coefficient outside of the parenthesis:
2t + 8 ≥ -4(t) -4(1)
2t + 8 ≥ -4t - 4
Add 4t to both sides:
6t + 8 ≥ -4
Subtract 8 from both sides:
6t ≥ -12
Divide both sides by 6:
t ≥ -2.
Answer: t ≥ -2/3
Step-by-step explanation:
Distribute the -4 into (t + 1). 2t + 8 ≥ - 4t - 4Add 4t on both sides. 6t + 8 ≥ -4Subtract 8 on both sides. 6t ≥ -4Divide by 6 on both side. Then , simplify -4/6 by 2 on both the numerator and denominator. t ≥ -2/3Five boxes of crackers cost $9 at this rate how much do 20 boxes cost
5 1.80, the crackers cost $1.80 per box: 20 3 1.80 5 36. So, 20 boxes cost $36.00.
Answer:
$36
Step-by-step explanation:
To find how much one box costs you divide 9÷5 = 1.8
Then you take 1.8 × 20 = 36
If you want me to go over it in depth, let me know! Have a great day!
Ben wants to try a new honey-glazed salmon recipe. He starts with 1 2/3 cups of honey. He uses 1/5 of it to make the glaze. How much honey does Ben have left?
Answer:
1 1/3
Step-by-step explanation:
Firstly, 1 2/3 is converted into an improper fraction being 5/3. Next, 1/5 of 5/3 is one portion of 5 equal portions. You can split 5/3 into five equal portions of 1/3. Therefore, 1/3 cup of honey was used to make the honey glaze. Lastly, that is subtracted from the 1 2/3 to end up with 1 1/3.
The required amount of honey left is given as 1 1/3.
Given that,
Ben wants to try a new honey-glazed salmon recipe. He starts with 1 2/3 cups of honey. He uses 1/5 of it to make the glaze.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Amount of honey = 1 2/3 = 5 / 3
Amount of honey used is 1/5 times = 1/5 [5 / 3] = 1 / 3
Amount of honey left = 5/3 - 1/3 = 4/3 or 1 1/3
Thus, the required amount of honey left is given as 1 1/3.
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Divide8/9 and 8. Express your answer in simplest form
Answer: The answer is 0.11 in decimal form.
Step-by-step explanation:
7 less than three times Heather's
age is 14. Write an equation and
solve to find Heather's age.
HELP PLS I NEED THIS >3
Answer:
56
Step-by-step explanation:
Here, n = 8, r = 3
[tex] \huge \orange{ \because \: ^nC_r = \frac{n!}{r!(n - r)!} } \\ \\ \huge \therefore \: ^8C_3 = \frac{8!}{3!(8 - 3)!} \\ \\ \huge \therefore \: ^8C_3 = \frac{8 \times 7 \times 6 \times 5!}{3 \times 2 \times 1 \times 5!} \\ \\ \huge \red{ \boxed{\therefore \:^8C_3 = \purple{56}}}[/tex]
Dave is driving to Dallas, TX for the weekend from Austin, TX for the weekend. He is traveling along the tollway 130. The speed limit is 80 mph. There are approximately 1.6 kilometers in 1 mile. What is this limit in kilometers per hour?
We need to multiply the 80mph by the 1.6 to make it KPH
When done correctly we get the answer of 128KPH
The limit is 128kph
HOPE THIS HELPED. DONT FORGET TO MARK THIS AS THE BRAINLIEST ANSWER AND GIVE IT A 5 STAR SO OTHER PEOPLE CAN BE HELPED BY THIS ANSWER!! HAVE A NICE DAY!
4 times as much as 3 is
Answer:
12
Step-by-step explanation:
4x3=12
3x – 1 > 4x + 7
What’s the answer
Answer:
[tex]x<-8[/tex]
Step-by-step explanation:
So we have the inequality:
[tex]3x-1>4x+7[/tex]
Add 1 to both sides. The left side cancels:
[tex]3x>4x+8[/tex]
Subtract 4x from both sides. The right side cancels:
[tex]-x>8[/tex]
Divide both sides by -1. Since we're dividing by a negative, we flip the sign:
[tex]x<-8[/tex]
And we're done!
Our solution is all numbers less than -8.
Answer:
x = -8
Step-by-step explanation:
I will be the brainliest, its hard to explain on a document, i could make you avideo how to do these problems, im a math teacher.
Please help me. I have been struggling with prob and stats.
Answer:
Step-by-step explanation:10
Graph [tex]g(x)=\frac{1}{2}|x+2|-3[/tex] as a transformation of [tex]f(x)=|x|[/tex]. Then identify the transformation.
Answer:
see below
Step-by-step explanation:
g(x) = 1/2 | x+2| -3
y = Cf(x) 0 < C < 1 compresses it in the y-direction
y = f(x + C) C > 0 moves it left
y = f(x) + C C < 0 moves it down
1/2 compression in the y direction moved to the left 2 units and down 3 units
Given: g(x) = 1/2|x + 2| - 3
0 < c < 1 means at the y-axis and makes it smaller
y = cf(x)
1/2 compression
c > 0 means that you move it to the left
y = f(x + c)
2 units to the left
c < 0 means that you move it down
y = f(x) + c
3 units down
Best of Luck!
A boy rolls down a hill on a skateboard. At time = 4 seconds, that boy has rolled 6 meters from the top of the hill. At time = 7 seconds, the boy has rolled to a distance of 30 meters. What is his average speed?
Answer:
His average speed is 4.75 m/s
Step-by-step explanation:
Here, we are interested in calculating the average speed of the boy.
At time t = 4 seconds, total distance traveled = 6 meters
The average speed here is distance/time = 6/4 = 1.5 m/s
Now at time 30 7 seconds , he has rolled 30 meters
What this actually means is that for the next 3 seconds after the initial 4 seconds, he rolled a total distance of 30-6 = 24 meters. Hence, he rolled 24 meters in the next three seconds
So mathematically, his average speed for the second part of the rolling is 24/3 = 8 meters per second
Conclusively therefore , his average speed will be (1.5 + 8)/2 = 9.5/2 = 4.75 meters per second