Answer:
x=20, y=17, and z=6 or (20,17,6)
Step-by-step explanation:
Hi there!
We're given the system of equations:
2x+z=46
3z=18
2y+z=40
and we need to solve for x, y, and z
first, let's find the value of z, as we have z by itself (no other variables) in 3z=18
divide both sides by z
z=6
the value of z is found :)
now we can use z=6 to find the value of the other variables; for example, plug z as 6 into 2x+z=46 to solve for x
2x+6=46
subtract 6 from both sides
2x=40
divide by 2
x=20
Finally, let's find y
once again, we can substitute z as 6 in the equation 2y+z=40 to find y
2y+6=40
subtract 6 from both sides
2y=34
divide by 2
y=17
so the answer is: x=20, y=17, and z=6; if you need it in a point it's (20,17,6)
Hope this helps! :)
Type the correct answer in the box.
Consider the table below.
х у
-3 0.5
-2
1
-1 2.5
0
5
18.5
Complete the standard form equation representing the quadratic relationship displayed above, where a, b, and care constants.
Answer:
Step-by-step explanation:
Use the standard form equation along with 3 of the coordinates from the table. I used (-1, 2.5), (0, 5), and (1, 8.5). Begin always with the coordinate where you have a 0:
[tex]5=a(0)^2+b(0)+c[/tex] and we get immediately that c = 5. We can use that value as move forward with the next coordinate pair.
[tex]8.5=a(1)^2+b(1)+5[/tex] and
8.5 = a + b + 5 and
3.5 = a + b Hold that thought while we come up with the second equation for this system.
[tex]2.5=a(-1)^2+b(-1)+5[/tex] and
2.5 = a - b + 5 and
-2.5 = a - b Now solve this system using the method of eliination:
a + b = 3.5
+ a - b = -2.5
so
2a = 1 and a = 1/2 Now we can plug that in and solve for b:
a + b = 3.5 becomes
1/2 + b = 3.5 so
b = 3 and the equation is
[tex]y=\frac{1}{2}x^2+3x+5[/tex]
You move down 2 units and up 8 units. You end at (0, 4). Where did you start?
Given:
You move down 2 units and up 8 units.
You end at (0, 4).
To find:
The starting point.
Solution:
Let the starting point be [tex](x,y)[/tex].
You move down 2 units and up 8 units. So, the rule of translation is:
[tex](x,y-2+8)=(x,y+6)[/tex]
You end at (0, 4).
[tex](x,y+6)=(0,4)[/tex]
On comparing both sides, we get
[tex]x=0[/tex]
[tex]y+6=0[/tex]
[tex]y=4-6[/tex]
[tex]y=-2[/tex]
Therefore, the starting point is (0,-2).
log base 16 of 256 -log base 16 of 16
Answer:
What’s the question
Step-by-step explanation:
The second term in a sequence is 13. The term to term rule is "add 6"
Write an expression, in terms of n, for the nth term of the sequence.
Answer:
[tex]a_{n}[/tex] = 6n + 1
Step-by-step explanation:
This is an arithmetic sequence with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 13 - 6 = 7 and d = 6 , then
[tex]a_{n}[/tex] = 7 + 6(n - 1) = 7 + 6n - 6 = 6n + 1
Answer:
the first few terms would be
7, 13, 19, 25, 31
nth term = 7 + 6(n+1)
nth term = 7+ 6n + 6
nth term = 6n + 13
If the angles are represented in degrees,find both angles: csc(2x+9) =sec(3x+26)
Angle 1: Angle 2:
Please respond quick
Answer:
31°,59°
Step-by-step explanation:
csc (2x+9)=sec(3x+26)
1/sin(2x+9)=1/cos (3x+26)
sin (2x+9)=cos(3x+26)
cos (90-2x-9)=cos(3x+26)
90=3x+26+2x+9
5x+35=90
5x=90-35=55
x=55/5=11
2x+9=2×11+9=31°
3x+26=3×11+26=59°
Help... A store owner collected data about the number of customers who came to the store in a day, y, for several days compared to the high temperature for that day, x. He found that the correlation coefficient was −0.76.
Answer:
strong, negative;
decreased
Step-by-step explanation:
A correlation coefficient that is close to 1, shows a strong association.
If the correlation coefficient is negative, it implies a negative association, meaning as one variable increases, the other decreases.
A positive correlation coefficient shows a positive association between two variables. This implies that as one variable increases, the other increases, or as one decreases, the other decreases as well.
In the case given, we are given that the correlation coefficient obtained is -0.76. This therefore shows a negative association. Also, the value is closer to 1.
This implies that there is a STRONG, NEGATIVE association association between x and y. This is because as the temperature (x) of the day increases across days, the number of customers who patronized the store DECREASED.
ReeeeeeeeeeeereEeeeeereeeee
Answer:
22
Step-by-step explanation:
B racket
I ndices
D division
M multiplication
A addition
Subtraction
Work out answer using the BIDMAS order
What are the lengths of AD, DB, AE, and EC? Measure and record them.
Help me !! Use the image to complete the equation below
m angle APD.
Hope It's help you.
Step-by-step explanation:
yeah angle m is APD so yeah
a freight elevator has a weight limit of 2 tons. Each crate that is loaded weighs 80 pounds. What is the greatest number of crates that can be loaded on to the elevator?
25
500
250
50
Please help meh TvT
Answer:
50 crates
Step-by-step explanation:
First we need to convert 2 tons into pounds; 2 short tons = 4000 pounds, so the greatest number of crates that can be loaded onto the elevator is 4000 Hope this helps >:D
which of the following exponential functions represents the graph below?
Answer:
D
Step-by-step explanation:
We can start by taking a look at the x and y intercepts. When x=0, y=3. Plugging this into each function,
5 * 3^(0) = 5
3 * 5^(0) = 3
5 * (1/3)^(0) = 5
3 * (1/5) ^ (0) = 3
Therefore, our answer must be either B or D. Then, although y=0 isn't given on the graph, based on where the graph is heading, we can say that y is getting smaller as x gets larger. For a big number, such as 100, we know that
3 * 5^(100) is something big and 3 * (1/5) ^ (100) is something small*. Therefore, as y must get small, not big, as x gets larger, D is our answer.
* We know that this is something small because anything less than 1 to the power of something greater than 1 makes it smaller. For example, 0.5² is 0.25, which is smaller than 0.5
Cuales son los terminos que siguen en cada sucesion:a)2,4,8,16,32,64,....B)1,3,5,7,9,....C)1,3,6,10,15,21,28,36,45
Answer:
a) Número siguiente = Número anterior * 2
b) Número siguiente = Número anterior + 2
c) Número siguiente = Número anterior + (n + 1)
Step-by-step explanation:
a) Para la secuencia 2,4,8,16,32,64, ....
El siguiente número es dos veces el número anterior.
Por ejemplo, 4 = 2 * 2, 8 = 4 * 2, 16 = 8 * 2 etc.
b) Para la secuencia 1,3,5,7,9, ....
El siguiente número es igual al número anterior + 2
Por ejemplo, 3 = 1 + 2, 5 = 3 + 2, 7 = 5 + 2 etc.
c) Para la secuencia1,3, 6,10,15,21,28,36,45
La diferencia entre los números aumenta en +1.
3-1 = 2
6-3 = 3
10-6 = 4
15-10 = 5
21-15 = 6
28-21 = 7
X, Y and Z are three points on a map. Y is 85km and on a bearing of 190° from X. Z is on a bearing of 140°, from Y. Z is due south of X. Calculate the distance between X and Z rounded to 1 DP
Answer:
The distance between X and Z is approximately 95.99 km
Step-by-step explanation:
Given, X, Y and Z are three points on a map. Y is 85km and on a bearing of 190° from X. Z is on a bearing of 140°, from Y. Z is due south of X.(For Diagram Please Find in Attachment)
Thus, The parameters areThe distance of Y from X = 85 km
The bearing of Y from X = 190°
The bearing of Z from Y = 140°
The bearing of Z from X = 180°
Now,
In triangle XYZ, we have∠YZX = 180° - (130° + 10°) = 40°
Therefore, Apply the sine rule here, we get
(85 km)/sin(40°) = XZ/(sin(130°))
XZ = sin(130°) × (85 km)/sin(30°) ≈ 95.99 km
The distance between X and Z ≈ 95.99 km
Find the solutions to the equation below.
Check all that apply.
30x^2 - 28x + 6 = 0
A. X = 4/5
B. X = 1/3
c. X = 1/2
D. X = 1/5
E. X = 3/5
F. X = 2/3
The solution to the equation 30x² - 28x + 6 = 0 is x = 3/5 and x = 1/3 option (B) and (E) are correct.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
We have a quadratic equation:
30x² - 28x + 6 = 0
a = 30, b = -28, and c = 6
Plug the values in the formula:
[tex]\rm x = \dfrac{-(-28) \pm\sqrt{(-28)^2-4(30)(6)}}{2a}[/tex]
After solving:
x = 3/5 or x = 1/3
Thus, the solution to the equation 30x² - 28x + 6 = 0 is x = 3/5 and x = 1/3 option (B) and (E) are correct.
Learn more about quadratic equations here:
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I’ve been stuck on these for a while, can someone help? Thank you :) !!
Answer:
6.32
5
254.34
Step-by-step explanation:
The lengths of the missing sides can be determined using Pythagoras theorem
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
first missing side
7² = 3² + x²
49 = 9 + x²
x² = 49 - 9
x² = 40
x = 6.32
second missing side
3² + 4²
9 + 16
= 25
√25 = 5
Area of a circle = πr²
Where : = π = pi = 3.14
3.14 x 9² = 254.34
You bought a shirt for 13.50 that was originally 45.00 in terms of percent what discount did you get the shirt?
Change 1/3 to a decimal number (show the working)
Answer:
0.33
Step-by-step explanation:
1/3 can also be written as 1 ÷ 3 which equals 0.33
Answer:
0.333333333
Step-by-step explanation
Look below at the picturess!!! pls help me i will give you 100 points !
Answer:
1/4
Step-by-step explanation:
because there 25% change
Answer:
for the blue its 1/4 or 2/8 and not likely.
For the yellow one it is 7/8 and likely.
Kevin correctly answered 75% of 32 test questions.
Part A
How many questions did Kevin answer correctly?
Part B
How many more questions would Kevin have to answer correctly to get more than 80% correct?
Answer:
part a-24 questions
part b-2 or 3 more questions
Step-by-step explanation:
part a-to find the number, change the percent into a decimal (.75) and multiply (24)
part b-first find how many questions need to be right to get 80% (.80 times 32=25.6). then subtract by how many he would get with a 75% (25.6-24=about 2 to 3 more questions, rounded 2)
Use trigonometric identities to simplify [tex]sec^2(\pi /2-(x))[sin^2(x) -sin^4(x)][/tex]
Answer:
Step-by-step explanation:
I am using trig identities and the formula for the difference of the cos of 2 angles to solve this. I'll do the steps one at a time. It's super tricky. First I'm just going to work on simplifying the sec² part and then I'll introduce the sin²(x) - sin⁴(x) when I need it. Beginning with the identity for the difference of the cos of 2 angles, knowing that sec²(x) = [tex]\frac{1}{cos^2(x)}[/tex]:
[tex]sec^2(\frac{\pi}{2}-x)=\frac{1}{cos^2(\frac{\pi}{2}-x )}[/tex] and expand that using the formula for the difference:
[tex]\frac{1}{cos(\frac{\pi}{2}-x)cos(\frac{\pi}{2}-x) }=[/tex] [tex]\frac{1}{(cos\frac{\pi}{2}cos(x)+sin\frac{\pi}{2}sin(x))(cos\frac{\pi}{2}cos(x)+sin\frac{\pi}{2}sin(x)) }[/tex] and all of that simplifies down to
[tex]\frac{1}{(0cos(x)+1sin(x))(0cos(x)+1sin(x))}[/tex] which simplifies further to
[tex]\frac{1}{(sin(x))(sin(x))}=\frac{1}{sin^2(x)}[/tex] Now we'll bring in the other term. This is what we have now:
[tex]\frac{1}{sin^2(x)}(\frac{sin^2(x)-sin^4(x)}{1})[/tex] and distribute in to get:
[tex]\frac{sin^2(x)}{sin^2(x)}-\frac{sin^4(x)}{sin^2(x)}[/tex] which simplifies to
[tex]1-sin^2(x)[/tex] and that, finally, simplifies down to a simple
[tex]cos^2(x)[/tex]
Please help i don't have enough time!! PISA: Exchange rate Mei-ling from Singapore has been preparing to go to South Africa for 3 months as an exchange student. She needed to convert some Singapore dollars (SGD) into South African Rand (ZAR). Mei-Ling discovered that the exchange rate between Singapore Dollar and South African Rand SeM 1 SGD = 4.2 ZAR Mei-Ling changed 3000 Singapore Dollars to South African Rand at this exchange rate. How much money did Mai Ling get in South African Rand?
Answer:
12600 (ZAR)
Step-by-step explanation:
4.2*3000
how tall is three feet
Answer: if you mean Inches, its 25.
Answer:
36 inches or 1 yard
Step-by-step explanation:
What is the value of the expression below?
2[3(4+1)]-2
Answer:
28
Step-by-step explanation:
2[3*5]-2
2*15-2
30-2
28
What are the solutions to the equation (2x+1)^2-(x+13)=3x^2-2x+2
how many real solutions does the equation sqrt 2x+4=1/2 x+1 have?
Answer:
unfortunately I do not have the answer, but this is like the only way to tell you something
The 3 real roots of the given equation.
To find the real roots.
What is quadratic equation?Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power. The quadratic formula to solve a quadratic equation ax2 + bx + c = 0 is x = [-b ± √(b2 - 4ac)]/2a.
Given that:
The equation are
[tex]\sqrt{2x+4}=\frac{1}{2x} +1\\[/tex]
By squaring both sides
[tex]2x+4=\frac{1}{4x^{2} }+1+\frac{1}{x} \\\\2x-\frac{1}{x}+3=\frac{1}{4x^{2} }\\\\8x^{3}-4x+12x^{2} -1=0\\ \\8x^{3}+12x^{2}-4x -1=0[/tex]
By solving quadratic equation ,Solutions for x
x1 = -1.74543
x2 = -0.17169
x3 = 0.41712
So, the 3 real roots of the given equation.
Learn more about quadratic equation here:
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is anyone good with Trigonometry word problems?
Answer:
maybe
Step-by-step explanation:
but what help do u want?
A business owner is paying for a dinner party that costs $212.00, including tax. If the tip is 20%, what is the total bill?
$218.40
$254.40
$276 60
$222.60
Answer:
$254.40
Step-by-step explanation:
Find the total bill by multiplying 212 by 1.2, which will calculate the cost included with the 20% tip:
212(1.2)
= 254.4
So, the total bill will be $254.40
Answer:
[tex]\$254.40[/tex]
Step-by-step explanation:
Since 20% as a decimal is 0.2, the total bill including tax is 1.2 times larger than the original bill.
Original bill of $212.00:
Final bill: [tex]212.00\cdot 1.2=\boxed{\$254.40}[/tex]
In the image, two circles are centered at A. The circle containing B was dilated to produce the circle containing B′. What is the scale factor of the dilation? A. 1 B. 2 C. 0.5 D. -0.5In the image, two circles are centered at A. The circle containing B was dilated to produce the circle containing B′. What is the scale factor of the dilation? A. 1 B. 2 C. 0.5 D. -0.5
Answer:
C. 0.5
Step-by-step explanation:
The diameter of B is from -2 to 2, which = 4 units.
The diameter of B' is from -1 to 1, which equals 2 units.
2/4 = 1/2 = 0.5 scale factor.
explain how you can use a model to find 4 x 3/4 include a drawing and a solution
Answer:
4 x 3/4 = 3
Step-by-step explanation:
Let f(x)=2(4)x+1−2. The graph of f(x) is translated 7 units to the left to form the graph of g(x).
