Answer:
(2,3)
Step-by-step explanation:
The given equations are:
[tex]y=-4x+11[/tex]
and
[tex]y=\frac{1}{2}x+2[/tex]
Equate both equations:
[tex]\frac{1}{2}x+2=-4x+11[/tex]
Multiply through by 2:
[tex]x+4=-8x+22[/tex]
[tex]x+8x=22-4[/tex]
[tex]9x=18[/tex]
x=2
Put x=2 into the first equation:
[tex]y=-4(2)+11[/tex]
[tex]y=-8+11[/tex]
y=3
The solution is (2,3)
Answer:
C. (2, 3)
Step-by-step explanation:
A system of linear equations is a set of (linear) equations that have more than one unknown. The unknowns appear in several of the equations, but not necessarily in all of them. What these equations do is relate the unknowns to each other.
Solve a system of equations is to find the value of each unknown so that all the equations of the system are met.
Ordering both equations
First equation
[tex]y=-4y+11[/tex]
[tex]4x+y=11[/tex]
Second equation
[tex]y=\frac{1}{2} x+2[/tex]
[tex]-\frac{1}{2}x+y=2[/tex]
Ordering in a system of equations
[tex]\left \{ {{4x+y=11} \atop {-\frac{1}{2}x+y=2}} \right.[/tex]
Using the reduction method which consists of operating between the equations, such as adding or subtracting both equations, so that one of the unknowns disappears. Thus, we obtain an equation with a single unknown.
We're going to subtract the second equation from the first to eliminate the unknown y.
4x + y = 11
- ((-1/2)x + y = 2)
(9/2)x = 9 ------> x= [(2)(9)]/9 -----> x = 2
Substituing the value x = 2 in [tex]y=\frac{1}{2} x+2[/tex]
y = (1/2)x + 2 ---------> y = (1/2)(2) + 2 -------> y = (2/2) + 2
y = 1 + 2 --------> y = 3
The solution of the system of equations is (2, 3).
Solve for x. Round to 3 decimal places
Answer:
x = 727Step-by-step explanation:
[tex]\log_ab=c\iff a^c=b\\\\Domain:\ x+2>0\to x>-2\\\\\log_3(x+2)-8=-2\qquad\text{add 8 to both sides}\\\\\log_3(x+2)=6\iff x+2=3^6\\\\x+2=729\qquad\text{subtract 2 from both sides}\\\\x=727\in D[/tex]
The answer is is x=727 ^^
PLEEEAAAASE HELLP!!!Tina is making a cylindrical sandbox that has a radius of 2 feet. She bought 18.84 cubic feet of sand for the sandbox. Which height does she need to make the sandbox to fit all the sand?0.5 ft, 0.75 ft, 1 ft, 1.5 ft.
Answer:
Step-by-step explanation:
The answer is 1.5 ft i just took the test
Answer:
The correct option is 4.
Step-by-step explanation:
The volume of a cylinder is
[tex]V=\pi r^2h[/tex]
where, r is radius of the base and h is height of the cylinder.
It is given that the radius of the cylindrical sandbox is 2 ft and the volume of cylindrical sandbox is 18.84.
[tex]18.84=(3.14)\times (2)^2\times h[/tex] [tex][\because \pi=3.14][/tex]
[tex]18.84=(3.14)\times 4\times h[/tex]
[tex]18.84=12.56\times h[/tex]
[tex]\frac{18.84}{12.56}=h[/tex]
[tex]1.5=h[/tex]
The height of the sandbox is 1.5 ft. Therefore the correct option is 4.
If h(x) = 3x − 1 and j(x) = −2x, solve h[j(2)] and select the correct answer below.
-11
11
-13
13
Answer:
- 13
Step-by-step explanation:
To evaluate h(j(2)) substitute x = 2 into j(x) then substitute the value obtained into h(x)
j(2) = - 2 × 2 = - 4, then
h(- 4) = (3 × - 4) - 1 = - 12 - 1 = - 13
Hence h(j(2)) = - 13
Which expression represents h(x)?
ANSWER
(f.g)(x)
EXPLANATION
From the table we can observe the following patterns:
f(-6)=12
g(-6)=-6
h(-6)=-72=12×-6
f(0)=3
g(0)=0
h(0)=0=3×0
f(6)=-6
g(6)=6
h(6)=-36=-6×6
Hence the h(x) is obtained by multiplying f(x) by g(x).
h(x)=(f.g)(x)
If you bought a stock last year for a price of $95, and it has gone down 2.6% since then, how much is the stock worth now, to the nearest cent?
Answer: $92.53
Step-by-step explanation:
95 x 0.026 = 2.47
95 - 2.47 = $92.53
In the 30-60-90 triangle below, side s has a length of _
length of
_and side q has a?
(e) is the homogeneous mixture
Answer:
it is E
Step-by-step explanation:
Just finished the test
Calculate the rate of change for the interval 45
Find the difference between 45 and 55:
55-45 = 10
Find the difference between the mpg for 45 and 55:
35 - 34.1 = 0.9
Divide the difference in mpg by the difference in x:
0.9 / 10 = 0.09
The answer is B.
Answer:
Option B: 0.09 mpg/mph
Step-by-step explanation:
You divide the delta (=difference) in F by the delta in x:
delta F is 35.0-34.1 = 0.9
delta x = 55-45 = 10
so rate of change is 0.9/10 = 0.09, answer B
Nate is wrapping a present the gift is a right rectangular prism with the base measuring 15“ x 12“ and a height of 8 inches what is the surface area?
What is 70 times five
Answer:
350
Step-by-step explanation:
Answer:
350
Step-by-step explanation:
First, do 7 x 5
7 x 5 is 35
Now just add a zero to the end to get 350
I hope this helps! :)
Select the number property that will justify the step in the following expression. 6 + (14 + 70) = (6 + 14) + 70 = 20 + 70 = 90
Answer: Associative property of addition.
Step-by-step explanation:
The rule for the Associative property of addition is:
[tex]a + (b + c) = (a + b) + c[/tex]
Therefore, this property establishes that it does not matter how you group the numbers, the sum will not change.
You can observe that, in this case, the numbers of the given addition can be grouped as [tex]6 + (14 + 70)[/tex] or [tex](6 + 14) + 70[/tex], and the sum will be the same.
Then, you get:
[tex]6 + (14 + 70) = (6 + 14) + 70 = 20 + 70 = 90[/tex]
which graph represents the function?
[tex]f(x) = \sqrt[3]{x + 2} [/tex]
Answer:
The top-right graph.
Step-by-step explanation:
Because f(-2) = 0.
The graph which represents the non-linear function with power 1/3 is similar graph in right side of upper option. Thus, the option B is correct.
What is non-linear graph?When the graph of the function represents the straight line, then it is called the linear function.
The graph of a function in which the power of variable is more than one is called the non-linear graph.
The function given in the problem is,
f(x)=∛(x+2)
It is a non-linear function. This function can be written as,
[tex]f(x)=(x+2)^\dfrac{1}{3}[/tex]
The graph of this function is attached below. This graph passes from the point (-2,0) and (0,1.26) and looks similar to the option B (right side of upper option).
Hence, the graph which represents the non-linear function with power 1/3 is similar graph in right side of upper option. Thus, the option B is correct.
Learn more about the linear and non-linear function here;
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NEED HELP FAST!!!!!!!!!
h= k/j
Multiply by j for the left and right hand side
(h)(j)= k/j(j)
Cross out j and j for the right hand side.
hj= k
answer is : k= hj
I think this is the answer
ANSWER
[tex]k = hj[/tex]
EXPLANATION
The given formula is:
[tex]h = \frac{k}{j} [/tex]
We want to solve this formula for k.
Let us multiply both sides by j.
[tex]h \times j = \frac{k}{j} \times j[/tex]
Cancel the common factors.
[tex]hj = k[/tex]
Or we rewrite to obtain,
[tex]k = hj[/tex]
k is now isolated on one side of the equation.
If csc B = b, which number below is not a possible value of b?
-1.75
0.5
1
1.05
Answer:
0.5Step-by-step explanation:
[tex]\csc B=\dfrac{1}{\sin B}\\\\-1\leq\sin B\leq1,\ \text{therefore}\ \csc B\leq-1\ or\ \csc B\geq1\\\\-1.75\leq-1\\\\0.5\to \bold{ANSWER}\\\\1\geq1\\\\1.05\geq1[/tex]
By definition, the cosecant is the inverse of the sine:
[tex]\csc(x) = \dfrac{1}{\sin(x)}[/tex]
Since the sine is never more than 1, the cosecant can never be smaller than 1.
So, the only impossible option is 0.5.
Given the point on a circle at (1,-7) and a center at (-6,-4), write the equation of the circle
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{-7})\qquad \stackrel{center}{(\stackrel{x_2}{-6}~,~\stackrel{y_2}{-4})}\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[-6-1]^2+[-4-(-7)]^2}\implies r=\sqrt{(-6-1)^2+(-4+7)^2} \\\\\\ r=\sqrt{(-7)^2+3^2}\implies r=\sqrt{58} \\\\[-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{-4}{ k})\qquad \qquad radius=\stackrel{\sqrt{58}}{ r}\\[2em] [x-(-6)]^2+[y-(-4)]^2=(\sqrt{58})^2\implies (x+6)^2+(y+4)^2=56[/tex]
To find the equation of the circle with a given point (1,-7) and center (-6,-4), calculate the radius using the distance formula to find that the radius is √58, then substitute the center coordinates and radius into the standard circle equation to get (x + 6)² + (y + 4)² = 58.
To write the equation of the circle given a point on the circle at (1,-7) and the center at (-6,-4), we will use the standard form of the circle's equation (x-h)² + (y-k)² = r², where (h, k) is the center of the circle and r is the radius. First, we calculate the radius of the circle using the distance formula: r =
√[(x_2-x_1)² + (y_2-y_1)²]. Plugging in our values, we get r = √[(1 - (-6))² + (-7 - (-4))²] = √[49 + 9] = √58. Therefore, the equation of the circle with center (-6,-4) and passing through the point (1,-7) is (x + 6)² + (y + 4)² = 58.
Help me with my math don't get it! ;(
Answer:
B
Step-by-step explanation:
So, we know that this inequality has an "at most" in its phrase, therefore signifying the sign x ≤ 5. Since the x is in the left side without any negatives, so the arrow goes left, and the circle is filled. So, B.
Please do this:) Thank you
Answer:
1) y = 12
2) x = 4
3) w = -3
4) k = -35
Step-by-step explanation:
Answer:
Question 1: y = 12
Question 2: x = 4
Question 3: w = -3
Question 4: k = -35
How to solve and check my solutions
Answer:
see explanation
Step-by-step explanation:
Subtract [tex]\frac{2}{3x}[/tex] from both sides
[tex]\frac{1}{6}[/tex] = [tex]\frac{4}{3x}[/tex] - [tex]\frac{2}{3x}[/tex] = [tex]\frac{4-2}{3x}[/tex] = [tex]\frac{2}{3x}[/tex]
Cross- multiply
3x = 12 ( divide both sides by 3 )
x = 4
As a check
Substitute x = 4 into the equation and if both sides are equal then it is the solution.
left side
[tex]\frac{2}{12}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{1}{6}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
right side
[tex]\frac{4}{12}[/tex] = [tex]\frac{1}{3}[/tex]
Both sides are equal hence x = 4 is the solution
Help plz!!!! This is precal
Answer:
The remainder is 0 ⇒ 3rd answer
Step-by-step explanation:
* In the synthetic calculation we use the coefficient of the dividend
with the value of x when the divisor = 0
∵ x - 1 = 0 ⇒ add 1 to both sides
∴ x = 1
Step 1 : Write down the coefficients of the f(x) , put x = 1 at the left
1 1 0 -1 1 -1
________________
Step 2 : Bring down the first coefficient to the bottom row.
1 1 0 -1 1 -1
________________
1
Step 3 : Multiply it by 1, and carry the result into the next column.
1 1 0 -1 1 -1
____ 1_________
1
Step 4 : Add down the column
1 1 0 -1 1 -1
____1__________
1 1
Step 5 : Multiply it by 1, and carry the result into the next column
1 1 0 -1 1 -1
_____1___1_______
1 1
Step 6 : Add down the column
1 1 0 -1 1 -1
____1___1______
1 1 0
Step 7 : Multiply it by 1, and carry the result into the next column
1 1 0 -1 1 -1
___1___1___0______
1 1 0
Step 8 : Add down the column
1 1 0 -1 1 -1
_____1____1__0_____
1 1 0 1
Step 9 : Multiply it by 1, and carry the result into the next column
1 1 0 -1 1 -1
____1____1___0___1___
1 1 0 1
Step 10 : Add down the column
1 1 0 -1 1 -1
____1____1___0___1___
1 1 0 1 0
∴ The quotient is (x³ + x² + 1 ) and the remainder is 0
* The remainder is 0
what is the sum of -5/7 + 4/7?
Answer:
1/7
Step-by-step explanation:
Answer: -1/7
Step-by-step explanation: Since the fractions have the same denominator you can add them together without trying to have to change it
30 points answer asap!!!!!!!!!!!!!!!!!!!!Which expression represents the lateral surface area of the cone?
Answer:
it would be b
if sin=3/5 then what does tan equal
Answer: [tex]tan(x)=\±\frac{3}{4}[/tex]
Step-by-step explanation:
You know that [tex]sin(x)=\frac{3}{5}[/tex] and you can identify that. Then:
[tex]sin^2(x)=(\frac{3}{5})^2[/tex]
[tex]sin^2(x)=\frac{9}{25}[/tex]
Remember that:
[tex]cos^2(x)=1-sin^2(x)[/tex]
Then [tex]cos^2(x)[/tex] is:
[tex]cos^2(x)=1-\frac{9}{25}\\\\cos^2(x)=\frac{16}{25}[/tex]
Apply square root to both sides to find cos(x):
[tex]\sqrt{cos^2(x)}=\±\sqrt{\frac{16}{25}}\\cos(x)=\±\frac{4}{5}[/tex]
Remember that:
[tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]
Then, this is:
[tex]tan(x)=\frac{\frac{3}{5}}{\±\frac{4}{5}}[/tex]
[tex]tan(x)=\±\frac{3}{4}[/tex]
The dot plot shows how many games of chess 8 different members of the chess club played in one month. If Jackson is a new member of the chess club, how many games of chess is he likely to play in one month?
Answer:
9
Step-by-step explanation:
Find the unit rate.
800 people per 20 square miles
-------- Peop
people per square mile
Type the correct answer.
Answer: 40 per square mile
Step-by-step explanation: 800/20
Convert 0.862862 to a fraction.
Answer:431⁄500
Step-by-step explanation:
2 = 6m what does m equal?
Answer:
m = 1/3
Step-by-step explanation:
When you multiply by a fraction it's actually dividing.
:)
The variable m equals 1/3 for the equation 2 = 6m obtained by dividing both sides by 6.
The given equation is 2=6m.
m is the variable in the equation.
To determine the value of m in the equation 2 = 6m, we need to isolate the variable m.
Divide both sides of the equation by 6:
2/6 = (6m)/6
1/3 = m
Therefore, m equals 1/3.
To learn more on Equation:
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Thanks for the help!
Answer:
x =34
Step-by-step explanation:
The sum of the angles of a triangle add to 180
The two angles in the middle are vertical angles to they are both 56 degrees
56+x+90 = 180
Combine like terms
146 +x = 180
Subtract 146 from each side
146-146 +x = 180-146
x = 34
Can someone help me with this thank you
Answer:
B
Step-by-step explanation:
This quadratic factors.
x^2 - 15x + 56
= (x - 7)(x - 8)
x - 7 = 0
x = 7
=====
x - 8 = 0
x = 8
====
{7,8}
A bank teller has some five-dollar bills and some twenty-dollar bills. The teller has a total of 32 bills. The total value of the money is $430.00. Find the number of five-dollar bills that he has
write and solve an equation
Answer:
14 five-dollar bills
Step-by-step explanation:
Let
x-----> the number of five-dollar bills
y----> the number of twenty-dollar bills
we know that
x+y=32 ----> y=32-x ----> equation A
5x+20y=430 ----> equation B
Substitute equation A in equation B and solve for x
5x+20(32-x)=430
5x+640-20x=430
20x-5x=640-430
15x=210
x=14 five-dollar bills
Find the value of y
y=32-x ----> y=32-14=18 twenty-dollar bills
according to the graph what is the value of the constant in the equation below
Answer: D or 36 just answered on apex
Step-by-step explanation:
To find the constant in an equation with a graph, examine the graph's features such as slope, intercept, or specific data points and compare them with theoretical constants provided, like k1, k2, k3, k4, and K3.
Explanation:The value of the constant in the equation being discussed is related to graphing functions and the characteristics of lines and curves on a graph. In general, when determining a constant from a graph in mathematics, it is essential to look at certain features such as the slope, the intercept, or specific data points depending on the context of the problem. For instance, if we are trying to find a constant of proportionality (k), we might use a linear fit of data points to determine the slope, which then gives us the value of k. Similarly, other constants may be deduced by comparing the theoretical values with the actual data points on the graph.
To determine the value of a constant such as k in a force (F) versus displacement (x) graph, one would label the transition region of the graph and use the given constants (e.g., k1, k2, k3, k4, K3) to measure the force. The slope (m) of the line on the graph is representative of how the value changes along the graph and is calculated using the change in y over the change in x. In situations where the graph does not display a constant force, the value may be represented by the area under the force versus distance graph.
Plz help me with this
Answer: A) y = -4
Step-by-step explanation:
The midline is usually at y = 0. In the given equation, the graph is shifted down 4 units so the new midline is at -4.