Answer:
D is false
Step-by-step explanation:
f(x) = -2x2 + 4x + 6 should be written with a " ^ " to indicate exponentiation:
f(x) = -2x^2 + 4x + 6.
Because of the - sign, we know that the graph of this function opens down, so there is a maximum at the vertex. We can determine the x-value at the vertex by using the formula x = -b/(2a), which here is x = -4/(2*-2), or 1.
Evaluating f(x) = -2x^2 + 4x + 6 at x = 1, we get -2 + 4 + 6, or 8. So statement A is true: there's a max at (1, 8). This is also the vertex of the graph.
Let's now look at C and D. We evaluate f(x) at x = 3 and x - 2. If the output (y) value is 0, we know we have an x - intercept:
f(3) = -2(9) + 4(3) + 6 = 0. Yes, C is true, (3, 0) is an x-intercept.
f(-2) = -2(4) - 8 + 6 is not 0. Therefore D is false; (-2, 0) is not an x-intercept.
Look at B: Let x = 0 and find y: it's 6. Thus, (0, 6) is the y-intercept. B is true.
Answer:
B) x + 12 < 8 − 3x
Step-by-step explanation:
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
PLZ HELP ME!!!!!!!!!!!!!!
Answer:
It's B. 1/6^9
Step-by-step explanation:
It is simplified to 6^-9 which is equal to 1/6^9.
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]
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
Kylie needs to pack her baton for a color-guard competition. The baton is 38 inches long. Will it fit in a rectangular box with a base of 13 inches by 35 inches and a height of 13 inches?
What is the diagonal??
Also, use the Pythagorean theorem
I really need it ASAP
Answer:
The baton will not fit in the rectangular box
Step-by-step explanation:
step 1
Find the diagonal of the base of the rectangular base and then compare with the length of the baton
Applying the Pythagoras Theorem
Let
x ----> the length of the diagonal base of rectangular box
we know that
[tex]x^{2}=13^{2}+35^{2} \\ \\x^{2} =1,394\\ \\x= 37.3\ in[/tex]
[tex]38\ in > 37.3\ in[/tex]
therefore
The baton will not fit in the rectangular box
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
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
I need a lot of help with many questions help
Answer:
2 cake donuts
Step-by-step explanation:
This is a question on probability, which means that we can find:
# of wanted outcomes/total outcomes.
Wanted outcomes: Vicky ate 3 cake donuts, so our value is 3.
Total outcomes: Vickey ate 3 + 4 + 8 = 15 donuts, so our value is 15.
Plug in: 3/15
Simplify: 1/5
So 1/5 of donuts Vicky eats will probably be cake donuts.
1/5 * 10 = 2
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
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.
I need help so this is so hard and this is not me
Answer:
No answer
Step-by-step explanation:
I don't think this equation has an answer.
Normally, you'd try to combine like terms
3 3/4 = 2 + 3/4
3 3/4 = 2 3/4
3 and 3/4 is not equal to 2 and 3/4.
So, I believe this equation has no answer
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
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
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.
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The difference of the same side interior angles of two parallel lines is 50°. Find all angles.
Answer:
The angles are 65° and 115°
Step-by-step explanation:
Let
x,y ----> the two side interior angles of two parallel lines
we know that
x+y=180° ----> equation A
x-y=50° ----> equation B
Adds equation A and equation B
x+x=180°-50°
2x=130°
x=65°
Find the value of y
x+y=180° -----> 65°+y=180° ----> y=180°-65°=115°
therefore
The angles are 65° and 115°
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)
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 ^^
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
Y’all answer this question
ANSWER
[tex]x = 11[/tex]
EXPLANATION
According to the exterior angle theorem, the sum of remote interior angles equal an exterior angle.
This implies that,
[tex](7x + 7) \degree + 66 \degree =(1 2x + 18) \degree[/tex]
We group the similar terms to get:
[tex]7 + 66 - 18 = 12x - 7x[/tex]
[tex]55= 5x[/tex]
Divide both sides by 5.
[tex]x = \frac{55}{5} [/tex]
[tex]x = 11[/tex]
I PROMISE BRINLIEST THIS IS VERY EASY I JUST DON'T KNOW!!!!!!!!!! Simplify the polynomial
3x2 + 5x – 5x2 – 4x + 5 – 2
A.)–8x2 – 9x + 3
B.)2x2 + x + 3
C.)–2x2– 9x + 3
D.)–2x2 + x + 3
Answer:
x-1
Step-by-step explanation:
(3)(2)+5x-(5)(2)-4x+5-2
=6+5x-10-4x+5-2
=x-1
Answer:
-2x2+x+3
Step-by-step explanation:
you have to combine like terms
-5x2+ 3x2= -2x2
5x-(-4x)= x
5-2=3
-2x2+x+3
Andre picks blocks out of a bag 60 times and notes that 43 of them were green. What should Andre estimate for the probability of picking out a green block from this bag?
43/60 would be the probability
The required estimation is [tex]P(A)=\frac{43}{60}[/tex]
Important information:
Number of observation=60
Number of expected outcomes =43
Probability: Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed between zero and one. So, the formula probability is,
P(A)=Expected observation/number of observations
Now, substituting the given values into the above formula we get,
[tex]P(A)=\frac{43}{60}[/tex]
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[02.05] Solve for x: 3 − (2x − 5) < −4(x + 2) x < −8 x > −8 x < −3 x > −3
ANSWER
[tex]x \: < \: - 8[/tex]
EXPLANATION
The given inequality is
[tex]3 - (2x - 5) \: < \: - 4(x + 2)[/tex]
Expand:
[tex]3 - 2x + 5 \: < \: - 4x - 8[/tex]
Group similar terms, to obtain:
[tex] - 2x + 4x\: < \: - 8 - 5 - 3[/tex]
Combine similar terms:
[tex]2x\: < \: - 16[/tex]
Divide both sides by 2 to get,
[tex]x \: < \: - 8[/tex]
Convert 0.862862 to a fraction.
Answer:431⁄500
Step-by-step explanation:
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}
30 points answer asap!!!!!!!!!!!!!!!!!!!!Which expression represents the lateral surface area of the cone?
Answer:
it would be b
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.
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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
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.
Simplify the expression
Answer:
the answer is c
Step-by-step explanation:
If F(x) = x+ 6 and G(x) = x^4, what is G(F(x))?
O
A. A +x+6
B. (X+6)^4
C.x^4+6
D.x^4(x+6)
ANSWER
B.[tex] (x + 6)^{4} [/tex]
EXPLANATION
The given functions are:
f(x)=x+6
and
[tex]g(x)= {x}^{4} [/tex]
We want to find
[tex]g(f(x)) = g(x + 6)[/tex]
This is the composition of functions, where one function becomes the input of the second function.
We plug in x+6 into the expression for g(x) to obtain,
[tex]g(f(x)) = (x + 6)^{4} [/tex]
The correct answer is B.