Answer:
list statements please or I cannot help you.
Step-by-step explanation:
or do you want me to make a statement?
Answer: Conditional Statement
A conditional is of the form "if, then" which is often found in math classes and formal logic classes as well.
If x= 7 - 4√3 then find the value of (a) (x+1/x) rais to 2 b) x rais 2+1/x rais to 2
The equation x = 7 - 4√3 is a radical expression, and the value of the radical expression is [tex](x + \frac 1x)^2 = 3650401 -2107560\sqrt 3[/tex]
How to solve the expressions?The equation is given as:
x = 7 - 4√3
So, we have:
[tex](x + \frac 1x)^2 = (7 - 4\sqrt 3 + \frac{1}{7 - 4\sqrt 3})^2[/tex]
Take the LCM
[tex](x + \frac 1x)^2 = (\frac{49 -56\sqrt3 + 48}{7 - 4\sqrt 3})^2[/tex]
Evaluate the like terms
[tex](x + \frac 1x)^2 = (\frac{97 -56\sqrt3 }{7 - 4\sqrt 3})^2[/tex]
Rationalize
[tex](x + \frac 1x)^2 = (\frac{(97 -56\sqrt3)(7 - 4\sqrt 3) }{49 -48})^2[/tex]
Evaluate the difference
[tex](x + \frac 1x)^2 = ((97 -56\sqrt3)(7 - 4\sqrt 3))^2[/tex]
Expand
[tex](x + \frac 1x)^2 = (679 -388\sqrt 3 -392\sqrt 3 + 672)^2[/tex]
Evaluate the like terms
[tex](x + \frac 1x)^2 = (1351 -780\sqrt 3 )^2[/tex]
Expand
[tex](x + \frac 1x)^2 = 1825201 +1825200 -2107560\sqrt 3[/tex]
[tex](x + \frac 1x)^2 = 3650401 -2107560\sqrt 3[/tex]
Hence, the value of the radical expression is [tex](x + \frac 1x)^2 = 3650401 -2107560\sqrt 3[/tex]
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Solve the compound inequality for x and identify the graph of its solution.
x+7 > 3 and x-5≤-1
O A. Solution: x < -4 or x ≥ 4
1 2 3 4 5
OB. Solution: x>-4 and x≤ 4
1
2 3 4 5
OC. Solution: x>-4 and x≤ 4
+
+
-5 -4 -3 -2 -1
1
2
3 4 5
OD. Solution: x²-4 and x < 4
1 2 3 4
5
-5 -4 -3 -2 -1 0
-5 -4 -3 -2 -1 0
0
-5 -4 -3 -2 -1 0
Answer:
x<-4 or x≤4
Step-by-step explanation:
The solution of the inequality is x > -4 and x ≤ 4.
So, the graph B is correct.
Given is an inequality, x+7 > 3 and x-5 ≤ -1, we need to solve and identify the graph,
To solve the compound inequality, let's solve each inequality separately and then find the intersection of the solutions.
Inequality 1: x + 7 > 3
Subtract 7 from both sides:
x > 3 - 7
x > -4
Inequality 2: x - 5 ≤ -1
Add 5 to both sides:
x ≤ -1 + 5
x ≤ 4
Now, we need to find the intersection of the solutions for both inequalities.
Since the conjunction between the two inequalities is "and," we need to find the common solution.
The common solution is the values of x that satisfy both x > -4 and x ≤ 4. From the two inequalities, we can see that the common solution range is from -4 to 4, including -4 but not including 4.
Therefore, the solution to the compound inequality is: -4 < x ≤ 4
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nth term of this quadratic sequence -1,2,7,14,23
Since we know it's quadratic, the n-th term will follow the pattern
[tex]x_n = an^2 + bn + c[/tex]
for some unknown coefficients a, b, and c.
Given that [tex]x_1=-1[/tex], [tex]x_2=2[/tex], and [tex]x_3=7[/tex], we have the following conditions on these coefficients:
[tex]\begin{cases} a + b + c = -1 \\ 4a + 2b + c = 2 \\ 9a + 3b + c = 7 \end{cases}[/tex]
Solve this system to get a = 1, b = 0, and c = -2. Then
[tex]\boxed{x_n = n^2 - 2}[/tex]
To solve the system, use elimination.
[tex](4a + 2b + c) - (a + b + c) = 2 - (-1) \implies 3a + b = 3[/tex]
[tex](9a + 3b + c) - (a + b + c) = 7 - (-1) \implies 8a + 2b = 8 \implies 4a + b = 4[/tex]
[tex](4a + b) - (3a + b) = 4 - 3 \implies a = 1 \implies b = 0 \implies c = -2[/tex]
Help!! Which of the following is equivalent to 3 6
— = —— ?
X X-4
Answer:
3rd Option - 3(x-4) = 6x
Step-by-step explanation:
To remove the fractions we escalate them up to the other side. So to remove the x under 3 we do the following :
[tex]\frac{3}{x} = \frac{6}{x-4}[/tex] -----> [tex]{3}= \frac{6x}{x-4}[/tex] (As you can see the x now goes to the numerator of the right side)
Now to remove x-4 under 6x we do the following :
[tex]{3}= \frac{6x}{x-4}[/tex] ------> [tex]3(x-4)= {6x[/tex]
Therefore giving our answer as the 3rd option.
Hope this helped and have a good day
6 A cube has a surface area of 54 mm². The length of its sides is: A 3 mm B 4 mm C 5
mm D 6 mm E 7 mm
Answer:
A
Step-by-step explanation:
A cube has 6 square faces
given surface area = 54 mm² , then
area of one face = 54 mm² ÷ 6 = 9 mm²
the area (A) of a square is calculated as
A = s² ( s is the side length ) , so
s² = 9 ( take square root of both sides )
s = [tex]\sqrt{9}[/tex] = 3 mm
necesito esto resuelto porfa! en 20 minutos
If f(x) = −5x − 4 and g(x) = -3x - 2, find (f+ g)(x).
Answer:
[tex](f+g)(x) = -8x-6[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]\displaystyle f(x) = -5x - 4 \text{ and } g(x) = -3x - 2[/tex]
And we want to find:
[tex](f+g)(x)[/tex]
Recall that this is equivalent to:
[tex]\displaystyle (f+g)(x) = f(x) + g(x)[/tex]
Substitute and simplify:
[tex]\displaystyle \begin{aligned} (f+g)(x) &= (-5x-4)+(-3x-2) \\ \\ &= -8x-6 \end{aligned}[/tex]
In conclusion:
[tex](f+g)(x) = -8x-6[/tex]
Select the correct answer. what is the solution set of y = x2 2x 7 and y = x 7? a. {(0, 7), (-1, 6)} b. {(0, 7), (-7, 0)} c. {(0, 7), (1, 8)} d. {(-2, 0), (4, 0)}
Answer:
a. {(0, 7), (-1, 6)}
Step-by-step explanation:
[tex]y = x^{2} +2x+7\\y=x+7[/tex]
subtract the equations
[tex]y = x^{2} +2x+7 \\- \ \ \ \ \ y=x+7\\y - y =x^{2} +2x+7-(x+7)\\0=x^{2} +x\\x = 0 \ and \ x= -1[/tex]
for [tex]y = x^{2} +2x+7[/tex], substitute x = 0
[tex]y = (0)^{2} +2(0)+7\\y = 0 +0+7\\y=7[/tex]
for [tex]y = x^{2} +2x+7[/tex], substitute x = 0
[tex]y = (-1)^{2} +2(-1)+7\\y = 1 -2+7\\y=6[/tex]
Answer:
A
Step-by-step explanation:
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Find the area of the shaded segment of the circle
Answer:
Exact Area =
16pi - 32 square meters
Decimal Approx:
A = 18.3 sq m
Step-by-step explanation:
In degrees, it's 360° all the way around a circle. The 270° in the image is to show you that the small piece (the triangle and yellow segment) are in a 90° part of the circle. That is 1/4 of the circle, this helps with area two ways. We'll find 1/4 of the circle area and also, that makes the triangle base 8 and height 8. This helps us find triangle area. See image.
what is the median and mean amount of sugar? pictures attached
Answer:
Step-by-step explanation:
mean is found by adding the numbers and dividing the sum by the number while the median is the middle value of the list ordered in an ascending order
Solve the following system of equations. Show all work and solutions.
y = 2x^2 + 6x + 1
y = −4x^2 + 1
Answer: (0, 1), (-1, -3)
Given two equation's:
y = 2x² + 6x + 1y = −4x² + 1Solve them simultaneously:
[tex]\sf 2x^2 + 6x + 1 = -4x^2 + 1[/tex]
[tex]\sf 2x^2 + 4x^2 = 1 - 1[/tex]
[tex]\sf 6x^2 + 6x = 0[/tex]
[tex]\sf 6x(x + 1) = 0[/tex]
[tex]\sf 6x = 0, \ x + 1 = 0[/tex]
[tex]\sf x = 0, \ x = -1[/tex]
(a) When x = 0, y = −4(0)² + 1 = 1
(b) When x = -1, y = -4(-1)² + 1 = -3
Solution: (x, y) → (0, 1), (-1, -3)
Answer:
System of equations
[tex]\large \begin{cases}y=2x^2+6x+1\\y = -4x^2+1\end{cases}[/tex]
To solve the given system of equations, use the substitution method:
[tex]\large\begin{aligned}2x^2+6x+1 & = -4x^2+1\\2x^2+6x+1+4x^2-1 & = 0\\6x^2+6x & = 0 \\6x(x+1) & = 0\\\implies x+1 & = 0 \implies x=-1\\\implies 6x & = 0 \implies x=0\end{aligned}[/tex]
Therefore the x-values of the solutions are:
[tex]\large \begin{aligned}x & =-1\\x & =0\end{aligned}[/tex]
Substitute the found values of x into the second equation to find the y-values:
[tex]\large \begin{aligned}x & =-1 & \implies &-4(-1)^2+1 =-3 & \implies & (-1,-3)\\x & =0 & \implies & -4(0)^2+1 =1 & \implies & (0,1)\end{aligned}[/tex]
Therefore, the solutions of the system of equations are:
(-1, -3) and (0, 1)
Given the Equation y squared-Ay-6=0, where A is a constant, find the solutions for y in terms of A
Answer:
do u still need help with this
Find the measure of the three missing angles in the parallelogram below.
Answer:
x= 67, y= 113 , z= 67........... ...........
The tables show linear functions representing the cost for purchasing different amounts of broccoli and cauliflower. which function has the greater slope and what does it indicate? the broccoli function has the greater slope, which shows that the cost per pound of broccoli is less than the cost per pound of cauliflower. the broccoli function has the greater slope, which shows that the cost per pound of broccoli is greater than the cost per pound of cauliflower. the cauliflower function has the greater slope, which shows that the cost per pound of cauliflower is less than the cost per pound of broccoli. the cauliflower function has the greater slope, which shows that the cost per pound of cauliflower is greater than the cost per pound of broccoli.
The function that has a greater slope will be B. The broccoli function has the greater slope, which shows that the cost per pound of broccoli is greater than the cost per pound of cauliflower.
What is a linear function?It should be noted that a linear function simply means a function whose graph is a straight line.
From the information given, the slope will be:
= (y2 - y1(/(x2 - x1)
= (3.6 - 3)/(3 - 2.5)
= 1.2
The slope for broccoli is 1.2
The slope of the cauli flower will be:
= (3.20 - 2.75)/(3.20 - 2.75)
= 1
Therefore, the broccoli function has the greater slope, which shows that the cost per pound of broccoli is greater than the cost per pound of cauliflower.
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Answer:
B
Step-by-step explanation:
right on 2022 edg
What is the distance around the perimeter of the garden? 60 ft 60 startroot 3 endroot ft 120 ft 120 startroot 3 endroot ft
The distance around the perimeter would be 120 ft.
What is perimeter?Perimeter is the distance around the edge of a shape.
The complete question is
A garden is designed in the shape of a rhombus formed from 4 identical 30°-60°-90° triangles. The shorter distance across the middle of the garden measures 30 feet.
A rhombus is shown. Lines are drawn from each point to the opposite point to form 4 right triangles. The other 2 angle measures are 30 and 60 degrees. The base length of each triangle is 15 feet.
What is the distance around the perimeter of the garden?
let AE is the half of the diagonal AC.
AC = 30 ft.
So, AE = ½ * 30
AE = 15 ft
Now, using trigonometry
sin 30 = 15/AD
0.5= 15/AD
AD= 30 ft
Hence, distance around the perimeter would be: AD+AD+AD+AD=
=30 ft + 30 ft + 30 ft + 30 ft
= 120 ft.
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Answer:A
Step-by-step explanation: just took it
Solve for the x in the inequality 6(2−6x)≤4−35x 6 ( 2 − 6 x ) ≤ 4 − 35 x .
Answer:
8 ≤ x
Step-by-step explanation:
6(2 − 6x) ≤ 4 − 35x
Expand bracket;
12 - 36x ≤ 4 − 35x
Add 36x to both sides to get;
12 ≤ 4 + x
Subtract 4 from both sides to get;
8 ≤ x
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to solve the inequality 6(2-6x)≤4-35x.
[tex]\triangle~\fbox{\bf{KEY:}}\star[/tex]
[tex]\star[/tex] We need to get x all by itself.First, we can use the distributive property and distribute 6:
[tex]\star\large\pmb{12-36x\leq4-35x}[/tex]
Now, add 35x to both sides:
[tex]\star\large\pmb{12-x\leq 4}[/tex]
And now, subtract 12 from both sides:
[tex]\star\large\pmb{-x\leq-8}[/tex]
Divide both sides by -1 and watch what happens:
[tex]\star\large\pmb{x\geq 8}[/tex]
Have you noticed that the inequality sign changed from "less than" to "greater than"?
Well, that happened because we divided both sides by a negative number, -1.
Thus, [tex]\star~\large\pmb{x\geq 8}[/tex]
Hope this helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
[tex]\pmb{M^ar_ib^el\:P^eri}[/tex]
1. Triangle STU is shown on the coordinate plane below. Triangle STU is transformed using the rule (x, y) -> (x+4, y-2). In the image of the transformation, triangle S'T'U', what is the x-coordinate of S'?
Using translation concepts, considering S(2,-1), the x-coordinate of S' is given by 6.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the rule is given by:
(x, y) -> (x+4, y-2).
Considering S(2,-1), 4 is added to the x-coordinate in the translation, hence:
2 + 4 = 6.
The x-coordinate of S' is given by 6.
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The function m is given in three equivalent forms.
Answer:
B; (-4, -8)
Step-by-step explanation:
The given forms of the equation are standard form, vertex form, and intercept form.
__
It is not surprising that the vertex form yields the vertex most quickly.
B) m(x) = 2(x +4)² -8
Compare this to the generic vertex form ...
f(x) = a(x -h)² +k . . . . . . . . . vertex (h, k)
We see that the vertex is (h, k) = (-4, -8).
The diagram shows a convex polygon.
What is the sum of the interior angle measures of this polygon?
°
Answer:
1080
Step-by-step explanation:
Which of the following are good ideas to use when gathering your resources?
Check all that apply.
A. Write down the facts.
B. Organize into a table.
C. Guess at the solution and see if you are close.
D. List potential formulas.
E. Form an equation.
F.Draw a diagram.
Answer:
a, b, d, e
maybe c
Step-by-step explanation:
Determine the value of X
AB is the mid segment of triangle LMN. Determine the value of X
Answer:
B. 4Step-by-step explanation:
Since ,AB is the mid segment of triangle LMN
Then
[tex]\Longleftrightarrow AB=\frac{MN}{2}[/tex]
[tex]\Longleftrightarrow x+8=\frac{5x+4}{2}[/tex]
[tex]\Longleftrightarrow 2\times(x+8)=5x+4[/tex]
[tex]\Longleftrightarrow 2x+16=5x+4[/tex]
[tex]\Longleftrightarrow 16-4=5x-2x[/tex]
[tex]\Longleftrightarrow 3x=12[/tex]
[tex]\Longleftrightarrow x=\frac{12}{3}=4[/tex]
What is the value of log 256/ log 1024
Answer:
0.8
Step-by-step explanation:
The change of base formula for logarithms can be used to find this value exactly. (Your calculator can also tell you.)
[tex]\log_b(a)=\dfrac{\log(a)}{\log(b)}[/tex]
__
Using this relation with the given numbers, we have ...
[tex]\dfrac{\log(256)}{\log(1024)}=\dfrac{\log(2^8)}{\log(2^{10})}=\dfrac{8\cdot\log(2)}{10\cdot\log(2)}=\dfrac{8}{10}\\\\\boxed{\dfrac{\log(256)}{\log(1024)}=0.8}[/tex]
Need the correct answers to select asap! Will give brainliest for correct answers
Answer:
first 2 options and 5th option are true
Step-by-step explanation:
locate y = - 4 on the y- axis. then a horizontal line through y = - 4 intersects the curve at x = - 2 and x = 1
----------------------------------------------------------
the axis of symmetry is a vertical line through the vertex with equation
x = c ( c is the value of the x- coordinate of the vertex )
vertex = ( - [tex]\frac{1}{2}[/tex], - 6 )
equation of axis of symmetry is x = - [tex]\frac{1}{2}[/tex]
------------------------------------------------------------
the minimum value is the y- coordinate of the vertex
that is the minimum value of f(x) is - 6
------------------------------------------------------------
given a parabola in standard form
ax² + bx + c ( a ≠ 0 )
• if a > 0 then graph opens up
• if a < 0 then graph opens down
Here the graph opens up , then coefficient of f(x) is positive
-------------------------------------------------------------
the solutions to f(x) = 0 are the values of x on the x- axis where the graph crosses.
the solutions are x = 2 and x = - 3
Which line is perpendicular to the line: y − 4 = 25(x +1)?
y² + 2y - 48 ( factor the polynomial )
Answer:
(y - 6)(y + 8)
Step-by-step explanation:
Find two numbers that add to 2 and multiply to -48. Then put them in the form above. Afterwards, use FOIL (First, Outside, Inside, Last) to check the factoring and you get: y² + 2y - 48
Have a great day! :)
Answer:
−8, 6
Step-by-step explanation:
Write the factored form using these integers. (y−8) (y+6)
Gerrie collects honey from a few
beehives. She scoops out the honey
with a small jar that holds of a cup.
Over the last two weeks Gerrie has
filled this jar 158 times. How many
cups of honey has she collected?
The number of the cups of honey has she collected will be 52 and 2/3 cups.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
Gerrie collects honey from a few beehives.
She scoops out the honey with a small jar that holds 1/3 of a cup.
Over the last two weeks, Gerrie has filled this jar 158 times.
1 small jar = 1/3 cup
But we have done this for 158 times. Then we have
158 small jar = 158 x 1/3 cups
158 small jar = 52 and 2/3 cups
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A runner runs a distance of 350 metres in a time of 50 seconds.
What is his average speed?
Answer:
7
Step-by-step explanation:
350÷50=7
................
If a doctor prescribes 75 milligrams of a specific drug to her patient how many milligrams of the drug will remain in the patients bloodstream after 6 hours if the drug decays at a rate of 20 percent per hour
After 6 hours the drug remains is 19.66 mg if the drug decays at a rate of 20 percent per hour.
What is exponential decay?During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.
We have:
If a doctor prescribes 75 milligrams of a specific drug to her patient how many milligrams of the drug will remain in the patients' bloodstream.
We know the exponential decay can be given as:
D = a(1 - r)ⁿ
a is the starting value and n is the number of hours.
D = 75(1 - 0.20)⁶
D = 19.66 milligrams
Thus, the after 6 hours the drug remains is 19.66 mg if the drug decays at a rate of 20 percent per hour.
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Can someone help me PLEASE I've been trying to get someone to help me for hours Come on I'm offering 20 points?!?!?!?
AND means multiply, so if probability is dependent on two things happening, then we will multiply the individual probabilities together.
1. P(A and 1) = 1/4 x 1/6 = 1/24
2. P(C and 2) = 1/4 x 2/6 = 2/24 = 1/12
3. P(B and 3) = 2/4 x 1/6 = 2/24 = 1/12
4. P(A and 4) = 1/4 x 2/6 = 2/24 = 1/12
5. P(C and 3) = 1/4 x 1/6 = 1/24
6. P(B and 2) = 2/4 x 2/6 = 4/24 = 1/6
7. P(a consonant and an odd #) = 3/4 x 2/6 = 6/24 = 1/4
8. P(a consonant and a prime #) = 3/4 x 3/6 = 9/24 = 3/8
9. P(a vowel and a 5) = 1/4 x 0/6 = 0
10. P(a vowel and a number less than 3) = 1/4 x 3/6 = 3/24 = 1/8
11. P(B and 1) = 2/4 x 1/6 = 2/24 = 1/12
Experimental probability is based on something that has already happened, or data that has already been collected.
12. P(1) = 3/30 = 1/10
13. P(2) = 8/30 = 4/15
14. P(3) = 7/30
15. P(4) = 5/30 = 1/6
16. P(5) = 3/30 = 1/10
17. P(6) = 4/30 = 2/15
Hope this helps!
Someone pleaseeeee helpp meeeeee!!!!
Answer:
The slope is 0.
Step-by-step explanation:
x is the gradient of the line, so multiplying the slope, zero, by the gradient, x, would make this equal to zero.