[tex]\bf \sqrt{24}\qquad \approx \qquad 4.899~\hfill \underset{\textit{nope, is outside}}{~\hfill \stackrel{\sqrt{24}}{4.899}}\rule[0.35em]{2em}{0.25pt}\boxed{5}\rule[0.35em]{10em}{0.25pt}\boxed{6}[/tex]
Find the value of a-b+c+d 2x+8y=7 4x-2y=9
Answer:
The value of a - b + c + d = -4
Step-by-step explanation:
* Lets explain the linear equation
- The linear equation is the equation that represented graphically
by a line
- The general form of its equation is ax + by = c
- The slope of the line is -a/b and the y-intercept of the line is c/a,
where a is the coefficient of x , b is the coefficient of y and c is the
numerical term
∵ We have two linear equation in the problem
∴ Their general form is ax + by = e , cx + dy = f
∵ The equation are 2x + 8y = 7 and 4x - 2y = 9
- By comparing the two equations with their general forms
∴ a = 2 , b = 8 , c = 4 , d = -2
- Now we can find the value of a - b + c + d
∵ a = 2 , b = 8 , c = 4 , d = -2
∴ a - b + c + d = 2 - 8 + 4 + (-2) = 2 - 8 + 4 - 2 = -4
* The value of a - b + c + d = -4
Solve for x.
5(х – 10) = 30 — 15х
x = 1
x = 4
х = 5
х = 8
In order to solve for x, we must do the following:
5(x - 10) = 30 - 15x
5x - 50 = 30 - 15x (Expand 5(x - 10) )
5x - 50 + 50 = 30 - 15x + 50 (Add 50 to both sides of the equation)
5x = 80 - 15x
5x + 15x = 80 - 15x + 15x (Add 15x to both sides)
20x = 80
20x/20 = 80/20 (Divide both sides by 20)
x = 4
Therefor, the correct answer is the second option (x = 4).
You can always check if this is correct by substituting your answer back into the original equation and seeing if the left side is equal to the right side (this is also a potential method for solving the question itself if it is multiple choice, but I find it is often better to actually solve the equation rather than substitute each answer to see which works):
5(x - 10) = 30 - 15x
if x = 4:
5(4 - 10) = 30 - 15(4)
5(-6) = 30 - 60
-30 = -30
The two sides are equal, therefor x = 4 is confirmed as the correct answer.
Final answer:
To solve the equation 5(x - 10) = 30 - 15x, we expand and rearrange to get 20x = 80 and divide both sides by 20 to find that x = 4.
Explanation:
The student is asking us to solve for x given the equation 5(x – 10) = 30 – 15x.
To solve for x, we first expand the left side of the equation:
5x - 50 = 30 - 15x. Next, we collect like terms by adding 15x to both sides and adding 50 to both sides to isolate x:
5x + 15x = 30 + 50.
This simplifies to:
20x = 80.
We then divide both sides by 20 to solve for x:
x = 80 / 20.
This results in:
x = 4. Therefore, x equals 4 is the solution.
As a check, substituting x = 4 back into the original equation yields the identity 5(4 - 10) = 30 - 15(4), or -30 = -30, confirming that x = 4 is indeed the correct solution.
Which algebraic rule describes the 180° counter-clockwise rotation about the origin?
A) (x, y) → (−x, y)
B) (x, y) → (x, −y)
C) (x, y) → (−x, −y)
D) (x, y) → (−y, −x)
Answer:
C
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 180°
a point (x, y ) → (- x, - y) → C
Answer: C) (x, y) → (−x, −y)
Step-by-step explanation:
When we rotate a figure 180°clockwise or counter-clockwise , the magnitude of x and y coordinates remains same but their signs got changed.
For example : After a rotation of 180°clockwise or counter-clockwise (3,4) becomes (-3,-4).
Algebraically , we can say
Ordered pair (x , y ) will become (-x, -y) after a rotation of 180°clockwise or counter-clockwise.
Thus , the algebraic rule describes the 180° counter-clockwise rotation about the origin will be :-
C) (x, y) → (−x, −y)
The recursive rule for a sequence is an=an-1+7, where a1=15.What is the explict rule for this sequence
well, the recursive rule of aₙ = aₙ₊₁ + 7, where a₁ = 15, is simply saying that
we start of at 15, and the next term is obtained by simply adding 7, and so on.
well, that's the recursive rule.
so then let's use that common difference and first term for the explicit rule.
[tex]\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=15\\ d=7 \end{cases} \\\\\\ a_n=15+(n-1)7\implies a_n=15+7n-7\implies a_n=7n+8[/tex]
What is the measure of JL (the minor arc)?
A.82
B.164
C.196
D.41
Answer:
B. 164°
Step-by-step explanation:
arc JL = 2 (<JKL)
arc JL = 2(82)
arc JL = 164°
The measure of JL is 164°.
The correct option is (B)
What is minor arc?An arc whose measure is less than 180 degrees is called a minor arc.
Given: angle JKL= 82°
We know by the theorem that
"When two angles are subtended by the same arc, the angle at the centre of a circle is twice the angle at the circumference."
Then,
JL= 2 (JKL)
JL= 2(82)
JL= 164°.
Hence, the measure of JL is 164°.
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Use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3).
f(x) = -x^2+6x-5
f'(x) =
Step 1: evaluate f(x+h) and f(x)
We have
[tex]f(x+h) = -(x+h)^2+6(x+h)-5 = -(x^2+2xh+h^2)+6x+6h-5[/tex]
[tex]= -x^2-2xh-h^2+6x+6h-5[/tex]
And, of course,
[tex]f(x)=-x^2+6x-5[/tex]
Step 2: evaluate f(x+h)-f(x)
[tex]f(x+h)-f(x)=-x^2-2xh-h^2+6x+6h-5-(-x^2+6x-5)=-2xh-h^2+6h[/tex]
Step 3: evaluate (f(x+h)-f(x))/h
[tex]\dfrac{f(x+h)-f(x)}{h}=-2x-h+6[/tex]
Step 4: evaluate the limit of step 3 as h->0
[tex]f'(x) = \displaystyle \lim_{h\to 0} \dfrac{f(x+h)-f(x)}{h}=-2x+6[/tex]
So, we have
[tex]f'(1) = -2\cdot 1+6 = 4,\quad f'(2) = -2\cdot 2+6 = 2,\quad f'(3) = -2\cdot 3+6 = 0[/tex]
What is the conversion factor to convert cups to liters?
Answer:
1 cup = 0.24 liters
Step-by-step explanation:
Tangent line i think please help me find x
Answer:
x= 6.5 cm
Step-by-step explanation:
When a tangent line touches the circle, it forms a right angle triangle at that point
Apply the Pythagorean relationship in this case
Given that the height is = 20.2 cm = b
The hypotenuse is = c= x+14.7 cm
General formulae is;
a² +b² =c²
x² + 20.2² =( x+ 14.7)²
x² + 408.04= x² +14.7x+14.7x+216.09
x² + 408.04= x² + 29.4 x +216.09.........................collect like terms
x²-x² + 408.04-216.09= 29.4x
191.95= 29.4x-------------------------------divide by 29.4 t0 get x
191.95/29.4 =x
x=6.5 cm
1 Point
The revenue from selling x bracelets is r(x) = 8x.
The cost of buying x bracelets is c(x) = 3x + 12.
The profit from selling x bracelets is p(x) = f(x) - c(x).
Write a function for p(x), the profit from selling x bracelets.
O A. p(x) = 11x - 12
O B. p(x) = 11x + 12
O C. p(x) = 5x - 12
O D. p(x) = 5x + 12
Answer:
C. p(x) = 5x - 12.
Step-by-step explanation:
p(x) = 8x - (3x + 12) (Note you have to put the 3x+12 in parentheses).
p(x) = 8x - 3x - 12
p(x) = 5x - 12
The sum of two numbers is 0. Twice the smaller number subtracted from 3 times the larger number is 10. Let x represent the larger number and y represent the smaller number. What is the equation
Answer:
3x - 2y = 10
Step-by-step explanation:
We are given that the sum of two numbers is 0 and twice the smaller number subtracted from 3 times the larger number is 10.
Assuming x to be the large number and y to be the smaller number we can write an equation to represent this.
Sum of two numbers is 0:
[tex]x+y=0[/tex]
Twice the smaller number subtracted from 3 times the larger number is 10:
[tex]3x-2y=10[/tex]
If f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to (fºg)(x)?
(3x + 2)(x2 + 1)
3x2 + 1 + 2
(3x + 2)2 + 1
3(x2 + 1) + 2
Answer:
3(x2 + 1) + 2
A. (3x + 2)(x2 + 1) WRONG bc = 3x^3
B. 3x2 + 1 + 2 Wrong bc 3x^+3
C. (3x + 2)2 + 1 wrong bc 6x+5
D. 3(x2 + 1) + 2Correct
What is the x-intercept of the function graphed below?
ed below?
ОА. (0, -4)
Ов. (-4, 0)
Ос. (0, 2)
OD. (2, 0)
Answer:
D
X - intercept is the point where the graph crosses the x-axis
in this case, the graph crosses at x = 2 and y = 0; or (2,0)
Answer:
(2, 0)
Step-by-step explanation:
The x- intercept is where the line crosses the x- axis at x = 2
x- intercept is (2, 0)
The y- intercept is where the line crosses the y- axis at y = - 4
y- intercept is (0, - 4)
A triangular brace has an angle measure of 30 degrees, with a side opposite this angle measuring 8 inches. The base of the triangular brace, which is adjacent to the given angle measure, is 11 inches in length. Which of the following statements is correct?
The problem can be solved using trigonometric principles where the hypotenuse measures 16 inches.
Explanation:The problem involving a triangular brace can be solved using trigonometry principles. As it involves a right triangle, you can use the sine function to solve the problem. In a right triangle, the sine of an angle (hypotenuse) is the length of the side opposite the angle divided by the length of the hypotenuse.
In this case, you have the opposite side (8 inches), the angle (30 degrees), and the adjacent side (base, 11 inches). Using these values and the sine rule, we can determine the length of the hypotenuse. In a 30-degree angle, the sine is 0.5, so the unknown length can be obtained by dividing the length of the opposite side by the sine of the angle. This gives: 8/0.5 = 16 inches.
Therefore, the correct statement will be that the hypotenuse of the triangular brace is 16 inches.
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Using the principles of trigonometry, specifically the sin and cos functions, applied to a triangle with a 30 degrees angle and known lengths of the sides opposite and adjacent to this angle, we can calculate the length of the hypotenuse.
Explanation:The question asked pertains to the principles of trigonometry. In particular, we have a triangle with one angle of 30 degrees, and we know the lengths of the side opposite this angle (8 inches) and the base of the triangle, which is adjacent to this angle (11 inches).
With a 30 degree angle, we can use sin, cos, and tan functions to form relationships with the opposite, adjacent, and hypotenuse sides of the triangle. In this scenario, the sin(30 degrees) = opposite length/hypotenuse = 8 inches/hypotenuse. Alternatively, the cos(30 degrees) = adjacent length/hypotenuse = 11 inches/hypotenuse.
To solve for the hypotenuse using the sin, you'd do 8/sin(30 degrees). From the cos, you'd do 11/cos(30 degrees).
Note that while you have two ways to solve for the hypotenuse, these should give you the same answer if your angle and side lengths are correct.
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Which angles are corresponding angles?
Check all that apply.
Answer: Options 'A', 'C' and 'F' are correct.
Step-by-step explanation:
Since we have given that
Corresponding angles are those angles which takes the same corresponding position at intersection when a transversal cut the two parallel lines.
so, According to this , we get that
∠1 and ∠5
∠2 and ∠6
∠3 and ∠7
∠4 and ∠8
so, Options 'A', 'C' and 'F' are correct.
which graph or graphs appear to show a sinusoid ?
Answer:
D
Step-by-step explanation:
Sinusoid graphs look like regular waves.
It is obvious that only I and III look like waves.
II is known as a stepwise function.
Option: D is the correct answer.
D. I and III only
Step-by-step explanation:The graph of a sinusoidal function is a smooth periodic graph.The graph is continuous all over the x-axis and also it repeats itself after every fixed interval.From the graph that is provided to us we observe that the graph I is a sinusoidal graph since it is similar to a graph of sine graph.
Also, the graph II is not a continuous graph and hence it can't be a graph of sinusoidal graph.
Also, graph III is similar to a graph of sine function and hence it represent a graph of a sinusoidal graph.
At Which values of x does the function f(x) have a vertical asymptote? Check all that apply
Answer:
C, D and E
Step-by-step explanation:
The denominator of f(x) cannot be zero as this would make f(x) undefined.
Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non zero for these values then they are vertical asymptotes.
solve 3x(x - 1)(x + 5) = 0
Equate each factor to zero and solve for x
3x = 0 ⇒ x = 0
x - 1 = 0 ⇒ x = 1
x + 5 = 0 ⇒ x = - 5
Vertical asymptotes at x = -5, x = 1 and x = 0
Answer:
0, 1, -5
Step-by-step explanation:
Find the area of the kite
Step-by-step answer:
Area of a kite is half of the product of the diagonals.
The length of diagonal in the x-direction is 4+5 = 9
The length of diagonal in the y-direction is 4+4 = 8
Therefore
Area of kite = 8*9/2 = 36 units.
ANSWER
The correct answer is A.
EXPLANATION
If you know the diagonals of a kite you can easily find the area.
The area of a kite is half the product of the diagonals.
From the graph, the from -5 to 4.
Using the number line approach. The longer diagonal is
[tex] |4 - - 5| = |4 + 5| = |9| = 9 \: \: units[/tex]
Similarly the shorter diagonal is from -4 to 4
[tex] |4 - - 4| = |4 + 4| = |8| = 8 \: \: units[/tex]
The area of the kite is:
[tex]Area= \frac{1}{2} \times 8 \times 9[/tex]
[tex]Area=4 \times 9[/tex]
This implies that
[tex]Area=36 \: square \: \: units[/tex]
The first choice is correct.
5 hatfields and five McCoys are up for 3 jobs. What is the probability that all 3 jobs go to the hatfields?
Answer:
[tex]P =\frac{1}{12}[/tex]
Step-by-step explanation:
The probability is defined as the number of ways to obtain the desired result among the number of possible outcomes.
The number of possible ways to select 3 hatfields from a group of 5 hatfields is:
[tex]3C5 =\frac{5!}{3!(5-3)!} =10[/tex]
The number of ways to select 3 people from a group of 10 is:
[tex]10C3 =\frac{10!}{3!(10-3)!} =120[/tex]
Then the probability is:
[tex]P =\frac{10}{120}[/tex]
[tex]P =\frac{1}{12}[/tex]
Solve for x. 9x + 2 = 5x + 22
Answer:
Here is your answer in the picture..
Answer:
x = 5
Step-by-step explanation:
Given
9x + 2 = 5x + 22 ( subtract 5x from both sides )
4x + 2 = 22 ( subtract 2 from both sides )
4x = 20 ( divide both sides by 4 )
x = 5
Help me out again Please thanks
Answer:
1x-4
Step-by-step explanation: Less than in this occasion means -4, and the product of one and a number x means 1x, so when you put it together it's 1x-4.
0.2x + 0.8 = 9.6 find x
Please and thank you.
Answer:
x=44
Step-by-step explanation:
Making the equation in terms of x:
0.2x + 0.8 = 9.6
-0.8 -0.8
0.2x=8.8
*5 *5
x=44
Answer:
x=44
Step-by-step explanation:
Multiply by 10 from both sides of equation.
0.2x*10+0.8*10=9.6*10
Simplify.
2x+8=96
Subtract by 8 from both sides of equation.
2x+8-8=96-8
Simplify.
96-8=88
2x=88
Divide by 2 from both sides of equation.
2x/2=88/2
Simplify, to find the answer.
88/2=44
x=44 is the correct answer.
I hope this helps you, and have a wonderful day!
what is Square root of -98 + 7i
Answer:
[tex]\sqrt{7(-14+i)}[/tex]
Step-by-step explanation:
We need to find the [tex]\sqrt{-98+7i}[/tex]
We know that 98/7 = 14.
Taking 7 common from both terms we get
[tex]\sqrt{7(-14+i)}[/tex]
Since 7 and -14 are not the perfect squares, so our answer is:
[tex]\sqrt{7(-14+i)}[/tex]
Write the inequality in slope-intercept form. 5x - 2y < -8 show work.
[tex]\bf 5x-2y<-8\implies -2y<-5x-8\implies \stackrel{\textit{multiplication by a negative}}{y~~\stackrel{\downarrow }{>}~~\cfrac{-5x-8}{-2}} \\\\\\ y>\cfrac{5x+8}{2}\implies y>\cfrac{5}{2}x+4\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
Find the measure of angle B in the following triangle
Answer:
27.6 degrees
Step-by-step explanation:
Use Cosine rule on Acute triangle
b² = a² + c² - 2ac Cos B
where b = 10, a = 14, c = 20
10² = 14² + 20² - 2(14)(20) Cos B
-496 = -560 Cos B
Cos B = (-496) / (-560)
B = [tex]Cos^{-1}[/tex] (-496) / (-560) = 0.483 radians = 27.6 degrees
Which statement accurately describes how to perform a 90° clockwise rotation of point A (1,4) around the origin?
I was expecting a choice that said A(1,4) is in the first quadrant so 90 degrees clockwise is fourth quadrant. For perpendicularity we reverse the coordinates, negating one of them. For the fourth quadrant, it must be the y coordinate that's negative. We end up at A'(4,-1).
The answer is the second choice: create a circle with the center at the origin. The image of A' will be on the circle, 90 degrees clockwise from A.
Please help IM OFFERING ALOT OF POINTS !!!!
Answer:
cos 2Ф = - 161/289 , tan 2Ф = - 240/161
Step-by-step explanation:
* Lets explain how to solve the problem
∵ cos Ф = - 8/17
∵ Ф lies in the 3rd quadrant
- In the 3rd quadrant sin and cos are negative values, but tan is
a positive value
∵ sin²Ф + cos²Ф = 1
∴ sin²Ф + (-8/17)² = 1
∴ sin²Ф + 64/289 = 1
- Subtract 64/289 from both sides
∴ sin²Ф = 225/289 ⇒ take √ for both sides
∴ sin Ф = ± 15/17
∵ Ф lies in the 3rd quadrant
∴ sin Ф = -15/17
∵ cos 2Ф = 2cos²Ф - 1 ⇒ the rule of the double angle
∵ cos Ф = - 8/17
∴ cos 2Ф = 2(-8/17)² - 1 = (128/289) - 1 = - 161/289
* cos 2Ф = - 161/289
∵ tan 2Ф = sin 2Ф/cos 2Ф
∵ sin 2Ф = 2 sin Ф × cos Ф
∵ sin Ф = - 15/17 and cos Ф = - 8/17
∴ sin 2Ф = 2 × (-15/17) × (-8/17) = 240/289
∵ cos 2Ф = - 161/289
∴ tan 2Ф = (240/289)/(-161/289) = - 240/161
* tan 2Ф = - 240/161
Answer:
so look the answer is 2090909876
Step-by-step explanation:
PLEASE HELP!!
We used these functions to represent the two sides of the equation:
f(x) = 3x
g(x) = 4x + 1
Graph the functions y = f(x) and y = g(x) on the same coordinate plane.
At which points are the functions y = f(x) and y = g(x) equal? What are the x-values of the solution?
How many solutions are there to the equation f(x) = g(x)? How do you know these are solutions?
Answer:
1. They are met on point (-1, -3)
2. They x- values of the solution is... -1
3. There is only one solution. Proof: The slope and the y intercept is different.
4. If you plug in -1 in the x, you get the same y
Explanation:
3x = 4x +1
0 = x +1
-1 = x
plug in... y = 3(-1) = -3
Answer:
The two functions are equal at the two graphs' points of intersection. The points of intersection are (0,1) and (2,9). The x-values of the solutions are x = 0 and x = 2.
Step-by-step explanation:
which is the completly factored form of 3x2-12x-15?
Answer:
(3x-15)(x+1)
Step-by-step explanation:
Given an expression in the form ax²+bx+c, where a,b and c are constants, we can factor it by first finding the two numbers that when multiplied equal to ac and when added equal to b
The expression 3x²-12x-15 can be factored as follows:
The two numbers that can be added to give 3×(-15) and when added result to -12 are -15 and 3.
Thus, 3x²+3x-15x-15
3x(x+1)-15(x+1)
The simplified form becomes: (3x-15)(x+1)
Answer:
A
Step-by-step explanation:
3(x + 1)(x – 5)
which function is even? check all that apply.
Answer:
Hi there!
The answer is A, and C
Step-by-step explanation:
cos(-x)=cos(x)
sec(-x)=sec(x)
Answer:
A and C.
Step-by-step explanation:
Graphs that have symmetry with respect to the y-axis are called even functions. So, let's check each of the graphs:
1. As we can see in the graph attached, y=cos(x) is symmetrical with respecto to the y-axis.
2. As we can see in the graph attached, y=sin(x) is not symmetrical with respecto to the y-axis.
3. As we can see in the graph attached, y=sec(x) is symmetrical with respecto to the y-axis.
4. As we can see in the graph attached, y=csc(x) is not symmetrical with respecto to the y-axis.
Solve (X + 6)(x - 4) = -16
O {-4, 6)
O {-4, 2]
O (-12, 22)
Final answer:
To solve the equation (x + 6)(x - 4) = -16, expand the brackets, rearrange the equation, and factorize to find the solutions.
Explanation:
To solve the equation (x + 6)(x - 4) = -16, we can start by expanding the brackets:
x2 - 4x + 6x - 24 = -16
x2 + 2x - 24 = -16
Next, we can rearrange the equation to one side:
x2 + 2x - 24 + 16 = 0
x2 + 2x - 8 = 0
Finally, we can factorize the quadratic equation:
(x + 4)(x - 2) = 0
This gives us two possible values for x: x = -4 or x = 2.