(A) Subtracting the right side from both sides, we get ...
... (20 -4x) -(12 -x +8 -3x) = 0
... (20 -12 -8) +x(-4 +1 +3) = 0
... 0 = 0 . . . . . true for all values of x (infinite solutions)
(B) Subtracting the right side from both sides, we get ...
... (5x +4x -3) -(24 +8x) = 0
... x(5 +4 -8) +(-3 -24) = 0
... x -27 = 0
... x = 27 . . . . . . (one solution)
(C) Subtracting the right side from both sides, we get ...
... (5x +6) -(2x +6 +3x -15) = 0
... x(5 -2 -3) +(6 -6 +15) = 0
... 15 = 0 . . . . . . . not true for any value of x (no solutions)
The straight line joining the points A(3,-5) and B(6,k) has a gradient of 4. Work out the value of k.
The straight line joining the points A(3,-5) and B(6,k) has a gradient of 4.
Gradient is the slope
So the slope of the line joining the points A(3,-5) and B(6,k) is 4
Slope of line joining two points = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
A(3,-5) and B(6,k) are (x1,y1) and (x2,y2)
slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
slope = [tex]\frac{k-(-5)}{6-3}=\frac{k+5)}{3}[/tex]
We know slope =4
[tex]\frac{k+5)}{3}=4[/tex]
Cross multiply and solve for k
k + 5 = 12
k = 7
The value of k = 7
Find the area of the sector of a circle with diameter 34 feet and an angle of π/5 radians. (Round your answer to four decimal places.)
The area of the sector of a circle with diameter 34 feet and an angle of π/5 radians is approximately 9.0095 square feet.
Explanation:To find the area of the sector of a circle, we need to use the formula A = πr2θ/360, where A is the area, r is the radius, and θ is the angle in radians. The given diameter is 34 feet, so the radius is 17 feet. The angle is π/5 radians. Plugging these values into the formula, we get A = π(17)2(π/5)/360. Simplifying, we find A = 9.0095 square feet. Rounded to four decimal places, the area of the sector is 9.0095 square feet.
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To find the area of the sector of a circle, you use the formula A = 0.5 * r² * θ where r is the radius (half of the diameter) and θ is the angle in radians. After plugging in the provided values, you calculate the area to four decimal points.
Explanation:The subject is related to finding the area of the sector of a circle. The formula to calculate the area of the sector is A = 0.5 * r² * θ, where r is the radius and θ is the angle in radians. In the given problem, the diameter of the circle is given as 34 feet, so the radius will be 17 feet, and the angle is given as π/5 radians.
Step 1: First, note down the radius from the given diameter, which would be 17 feet, as radius = diameter/2.
Step 2: Plug the value of the radius and the angle into the formula for the area of a sector. The calculation will look like this: A = 0.5 * (17)² * (π/5).
Step 3: Calculate the area by multiplying the values. The final answer will be rounded to four decimal places.
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Lee converted 500 U.S. dollars to 625 Singapore dollars. If x represents U.S. dollars and s represents Singapore dollars, which of these equations represents the relationship between the two currencies?
Given
Lee converted 500 U.S. dollars to 625 Singapore dollars.
x represents U.S. dollars and s represents Singapore dollars.
Find out equations represents the relationship between the two currencies.
To proof
As given in the question
x represents U.S. dollars and s represents Singapore dollars.
converted 500 U.S. dollars to 625 Singapore dollars
500 x = 625 s
[tex]x = \frac{625}{500} s[/tex]
x = 1.25 s
This shows that the U.S dollars is equal to 1.25 times of singapore dollars.
Hence proved
Consider the following investment. (Round your answers to the nearest cent.)
$3,000 at 6% compounded annually for 15 years
(a) FIND the future value of the given amount.
(b) INTERPRET the future value of the given amount.
After 15 years, the investment is worth $?
(a) 6% of the value of the investment is added each year. This means the value of the investment is multiplied by 1.06 each year. After 15 multiplications, the value is ...
... $3000×1.06¹⁵ ≈ $7189.67
(b) The interpretation of this result is ...
... After 15 years, the investment is worth $7189.67.
The future value of a $3000 investment at an annual interest rate of 6%, compounded annually for 15 years, is approximately $8093.97. This means that the original sum will grow to this amount after the set period.
Explanation:To find the future value of an investment, we use the formula for compound interest which is A = P(1 + r/n)^(nt). Where:
A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount you borrowed or deposited). r is the annual interest rate (in decimal form). n is the number of times that interest is compounded per unit t. t is the time the money is invested for in years.Given are P = $3000, r = 6%/100 = 0.06 (annually), n = 1 (since it's compounded annually), and t = 15 years. Plugging these into the formula, we get A = $3000(1 + 0.06/1)^(1*15) = $3000(1.06)^15 = $8093.97.
Interpreting this, it means that investing $3000 at 6% compounded annually would grow to approximately $8093.97 after 15 years.
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The bird population on an island is declining at a rate of 2.2% per year. The population was 3500 in the year 2009.
Which answer is the best prediction of the population in the year 2014?
A 2730
B 3062
C 3132
D 3423
The population is multiplied by 100% -2.2% = 97.8% each year. After 5 years, the population will have been multiplied by this value 5 times, so will be ...
... 3500×0.978⁵ ≈ 3132
The appropriate choice is ...
... C. 3132
Use the three steps to solve the problem.
One number is 11 more than twice another number. If the sum of the numbers is twice their difference, find the numbers.
Let x be the bigger number and y be the smaller number.
One number is 11 more than twice another number. Thus,
x = 2y + 11
The sum of the numbers is twice their difference, thus,
x + y = 2(x-y), which simplifies to:
x + y = 2x - 2y
3y = x (Now plug this back to the first equation:
3y = 2y + 11, and solve:
y = 11
Plug in y = 11 to the first equation:
x = 2(11) + 11 = 22 + 11 = 33
Thus the numbers are: x = 33, y = 11.
there is a photo attached
drop down 1:
161/289 -- incorrect
-161/289 -- CORRECT
64/289
-64/289
drop down 2:
-30/217 -- incorrect
-30/161 -- INCORRECT
-240/217 -- incorrect
-240/161
Your question answers itself.
You have shown the correct answer for the first drop-down: -161/289
You have shown the 3 incorrect answers out of the 4 choices for the second drop-down. The correct choice is the remaining one: -240/161.
_____
Even if all you know is that tan = sin/cos, you would suspect that answer choice based on the numerator of the cosine: 161. That value is likely the one in the denominator of the tangent value.
_____
cos(2θ) = 2cos(θ)² . . . . trig identity
... = 2(-8/17)² -1 = 128/289 -1 = -161/289
sin(2θ) = √(1-cos(2θ)²) . . . . trig identity
... = √(289² -161²)/289 = √57600/289 = 240/289
tan(2θ) = sin(2θ)/cos(2θ) . . . . trig identity
... = (240/289)/(-161/289) = -240/161
97 POINTS WILL MARK BRAINLESS
I need help with these i'm so confused could you show me on how you got the answers Thank you so much
Answer:
2.
x = 15∠1 = 45°1.
x = 5∠A = 85°Step-by-step explanation:
2.Angles 135° and (2x+15)° together make up a line (the transversal crossing m and n). Such angles are called a "linear pair" and their sum is always 180°. That means we can write the equation ...
... 135° + (2x+15)° = 180°
... 150 +2x = 180 . . . . . . . remove the degree symbol, combine terms
... 2x = 30 . . . . . . . . . . . . subtract 150
... x = 15 . . . . . . . . . . . . . . divide by 2
Angle 1 and angle (2x+15)° are on opposite sides of the transversal line, and are both between the parallel lines m and n. This makes them alternate interior angles. Such angles are congruent—they have the same measure. We know the measure of angle (2x+15)° is (2·15+15)° = 45°, so we know the measure of ∠1 is also 45°.
1.a) The sum of angles in a triangle is always 180°. This means ...
... (15x +10)° + (15x -10)° + (3x +15)° = 180°
... 33x +15 = 180 . . . . . . . drop the ° symbol, combine terms
... 33x = 165 . . . . . . . . . . subtract 15
... x = 5 . . . . . . . . . . . . . . . divide by 33
b) ∠A = (15x+10)° = (15·5 +10)°
... ∠A = 85°
(1)
(a)
the sum of the angles in a triangle = 180°, hence
3x + 15 + 15x - 10 + 15x + 10 = 180
33x + 15 = 180 ( subtract 15 from both sides )
33x = 165 ( divide both sides by 33 )
x = 5
(b) ∠A = 15x + 10 = (15 × 5 ) + 10 = 75 + 10 = 85°
(2)
2x + 15 + 135 = 180 ( straight angle )
2x + 150 = 180 ( subtract 150 from both sides )
2x = 30 ( divide both sides by 2 )
x = 15 ⇒ 2x + 15 = 45
∠1 = 45° ( alternate angles are congruent )
Jordan and Sharla are saving money to go on a study abroad trip. They must provide a down payment of $650 to sign up for the trip, and they can pay the remaining balance later. Jordan raises money by mowing lawns in his neighborhood and charges $25 per lawn. Sharla raises money by selling handmade necklaces for $15 each. Sharla raises less money than Jordan does because Sharla 3. only has enough materials to make 40 necklaces. (A) write two constraints to model the problem. Let x respresent the number of lawns Jordan mows and y represent the number of necklaces Sharla sells. (B) can sharla afford the down payment with the money she earns selling her necklaces? Explain your answer Please HELP ASAPm
Amount needed for down payment = $650
Amount charged by Jordan for mowing 1 lawn = $25
Amount charged by Sharla for 1 necklace = $ 15
Let the number of lawns mowed by Jordan = x
Let the number of necklace made by Sharla = y
Part A:
[tex]25x+15y=650[/tex]
As it is given, Sharla can make 40 necklace so,
[tex]25x+15(40)=650[/tex]
Or it could be 25x=650 and 15y=650
Part B:
No, Sharla cannot afford the down payment because she makes $15 for every necklace and she only has 40 necklaces which is [tex]15*40=600[/tex]
Point A is located at (4, 8) and point B is located at (14, 10) . What point partitions the directed line segment AB⎯⎯⎯⎯⎯ into a 1:3 ratio? (612, 812) (9, 9) (1112, 912) (6, 6)
The 1:3 ratio means that the distance from A to the point is 1/4 of the distance from A to B.
The difference of y-coordinates is 10-8 = 2. 1/4 of that is 2·1/4 = 1/2, so the point of interest will have y-coordinate 8 + 1/2 = 8 1/2. This apparently corresponds to the first selection:
... (6 1/2, 8 1/2)
Make a frequency distribution and find the relative frequencies for the following number set. Round the relative frequency to the nearest tenth of a percent. Some of the answers will be used more than once and some may not be used. 10, 21, 21, 21, 21, 22, 22, 23, 23, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 27, 27, 27, 27, 27, 28, 28, 28, 29, 29, 29, 29 Number Frequency Relative Frequency 20 ______ ______% 21 ______ ______% 23______ ______% 24 ______ ______% 25 ______ ______% 26______ ______% 27 ______ ______% 28 ______ ______% 29 ______ ______%
Solution: We have to find the Frequency and Relative frequency of the given data:
Frequency is the number of times a number occurs.
Relative Frequency is the number of times a number occurs divided by the total number of items.
Therefore, the frequency and relative frequency are calculated as below:
Number Frequency Relative Frequency
20 1 [tex]\frac{1}{31} \times 100 =3.2\%[/tex]
21 4 [tex]\frac{4}{31} \times 100 =12.9\%[/tex]
22 2 [tex]\frac{2}{31} \times 100 =6.5\%[/tex]
23 4 [tex]\frac{4}{31} \times 100 =12.9\%[/tex]
24 3 [tex]\frac{3}{31} \times 100 =9.7\%[/tex]
25 2 [tex]\frac{2}{31} \times 100 =6.5\%[/tex]
26 3 [tex]\frac{3}{31} \times 100 =9.7\%[/tex]
27 5 [tex]\frac{5}{31} \times 100 =16.1\%[/tex]
28 3 [tex]\frac{3}{31} \times 100 =9.7\%[/tex]
29 4 [tex]\frac{4}{31} \times 100 =12.9\%[/tex]
Total 31
please help!!!
The value of " X " is...
2x + y − z = 3
−x + y + 2z = 0
3x + 2y + z = 9
12
2
3
-4
x = 3
2x + y - z = 3 → (1)
- x + y + 2z = 0 → (2)
3x + 2y + z = 9 → (3)
we require to eliminate the y and z terms from the equations
(1) + (3) : 5x + 3y = 12 → (4)
multiply (1) by 2
4x +2y - 2z = 6 → (5)
(2) + (5) : 3x + 3y = 6 → (6)
(4) - (6) : 2x = 6 ⇒ x = 3
ANSWER = BRAINLIEST
Why does a = 8sin40?
look at the shaded right-angled triangle on the left
8 is the hypotenuse n a is opposite to the 40-degree angle
by definition, sin = opposite side / hypotenuse
so sin40=a/8
rearranging a=8sin40
Two right-angled triangles share a common side with length a.
For the inverted triangle on the left, a is the opposite side to the 40-deg angle.
Its longest side, hypotenuse, is 8cm.
Use the sine function, sin40 = opposite/hypotenuse = a/8
Multiply 8 on both sides, a = 8sin40
what is 352 divided by 53 please reply to this within a hour im timed....
352 divided by 53 is 6.64150943
Hi TaeArmy23,
352 / 53
= 6.6415
= 6.6
Hope This Helps!
solve the system by graphing or using a table.
2x+4y=12
x+y=2
Answer: x = -2 and y = 4
Step-by-step explanation:
We have given a system of equations
2x + 4y =12 ...........(1)
and
x + y = 2 .............(2)
Now to plot them in graph we need to find the points of the above linear equations .
From equation 1 ,we get
[tex]4y=12-2x\\\Rightarrow\ y=\frac{12-2x}{4}\\ \Rightarrow\ y=3-\frac{x}{2}\\\text{Put x=0, then} \\y=3-\frac{0}{2}=3\\\Rightarrow\ \text{Put x=6}\\y=3-\frac{6}{2} =3-3=0[/tex]
So get the points (0,3) and (6,0).
From equation 2 ,we get
[tex]y=2-x\\\text{Put x=0}\\y=2-0=2\\\text{Put x=2}\\y=2-2=0[/tex]
So we get the points (0,2) and (2,0).
So after plotting these points we get two lines intersecting at (-2,4).
Therefore our solution is x=-2 and y= 4.
Answer:
(-2, 4)
Step-by-step explanation:
How can the Angle-Angle Similarity Postulate be used to prove the two triangles below are similar? Explain your answer using complete sentences, and provide evidence to support your claims
To use the AA postulate directly, you need to show that two corresponding angles are congruent. In order to show that here, you must calculate the value of one of the missing angle measures. Either of the missing angles can be found by invoking the fact that the sum of angles in a triangle is 180°.
After finding either missing angle, you can show that the measures of two angles in one triangle are identical to the measures of two angles in the other triangle, hence the triangles are similar by the AA postulate.
Answer:
I wrote the answer below :) hope it makes sense
Step-by-step explanation:
The Angle-Angle Similarity postulate can be used to prove that these two triangles are similar. To demonstrate I will use an example, and try to make sense to the reader. on triangle ABC, the 2 angles that are given to us are 32 degrees and 49 degrees. Since all triangles have an angle sum of 180 degrees, the missing degree would have to be 99 degrees. Same for the triangle A'B'C'. The 2 angles given are 99 degrees and 49 degrees, which means the missing angle has to be 32 degrees. Therefore, the triangles are similar.
I just took the test and this is correct.
Happy Holidays!
y = 12x2 - 9x + 4 how many real solution 10x + y = -x2 + 2 how many real solution(s) 4y - 7 = 5x2 - x + 2 + 3y how many real solution(s) y = (-x + 4)2 how many real solution(s)
Answer:
(a) 0
(b) 2
(c) 0
(d) 1
Step-by-step explanation:
All of these can be solved easily by a graphing calculator. The attached graphs show the real solutions of those equations that have them. Here, you can also answer the question from the sign of the discriminant.
For y = ax² +bx +c
the value of the discriminant is
... b² -4ac
When the discriminant is negative, both solutions are complex. When 0, there is one solution. When positive, there are two real solutions.
(a) The discriminant is ...
... (-9)² -4(12)(4), a negative number. There are no real solutions.
(b) This needs to be rearranged to ...
... y = -x² -10x +2
Then the discriminant is ...
... (-10)² -4(-1)(2), a positive number. There are 2 real solutions.
(c) This needs to be rearranged to ...
... y = 5x² -x +9 . . . . add 7-3y
Then the discriminant is ...
... (-1)² -4(5)(9), a negative number. There are no real solutions.
(d) This equation is in vertex form, and the vertex is (4, 0). Since the vertex is the only x-intercept, there is one real solution.
If f(x) = 4x + 1 and g(x) = x^2 - 5, find (f - g)(x)
Answer:
The Answer is B
Step-by-step explanation:
Subtract f-g
4x + 1 - x^2 - 5
Distribute the - sign
4x + 1 - x^2 + 5
Combine like terms
-x^2 + 4x + 1 + 5
-x^2 + 4x + 6
y=f(x)=-3x find f(x) when x is 3
f(3) = -9 for the function [tex]\( y = f(x) = -3x \) when \( x \) is 3.[/tex]
To find f(x) when ( x ) is 3 for the given function [tex]\( y = f(x) = -3x \),[/tex] you substitute 3 for ( x ) in the function: [tex]\[ f(3) = -3 \times 3 \][/tex]
Now, calculate the value: [tex]\[ f(3) = -9 \][/tex]
Therefore, when ( x ) is 3, f(x) is -9 for the function [tex]\( y = f(x) = -3x \).[/tex]
In more detail, this means that if you plug ( x = 3 ) into the function, it will result in ( y = -9 ). The function ( y = -3x ) represents a linear relationship where the coefficient of ( x ) is -3. This indicates that for each unit increase in ( x ), ( y ) decreases by 3 units. In the specific case of ( x = 3 ), substituting this value into the function gives [tex]\( y = -3 \times 3 = -9 \).[/tex]
This kind of analysis is fundamental in understanding the behavior of linear functions. It provides insight into how the function's output (y) changes in response to changes in the input ( x ). In this case, when ( x ) increases by 1, ( y ) decreases by 3, leading to the slope of -3 in the function ( y = -3x ).
What’s is the product of the two solutions of the quadratic equation ax^2+bx+c=0
The product of the two roots is c/a.
_____
Consider the equation
... a(x -p)(x -q) = 0
which has solutions x=p and x=q.
When multiplied out, it becomes ...
... a(x² -(p+q)x +pq) = ax² -a(p+q)x +apq = 0
When apq = c, the product pq is c/a.
name a plane two different ways
3 and 5 form what type of angle pair? A. corresponding angles B. alternate interior angles C. consecutive interior angles D. alternate exterior angles
Answer:
C. consecutive interior angles
Step-by-step explanation:
The subject angles are between lines a and b, so are interior (not exterior). They are on different corners of the intersection, so are not corresponding. They are on the same side of line c, so are not alternate. The share a side, but not a vertex, so they are consecutive. The appropriate choice is ...
... C. consecutive interior angles
Answer: C. consecutive interior angles
A segment has endpoints (a,b) and (c,d). The segment is translated so that its image is 6 units up and 3 units left of the preimage. Are the two segments parallel, perpendicular, or neither? Also need a picture of the image and preimage, thanks!
Answer:
parallel
Step-by-step explanation:
Translation moves each point the same amount in the same direction. Essentially, the original segment becomes the side of a parallelogram, whose other side is the image, and whose ends are the vectors specifying the translation.
In the attachment, we have designated (a, b) as point A, and (c, d) as point B. We had to choose specific values for these in order to plot them, but the description of the effect of translation applies no matter what the point coordinates are chosen to be.
Please help! 15 Points! How do i do this? (View the picture down below)
Make 6 moves of [tex]\frac{2}{5}[/tex] to find the product.
Plot the product of the expression 6 ⋅ ( [tex]\frac{2}{5}[/tex] ) on the number line.
Ok, so what this question is really asking you is: [tex]2/5=0.4[/tex]
What is [tex]6*0.4[/tex] and that equals [tex]6*0.4=2.4[/tex]
Now because the the number is 2.4 plot that point
Rewrite using a single exponent. 7^4 - 7^4
A number added to its opposite is zero (0). No exponent is needed.
7^4 - 7^4 = 0
Jillian had
5
6
of a whole and took
3
6
away from it. How much does she have left?
2/6 is remaining from Jillian's whole.
[tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
Since the denominators of both fractions are common , that is 6
To subtract, subtract the numerators leaving the denominator
[tex]\frac{5}{6}[/tex] - [tex]\frac{3}{6}[/tex] = [tex]\frac{5-3}{6}[/tex] = [tex]\frac{2}{6}[/tex]
This fraction may be simplified by dividing the numerator/ denominator by 2
[tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex] ← in simplest form
how many times larger is 9 X 10 to the 6 exponent than 3 x 10 to the 4th exponent
300
divide 9 × [tex]10^{6}[/tex] by 3 × [tex]10^{4}[/tex]
= [tex]\frac{9}{3}[/tex] × [tex]10^{6}[/tex] / [tex]10^{4}[/tex]
= 3 × [tex]10^{6-4}[/tex] = 3 × [tex]10^{2}[/tex] = 300
What is the slope of your line perpendicular to y=5x-12
The slope of your line is the x-coefficient: 5.
The slope of a perpendicular line is the negative reciprocal of that: -1/5.
if 3x + 5y = 2 and 2x - 6y = 20 what is 5x - y
Hey!
We have:
... 3x + 5y = 2
... 2x - 6y = 20
In order to get 5x - y , we will need to add both the equations.
3x+5y=2
2x-6y=20
____________________________________________________
...5x - y = 22
Hence, the required answer is 22.
Hope it helps!
Linear equations in two variables are solved to obtain the values of variables. Thus, the value of the equation [tex]5x - y[/tex] is [tex]\bold{22}[/tex].
Given equations are mentioned below:
[tex]3x + 5y = 2\\2x - 6y = 20[/tex]
We need to determine the values of the expression [tex]5x - y[/tex].
For calculating the value of the above expression, first we need the value of the variables x and y.
How to calculate the values of the variables?The solution of linear equation in two variables can be calculated by different methods such as substitution, elimination and graphical methods.Here, in this question we used substitution method to calculate the desired value. Calculations:[tex]\begin {aligned}3x + 5y &= 2\\3x&=2-5y\\x&=\dfrac{2-5y}{3} \end{aligned}[/tex]
Now, substitute the value of the x in another expression and solve it further.
[tex]\begin{aligned}2 \times \dfrac{2-5y}{3} -6y&=20\\ \dfrac{4-10y}{3}-6y&=20\\4-10y-18y&=60\\28y&=-56\\y&=-2 \end{aligned}[/tex]
Now, calculate the value of x.
[tex]\begin{aligned}x&=\dfrac{2-5 \times -2}{3}\\&=\dfrac{12}{3}\\&=4 \end{aligned}[/tex]
Now, calculating the value of [tex]5x - y[/tex].
[tex]5\times4 - (-2)=22[/tex]
Hence, the value of the expression [tex]5x - y[/tex] is 22.
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Since it's Wednesday, Buy for Less gives a 5% discount for purchases. The items in Rhonda's cart total $53.75. She needs to know the cost of the items with the discount. So, she multiplies 5% times $53.75 and subtracts the amount from $53.75. Which expression would give Rhonda the same result in one step? A) .90(53.75) B) .95(53.75) C) 1.05(53.75) D) 53.75 - .05(53.75)
First we need to know how much the discount was so 5% is actually 0.05 then we need to multiply it by 53.75 which would equal 2.6875 then subtract it by 53.75 which would equal -51.0625.
B) .95(53.75)
This is a trick question because D) could also be correct if they said you could subtract it but it's not saying use the distributive property.
The answer would be B) .95(53.75)