[tex]x - 3y = 15 \\ x = 15 + 3y[/tex]
[tex](15 + 3y) {}^{2} + y {}^{2} = 25[/tex]
[tex]225 + 90y + 9y {}^{2} + y {}^{2} = 25[/tex]
[tex]10y {}^{2} + 90y + 200 = 0[/tex]
[tex]y {}^{2} + 9y + 20 = 0[/tex]
[tex](y + 4)(y + 5) = 0[/tex]
[tex]y = - 4 \: \: \: \: \: \: y = - 5[/tex]
[tex]for \: y= - 4 \\ x = 15 + 3( - 4) = 15 - 12 = 3[/tex]
[tex]for \: y = - 5 \\ x = 15 + 3( - 5) = 15 - 15 = 0[/tex]
Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted: rectangle with a length of x plus 15 and width of x plus 10 with a rectangle in the bottom right corner labeled bench that has a length of 5 and width of 1 write an equation to determine the area, a, of the patio that will be painted. a = (x 20)(x 11) a = (x 15)(x 10) 5 a = (x 15)(x 10) − 5 a = (x 9)(x 10)
The equation which determines the painted area is (x+15)(x+10)-5.
Given that there is a rectangle with a length of x plus 15 and width of x plus 10 with a rectangle in the bottom right corner labeled bench that has a given length of 5 and width of 1.
A rectangle is a two-dimensional (2D) form in which the four angles are all right angles and the opposite sides are parallel and equal to one another. The region that the rectangle's perimeter encloses is known as its area, which is equal to the product of its length and width.
Let the length of the patio be L=x+15.
The width of the patio be W=x+10.
So, the Area of the patio will be painted is, A₁=L×W
A₁=(x+15)(x+10)
Let the Length of the bench be L₁=5
The width of the bench be W₁=1
So, the Area of the bench will be painted is, A=L₁×W₁
A₂=5×1
A₂=5
The net area of the patio that will be painted is
A=A₁-A₂
A=(x+15)(x+10)-5
Hence, the equation which is used determines the area, A, of the patio that will be painted is (x+15)(x+10)-5.
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Which pair of complex numbers has a real-number product? (1 3i)(6i) (1 3i)(2 – 3i) (1 3i)(1 – 3i) (1 3i)(3i)
Answer:
(1+3i)(1-3i)
Step-by-step explanation:
When these terms have the same pair of numbers in them, but one set has a PLUS and one set has a MINUS, these are called CONJUGATES.
When you multiply CONJUGATES, you will eliminate the imaginary number, i.
Remember i^2=-1
see image.
If the zeros of a quadratic equation are -3
and 5, what would be the x-intercepts?
Answer:
To find the x-intercepts of a quadratic equation, let y = 0. Write down the new equation ax squared + bx + c = 0 and the quadratic formula that gives the solution as x = -b plus or minus the square root of (b squared - 4ac), all divided by 2a.
Step-by-step explanation:
Hope this helps.
Answer:
-3, 5
Step-by-step explanation:
The x-intercepts are the same as the zeros.
I REALLY NEED HELP WITH THESE GRADIENT QUESTIONS
PLS HELP ILL GIVE BRAINLIEST
Answer:
For the first picture, the answer is either A or B, but I think it's A. For the second picture, the answer should also be 4, because the lines are parallel to each other and therefore have the same gradient.
Four teachers offer an after-school chess club the table shows the number of students who joined
Because you make a "half circle" when you bisect an angle, neither a ruler nor a compasses are needed. Because a bisected angle wouldn't be straight, you wouldn't need either of the two.
Teams of no more than six pupils will be formed from the total group of participating students by the teachers.
What is the smallest number of teams that may be formed with every student?Four teachers offer an after-school chess club the table shows the number of students who joined In the box, type your response. teams Part B With 18 chess sets at its beginning, the chess club. Three cases of 15 chess sets were ordered by the professors. To provide each teacher an equal number of chess sets, they will divide the total number of chess sets. Any extra sets will then be donated to the school library.
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you have two exponential functions. one has the formula h(x)=2^x +3. the other function, g(x), has the graph shown below. which equation or inequality below is true
g(2)>h(2)
g(2)>h(2)=7
g(7)=h(7)=2
g(2)
please i rlly need helpppppp!!!!
The true equation about the functions is (d) g(2) = h(2) = 7
How to determine the true statement?The graph that completes the question is added as an attachment
The function is given as:
h(x) = 2^x + 3
Calculate h(2) and h(7)
h(2) = 2^2 + 3 = 7
h(7) = 2^7 + 3 = 131
From the graph, we have:
g(2) = 7
g(7) = 610
By comparison, we have:
g(2) = h(2) = 7
Hence, the true equation is (d) g(2) = h(2) = 7
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Choose the most convenient method to graph the line 3x−2y=−12.
Select the correct answer below:
Recognize the equation as that of a vertical line passing through the x-axis at −12.
Recognize the equation as that of a horizontal line passing through the y-axis at −12.
Identify the slope and y-intercept, and then graph.
Find the x- and y-intercepts and then graph.
Determine the quadrant ( I, II, III, and IV ) or axis (x and y ) where each of the following point is located.
1. ( 0,-6 )
2. ( 15,4 )
3. ( 100, -5 )
4. ( 0.004, .05 )
5. ( -4,0 )
8. ( -7.5, -6.3 )
9. ( 0.1000)
Answer:
1. ( 0,-6 ) is y-axis
2. ( 15,4 ) is l quadrant
3. ( 100, -5 ) is lV quadrant
4. ( 0.004, .05 ) is l quadrant
5. ( -4,0 ) is x-axis
8. ( -7.5, -6.3 ) is lll quadrant
9. ( 0.1000) is y-axis.
HELP!! What is the equation of the graphed line?
(y=mx+b)
factorise 25x^2-20xy-21y^2+10yz-z^2
The factorization of the given expression is 5x(5x - 4y) - y(21y + 10z) - z².
Factorization of algebraic expression:The factorization of an algebraic expression is the process of finding two or more factors, whose multiplication results back in the given expression.
From the information given:
The factorization of 25x^2-20xy-21y^2+10yz-z^2 can be computed as:
= 5x(5x - 4y) - y(21y + 10z) - z²
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Which descriptions from the list below accurately describe the relationship
between AABC and ADEF? Check all that apply.
E
5/37
53
A 3 C D
10
53
6
37
A. Same area
B. Same size
8
C. Congruent
D. Congruent after a dilation
Triangle ABC was dilated to form triangle DEF, hence both triangles have the same shape and are similar.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
Dilation preserves the shape but not the size.
Triangle ABC was dilated to form triangle DEF, hence both triangles have the same shape and are similar.
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What is the missing value for x
Answer:
x° = 43°
Step-by-step explanation:
You want the measure of the angle marked x° in the circle with arcs of 152° and 122° shown.
Inscribed angleThe arc subtended by the inscribed angle x° will be the measure of the arc that makes up the rest of the 360° circle:
360° -152° -122° = 86°
The measure of angle x° is half the measure of the subtended arc:
x° = 86°/2
x° = 43°
<95141404393>
he graph shows the velocity f(t) of a runner during a certain time interval:
Graph of line segment going through ordered pairs 0, 6 and 6, 8. Graph of another line segment going through the ordered pairs 6, 8 and 8, 0. Label on the x axis is time in seconds, and label on the y axis is velocity in meters per second.
Which of the following describes the intercepts on the graph?
Option D. The description that best fits the intercept of the graph is The initial velocity of the runner was 6 m/s, and the runner stopped after 8 seconds.
How to solve for the intercept of the graphThe graph has lines that would go through these points, (0,6) and pair (6,8). In the other graph, it goes through 6, 8 and 8, 0.
The initial velocity of this runner is seen to be 6m/s. As he runs this would increase and while he slows down it would fall. The stop time of the runner is going to be at 8 minutes.
Complete question
Which of the following describes the intercepts on the graph?
The initial acceleration of the runner was 8 m/s2, and the runner stopped after 6 seconds.
The initial acceleration of the runner was 6 m/s2, and the runner stopped after 8 seconds.
The initial velocity of the runner was 8 m/s, and the runner stopped after 6 seconds.
The initial velocity of the runner was 6 m/s, and the runner stopped after 8 seconds.
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PLEASE HELP
Which linear equation can be derived from this proportion?
12/( x + 8 ) = 7/( x + 1 )
A.
12x + 8 = 7x + 1
B.
12x + 12 = 7x + 56
C.
12x + 1 = 7x + 8
D.
12x + 96 = 7x + 7
Answer:
B. 12x + 12 = 7x + 56
Explanation:
[tex]Given : \ \sf \dfrac{12}{ x +8} = \dfrac{7}{x + 1}[/tex]
cross multiply formula: if [tex]\sf \dfrac{a}{b} = \dfrac{c}{d}[/tex] then [tex]\sf ad = cb[/tex]
[tex]\sf 12(x +1) = 7(x + 8)[/tex]
distribute inside parenthesis
[tex]\sf 12x + 12= 7x + 56[/tex]
collect like terms
[tex]\sf 12x -7x = 56 - 12[/tex]
simplify the following
[tex]\sf 5x = 44[/tex]
dividing both sides by 5
[tex]\sf x = 8.8[/tex]
can you please help with these two gradient questions I'm giving brainliest :)
The line with a gradient of 6 is line A, and the gradient of line A is 4
The line with a gradient of 6The gradients are given as:
-0.5, 0, 2 and 6
A line with a negative gradient (i.e. -0.5) would decrease as the x values increase.
This is represented by line D
A line with a 0 gradient is a horizontal line
This is represented by line C
The line closer to the y-axis have a higher gradient.
This means that line A has a higher gradient than line B, because of its proximity to the y-axis
Hence, the line with a gradient of 6 is line A
The gradient of line AThe gradient of line B is given as:
Gradient = 4
Line A and line B are parallel lines
Parallel lines have the same gradient
Hence, the gradient of line A is 4
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Use distributive law evaluate
Answer:
The distributive property allows you multiply a sum in parenthesis by multiplying each addend separately, then add the products.
Step-by-step explanation:
How to use the distributive law example.
2(x+4) = 16
To use the distributive law in this example multiply 3 by all terms in the parenthesis. Multiply 2 and x, then 2 and 4 to open the parenthesis.
2x+8=16
That is how you use the distributive law.
To continue solving, subtract 8 from both sides.
2x+8-8=16-8
2x=8
Divide 2 from both sides.
2x/2=8/2
x=4
Hope this helps!
If not, I am sorry.
Draw a ratio box for this problem. Then solve the
problem using a proportion.
her piano students and that 40% of the
Ms. Smith noted that there were 12 girls among
students were boys. How many piano students
did Ms. Smith teach?
There are total 30 students in the piano class.
What is Ratio and Proportion ?When a number can be divided by another number then they can be written as p : q , when two ratios can be equated using an equal sign then they are said to be in proportion.
It is given that the total number of girls is 40% of the total students
The ratio of total students to girls is 100 :40
= 10 :4
= 5 : 2
It is also given that in the total number of students 12 were girls
Let total students be x
Then the ratio is x : 12
As both the ratio are same and so can be equated and the proportion will be
5 : 2 = x : 12
5/2 = x /12
x = 30
Therefore there are total 30 students in the piano class.
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1. Factor 250² - 81b².
О (5а - 9ь)(5а + 90)
-
О (5а - 9b)(5а - 9b)
О (5а + 9ь)(5а + 9ь)
(12.5a-4.5b) (12.5a + 4.5b)
Answer: The answer is option
Step-by-step explanation:
The solution is in the attached
19. For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither?
19. Line 1: Passes through (-8, -55) and (10, 89)
Line 2: Passes through (9, -44) and (4, -14)
Answer:
The given lines are un-related.
Step-by-step explanation:
In the question, two lines are given as line 1 passes through (-8,-55) and (10,89). Whereas, line 2 passes through (9,-44) and (4,-14).
It is required to find the slope of given lines and figure out whether they are perpendicular, parallel or neither.
To solve this question, first find the slope of both lines. Check if their product is equal to -1, then they are perpendicular. If the slopes are equal the lines are parallel.
Step 1 of 2
Find the slope of first line.
[tex]$$\begin{aligned}&m_{1}=\frac{89-(-55)}{10-(-8)} \\&m_{1}=\frac{144}{18} \\&m_{1}=8\end{aligned}$$[/tex]
Step 2 of 2
Find the slope of first line.
[tex]$$\begin{aligned}&m_{2}=\frac{-14-(-44)}{4-9} \\&m_{2}=\frac{30}{-5} \\&m_{2}=-6\end{aligned}$$[/tex]
Since, both slopes are neither equal nor reciprocal of each other.
Therefore, the lines are un-related.
A company invests $32000. after 4 years of growth at the same rate each year, the investment is worth $42692. find the annual growth rate as a percentage.
Answer:
R = 33.35%
Step-by-step explanation:
that is the solution above
help me quik please!! 20 points
What is the opposite of –(–24)
And, what is the opposite of +(+15)
Answer:
Step-by-step explanation:
hello :
the opposite of +(+15) is : +(-15)
the opposite of -(-24) is : +(-24)
[tex]\huge\fbox\purple{Question}[/tex]
1)Find the H.C.F of the following set of numbers by finding all the possible factors.
a)6 and 15
b)12 and 18
c)15 and 24
d)24 and 36
e)30 and 48
f)36 and 54
g)32,40 and 56
h)28,42 and 70
I)30,75 and 90
Note=
Answer with proper explanation required and all steps to be mentioned .
The HCF are
3631261881415What is HCF?This is the common factor that is the highest that a group of numbers can have in common.
1. 6 and 15
factors of 6 = 1, 2, 3, 6
factors of 15: 1, 3, 5, 15
The HCF is the number they have in common = 3
2. 12 and 18
The factors of 12: 1, 2, 3, 4, 6, 12
The factors of 18: 1, 2, 3, 6, 9, 18
The HCF = 6
3. 15 and 24
Factors of 15: 1, 3, 5, 15
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
The HCF = 3
4. 24 and 36
The factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
The HCF : 12
5. 30 and 48
The factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
The factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The HCF = 6
6. 36 and 54
The factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
The hcf = 18
7. 32,40 and 56
The factors of 32: 1, 2, 4, 8, 16, 32
The factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
The factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
The HCF is 8
8. 28,42 and 70
The factors of 28: 1, 2, 4, 7, 14, 28
The factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
The factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
The HCF = 14
9. 30,75 and 90
The factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
The factors of 75: 1, 3, 5, 15, 25, 75
The factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The HCF is 15
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4 12-sided dice are rolled. What is the probability that the number of dice showing a two digit number is equal to the number of dice showing a one digit number
Probability means Possibility. It states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty.
I'll take a stab at this one. if the number of dice showing a two-digit number = the number of dice showing a one-digit number, then 2 must show a two-digit number and 2 must show a one-digit number
There are 3 two-digit numbers and 9 one-digit numbers on each die
So....the probability is
C(4,2) (3/12)^2 (9/12)^2 =
C(4,2) (1/4)^2 (3/4)^2 =
27/128.
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Given that n is an integer. write down expression for next two odd numbers after 2n-1.
explain why the sum is multiples of 3
The expressions for the next two odd numbers after 2n -1 are; 2n +1 and 2n +3.
What are the expressions for the next two odd numbers?If follows from the task content that the expressions for the next two odd numbers after 2n-1 are required.
Since odd numbers are have difference 2, it follows that the next 2 odd numbers must be obtained by adding each time. Hence, we have, 2n +1 and 2n +3.
The sum is a multiple of 3 because; 2n -1 + 2n +1 + 2n +3 = 6n +3 = 3(2n+1).
Hence, the sum is multiples of 3.
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There is a reflection at the boundary between two materials if there is a change of __________ at the boundary.
There is a reflection at the boundary between two materials if there is a change of the speed of light in the material at the boundary.
This bending is referred to as refraction. whilst a wave traveling at an angle adjusts its velocity upon crossing a boundary among materials,. This bending is known as refraction. As a wave crosses a boundary into a new medium, its pace, and wavelength exchange simultaneously as its frequency stays equal.
While light from air hits a smooth piece of glass (n = 1. five) with the ray perpendicular to the glass floor, of the subsequent will occur while light from air hits a clean piece of glass with the ray perpendicular to the glass surface, the part of the light passing into the glass: will now not exchange its frequency.
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What is the formula for the sum of the first n terms in the following sequence in terms of n:
1, 1+2, 1+2+2^2, 1+2+2^2+2^3, ...
Let [tex]S_n[/tex] be the [tex]n[/tex]-th term in this sequence, so
[tex]S_1 = 1[/tex]
[tex]S_2 = 1 + 2[/tex]
[tex]S_3 = 1 + 2 + 2^2[/tex]
and so on, with general [tex]n[/tex]-th term
[tex]S_n = 1 + 2 + 2^2 + \cdots + 2^{n-1} = \displaystyle \sum_{i=1}^n 2^{i-1}[/tex]
Observe that
[tex]2 S_n = 2 + 2^2 + 2^3 + \cdots + 2^n[/tex]
and by subtracting this from [tex]S_n[/tex], we eliminate all but the outermost terms, namely
[tex]S_n - 2S_n = 1 - 2^n[/tex]
so that
[tex]-S_n = 1 - 2^n[/tex]
[tex]S_n = 2^n - 1[/tex]
Now, the sum of the first [tex]n[/tex] terms of the sequence [tex]\{S_1,S_2,S_3,\ldots,S_n\}[/tex] is
[tex]S = S_1 + S_2 + S_3 + \cdots + S_n[/tex]
[tex]S = \displaystyle \sum_{i=1}^n S_i[/tex]
[tex]S = \displaystyle \sum_{i=1}^n (2^i - 1)[/tex]
[tex]S = \displaystyle \sum_{i=1}^n 2^i - \sum_{i=1}^n 1[/tex]
[tex]S = \displaystyle 2 \underbrace{\sum_{i=1}^n 2^{i-1}}_{S_n} - n[/tex]
[tex]S = 2(2^n - 1) - n[/tex]
[tex]S = \boxed{2^{n+1} - n - 2}[/tex]
use the geometric model to factor 3x^2+4x+1
The geometric model to factor 3x²+4x+1 can be shown as given below in the form of geometric tiles.
\What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
The geometric model to factor 3x²+4x+1 can be shown as given below in the form of geometric tiles.
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Given the equation startfraction 2 x 2 over y endfraction = 4 w 2 what is the value of x?
The value of x is 2wy + y - 1.
Given: (2x + 2)/y = 4w + 2
To find: the value of x
the following steps will be used.
First, Multiply both sides by y
y * (2x + 2)/y = (4w + 2) * y
2x + 2 = 4wy + 2y
Subtract 2 from both sides
2x + 2 - 2 = 4wy + 2y - 2
2x = 4wy + 2y - 2
Multiply both sides by ½
½ * 2x = ½(4wy + 2y - 2)
x = ½(4wy + 2y - 2)
Open bracket
x = ½ * 4wy + ½ * 2y - ½ * 2
x = 2wy + y - 1
Hence, the value of x is 2wy + y - 1.
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Can someone help with this section? Please ASAP
The values of the trigonometric functions are
7. [tex]sin\theta = \frac{12}{13}[/tex]
[tex]cos\theta = \frac{5}{13}[/tex]
[tex]tan\theta = \frac{12}{5}[/tex]
[tex]csc\theta =\frac{13}{12}[/tex]
[tex]sec\theta =\frac{13}{5}[/tex]
[tex]cot\theta =\frac{5}{12}[/tex]
8. [tex]sin\theta = \frac{\sqrt{7} }{4}[/tex]
[tex]cos\theta = \frac{12}{16}[/tex]
[tex]tan\theta =\frac{\sqrt{7} }{3}[/tex]
[tex]csc\theta = \frac{4}{\sqrt{7} } \ OR \ \frac{4\sqrt{7}}{7}[/tex]
[tex]sec\theta =\frac{16}{12}[/tex]
[tex]cot\theta = \frac{3}{\sqrt{7}} \ OR \ \frac{3\sqrt{7}}{7}[/tex]
Trigonometric functionsFrom the question, we are to determine the values of the given trigonometric functions
7.
In the given triangle,
Opposite = 12
Adjacent = 5
Hypotenuse = ?
Hyp² = Opp² + Adj² (Pythagorean theorem)
∴ Hyp² = 12² + 5²
Hyp² = 144 + 25
Hyp² = 169
Hyp =√169
Hyp = 13
Using SOH CAH TOA
[tex]sin\theta = \frac{12}{13}[/tex]
[tex]cos\theta = \frac{5}{13}[/tex]
[tex]tan\theta = \frac{12}{5}[/tex]
[tex]csc\theta =\frac{1}{sin\theta} =\frac{13}{12}[/tex]
[tex]sec\theta =\frac{1}{cos\theta} =\frac{13}{5}[/tex]
[tex]cot\theta =\frac{1}{tan\theta} =\frac{5}{12}[/tex]
8.
Hypotenuse = 16
Adjacent = 12
Opposite = ?
Hyp² = Opp² + Adj² (Pythagorean theorem)
Opp² = Hyp² - Adj²
∴ Opp² = 16² - 12²
Opp² = 256 - 144
Opp² = 112
Opp =√112
Opp = 4√7
Using SOH CAH TOA
[tex]sin\theta = \frac{4\sqrt{7} }{16} = \frac{\sqrt{7} }{4}[/tex]
[tex]cos\theta = \frac{12}{16}[/tex]
[tex]tan\theta = \frac{4\sqrt{7} }{12}= \frac{\sqrt{7} }{3}[/tex]
[tex]csc\theta =\frac{1}{sin\theta} =\frac{16}{4\sqrt{7} } = \frac{4}{\sqrt{7} } \ OR \ \frac{4\sqrt{7}}{7}[/tex]
[tex]sec\theta =\frac{1}{cos\theta} =\frac{16}{12}[/tex]
[tex]cot\theta =\frac{1}{tan\theta} =\frac{12}{4\sqrt{7}} = \frac{3}{\sqrt{7}} \ OR \ \frac{3\sqrt{7}}{7}[/tex]
Hence, the values of the trigonometric functions are
7. [tex]sin\theta = \frac{12}{13}[/tex]
[tex]cos\theta = \frac{5}{13}[/tex]
[tex]tan\theta = \frac{12}{5}[/tex]
[tex]csc\theta =\frac{13}{12}[/tex]
[tex]sec\theta =\frac{13}{5}[/tex]
[tex]cot\theta =\frac{5}{12}[/tex]
8. [tex]sin\theta = \frac{\sqrt{7} }{4}[/tex]
[tex]cos\theta = \frac{12}{16}[/tex]
[tex]tan\theta =\frac{\sqrt{7} }{3}[/tex]
[tex]csc\theta = \frac{4}{\sqrt{7} } \ OR \ \frac{4\sqrt{7}}{7}[/tex]
[tex]sec\theta =\frac{16}{12}[/tex]
[tex]cot\theta = \frac{3}{\sqrt{7}} \ OR \ \frac{3\sqrt{7}}{7}[/tex]
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