The answer is:
Whether you add or subtract the equations, you get the same resulting equation in one variable.
y=-4x+12
6x+ 5y = 11
The value of x = 7/2 and y = -2, Given equation are linear.
What is a linear equation?
When the greatest power of the variable is consistently 1, an equation is considered to be linear. A one-degree equation is another name for it. The typical form of a linear equation with one variable is Ax + B = 0.
The equation are,
y=-4x+12 --------(i)
6x+ 5y = 11 --------(ii)
for eq(i),
y + 4x = 12
4x + y = 12
Now, put together both the equation and multiply with coefficient of x to make common value of x so that we can cut by opposite signs,
(4x + y = 12) * 6
(6x+ 5y = 11) * 4
After multiplying, we get
24x + 6y = 72
24x + 20y = 44
Now change the signs with + to - and - to +, like that
24x + 6y = 72
24x + 20y = 44
- - -
-----------------------
0 + 6y - 20y = 72 - 44
=> -14y = 28
=> y = 28/(-14)
=> y = -2
Put y = -2 in eq(i),
4x + y = 12
4x - 2 = 12
4x = 12 + 2
x = 14/4
x = 7/2
Hence, the values we get after solving given equation is x=7/2 and y= -2.
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what are the appropriate tools to measure the lengths of the sides and the angles of a trapizoid
Answer: A ruler and a protracor
Step-by-step explanation:
Suppose that ab = 5 cm. If we continually duplicated segment ab, what are the lengths of the first four segments you would be able to construct?
After solving the arithmetic sequences, he lengths of the first four segments will be 20 cm.
What is arithmetic sequences?Arithmetic sequences take the following format: a, a+d, a+2d, a+3d, etc. up to n terms. A is the first term; d is a frequent difference; and n is the total number of terms.
Find the AP, the number of terms, and the common difference for the calculation using the arithmetic sequence formulas. To determine the nth term, sum, or common difference of a given arithmetic sequence, various arithmetic series formulas are used.
To find the lengths of the first four segments we use the Arithmetic progression formula that is
[tex]a_n =[/tex] a₁ + (n - 1)d
Where
an = the nᵗʰ term in the sequence
a₁ = the first term in the sequence
d = the common difference between terms
We have a₁ as 5 cm and as it is being duplicated the common ration d is 5
and we have been asked the length of the first four segments, so n = 4
Lets substitute the given information
[tex]a_n =[/tex] 5 + (4 - 1)5
= 5 +(3)5
= 5 + 15
= 20
Thus, after continually duplicated segment ab, the lengths of the first four segments will be 20Cm
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Helps me please I’m having trouble
a) The slope of the equation is m = 291.5
b) The y intercept is y = 2944.01
What is y- intercept ?An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx+c, where m denotes slope and c denotes the y-intercept.
Given : y = 291.5x + 2944.01
and x = number of years after 2000
y = total cost
a) The given equation is of the form y = mx + c
On comparing these two equations , we get that the slope m = 291.5
b) The y intercept is y = 2944.01
The y intercept means the value of the y when x = 0 .
Thu when we substitute the value of x as 0
we get y = 2944.01
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4 of 4
A notebook costs £1.10, a pen costs 43p, a pencil costs 24p and a sharpener costs 88p.
Remi buys 2 pencils, 2 pens, 3 sharpeners and some notebooks.
He pays with £7 and receives 82p change.
How many notebooks did he buy?
Answer:
He bought 2 notebooks
Step-by-step explanation:
Add up the cost of the pens, pencils, sharpeners, and the change.
This will give you £4.80, subtract that from £7.00 and you get £2.20
Since the notebooks are only £1.10, he could've only bought 2.
Please mark brainliest!!!
Write an equation of the line that passes through the given point and is (a) parallel and b) perpendicular to the given line.
a. y =
b. y=
(a) The equation of the parallel line is y = 3x - 11.
(b) The equation of the perpendicular line is y = - x/3 - 1.
Consider the line graphed,
The two points on the line are ( 1, - 4 ) and ( 2, - 1 ).
Now, the slope of the line with two points ( x₁, y₁ ) and ( x₂, y₂ ) is:
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Then,
m = ( - 1 - (-4) ) / ( 2 - 1 )
m = 3
(a) The lines which are parallel have the same slope.
Now, the parallel line passes through ( 3, - 2 ).
Therefore, the equation of the line is y = mx + b where b is the y-intercept.
y = mx + b
- 2 = 3 × 3 + b
- 2 = 9 + b
b = - 11
Therefore, the equation of the line is y = 3x - 11.
(b) The slope of the line perpendicular to the line with slope m is equal to - 1/m.
Then the slope of the perpendicular line is - 1/3.
The line passes through the point ( 3, - 2 ).
y = mx + b
- 2 = ( - 1/3 ) × 3 + b
- 2 = - 1 + b
b = - 1
Then the equation of the perpendicular line is:
y = - x/3 - 1
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Need help asap, 30 points
Answer:
Combining like terms
Step-by-step explanation:
Answer: Combing like terms
The answer to the math problem is 76.2 if the r means remainder
Step-by-step explanation: Hope this helps
Thanks for the points:)
The domain for f(x) and g(x) is the set of all real numbers.
Let fix)=x²+1 and g(x) = 3x.
Find f-g-
A. x²+3x+1
B. 3x³ +3x+1
C. x² + 3x
D. x²-3x+1
The value of the composite function (f - g)(x) is x² - 3x + 1
How to evaluate the function?The functions are given as
f(x) = x² + 1
g(x) = 3x
The composite function definition is given as
(f - g)(x)
This composite function is calculated using the following composite function formula
(f - g)(x) = f(x) - g(x)
Substitute the known values in the above equation
So, we have the following equation
(f - g)(x) = x² + 1 - 3x
Evaluate the like terms
(f - g)(x) = x² - 3x + 1
Hence, the composite function is (f - g)(x) = x² - 3x + 1
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PLS HELP 40 POINTS IF YOU GET THIS RIGHT AND BRAINLIST. PRETTY SIMPLE.
• Jackie made a mistake when he _________.
• The Triangle Congruence Postulate or Theorem that is easiest for me to use is ____ because _____.
• The Triangle Congruence Postulate or Theorem that is the most difficult for me to use is ____ because _____.
Answer:
12
Step-by-step explanation:
bla bla bla is not 12 and I know that thanks for my points is not 12 thanks
Calculate the value of a in the triangle below.
15 cm
12 cm
a cm
Answer:
a = 9 cm
Step-by-step explanation:
Calculate the value of a in the triangle below.15 cm12 cma cmit is a right triangle and we use the Pythagorean theorem
a = √(15²-12²)
a = √(225 - 144)
a = √81
a = 9 cm
How much would Haiti’s balance be from account two over 3.4 years round to two decimal place
Solution:
Given:
Account 2 details:
Assume a year is 365 days;
[tex]\begin{gathered} P=\text{ \$}8100 \\ t=3.4years \\ r=5.1\text{ \%}=\frac{5.1}{100}=0.051 \\ n=365days \end{gathered}[/tex]Using the compound interest formula to get the amount;
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Hence, substituting the values;
[tex]\begin{gathered} A=8100(1+\frac{0.051}{365})^{365\times3.4} \\ A=8100(1+\frac{0.051}{365})^{1241} \\ A=9633.55 \end{gathered}[/tex]Therefore, the balance in account 2 will be $9633.55
Write the following expression using the fewest possible terms.
(−2x − 13) + (19 + 5x)
3x + (−6)
7x + (−6)
7x + 32
3x + 6
There is nothing more we can do with these binomials, so we break them up and combine like terms.
-2x - 13 + 19 + 5x
5x - 2x + 19 - 13
3x + 19 - 13
3x + 6
Answer:
[tex]\boxed{\sf 3x+6}[/tex]
Step-by-step explanation:
[tex]\sf \left(-2x-13\right)+\left(19+5x\right)[/tex]
Simplify:-
[tex]\sf -2x-13+19+5x[/tex]
Combine like terms/Add numbers:-
[tex]\sf -2x+5x-13+19[/tex]
[tex]\sf (-2x+5x)=\bf 3x[/tex]
[tex]\sf (-13+19)=\bf 6[/tex]
[tex]\boxed{\sf 3x+6}[/tex]
Therefore, your answer is D. 3x + 6!!
_______________________
Hope this helps!
Have a great day!
On a coordinate plane, a curved line with a minimum value of (negative 1.25, negative 3.25) and a maximum value of (0.25, negative 1.75), crosses the x-axis at (negative 2.25, 0), and crosses the y-axis at (0, negative 2). The line exits the plane at (negative 2.75, 6) and (1.5, 6).
Which statement is true about the end behavior of the graphed function?
As the x-values go to positive infinity, the function's values go to negative infinity.
As the x-values go to zero, the function's values go to positive infinity.
As the x-values go to negative infinity, the function's values are equal to zero.
As the x-values go to positive infinity, the function's values go to positive infinity.
The true statement about the end behaviour of the described function is the fourth option;
As the x–values go to positive infinity, the function's value go to positive infinity What is the end behaviour of a function?The end behaviour of a function is the description of the shape of the function's graph towards the left and right extremities of the x–axis
The points on the graphed function, obtained from the description are;
Minimum point; (-1.25, -3.25)
Maximum point; (0.25, -1.75)
x–intercept; (-2.25, 0)
y–intercept; (0, -2)
Exit points of the graph on the plane; (-2.75, 6), and (1.5, 6)
Arranging the above points with respect to their location on the x–axis gives;
(-2.75, 6), (-2.25, 0), (-1.25, -3.25), (0, -2), (0.25, -1.75), (1.5, 6)
Observing the y–values indicates that the y–values decreases in the region; -2.75 ≤ x < -1.25, and the y–values increases in the region; -1.25 < x ≤ 1.5
Which gives;
The turning point on the graph are the points (-1.25, -3.25) and (0.25, -1.75)
However, as the x–values increases towards+1.5, the y–value increases to 6
The correct option is therefore;
As the x–value go to positive infinity, the function value goes to positive infinity
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Answer:
its A
Step-by-step explanation:
e. Write an equation for the line containing all possible images of point C.
Following a dilation with a scale factor of s, the coordinates of point C are 3.s +2,s. The line's equation is 3y = x - 2
What is the slope intercept equation for this line?When you know the slope of the line to be examined and the point given is also the y intercept, you can use the slope intercept formula
y = mx + b. (0, b).
The y value of the y intercept point is represented by b in the formula.
First part
The scale factor of dilation = 2
Given that the center of dilation is the point (2, 0) on the preimage, we have;
The coordinates of the image are;
(2, 0), (2 ×(5 - 2) + 2, (2 × (1 - 0)), (2 × (5 - 2) + 2, 0)
Which gives;
The coordinates of the vertices of the image are; (2, 0), (8, 2), (8, 0)
Please find the drawing of the image of the dilation of triangle ΔABC with a scale factor of 2 attached.
Second [part;
The scale factor = 3
Center of dilation = (2, 0)
The coordinates of the image are therefore;
(2, 0), (3 × (5 - 2) + 2, (3 × (1 - 0)), (3 × (5 - 2) + 2, 0)
Which gives;
(2, 0), (11, 3), and (11, 0)
Please find attached the drawing of the image of the dilation of triangle ΔABC with a scale factor of 3
Third part;
The scale factor = 12
Center of dilation = (2, 0)
The coordinates of the image are;
(2, 0), (12 × (5 - 2), 12 × (1 - 0)), (12 × (5 - 2), 0)
Which gives;
(2, 0), (36, 12), (36, 0)
Please discover connected the drawing of the image of ΔABC having a scale factor of 12
Fourth part
Center of dilation = (2, 0)
Scale factor of dilation = s
The coordinates of the image are;
A(2, 0), C(s × (5 - 2) + 2), s × (1 - 0)), B(s × (5 - 2) + 2, 0)
Which gives;
The coordinate of point C is 3.s +2,s.
Fifth part
The slope of the line is m, which is equal to the slope of the side AC of Δ A B C, which is given as follows;
[tex]$m=\frac{1-0}{5-2}=\frac{1}{3}[/tex]
The equation of the line in point and slope form is therefore;
[tex]$y=\frac{1}{3} \times(\mathrm{x}-2)[/tex]
Which gives;
3y = x - 2
- The equation of the line is 3y = x - 2
The complete question is:
Here is triangle ABC. Draw the dilation of triangle ABC with center (2,0) and scale factor 2. Draw the dilation of triangle ABC with center (2,0) and scale factor 3. Draw the dilation of triangle ABC with center (2,0) and scale factor 12. What are the coordinates of the image of point C when triangle ABC is dilated with center (2,0) and scale factor s? Write an equation for the line containing all possible images of point C.
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in the given picture, the measure of x is __°
*no multiple choice*
Answer:
x = 52°
Step-by-step explanation:
Exterior Angle Theorem
The interior angles of a triangle sum to 180°. Angles on a straight line sum to 180°. Therefore, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.
⇒ x + 90° = 142°
⇒ x + 90° - 90° = 142° - 90°
⇒ x = 52°
Let us assume that,
→ x + y + 90° = 180°
Now the required value of y is,
→ y + 142° = 180°
→ y = 180° - 142°
→ [ y = 38° ]
Then the value of x will be,
→ x + 38° + 90° = 180°
→ x = 180° - 128°
→ [ x = 52° ]
Hence, the value of x is 52°.
Marissa is selling paintings for $15 each and bracelets for $7 each. Her goal is to sell at least $800 in products, and she must sell at least 60 bracelets. Which of the
following combinations will satisfy these constraints?
O20 paintings and 65 bracelets
O25 paintings and 60 bracelets
O26 paintings and 61 bracelets
014 paintings and 45 bracelets
Answer:
the answer is: 026 paintings and 61 bracelets
Step-by-step explanation:
20•15=300+65•7=755
25•15=375+60•7=795
26•15= 390+61•7=817
14•15= 210+41•7=497
Answer: 26 paintings and 61 bracelets
Step-by-step explanation:
Find the volume of this cone.Use 3 for T.10 ft=115 ftTr²hV=3Hint: The radius (1) is1/2 of the diameter.V ~ [?]ft3
Given:-
[tex]V=\frac{\pi r^2h}{3}[/tex]To find the volume of the cone.
From the given image it is clear,
[tex]h=5,r=5[/tex]So now we substitute the known values. so we get,
[tex]\begin{gathered} V=\frac{\pi r^2h}{3} \\ V=\frac{3(5)^25}{3} \\ V=5^3 \\ V=125 \end{gathered}[/tex]So the required volume is 125ft^3.
Find the least common multiple of 3x and 3(x−2)
The least common multiple of the 3x and 3(x−2) is 9x(x - 2)
How to determine the least common multiple of the expressions?From the question, the expressions are given as
3x and 3(x−2)
The expressions do not have direct factors or multiples
So, we multiply both expressions to calculate the least common multiple
This above computation can then be represented as
Least common multiple = Product of the two expressions
Substitute the known values in the above equation
So, we have the following representation
Least common multiple = 3x * 3(x - 2)
Evaluate the product of 3x and x in the above equation
So, we have the following equation
Least common multiple = 9x(x - 2)
Hence, the least common multiple of the expressions is 9x(x - 2)
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The division law of exponents says that if b is a non zero number and n and m are any numbers then bm/bn = bm-n true or false?
it is True that the division law of exponents says that if b is a non zero number and n and m are any numbers in the exponents of b then b^m/b^n = b^(m-n)
What is division law of exponents?This is the law that governs numbers that are have exponents or power.
According to the question b is the number while m and n represents the value of the exponents or the numbers for which number b is raised to their power say: b^m and b^n
The division law of exponents holds as:
= b^m ÷ b^n
= b ^ ( m - n )
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Triangles worksheet
We can tell if the components on each side of the equation are congruent when you see the equals sign with a squiggly line on top. Name the corresponding sides after that. Two triangles with corresponding sides have matching sides. Congruent triangles will have the same length.
How did you recognize the triangles' matching sides?The same two angle pairs are touched by corresponding sides. When the sides are equivalent, you can multiply each side by the same value to move from one triangle to another. The corresponding sides of the triangles in the similar triangles diagram are the same color.The side a (next to b) must match either v or x, for instance, if one polygon has the sequential sides a, b, c, d, and e and the other has the sequential sides v, w, x, y, and z. (both adjacent to w).If two triangles have sides A,B,C and a,b,c, respectively, and they are similar, then the pair of matching sides are proportionate, meaning that A: a = B: b = C.The relationship between the sides and angles of two congruent triangles is referred to as "corresponding parts of congruent triangles," or cpct.To learn more about Triangles refer to:
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Find the median number of points.
4
5
5
8
8
8
9
12
13
Answer:
8
Step-by-step explanation:
Hello, no worries! It's a pleasure to meet and help you out today.
Median refers to the number that is in the middle of a data set.
The data set you provided has the numbers listed in order, which is great! However, if it's not listed in order, then you must list it in order by yourself.
Data Set: 4, 5, 5, 8, 8, 8, 9, 12, 13
As I said previously, we must find the middle value in the data set.
Data Set: 4, 5, 5, 8, 8, 8, 9, 12, 13
Clearly, the middle value in the data set is 8, so that's the median.
I hope my work has helped you in a way, and I wish you the best of luck with the rest of your assignment! (:
(p+2) is a factor of (3p^3-4p^2-13p+14)
Answer:
true
Step-by-step explanation:
3p^3-4p^2-13p+14 = (p-1)(3p-7)(p+2)
The sides of a triangle are 7 cm, 18 cm, and 16 cm. Find the length of the longest side of a similar triangle whose shortest side is 14.7 cm.
The longest side of the other triangle is 37.8 cm
How to determine the longest side of the other triangle?From the question, the sides of the triangle are given as
Sides of a triangle = 7 cm, 18 cm, and 16 cmThe shortest side on a similar triangle is 14.7 cm.This means that
Ratio = Corresponding sides of the triangles
So, we have
Ratio = Longest sides : Shorters sides
Substitute the known values in the above equation
So, we have the following equation
18 : 7 = Longest side : 14.7
Multiply 18 : 7 by 2.1
So, we have
37.8 : 14.7 = Longest side : 14.7
So, we have
Longest side = 37.8
Hence, the longest side is 37.8 cm
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How do yu solve this problem right here 25m^2 - 17= -1
Answer:
The answer will be 4/5
Step-by-step explanation:
25m^2-17=-1
25m^2=-1+71
√25m^2=√16
5m=4
m=4/5
Find the quotient of
30 x 10-24
5x10-24
Write the final answer in scientific notation.
Answer: The quotient of (30 x 10^-24)/(5 x 10^-24) is 6, which means that in scientific notation, it’s written as 6 x 10^0.
- Without looking, Jeff threw a small beanbag on a target with a radius of 20 cm. Adiagram of the target is shown below.10 cm 10 cmcIf the beanbag lands on the target, what is the probability it will land on the shadedarea?
To find the probability, we will need to first find the area of the whole circle and the area of the shaded part.
Area of the Big Circle
Given that the radius, R, is 20cm, the area is
[tex]\begin{gathered} A=\pi R^2 \\ =\pi\times20^2 \\ =400\pi \end{gathered}[/tex]Area of the Shaded Part
We can find the area of the shaded part by calculating the area of the small circle (r = 10cm) and subtract it from the big circle.
Hence
[tex]\begin{gathered} a=\pi r^2 \\ a=\pi\times10^2 \\ a=100\pi \end{gathered}[/tex]The area of the shaded portion is
[tex]\begin{gathered} A_s=A-a \\ A_s=400\pi-100\pi \\ A_s=300\pi \end{gathered}[/tex]Probability of landing on the shaded portion:
The probability is calculated by
[tex]\begin{gathered} P(A_s)=\frac{A_s}{A} \\ =\frac{300\pi}{400\pi} \\ P(A_s)=\frac{3}{4} \end{gathered}[/tex]Therefore, the probability that the ball will land on the shaded area is 3/4.
The FOURTH OPTION is correct.
Graph the equation y-2=1/5(x-5)
The points to be graphed are (0, 1) and (-0.2, 0). The graph of the equation is shown in the attached image
How to graph the equation of a line?
Given y-2=1/5(x-5)
In order to graph the equation of the line:
First, find the value of x when y = 0:
y-2=1/5(x-5), when y = 0:
0 -2 = 1/5(x-5)
-2 = 1/5x - 1
1/5x = -2 + 1
1/5x = -1
-5x = 1
x = -1/5 = -0.2
Also, find the value of y when x = 0:
y-2= 1/5(x-5), when x = 0:
y-2= 1/5(0-5)
y-2 = 1/5(-5)
y-2 = -1
y = 1
Therefore, the values to be plotted on our graph are (0, 1) and (-0.2, 0). The image of the graph is attached
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this is due now pls explain how u got the anser
Answer:
The correct answer is C.
Step-by-step explanation:
I got the answer by plotting the points on a graph. Then count how many places you have to go from one point to the other to find the slope. To find the y - intercept, look at where the point passes or is on the y-intercept. Sorry if this isn't a good explanation.
What is the slope of the linear relationship shown on the graph?
4/3
-4/3
3/4
-3/4
The slope of the linear graph is - 4 / 3.
How to find the slope of a linear graph?The slope of a linear graph is the change in the dependent variable with respect tot he change in the independent variable.
The slope is describe as rise over run.
Therefore, the slope can be represented mathematically, as follows;
Hence,
slope = y₂ - y₁ / x₂ - x₁
Therefore, using (0, -2) and (- 3 / 2, 0)
x₁ = 0
x₂ = - 3 / 2
y₁ = - 2
y₂ = 0
Therefore,
slope = 0 + 2 / - 3 / 2 - 0
slope = 2 ÷ - 3 / 2
slope = 2 × 2 / -3
Therefore,
slope = - 4 / 3
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Yessenia works at The Buckle. She earns $350 per week plus 3% commission on her sales. If Yessenia sells $8,500 worth of clothing this week,
what would her hourly rate be if she worked 40 hours?
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
The total amount earned in a week including the commission is $605 working for 40 hours.
The hourly rate is $15.125.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
The amount earned in a week = $350
Amount earned in commission = 3% of $8,500
= 3% of 8500
= 3/100 x 8500
= 3 x 85
= $255
The number of hours worked = 40 hours.
The hourly rate for the week:
= (350 + 255) / 40
= 605 / 40
= $15.125
Thus,
The hourly rate is $15.125.
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