Answer:
1800
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = - 27 and d = 6, thus
[tex]S_{30}[/tex] = [tex]\frac{30}{2}[/tex] [ (2 × - 27) + (29 × 6) ]
= 15( - 54 + 174)
= 15(120)
= 1800
The sum of the first 30 terms of the arithmetic sequence, is 1800.
In an arithmetic sequence, the sum of the first n terms can be calculated using the formula:
Sum = n/2 × (2a + (n-1)d), where:
n is the number of termsa is the first termd is the common differenceGiven:
First term (a) = -27Common difference (d) = 6Number of terms (n) = 30Plugging in these values, we get:
Sum = 30/2 × (2(-27) + (30-1) × 6)
Calculating step-by-step:
Calculate the first part: 30/2 = 15Calculate inside the parentheses: 2(-27) + (30-1)6 = -54 + 29*629 × 6 = 174-54 + 174 = 120Final calculation: 15 × 120 = 1800Therefore, the sum of the first 30 terms of the arithmetic sequence is 1800.
At the park there is a pool shaped like a circle with diameter 22 yd. A ring-shaped path goes around the pool. Its width is 6 yd.
We are going to give a new layer of coating to the path. If one gallon of coating can cover 5 yd", how many gallons of coating do we need? Note that coating
comes only by the gallon, so the number of gallons must be a whole number. (Use the value 3.14 for n).
Answer:
106 gal
Step-by-step explanation:
step 1
Find the area of the path
we know that
The area of the path is given by the formula
[tex]A=\pi r_2^{2} -\pi r_1^{2}[/tex]
[tex]A=\pi [r_2^{2} -r_1^{2}][/tex]
where
r_2 is the radius of the pool plus the width of the path
r_1 is the radius of the pool
we have
[tex]r_1=22/2=11\ yd[/tex] ---> the radius is half the diameter
[tex]r_2=11+6=17\ yd[/tex]
substitute
[tex]A=\pi [17^{2}-11^{2}][/tex]
[tex]A=168\pi\ yd^2[/tex]
assume
[tex]\pi =3.14[/tex]
[tex]A=168(3.14)=527.52\ yd^2[/tex]
step 2
Find the gallons of coating needed
Divide the area of the path by 5
so
[tex]527.52/5=105.5\ gal[/tex]
Round up
therefore
106 gal
To calculate how many gallons of coating are needed, we find the area of the path by subtracting the area of the pool from the total area covered. This equals to 527.52 yd². As each gallon of coating covers 5 yd², we need 105.504 gallons. However, since the paint is sold in whole gallons, we round it up to 106 gallons.
Explanation:To determine how many gallons of coating are needed, we first need to calculate the area of the ring-shaped path around the pool.
The pool is a circle with a diameter of 22 yd, so its radius is 11 yd. The path is around this pool and has a width of 6 yd. Therefore, the outer radius of the path is 11yd (radius of pool) + 6yd (width of path)=17 yd. The area of a circle is given by the formula πr² where r is the radius and π is a constant, approximately equal to 3.14.
So, the area of the outer circle is 3.14 × (17 yd)² = 907.46 square yards, and the area of the inner circle (pool) is 3.14× (11 yd)² = 379.94 square yards. The area of the path is the difference of those two areas, 907.46 yd² - 379.94 yd² = 527.52 yd².
Since one gallon of the coating can cover 5 sq yd, the number of gallons required is the total area divided by the area that one gallon can cover, which is 527.52 yd² / 5 yd²/gallon = 105.504 gallons. Since paint comes in whole gallons, you'll need to round up to the next whole number, which is 106 gallons.
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A football field is 120 yards long by 53 yards wide if a player runs diagonally from one corner to the opposite corner. How far will they travel?
Answer: They will travel about 131.18 yards.
Step-by-step explanation:
Given : A football field is 120 yards long by 53 yards wide.
We know that a football field is rectangular in shape.
Each interior angle in a rectangle is a right angle.
Then, by Pythagoras theorem, we have
(Diagonal)² = (Length)² + (Width)²
If a player runs diagonally from one corner to the opposite corner, then the length of the diagonal is given by :-
[tex](\text{Diagonal})=\sqrt{(120)^2+(53)^2}\\\\\Rightarrow\ (\text{Diagonal})=\sqrt{14400+2809}\\\\\Rightarrow\ (\text{Diagonal})=\sqrt{17209}\\\\\Rightarrow\ (\text{Diagonal})=131.183078177\approx131.18\text{ yards}[/tex]
Hence, they will travel about 131.18 yards.
Final answer:
The distance a player would travel running diagonally across a football field that is 120 yards long and 53 yards wide is approximately 131.183 yards.
Explanation:
The student asked about the distance a player would travel if they ran diagonally from one corner to the opposite corner of a football field that is 120 yards long and 53 yards wide.
To solve this, we need to apply the Pythagorean theorem in which the length and width of the football field will be the legs of the right triangle and the diagonal the player runs will be the hypotenuse.
The formula for the Pythagorean theorem is a² + b² = c², where a and b are the lengths of the legs and c is the length of the hypotenuse.
Therefore, the calculation will be as follows:
(120 yd)² + (53 yd)² = c².
Simplifying,
14400 yd² + 2809 yd² = c².
Adding these together gives us 17209 yd², and taking the square root of that gives us the length of the diagonal, which is the distance the player will travel.
Thus, c = √17209 yd2 ≈ 131.183 yards.
About 53.6% of the students in class got an A. If 15 students got an A, how many students were in the class?
Answer:
Step-by-step explanation:
56.3% of the student got A
15 students got A
Then,
Let the total number of students be x
56.3% of x= got A
56.3/100 × x =15
0.563x=15
Then x=15/0.563
x=26.6
The number of students can't or be 26.6 so let approximate it
Then, x=27
Therefore 27students are in the class
Can anyone help me solve this?
Answer:
a- 16/100
b- 1/6
c- not sure
Step-by-step explanation:
What fractions are equivalent to 20/22
Answer:
10/11
Step-by-step explanation:
You can find this answer by dividing the top and bottom numbers by 2.
Final answer:
Equivalent fractions of 20/22 can be found by simplifying it to 10/11 or by scaling it up, such as 40/44 or 60/66, by multiplying the numerator and denominator by the same whole number.
Explanation:
To find fractions equivalent to 20/22, you can simplify or scale the fraction up by multiplying both the numerator and the denominator by the same nonzero whole number. An equivalent fraction is one that represents the same value when both the top number (numerator) and the bottom number (denominator) are multiplied or divided by the same value.
Simplifying 20/22 means finding the greatest common divisor of 20 and 22, which is 2. So, dividing both by 2, we get 10/11. To scale up, you can multiply both the numerator and the denominator by any nonzero whole number, such as 2, to get 40/44, or 3 to get 60/66, and so on. Each of these fractions represents the same part of a whole as 20/22.
G(F(x)) is always equal to F(G(x)).
O
A. True
OB. False
B. False
There are cases where this is not true, but if you want to prove that, you'll need to know what f and g are. For example, if f(x) = x - 3 and g(x) = x2, then f(g(x)) is not equal to g(f(x)) because
f(g(x)) = x2 - 3 and g(f(x)) = (x - 3)2. Those 2 functions are not the same because f(g(0)) = -3 ≠ 9 = g(f(0)).
What are the rules of functions?Function rules by equations | Algebra functions that match 1 variable to the other in a 2-variable equation. Functions are written using function notation. Create functions that match 1 variable to the another in a 2-variable equation.
What are some examples of mathematical functions?there are Some Examples of Functions
x2 (squaring) is the functionx3+1 is also a functionSine, Cosine or Tangent are functions used in trigonometryLearn more about functions here https://brainly.com/question/12431044
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how do I solve system of equations elimination method
Step-by-step explanation:
To Solve a System of Equations by EliminationTo Solve a System of Equations by EliminationWrite both equations in standard form. ...To Solve a System of Equations by EliminationWrite both equations in standard form. ...Make the coefficients of one variable opposites. ...To Solve a System of Equations by EliminationWrite both equations in standard form. ...Make the coefficients of one variable opposites. ...Add the equations resulting from Step 2 to eliminate one variable.To Solve a System of Equations by EliminationWrite both equations in standard form. ...Make the coefficients of one variable opposites. ...Add the equations resulting from Step 2 to eliminate one variable.Solve for the remaining variable.To Solve a System of Equations by EliminationWrite both equations in standard form. ...Make the coefficients of one variable opposites. ...Add the equations resulting from Step 2 to eliminate one variable.Solve for the remaining variable.Substitute the solution from Step 4 into one of the original equations.To Solve a System of Equations by EliminationWrite both equations in standard form. ...Make the coefficients of one variable opposites. ...Add the equations resulting from Step 2 to eliminate one variable.Solve for the remaining variable.Substitute the solution from Step 4 into one of the original equations.More items...explain why an inverse variation function is not the best model for the data set
Answer: The products of corresponding x- and y- values of an inverse variation function are constant.
As x increases, y also increases.
The product of coordinate pairs are not equal: (165) (198) = 32,670 and (170) (204) = 34,680.
Step-by-step explanation:
What is the radius of a sphere with the volume of 972pi mm
[tex]\large\text{Hey there!}[/tex]
[tex]\mathsf{The\ sphere\ formula\ is: \dfrac{4}{3}\pi\times r^3}[/tex]
[tex]\mathsf{Now, that\ we\ have\ our\ formula\ let's\ solve\ for\ the\ equation}[/tex]
[tex]\mathsf{So,\ first\ \bf{\underline{DIVIDE}}}\mathsf{\ both\ of\ your\ sides\ by\ \pi}[/tex]
[tex]\mathsf{\dfrac{4}{3}r^3=972}\\\\\rightarrow\ \mathsf{r^3=972\times\dfrac{3}{4}}\\\\\mathsf{972\times\dfrac{3}{4}=729}\\\\\mathsf{\rightarrow\ r^3=729}[/tex]
[tex]\mathsf{\sqrt[\mathsf{3}]{\mathsf{729}} = 81}\\\\\mathsf{\sqrt{81}=81\div9=9}\\\\\mathsf{\sqrt{81}=9}\\\\\mathsf{r=9}[/tex]
[tex]\boxed{\boxed{\mathsf{\bf{Answer: \boxed{\mathsf{radius = \bf{9}}}}}}}\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]
Find the approximate side length of a square game board with an area of 136in^2
Answer:
68in
Step-by-step explanation:
Divide the area by 2 because a= l x w and squares sides are all the same.
PLEASE MARK BRAINLIEST! :]To find the approximate side length of a square game board with an area of 136in^2, you can use the formula for the area of a square and take the square root of the given area. The approximate side length is 11.66 inches.
Explanation:To find the approximate side length of a square game board with an area of 136in2, we can use the formula for the area of a square, which is length * length. In this case, we need to find the square root of 136 to get the side length. The square root of 136 is approximately 11.66 inches.
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What is the equation of a circle with center (-3,-5) and radius 4?
O A. (x+3)2 + (y + 5)2 = 4
O B. (x-3)2 + (y- 5)2 = 16
O C. (x-3)2 + (y- 5)2 = 4
O D. (x + 3)2 + (y + 5)2 = 16
Answer: D) (x + 3)² + (y + 5)² = 16
Step-by-step explanation:
The equation of a circle is: (x - h)² + (y - k)² = r²
where (h, k) = center and r = radius
Given: (h, k) = (-3, -5) r = 4
Equation: (x - (-3))² + (y - (-5))² = 4²
(x + 3)² + (y + 5)² = 16
Tyree is determining the distance of a segment whose endpoints are A(–4, –2) and B(–7, –7).
Step 1: d = StartRoot (negative 7 minus (negative 7)) squared + (negative 4 minus (negative 2)) squared EndRoot
Step 2: d = StartRoot (negative 7 + 7) squared + (negative 4 + 2) squared EndRoot
Step 3: d = StartRoot (0) squared + (negative 2) squared EndRoot
Step 4: d = StartRoot 0 + 4 EndRoot
Step 5: d = StartRoot 4 EndRoot
Therefore, d = 2.
Which best describes the accuracy of Tyree’s solution?
Tyree’s solution is accurate.
Tyree’s solution is inaccurate. In step 1, he substituted incorrectly.
Tyree’s solution is inaccurate. In step 2, he simplified incorrectly.
Tyree’s solution is inaccurate. In step 3, he added incorrectly.
Answer:
Tyree’s solution is inaccurate. In step 1, he substituted incorrectly.
Step-by-step explanation:
to find the distance between two point A(-4, -2) and B(-7, -7) we use the following distance formula
[tex]d=\sqrt{(x_{2} -x_{1})^2+(y_{2}-y_{1} )^2 \\\\[/tex]
x1=-4, x2=-7
y1=-2, y2=-7
so,
[tex]d=\sqrt{(-7-(-4))^2+(-7-(-2) )^2\\}\\\\d=\sqrt{(-7+4)^2+(-7+2)^2 }\\\\d=\sqrt{(-3)^2+(-5)^2 }\\\\\\\\d=\sqrt{9+25}\\ \\d=\sqrt{34}[/tex]
Answer:
Tyree’s solution is inaccurate. In step 1, he substituted incorrectly.
Explanation:
I got it right,
Hope this Helps!
Select all that apply.
What types of triangles have at least two acute angles?
right
obtuse
equilateral
isosceles
Answer:
Step-by-step explanation:
An obtuse triangle must contain an obtuse angle and two acute angles. An equilateral triangle must be 60 degrees in every corner, and thus there are 2+ acute angles. An isosceles triangle can have two angles that are 30 degrees (thus two acute), and a 120 degree angle
Which system of equations could be used to solve for the point of intersection of the lines on the graph?
A)
y-2x+1 and - x+9
B)y=2x-1 and = x +9
C)y=xx-1 and 7x+9
D)y=-x-1 and - *+9
9
Answer:
[tex]y=\frac{3}{4}-1[/tex] and [tex]y=-\frac{4}{3}+9[/tex]
Step-by-step explanation:
step 1
Find the equation of the blue line
take the points
(0,-1) and (8,5) from the graph
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{5+1}{8-0}[/tex]
[tex]m=\frac{6}{8}[/tex]
simplify
[tex]m=\frac{3}{4}[/tex]
Find the equation of the line in slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=\frac{3}{4}[/tex]
[tex]b=-1[/tex] ---> see the graph
substitute the given values
[tex]y=\frac{3}{4}-1[/tex]
step 2
Find the equation of the black line
take the points
(0,9) and (3,5) from the graph
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{5-9}{3-0}[/tex]
[tex]m=-\frac{4}{3}[/tex]
Find the equation of the line in slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=-\frac{4}{3}[/tex]
[tex]b=9[/tex] ---> see the graph
substitute the given values
[tex]y=-\frac{4}{3}+9[/tex]
therefore
The system of equations is
[tex]y=\frac{3}{4}-1[/tex] and [tex]y=-\frac{4}{3}+9[/tex]
The equations of the blue and black lines are y = 3/4x - 1 and y = -4/3x + 9, respectively, based on their respective slopes and given points.
To find the equations of the blue and black lines, we start by determining their slopes using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on each line.
For the blue line:
Points: (0, -1) and (8, 5)
m = (5 - (-1)) / (8 - 0) = 6/8 = 3/4
Now, using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we substitute the slope m = 3/4 and the given point (0, -1):
y = 3/4x - 1
For the black line:
Points: (0, 9) and (3, 5)
m = (5 - 9) / (3 - 0) = -4/3
Substituting the slope m = -4/3 and the given point (0, 9) into the slope-intercept form, we get:
y = -4/3x + 9
Therefore, the system of equations representing the blue and black lines is:
y = 3/4x - 1
y = -4/3x + 9
The question probable may be:
Write system of equations could be used to solve for the point of intersection of the lines on the graph?
Elmer deposited $2250 into a savings account that pays annual simple interest at the end of seven years he earned $157.50 in interest what is the interest rate on a savings account round to the nearest 10th of a percent
Work Shown:
i = P*r*t
157.50 = 2250*r*7 ... plug in given values
157.50 = 2250*7*r
157.50 = 15750r
15750r = 157.50
r = 157.50/15750 ... divide both sides by 15750
r = 0.01
The interest rate is 1%
To go from 0.01 to 1%, you move the decimal point 2 spots to the right.
Alternatively, you would multiply by 100.
Answer:7%
Step-by-step explanation:
select the quadratic equation that has roots x=8 and x=-5
Step-by-step explanation:
Since, x=8 and x=-5 are the roots.
Therefore, (x - 8) & (x - 5) will be factors.
Hence, required quadratic equation can be given as:
[tex](x - 8)(x - 5) =0 \\ \\ \therefore {x}^{2} + ( - 8 - 5) x+ ( - 8) \times ( - 5) = 0 \\ \\ \therefore {x}^{2} + ( - 13) x+ 40= 0 \\ \\ \huge \red{ \boxed{ \therefore {x}^{2} - 13x+ 40= 0 }} \\ is \: the \: required \: quadratic \: equation.[/tex]
Hannah finds purple, blue, and silver space rocks while exploring.
2
3
of the rocks are purple and
3
4
of the remainder are blue. If there are 3 silver rocks, how many space rocks does Hannah have?
Answer:
There were 36 space rocks in total.
Write an equation in slope intercept form of the line that passes through (-1,2) and has a slope of 1/2.
Answer:
[tex]y=\frac{1}{2} x+2.5[/tex]
Step-by-step explanation:
I graphed the equation on the graph below.
If this answer is correct, please make me Brainliest!
If X || Y and Y || Z, then _____
A) A || B
B) X || Z
C) X⊥A
D) A⊥Z
Answer:
B) X || Z
Step-by-step explanation:
Hope it helps you in your learning process.
What is the measure of minor arc BD?
Angle BCD is a circumscribed angle of circle A. Angle BCA
measures 40°
B
40°
© 50°
80°
100°
Answer:
[tex]minor\ arc\ BD=100^o[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
we know that
A circumscribed angle is the angle made by two intersecting tangent lines to a circle
so
In this problem
BC and CD are tangents to the circle
BC=CD ----> by the Two Tangent Theorem
That means
Triangle ABC and Triangle ADC are congruent
so
[tex]m\angle BAC=m\angle DAC[/tex]
Find the measure of angle BAC
In the right triangle ABC
[tex]m\angle BAC+m\angle BCA=90^o[/tex]
substitute given value
[tex]m\angle BAC+40^o=90^o[/tex]
[tex]m\angle BAC=90^o-40^o=50^o[/tex]
Find the measure of angle BAD
[tex]m\angle BAD=2m\angle BAC[/tex]
[tex]m\angle BAD=2(50^o)=100^o[/tex]
Find the measure of minor arc BD
we know that
[tex]minor\ arc\ BD=m\angle BAD[/tex] -----> by central angle
therefore
[tex]minor\ arc\ BD=100^o[/tex]
Final answer:
The measure of the minor arc BD is d. 80°, because it is twice the measure of the inscribed angle BCA, which is 40°.
Explanation:
When we are looking for the measure of a minor arc in a circle, and we know the measure of the inscribed angle that subtends that arc, we can find the measure of the arc by understanding that the inscribed angle is half the measure of the arc it cuts from the circle. Given that angle BCA measures 40°, and assuming BCD is an inscribed angle that subtends the arc BD, we can deduce that the minor arc BD is actually twice the measure of the inscribed angle BCA.
Therefore, to find the measure of minor arc BD, we double the measure of angle BCA:
Measure of minor arc BD = 2 × measure of angle BCA
Measure of minor arc BD = 2 × 40°
Measure of minor arc BD = 80° (d.)
Need help with this ASAP!! Will award brainliest to answer with steps!! Anthony has a sink that is shaped like a half-sphere. The sink is 660pi in.^3. One day his sink clogged. He has to use one of two cylindrical cups to scoop the water out of the sink. The sink is completely full when he begins scooping.
Answer:
part a) 13 scoops
part b) 3 scoops
Step-by-step explanation:
1) so we know that the volume of the sink is 660pi in^3
we have to divide this with the volume of each cup to find out the number of scoops it takes to get all the water out.
since we are dividing, I don't like leaving answers in terms of pi so
660*pi= 2073.45115137
formula for volume of cylinder(diameter) [tex]pi(\frac{d}{2} )^2 h[/tex]
pi*(5/2)^2*h=157.079632679
so
2073.45115137/157.079632679= 13.2 - for cup 1
for cup 2:
pi*(10/2)^2*8= 628.318530718
so
2073.45115137/628.318530718= 3.3- for cup 2
Hope this helps!
Deon estimated the length of a room is his house to be 13 ft. The actual length of the room is 11 ft.
Find the absolute error and the percent error of Deon's estimate. If necessary, round your answers to the nearest tenth.
absolute error = [lt
The absolute error is 2 feet and percent error is 18.18%
Step-by-step explanation:
Given,
Estimated length = 13 feet
Actual length = 11 feet
Absolute error = Estimated length - Actual length
Absolute error = 11 - 13 = -2 feet
Absolute error = 2 feet
Percent error = [tex]\frac{Absolute\ error}{Exact\ value}*100[/tex]
Percent error = [tex]\frac{2}{11}*100[/tex]
Percent error = [tex]\frac{200}{11}=18.18 \%[/tex]
The absolute error is 2 feet and percent error is 18.18%
The absolute error is 2 feet and the percent error is approximately 18.2%
Explanation:The absolute error in Deon's estimate can be found by subtracting the actual value from the estimated value and taking the absolute value. So that's |13 - 11| which equals 2 feet.
The percent error can be found by dividing the absolute error by the actual value and then multiplying by 100 to convert it into a percentage. That's (2 / 11) * 100 which equals approximately 18.2%. If we round to the nearest tenth, we get 18.2%.
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I Need help Asap no decimal please just plot the point!
Step-by-step explanation:
if you see the number the line is divided into 6 or to get from 0 to 1 or 2 to 3 it takes 6 space that means the fraction should n/6.
n= a number
2 5/6 that means that there is 2 wholes or 2 6/6
6/6= 1
it is easy to plot 2 5/6 because it is already 5/6, you plot it right on the line that is before 3 or 5 spaces after 2.
1 2/3 is the same as 1 4/6
there is 1 whole or one 6/6. now it is easy you plot it on the line that is 4 spaces away from 1.
Plotted the points on the line. Please see attached.
2 5/6 = 17/6 = 2.83
1 2/3 = 5/3 = 1.67
Find the surface area, will give Brainliest
Answer:
96 units^2
Step-by-step explanation:
Base: 6 × 6 = 36
Faces: 5 × 6 = 30 (×2 = 60)
Add: 36 + 60 = 96
Answer:
96 units^2
Step-by-step explanation:
The Base: 6 × 6 = 36
The Faces: 5 × 6 = 30 (×2 = 60)
Then Add: 36 + 60 = 96
Hope to help.
isolate the variables of 110=m+95
Answer:
15
Step-by-step explanation:
To isolate the variable, subtract 95 on both sides.
110=m + 95
m=15
Hope this helped! :)
Answer:
m=15
Step-by-step explanation:
110=m+95
Just subtract 95 from each side to isolate m and get your answer
110=m+95
-95 -95
15=m
30 out of 40 is equal to what percent
Answer:
%75
Step-by-step explanation:
30/40 is equal to 0.75
0.75 is also %75
Answer: %75
| If f(x) = 7 + 4x and g(x)= 7, what is the value of (f/g)(5)
Answer:
27/7.
Step-by-step explanation:
(f/g)x = (7 + 4x) / 7
(f/g)(5) = (7 + 4(5)/ 7
= 27/7.
Yo sup??
f(x)=7+4x
g(x)=7
f/g(5)
=7+4*5/7
=27/7
Hope this helps
x2 - 6x + 12 and y = 2x - 4, algebraically are
The first two steps in determining the solution set of the system of equation
shown in the table.
Step
Step 1
Step 2
Equation
x² - 6x + 12 = 2x - 4
x2-8x+16=0
Which represents the solution(s) of this system of equations?
(4.4)
(-4,-12)
(4.4) and (-4, 12)
(-4, 4) and (4, 12)
Answer:
its A (4,4)
Step-by-step explanation:
The solution of the system y = x² - 6x + 12 and y = 2x - 4 is (4, 4).
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, y = x² - 6x + 12 and y = 2x - 4.
∴ The solution set of this system is,
x² - 6x + 12 = 2x - 4.
x² - 8x + 16 = 0.
x² - 4x - 4x + 16 = 0.
x(x - 4) - 4(x - 4) = 0.
(x - 4)(x - 4) = 0.
x - 4 = 0 Or x - 4 = 0.
x = 4 Or x = 4.
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37.5% of what number is 6
To find the number that 37.5% of it equals 6, set up an equivalent fractions equation, cross-multiply, and solve for the unknown number. In this case, 37.5% of 16 is 6.
Explanation:The question pertains to finding a certain number when given a percentage of that number. Here, we're asked to find the number of which '37.5% is 6'. We can solve this through simple arithmetic and the use of equivalent fractions. An important rule to remember is that 'percentage' literally means 'per 100', so 37.5% can be written as the fraction 37.5/100.
To find the unknown number (let's call it X), you can set up the equation 37.5/100 = 6/x, where 'x' is the number we're trying to find. Then you cross-multiply to solve for 'x': 37.5 * X = 6 * 100. Simplifying this, X = (6 * 100) / 37.5. Calculating that out gives X = 16. Therefore, 37.5% of 16 is 6.
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The value of the unknown number whose 37.5 percent equals 6 is 16.
What number does its 37.5% gives 6?Given the parameter:
37.5% of what number is 6
The problem is asking for 37.5% of some unknown number which gives 6.
We can represent the unknown number as x.
Now, the equation to find the unknown number will be:
37.5% of x = 6
Replace 37.5% with 37.5/100:
37.5/100 of x = 6
37.5/100 × x = 6
Solve for x:
0.375 × x = 6
0.375x = 6
Divide both sides by 6:
x = 6/0.375
x = 16
Therefore, the value of the number is 16.
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Identify the property used in each step of solving the inequality 3x-2>-4.
Addition property of equality
Division property of equality
Solution:
Given inequality is:
3x - 2 > 4
[tex]\mathrm{Add\:}2\mathrm{\:to\:both\:sides}[/tex]
Here, Addition property of equality is used
When the same amount is added to both sides of an inequality, then the inequality is still true
3x - 2 + 2 > 4 + 2
3x > 6
[tex]\mathrm{Divide\:both\:sides\:by\:}3[/tex]
Here, Division property of equality is used
When we divide both sides of an equation by the same nonzero number, the sides remain equal.
[tex]\frac{3x}{3}>\frac{6}{3}\\\\x > 2[/tex]
Thus the property used in each step of solving the inequality is found