Area of a circle:
[tex]A=\pi r^2[/tex] "r" is the radius
Since you know [tex]A=196\pi[/tex] in², you can plug (196[tex]\pi[/tex]) for "A" in the equation
[tex]A=\pi r^2[/tex]
[tex]196\pi=\pi r^2[/tex] Divide pi on both sides
196 = r² Square root both sides
14 = r
The exact length of the circle's radius is 14 inches.
The formula to calculate the area (A) of a circle is given by:
[tex]A = π * r^2[/tex]
where "r" is the radius of the circle.
In this case, we are given that the area of the circle is 196π square inches. So we can set up the equation:
196π = π * [tex]r^2[/tex]
To find the radius (r), divide both sides of the equation by π:
[tex]r^2[/tex] = 196
Now, solve for the radius:
r = √196
r = 14
Therefore, the exact length of the circle's radius is 14 inches.
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A motorist traveled 250 miles on 11 gallons of gas. With the same vehicle, about how far could he go on 16 gallons of gas? Round to the nearest tenth.
Answer:
363.6
Step-by-step explanation:
250/11= 22.72
22.72 x 16= 363.3636
when rounded tot he nearest tenth its 363.6 because the three is less than five and cannot bump up the 6
if possible make my answer the brainliest
Ann is surveying people in the city about their interest in a new shopping mall. She found that 180 people or 37.5% of those who surveyed do not want a new shopping mall. How many people did Annette survey
Answer:
480
Step-by-step explanation:
Divide 100 by 37.5
Multiply 180 by that number
100/37.5=2.667'
180*2.667=480
Anne surveyed 480 people.
write the slope-intercept form of the equation of the line described.
through:(-2,-4), perpendicular to y=2x+5
Answer:
Find the negative reciprocal of the slope of the original line and use the slope-intercept form
y=mx+b to find the line perpendicular to [tex]y=2x+5[/tex].
[tex]y=−12x−5[/tex]
Hope this helps!!
[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\\text{We have}\ k:y=2x+5\to m_1=2.\\\\l:y=mx+b\to m=-\dfrac{1}{2}\to y=-\dfrac{1}{2}x+b.\\\\\text{The line passes through the point (-2, -4).}\ \text{Put the coordinates to the equation:}\\\\-4=-\dfrac{1}{2}(-2)+b\\\\-4=1+b\qquad\text{subtract 1 from both sides}\\\\-5=b\to b=-5\\\\Answer:\ \boxed{y=-\dfrac{1}{2}x-5}[/tex]
A line passes through (3, -2) and (6, 2). a. Write an equation for the line in point-slope form. b. Rewrite the equation in standard form using integers
Answer:
(a)
Given: A line passes through the points (3, -2) and (6, 2)
Point slope form: An equation of line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by:
[tex]y -y_1=m(x-x_1`)[/tex] .....[1] where m is the slope of the line.
Calculate first the slope of the line:
Slope(m) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given points;
[tex]m = \frac{2-(-2)}{6-3}=\frac{2+2}{3} =\frac{4}{3}[/tex]
Substitute the value of m in [1] ;
[tex]y - (-2) = \frac{4}{3}(x-3)[/tex]
[tex]y+2=\frac{4}{3}(x-3)[/tex] ......[1]
therefore, the equation of line in point slope form is, [tex]y+2=\frac{4}{3}(x-3)[/tex]
(b)
to find the standard form of the equation [1]
Multiply both sides by 3 in [1] we get;
[tex]3(y+2) = 4(x-3)[/tex]
using distributive property; [tex]a\cdot (b+c) = a\cdot b + a\cdot c[/tex]
3y + 6 = 4x -12
Subtract 3y to both sides we get;
3y + 6 -3y = 4x - 12 - 3y
Simplify:
6 = 4x - 3y -12
Subtract 6 from both sides we get;
0 = 4x - 3y -12-6
Simplify:
4x - 3y - 18 =0
Therefore, the standard form of the equation is; 4x - 3y - 18 =0
What monomial do you have to raise to the power of 2 to get the given monomial? What monomial do you have to raise to the power of 3 for this? a x6y12
When raising a monomial to a power, you multiply the exponents of each variable by that power.
Explanation:When you raise a monomial to the power of 2, you multiply the exponents of each variable by 2. So in the given monomial ax6y12, you would raise each exponent to the power of 2 to get a2x12y24.
Similarly, when you raise a monomial to the power of 3, you multiply the exponents of each variable by 3. So in the given monomial ax6y12, you would raise each exponent to the power of 3 to get a3x18y36.
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a proportional relationship is represented by the equation 2x=18y . If y=x , where k is the constant of proportionality, then what is the value of k.
Answer: [tex]\bold{k=\dfrac{1}{9}}[/tex]
Step-by-step explanation:
The constant of proportionality is y = kx. Solve the given equation for "y" to find k-value in front of "x".
18y = 2x
[tex]\dfrac{18y}{18}=\dfrac{2x}{18}[/tex]
[tex]y=\dfrac{1}{9}x[/tex]
[tex]k=\dfrac{1}{9}[/tex]
properties of isoceles trapezoids??
Answer:
Parallel bases.
The legs are congruent by definition.
The lower base angles are congruent.
The upper base angles are congruent.
Any lower base angle is supplementary to any upper base angle.
The diagonals are congruent.
Step-by-step explanation:
identify the slope x + y= -3 solve for b
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
x + y = -3 subtract x from both sides
y = -x - 3
slope = -1Karin wants to use the distributive property to mentally find the value of 19 x 42+ 19x 58. Which expression can she use?
19 x (42 + 58) or 19*(42 + 58) is the expression she can use. You factor out the common term 19. The distributive rule says that we can multiply the outer 19 with each term inside to get the original expression again.
a. 0.98 – 0.053 b. 0.67 – 0.4 c. 0.3 – 0.002 d. 3.2 – .789 e. 6.53 – 4.298 f. 6 – 4.32 g. 7 – 3.574 h. 4.83 – 1.8 i. 3.7 – 1.8 j. 16.17 – 11.632
a. 0.927
We have:
0.98 – 0.053
We can re-write it as:
0. 9 8 0 -
0. 0 5 3
Moving digits to the right:
0. 9 7 10 -
0. 0 5 3
Digit-per-digit subtraction:
0. 9 2 7
b. 0.27
We have:
0.67 – 0.4
We can re-write it as:
0. 6 7 -
0. 4 0
Digit-per-digit subtraction:
0. 2 7
c. 0.298
We have:
0.3 – 0.002
We can re-write it as:
0. 3 0 0 -
0. 0 0 2
Moving digits to the right:
0. 2 10 0 -
0. 0 0 2
Again:
0. 2 9 10 -
0. 0 0 2
Digit-per-digit subtraction:
0. 2 9 8
d. 2.411
We have:
3.2 – .789
We can re-write it as:
3. 2 0 0 -
0. 7 8 9
We need to rewrite the first term by moving digits to the right several times:
3. 2 0 0 = 2. 12 0 0 = 2. 11 10 0 = 2. 11 9 10
So now we have:
2. 11 9 10 -
0. 7 8 9
Digit-per-digit subtraction:
2. 4 1 1
e. 2.232
We have:
6.53 – 4.298
We can re-write it as:
6. 5 3 0 -
4. 2 9 8
We need to rewrite the first term by moving digits to the right several times:
6. 5 3 0 = 6. 5 2 10 = 6. 4 12 10
So now we have:
6. 4 12 10 -
4. 2 9 8
Digit-per-digit subtraction:
2. 2 3 2
f. 1.68
We have:
6 – 4.32
We can re-write it as:
6. 0 0 -
4. 3 2
We need to rewrite the first term by moving digits to the right several times:
6. 0 0 = 5. 10 0 = 5. 9 10
So now we have:
5. 9 10 -
4. 3 2
Digit-per-digit subtraction:
1. 6 8
g. 4.426
We have:
7 – 3.574
We can re-write it as:
7. 0 0 0 -
3. 5 7 4
We need to rewrite the first term by moving digits to the right several times:
7. 0 0 0 = 6. 10 0 0 = 6. 9 10 0 = 6. 9 9 10
So now we have:
6. 9 9 10 -
3. 5 7 4 =
Digit-per-digit subtraction:
3. 4 2 6
h. 3.03
We have:
4.83 – 1.8
We can re-write it as:
4. 8 3 -
1. 8 0
We can immediately do the digit-per-digit subtraction:
3. 0 3
i. 2.9
We have:
3.7 – 1.8
We can re-write it as:
3. 7 -
1. 8
We need to rewrite the first term by moving digits to the right:
3. 7 = 2. 17
So now we have:
2. 17 -
1. 8 =
Digit-per-digit subtraction:
2. 9
j. 4.538
We have:
16.17 – 11.632
We can re-write it as:
1 6 . 1 7 0 -
1 1 . 6 3 2
We need to rewrite the first term by moving digits to the right:
1 6. 1 7 0 = 1 6. 1 6 10 = 1 5. 11 6 10
So now we have:
1 5. 11 6 10 -
1 1. 6 3 2 =
Digit-per-digit subtraction:
0 4. 5 3 8
Analyze the reflectional symmetry of the regular polygons. The square has -fold reflectional symmetry. The regular octagon has -fold reflectional symmetry.
Answer:
The square has 4-fold reflectional symmetry. The regular octagon has 8-fold symmetry.
Step-by-step explanation:
For a square,
There are two lines of symmetry along two diagonals and
two lines of symmetry along midpoints of two pairs of opposite sides.
Therefore, there are 4 lines of reflectional symmetry in total.
For a regular octagon,
There are four lines of symmetry along four diagonals and
four lines of symmetry along midpoints of four pairs of opposite sides.
Therefore, there are 8 lines of reflectional symmetry in total.
Final answer:
A square has 4-fold reflectional symmetry, while a regular octagon has 8-fold reflectional symmetry.
Explanation:
Reflectional symmetry refers to a property of a shape where it can be divided into two mirror-image halves. The -fold reflectional symmetry of a regular polygon refers to the number of lines of symmetry it possesses. A line of symmetry is an imaginary line that divides the shape into two equal halves that are mirror images of each other.
For example, a square has 4-fold reflectional symmetry because it has 4 lines of symmetry, dividing it into 4 equal halves. Each line of symmetry passes through the midpoints of opposite sides.
On the other hand, a regular octagon has 8-fold reflectional symmetry because it has 8 lines of symmetry, dividing it into 8 equal halves. Each line of symmetry passes through the midpoints of opposite sides or vertices.
please help!! Which shape is a continuous line of equal distance from its center?
Answer: I know it’s a circle but I forget why actually sorry that doesn’t help much
Step-by-step explanation:
Which reason justifies the statement below
“If CD = EF, then CD = EF”
A. Defintion of congruence B. Reflexie property C. Symmetric property D. Definition of midpoint
The reflexive property justifies the statement "If CD = EF, then CD = EF".
Explanation:The reason that justifies the statement "If CD = EF, then CD = EF" is the reflexive property.
The reflexive property states that any geometric shape or object is always equal to itself. In this case, CD is equal to itself, and EF is equal to itself, so if CD = EF, then CD will always be equal to EF.
Therefore, option B, the reflexive property, is the correct reason for the given statement.
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the sum of two numbers is 17 and their difference is 29 what are the two numbers
Answer:
According to the question,
Numbers are : 23 and -6
The two numbers are -6 and 23.
To find the two numbers, we can set up a system of equations based on the given information. Let the two numbers be [tex]\( x \) and \( y \), where \( x > y \)[/tex]. According to the problem, we have:
1. The sum of the two numbers is 17:
[tex]\[ x + y = 17 \][/tex]
2. The difference between the two numbers is 29:
[tex]\[ x - y = 29 \][/tex]
Now, we can solve this system of equations. We can add the two equations together to eliminate [tex]\( y \)[/tex] :
[tex]\[ (x + y) + (x - y) = 17 + 29 \] \[ 2x = 46 \] \[ x = \frac{46}{2} \] \[ x = 23 \][/tex]
Now that we have the value of [tex]\( x \)[/tex], we can substitute it back into one of the original equations to find [tex]\( y \)[/tex]. Let's use the first equation:
[tex]\[ 23 + y = 17 \] \[ y = 17 - 23 \] \[ y = -6 \][/tex]
Therefore, the two numbers are 23 and -6.
Point A lies on the circle and has an x-coordinate of 3.
Answer:
y = √7
Step-by-step explanation:
This circle has a center at (0,0) and a radius of 4 so its equation is:-
x^2 + y^2 = 16
when x= -3, (-3)^2 + y^2 = 16
9 + y^2 = 16
y^2 = 7
y = √7
what is the volume of this cuboid?
Please help me!!!?!
The formula of a volume of a cuboid:
[tex]V=lwh[/tex]
l - length
w - width
h - height
We have:
l = (x + 4) cm
w = (x + 1) cm
h = 3 cm
Substitute:
[tex]V=(x+4)(x+1)(3)[/tex] use distributive property
[tex]V=(x+4)(3x+3)[/tex]
[tex]V=(x)(3x)+(x)(3)+(4)(3x)+(4)(3)[/tex]
[tex]V=3x^2+3x+12x+12[/tex] combine like terms
[tex]\boxed{V=3x^2+15x+12}[/tex]
f(x)=-x^2+1 find f(-3)
Answer:
-8
Step-by-step explanation:
All you have to do to solve this equation is plug "-3" into the equation where you see "x"
[tex]f(x)=-x^2+1\\f(-3)=-(-3)^2+1\\f(-3)=-(9)+1\\f(-3)=-9+1\\f(-3)=-8[/tex]
I need help could you please help me
Item 1 Solve the system of linear equations by graphing. 5x+5y=15 2x−2y=10
After graphing both lines, we're able to tell the solution by looking at the point where the lines cross. In this case, it's at (4, -1). And so that is the solution set.
What is the value of 1/2 divided by 3/5
Answer:
5/6
Step-by-step explanation:
1/2 / 3/5
1/2*5/3
5/6
Answer:
5/6
Step-by-step explanation:
1/2 ÷ 3/5
Copy dot flip
1/2 * 5/3
5/6
Solve for y in terms of x.
2/3y - 4 = x
y = x + 6
y = -x + 4
y = -x + 6
y = x + 4
Answer:
[tex]y=\frac{3}{2} x+6[/tex]
Step-by-step explanation:
We are given the following equation and we are supposed to solve y in terms of x. It simpler terms, it means that we have to make y the subject of the equation while x being used in it as it is:
[tex]\frac{2}{3} y-4=x[/tex]
Taking the constant 4 to the side where x is to get:
[tex]\frac{2}{3} y=x+4[/tex]
Multiplying the denominator 3 to the other side of the equation to get:
[tex]2y=3x+12[/tex]
Isolating y to make it the subject:
[tex]y=\frac{3}{2} x+\frac{12}{2}\\ \\y=\frac{3}{2} x+6[/tex]
what is the importance of the quadratic formula?
Answer:
It solves all quadratic equations for any real or imaginary solutions.
Step-by-step explanation:
The quadratic formula is
[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex].
It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions.
Threeangles of a quadrilateral are equal and its fourth angel is 120° . Find all the angels
Answer:
80°
Step-by-step explanation:
Three angles are equal
Let the equal angle be x
3x+120=360
3x=240
x=240/3
=80
Hence the three angles are 80∘
Answer:
Each of the three congruent angles has measure 80 deg. The fourth angle has measure 120 deg.
Step-by-step explanation:
The sum of the measures of the angles of an n-sided polygon is (n - 2)180.
A quadrilateral has 4 sides, so n = 4 in the formula above.
(n - 2)180 = (4 - 2)180 = 2(180) = 360
The sum of the measures of the angles of a quadrilateral is 360 degrees.
Three angles are congruent. Let the measures of the three congruent angles be x. The sum of the measures of the 3 angles is x + x + x = 3x.
The sum of the measures of the angles is 360 deg.
3x + 120 = 360
Subtract 120 from both sides.
3x = 240
Divide both sides by 3.
x = 80
Answer: Each of the three congruent angles has measure 80 deg. The fourth angle has measure 120 deg.
Which is equivalent to (-2ab^3) (-3a^2b^5)
Answer:
6 a^3 b^8
Hope That Helps!
What is the equation of the line that passes through the points (-3,2) and (-5,8)
Answer:
y = -3x - 7
Step-by-step explanation:
Slope = (8 - 2)/(-5 + 3) = 6/-2 = -3
Equation
y - 2 = - 3(x + 3)
y - 2 = -3x - 9
y = -3x - 7
Answer
y=-3x-7
is the equation of line that passes through the points (-3,2) and (-5,8)
step by step explanation:
we are given
(x1,y1)=(-3,2)
(x2,y2)=(-5,8)
formula of slope
m=(y2-y1 )/ (x2-x1)
putting value in formula
m=(8-2) /-5-(-3)
m=6/-5+3
m=6/-2
m=-3
Formula of line slop form of equation is
y-y1=m(x-x1)
putting the values in the formula
y-2= -3(x-(-3))
y-2= -3(x+3)
y-2=-3x-9
y=-3x-9+2
y=-3x-7
is the equation of line that passes through the points (-3,2) and (-5,8)
6 painters can paint the fence in 15 hours. How long would it take 5 workers to do the same job? 12.5 is not the right answer
Answer:
It will take them 18 hours.
Step-by-step explanation:
To find the answer of this, you must first multiply the amount of people by the time:
6 * 15 = 90
Then to find the time it takes 5 workers, divide this by 5:
90 ÷ 5 = 18
So it will take them 18 hours!
A jar contains 133 pennies. A bigger jar contains 1 2/7 times as many pennies. What is 5he value of the pennies in the bigger jar
Answer:
The Jar contained 5^67 pennis of nickels and quaters. Making a lot of money in 1/4 of a month. The 5he value of the pennies in the bigger than the amount of the total fitting of itself. The Largest pennies in the jar depended on the nickels and quaers inside. The 133 pennies wer the jar that contained the lesser amount of pennies, therfore the bigger jar standes with a larger value
Step-by-step explanation:
A rectangle has a length of 6 inches and a width of x inches. The value of the perimeter of the rectangle is equal to the value of the area of the rectangle. Graph a system of linear equations to find x .
The value of x is the point of intersection of the graphs of [tex]\mathbf{P =12 + 2x}[/tex] and [tex]\mathbf{A =6x}[/tex]
The value of x is 3
The given parameters are:
[tex]\mathbf{Length = 6}[/tex]
[tex]\mathbf{Width = x}[/tex]
The perimeter is calculated as:
[tex]\mathbf{P =2 \times (Length + Width)}[/tex]
So, we have:
[tex]\mathbf{P =2 \times (6 + x)}[/tex]
Expand
[tex]\mathbf{P =12 + 2x}[/tex]
The area is calculated as:
[tex]\mathbf{P = Length \times Width}[/tex]
So, we have:
[tex]\mathbf{A =6 \times x}[/tex]
[tex]\mathbf{A =6x}[/tex]
See attachment for the graphs of [tex]\mathbf{P =12 + 2x}[/tex] and [tex]\mathbf{A =6x}[/tex]
From the attached graph, the lines of both functions meet at x =3.
Hence, the value of x is 3
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Which is the simplified form of the expression 3(7/5x+4)-2(3/2-5/4x)
Simplify 7/5x to 7x/5
3(7x/5 + 4) -2(3/2 - 5/4x)
Simplify 5/4x to 5x/4
3(7x/5 + 4) -2(3/2 - 5x/4)
Expand
21x/5 + 12 - 3 + 5x/2
Collect like terms
(21x/5 + 5x/2) + (12 - 3)
Simplify
67x/10 + 9
The simplified form of the expression 3(7/5x+4)-2(3/2-5/4x) is (67x + 90)/10
What is an Expression ?Expression is a mathematical statement which consists of variables , constant and mathematical operators all together simultaneously.
The given expression is 3(7/5x+4)-2(3/2-5/4x)
[tex]\rm 3 ( \dfrac{7}{5} x+4) -2 ( \dfrac{3}{2}-\dfrac{5}{4}x)[/tex]
(21/5)x +12 - 3 + (5/2)x
((42+25)/10)x + 9
(67x + 90)/10
The simplified form of the expression 3(7/5x+4)-2(3/2-5/4x) is (67x + 90)/10
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Find the measure of angle x in the diagram below.
A. 25°
B. 45°
C. 105°
D. 145°
Answer:
C. 105°
Step-by-step explanation:
To find the answer, we can use the method of exterior angle of triangles, which would be <A + <B = <C, in which A and B is any interior angles of triangles and C would be the exterior angle for the remaining angle.
In this case:
45°+60° = 105°
Therefore the answer is C. 105°
Hope it helps!
The measure of the angle x is 105 degrees option (C) is correct.
What is the triangle?In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
We have a triangle shown in the picture.
As we know,
The sum of two interior angles is equal to the exterior angle;
The measure of the angle x:
x = 60 + 45
x = 105 degrees
Thus, the measure of the angle x is 105 degrees option (C) is correct.
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