Answer:
It's 53.
Step-by-step explanation:
Let the number be xy so the digits are x and y, so:
x + y = 8...........(1)
Reversing the 2 digits we have the number 10y + x and this equals
10x + y - 18 so we have the equation:-
10x + y - 18 = 10y + x
9x - 9y = 18
x - y = 2...........(2) Adding equations (1) and (2) we have:
2x = 10
x = 5
and y = 8 - 5 = 3.
So the original number is 53.
We can check this as follows
Original number is 53 so the reverse is 35 .
53 - 35 = 18 which checks out.
can someone explain it to me, i don't need the answer, i just need an detailed explanation of how they got the answer using the method that they provided
Answer:
Step-by-step explanation:
Good idea to review quadratic functions and the quadratic formula.
Quadratics have three coefficients: ax² + bx + c, and the "discriminant" is defined as b²-4ac. Please review these rules:
1) if the discriminant is +, the quadratic equation has two real, unequal roots.
2) if the disc. is 0, the equation has two real, equal root.
3) If the disc. is - , the equation has two complex roots.
Here a = 1, b = -3 and c = 4. Therefore the discriminant is (-3)²-4(1)(4), or
-7. Rule 3) applies: the equation has two complex roots, but no real ones. Thus we know that the graph does not cross the x-axis.
Graphing the given quadratic, x² - 3x + 4, using a dashed "line," is helpful. As you can see in the illustration of this graph, the graph neither touches nor crosses the x-axis. Thus, y = x² - 3x + 4 is greater than 0 for all x. The answer: All real numbers.
I need help putting this in corresponding factored form. I got two wrong but I’m not sure how to do it and show my work.
Answer:
x^2-16 goes with (x+4)(x-4)
x^2+10x+16 goes with (x+8)(x+2)
Step-by-step explanation:
The first one you got wrong is known as a difference of squares.
To factor a difference of squares, a^2-b^2, you just write it as (a-b)(a+b) or (a+b)(a-b) would work too.
So x^2-16=(x-4)(x+4) or (x+4)(x-4).
Let's check (x+4)(x-4) using foil!
First: x(x)=x^2
Outer: x(-4)=-4x
Inner: 4(x)=4x
Last: 4(-4)=-16
----------------------Add
x^2-16
Bingo! (x+4)(x-4) definitely corresponds to x^2-16.
Here are more examples of factoring a difference of squares:
Example 1: x^2-25 = (x+5)(x-5)
Example 2: x^2-81 = (x+9)(x-9)
Example 3: x^2-100 =(x+10)(x-10)
Onward to the next problem:
x^2+10x+16
When the coefficient of the leading term of a quadratic is 1, all you have to do is find two numbers that multiply to be c=16 and add up be b=10.
Those numbers would be 8 and 2
because 8(2)=16 and 8+2=10.
So the factored form of x^2+10x+16 is (x+2)(x+8) or (x+8)(x+2).
Here is another example of when the leading coefficient of a quadratic is 1:
Example 1: x^2+5x+6=(x+2)(x+3) since 3(2)=6 and 3+2=5.
Example 2: x^2-x-6=(x-3)(x+2) since -3(2)=-6 and -3+2=-1.
8. Point O is the circumcenter of the triangle ABC shown below.
Which segment passes through point O for all lengths of sides of the triangle?
A. angle bisector of angle ABC
B. perpendicular bisector of side AB
C. a line segment drawn from vertex C to bisect side AB
D. a line segment drawn from vertex A to cut side BC at right angles
The circumcenter O, formed by the intersection of the perpendicular bisectors of sides AB and BC, is equidistant from all vertices, with OA = OB = OC. Here option B is correct.
In a triangle, the circumcenter is the point where the perpendicular bisectors of its sides intersect. In this case, the circumcenter O is formed by the intersection of the perpendicular bisector of side AB and the perpendicular bisector of side BC.
The circumcenter is equidistant from all three vertices, making OA, OB, and OC equal, and these distances represent the radius of the circumcircle.
This line not only bisects side AB but also intersects with the perpendicular bisector of side BC at the circumcenter O. The equality of OA, OB, and OC ensures that the circumcircle passes through all three vertices of the triangle, making it a significant point in the context of the triangle's geometry. Here option B is correct.
Find the length of RW
Answer:
A 54
Step-by-step explanation:
RC = 126
WC = 72
RC = WC + RW
126 = 72+RW
Subtract 72 from each side
126-72 = 72-72+RW
54 = RW
Answer: First option
[tex]RW=54[/tex]
Step-by-step explanation:
Notice in the image that the distance from R to C is equal to 126.
Then we write:
[tex]RC = 126[/tex]
Also note that the distance between W and C is 72.
We know that:
[tex]RC=RW + WC[/tex]
In this case we want to find RW, so we solve the equation for RW
[tex]RC-WC=RW + WC-WC[/tex]
[tex]RC-WC=RW[/tex]
[tex]RW=RC-WC[/tex]
Now we substitute the values of RC and WC into the equation
[tex]RW=126-72[/tex]
[tex]RW=54[/tex]
The point slip form of a line that has a slope of 1/4 and passed through the point (3,0) is shown. Y-0=1/4(x-3) what is the equation in slope intercept form
[tex]\bf y-0=\cfrac{1}{4}(x-3)\implies y=\cfrac{1}{4}(x-3)\implies \stackrel{\textit{distributing}}{y=\cfrac{1}{4}x-\cfrac{3}{4}}[/tex]
For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
According to the data we have to:
[tex]m = \frac {1} {4}[/tex]
Then, the equation is of the form:
[tex]y = \frac {1} {4} x + b[/tex]
We substitute point (3.0):
[tex]0 = \frac {1} {4} (3) + b\\b = - \frac {3} {4}[/tex]
Finally, the equation is:
[tex]y = \frac {1} {4} x- \frac {3} {4}[/tex]
Answer:
Option B
F(x)=x^2+9x-16
What is vertex
Axis of semetry
Answer:
axis of symmetry is [tex]x=\frac{-9}{2}[/tex].
The ordered pair of the vertex is [tex](\frac{-9}{2},\frac{-145}{4})[/tex].
Step-by-step explanation:
Your function is a quadratic.
Compare [tex]x^2+9x-16[/tex] to [tex]ax^2+bx+c[/tex].
You should see that [tex]a=1,b=9,c=-16[/tex].
The x-coordinate of the vertex or the axis of symmetry since the axis symmetry goes through the vertex can be found by computing [tex]\frac{-b}{2a}[/tex].
So here we go!
The axis of symmetry is [tex]x=\frac{-9}{2(1)}=\frac{-9}{2}[/tex].
When you write your axis of symmetry be sure to write it as an equation.
That is the axis of symmetry is [tex]x=\frac{-9}{2}[/tex].
Now that was also the x-coordinate of your vertex. To find the corresponding y-coordinate of the vertex, plug your value for [tex]x[/tex] into
[tex]y=x^2+9x-16[/tex].
[tex]y=(\frac{-9}{2})^2+9(\frac{-9}{2})-16[/tex]
Put into calculator:
[tex]y=\frac{-145}{4}[/tex] when [tex]x=\frac{-9}{2}[/tex]
The ordered pair of the vertex is [tex](\frac{-9}{2},\frac{-145}{4})[/tex].
Answer:
Vertex: [tex](h,k)\rightarrow(-4.5,-36.25)[/tex]
Axis of symmetry: [tex]x=-4.5[/tex]
Step-by-step explanation:
Finding the Axis of Symmetry:First I'll find the axis of symmetry. This formula lets us find the a.o.s: [tex]x=\frac{-b}{2a}[/tex].
In [tex]x^2+9x-16[/tex], the values of a, b, and c are:
a: 1b: 9c: -16We only need a and b to find the axis of symmetry. Substitute these values into the formula.
[tex]x=\frac{-(9)}{2(1)}[/tex]Simplify this fraction.
[tex]x=\frac{-9}{2} =-4.5[/tex]The axis of symmetry of this quadratic function is x = -4.5.
Finding the Vertex:Now to find the vertex, we have to take into account that this quadratic is in standard form, making it a little harder. We have to convert this function into vertex form.
Start by changing f(x) to 'y' and adding 16 to both sides.
[tex]y+16=x^2+9x[/tex]Use the completing the square formula: [tex](\frac{b}{2} )^2[/tex]
[tex](\frac{9}{2} )^2=20.25[/tex]Keep the balance by adding 20.25 on the left side and adding it on the right side of the equation.
[tex]y+16+20.25=x^2+9x+20.25[/tex]Combine like terms.
[tex]y+36.25=x^2+9x+20.25[/tex]Factor the right side of the equation. Ask yourself, "What two numbers multiply to 20.25 (c) and add up to 9 (b)?" These two numbers are 4.5 and 4.5. Rewrite the right side with factors.
[tex]y+36.25=(x+4.5)(x+4.5)[/tex][tex]y+36.25=(x+4.5)^2[/tex]Isolate y by subtracting 36.25 from both sides of the equation.
[tex]y=(x+4.5)^2-36.25[/tex]Now this quadratic function is in vertex form, making it super simple to find the vertex using [tex](h, k)[/tex].
Vertex form of a quadratic is:
[tex]y=a(x-h)^2+k[/tex]Compare [tex]y=(x+4.5)^2-36.25[/tex] with the original vertex form and find where h and k are. Those are the x (h) and y (k) values of the vertex.
Since the original vertex form has x - h, the h value in [tex]y=(x+4.5)^2-36.25[/tex] would be a negative since two negatives make a positive. The k value would stay "normal"---negative would mean it is a negative and positive would mean it is a positive number.
Therefore the h value is -4.5, and the k value is -36.25.
The ordered pair of the vertex is [tex](-4.5, -36.25)[/tex].
Mapping congruent Triangles
Mis the midpoint of AD.
What single transformation is required to map one of
these congruent triangles onto the other?
Reflection
O Rotation
O Translation
O Dilation
27
) Intro
✓ Done
4 of 9
Reflection is the correct answer
A reflection would be the single transformation required to map one congruent triangle onto the other in this scenario, with the line AD serving as the line of reflection.
Explanation:The single transformation required to map one congruent triangle onto the other is a translation.
In the context of two congruent triangles, when point M is the midpoint of AD, the single transformation to map one triangle onto the other would be a reflection. Imagine the line segment AD as the mirror or line of reflection. Because M is the midpoint, both halves of the line segment would mirror each other exactly, corresponding to the two congruent triangles. This means the triangle on one side of the line AD can be reflected over the line AD to coincide exactly with the triangle on the other side.
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Dante is standing at horizontal ground level with the base of the Empire State Building in New York City. The angle formed by the ground and the line segment from his position to the top of the building is 48.4°. The height of the Empire State Building is 1,472 feet. Find his distance from the Empire State Building to the nearest foot.
A. 7.65 ft
B. 1, 968 ft
C. 1,307 ft
D. 2, 217 ft
Answer:
C. 1307 ft
Step-by-step explanation:
Given:
Angle = 48.4 degrees
Height, opposite side= 1472 feet
his distance from the Empire State Building, base=x
Now as per the trigonometric ratios:
Tan∅= Opposite/base
tan(48.4)= 1472/x
x=1472/(1.13)
x=1302.65
his distance from the Empire State Building is 1302.65 feet!
Answer:
The correct answer is option C.
Step-by-step explanation:
Height of Empire State Building = 1,472 feet
Angle formed by the line segment from the point of ground on which Dante is positioned to the top of the building is 48.4°.
Distance of Dante from the Empire State Building =?
In the fig ,ΔABC
AB = 1,472 feet, BC = ? , θ= 48.4°
[tex]\tan\theta =\frac{Perpendicular}{base}[/tex]
[tex]\tan 48.4^o=\frac{AB}{BC}[/tex]
[tex]BC=\frac{AB}{\tan 48.4^o}=\frac{1,472 feet}{1.1263}=1,306.9 feet\approx 1,307 feet[/tex]
Distance of Dante from the Empire State Building is 1,307 feet.
A rectangle's length is 4 feet more than its width. Write a quadratic function
that expresses the rectangle's area in terms of its width.
A. A(W) = w^2 – 4w
B. A(w)= w^2+4w
c. A(w)=w+4
D. A(w) = lw
Answer:
B. A(w)=w∧2+4w
Step-by-step explanation:
Let the width of the rectangle be w.
The length is 4 feet longer than the width= w+4
Area of a rectangle= length× width
A=L×W
=(w+4)×w
Opening the brackets gives the:
A=w²+4w
Therefore the expression for the area in terms of width is A(w)=w∧2+4w
The Big Burger recipe calls for 3 meat patties, 2 slices of cheese, and four pickles. How many meat patties are needed if 52 pickles are used?
Answer:
39 meat patties
Step-by-step explanation:
Given,
The Big Burger recipe calls for 3 meat patties, 2 slices of cheese and 4 pickles,
That is, the ratio of meat patties, cheese and pickles in the recipe = 3 : 2 : 4
Let in a recipe,
Meat patties = 3x, Cheese = 2x, pickles = 4x
Where, x is a positive real number,
If there are 52 pickles,
⇒ 4x = 52 ⇒ x = 13
Hence, meat patties = 3 (13) = 39
WILL GIVE BRAINLIEST!
The table below shows part of the texting skills’ data collected by the cell phone company.
Use the table to interpret the axes labels of the scatterplot as either time or texting speed.
The y-axis label of the scatterplot is...
A. Number of Words
B.Texting Speed
C.Time
Answer:
Texting speed
Step-by-step explanation:
It's the dependent variable
Answer:
B
Step-by-step explanation:
I has the most numbers varied and has bigger numbers which means it can't be the time which is either 1 2 or 3. The number of words will almost never be the answer!
During the first four months of the year, Jack earned $1270, $1150, $870 and $1450 If Jack must have an average salary of at least $1150 in order to earn retirement benefits, what must Jack earn in the fifth month in order to qualify for benefits?
Answer:
1010
Step-by-step explanation:
There are a whole class of questions that rely on the method to this one.
First add up what you know
1270 + 1150 + 870 + 1450 = 4740
Now add on the 5th month (which you don't know. Call it x)
4740 + x
Divide by 5
(4740 + x)/5 = 1150 and that is your equation
Solution
Multiply both sides by 5
5*(4740 + x) / 5 = 1150 * 5
4740 + x = 5750
Subtract 4740 from both sides
4740 - 4740 + x = 5750 - 4740
x = 1010
Which seems kind of low, but that's what the numbers come to.
34 + 3 ⋅ 5 = ____. (Input only whole numbers.)
[tex]34+3\cdot5=34+15=49[/tex]
Hope this helps.
r3t40
Answer:
[tex]\huge \boxed{49}\checkmark[/tex]
Step-by-step explanation:
Order of operations
PEMDAS
Parenthesis
Exponent
Multiply
Divide
Add
Subtract
Do multiply first.
[tex]\displaystyle 34+3\times5[/tex]
[tex]\displaystyle 3\times5=15[/tex]
Add from left to right to find the answer.
[tex]\displaystyle 34+15=49[/tex]
[tex]\huge \boxed{49}[/tex], which is our answer.
Hope this helps!
Which ordered pair is a solution of the equation 2x − y = 9?
Answer:
The answer is C; (5, 1).
Step-by-step explanation:
2(5) - 1 = 9
10 - 1 = 9
9 = 9
9 = 9 is a true statement so the answer is C.
Which is a diagonal through the interior of the cube?
Answer:
AH
Step-by-step explanation:
we know that
A cube has 6 faces and on each face there are two diagonals joining nonadjacent vertices and there are 4 diagonals through the interior of the cube. Thus in total there are 6×2+4=16 diagonals in a cube.
In this cube, the diagonals through the interior of the cube are
AH, CF, DE and BG
therefore
The answer is AH
Answer:
The correct answer is first option. AH
Step-by-step explanation:
From the figure we can see a cube ABCDEFGH.
In a cube thee are 4 interior diagonals
To find the diagonal of the cube
AH, BG, CF and DE
There are 4 interior diagonals.
The given options contain only one interior diagonal.
Therefore the correct answer is first option. AH
Given: DE || BC. Find the measure of AED in the triangle AED.
Answer:
<AED = 60
Step-by-step explanation:
Since triangle ADE is similar to triangle ABC
Angle ADE equals angle ADC
The angles of a triangle add to 180 degrees
<A + <ADE + <AED = 180
36 + 84+ <AED = 180
Combine like terms
120 + <AED = 180
Subtract 120 from each side
120-120 +<AED = 180-120
<AED = 60
Answer:
58°
Step-by-step explanation:
Since DE and BC are parallel, ADE will be equal to ABC.
So ADE is 84°.
And, the sum of the angles of a triangle is 180°. So AED will be equal to 180-(38 + 84),which is 58°
[Only if Angle A is 38°]
Carl's Candies has determined that a candy bar measuring 3 inches long has a z-score of +1 and a candy bar measuring 3.75 inches long has a z-score of +2.
What is the standard deviation of the length of candy bars produced at Carl's Candies?
A 0.75
B 3
C 3.75
D 2
Answer:
A. d = 0.75.
Step-by-step explanation:
The z-score =( x - m) / d where m = the mean and d = the standard deviation.
So we have
(3 - m) / d = 1
3 - m = d.............(1)
and
(3.75 - m) / d = 2
3.75 - m = 2d....... (2)
Subtract (2) - (1):
0.75 = d.
Answer: A 0.75
Step-by-step explanation:
Formula for z-score :
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
, where x= random variable
[tex]\mu[/tex] = Population mean
[tex]\sigma[/tex] = Standard deviation
As per given , we have
[tex]+1=\dfrac{3-\mu}{\sigma}\\\\\Rightarrow\ \sigma=3-\mu\\\\\Rightarrow\ \mu=3-\sigma---(i)[/tex]
[tex]+2=\dfrac{3.75-\mu}{\sigma}\\\\\Rightarrow\ \mu=3.75-2\sigma---(ii)[/tex]
From (i) and (ii) , we have
[tex]3-\sigma=3.75-2\sigma\\\\\Rightarrow\ 2\sigma-\sigma=3.75-3\\\\\Rightarrow\ \sigma=0.75[/tex]
Hence, the standard deviation of the length of candy bars produced at Carl's Candies is 0.75.
Thus , the correct answer is A. 0.75.
Algebra 2 help please ASAP
Answer:
The option A,D and E are correct.
Step-by-step explanation:
Given: 2x^3-250x^2
Factor : 2x^2(x-125)
So, GCF = 2x^2
Now a = 1 and b= 5
we know that a^3-b^3 = (a-b)(a^2+ab+b^2)
(x)^3 - (5)^3 = (x-5)(x^2+5x+25)
So, the option A,D and E are correct.
What is the area of the rhombus shown below? MK=13 JL= 17
Answer:
110.5 units²
Step-by-step explanation:
The area (A) of a rhombus is calculated as
A = [tex]\frac{1}{2}[/tex] product of diagonals, that is
A = 0. 5 × MK × JL = 0.5 × 13 × 17 = 110.5
The area of the rhombus will be 110.5 square units.
How to calculate the area of the rhombus?The area of the rhombus can be calculated by half of the product of its two diagonals.
Here given,
JKLM is a rhombus.
The length of its diagonals will be MK=13
JL=17
The diagonal MK and JL intersect each other by 90° at point O.
Now the rhombus is divided by 4 right-angled triangle,
Area of the rhombus will be 4 times of the right-angled triangle ΔMJO
Area of the rhombus= 4*Area of right-angled triangle ΔMJO
=4*(1/2)*MO*JO
= 4*(1/2)*(MK/2)(JL/2)
=(1/2)*MK*JL
=(1/2)*the product of its two diagonals
=(1/2)*13*17
=110.5 Square unit
Therefore the area of the rhombus will be 110.5 square units.
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What’s the y-intercept of the graph
Answer:
-3
explanation:
since the line crosses the y-axis on the point -3
Answer:
c = - 3
Step-by-step explanation:
The y- intercept is the point on the y- axis where the line crosses.
The line crosses the y- axis at (0, - 3), hence y- intercept = - 3
A plane is taking off from Bangladesh headed to
New York City. At the same time, a plane from
New York City is headed to Bangladesh is also
taking off. The plane bound to New York City is
traveling at 600 mph, while the plane traveling
to Bangladesh is traveling at 400 mph. How far
from New York City will the two planes meet
if the distance between New York City and
Bangladesh is 8,000 miles?
Answer:
4800 miles
Step-by-step explanation:
Use a calculator to find the approximate value of arccos(0.67).
Answer:
The approximate value of arc cos(0.87) is 29.54°
Step-by-step explanation:
we know that
The arc cosine of x is defined as the inverse cosine function of x
so
if y=cos(x)
then
arc cos (y)=x
In this problem we have
y=0.67
so
x=arc cos(0.87)
using a calculator
x=29.54°
So, the approximate value of arccos(0.67) is about 0.84108 radians.
To approximate arccos(0.67) using a calculator, we find it to be approximately 0.84108 radians. This value represents the angle whose cosine is 0.67. Arccos, or inverse cosine, returns the angle in radians between 0 and π (approximately 3.14159) whose cosine is the input value. In this case, 0.67 is the cosine of the angle 0.84108 radians. This angle is commonly used in trigonometric calculations, such as determining the angle of a vector or solving geometric problems involving cosine functions.Let's use a calculator to find the approximate value of arccos(0.67).
Using a calculator:
[tex]arccos(0.67) \approx 0.84108 radians[/tex]
HELP ASAP!!!
Lena makes home deliveries of groceries for a supermarket. Her only stops after she leaves the supermarket are at traffic lights and the homes where
she makes the deliveries. The graph shows her distance from the store on her first trip for the day. What is the greatest possible number of stops she
made at traffic lights?
answers:
a) 9
b) 5
c) 3
d) 4
Answer:
3
Step-by-step explanation:
3 is the greatest possible number of stops she made at traffic lights.
What is a Distance-Time Graph?A distance-time graph suggests how the distance an item has traveled in a given time. it's far a simple line graph that denotes distance as opposed to time findings the graph. Distance is plotted on the Y-axis.
How to read a distance graph?In a distance-time graph, the gradient of the line is equal to the velocity of the object. The more the gradient (and the steeper the road) the faster the object is transferring.
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What is the lateral area of a regular pyramid with a square base which has a slant height of 9 units and base side lengths of 7 units?
Answer:
126 units
Step-by-step explanation:
the lateral area of a regular pyramid with a square base of 126 units has a slant height of 9 units and base side lengths of 7 units.
What is the smallest positive integer that will make x^x > 500,000? What
is the largest negative integer that will make x^(-x) > 500,000?
Answer:
For [tex]x^x > 500,000[/tex] [tex]x=7[/tex]
For [tex]x^{(-x)} > 500,000[/tex] [tex]x=-7[/tex]
Step-by-step explanation:
We need to find the smallest positive whole number that satisfies the inequality:
[tex]x^x > 500,000[/tex]
We tested with x = 6
[tex]6^6=46,656\\\\46,656 > 500,000[/tex]
Inequality is not met because [tex]46,656 < 500,000[/tex]
We test with the following integer x = 7
Then we have that:
[tex]7^7=823,543\\\\823,543 > 500,000[/tex]
Then the smallest positive integer that will make [tex]x^x > 500,000[/tex] is 7 because Inequality is met.
In the same way the largest negative integer that will make [tex]x^{(-x)} >500000[/tex] is [tex]x=-7[/tex] Beacuse [tex]7^{-(-7)}=823,543>500,000[/tex]
Answer:
Smallest positive integer value for [tex]x^x>500000[/tex] is,
x = 7,
Largest negative integer value for [tex]x^{-x}>500000[/tex] is,
x = -8
Step-by-step explanation:
If [tex]x^x>500000[/tex]
By graphing calculator,
[tex]x>6.83[/tex]
Thus, the smallest possible positive integer value of x is 7,
Now,
[tex]x^{-x}>500000[/tex]
Possible negative integer values of x are -6, -7 and -8,
If x = -6, -7, and -8,
[tex](-6)^{6}=46656[/tex]
[tex](-7)^{7}=-823543[/tex]
[tex](-8)^{8}=16777216[/tex]
[tex]\because 16777216 > 500000[/tex]
Thus, the largest negative integer value of the inequality [tex]x^{-x}>500000[/tex] is,
x = -8.
Simplify 7(x - 2) - 4x + 9
Answer:
3x - 5
Step-by-step explanation:
Perform the indicated multiplication. We get:
7x - 14 - 4x + 9.
Combining like terms, we get 3x - 5
Find the area of a regular octagon whose side length is 4.7 in. and the apothem is 6.5 in
Answer:
122.2 in^2.
Step-by-step explanation:
WE can divide a regular octagon into 8 triangles with height ( = the apotherm) = 6.5 and base = 4.7.
The area of each triangle is 1/2 * 4.7 *6.5 so #the area of the octagon
= 8 * 1/2 * 4.7 * 6.5
= 122.2 in^2.
For this case we have by definition, that the area of an octagon is given by:
[tex]A = \frac {p * a} {2}[/tex]
Where:
p: perimeter
a: apothem
We have that the perimeter is given by the sum of the sides of the octagon:
[tex]p = 8 * 4.7 = 37.6 \ in\\a = 6.5 \ in[/tex]
Substituting:
[tex]A = \frac {37.6 * 6.5} {2} = 122.2[/tex]
So, the area of the octagon is[tex]122.2 \ in ^ 2[/tex]
Answer:
[tex]122.2 \ in ^ 2[/tex]
What are the zeros of the polynomial function f(x) =x^2+5x-6
Answer:
The zeros are x=1, x=-6
Step-by-step explanation:
f(x) =x^2+5x-6
Factor: What two numbers multiply to -6 and add to 5
-1 *6 = -6
-1 +6 = 5
f(x) = (x-1) (x+6)
Using the zero product property
0 = (x-1) (x+6)
x-1 =0 x+6=0
x=1 x=-6
The zeros are x=1, x=-6
Find the equation of the horizontal line that passes through the point (-5,6) using the point slope formula
Answer:
So first blank=6
Second blank=0
Third blank=-5
Fourth blank=6
Step-by-step explanation:
It is a horizontal line so the equation is just going to be
[tex]y=\text{ whatever y-coordinate they gave you in that one point}[/tex].
So it will be [tex]y=6[/tex]
We are going to do the point-slope form too as I requested.
Point-slope form is [tex]y-y_1=m(x-x_1)[/tex].
We have m=0 since you said the slope was 0 and since it said your have a horizontal line (which means the slope slope or m is 0).
You also that it contains the point [tex](-5,6)=(x_1,y_1)[/tex].
So our line in point-slope form is [tex]y-6=0(x-(-5))[/tex].
AB ll CD and EF ll GH use the figure above to find the value of each angle
Answer:
[tex]x=k=117\°[/tex]
Step-by-step explanation:
Givens
AB || CD
EF || GH
These parallels gives us certain pair of angles which are congruent.
The given angle 63° is congruent with its corresponding angles. The image attached shows all corresponding angles that are equal to 63° (red angles).
Basically,
[tex]x+63=180[/tex] and [tex]k+63=180[/tex], by suplementary angles and straight angle definition.
Then, solving for [tex]x[/tex] and [tex]k[/tex], we have
[tex]x=180-63\\x=117\°[/tex]
[tex]k=180-63\\k=117\°[/tex]
Therefore, both angles are equal to 117°.
The measure of each angle are:
<m = 63 <n = 117<k = 63 <x = 63 <w = 63 <p = 63Given:
AB || CD
EF || GH
As, the lines are parallel and parallel line have following properties
Corresponding angleAlternate Interior angleAlternate Exterior angleCo- interior angleSo, <m = 63 {Corresponding angle}
Now, <m + <n = 180 {Linear pair}
63 + <n =180
<n =180 - 63
<n = 117
and, <k = 63 {Vertical opposite angle}
and, <k = <x = 63 {Corresponding angle}
and, <w = <x = 63 (alternate Interior angle}
and, <p = <w = 63 {Vertical opposite angle}
Learn more about Parallel lines here:
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