8a)
x = width
x+3 = length, since its 3 ft longer than the width
A = length*width
A = LW
A = (x+3)*x
A = x^2+3x
Set this equal to 108 since this is the area of the rectangle.
Answer: x^2 + 3x = 108=========================================================
8b)
x^2+3x = 108
x^2+3x-108 = 0
Use the quadratic formula with a = 1, b = 3, c = -108
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(3)\pm\sqrt{(3)^2-4(1)(-108)}}{2(1)}\\\\x = \frac{-3\pm\sqrt{441}}{2}\\\\x = \frac{-3\pm21}{2}\\\\x = \frac{-3+21}{2} \ \text{ or } \ x = \frac{-3-21}{2}\\\\x = \frac{18}{2} \ \text{ or } \ x = \frac{-24}{2}\\\\x = 9 \ \text{ or } \ x = -12\\\\[/tex]
Ignore the negative solution because we cannot have a negative width.
x = 9 is the width
x+3 = 9+3 = 12 is the length being 3 longer.
The rectangle is 12 ft by 9 ft to get an area of 12*9 = 108 sq ft, which confirms the answer.
Answer: 12 feet by 9 feetfind the measure of minor arc AB when the angle is 85 degrees
Answer:
170 degrees
Step-by-step explanation:
The minor arc will always be twice as much as the inscribed angle.
Simplify 3√8w - 3√216w + 3√216w
Answer:
6√2w
Step-by-step explanation:
3√8w - 3√216w + 3√216w
6√2w -18√6w +18√6w
6√2w +0
6√2w
HELP PLS
Find the Area for the following shapes
PLEASE MAR BRAINLIEST
Answer: THE TRIANGLE HAS AN AREA OF 25 IN ND THE OTHER SHAPE HAS AN AREA OF 156
Step-by-step explanation:
Find the slope of the line that passes through(5,7) and (7,6)
Answer:
Equation: y = -0.5x + 9.5.
Answer:
-0.5 or -1/2
Step-by-step explanation:
The formula to find the slope of a line given two points if [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].
[tex]\frac{(6)-(7)}{(7)-(5)}[/tex] [tex]\frac{-1}{2}[/tex] [tex]-0.5[/tex]Therefore, the slope is -0.5 or -1/2.
Use the remainder theorem and synthetic division
to find the value of f(3) if f(x) = x^3 - 6x^2 + 13x - 11
VIEW IMAGE
Show the steps of the synthetic division!
Answer:
f(3) = 1
Step-by-step explanation:
The value of f(3) is told by the remainder theorem to be the remainder from division of f(x) by (x -3). That division is shown in the attachment. The remainder is 1, so ...
f(3) = 1
__
The number at upper left in the synthetic division table is the value of x for which we are evaluating f(x).
_____
Additional comment
When the polynomial is written in Horner Form:
f(x) = ((x -6)x +13)x -11
the coefficient of x at each point in the evaluation is the same as the number on the bottom row of the synthetic division. The result of the evaluation is the same as the remainder from the division.
it said draw a line representing the rise and a line representing the run of the line. state the slope of the line in simplest form
Answer:
The slope of the line is 2/3
Step-by-step explanation:
You lose an online auction for an autograph. Your losing bid of $28 is 40% of the winning bid. How much less was your bid than the winning bid?
Answer:
My bid was $42 less than the winning bid.
Step-by-step explanation:
The winning bid is x.
$28 is 40% of x
0.4x = 28
x = 28/0.4
x = 70
The winning bid was $70.
$70 - $28 = $42
Answer: My bid was $42 less than the winning bid.
Find the perimeter of a triangle 20cm and 29cm
Answer:
Unclear.
To find the perimeter you need all three sides of the triangle. You have only given two.
All you need to do is add up all three sides and you have your perimeter.
Formula: P=a+b+c
Answer:
Unknown unless you give the amount of cm for the last side
Which statement describes characteristics of a convex lens?
A convex lens diverges light and curves inward.
A convex lens diverges light and curves outward.
Aconvex lens converges light and curves inward.
A convex lens converges light and curves outward.
Answer:
A convex lens converges light and curves outward.
Step-by-step explanation:
A convex lens converges light and curves outward.
We have given that,
A convex lens diverges light and curves inward.
A convex lens diverges light and curves outward.
A convex lens converges light and curves inward.
A convex lens converges light and curves outward.
We have to determine Which statement describes the characteristics of a convex lens.
What is the convex lens?
A convex lens is a converging lens. When parallel rays of light pass through a convex lens the refracted rays converge at one point called the principal focus.
A convex lens converges light and curves outward.
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Question 2 of 10
Which are the better statistics to use to compare the distributions? Assume
you know the mean, median, standard deviation, and IQR for each.
35 36 37 38 39 40 41 42 43 44 45
35 36 37 38 39 40 41 42 43 44 45
The better statistics which can be used to compare the given distributions are mean and standard deviation.
What is a z-core?A z-core is also referred to as a standard score and it can be defined as a statistical measure of the distance between a data point (raw score) and the mean, especially when standard deviation units are used.
In Mathematics, z-scores can either be negative or positive and it is generally calculated by using this formula:
[tex]Z=\frac{x\;-\;u}{\delta}[/tex]
Where:
x is the observed data or sample mean.u is the mean.[tex]\delta[/tex] is the standard deviation.In conclusion, the better statistics which can be used to compare the given distributions are mean and standard deviation.
Read more on standard deviation here: https://brainly.com/question/4302527
A land mass is roughly in the shape of a rectangle whose perimeter is 1280 miles. the width is 120 miles less than the length find the length and the width.
HELP!!!!
Felicia filled the bathroom sink with water. Is the amount more than
1 liter, about 1 liter, or less than 1 liter
y=3x-11
y-3x=-13
Solving using systems of equations
Answer: There are no possible solutions because
If you were to plot these two equations on the graph you would notice they are parallel because both have the same slope (3x) but still have different intercepts. This means there are no possible solutions as in order to have a solution for x and y they need to intercept and the point of interception is the solution for x and y but that cannot happen in a system of equations that result in parallel lines ( they’ll never intercept)
Answer:
Ø
Step-by-step explanation:
These equations are parallel, meaning they have SIMILAR rate of changes [slopes]. To prove it, convert the second equation from Standard Form to Slope-Intercept Form:
[tex]\displaystyle y - 3x = -13 \hookrightarrow y = 3x - 13 \\ \\ \left \{ {{y = 3x - 13} \atop {y = 3x - 11}} \right.[/tex]
As you can see, both equations have a rate of change of 3, meaning we CANNOT obtain a solution here, therefore we have no solution.
I am joyous to assist you at any time.
help me please i need it rn
[tex] \rm \: this \: month, \: Mikasa \: earned \: only \rm \frac{-3}{4} \:of \: his \: earning \: last \: month\: if \: his \: earning \: last \: month \: is \: 12,600 \: how \: much \: did \: he \: earn \: this \: month[/tex]
Step-by-step explanation:
Multiply 12600 by -3/4 to determine the amount earned.
*12600 can be put over 1.
Multiply:
[tex] \frac{12600}{1} \times \frac{ - 3}{4} = \frac{37800}{4} [/tex]
Simplify by dividing the fraction by 4:
[tex] \frac{ - 37800 \div 4}{4 \div 4} = \frac{ - 9450}{1} [/tex]
Mikasa has lost $9450.
please answer the question
Answers:
A) 2,600 cubes (13 x 40 x 5 = 2,600)
B) 6,600 cubes (11 x 20 x 30 = 6,600)
C) Boxes A and C or boxes B and C
D) 11,200 cubes (13 x 40 x 5) + (11 x 20 x 30) + (8 x 10 x 25) = 11,200
Select the correct answer.
Chase is constructing equilateral triangle EFG inscribed in a circle.
He begins by using a compass to draw circle X. He then uses a straightedge to draw a diameter of the circle and labels the endpoints D and E.
How can Chase find points F and G?
A.
Points F and G are endpoints of a chord that is perpendicular to and bisects DE.
B.
Points F and G are the points where circle X intersects a congruent circle centered at D.
C.
Points F and G are the points where circle X intersects a congruent circle centered at E.
D.
Points F and G are points of intersection of two congruent circles centered at D and E
Answer: A
Step-by-step explanation:
To construct equilateral triangle in a circle F and G as D. Points F and G are points of intersection of two congruent circles centered at D and E. The correct answer is option A.
What is a circumscribed circle?The circumscribed circle or circumcircle of a polygon in geometry is a circle that passes through each of the polygon's vertices. This circle's circumcenter and circumradius are its center and radius, respectively.
It should be noted that an equilateral triangle simply means a triangle that has all the sides and angles to be equal.
After drawing the diameter of the circle through the center, it's important to open the compass to a width that's equivalent to the radius of the circle.
In this case, it can be deduced that Points F and G are points of intersection of two congruent circles centered at D and E.
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HelP KE PLEASE HELP HELP
Answer:
C (14 aq units)
Step-by-step explanation:
Area of a triangle = 1/2 x base x height
Base = MY = 4 UNITS
Height = AM = 7 UNITS
Area = 4 x 7 x 1/2 = 14
Answer:
Area=1/2×base×height
But base=4 units and height=7 units
So the area is
1/2×4×7
which is 14 sq units
2c+3a
c=6
a=3
Evaluate the expression
Answer:
21
Step-by-step explanation:
2c + 3a
= 2(6) + 3(3)
= 12 + 9
= 21
NO LINKS!! A blimp, suspended in the air of 500 feet, lies directly over a line from Soldier Field to the Adler Planetarium on Lake Michigan (see the figure). If the angle of depression from the blimp to the stadium is 32° and from the blimp to the Planetarium is 23°, find the distance between Soldier Field and the Adler Planetarium.
Answer:
1978 ft (nearest foot)
Step-by-step explanation:
Using the Alternate Interior Angles theorem, we can deduce that the left base angle of the triangle is 32° and the right base angle of the triangle is 23°.
The triangle can be divided into 2 right triangles, both with height of 500ft (see attached diagram).
Using the tan trig ratio, we can calculate the base of each triangle.
[tex]\mathsf{\tan(\theta)=\dfrac{O}{A}}[/tex]
where:
[tex]\theta[/tex] = angleO = side opposite the angleA = side adjacent the angleLeft triangle
let [tex]x[/tex] = the base length
[tex]\implies \tan(32)=\dfrac{500}{x}[/tex]
[tex]\implies x=\dfrac{500}{\tan(32)}[/tex]
Right triangle
let [tex]y[/tex] = the base length
[tex]\implies \tan(23)=\dfrac{500}{y}[/tex]
[tex]\implies y=\dfrac{500}{\tan(23)}[/tex]
To find the distance between the Soldier Field and Adler Planetarium, simply sum [tex]x[/tex] and [tex]y[/tex]:
[tex]\implies \dfrac{500}{\tan(32)}+\dfrac{500}{\tan(23)}=1978.093447...[/tex]
Therefore, the distance is 1978 ft (nearest foot)
please help answer and explanation im very confused.
Answer:
1) 18m²
2) 25cm²
Step-by-step explanation:
1)
a = ½ × b × ha = ½ × 9 × 4a = ½ × 36a = 18m²2)
a = ½ × b × ha = ½ × 10 × 5a = 5 × 5a = 25 cm²Find the height of a rectangle if the base is 24 in and the perimeter is 102 in.
Answer:
The answer is A: 27 inches (not squared because it's not area)
Step-by-step explanation:
In a rectangle the angles are [tex]2y[/tex] and [tex]2x[/tex]
let's say [tex]24=x[/tex]
so then:
[tex]2x=48[/tex]
now to solve for [tex]y[/tex]
[tex]102-48=2y[/tex]
[tex]y=27[/tex]
The answer is A: 27 inches (not squared because it's not area)
Given x= -2, mark and place these six expressions
on the same number line below.
X, -X, |-1.5], -4, 15, 16||
Answer:
-4, x, |-1.5| , -x, |5|, |6|
Step-by-step explanation:
X = -2
-X = 2
|-1.5| = 1.5
|5| = 5
|6| = 6
A study found that 9% of dog owners brush the dogs teeth. Of 578 dog owners, about how many would be expected to brush their dog’s teeth? explain.
Answer:
52
Step-by-step explanation:
Step 1: Our output value is 578.
Step 2: We represent the unknown value with [tex]x[/tex].
Step 3: From step 1 above, [tex]578=100%[/tex]%
Step 4: Similarly, x=9%
Step 5: This results in a pair of simple equations:
578 = 100% (1)
x = 9% (2)
Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both
equations have the same unit (%); we have
578/x = 100% /9%
Step 7: Again, the reciprocal of both sides gives
x/578 = 9 /100
⇒ x = 52.02
Therefore, 9% 578 is 52.02
Round:
Answer: About 52 dog owners are expected to brush their dogs teeth.
Use the pythagorean theorem a + b = c to find the length of a triangle when a = 9 ft and b = 40 ft
Answer:
41
Step-by-step explanation:
a^2 + b ^2 =c^2
9^2 + 40^2 = c^2
81+ 1600 = c^2
1681= c^2
[tex]\sqrt{1681[/tex] = [tex]\sqrt{c^{2}[/tex]
41 = c
. Express this number in standard form:
?
4.39 х 10^-7
Answer:
4.39e-7
Step-by-step explanation:
Cooper's father is 120% of Cooper's height of his father measures 180 cm, how tall is Cooper?
Answer:
Cooper's height is 150 cm
Step-by-step explanation:
To find this answer you can divide 180 by 1.2 (1.2 is 120% in decimal form)
Hope that helps!
A number divided by 7 is –35.
Answer:
-245
Step-by-step explanation:
multiply 7 and -35 to get your answer.
I hope this helped <3
Answer:
The number is (-245)
Step-by-step explanation:
Let the number be 'x'
x ÷ 7 = -35
[tex]\dfrac{x}{7}=-35\\\\\\Multiply \ the \ entire \ equation \ by \ 7\\\\x =-35*7\\\\x = - 245[/tex]
32,8,83,88,58,58,66,11,34,23 calculate the range
Answer:
80
Step-by-step explanation:
After spending some time arranging the numbers in order, we get the sequential order as 8, 11, 23, 32, 34, 58, 58, 66, 83, 88.
Next, we need to find the range. The Range of a data set is the difference between the largest and smallest number.
Thus, 88 - 8 = 80 as the range.The expression 3b +2.2 is equal to for b = 1.8.
(Type a whole number or a decimal.)
Enter your answer in the answer box and then click Check Answer.
2
parts
remaining
Clear All
What is the answer?
Select all x values that are solutions to the equation
Answer:
The answers are 3 and 5
The only thing u had to do is
x-5=0
x=5
7x-21=0
7x=21
x=3