Answer:
4 feet
Step-by-step explanation:
We know the the area of a triangle can be represented as [tex]\frac{bh}{2}[/tex].
Since the height is twice the base, we can substitute the value [tex]2b[/tex] in as [tex]h[/tex] in the expression, making it [tex]\frac{b\cdot2b}{2}[/tex]. If the area is 16, we can make the equation
[tex]\frac{b\cdot2b}{2} = 16[/tex]
Now to solve for b.
[tex]\frac{2b^2}{2} = 16\\\frac{2b^2}{2}\cdot2 = 16\cdot2\\\\2b^2 = 32\\\\2b^2\div2 = 32\div2\\\\b^2 = 16\\\\b=4[/tex]
Hope this helped!
Which expression is equivalent to 10i/2-i
Answer:
A reduce the fraction is
5\1
Answer:
C. 4i-2
Step-by-step explanation:
EDGE 2020
Given: f(x) = X^2 - 3 and g(x) = X + 1 The composite function g°f is:_______.
Answer:
x² - 2
Step-by-step explanation:
To obtain (g ￮ f)(x), substitute x = f(x) into g(x), that is
g(x² - 3)
= x² - 3 + 1
= x² - 2
Answer:
✔ x² - 2
Step-by-step explanation:
EDG 2020
Subtract 5 - 4i from 19 - 3i.
Answer:
Step-by-step explanation:
19 - 3i - 5 + 4i
14 + i
x + 2y = 33
x-y = 11
Answer:
[tex]x=\frac{55}{3},\:y=\frac{22}{3}[/tex]
Step-by-step explanation:
Solve by Substitution ;
[tex]\begin{bmatrix}x+2y=33\\ x-y=11\end{bmatrix}\\\\\mathrm{Isolate}\:x\:\mathrm{for}\:x+2y=33:\quad x=33-2y\\\\\mathrm{Subsititute\:}x=33-2y\\\\\begin{bmatrix}33-2y-y=11\end{bmatrix}\\\\Simplify\\\begin{bmatrix}33-3y=11\end{bmatrix}\\\\\mathrm{Isolate}\:y\:\mathrm{for}\:33-3y=11:\quad y=\frac{22}{3}\\\mathrm{For\:}x=33-2y\\\\\mathrm{Subsititute\:}y=\frac{22}{3}\\x=33-2\times\frac{22}{3}\\\\x=\frac{55}{3}\\\\x=\frac{55}{3},\:y=\frac{22}{3}[/tex]
It is estimated that 65.5% of the students at Foster Middle School will attend the benchmark reward party. Which number is NOT equivalent to 65.5%
Answer:
I am not totally sure but the answer might be 0.0655.
PLS ANSWER BEST ANSWER GETS BRAINLIEST Tim wants to decorate a rectangular card with a width of 1/2 inch and an area of 7/4 square inches. Find the length of the card in inches?
Answer:
[tex]\frac{7}{2}[/tex]in
Step-by-step explanation:
First you must set up an equation. [tex]\frac{1}{2}x=\frac{7}{4}[/tex]
Then, you must solve for x. [tex]x=\frac{7}{2}[/tex]
Make the number 18 using six "1"s.
Answer:
(11-1-1)(1+1)
Step-by-step explanation:
revised
A number cube numbered 1-6 is rolled once. What is the probability that the side facing up shows a 4
Answer:
it will be one out six to roll a four
Step-by-step explanation:
there is one being rolled to be a 4 out of six
if you're currently making $6.75 per hour and you were offered a new job that pays $7.47 per hour, what will be your percent of increase in pay?
Answer:
10.67% increase
Step-by-step explanation:
We can find percent increase with (difference/original) x 100
7.47 - 6.75
= 0.72 (difference)
(0.72/6.75) x 100
= 10.67% increase
Match each fraction with its percent equivalent.
1/5 9/10 21/25 3/4 75% 84% 90% 20%
This is the last one, i truly appreciate all the help u guys have given me.
Answer:
it's rational ..........
Select the correct inequality to make a true statement
Please help
Answer:
2/5 is greater
Step-by-step explanation:
to compare you need to make them common denominator, and that could be10. to make both denominators equal to ten just multiply the top and bottom of 2/5 by 2. this will turn it into 4/10. 4/10 is greater than 3/10
The solution is : 2/5> 3/10
2/5 is greater than 3/10
What is fraction?A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.
Here, we have,
the given fractions are,
2/5 and 3/10
now, we have,
to compare you need to make them common denominator,
and that could be10.
to make both denominators equal to ten just multiply the top and bottom of 2/5 by 2.
i.e. 2*2/5*2
=4/10
this will turn it into 4/10.
now, we get,
4/10 is greater than 3/10
Hence, 2/5> 3/10 , 2/5 is greater than 3/10.
To learn more on fraction click:
brainly.com/question/10354322
#SPJ2
Linda had 72 fliers to post around town. Last week, she posted 1/3
of them. This week, she posted 1/4 of the remaining fliers. How many fliers has she still not
posted?
Answer:
36 fliers
Step-by-step explanation:
1/3*72 = 24 fliers posted last week (.333*72)
72-24 = 48 fliers left
1/4*48 = 12 fliers posted this week (.25*48)
48-12= 36 fliers not posted
Linda has 36 fliers left to post.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given: Linda had 72 fliers to post around town. Last week, she posted 1/3
of them. This week, she posted 1/4 of the remaining fliers.
1st-week Linda posted 72/3=24 and remaining fliers72-24=48
2nd the week Linda posted 48/4=12 and remaining fliers 48-12=36
∴The remaining fliers left to be posted are 36
Hence, Linda has 36 fliers left to post.
Learn more about the unitary method here:
https://brainly.com/question/22056199
#SPJ2
Designer wants to create a whisper chamber in the shape of an ellipse. He has a warehouse space with a longest length of 30 feet which he decides will be the major axis of his elliptical chamber. He determines the best spots for his guest to stand to experience his whisper chamber will be 4 feet from the center of the warehouse space, which will act as the foci. How far out from the center along the minor axis should he built his whisper chamber.
Answer:
14.48 ft
Step-by-step explanation:
The relation between the location of the focus (c), the vertex on the major axis (a) and the vertex on the minor axis (b) with respect the center is:
b² = a² - c²
From the question:
c = 4 ft
a= 30/2 = 15 ft
Replacing into the equation:
b² = 15² - 4²
b = √209
b = 14.48 ft
So, he should build the whisper chamber at 14.48 ft out from the center along the minor axis
Answer: The answer to this questiojn is 14.48 feet, but if rounded to the nearest tenth, then it should be 14.5 (As it was on my question)
There is 26 letters in the alphabet A=1 B=2 C=3 and so on Z+Z=?+D-A then take the number you get then turn it into a letter ?+F-K+L=? This is One of the hardest questions i made!!!!
Answer:
I got (G^B) +F-K+L= (G^B)
Step-by-step explanation:
The number of students in a school's math club is ten less than twice the number of students in the art club. Let a represent the number of students in the art club. Write an expression for the number of students in the math club.
Answer: 2a - 10
Step-by-step explanation:
a represents the number of students in the art club.
The number of students in a school's math club is ten less than twice the number of students in the art club.
ten less = - 10
twice the number of students in the art club = 2*a
2a - 10 = the number of students in the math club
A bicycle tire is 28 inches in diameter. Approximately how far does the bicycle move forward each time the wheels go around (use22/7 as an approximation for pie
Answer: About 88 inches
=============================================
Explanation:
Find the circumference
C = pi*diameter
C = (22/7)*28
C = 88
The tire's circumference is approximately 88 inches. This is the perimeter or distance around the circle. As the bike moves forward one full rotation of the wheel, all of the wheel will touch the ground at some point. The bike will move about 88 inches forward when the wheel does one full rotation.
A good way to visualize this is to imagine cutting the tire so that you can unroll it to lay it out completely flat forming a straight line. This line will be roughly 88 inches long.
how to do this problem
−2(3x−2)+3x+3=34
Answer:
answer is -3
Step-by-step explanation:
-6x+4+3x+3=34
-3x+7=34
-3x=34-7
-3x=27
x=27/-3
x=-3
(23.0lb/gal)(2ft) report in correct number of significant figures and units
Answer:
344.1 Ib/ft²
Step-by-step explanation:
This has to do with conversion
23.0Ib/gal × 2ft
Step 1
First we convert 23.0lb/gal to Ib/ft³
1 Ib/gal = 7.48051948 Ib/ft³
23.0lb/gal = X Ib/ft³
Cross Multiply
1 Ib/gal × X Ib/ft³ = 23.0lb/gal × 7.48051948 Ib/ft³
X Ib/ft³ = 23.0lb/gal × 7.48051948 Ib/ft³/1 Ib/gal
X Ib/ft³ = 172.05194804 Ib/ft³ =
Step 2
Since 23.0lb/gal = 172.05194804 Ib/ft³
172.05194804 Ib/ft³ × 2 ft
= 344.10389608Ib/ft²
Approximately to 1 significant figure
= 344.1 Ib/ft²
please help!! What is the solution to the quadratic inequality? 6x2≥10+11x
answers:
(−∞,−52]∪[23,∞)
(−∞,−23]∪[52,∞)
[−23,52]
[−32,14]
Answer:
The solution of the inequation [tex]6\cdot x^{2} \geq 10 + 11\cdot x[/tex] is [tex]\left(-\infty,-\frac{2}{3}\right]\cup\left[\frac{5}{2},+\infty\right)[/tex].
Step-by-step explanation:
First of all, let simplify and factorize the resulting polynomial:
[tex]6\cdot x^{2} \geq 10 + 11\cdot x[/tex]
[tex]6\cdot x^{2}-11\cdot x -10 \geq 0[/tex]
[tex]6\cdot \left(x^{2}-\frac{11}{6}\cdot x -\frac{10}{6} \right)\geq 0[/tex]
Roots are found by Quadratic Formula:
[tex]r_{1,2} = \frac{\left[-\left(-\frac{11}{6}\right)\pm \sqrt{\left(-\frac{11}{6} \right)^{2}-4\cdot (1)\cdot \left(-\frac{10}{6} \right)} \right]}{2\cdot (1)}[/tex]
[tex]r_{1} = \frac{5}{2}[/tex] and [tex]r_{2} = -\frac{2}{3}[/tex]
Then, the factorized form of the inequation is:
[tex]6\cdot \left(x-\frac{5}{2}\right)\cdot \left(x+\frac{2}{3} \right)\geq 0[/tex]
By Real Algebra, there are two condition that fulfill the inequation:
a) [tex]x-\frac{5}{2} \geq 0 \,\wedge\,x+\frac{2}{3}\geq 0[/tex]
[tex]x \geq \frac{5}{2}\,\wedge\,x \geq-\frac{2}{3}[/tex]
[tex]x \geq \frac{5}{2}[/tex]
b) [tex]x-\frac{5}{2} \leq 0 \,\wedge\,x+\frac{2}{3}\leq 0[/tex]
[tex]x \leq \frac{5}{2}\,\wedge\,x\leq-\frac{2}{3}[/tex]
[tex]x\leq -\frac{2}{3}[/tex]
The solution of the inequation [tex]6\cdot x^{2} \geq 10 + 11\cdot x[/tex] is [tex]\left(-\infty,-\frac{2}{3}\right]\cup\left[\frac{5}{2},+\infty\right)[/tex].
From the given figure 7 ,find the value of x if AB is parallel CF and AE = DE, angle BAE = 38°.
*see the given given in the attachment below
Answer:
x = 109°
Step-by-step Explanation:
Since AB is parallel to CF, m<BAE = m<AED = 38° (alternate interior angles are congruent)
Since AE = DE, ∆AED is an isosceles ∆.
The two base angles of any given isosceles ∆ are said to be congruent.
This means, m<EAD = m<EDA = ½(180 - m<AED)
m<EDA = [tex] \frac{1}{2}*(180 - 38) [/tex]
m<EDA = [tex] \frac{1}{2}*(142) = 71 [/tex]
x + m<EDA = 180° (angle on a straight line)
[tex] x + 71 = 180 [/tex]
[tex] x + 71 - 71 = 180 - 71 [/tex]
[tex] x = 109 [/tex]
Value of x = 109°
find the area of the blue shaded shape
Answer:
Hey there!
The big square has an area of 6x6 or 36 units.
However, we subtract 8 to get 28 because the 8 white squares do not count.
Let me know if this helps :)
Answer:
28units²
Step-by-step explanation:
6² = 36
36 - 8 = 28
15m + (- 5m) combine like terms
Answer:
10 m
Step-by-step explanation:
15m - 5m = 10 m
both numbers have m which are alike
Answer: 10m
Step-by-step explanation: you subtract five from fifteen
Determine the number and type of roots for the equation using one of the given roots. Then find each root. (inclusive of imaginary roots.) 1. x^3-7x+6=0;1 2. x^3-3x^2+25x+29=0;-1 3.x^3-4x^2-3x+18=0;3 Find all the zeros of the function 4. f(x)=x^2+4x-12 5.f(x)=x^3-3x^2+x+5 6. f(x)=x^3-4x^2-7x+10 Write the simplest polynomial function with integral coefficients that has the given zeros. 7. -5,-1,3,7 8. 4,2+3i (thank you so much in advance, it would mean a lot, and it is urgently needed, hence the high reward, thank you! Have a great day)
Step-by-step explanation:
"Determine the number and type of roots for the equation using one of the given roots. Then find each root. (inclusive of imaginary roots.)"
Given one of the roots, we can use either long division or grouping to factor each cubic equation into a binomial and a quadratic. I'll use grouping.
Then, we can either factor or use the quadratic equation to find the remaining two roots.
1. x³ − 7x + 6 = 0; 1
x³ − x − 6x + 6 = 0
x (x² − 1) − 6 (x − 1) = 0
x (x + 1) (x − 1) − 6 (x − 1) = 0
(x² + x − 6) (x − 1) = 0
(x + 3) (x − 2) (x − 1) = 0
The remaining two roots are both real: -3 and +2.
2. x³ − 3x² + 25x + 29 = 0; -1
x³ − 3x² + 25x + 29 = 0
x³ − 3x² − 4x + 29x + 29 = 0
x (x² − 3x − 4) + 29 (x + 1) = 0
x (x − 4) (x + 1) + 29 (x + 1) = 0
(x² − 4x + 29) (x + 1) = 0
x = [ 4 ± √(16 − 4(1)(29)) ] / 2
x = (4 ± 10i) / 2
x = 2 ± 5i
The remaining two roots are both imaginary: 2 − 5i and 2 + 5i.
3. x³ − 4x² − 3x + 18 = 0; 3
x³ − 4x² − 3x + 18 = 0
x³ − 4x² + 3x − 6x + 18 = 0
x (x² − 4x + 3) − 6 (x − 3) = 0
x (x − 1)(x − 3) − 6 (x − 3) = 0
(x² − x − 6) (x − 3) = 0
(x − 3) (x + 2) (x − 3) = 0
The remaining two roots are both real: -2 and +3.
"Find all the zeros of the function"
For quadratics, we can factor using either AC method or quadratic formula. For cubics, we can use the rational root test to check for possible rational roots.
4. f(x) = x² + 4x − 12
0 = (x + 6) (x − 2)
x = -6 or +2
5. f(x) = x³ − 3x² + x + 5
Possible rational roots: ±1/1, ±5/1
f(-1) = 0
-1 is a root, so use grouping to factor.
f(x) = x³ − 3x² − 4x + 5x + 5
f(x) = x (x² − 3x − 4) + 5 (x + 1)
f(x) = x (x − 4) (x + 1) + 5 (x + 1)
f(x) = (x² − 4x + 5) (x + 1)
x = [ 4 ± √(16 − 4(1)(5)) ] / 2
x = (4 ± 2i) / 2
x = 2 ± i
The three roots are x = -1, x = 2 − i, x = 2 + i.
6. f(x) = x³ − 4x² − 7x + 10
Possible rational roots: ±1/1, ±2/1, ±5/1, ±10/1
f(-2) = 0, f(1) = 0, f(5) = 0
The three roots are x = -2, x = 1, and x = 5.
"Write the simplest polynomial function with integral coefficients that has the given zeros."
A polynomial with roots a, b, c, is f(x) = (x − a) (x − b) (x − c). Remember that imaginary roots come in conjugate pairs.
7. -5, -1, 3, 7
f(x) = (x + 5) (x + 1) (x − 3) (x − 7)
f(x) = (x² + 6x + 5) (x² − 10x + 21)
f(x) = x² (x² − 10x + 21) + 6x (x² − 10x + 21) + 5 (x² − 10x + 21)
f(x) = x⁴ − 10x³ + 21x² + 6x³ − 60x² + 126x + 5x² − 50x + 105
f(x) = x⁴ − 4x³ − 34x² + 76x − 50x + 105
8. 4, 2+3i
If 2 + 3i is a root, then 2 − 3i is also a root.
f(x) = (x − 4) (x − (2+3i)) (x − (2−3i))
f(x) = (x − 4) (x² − (2+3i) x − (2−3i) x + (2+3i)(2−3i))
f(x) = (x − 4) (x² − (2+3i+2−3i) x + (4+9))
f(x) = (x − 4) (x² − 4x + 13)
f(x) = x (x² − 4x + 13) − 4 (x² − 4x + 13)
f(x) = x³ − 4x² + 13x − 4x² + 16x − 52
f(x) = x³ − 8x² + 29x − 52
PART 5 - Mathematical knowledge
What is the area of a parallelogram if its length is x +4 and its height is x +3?
A 4x + 14
B
2x + 7
C x2 + 12x + 7
D x2+ 7x + 12
Click the button or type the letter to the left of your answer
A work shift for an employee at a restaurant consist of 8 hours.What fraction of the employee’s work shift is represented by 6 hours ?
Answer:
Fraction of work shift represented by 6 hours = 0.6
Step-by-step explanation:
Total work shift of employee = 10 hours
Time considered to find fraction = 6 hours
Fraction of work shift represented by 6 hours 6/10=3/5=0.6=60%
Fraction of work shift represented by 6 hours = 0.6
Answer:
0.75
Step-by-step explanation:
Total work shift of an employee is 8 hours
Time consist to find fraction is 6 hours
The fraction of work shift by 6 hours :
[tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex] = 0.75 = 75%
The ABC company's brand has a market share of 30%. Suppose that in a survey, 800 consumers of the product are asked which brand they prefer. What is the probability that more than 32% of the respondents say they prefer ABC's brand?
Answer: 0.68
Step-by-step explanation:
given data:
ABC market share = 30%
number of customers surveyed = 800
probability that more than 32% prefers ABC
Solution:
32% of 800
= 256 persons
p ( x ≥ 256 )
= 1 - ( 256/800 )
= 1 - 0.32
= 0.68
the probabiliy that more than 32% of those who carried out the survey would prefer ABC brand is 0.68.
If you go on a road trip of 270 miles in the mountains and 7/10 of the trip is downhill, how many miles of the trip are not downhill? Reduce to the lowest terms.
Answer:Answer:
81 miles
Step-by-step explanation:
From the question 7/10 of the trip has been said to be downhill. It therefore means that 3/10 is not downhill.
Miles = 270
Downhill = 7/10
Not downhill = 3/10
Now we have To calculate Miles that are not downhill (uphill)
But first I calculated for the number of downhill miles
270x7/10
Downhill = 189 miles
To get the number of not downhill miles
I subtracted 189 from the total number of miles on the question.
270 - 189
= 81 Miles.
Therefore 81 Miles of the trip are not downhill.
If you have anymore questions or need clarity please let me know on the comment section. Thank you and Good luck!
Step-by-step explanation:
Need the answer ASAP
Answer:
Approximately 201 squared inches.
Step-by-step explanation:
So, the composite figure is made up of a square and a semi-circle. The square has side lengths of 12 and the semi-circle has a radius of 6.
The total area of the figure would be the area of the square plus the area of the semi-circle. Thus, find the area of each individual figure.
Square:
The area of a square is given by:
[tex]A=l^2[/tex]
Where l is the side length.
Substitute 12 for l:
[tex]A=(12)^2\\A=144\text{ in}^2[/tex]
So the square is 144 square inches.
Semi-circle:
The area of a semi-circle is given by:
[tex]A=\frac{1}{2}\pi r^2[/tex]
Substitute 6 for r and 3.14 for π:
[tex]A=\frac{1}{2}(3.14)(6)^2\\ A=56.52[/tex]
Therefore, the total area is:
[tex]TA=144+56.52\\TA=200.52\text{ in}^2\approx201\text{ in}^2[/tex]
An object has a potential energy of 14 J and a mass of 17 kg , how far above the ground is the object? An object moving with a speed of 35 m/s and has a kinetic energy of 1500 J, what is the mass of the object. What is the Potential Energy of a 1200 kg object that is 24 m above the ground? What is the Potential Energy of a 478 kg object that is150 m above the ground? What is the Potential Energy of a 100 kg object that is 12.5 m above the ground? An object has a potential energy of 14 J and a mass of 17 kg , how far above the ground is the object? An object is 35 m above the ground and has a potential energy of 1500 J, what is the mass of the object?
1. Potential Energy = mgh
h = U_g / (mg) = 14 / (17 * 9.81) = 0.084 m above the ground.
2. Kinetic Energy = 1/2 mv^2
m = 2K_e / (v^2) = 2.45 kg
3. U_g = mgh = (1200)(9.81)(24) = 282528 J
4. U_g = mgh = (478)(9.81)(150) = 703377 J
5. U_g = mgh = (100)(9.81)(12.5) = 12262.5 J
6. h = U_g / (mg) = 14 / (17 * 9.81) = 0.084 m above the ground.
7. m = U_g / (gh) = 1500 / (9.81 * 35) = 4.37 kg