Answer:
9^2 = 81
12^2 = 144
63^= 3969
A^2 + B^2 = C^2
81 + 144 = 225
so these numbers do not make a right triangle
Final answer:
The numbers square root of 63, 9, and 12 do make a right triangle as their squares satisfy the Pythagorean theorem. The sum of the squares of 9 and square root of 63 equals the square of 12, which validates that we have a right triangle.
Explanation:
To determine if the numbers square root of 63, 9, and 12 make a right triangle, we can apply the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides must be equal to the square of the longest side (the hypotenuse). Let's calculate the squares of each provided number:
The square root of 63 squared is 63 (because \ \ \ equals 63).9 squared is 81.12 squared is 144.Since the longest side here must be 12 (as it is the largest number), the Pythagorean theorem for these numbers would be as follows:
81 + 63 = 144?
That simplifies to:
144 = 144?
This is a true statement, which means that these numbers do indeed represent the sides of a right triangle.
PLEASE ANSWER RIGHT AWAY
ANSWER
The second term is 7.
EXPLANATION
The given sequence has it's first term to be:
[tex]t_1 = 3[/tex]
The recursive definition is :
[tex]t_{n+1}=2t_n+n[/tex]
To find the second term , we substitute n=1,
to obtain,
[tex]t_{1+1}=2t_1+1[/tex]
This implies that:
[tex]t_{2}=2t_1+1[/tex]
[tex]t_{2}=2(3)+1[/tex]
Simplify:
[tex]t_{2}=6+1[/tex]
[tex]t_{2} = 7[/tex]
Answer:
The second term of the sequence is 7 ⇒ the 2nd answer
Step-by-step explanation:
* Lets revise the recursive formula
1. Determine if the sequence is arithmetic (Do you add, or subtract, the
same amount from one term to the next?)
2. Find the common difference. (The number you add or subtract.)
3. Create a recursive formula by stating the first term, and then stating
the formula to be the previous term plus the common difference.
a1 = first term;
an+1= an + d
- Where:
# a1 = the first term in the sequence
# an = the nth term in the sequence
# an+1 = the term after the nth term
# n = the term number
# d = the common difference.
* Now lets solve the problem
∵ The recursive definition is tn+1 = 2 tn + n and t1 = 3
- Lets find the 2nd term
∵ t1 = 3
∵ tn+1 = 2 tn + n
* To find the second term put n = 1
∴ t2 = 2 (3) + 1
∴ t2 = 6 + 1 = 7
∴ t2 = 7
* The second term of the sequence is 7
A football team has a budget of $2500 for supplies. The team purchased new helmets for $975. Each new football costs $34. The inequality 975 + 34f ≤ 2500 can be used to describe the number of footballs (f) the team can purchase. Which statement about the number of footballs they can purchase is true?
a) The team can purchase 45 footballs.
b) The minimum number of footballs the team can purchase is 44.
c) The team can purchase 49 footballs.
d) The maximum number of footballs the team can purchase is 44.
Answer:
d) The maximum number of footballs the team can purchase is 44.
Step-by-step explanation:
975+34f≤ 2500
Subtract 975 from both sides: 975-975+34f≤ 2500-975
34f≤ 1525
Divide both sides by 34: 34f/34≤ 1525/34
f≤ 44.853
You can't purchase 0.853 of a helmet so the maximum you can buy is 44
The maximum number of footballs the team can purchase is 44.
What is inequality?Inequality directs to the phenomenon of unequal and/or unjust distribution of resources and possibilities among members of a given society. The word inequality may mean different things to various people and in different contexts.
A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
Given
975+34f≤ 2500
Subtracting 975 from both sides: 975-975+34f≤ 2500-975
34f≤ 1525
Dividing both sides by 34: 34f/34≤ 1525/34
f≤ 44.853
so the maximum you can buy is 44
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A discount store promises that all items it sells are 40% of their normal asking retail price. If one buys shoes that normally retail for $60.99 what is the price you would expect to pay? ( NOTICE IT IS 40% of not 40% off. Which plays a big difference) someone please help me find the answer and explain how you got the answer. I’m in algebra 1 and I am no good at math. Thanks.
Answer:
$24.4
Step-by-step explanation:
We are given that a discount store promises that all items it sells are 40% of their normal asking retail price.
If a shoes have a retail price of $60.99, we are to find the expected price of the shoes at this store.
Expected price of shoes = 40% of $60.99 = [tex] \frac { 4 0 } { 1 0 0 } \times 6 0 . 9 9 [/tex] = $24.4
Dyson hikes 1/2 mile every 15 minutes or 1/4 hour how far dose he hike in 1 hour
Answer:
2 miles.
Step-by-step explanation:
What are the solutions for x when y is equal to 0 in the following quadratic
function?
y = x^2 - 13x
OA) x = 0
OB) x = 13
OC) x = 0 or x = 13
OD) x = 0 or x = -13
O E) no real solutions
Answer: Option C
Step-by-step explanation:
Given the quadratic equation [tex]y = x^2 - 13x[/tex], substitute [tex]y=0[/tex]:
[tex]0 = x^2 - 13x[/tex]
In this case, to find the solutions of the given quadratic equation, you must factor out the variable "x". Then:
[tex]0=x(x-13)[/tex]
Therefore, you get that the solutions of this equation are the following:
[tex]x=0\\\\\\x-13=0\\x=13[/tex]
Then, the answer is:
[tex]x = 0\ or\ x = 13[/tex]
This matches with the option C.
Compute the value of the discriminant and give the number of real solutions of the quadratic equation.
5x²-7X+2=0
Answer:
2 reals and 2 rationals.
Step-by-step explanation:
The discriminate gives
b^2 - 4*a*c
b = -7
a = 5
c = 2
(-7)^2 - 4(5)(2)
49 - 40
9
Taking the square root gives you +/-3
The discriminate tells you that there are 2 roots, both real and both rational
x = [(-7) +/- 3 ]/2*5
x = (- 7 - 3)/10 = - 1
x = (- 7 + 3)/10 = -0.4
You walk 3/8 miles to a music store. Then you walk another 1/3 miles to a clothing store. How many miles have you walked in all?
Answer:
You have walked [tex]\frac{17}{24}[/tex] miles
Step-by-step explanation:
In order to add these two fractions, we must find a common denominator. In this case, I used 24
[tex]\frac{3}{8} +\frac{1}{3} \\\\\frac{9}{24} +\frac{8}{24} =\frac{17}{24}[/tex]
Answer:
3/8 + 1/3 = 9/24 + 8/24 = 17/24
Step-by-step explanation:
What is the average rate of change of the function g(x) = 3(2x) - 6 over the interval 0<=x<=3? Show all work.
Definition of average rate of change a function g(x) over an interval [a,b]:
[tex]A = \dfrac{g(b)-g(a)}{b-a}[/tex]
Substitute your function and your interval:
[tex]A = \dfrac{(3^6-6)-(3^0-6)}{3-0} = \dfrac{3^6-6-3^0+6}{3} = \dfrac{3^6-1}{3} = \dfrac{728}{3}[/tex]
The average rate of change of the function gx) = 3(2x) - 6 over the interval [0,3] is calculated as (g(3) - g(0)) / (3 - 0) which equals to 6.
Explanation:The average rate of change of a function over an interval [a,b] is defined as:
(g(b) - g(a)) / (b - a)
Here, the function g(x) = 3(2x) - 6, and the interval is [0,3]. Let's calculate g(3) and g(0).
g(3) = 3(2*3) - 6 = 12
g(0) = 3(2*0) - 6 = -6
Now, apply these values to the average rate of change formula:
(g(3) - g(0)) / (3 - 0) = (12 - (-6)) / 3 = 18 / 3 = 6.
So, the average rate of change of the function g(x) over the interval [0,3] is 6.
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Which of the following is a solution of y + x < -5?
(-4, -2)
(-3, -2)
(-2, -3)
(-1, -3)
Answer:
FIRST OPTION: (-4, -2)
Step-by-step explanation:
Given the inequality [tex]y + x < -5[/tex], substitute each solution given in the options:
1) For (-4, -2) :
[tex](-2)+ (-4) < -5[/tex]
[tex]-6 < -5[/tex] (This is true)
2) For (-3, -2):
[tex](-2)+ (-3) < -5[/tex]
[tex]-5 < -5[/tex] (This is not true)
3) For (-2, -3):
[tex](-3)+ (-2) < -5[/tex]
[tex]-5 < -5[/tex] (This is not true)
4) For (-1, -3):
[tex](-3)+ (-1) < -5[/tex]
[tex]-4 < -5[/tex] (This is not true)
You can observe that (-4, -2) is a solution of [tex]y + x < -5[/tex]
The answer is A.
Hope this helps :)
The ground temperature at an airport is 12 °C. The temperature decreases by 5.4 °C for every increase of 1 kilometer above the ground. What is the temperature outside a plane flying at an altitude of 5 kilometers?
Decrease in the temperature: 5.4×5=27°C
Final temperature: 12-27=-15°C
1/3(4y-2)+ 1/9(6y+10)
-Use the distributive property to take away the parentheses
- Combine like terms
Each month a retail store awards a blue ribbon to its employee of the month. The probability that Chloe is the employee of the month is 29% in January and 49% in February. What is the probability that she is awarded a blue ribbon in both January and February?
The probability that Chloe is awarded a blue ribbon in both January and February is 0.1421 or 14.21%.
To calculate this, we simply multiply the probabilities of Chloe being awarded a blue ribbon in January and February:
Probability in January = 0.29
Probability in February = 0.49
Probability in January and February = 0.29 * 0.49 = 0.1421
Explanation:
1. Given probabilities:
- Probability of Chloe being awarded a blue ribbon in January = 29% = 0.29
- Probability of Chloe being awarded a blue ribbon in February = 49% = 0.49
2. To find the probability of Chloe being awarded a blue ribbon in both January and February, we multiply the probabilities together:
- Probability in January and February = 0.29 * 0.49 = 0.1421
Therefore, the probability that Chloe is awarded a blue ribbon in both January and February is approximately 14.21%.
Complete question:
Each month a retail store awards a blue ribbon to its employee of the month. The probability that Chloe is the employee of the month is 29% in January and 49% in February. What is the probability that she is awarded a blue ribbon in both January and February?
cone-shaped paperweight has a diameter of 3 inches and a height of 5 inches.
What is the volume of the paperweight?
Use 3.14 for pi.
Enter your answer, as a decimal, in the box.
Answer: [tex]V=11.775\ in^3[/tex]
Step-by-step explanation:
You need to use the formula for calculate the volume of a cone. This is:
[tex]V=\frac{1}{3}\pi r^2h[/tex]
Where "r" is the radius and "h" is the height.
You know that the diameter of the cone-shaped paperweight is 3 inches. Then, you need to divide the diameter by 2 to find the radius:
[tex]r=\frac{3in}{2}\\\\r=1.5\ in[/tex]
Now you know that:
[tex]r=1.5\ in\\h=5\ in\\\pi=3.14[/tex]
Substituting these values into the formula [tex]V=\frac{1}{3}\pi r^2h[/tex], you get that the volume of the paperweight is:
[tex]V=\frac{1}{3}(3.14)(1.5\ in)^2(5\ in)[/tex]
[tex]V=11.775\ in^3[/tex]
The volume of the paperweight will be 11.76 cubic inches.
What is the volume of a cone?Let d be the diameter of the base circle and h be the height of the cone.
Then the volume of the cone will be
V = 1/12 x πd² x h
The cone-shaped paperweight has a diameter of 3 inches and a height of 5 inches.
Then the volume of the paperweight will be
V = 1/12 x π(3)² x 5
V = 1/12 x 3.14 x 9 x 5
V = 11.76 cubic inches
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adam bought a new flat screen tv with an area of 21 ft the screen is 3 feet wide how tall is it
Answer:
7 ft bRo
Step-by-step explanation:
wow i took 21 and divided it by three and i got SEVEN
how old are you like four
The height of the flat screen TV can be calculated by dividing the given area (21 square feet) by the given width (3 feet). This gives us a height of 7 feet.
Explanation:In this problem, we are given the area of the flat screen TV and the width. The area of a rectangle is calculated by multiplying the width and the height, so to find the height, we can divide the area by the width.
Let's denote the height as 'h'. So, the formula will be: Width times height = Area of the screen, or in our case, 3 feet times h = 21 square feet. Solving this equation gives us h = 21 ÷ 3 = 7 feet.
So, the height of the TV is 7 feet.
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Divide the sum of 9/10 and 2/5 by the product of 11/6 and 5/9
Answer:
[tex]\bold{\dfrac{\,351\,}{275}}[/tex]
Step-by-step explanation:
[tex]\left(\dfrac9{10}+\dfrac25\right)\div\left(\dfrac{11}{6}\cdot\dfrac59\right)\ =\ \left(\dfrac9{10}+\dfrac4{10}\right)\div\dfrac{55}{54}=\\\\\\ =\ \dfrac{13}{10}\times\dfrac{54}{55}\ =\ \dfrac{13}{5}\times\dfrac{27}{55}\ =\ \dfrac{351}{275}[/tex]
Joan went to the bookstore. At
this bookstore, 3/4 of the books
are fiction. Of the fiction books,
1/3 are mystery books. What
fraction of the books at the
bookstore are mystery fiction
books?
Answer:
[tex]\frac{1}{4}[/tex] of the books in the book store are mystery fiction books.
Step-by-step explanation:
Let x represent all the books in the books store.
Then, the fraction of books that are fiction books is [tex]\frac{3}{4}x[/tex]
We have that; [tex]\frac{1}{3}[/tex] of the fiction books are mystery books.
The fraction of the books at the bookstore that are mystery fiction books is [tex]\frac{1}{3}\times \frac{3}{4}x=\frac{1}{4}x[/tex].
Therefore [tex]\frac{1}{4}[/tex] of the books in the bookstore are mystery fiction books.
Answer:
1/4
Step-by-step explanation:
PLZ HELP I PROMISE I WILL GIVE BRAINLIEST!!!! ASAP
Answer:
[tex]4c^{7}d^{13}[/tex]
Step-by-step explanation:
[tex](2cd^{4} )^{2} *(cd)^{5}[/tex]
[tex]4c^{2}d^{8} *c^{5} d^{5}[/tex]
[tex]4c^{7}d^{13}[/tex]
Please help will give brainliest. Drag each label to the correct location on the image. Each label can be used more than once, but not all labels will be used.
Determine the unknown angle measures.
Answer:
1= 115
2=45
3=110
4=115
5=115
Step-by-step explanation:
Answer:
1:
[tex]180-(70+45)=65[/tex] degrees(3rd angle of triangle)
Angle 1 is [tex]180-65=115[/tex] degrees.
2:
Angle 2 is 45 degrees as vertically opposite is also 45 degrees.
3:
[tex]180-(65+45)=70[/tex] degrees(third angle of lower triangle)
Its opposite will also be 70 degrees.
So, 3rd can be found as : [tex]360-(70+110+70)=110[/tex] degrees
You can also say that 3 is vertically opposite of 110 degrees.
4:
[tex]180-65=115[/tex] degrees
5:
This is also 115 degrees as its vertically opposite angle to 4.
Without actual division show that f(x) = (x3 − 3x2 − 13x + 15) is exactly divisible by g(x) = (x2 + 2x − 3).
Answer:
see explanation
Step-by-step explanation:
Note that the sum of the coefficients of g(x)
1 + 2 - 3 = 0
Hence x = 1 is a root of g(x) and (x - 1) is a factor
Note the sum of the coefficients of f(x)
1 - 3 - 13 + 15 = 0
hence x = 1 is a root of f(x) and (x - 1) is a factor
Since (x - 1) is a factor of both
Then f(x) is also divisible by x² + 2x - 3
If y varies inversely with x, and the constant of variation
is 4.5, what are the values missing in the table?
Answer:
A. 0.5
B. 4.5
C. 1.5
D. 0.5
Step-by-step explanation:
y varies inversely with x can be written as:
y = k/x
where k is constant of variation.
1. value of A
x=A, y = 9 and k = 4.5 (given)
y = k/x
9 = 4.5/A
=> A = 4.5/9
=> A=0.5
2. Value of B
x =1, y= B, k = 4.5
y = k/x
B = 4.5/1
B= 4.5
3. Value of C
x=C, y=3. k=4.5
y = k/x
3 = 4.5/C
3C = 4.5
C = 4.5/3
C = 1.5
4. Value of D
x= 9, y=D, k=4.5
y = k/x
D = 4.5/9
D = 0.5
Answer:
[tex]A=0.5[/tex]
[tex]B=4.5[/tex]
[tex]C=1.5[/tex]
[tex]D=0.5[/tex]
Step-by-step explanation:
The form an the equation of inverse variation is:
[tex]y=\frac{k}{x}[/tex]
Being "k" the constant of variation.
Since we know "k" and we have the values given in the table, we can find the missing values:
To find A we need to substitute the [tex]y=9[/tex], the value of "k" and [tex]x=A[/tex] into the equation and solve for "A":
[tex]9=\frac{4.5}{A}[/tex]
[tex]A=\frac{4.5}{9}=0.5[/tex]
To find B we need to substitute the [tex]x=1[/tex], the value of "k" and [tex]y=B[/tex] into the equation:
[tex]B=\frac{4.5}{1}=4.5[/tex]
To find C we need to substitute the [tex]y=3[/tex], the value of "k" and [tex]x=C[/tex] into the equation and solve for "C":
[tex]3=\frac{4.5}{C}[/tex]
[tex]C=\frac{4.5}{3}=1.5[/tex]
To find D we need to substitute the [tex]x=9[/tex], the value of "k" and [tex]y=D[/tex] into the equation:
[tex]D=\frac{4.5}{9}=0.5[/tex]
What is the discriminate of the quadratic equation 0=2x^2+3x-5
ANSWER
The discriminant is 49.
EXPLANATION
The given quadratic equation is:
[tex]0 =2{x}^{2} + 3x - 5[/tex]
We can rewrite this as
[tex]2{x}^{2} + 3x - 5 = 0[/tex]
Comparing this to
[tex]a{x}^{2} + bx + c = 0[/tex]
We have a=2,b=3, c=-5.
The discriminant is given by:
[tex]D = {b}^{2} - 4ac[/tex]
We plug in the values to get:
[tex]D = {3}^{2} - 4(2)( - 5)[/tex]
[tex]D =9 + 40[/tex]
[tex]D = 49[/tex]
Answer:
D IS THE ANSWER (49)
Step-by-step explanation:
how many solutions are there to this equation 7x-3(x-1)=2(2x+3)
Answer:
there are no answers it is false just did it
Step-by-step explanation:
What is ( x + y + 2 )( y + 2 )?
Answer:
y²+4y+2x+xy+4
Answer:
xy+y^2+2x+4y+4
Step-by-step explanation:
simplify by multiplying variable in the first parentheses set with the ones in the second parentheses set:
(x+y+2)(y+2)
=(x)(y)+(x)(2)+(y)(y)+(y)(2)+(2)(y)+(2)(2)
=xy+2x+y^2+2y+2y+4
=xy+y^2+2x+4y+4
hope this helps!
The area of a park was increased from
22,250 square yards to 25,587.5 square
yards. What was the percent of increase in
square yards?
A. 15%
B. 22%
C. 25%
. 33%
Answer:
A. 15%
Step-by-step explanation:
percent change = (new number - old number)/(old number) * 100%
The new number is the increased area, 25,587.5 sq yd, and the old number is the original area, 22,250 sq yd.
percent change = (25,587.5 sq yd - 22,250 sq yd)/(22,250 sq yd) * 100%
percent change = (3,337.5 sq yd)/(22,250 sq yd) * 100%
percent change = 0.15 * 100%
percent change = 15%
Since the percent change is a positive number, it is a percent increase.
The percent increase was 15%.
Answer: A. 15%
Find the area of a circle with a circumference of 30 pie meters
Step-by-step explanation:
Cir=30π=2πr , thus r=15 , Area=π(r^2)=225 pie meters
The area of circle is 225π m².
What is circle ?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry around the center.
Given that,
Circumference of the circle = 30π m
Let r be the radius of circle.
Since we know that,
circumference of the circle = 2πr
Therefore,
⇒ 2πr = 30π
⇒ r = 15 m
Area of circle = πr²
= (15)²π
= 225π
Hence required area is 225π square meter.
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Laura makes 10.5% commission on each of her sales. How much does she make when she sells a house for 85,000
Answer:
85000/100*10.5 = $8925
Step-by-step explanation:
N/A
Which statement are true about the angles in the diagram? Check all that apply
Answer:
Options B,C,E are true.
Step-by-step explanation:
It has been given in the question ∠ACD is supplementary to ∠ACE and ∠BCD
∠ACD ≅ ∠BCE
Option A. ∠ACE is supplementary to ∠BCD
False. They are not lying on a point of straight line.
∠ACE + ∠BCD ≠180°
Option B. ∠BCE is supplementary to ∠ACE
Since ∠ACD + ∠ACE = 180° [Given]
and ∠ACD ≅ ∠BCE [Given]
Therefore, ∠BCE + ∠ACE = 180°
TRUE.
Option C. ∠BCD is supplementary to ∠BCE
Since ∠ACD + ∠BCD = 180°[Given]
and ∠ACD ≅ ∠BCE [Given]
So ∠BCE + ∠BCD = 180°
TRUE.
Option D. ∠ACE ≅ ∠BCE
Since ∠ACD + ∠ACE = 180°
And ∠ACD + ∠BCD = 180°
This is clear from these equations that ∠ACE is supplementary to ∠BCD.
FALSE :
Option E. ∠BCD is congruent to ∠ACE
As we have already proved in option D. ∠BCD ≅ ∠ACE
TRUE
Therefore, Options B, C, E are TRUE
Crystal's soccer team won 14 of the 20 games they played. What percent of games played did they win?
A) 14%
B) 20%
C) 70%
D) 34%
Answer:
Option C) 70%
Step-by-step explanation:
we know that
To determine the percentage of games played that won, divide the number of games won by the total number of games played.
so
[tex]P=14/20=0.70[/tex]
Convert to percentage (multiply by 100)
[tex]0.70*100=70\%[/tex]
Please help! Pythagorean Theorem things...
The answer is 16
The Pythagorean theorem is a^2+b^2=c^2
You already have one side and the hypotenuse (c)
15^2+b^2=17^2
15^2= 225
17^2= 289
Now you have 225+b^2= 289
Subtract 225 from both sides and you get
b^2=64
Then take the square root of both sides to get b alone
b=8
Now, since the base of the inner triangle is half of the base of the pyramid, multiply your answer by 2
You will get 16
A football team lost 5 yards and then gained 9. What is the team’s progress?
Answer:
4
Step-by-step explanation:
-5+9=4