7. Matéd is 41 years old. Mateo's brother
is younger than him. Mateo writes
the inequality b > 41, where b equals
the number of years, to represent
his brother's age. Is Mateo correct?
Explain.
Solve the following quadratic by
completing the square.
y = x2 – 8x + 5
Answer:
x = 4 ± √11
Step-by-step explanation:
hello :
x²-8x+5= x² -2(4 )(x)+5
x²-8x+5= x² -2(4 )(x)+5 = ( x² -2(4 )(x) +4²) -4²+5
= (x-4)²-11 .....( completing the square )
x²-8x+5= 0 means : (x-4)²-11 = 0
(x-4)²=11 but : 11 = (√11)² = ( - √11)²
x-4 =√11 or x-4 = -√11
x = 4 ± √11
Answer:
x = 4 ± [tex]\sqrt{11}[/tex]
Step-by-step explanation:
To solve the equation let y = 0 , that is
x² - 8x + 5 = 0 ( subtract 5 from both sides )
x² - 8x = - 5
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 4)x + 16 = - 5 + 16
(x - 4)² = 11 ( take the square root of both sides )
x - 4 = ± [tex]\sqrt{11}[/tex] ( add 4 to both sides )
x = 4 ± [tex]\sqrt{11}[/tex]
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
Answer:
D.) the amount in the account increase by 4% each year
Step-by-step explanation:
Compound interest formula: P*(1+r/n)^(nt)
P=initial principal balance
r=interest rate
n=times applied per [time (eg year)]
t=number of time periods gone by
The expression: 2500(1.04)^x
The expression: 2500(1+1/25)^(nt)
1.04=1+1/25=increases by 4% each year
Marris decides to bake his parents a cookie in the shape of a regular dodecagon (12‑gon) for their 12-day anniversary.
A.) If the edge of the dodecagon is 6 cm, what is the area of the top of the cookie?
B.) His parents decides to divide the cookie into 12 congruent pieces.
After 9 of the pieces have been eaten, what area of the cookie is left?
Answer:
The answer to each question is:
A.) 403.2 [tex]cm^{2}[/tex] B.) 100. 8 [tex]cm^{2}[/tex]Step-by-step explanation:
A.) To obtain the area of the dodecagon, you can use the next formula:
Area of a dodecagon = 6 * apothem * edgeIn the exercise, we have the edge (6 cm), but, to find the apothem of a dodecagon, that is the distance between the center of the polygon, and the middle point of each side, you can use the next formula:
Apothem = Edge * [tex]\frac{2+\sqrt{3}}{2}[/tex]If we replace the value of the edge, we obtain:
Apothem = 6 cm * [tex]\frac{2+\sqrt{3}}{2}[/tex]Apothem = 11.2 cm (approximately).With this data, we can find the area:
Area of a dodecagon = 6 * apothem * edgeArea of a dodecagon = 6 * 11.2 cm * 6 cmArea of a dodecagon = 403.2 [tex]cm^{2}[/tex]Then, the area of the dodecagon is 403.2 [tex]cm^{2}[/tex] approximately.
B.) As the area obtained is for 12 pieces, when the parents ate 9 pieces, just left 3 pieces, with these values you can make a rule of three.
If:
12 pieces = 403.2 [tex]cm^{2}[/tex]3 pieces = XThen:
X = (3 * 403.2 [tex]cm^{2}[/tex]) / 12X = 1209.6 [tex]cm^{2}[/tex] / 12X = 100. 8 [tex]cm^{2}[/tex]In this form, when the cookie has 3 pieces, its area is 100. 8 [tex]cm^{2}[/tex] approximately.
Shane hit the ball 3 out of times. How is this written as a ratio?
Question is incomplete as number of trials isn't given. We'll use an hypothetical value to make x plain the situation
Answer:
Kindly check explanation
Step-by-step explanation:
Given that the number of trials = x
If the number of tines the ball was hit out if 'x' trials = 3
The ratio of the number of hits to the number of trials is written as :
Number of hits : Number of trials
3 : x
Just put the exact value of x in the equation above and if possible, reduce to simplest form.
pls help!! n33d help
Answer:
6 and 12
Explanation:
(b.) is under set A but not set B, meaning that all the elements there are multiples of 3 that are not odd numbers.
all the multiples of 3 that are less than 16: 3 6 9 12 15
all the multiples of 3 that are even numbers: 6 12
thus, the elements that go in (b.) are 6 and 12.
i hope this helps! :D
URGENT - PLEASE HELP 25 POINTS AND BRAINIEST
A right triangle has legs that measure 5 and x - 1
Its hypotenuse measures x.
Solve for x
The value of x can be 2 or 5
The value of y can be 3 or 12
List the possible values of
XY
Step-by-step explanation:
[tex]when \: x = 2 \: and \: y = 3 \\ xy = (2 \times 3) = 6 \\ when \: x = 2 \: and \: y = 12 \\ xy = (2 \times 12) = 24 \\ when \: x = 5 \: and \: y = 12 \\ xy = (5 \times 12) = 60 \\ when \: x = 5 \: and \: y = 3 \\ xy = (5 \times 3) = 15 \\ values \: of \: xy \: are \: 6, \: 24, \: 60, \: 15[/tex]
Cindy's car used 15 gallons to travel 390 miles. How many gallons of gas would she need to travel 156 miles?
Answer: 6 gallons
Step-by-step explanation: 15/390 then answer x 156
A six sided die is rolled and a spinner with 5 equal spaces labeled A-E is spun. Find the P(rolling
a 1 and spinning A). Answer as simplified fraction.
Answer:
1 / 30
Step-by-step explanation:
For a six - sided die :
Sample space = (1, 2, 3, 4, 5, 6)
P(rolling a 1) = required outcome / sample space = 1/6
Sample space for spinner = (A, B, C, D, E)
P(spinning A ) = required outcome / sample space = 1/5
P(spinning A) = 1 / 5
P(rolling a 1 and spinning A) = P(rolling a 1) * P(spinning A) = 1/6 * 1/5 = 1 / 30
Mark's scores on his first nine assignments were: 10, 10, 9, 9, 10, 8, 9, 10, and 8.
a. What are the median and range of his scores?
b. What is his mean (average) score so far?
c. Mark did not do the tenth assignment, so he got a zero on it. Zero is an outlier for these assignments. What is his new mean?
If you help me with my last question I will help you with this one
Answer:
Median= 9
Range= 2
Mean= 9.2
Mean after zero= 8.3
Step-by-step explanation:
8, 8, 9, 9, 9, 10, 10, 10, 10
Median= order from least to greatest then eliminate from left to right until you get to the middle
Range= Subtract biggest # minus smallest #
Mean= add up all the numbers then divide by 9
Mean after zero= add 0 with other numbers then divide by 10
Decide if each expression represents one third the sum of 5 and 4. choose yes or no for each expression.
Answer:
yes
no
yes
no
Step-by-step explanation:
pls mark brainliest
A right triangle has an area of 98 square inches. If the triangle is not an Isosceles triangle, what are the all possible lengths of the legs?
Answer:
The possible length of the triangle =
1) (1inches, 196inches)
2) (2incheq, 98inches)
3) (4inches , 49 inches)
4) (7 inches , 28 inches)
Step-by-step explanation:
We are told the above Triangle is not an Isosceles Triangle
Hence, we assume it is a right angle triangle
The area of a triangle is = 1/2 × Base × Height
= let us represent Base and Height = x
Hence:
1/2 × x × x = 98
x² /2 = 98
Cross Multiply
x² = 98 × 2
x² = 196
Step 2
We find the factors of 196
1× 196 = 196 (1, 196)
2 × 98 = 196 (2, 98)
4 ×49 = 196 (4, 49)
7 × 28 = 196 (7, 28)
Therefore, all the possible length of the triangle =
1) (1inches, 196inches)
2) (2incheq, 98inches)
3) (4inches , 49 inches)
4) (7 inches , 28 inches)
(1)/(4p)(x-h)^(2)+k=0 Multiply the equation by 4p. Explain how different values of k affect the number of zeros of the polynomial. Consider k > 0, k = 0, and k < 0. Assume p > 0.
Answer:
Step-by-step explanation:
Assume that and multiply the equation by 4p. Then you obtain the equation (x-h)^2+4pk=0.
1) If k>0, then 4pk>0 and the equation does not have real solutions and there is no zero.
2) If k=0, then 4pk=0 and . There is one solution x=h and there is one zero.
2) If k<0, then 4pk<0 and the equation has two different solutions and there are two zeros.
Answer:
Given equation:
[tex]\frac{1}{4p} (x - h)^2 + k = 0[/tex]Multiply this by 4p to get:
(x - h)² + 4pk = 0Rewrite this as:
(x - h)² = 4pk1) If p > 0 and k < 0
(x - h)² < 0, then no real solutions as left side is always positive2) If p > 0 and k = 0
(x - h)² = 0, then x = h, one solution = 1 zero3) If p > 0 and k > 0
(x - h)² > 0, then there 2 real solutions = 2 zeros:x = h ± 2[tex]\sqrt{pk}[/tex]Please help will give brainliest
Answer:
A
Step-by-step explanation:
Volume = lwh
Volume = (8/3) x (13/4) x (3)
Volume = 26 cubic meters
please helppppppppppp
i put it at 50 points-
Answer:
98
Step-by-step explanation:
6 times the quotient of 3 and 5
Answer:
ten less the quotient of a number and 3 is 6. help needed with equation!Step-by-step explanation:
Answer: I’m not sure if you’re asking for me to solve this or how to set it up. But if you solve it you get 3.6. if you have to sit it up it would be 6 x 3/5
Step-by-step explanation:
Write the equation of the line passing
through the point (2, -1) with a slope of -3.
Answer:
y = -3x + 5
Step-by-step explanation:
(2, -1); m = -3
y - y1 = m(x - x1)
y + 1 = -3(x - 2)
y + 1 = -3x + 6
y = -3x + 5
Plz help me. Giving branliest
Answer: im not sure about this but I’ll try
24 because if you look at the side that says 12mi And then look at the side withe the x where they are both standing which says 48 and 72 are really similar wand looks like they have the same distance so you can add 12 + 12 and is 24 miles
Step-by-step explanation:
if the 55 employees who work overtime make up approximately 42% of all employees at the company, how many employees are there in total
Answer:
Approximately = 131 employees in total
Step-by-step explanation:
if the 55 employees who work overtime make up approximately 42% of all employees at the company, how many employees are there in total?
Let us represent total number of employees = x
Hence,
42% of x = 55 employees
42/100 × x = 55
42x/100 = 55
Cross Multiply
42x = 100 × 54
x = 100 × 55/42
x = 130.95238095 employees
Therefore, there is approximately a total 131 employees
Please answer this question correctly
Answer: it is 6
Step-by-step explanation: because they are the same length.
What can it be solved by?
-4 (b + 2) = 20 answer
The power,
P
(watts)
, of a car engine is proportional to the square of its speed,
s
(
m
/
s
)
.
When
s
=
20
,
P
=
2000
.
Work out the speed (to 1 DP) when the power is
1960
watts
Answer:
30
Step-by-step explanation:
6 cm 4 cm 10 cm What is the surface area of the figure?
Answer:
248 cm^2
Step-by-step explanation:
in order to get the figures surface area you only need to find the area of all 6 sides
in this case the two ends are 4 by 6
the front and back are 10 by 6
and the top and bottom are 10 by 4
this would mean that we need to multiply
(4*6)*2
(10*6)*2
(10*4)*2
which would look like
(4*6)*2= (24)*2= 48
(10*6)*2= (60)*2=120
(10*4)*2= (40)*2=80
and finally the sum of the equations is the surface area of the figure
48+120+80=248
A clothing manufacturer offers 2 different styles of jeans, relaxed fit and regular fit, in 5 different colours. How many combinations of a style and a colour are possible?
Answer:
10 combinations
Step-by-step explanation:
We can solve the above question using the Fundamental Counting Principle.
This states that:
If an event has x possible outcomes and a other event has y possible outcomes, then there are x and y total possible outcomes for the two events together.
We are told in the above question that:
Styles of jeans = 2
Number of colors = 5
Hence,the number of combinations of a style and a colour that are possible is calculated as:
5 × 2 = 10 combinations
what is the mathematical equation of 9932x6394=
Answer:
Step-by-step explanation:
63,505,208
can you choose me brainliest?
Sally averaged that she spent about 6.8×10^4 seconds training for her weight lifting competition in the month of May. Write this time in standard notation.
Answer:
t = 68000 s
Step-by-step explanation:
Given that,
The average time Sally spent for training for her weight lifting competition in the month of May is [tex]6.8\times 10^4\ s[/tex].
We need to write this time in standard notation.
The power of 10 is 4. 10⁴ can be written as 10000.
[tex]6.8\times 10^4=\dfrac{68}{10}\times 10000\\\\=68000[/tex]
So, the standard time is equal to 68000 s.
X2+2x-8 factorised.
Answer:
( x− 2 ) ( x + 4 )
Step-by-step explanation:
Answer:
[tex] {x}^{2} + 2x - 8 \\ sum = 2 \: and \: product = - 8 \\ factors = 4 \: and \: - 2 \\ = > {x}^{2} + 4x - 2x - 8 \\ = x(x + 4) - 2(x + 4) \\ = (x - 2)(x + 4)[/tex]
A sphere has a volume of 1,436 in3. What is its radius?
Answer:
7
Step-by-step explanation:
So first you would have to know the formula for the volume of a sphere to solve for the radius. The formula is:
V=4 /3πr3
so now we plug in the variables
1,436=4/3πr3
divide by pi
457.09=4/3r3
divide by 4/3 (multiply by the reciprocal which is 3/4)
342.82=r3
Take the third root to get r by itself
r=6.998 or 7 if you will.