Answer:
[tex]y_1 = -2[/tex] and [tex]y_2 = 4[/tex]
Step-by-step explanation:
[tex] \sqrt{10y + 24} - 3 = y + 1[/tex]
Move the constant to the right-hand side and change their sign.
[tex] \sqrt{10y + 24} = y + 1 + 3 [/tex]
combine like terms
[tex] \sqrt{10y + 24} - 3 = y + 4[/tex]
Square both side to remove square brackets.
10y + 24 - 3 = y²+ 8y + 16
Move the expression to the left-hand side and change its sign.
10y + 24 - y² - 8y - 16 = 0
Combine like terms
10y - 8y + 24 - 16 - y² = 0
2y + 8 - y² = 0
Use commutative property to reorder the terms.
-y² + 2y + 8 = 0
Change the sign of expression.
y² -2y -8 = 0
split -2y
y² + 2y - 4y - 8 = 0
Factor out y from the first pair and -4 from the second equation.
y ( y + 2 ) - 4 ( y + 2 ) = 0
Factor out y+2 from the expression.
( y + 2 ) ( y - 4)
When the products and factors equals 0, at least one factor is 0.
y + 2 = 0
y - 4 = 0
Solve for y
y = -2
y = 4
When we plug the both solution as y we found that both is true solution of this equation.
This equation has two solutions which are -2 and 4.
Answer:
Solution given:
[tex] \sqrt{10y + 24} - 3 = y + 1[/tex]
keep the constant term in one side
[tex] \sqrt{10y + 24} =y+1+3[/tex]
solve possible one
[tex]\sqrt{10y+24}=y+4[/tex]
now
squaring both side
[tex](\sqrt{10y+24})²=(y+4)²[/tex]
10y+24=y²+8y+16
taking all term on one side
10y+24-y²-8y-16=0
solve like terms
8+2y-y²=0
doing middle term factorisation
8+4y-2y-y²=0
4(2+y)-y(2+y)=0
(2+y)(4-y)=0
either
y=-2
or
y=4
y=-2,4
2 Select THREE expressions that are equivalent to 16x - 68 A. -4(4x - 17) B-28x + 3) c. 21-8-34) D 4 - 4 - 17) E 8 - 2x-8)
pls help:(
Answer:
Step-by-step explanation:
let's try a:
-4*4x-4*(-17) - expand the distributing terms
-16x-4*(-17) - simplify
-16x-(-68) - simplify again
-16x+68 - remove parentheses
-16x+68 does not equal to 16x-68
lets try b:
-28x+3... dont know what u mean
lets try c:
13-34 first
-21
lets try d:
0-17
-17
lets try e:
-2x+(8-8)
-2x
fortunally dont know what you mean.
Can someone help me I don't understand
Answer:
Okay,So lines of symmetry are basically how many different ways you can fold that shape without any hanging out etc.
Answer:
There are 3 lines of symmetry
Step-by-step explanation:
The lines of symmetry are
horizontal
vertical.
diagonal
Hope this helped! Please tell me if there is something wrong with my answer.
In ΔEFG, the measure of ∠G=90°, EG = 11, FE = 61, and GF = 60. What ratio represents the sine of ∠F?
Answer:
sinF = [tex]\frac{11}{61}[/tex]
Step-by-step explanation:
sinF = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{EG}{FE}[/tex] = [tex]\frac{11}{61}[/tex]
The ratio which represents the sine of ∠F is [tex]\frac{11}{61}[/tex].
What is sine of an angle?In a right angled triangle, the sine of an angle is the length of the side opposite the angle divided by the length of the hypotenuse.
Formula for sine of an anglesin θ = opposite side w.r.t θ / hypotenuse
According to the given question
We have
A right angle triangle EFG, in which
∠G = 90 degree
EG = 11
FE = 61
and, GF = 60
Now, the opposite side with respect to ∠F is GE
and the hypotenuse is EF
Therefore, sine of ∠F = side which is opposite w.r.t ∠F/ hypotenuse
⇒ [tex]sinF=\frac{GE}{EF}[/tex]
⇒ [tex]SinF=\frac{11}{61}[/tex]
Hence, the ratio which represents the sine of ∠F is [tex]\frac{11}{61}[/tex].
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Statement Reason
Check Answers
Answer:
Question?
Step-by-step explanation:
b) Tìm ba cách viết số hữu tỉ -11/25 dưới dạng tổng của hai số hữu tỉ dương.
f The difference of 8 and 3 is multiplied by one-quarter of the sum of 7 and 5 37 vedanta Excel in Mathematics
Answer:
15
Step-by-step explanation:
first find f which is (8-3) × ( 1/4 × 7 + 5)
simplify
5 × (1/4 ×12)
5 × 3
15 is thw answer
If p:q=3:4 and q:r=14:9, find p:r
Answer:
7/6
Step-by-step explanation:
p=3/4*q
q=14/9*r
so p=3/4*14/9r=7/6r
12
Use upper rectangles with areas equal to
Marks: 1
Area = f(x) · A3
to estimate the area under the curve of f(x) = x, on the interval from (1,3). Partition the interval into four subintervals. Hint:
Area = (F(1.5) + f(2) + f(2.5) + f(3))Ar = (1.53 +23 +2.53 +33)Az, where Ax =
Choose one answer.
ST
3-1
4
a. 35
b. 42
c. 27
d d. 19
Answer:
42
Step-by-step explanation:
Please hurry I will mark you brainliest
Answer:
q = 1/4
Step-by-step explanation:
-5/4 - (-1/4) = -1
-1/(q-1/2) = 4
-1 = 4(q-1/2)
-1 = 4q - 2
1 = 4q
q = 1/4
Solve for hhh: h-\left(-2.22\right)=-7.851h−(−2.22)=−7.851h, minus, left parenthesis, minus, 2, point, 22, right parenthesis, equals, minus, 7, point, 851 h =h=h, equals
The question isn't well formatted ; however, from what can be deduced from the question posted :
Answer:
- 10.071
Step-by-step explanation:
Given the expression :
Solve for hhh: h-\left(-2.22\right)=-7.851h−(−2.22)=−7.851h, minus, left parenthesis, minus, 2, point, 22, right parenthesis, equals, minus, 7, point, 851 h =h=h, equals
Expressing Mathematically :
h - (- 2.22) = - 7.851
Opening the bracket :
h + 2.22 = - 7.851
Subtract 2.22 from both sides :
h + 2.22 - 2.22 = - 7.851 - 2.22
h = - 10.071
The temperature is 45°F The temperature will decrease by 2°F each hour. Let
h be the number of hours.
When will the temperature be below 32°F?
Write an inequality for this problem.
A. 45 + 25 = 32
B. 45 - 2.32
C. 45 + 25 32
D. 45 - 253
Find the value of x for which (4/5)-4 x (4/5)-7 =(4/5)2x-1 Can some1 say this ans fast plz
Answer:
Fraction form: x = -21/4
Decimal Form: x = -5.25
Step-by-step explanation:
See the picture for steps :)
If the amount of waking time 4 year old children spend with their fathers each day is 42 minutes while the daily waking time spent in daycare is 6 hours, what is the ratio of time with father to time in daycare?
Answer:
7/60
Step-by-step explanation:
Because the question is phrased such that it asks "the ratio of time with father to....", we know to put the time with father on top, or first. Similarly, since it is asked to put the ratio of time with the father to the time in daycare, we can put the daycare amount second/on the bottom. Therefore, we can write the ratio as
(42 minutes)/(6 hours)
To make both of these in terms of minutes to simplify it, we know that 60 minutes = 1 hour, so 1 hour / 60 minutes =1 . Since multiplying something by 1 keeps it the same, we can multiply our ratio by this amount. We want to multiply with the hour on top so the hours cancel out, as so:
[tex]\frac{42 minutes}{6 hours} * \frac{1 hour}{60 minutes} = \frac{42 minutes * hours}{360 minutes * hours} = \frac{42}{360}[/tex]
To simplify this even further, we can note that 6 is a factor of both 42 and 360*, so we can multiply this fraction by (1/6) / (1/6) to get
(42/360) * (1/6)/(1/6) = 7/60 as our final answer
If this doesn't come up immediately, you can always find the greatest common factor by listing the factors of each number and finding the highest one that fits both, e.g.
for 42: 42, 21, 14, 7 , 6...
for 360: 360,180, ... 6,5....
help me please and thank youu
Answer:
-3
Step-by-step explanation:
The shape on the left is translated to the shape on the right which statement about transformation is true?
Sally spent half of her allowance going to the movies. She washed the family
car and earned 6 dollars. What is her weekly allowance if she ended with
17 dollars ?
does it give the answer choice or is it a blank space?
How do I write a verbal expression for each algebraic expression?
23f
Answer:
Twenty three times f
Step-by-step explanation:
If x / 2y = 0.4 , A / 5B = 0.25 Then A + y / 5 =…....
Answer:
[tex] \frac{x}{2y} = \frac{4}{10} \\ 8y = 10x \\ y = \frac{10x}{8} - - - - - 1 \\ \\ \frac{a}{5b} = \frac{25}{100} \\ \frac{a}{5b} = \frac{1}{4} \\ 4a = 5b \\ a = \frac{5b}{4} - - - 2 \\ \\ so \: \: \frac{a + y}{5} \\ = (a + y) \times \frac{1}{5} \\ = ( \frac{5b}{4} + \frac{5x}{4} ) \times \frac{1}{5} \\ = \frac{5b + 5x}{4} \times \frac{1}{5} \\ = \frac{5(b + x)}{4} \times \frac{1}{5} \\ = \frac{b + x}{4} \\ \\ so \: \: \: \frac{a + y}{5} = \frac{b + x}{4} [/tex]
Given that [tex]\frac{x}{2y} = 0.4 \ and \frac{A}{5B} = 0.25.[/tex] The value of equation [tex]\ \frac{A+y}{5} = \frac{x+10B}{40}[/tex]
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. The expressions may contain any constants, variables and algebraic operators.
Given the equations,
equation 1:
[tex]= \frac{x}{2y} = 0.4 = \frac{4}{10} \\\\= 10x = 80y \\\\= x = 8y\\\\=y = \frac{x}{8}[/tex]
equation 2:
[tex]\frac{A}{5B} = 0.25 = \frac{25}{100} = \frac{1}{4}\\ \\=4A = 5B\\\\=A = \frac{5B}{4}[/tex]
We need to find [tex]\frac{A + y}{5}[/tex],
putting the value of A and y in the equation,
[tex]= \frac{A + y}{5}\\\\=\frac{\frac{x}{8}+\frac{5B}{4} }{5} \\\\= \frac{x+10B}{40}[/tex]
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What is the distance between (1, 9) and (1, -4)? Use the distance formula.
D=(x2-x1)2+(y2-y1)2
Answer:
D. 13
Step-by-step explanation:
You just have to plug in numbers then solve.
(1,9) and (1,-4). Every coordinate is placed as (x,y)
(1,9) is labeled as (x1, y1)
(1,-4) is labeled as (x2,y2)
Now plug in the numbers.
d= Square root of (1-1)^2 + (-4-9)^2
d= Square root of 1^2 +-13^2
d= Square root of 1+169
d= Square root of 170
d= 13.04
Rounded to a whole number, the answer is 13
Answer:
D
Step-by-step explanation:
you have to substitute the values in the distance formula,in this case x2 is 1,x1 is 1,y2 is -4 and y1 is 9
d=√(x2-x1)²+(y2-y1)²
=√(1-1)²+(-4-9)²
=√(0)²+(-13)²
=√169
=13
I hope this helps
In this figure, a line through points X and Y will _____
Answer:
D.
Step-by-step explanation:
The line will be a straight line and will go through AB in the center. Therefore, it will be the perpendicular bisector.
HELP HURRY PLEASE i dont understanddd
Answer:
see image
Step-by-step explanation:
put a point on .5 on the x axis and a point on -3 on the y axis draw a line through them and shade the space under the line
I NEEDDD HELPPPP ASAPPPP ITS URGENTTT!!!!
Answer:
(x-6)^2+(y-14)^2=4
Step-by-step explanation:
The present age of Madison's Mother is 3 time that of Madison. After 6 1/4 years, the sum of their age will be 53 3/4 years. Find their present ages. (Estimate to the nearest whole number)
Answer: [tex]10, 31\ \text{years}[/tex]
Step-by-step explanation:
Given
The present age of Madison's Mother is three time that of Madison
Suppose the Present age of Madison is [tex]x[/tex], so age of her mother is [tex]3x[/tex]
After [tex]6\dfrac{1}{4}\ \text{years}[/tex], the sum of their age will be [tex]53\dfrac{3}{4}\ \text{years}[/tex]
[tex]\therefore (x+6\dfrac{1}{4})+(3x+6\dfrac{1}{4})=53\dfrac{3}{4}\\\\\Rightarrow 4x+2\times \dfrac{25}{4}=\dfrac{53\times 4+3}{4}\\\\\Rightarrow 4x+\dfrac{50}{4}=\dfrac{215}{4}\\\\\Rightarrow 4x=\dfrac{215-50}{4}\\\\\Rightarrow x=\dfrac{165}{16}\\\\\Rightarrow x= 10.31\approx 10[/tex]
Madison mother's age [tex]3x=30.93\approx 31\ \text{years}[/tex]
need help with this!!
what is the equation of the graph ?
Answer:
what graph
Step-by-step explanation:
A certain country is divided into 5 provinces. Each province consists entirely of Progressives and Traditionalists. If each province contains the same number of Traditionalists and the number of Traditionalists in any given province is 1/10 the total number of Progressives in the entire country, what fraction of the country is Traditionalist
Answer:
one third (1/3)
Step-by-step explanation:
we have 5 provinces.
Each province contains the same number of Traditionalists, let's say that there are T traditionalists per province, thus, there are:
5*T in the country.
now we know that in each province, the number of traditionalists is equal to 1/10 of the total number of progressives in the entire country.
If there are a total of P progressives in the entire country, we will have that:
T = P/10
Then the total number of traditionalists in the entire country is:
5*T = 5*(P/10) = P/2
So in the whole country, there are P progressives and P/2 traditionalists.
So the total population is:
total = P + P/2 = (3/2)*P
We want to know what fraction of the country is traditionalist, this is equal to the quotient between the traditionalist population, P/2, and the total population, (3/2)*P
This is:
[tex]c = \frac{P/2}{(3/2)*P} = 1/3[/tex]
So one third of the country is traditionalist.
Please help explanation if possible
Answer:
y = 1/7x + 0
Step-by-step explanation:
3x + 21y = 21
21y = -3x + 21
y = -3/21x
y = 1/7x
A kindergarten class had a total of 15 boys 9 girls , what is the ratio of girls to boys in that class ?
Answer:
9:15
girls : boys
Step-by-step explanation:
Answer:
9:15
Or 3:5 when reduced
Step-by-step explanation:
15/2 divided by 5/3
Brainlest is one the line
Answer:
[tex] \frac{9}{2} [/tex]
Step-by-step explanation:
[tex] \frac{15}{2} \div \frac{5}{3} = \frac{15}{2} \times \frac{3}{5} = \frac{3}{2} \times \frac{3}{1} = \frac{9}{2} [/tex]
In a survey of women in a certain country the mean height was 62.9 inches with a standard deviation of 2.81 inches answer the followinv questions about the specified normal distribution
The question is incomplete. The complete question is :
In a survey of women in a certain country ( ages 20-29), the mean height was 62.9 inches with a standard deviation of 2.81 inches. Answer the following questions about the specified normal distribution. (a) What height represents the 99th percentile? (b) What height represents the first quartile? (Round to two decimal places as needed)
Solution :
Let the random variable X represents the height of women in a country.
Given :
X is normal with mean, μ = [tex]62.9[/tex] inches and the standard deviation, σ = [tex]2.81[/tex] inches
Let,
[tex]$Z=\frac{X - 62.9}{2.81}$[/tex] , then Z is a standard normal
a). Let the [tex]99th[/tex] percentile is = a
The point a is such that,
[tex]$P(X<a)=0.99$[/tex]
[tex]$P \left( Z < \frac{a-62.9}{2.81} \right) = 0.99$[/tex]
From standard table, we get : [tex]P( Z < 2.3263) =0.99[/tex]
∴ [tex]$\frac{(a-62.9)}{281} = 2.3263$[/tex]
[tex]$a= (2.3263 \times 2.81 ) +62.9$[/tex]
= 6.536903 + 62.9
= 69.436903
= 69.5 (rounding off)
Therefore, the height represents the [tex]99th[/tex] percentile = 69.5 inches.
b). Let b = height represents the first quartile.
It is given by :
[tex]P( X < b) =0.25[/tex]
[tex]$P \left( Z < \frac{(b-62.9)}{2.81} \right) = 0.25$[/tex]
From the standard normal table,
[tex]P( Z < -0.6745) =0.99[/tex]
∴ [tex]$\frac{(b-62.9)}{2.81}= 0.6745$[/tex]
[tex]$b=(0.6745 \times 2.81) +62.9$[/tex]
= 1.895345 + 62.9
= 64.795345
= 64.8 (rounding off)
Therefore, the height represents the 1st quartile is 64.8 inches.
