Really struggling with these problems please help!
Solve.
[tex] \sqrt{10y + 24} - 3 = y + 1[/tex]

Answers

Answer 1

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 2

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


Related Questions

Can someone help me I don't understand

Answers

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 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

Answers

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.

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

Answers

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

I NEEDDD HELPPPP ASAPPPP ITS URGENTTT!!!!

Answers

Answer:

(x-6)^2+(y-14)^2=4

Step-by-step explanation:

need help with this!!

Answers

Answer: C. 40



Explanation: Since the correct graph is 3 (based on the information given), you would look at the part of the graph where only circles BM and NT overlap. The number inside that section would be the amount of people who watched both Batman and Ninja Turtles but not Looney Tunes. By observing the graph, you can tell that the number 40 is in the section where BM and NT overlap, so therefore the answer would be 40.



Hope that helps シ

If x / 2y = 0.4 , A / 5B = 0.25 Then A + y / 5 =….... ​

Answers

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]

Learn more about equations here

https://brainly.com/question/33622350

#SPJ2

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)

Answers

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]

How do I write a verbal expression for each algebraic expression?

23f

Answers

Answer:

Twenty three times f

Step-by-step explanation:

The shape on the left is translated to the shape on the right which statement about transformation is true?

Answers

When. Dbhdbhsbbsb send Sheba ebbs she be be she ehehhd rhehebjebd jehd Ivan’s shhdbdhs ehuehe while she dhhe e hehebehe

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

Answers

Answer:

42

Step-by-step explanation:

HELP HURRY PLEASE i dont understanddd

Answers

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

Statement Reason
Check Answers

Answers

Answer:

Question?

Step-by-step explanation:

help me please and thank youu

Answers

Answer:

-3

Step-by-step explanation:

y - y1 = m(x - x1) m = slope

y - 5 = -3(x - 17) slope = -3

Answer:

-3

Step-by-step explanation:

b) Tìm ba cách viết số hữu tỉ -11/25 dưới dạng tổng của hai số hữu tỉ dương.

Answers

Bạn ơi tổng hai số hữu tỉ dương làm sao bằng âm được ạ? Bạn xem lại đề có sai không ạ ^^

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

Answers

Answer:

Fraction form: x = -21/4

Decimal Form: x = -5.25

Step-by-step explanation:

See the picture for steps :)

If p:q=3:4 and q:r=14:9, find p:r

Answers

Answer:

7/6

Step-by-step explanation:

p=3/4*q

q=14/9*r

so p=3/4*14/9r=7/6r

f The difference of 8 and 3 is multiplied by one-quarter of the sum of 7 and 5 37 vedanta Excel in Mathematics​

Answers

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

15/2 divided by 5/3

Brainlest is one the line

Answers

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]

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:(​

Answers

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.

In this figure, a line through points X and Y will _____

Answers

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.

Please help explanation if possible

Answers

Answer:

y = 1/7x + 0

Step-by-step explanation:

3x + 21y = 21

21y = -3x + 21

y = -3/21x

y = 1/7x

Please hurry I will mark you brainliest

Answers

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

What is the distance between (1, 9) and (1, -4)? Use the distance formula.

D=(x2-x1)2+(y2-y1)2

Answers

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

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 ?

Answers

does it give the answer choice or is it a blank space?

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?

Answers

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....

In ΔEFG, the measure of ∠G=90°, EG = 11, FE = 61, and GF = 60. What ratio represents the sine of ∠F?

Answers

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 angle

sin 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].

Learn more about sine of an angle here:

https://brainly.com/question/13656175

#SPJ2

what is the equation of the graph ?

Answers

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

Answers

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.

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

Answers

The answer is going to a: 45+ 25 = 32

A kindergarten class had a total of 15 boys 9 girls , what is the ratio of girls to boys in that class ?

Answers

Answer:

9:15

girls : boys

Step-by-step explanation:

Answer:

9:15

Or 3:5 when reduced

Step-by-step explanation:

Other Questions
The nation that Georgia belongs to: the length of a rectangular box is 8cm. If its diagonal is 10cm. Find its width 1. Choose the correct decimal for "three tenths."30.030.0030.3 Please hurry, if you do reply thank u, it means alot! what good things we can do for our country by becoming football players? plz help me Complete the table y+1=7/8x A day i will never forget Alejandro moves to Australia because he found a new job. Which word bestdescribes Alejandro?O A. TouristB. ImmigrantC. WorkerD. Transient Tell whether the line for x = -5 is horizontal, vertical, or neither. What is the best example of a person displaying a high level of muscular endurance?(Select all that apply.)Performing consecutive curl-ups for one minute.Completing a heavy squat exercise for three repetitions.,Completing a heavy bench press exercise for three repetitionsPerforming consecutive push-ups for one minute. what is the best word choice bused to describe the probalility of beatingt your friem easy biology question below first correct answer gets brainliest During the testing phase of an ERP system, the system implementation assurers should review: Group of answer choices Program change requests Vendor contracts Error reports Configuration design specifications . Error Analysis Describe and correct the errora student made when ordering numbers fromleast to greatest.HELP ASAP How do you calculate percentage or find the per cent value 40 POINTS ASAP PLEASE Read the sentence: Rafael finds fossils. Select the sentence that correctly uses a prepositional phrase to add detail. Rafael finds fossils around his neighborhood. Rafael finds fossils but never shark's teeth. Rafael finds fossils when he goes digging. Rafael finds fossils, which he thinks are cool. PLS HELP ME!!!A sample is generated from a population of 20 items. Each of the 20 items are given a label, and a 20-sided die is rolled 3 times to determine which 3 items are in the sample. This is an example of a __________.A. systematic sampleB. random sampleC. convenience sampleD. self-selecting sample Anyone could please answer this?? A consumer must decide between purchasing a new television or a new computer. What limited resource is responsible for this trade-off decision? A. The consumer has a different benefit from each possible product. B. The profit the producers receive from each possible purchase. C. The producers have a limited number of televisions and computers. D. The consumer has a limited amount of money available for purchases. An AED automatically detects if ais needed. *Your answerOThis is a required question