5a + 4b = 31
5a + 6b = 39
What is a and what is b

Answers

Answer 1

Answer:

a = 3 and b = 4

Step-by-step explanation:

5a + 4b = 31 --(1)

5a + 6b = 39 --(2)

(2) - (1) : 2b = 8

               b = 4 -- (3)

Substituting (3) into (1),

5a + 16 = 31

5a = 15

a = 3 -- (4)

Therefore, a = 3 and b = 4

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Related Questions

Robert and Chris can skate 4 miles in 18 minutes. How far can they ride in 45 minutes?​

Answers

Answer: Robert and Chris can skate 10 miles in 45 minutes.

Step-by-step explanation:

Let's start by finding the unit rate.

[tex]\frac{4}{18} =\frac{2}{9} \\\frac{18}{18} =1[/tex]

Robert and Chris can skate [tex]\frac{2}{9}[/tex] of a mile in 1 minute. Now we can multiply both by 45 to see how far the can go in 45 minutes.

[tex](\frac{2}{9}) (\frac{45}{1} )\\\frac{(2)(45)}{(9)(1)} \\\frac{90}{9} \\10[/tex]

45x1=45

The can skate 10 miles in 45 minutes.

How many different license plates are possible if digits and letter can be repeated if the configuration is 3 letters, 2 digits, 2 letters?

Answers

Answer:

1,188,137,600 possible combinations

Step-by-step explanation:

The first three and last two digits can be any letter while the middle two digits can be any number.

26*26*26*10*10*26*26=1,188,137,600

Solve the system x-2y+2z=9 y+2z=5 z=3
Enter the answer as an ordered triple, (X,Y,Z)

Answers

The last equation says z = 3, so that in the second equation we get

y + 2z = y + 6 = 5   ==>   y = -1

and in turn, the first equation tells us

x - 2y + 2z = x + 2 + 6 = x + 8 = 9   ==>   x = 1

So the solution to the system is (x, y, z) = (1, -1, 3).

The answer is (1, -1, 3)

which values are solutions to the inequality below? Check all that apply. √x <7
A. -15
B. 48
C. 14
D. 2
E.51
F. No Solutions

Answers

Answer:

B,C,D

Step-by-step explanation:

Square both sides of the equation to get rid of the square root surrounding x.

sqrtX^2 = x and 7^2 = 7*7 = 49

x<49

And since we have a radical, we have to have non-negative solutions (the radical used in the equation actually only means the positive square root) meaning x>0

So which one of the choices is less than 49 and greater than 0?

B,C, and D are all less than 49, and greater than 0

given 12 consecutive integers in how many ways can three of these integers be selected to give a sum which divides by 4?

Answers

There are  [tex]55[/tex] ways of these integers be selected to give a sum.

Given that:

It has [tex]12[/tex] consecutive integers .

Now,

Definition of consecutive integers :

" Consecutive integers are the integers that follow in the fixed sequence .

Consecutive integers is represented by  [tex]n,n+1,n+2,n+3,....[/tex] where [tex]n[/tex] is an integer."

By given :

we have [tex]12[/tex] consecutive integers .

Thus,[tex]n=1[/tex] and substitute the equation is,

[tex]1,(n+1),(1+2),(1+3),(1+4),(1+5),(1+6),(1+7),(1+8),(1+9),(1+10),(1+11)\\\\\implies 1,2,3,4,5,6,7,8,9,10,11,12[/tex]

Now,

Split all the integers into 4 equal parts,

Part 1:  Those integers are divisible by [tex]4[/tex] and the remainder be 0.

Then,  

   [tex]a=0(mod 4)[/tex]

Part 2:  Those integer producing the remainder [tex]1[/tex] when it is divisible by [tex]4[/tex].

Then,

   [tex]a=1(mod 4)[/tex]

Part 3:  Those integer producing the remainder [tex]2[/tex]  when it is divisible by[tex]4[/tex].

Then,

    [tex]a=2(mod 4)[/tex]

Part 4: Those integer producing the remainder [tex]3[/tex]  when it is divisible by[tex]4[/tex].

Then,

   [tex]a=3(mod4)[/tex]

Since, three of these integers be selected to give a sum which divides by [tex]4[/tex] is,

In any 12 consecutive integers there are [tex]12\div4[/tex]

i.e. exactly 3 numbers of each category of mod4 namely ,

[tex]0(mod4), 1(mod4), 2(mod4), 3(mod4)[/tex]

Thus, the  total combinations of above [tex]5[/tex] categories of sets of [tex]3[/tex] integers are

All the 3 numbers are  [tex]0(mod4)[/tex]

                 [tex]3C_1=3(1)=3[/tex]

One number be   [tex]0(mod4)[/tex]  and other two numbers are  [tex]2(mod4)[/tex]

            [tex]3C_1*3C_2=3(1)*3=9[/tex]

One number  [tex]0(mod4)[/tex]  and other numbers  [tex]1(mod4)[/tex] & [tex]3(mod4)[/tex]

           [tex]3C_1*3C_1*3C_1=3*3*3=27[/tex]

Two numbers be [tex]1(mod4)[/tex] and one  number be [tex]2(mod4)[/tex]  

           [tex]3C2 * 3C1 = 3*3 = 9[/tex]

One number  be  [tex]2(mod4)[/tex] and two numbers be [tex]3(mod4)[/tex]

           [tex]3C1 * 3C2 = 3*3 = 9[/tex]

Thus, sum of the total ways be [tex]12[/tex] consecutive integers of three integers is divisible by 4 is,

       [tex]3+9+27+9+9=55[/tex]

Hence, it has [tex]55[/tex] ways.

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Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.7 feet and a standard deviation of 0.4 feet. A sample of 74 men’s step lengths is taken. Step 1 of 2 : Find the probability that an individual man’s step length is less than 2.5 feet. Round your answer to 4 decimal places, if necessary.

Answers

Answer:

0.3085 = 30.85% probability that an individual man’s step length is less than 2.5 feet.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 2.7 feet and a standard deviation of 0.4 feet.

This means that [tex]\mu = 2.7, \sigma = 0.4[/tex]

Find the probability that an individual man’s step length is less than 2.5 feet.

This is the p-value of Z when X = 2.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.5 - 2.7}{0.4}[/tex]

[tex]Z = -0.5[/tex]

[tex]Z = -0.5[/tex] has a p-value of 0.3085

0.3085 = 30.85% probability that an individual man’s step length is less than 2.5 feet.

SOMENE PLS PLS HELP IL GIVE OYU A KISS AND A COOKIE FI YOU HHELP E IM BEGGING

Answers

Answer:

B

Step-by-step explanation:

SOH CAH TOA

sin theta = opp/hyp

csc theta = hyp/opp

csc theta = 10/8 = 5/4

cos theta = adj/hyp

sec theta = hyp/adj

sec theta = 10/6 = 5/3

Answer: B

Can someone please help me?

Answers

Answer:

A is the correct answer

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Remember X intercept is when y is equal to zero

So basically f(x-4) is literally equal to y=radical (x-4)

When graphing them you will notice that the x intercept is 4 units lower

Suppose the mean height for men is 70 inches with a standard deviation of 2
inches. What percentage of men are between 68 and 74 inches tall? Enter
the value of the percentage without the percent sign.

Answers

Answer:

81.85.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Suppose the mean height for men is 70 inches with a standard deviation of 2 inches.

This means that [tex]\mu = 70, \sigma = 2[/tex]

What percentage of men are between 68 and 74 inches tall?

The proportion is the p-value of Z when X = 74 subtracted by the p-value of Z when X = 68.

X = 74

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{74 - 70}{2}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772.

X = 68

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{68 - 70}{2}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a p-value of 0.1587.

0.9772 - 0.1587 = 0.8185

0.8185*100% = 81.85%.

Thus the percentage is 81.85%, and the answer is 81.85.

Bradley was passing out fliers to different neighborhoods. There were 20 neighborhoods that he wanted to hit. If each neighborhood had 83 houses, how many fliers would Bradley need?
(PLEASE HELP ME I WILL GIVE BRAINLIEST)

Answers

Answer:

1660

Step-by-step explanation:

Type the correct answer in the box.
The formula for the volume, V, of a cone having the radius, r, and the height, h, is shown below.
V r2h
-
Write the formula to calculate the height, h.

Answers

Step-by-step explanation:

V should be written as (1/3) pi r^2 h

V = (1/3) pi r^2 h multiply by 3

3V = pi r^2 h Divide by pi

3V/ pi = r^2 h Divide by r^2

3V / (pi *r^2 ) = h

What’s the value of the expression below

Answers

Answer:

8

Step-by-step explanation:

When multiplying numbers with the same base

the exponents are added

1/4 + 1/4 + 1/4 + 1/4  = 1

8¹ = 8

What is the surface area of the regular pyramid below?

Answers

D. 304 sq units

Surface area is just finding the area of each face of a 3d figure and adding it up together:

Area of square base:
8 • 8 = 64 sq units

Area of ONE triangle face:
1/2 • 15 • 8 = 60 sq units
MULTIPLY that by 4 because we have 4 triangle faces: 60 • 4 = 240 sq units

ADD area of square base and 4 triangle faces: 240 + 64 = 304

FINAL ANSWER OF SURFACE AREA:
304 sq. units

BRAINLIEST will be much appreciated!
-SpaceMarsh, have a nice day/night!

I would if someone could answer this :)

Answers

1- 90
2- 60
3- 60
4- 30
90 primera opcion
60 segunda opcion
60 tercera opcion
30 cuarta opcion

Using a Simple Radom Sample of 500 rental property owners in Washington State, a 95% confidence interval estimate of the proportion who own rental property by the water is (0.281, 0.392). Which of the following is the correct interpretation of this interval?

a. Ninety-five percent of all samples of size 500 will result in a proportion of rental property between 0.281 and 0.392.
b. There is probability equal to 0.95 that the proportion of owning a rental property by the water is between 0.281 and 0.392
c. 95% confident that the sample proportion of rental propery owners in Washington is between 28.1% and 39.2%.
d. We can be 95% confident that between 28.1% and 39.2% of all rental property owners own a property by the water

Answers

Answer:

Hence the correct option is option d.

Explanation:

We can 95% confident that between 28.1% and 39.2% of all rental property owners own a property by the water.  

Here correct option for interpretation of the 95% confidence interval. The remaining options are about probabilities and sample proportions.

6
Which expression is equivalent

Answers

Answer:

I thimk it is B

Step-by-step explanation:

❗️‼️❗️❗️‼️‼️‼️❗️‼️

What’s the area help please and please attach work

Answers

Answer:

106

Step-by-step explanation:

5 x 2 = 10

7 + 5 = 12

8 x 12 = 96

96 + 10 = 106 :)

Helpppp plssssss I need to get my grade up in math

Answers

Answer: 1.25 square feet

This converts to the improper fraction 5/4

===========================================================

Explanation:

The area of the triangle on the left is base*height/2 = 0.5*2/2 = 0.5 square feet. Note that 1/2 = 0.5

The area of the triangle on the right side is base*height/2 = 0.2*3/2 = 0.75 square feet. This converts to the fraction 3/4

Add up the two results: 0.5+0.75 = 1.25 square feet

-----------

If you need the answer as an improper fraction, then,

1.25 = 1 + 0.25

1.25 = 1 + 1/4

1.25 = 4/4 + 1/4

1.25 = (4+1)/4

1.25 = 5/4

Write the following equation in the general form Ax + By + C = 0.

y - x - 1 = 0

2x - 3y + 6 = 0
2x - 3y - 6 = 0
-2x + 3y - 6 = 0

Answers

Answer:

C. -2x +3y-6=0

this is the answer

Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following: 22 Pennies 27 Dimes 9 Nickels 30 Quarters What is the probability that you reach into the jar and randomly grab a penny and then, without replacement, a dime

Answers

Answer:

[tex]P(Penny\ and\ Dime) = \frac{9}{116}[/tex]

Step-by-step explanation:

Given

[tex]Pennies = 22[/tex]

[tex]Dimes = 27[/tex]

[tex]Nickels = 9[/tex]

[tex]Quarters = 30[/tex]

Required

[tex]P(Penny\ and\ Dime)[/tex]

This is calculated as:

[tex]P(Penny\ and\ Dime) = P(Penny) * P(Dime)[/tex]

Since it is a selection without replacement, the computation is:

[tex]P(Penny\ and\ Dime) = \frac{Penny}{Total} * \frac{Dime}{Total-1}[/tex]

So, we have:

[tex]P(Penny\ and\ Dime) = \frac{22}{22+27+9+30} * \frac{Dime}{22+27+9+30-1}[/tex]

[tex]P(Penny\ and\ Dime) = \frac{22}{88} * \frac{27}{87}[/tex]

[tex]P(Penny\ and\ Dime) = \frac{1}{4} * \frac{9}{29}[/tex]

[tex]P(Penny\ and\ Dime) = \frac{9}{116}[/tex]

HELP ASAP PLS 10 points AND BRAINLEST

Answers

Answer:

ABC is congruent to EDC because m<3 = m<4 and m<1 = m<5

Step-by-step explanation:

m<3 and m<4 are vertical angles so they are congruent. m<1 and m<5 are alternate interior angles so they are also congruent.

Find the equation of the line that has a slope of 7 and a y intercept of -10. Write you answer in the form of y = mx + b

Answers

Answer:

Step-by-step explanation:

y = mx + b is the slope-intercept form of a line where m is the number value of the slope and b is the number value of the y-intercept. Our slope is given as 7, therefore, m = 7 in our equation. Our y-intercept is given as -10; thus, b = -10. Filling that in gives us y = 7x - 10

Answer: y=7x-10

Step 1: Rewrite information

y=mx+b
Slope of 7
Y intercept of -10

Step 2: Understand each component

To properly solve this equation, it helps to understand each part of the equation.
Y- Answer
M- Slope
X- Variable
B- Y intercept

Step 3: Substitute numbers

Using the information from step 2, substitute each number in the correct part.

y=7x+ -10

Step 4: Final equation

The equation y=7x+ -10 is almost correct, except that we cannot have a + and - sign next to each other. The equation will hav the same meaning if we were to remove the plus sign.

y=7x-10 is the final answer!

Hope this helps :)

a line through (4,2) with slope 1/2

Answers

Answer:

Step-by-step explanation:

Use the formula P=MX+B

Cheryl is making homemade fruit soda. She needs 14 pints of fruit juices and club soda for her recipe. How many cups of homemade fruit soda does Cheryl make?

Answers

Well, if one pint is equal to 2 cups then, we are able to multiply 14 by 2 which gives us 28. Therefore, Cheryl can make 28 cups of homemade soda.

A. State whether each figure is a polygon​

Answers

All the shapes except the circle & heart are polygons
All except circle and heart

can anyone ps answer this? it's urgent! ​

Answers

Answer:

9:125

Step-by-step explanation:

To write a ratio correctly, you need the same units for both numbers.

Let's convert liters into milliliters.

1 L = 1000 mL

Ratio of 72 mL to 1000 mL =

= 72:1000

Divide both numbers by their GCF, 8.

= 9:125

Sarah bought a TV for £250
Three years later she sold it for £180
Work out her percentage loss

Answers

Answer:

36%

Step-by-step explanation:

Step-by-step explanation:

Loss percentage= loss/cost× 100%

250-180=70

70/180=0.3888

0.3888×100%=39%

Determine whether the source given below has the potential to create a bias in a statistical study. A certain medical organization tends to oppose the use of meat and dairy products in our​ diets, and that organization has received hundreds of thousands of dollars in funding from an animal rights foundation.
A. There does not appear to be a potential to create a bias. The organization would not gain from putting spin on the results.
B. There does appear to be a potential to create a bias. There is an incentive to make the results statistically insignificant.
C. There does appear to be a potential to create a bias. There is an incentive to produce results that are in line with the​organization's creed and that of its funders.
D. There does not appear to be a potential to create a bias. The organization is reputable and has many professional and credible members.

Answers

The answer is C. Hope this helps

3x-6y-2z=-17
−6x+4y+5z=13
−3x−4y−3z=22

Answers

Answer:

1) x = -17 +6y + 2z/3

2) x= -13 - 4y - 5z/6

3) x= -22 +4y + 3z/3

Step-by-step explanation:

1) 3x-6y-2z=-17

3x- 6y -2z- (-6y -2z)= - 17 - ( 6y -2z )

3x=-17+6y+2z

3x/3= -17/3 +6y/3 + 2z/3

x = -17 +6y + 2z/3

2) −6x+4y+5z=13

-6x+4y+5z- ( 4y + 5z )= 13 - ( 4y + 5z )

-6x=13-4y-5z

-6x/-6= 13/-6 - 4y/-6 - 5z/-6

x= -13 - 4y - 5z/6

3) −3x−4y−3z=22

-3x=22+4y+3z

-3x/-3 = 22/-3 + 4y/-3 +3z/-3

x= -22 +4y + 3z/3

Which of the following is true regarding the sequence graphed below?
an
35
30
25
• (5, 25)
20
15-
• (4. 16)
10 -
• (3,9)
5
• (2, 4)
1 2 3
4
5 6
7 8
9
n
The sequence is arithmetic because the terms have a common difference.
O The sequence is arithmetic because the terms do not have a common difference

Answers

Answer:

I think the answer is the sequence is arithmetic because the term have a common difference

The correct option is The sequence is not arithmetic because the terms do not have a common difference.

What is an arithmetic sequence?

An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k.

This is in contrast to a geometric sequence where each term increases by dividing/multiplying some constant k called the common difference.

Given is graph, we need to conclude the true about the graph,

Finding the common difference,

4-1 = 3    

9-4 = 5

16-9 = 7

25-16 = 9

Clearly from the set of values that are given in the graph we could observe that the function that is formed using these set of values is:

y=f(n)=n² where n=1,2,3,4,5,.....

That mean, the following sequence is not an arithmetic sequence as the common difference is different.

Hence, the correct option is The sequence is not arithmetic because the terms do not have a common difference.

Learn more about arithmetic sequence click;

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