The sum of two numbers is 90. The larger
number is 14 more than 3 times the smaller
number. Find the numbers.

Answers

Answer 1

Answer:

The numbers are 19 and 71.

Step-by-step explanation:

Let x and y represent the two numbers.  Then x + y = 90.  

Also, if we assume that the larger number is y, then y = 3x + 14.

We must solve this system of linear equations.  Since we already have the result of solution for y  (y = 3x + 14), let's use the substitution method to find the solution:

x + y = 90 becomes x + 3x + 14 = 90, or:

4x = 76.  Thus, x = 76/4, or 19.       If x = 19, then y = 3(19) + 14, or y = 71.

The numbers are 19 and 71.

Note that these add up to 90, as they must, and that 71 is 14 more than 3 times 19.

Answer 2

Answer:

[tex]19\text{ and }71[/tex]

Step-by-step explanation:

Let the smaller number be [tex]x[/tex]. The larger number can be represented by [tex]3x+14[/tex]

Solving, we get:

[tex]x+3x+14=90,\\4x+14=90,\\4x=76,\\x=\boxed{19}[/tex]

The larger number is therefore [tex]90-19=\boxed{71}[/tex]


Related Questions

What is 1/6 divided by 1/2/3 in simplest form

Answers

Answer:

1

Step-by-step explanation:

Given :

[tex]\frac{1}{6}[/tex]   divided by [tex]\frac{1/2}{3}[/tex]

Now, it can be solving as:

[tex]\frac{1/6}{\frac{\frac{1}{2} }{3} } \\=\frac{\frac{1}{6} }{\frac{1}{6} } \\=1[/tex]

Simplest form of given equation is 1

What is the volume of a sphere with a radius of 30.5 cm

Answers

118,847 is the volume

Can someone help me which expression is equal to 16

Answers

Answer:

D.(4^1/2)^4

hope this helps

have a good day :)

Step-by-step explanation:

what is tangent (260) rounded to the nearest hundredth

Answers

Answer:

tan 260 = 5.670

Step-by-step explanation:

What is tangent (260) rounded to the nearest hundredth

Given data

θ=260

We want to find the value of

tan θ

Hence, from table

tan 260= 5.670

the graph of the function f(x)=ax^2+bx+c is given below could the factor of f(x) be ( x + 2) (x - 3)?

Answers

Step-by-step explanation:

everything can be found in the picture

The graph of the function f(x)=ax²+bx+c could have the factor of f(x) be ( x + 2) (x - 3)

What is a function?

A relation is a function if it has only One y-value for each x-value.

We can set two functions y₁=x+2 and y₂=x-3

Let us draw these two functions on the graph

We observe that the function  f(x)=ax²+bx+c  intersects y₁ and y₂.

y₁ intersects x axis at (-2, 0)

y₁ intersects y axis at (0, 2)

y₂ intersects x axis at (3, 0)

y₂ intersects y axis at (0, -3)

Hence, the graph of the function f(x)=ax²+bx+c could have the factor of f(x) be ( x + 2) (x - 3)

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Two mechanics worked on a car. The first mechanic charged S75 per hour, and the second mechanic charged S50 per hour. The mechanics worked for a
combined total of 25 hours, and together they charged a total of $1750. How long did each mechanic work

Answers

Step-by-step explanation:

t8d0dt80dtidt8cyxyyx9uf0

Warm-Up
Construct a perpendicular bisector to PQ
by following these steps.
1. Move the compass center to P and
draw a long arc that intersects PQ.
Then move the compass to Q and
draw an arc that intersects the first
arc in two places.

Answers

Note that the perpendicular bisector to line PQ is constructed and attached accordingly. Here is how to do it.


How do you construct a perpendicular bisector to PQ?

Note that the first stage is to draw a line PQ. But this has already been done.

Next is to place the compass on P as shown in the image above. If you allow you compass (locked at the same degree) to rotate about point P, you will get a circle. However, that is not the objective.

If you also place your compass on point Q, locked to the same degree as when it was on P, and take a rotation around point Q, you will also get a circle.

At some point, you will notice that both circles intersect at two point, which we can call AB₁ and AB₂.

Now you are done with the compass. Take up your ruler, and place it such that it meet both AB₁ and AB₂ but allowing you space to mark a line connecting both points.

Next, using your live or online pencil tool, draw the line from AB₁ to AB₂. Now you have the Perpendicular bisector which you can call AB₁₂.

Note that a perpendicular bisector is a line or plane that intersects a line segment at its midpoint, forming a right angle and dividing the segment into two equal parts.

Learn more about Perpendicular Bisector on:

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I will give brainliest to whoever explains answer thouroughly.

There is a spinner with 15 equal areas, numbered 1 through 15. If the spinner is spun one time, what is the probability that the result is a multiple of 5 or a multiple of 2?

Answers

Answer:

67

The multiples of 2 between 1 and 15 are

2, 4, 6, 8, 10, 12, 14

The multiples of 5 are

5, 10, 15

So, there are seven multiples of 2 and three multiples of 5.

The probability of getting a multiple of 2 is

P=\frac{7}{15}= 0.47 (or \ 47\%)P=

15

7

=0.47(or 47%)

The probability of getting a multiple of 5 is

P=\frac{3}{15}=0.2 (or \ 20\%)P=

15

3

=0.2(or 20%)

Now, the probability of getting a multiple of 2 or 5 is

P=0.47+0.20=0.67 (or \ 67\%)P=0.47+0.20=0.67(or 67%)

Therefore, the answer is 67%.

Remember that the probability of one event happening OR another event happening is the sum of the probabilities of those events.

Step-by-step explanation:

hope it helps

Please only correct answers only I need to past this

Answers

Answer:

Multiplication properly of equality

Why are (1, 2) and (2, 1) sot equal ordered pairs​

Answers

Answer:

Step-by-step explanation:

(1,2) and (2,1) are not equal ordered pairs becasue their corresponding elements are not equal.

Two Ordered Pairs are said to be equal if the corresponding first components are equal alongside the corresponding second components are equal.

for example:

(3,1) and (3,1)

here corresponding element of 3 is 3 and of 1 is 1 .so they are called equal ordered pairs.

after reading the directions to paint,on the paint drum, the information indicated two coats of paints is required when using the 5 liter paint and one coat with the 20 liter drum. With both paints 1 litre of paint covers 9 meter squared.

There are 28 rooms to be painted.Show with calculations which will be cheaper paint to buy​

Answers

29 rooms left to uncover the paint from the 9 meter squared rooms

5p + 2 = 3p - 8 please help

Answers

Answer:

p=-5

Step-by-step explanation:

5p-3p=-2-8

2p=-10

p=-5

The answer would be -5

Write the equation of the line that passes through the points (0, 3) and (2. 6)

Answers

Answer:

Y=3/2X + 3

Step-by-step explanation:

Y= mX + b

b is the y intercept or the Y number for when the point is in place o for X

(0, 3) is the Y intersect so b is 3

this is shown on the diagram I drew below

m is the slope of the line and can be calculated

m = change in Y/ Change in X

Our change in Y is 6-3

And out change is X is 2-0

So

m = 3/2

This is shown on the image below

Y=3/2X + 3

write an equation to represent the function.
input (x)
0
3
9
output
(y)
0
1
3

Answers

Answer:

Step-by-step explain

the answer is c

9th one pls fast as soon as possible

Answers

The answer is -1... which is option a. I had a to be -0.69 and b to be -0.31.. l hope it helped??

Answer

Value of a3³+b³-3ab = -1

Explanation

Given a+b=-1----(1)

On cubeing both sides of equation (1), we get

(a+b)³ = (-1)³

Call 98%

we know the algebraic identity:

(x+y)³ = x³+y³ + 3xy(x+y)

=> a³ + b³ +3ab(a+b)= -1

=> a³ + b³ +3ab(-1)=-1

/* from (1)*/

=> a³ + b³-3ab = -1

Therefore,

Value of a³+b³-3ab = -1

Please give me brainliest (click on the crown) Thank you :)

What is three and seventeen-thousandths written in standard form?

Answers

Answer:

Step-by-step explanation:

That would be 3.017:  three and seventeen thousandths

^^the question above in the photo

Answers

Answer:

11

Step-by-step explanation:

who do I solve this I have only 10 minuted​

Answers

Answer:

[tex]\sum {{n} \atop {1}} \right 6n+2n^2[/tex]

Step-by-step explanation:

Given the series 8 + 12 + 16 + 20+ ...

Sum of nth term Sn = n/2[2a+(n-1)d]

a is the first term = 8

d is the common difference = 12 - 8 = 16 - 12 = 4

Substitute

Sn = n/2[2(8)+(n-1)(4)]

Sn = n/2[16+4n-4]

Sn = n/2[12+4n]

Sn  2n/2[6+2n]

Sn = n(6+2n)

Sn = 6n + 2n²

Hence the sigma representation is expressed as;

[tex]\sum {{n} \atop {1}} \right 6n+2n^2[/tex]

What is the point used to write the equation y-2=4(x+5) in point slope form?

Answers

Answer: y−26=4(x−1)

Step-by-step explanation:

A rectangle has vertices E(4,8), F(2,8), G(2,-2) and H(-4,-2). The rectangle is dilated with the origin as the center of dilation so that G's is located at (5,5). Which algebraic reprensentation represents this dilation

Answers

Note: The image of G after the dilation must be G'(5,-5) instead of G'(5,5).

Given:

The vertices of a rectangle are E(4,8), F(2,8), G(2,-2) and H(-4,-2).

The rectangle is dilated with the origin as the center of dilation so that G's is located at (5,-5).

To find:

The algebraic representation that represents this dilation.

Solution:

If a figure is dilated by factor k with origin as the center of dilation, then the dilation is defined as:

[tex](x,y)\to (kx,ky)[/tex]              ...(i)

Let the given rectangle is dilated by factor k with origin as the center of dilation. Then,

[tex]G(2,-2)\to G'(k(2),k(-2))[/tex]

[tex]G(2,-2)\to G'(2k,-2k)[/tex]

The image of G after dilation is G'(5,-5). So,

[tex](2k,-2k)=(5,-5)[/tex]

On comparing both sides, we get

[tex]2k=5[/tex]

[tex]k=\dfrac{5}{2}[/tex]

So, the scale factor is [tex]k=\dfrac{5}{2}[/tex].

Substituting [tex]k=\dfrac{5}{2}[/tex] in (i), we get

[tex](x,y)\to \left(\dfrac{5}{2}x,\dfrac{5}{2}y\right)[/tex]

Therefore, the required algebraic representation to represents this dilation is [tex](x,y)\to \left(\dfrac{5}{2}x,\dfrac{5}{2}y\right)[/tex].

what is. perfect square

Answers

Answer:

a four sided parallelogram where all angles are the same and all sides are the same length

A $350 suit is marked down by 25%. What is the sale price of the suit after the markdown?

Answers

Answer:

262.50

Step-by-step explanation:

350 x .25 (25 %)=87.50

350-87.50=262.50

or

350x.75=262.50

the age of nicole is 3 times of christine now after five years nicole will be twice as old as krisin

Answers

what’s the question?


Pls help I have to find the area

Answers

Answer:

28 square units

Step-by-step explanation:

The area of a rectangle is A = l x w.

The length of this rectangle is 7 square units.

The width is 4 square units.

7 x 4 = 28 square units

Help plzzzz !!!!!!!!!

Answers

Area
= 3^2*pi*150/360
=11.8 m^2 to nearest tenth

1. The function h defined by h(t)=(49 + 4.9t)(10 - t) models the height, in meters, of an object t seconds after it is dropped from a helicopter. Find or approximate the time when the object hits the ground. Explain your method.
2.The function h defined by h(t)=(49 + 4.9t)(10 - t) models the height, in meters, of an object t seconds after it is dropped from a helicopter.
From what height is the object dropped? Explain how you know.

Answers

Answer:

Step-by-step explanation:

Let's FOIL this out and get it into standard form. That gives us:

[tex]h(t)=-4.9t^2+490[/tex] For #1, then:

The height of something when it is on the ground is 0; that means that the h(t) is 0. This allows us to factor the quadratic and solve for t:

[tex]-4.9t^2=-490[/tex] and divide both sides by 4.9 to get

[tex]t^2=100[/tex] so

t = 10. Notice that one of the factors for that quadratic is 10 - t. That factor represents the time it takes to hit the ground. So you might ask why, then, we FOILed this out in the first place if the answer was ight in front of our noses. The reason is becase of #2 that is asking us what the initial height of the object was. That is found in the standard form...in the constant in particular. The initial height is 490 m. That's how you know (because the constant represents the height from which an object is dropped in either free fall, which this is, or in parabolic motion).

write an inequality that represents the real-world problem. then select all that apply

Answers

Answer:

where is the problem

Step-by-step explanation:

Max is training for a race. Based on the graph, how long did it take Max to run 12 mi?

A) 1.2 hr.
B) 3 hr.
C) 5 hr.
D) 7.5

Answers

3 hrs. since 12 and 3 meet at that point
B.3 hours to run 12 miles

How do you know you're good at sleeping I need help

Answers

Answer:

You can do it with your eyes closed

Step-by-step explanation:

1.2.1 AFB is congruent to CHB
1.2.2 DF // HB
1.2.3 DFBH is a parallelogram

Answers

Answer:

this statement is true

hope it helps you

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