All categories

3 years ago

Find the larger of two consecutive integers if the larger is 149 less than twice the smaller.

Mathematics

1 answer:

snow_tiger [21]3 years ago

4 0

Answer:

151

Step-by-step explanation:

Let x = the smaller integer and y = the larger integer.

We have two conditions:

(1) x + 1 = y

(2) y = 2x - 149 Substitute (1) into (2)

x + 1 = 2x - 149 Add 150 to each side

x + 150 = 2x Subtract x from each side

x = 150 Substitute into (1)

150 +1 = y

y = 151

The larger integer is 151.

<em>Check: </em>

(1) 150 + 1 = 151

151 = 151

(2) 151 = 2×150 -149

151 = 300 -149

151 = 151

You might be interested in

Manuel bought a balloon (that is a perfect sphere) with a radius of 2 \text{ cm}2 cm2, start text, space, c, m, end text. He wan

mote1985 [20]

Answer:

<h2>The required ratio is 8</h2>

Step-by-step explanation:

Volume of a sphere = $\frac{4}{3}\pi r^{3}$ where r is the radius of the sphere.

If manuel bought a balloon (that is a perfect sphere) with a radius of 2cm, the original volume of the sphere is expressed as;

Vo = $\frac{4}{3}\pi (2)^{3}$

$Vo = \frac{4}{3}\pi *8\\Vo = \frac{32 \pi}{3}$

If he wanted his balloon to be bigger and he blew 2 big breaths of air into the balloon, if each big breath increased the balloon's radius by 1cm, the total radius will be the initial radius of the sphere plus the new radius after expansion.

radius of current sphere = 2cm+(1cm+1cm) = 4cm

Volume of the current sphere Vc = $\frac{4}{3}\pi (4)^{3}$

$Vc = \frac{4}{3}\pi *64\\Vc = \frac{256 \pi}{3} \\$

The ratio of the current volume of the balloon Vc to the original volume of the balloon Vo will be expressed as;

Vc/Vo = $\frac{\frac{256\pi}{3} }{\frac{32\pi}{3} }$

$\frac{Vc}{Vo}=\frac{256\pi}{3}*\frac{3}{32\pi} \\\frac{Vc}{Vo}=\frac{256}{32}\\\frac{Vc}{Vo}= 8$

The required ratio is 8

3 0

2 years ago

Sharon is conducting research on two species of birds at a bird sanctuary. The number of birds of species A is represented by th

e-lub [12.9K]

Answer: After 7 years the number of birds of species A and B are same. and the number of birds during that year will be 140.

Step-by-step explanation:

Given: Sharon is conducting research on two species of birds at a bird sanctuary.

The number of birds of species A is represented by the equation below,where S represents the number of birds, x years after beginning her research.

$S=2^x+12$

The number of birds of species B is represented by the equation below,where S represents the number of birds, x years after beginning her research.

$S=15x+35$

To plot the above function, first find points by which they are passing.

For species A, At x=0 , $S=1+12=13$

At x=2 , $S=2+12=14$

Similarly find more points and plot curve on graph.

For species A, At x=0 , $S=0+35=35$

At x=2 , $S=15+35=50$

Plot a line with the help of these two points.

Now, from the graph the intersection of curve (for A) and line (for B) is at (7,140) which tells that After 7 years the number of birds of species A and B are same. and the number of birds during that year will be 140.

8 0

3 years ago

Read 2 more answers

Lenny and Lisa have obtained a 30-year, fixed rate mortgage for $675,250 with a 7.25% interest rate. They purchased 3 points and

Vikentia [17]

Answer:

119 months

Step-by-step explanation:

In this question, we are asked to calculate the amount of time it would take for a break-even point on a mortgage, if there is a factoring in the cost of points.

We proceed to answer the;

Mathematically,

The Break Even Point = Amount Paid for purchasing Discount Points divided by Monthly savings in the interest payments

We lost out the important values given in the question as follows:

Amount of Mortgage - $675,250

Tenure - 30 Years

The Rate of interest without points = 7.25%

The number of points = 3 points

The rate of interest with the 3 points = 6.875%

The amount to be paid for purchasing the discount point is now calculated below;

Since 1 discount point = 1% of mortgage value;

Therefore, 3 discount points = 3% of mortgage value

The amount paid is thus = 3% of $675,250 = $20,257.5

To calculate Monthly payment without points, we use the mathematical formula;

M = P[r(1+r)^n/((1+r)^n)-1)]

Where M

Is monthly payment, r is the interest rate, n is the number of months.

According to the question M = 675,250, r = 7.25% = 7.25/100 = 0.0725 , n= 30 * 12 months = 360 months

M = 675,250[0.0725(0.0725+1)^30/(1+0.0725)^360)-1) = $4606.40

To get the monthly payment with points, we simply use the formula again but this time interest rates will be 6.875% = 0.06875 I.e r = 0.06875

Inputting the terms in the formula will yield a value of $4435.91. This means monthly payment with discount will be $4435.91

Savings in monthly payments after purchasing the discount points = $4,606.40 - $4,435.91 = $170.48

Break Even = Purchase cost of Discount Points / Monthly savings

= $20,257.5 / $170.48

= 119 Months

Hence, the number of months it will take Lisa and Lenny to break-even point on their mortgage will be 119 months

6 0

3 years ago

In a right triangle, the measure of one acute angle is 12 more than twice the measure of the other acute angle. Find the measure

soldi70 [24.7K]

Given:

In a right triangle, the measure of one acute angle is 12 more than twice the measure of the other acute angle.

To find:

The measures of the 2 acute angles of the triangle.

Solution:

Let x be the measure of one acute angle. Then the measure of another acute is (2x+12).

According to the angle sum property, the sum of all interior angles of a triangle is 180 degrees. So,

$x+(2x+12)+90=180$

$3x+102=180$

$3x=180-102$

$3x=78$

Divide both sides by 3.

$x=\dfrac{78}{3}$

$x=26$

The measure of one acute angle is 26 degrees. So, the measure of another acute angle is:

$2x+12=2(26)+12$

$2x+12=52+12$

$2x+12=64$

Therefore, the measures of two acute angles are 26° and 64° respectively.

8 0

3 years ago

Sarah saw seven sharks while swimming now how many S is in the sentence

Katen [24]

Answer:

6 S's in the sentence

Step-by-step explanation:

5 0

3 years ago