Final answer:
To find the two numbers, we created a system of equations with the sum being 70 and the larger number as five less than twice the smaller number. Solving the equations, we found that the smaller number is 25 and the larger number is 45.
Explanation:
The question asks us to find two numbers where the sum is 70, and the larger number is five less than twice the smaller number. To solve this, we'll set up a system of equations with two variables, which we'll call x and y. The first equation would be x + y = 70, since their sum is 70. The second equation is derived from the statement that the larger number is five less than twice the smaller number, which can be expressed as y = 2x - 5. Now we substitute the second equation into the first to solve for x. We get x + (2x - 5) = 70. Simplifying, we have 3x - 5 = 70, thus 3x = 75, and therefore x = 25. With the smaller number found, we can determine the larger number using the second equation y = 2(25) - 5, resulting in y = 45. Hence, the two numbers are 25 and 45.
Which is the equation of the line with slope 5 that contains point (-2, -3)
A. y + 2 = 5(x – 3) B. y + 3 = 5(x + 2) C. y – 3 = 5(x – 2) D. y – 2 = 5(x – 3)
The answer is y = 5x + 7
here's how you get it:
Start with the base y = mx + b
then imput the points and the slope:
-3 = 5 ( -2 ) + b
Then solve for b
-3 = 5 ( -2 ) + b
-3 = -10 + b
-b = -7
b = 7
so the equation is:
y = 5x + 7
Expand the fraction 72/125 .so that it has a denominator of 1000.
Find the common ratio of the geometric sequence: −320,80,−20,5,…−320,80,−20,5,… A. −14−14 B. 1414 C. -4 D. 4
What property describes the number sentence? 6+0=6
A rectangular greenhouse has an area of 6480 square meters and a length of 120 meters. How many meters is it in width?
which algebraic expression shows the average melting points of helium, hydrogen, and neon if h represents the melting point of helium, j represents the melting point of hydrogen, and k represents the melting point of neon?
A. h + j + k
B. hjk
c. h+j+k over 3
d. hjk over 3
Answer:
c. h+j+k over 3
Step-by-step explanation:
We know that,
[tex]\text{Average}=\frac{\text{Sum of observations}}{\text{Total number of observation}}[/tex]
Here, h, j and k represents the melting point of helium, hydrogen and Neon respectively,
Since, the sum of melting points = h + j + k,
Also, the total number of gases = 3,
Thus,
[tex]\text{Average melting points}=\frac{h+j+k}{3}[/tex]
Or (h+j+k) over 3
⇒ Option c is correct.
The algebraic expression which shows the average melting
points of helium, hydrogen, and neon is h+j+k over 3.
What is Average?
This is calculated with the sum of the items divided by the
number of items.
In this scenario, we were given the items as h, j and k. The
total number of items is 3.
The average will therefore be = h+j+k/3
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Ann is grouping 38 rocks. She can put them into groups of 10 rocks or as single rocks.what are different ways Ann can group the rocks?
A new cruise ship line just launched 3 new ships: the Pacific Paradise, the Caribbean Paradise, and the Mediterranean Paradise.
The Caribbean Paradise has 29 more than the Pacific Paradise. The Mediterranean Paradise has 30 fewer deluxe staterooms than twice the number of deluxe staterooms on the Pacific Paradise. Find the number of deluxe staterooms for each of the ships if the total of deluxe staterooms for the total of the three ships is 719.
To find the number of deluxe staterooms for each of the three ships, we can set up and solve an equation based on the given information.
Explanation:Let's represent the number of deluxe staterooms on the Pacific Paradise ship as x.
The number of deluxe staterooms on the Caribbean Paradise is 29 more than the Pacific Paradise, so it can be represented as x + 29.
The number of deluxe staterooms on the Mediterranean Paradise is 30 fewer than twice the number of deluxe staterooms on the Pacific Paradise, so it can be represented as 2x - 30.
We can form an equation with the sum of the deluxe staterooms on all three ships: x + (x + 29) + (2x - 30) = 719.
Simplifying the equation gives us 4x - 1 = 719.
By adding 1 to both sides and dividing by 4, we can find the value of x which represents the number of deluxe staterooms on the Pacific Paradise ship.
Finally, we can substitute the value of x into the expressions for the other two ships to find their number of deluxe staterooms.
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Find a_1 and d for an arithmetic sequence with these terms. a_4=9and a_7=18
You are trying to determine the half-life of a new radioactive element you have isolated. You start with 1 gram, and 5 days later you determine that it has decayed down to 0.7 grams. What is its half-life? (Round your answer to three significant digits.)
The table below represents the distance of a train from its destination as a function of time: Time (hours) x Distance (miles) y 0 665 1 570 2 475 3 380 4 285 Part A: What is the y-intercept of the function, and what does this tell you about the train? (4 points) Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 4 hours, and tell what the average rate represents. (4 points) Part C: What would be the domain of the function if the train continued to travel at this rate until it reached its destination? (2 points)
1 + 2 + 3 + 4 + 5 + . . . is an example of a finite series. True False
The figure has ____ lines of symmetry. A. 0 B. 4 C. 6 D. 8
an airline ramp with a base of 50 makes an angle of 27 with the ground. find the distance a person will walk on a ramp round to the nearest foot
What is the greatest common factor of 4k, 18k4, and 12?
A pea seller had some peas. He sold 40% of his stock and still had 420 peas. Originally, he had how many peas?
100-40= 60%
60% = 0.60
420/0.60 = 700
he had 700 peas
A cone has a volume of 12 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of?
find the values of x between 0 and 2pi where the tangent line to the graph of y=sinxcosx is horizontal.
Evaluate the limit using the appropriate limit law(s). (if an answer does not exist, enter dne.) lim x → 1 2x2 + 4 x2 + 4x − 4
what is the remainder when 3 is synthetically divided into the polynomial -x^2+5x-9
Answer:
REmainder is -3
Step-by-step explanation:
find remainder when 3 is synthetically divided into the polynomial -x^2+5x-9
In synthetic division we write all the coefficient of the polynomial and divide by 3
3 -1 5 -9
0 -3 6
-------------------------------
-1 2 -3 ----> Remainder
So the remainder is -3
Out of 30 students surveyed 17 have a dog based on these results predict how many of the 300 students in the school have a dog
17/30 = 0.5666 so about 57% of the sample had dogs
300 x 0.57 = 171 would have dogs
Suppose an isosceles triangle ABC has A = 45° and b = c = 4. What is the length of a2?
Which of the following is not an appropriate method of proving triangles congruent a) AAA b)SSS c) AAS D) SAS
Answer:
a) AAA.
Step-by-step explanation:
Triangles which are of the same shape and size are called congruent triangles. Triangles of same shape are similar triangles.
Two triangles can be proved congruent by SSS ,SAS AAS ,ASA ,HL postulates.
Two triangles can be proved similar by AAA method.
All congruent triangles are similar but all similar triangles are not congruent.
Hence option a) AAA is not an appropriate method of proving triangles congruent.
If a wheel with a radius of 80 inches spins at a rate of 50 revolutions per minute, find the approximate linear velocity in miles per hour.
Which of the following gives all of the sets that contain -1/2?
A.the set of all rational numbers and the set of all real numbers
B.the set of all natural numbers and the set of all irrational numbers
C.the set of all integers and the set of rational numbers
D.the set of all natural numbers, the set of rational numbers, and the set of all real numbers
Answer:
Option A is Correct Option.
Step-by-step explanation:
Given: [tex]\frac{-1}{2}[/tex]
[tex]\frac{-1}{2}[/tex] is a rational no.
Option A:
Given no is a rational no.
⇒ Both Set of rational no and real nos. contain rational nos..
Thus, Correct Option.
Option B:
set of natural nos and irrational nos does not contain rational nos.
Thus, Not correct option.
Option C:
Set of integers does not contain rational numbers.
Thus, Incorrect Option.
Option D:
Set of all Natural Nos. does not contain rational nos.
Thus, This option is not correct option
Therefore, Option A is Correct Option.
The length of a shadow of a building is
29 m
. The distance from the top of the building to the tip of the shadow is
35 m
. Find the height of the building
Kathy walked 3 1/2 miles per hour for 1 1/4 hours. During 1/2 of her walking time it rained. How many miles did she walk while it was raining?
1 1/4 = 5/4 * 1/2 = 5/8
3 1/2 = 7/2 * 5/8 = 35/16 = 2 3/16 miles
Many practical applications require calculations of area. some of these calculations are straightforward, but others are more difficult, and it turns out that the idea of the definite integral can help us with the more difficult cases. let’s start with some familiar shapes. what is the area of a rectangle of length l and width w? express your answer in terms of l and w.
The area of a rectangle with length l and width w is given by the product l * w.
what is the area of a rectangle of length l and width w?The area of a rectangle is calculated by multiplying its length (l) by its width (w).
Therefore, the area (A) of a rectangle can be expressed as:
A = l * w
So, the area of a rectangle with length l and width w is given by the product l * w.
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EASY 5 POINTS!!! A spherical ball just fits inside a cylindrical can, 16 centimeters tall, with a diameter of 16 centimeters. Which expression gives the volume of the sphere in cubic centimeters?
formula for volume of a sphere is V=4/3 x pi x R63
if diameter = 16 than radius = 16/2 = 8
so the equation would be 4/3 x pi x 8^3
Find the exact value of cos 105°.