To find the two numbers, we set up a system of equations and solve for the variables using substitution.
Explanation:To solve this problem, we can set up a system of equations. Let's call the smaller number 'x' and the larger number 'y'. We know that the sum of the two numbers is 32, so our first equation is x + y = 32.
We are also given that the larger number is one less than twice the smaller number. This can be written as y = 2x - 1. Now we have two equations:
x + y = 32y = 2x - 1We can solve this system of equations by substitution or elimination. Let's use substitution:
Starting with the second equation, we can substitute y with its value from the first equation:
2x - 1 = 32 - x
Now we can solve for x:
3x = 33
x = 11
Substituting this back into the first equation, we can find the value of y:
11 + y = 32
y = 21
Therefore, the smaller number is 11 and the larger number is 21.
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a wallet that holds $25 contains the same number of $1 bills, $5 bills, and quarters. how many of each type of bill or coin does the wallet contain?
The number of each type of bill or coin the wallet contains is:
4
Step-by-step explanation:It is given that:
A wallet holds $ 25 in total.
Also, the number of $ 1 bills,$ 5 bills and qaurters are present in equal number in the wallet.
Let the number of each coin or bill in the wallet be: x
Also, we know that:
1 quarter= 1/4 dollar
i.e.
1 quarter= 0.25 dollar
Hence, we get:
x+5x+0.25x=25
i.e.
6.25 x=25
On dividing both side of the equation by 6.25 we get:
x=25/6.25
i.e.
x=4
Hence, the number of each kind of coin or bill are: 4
The center of a circle is at the origin. An endpoint of a diameter of the circle is at (-3, -4). How long is the diameter of the circle?
5
10
25
what is the ratio 15:75 in lowest terms? as a ratio
Answer:
1 : 5
Step-by-step explanation:
did anyone do the Algebra 1 interim assessment 2??? and can someone help me with it please!!!
In the diagram, g ∥ h, m∠1 = (4x + 36)°, and m∠2 = (3x – 3)°. What is the measure of ∠3? 21° 60° 120° 159°
The measure of angle m∠3 would be 60°.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
Given;
g ∥ h, m∠1 = (4x + 36)°,
m∠2 = (3x – 3)°.
m∠2 = m∠3 ( alternate interoir angle)
we know that
m∠1 + m∠2 = 180
4x + 36 + 3x – 3 = 180
7x + 33 = 180
7x = 147
x = 21
Substituting
m∠2 = 3x – 3
m∠2 = 3(21) - 3
m∠2 = 63 - 3
m∠2= 60
Therefore, m∠3 = m∠2 = 60
Hence, The measure of angle m∠3 would be 60°.
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considering the one-time deposit and monthly rent, the equation y=1200+400x can be used to represent y, the total cost of renting an apartment for x months. what is the amount of the deposit?
What is the quotient (2x3 − 3x2 − 14x + 15) ÷ (x − 3)?
a. 2x2 + 3x − 5
b. 2x2 − 3x + 5
c. 2x2 − 3x − 5
d. 2x2 + 3x + 5
Answer: The correct option is (a) [tex]2x^2+3x-5.[/tex]
Step-by-step explanation: We are given to find the quotient in the following division :
[tex]Q=\dfrac{2x^3-3x^2-14x+15}{x-3}.[/tex]
To find the quotient, first we will try to factorize the numerator and then we will try to divide by the denominator.
We have
[tex]Q\\\\\\=\dfrac{2x^3-3x^2-14x+15}{x-3}\\\\\\=\dfrac{2x(x-3)+3x(x-3)-5(x-3)}{x-3}\\\\\\=\dfrac{(x-3)(2x^2+3x-5)}{(x-3)}\\\\=2x^2+3x-5.[/tex]
Thus, the required coefficient is [tex]2x^2+3x-5.[/tex]
Option (a) is CORRECT.
My last question someone help
Solve x2 + 5x + 3 = 0.
The solutions to the quadratic equation x² + 5x + 3 = 0 are:
x = (-5 + √13) / 2
x = (-5 - √13) / 2
How did we get the values?To solve the quadratic equation x² + 5x + 3 = 0, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
In this equation, a = 1, b = 5, and c = 3. Substituting these values into the quadratic formula, we get:
x = (-5 ± √(5² - 4×1×3)) / (2×1)
Simplifying further:
x = (-5 ± √(25 - 12)) / 2
x = (-5 ± √13) / 2
Therefore, the solutions to the quadratic equation x² + 5x + 3 = 0 are:
x = (-5 + √13) / 2
x = (-5 - √13) / 2
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How would you graph the solution set of x + 4 > -9?
open circle on -13 and shaded to the right
closed circle on -13 and shaded to the right
open circle on -5 and shaded to the right
closed circle on -5 and shaded to the right
Answer:
give the other person brainly
its A
Step-by-step explanation:
All the angles are measured in degrees, show that the triangle is isosceles.
The triangle is isosceles.
What is a triangle?A triangle is a polygon that has three vertices on each of its three sides. The angle that is created within the triangle is 180 degrees. It indicates that the sum of a triangle's interior angles is 180 degrees. This is a polygon with the fewest sides. At the end of the day, a triangle is characterized as a three-sided two-layered figure whose inside points are equivalent to 180°.
Given a triangle let the triangle be ΔABC
given angles (4x + 8), (5x + 2) and (6x - 10)
let ∠A = (4x + 8), ∠B = (5x + 2) and ∠C = (6x - 10)
we know that sum of angle of triangle is 180⁰
∠A + ∠B + ∠C = 180
4x + 8 + 5x + 2 + 6x - 10 = 180
15x = 180
x = 180/15 = 12
∠A = 4x + 8 = 4(12) + 8 = 56⁰
∠B = 5x + 2 = 5(12) + 2 = 62⁰
∠C = 6x - 10 = 6(12) - 10 = 62⁰
since ∠B = ∠C
it is the property of an isosceles triangle, An isosceles triangle is a triangle with any two sides that are the same length and angles on opposite sides that are the same size.
Hence the Given triangle is isosceles.
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2.8y + 6 +0.2 y =5y -14
Determine the n-intercept of the graph of the graph of the car value equation v= -1385n + 18,790
Answer:
13.57
Step-by-step explanation:
We have been given an equation [tex]v=-1385n+18,790[/tex], which represents the value of a car. We are asked to find the n-intercept of our given equation.
We know that the n-intercept will be at [tex]v=0[/tex].
[tex]0=-1385n+18,790[/tex]
Subtracting 18,790 from both sides of our equation we will get,
[tex]0-18,790=-1385n+18,790-18,790[/tex]
[tex]-18,790=-1385n[/tex]
Now, we will divide both sides of our equation by [tex]-1385[/tex].
[tex]\frac{-18,790}{-1385}=\frac{-1385n}{-1385}[/tex]
[tex]13.566787=n[/tex]
[tex]n\approx 13.57[/tex]
Therefore, the n-intercept of our given graph is approximately 13.57.
Identify which type of correlation the given scatterplot possesses, if a correlation exists.
A.
no correlation
B.
positive correlation
C.
negative correlation
D.
correlation is impossible to determine
Answer:
B. Positive correlation
Step-by-step explanation:
Positive correlation is nothing but when the values of x increase, the corresponding y values are also increase.
When we look at the scatter plot, when x increase, the y also increase.
Therefore, it is a positive correlation.
Hope this will helpful.
Thank you.
Stephen wants to use the Triangle Proportionality Theorem to determine the relationships on his map. He knows the angle between the park, the bus stop, and his home. Which other angle does he need to know?
Select one:
a. Bus stop, park, and his friend's house
b. Bus stop, park, and his home
c. His friend's house, grocery store, and his home
d. Park, his home, and grocery store
Answer:
C. His friend's house, grocery store, and his home.
Step-by-step explanation:
Triangle Proportionality Theorem-
If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.
So if the line joining the park, bus stop and friend's house, grocery store will be parallel, Stephen can use triangle proportionality theorem.
When two lines are crossed by another line i.e the transversal, the angles in matching corners are called corresponding angles. And when the corresponding angles are equal then the two lines are parallel.
The corresponding angle of the angle between the park, the bus stop, and his home is the angle between his friend's house, grocery store, and his home.
Therefore, he needs to measure that angle.
Which statements are true about the ordered pair (7, 19) and the system of equations?
{2x-y=-5
{x+3y=22
select each correct answer.
A.The ordered pair (7, 19) is a solution to the first equation because it makes the first equation true.
B.The ordered pair (7, 19) is a solution to the second equation because it makes the second equation true.
C.The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false.
D.The ordered pair (7, 19) is a solution to the system because it makes both equations true.
A scale model of a human heart is 196 inches long. The scale is 30 to 1. How many inches long is the actual heart? Round your answer to the nearest whole number.
what is 5p+2q-3p-3q
Coldwell elementary has a goal to collect 1,500 box tops in 6 months. the pta brought 458 box tops within two weeks. write and solve an inequality to describe how many box tops need to be collected to meet or exceed their goal.
100 envelopes cost $0.70 how much would it be for 250
If 100 envelopes cost $0.70 then it would cost $1.75 for 250 envelopes.
If 100 envelopes cost $0.70, we can set up a proportion to determine the cost of 250 envelopes:
100 envelopes / $0.70 = 250 envelopes / x
Cross-multiplying:
100 × x = 250 × $0.70
Simplifying:
100x = 175
Dividing both sides by 100:
x = 175 / 100
x = $1.75
Therefore, it would cost $1.75 for 250 envelopes.
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What is the reason for each step in the solution of the equation? −5(x−6)=10x
−5(x−6)=10x
−5x+30=10x
30=15x
2=x
Division Property of Equality
Commutative Property
Addition Property of Equality
Given
Distributive Property
How to find the multiplicity of a zero of a polynomial function?
Annabelle traded $2250 for euros, immediately changed her mind, and then promptly traded her euros back into dollars. Which of these amounts is she most likely to have?
Train a has a speed of 15 miles per hour greater than that of train
b. if train a travels 150 miles in the same time train b travels 120 miles, what are the speeds of the two trains
Divide: 1,485 ÷ 0.09
Mr.collins wrote a number between 7000 and 8000. there were more hundreds than tens. there were more ones than hundreds. what could mr.collins number be
What is the value of x?
a. 71°
b. 142°
c. 152°
d. 76°
Which of the following inequalities is equivalent to -6 > x?
A staircase handrail is made from congruent parallelograms. in parallelogrampqrs, pq = 17.5, st = 18, and m∠ qrs = 110° . find m∠ pqr.
To find angle PQR in a parallelogram, we can use the Exterior Angle Theorem. By subtracting the measures of the other two angles in triangle QRS from 180 degrees, we find that angle PQR is 70 degrees.
Explanation:To find the measure of angle PQR, we can use the fact that opposite angles in a parallelogram are congruent. This means that angle PQR is equal to angle STQ. Since STQ is an exterior angle of triangle QRS, we can use the Exterior Angle Theorem to find its measure by subtracting the measures of the other two angles in the triangle from 180 degrees.
Given that angle QRS is 110 degrees, we can find angle STQ by subtracting the measures of angles QRS and QSR from 180 degrees:
angle STQ = 180 - (110 + 180) = -110 degrees
However, angles cannot have negative measures, so we need to find the equivalent positive measure. Adding 180 degrees to -110 degrees gives us angle STQ = 70 degrees. Therefore, angle PQR is also equal to 70 degrees.
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It costs a flat fee of $3.15 to make an international call plus $0.05 for every minute that you talk. if you were charged $5.10 for making an international call, for how many minutes did you talk?