The solution to the system of linear equations 4x - 2y = 8 and y = (3/2)x - 2 is x = 4 and y = 4, found by substituting y in the first equation with the expression from the second equation and solving for x.
The student is asking to solve a system of linear equations. The equations provided are:
4x - 2y = 8
y = (3/2)x - 2
We will solve this system using substitution since the second equation is already solved for y. Here are the steps:
Substitute y in the first equation with the expression from the second equation: 4x - 2((3/2)x - 2) = 8.
Simplify the equation: 4x - 3x + 4 = 8.
Solve the simplified equation for x: x + 4 = 8, which leads to x = 4.
Substitute x back into the second equation to find y: y = (3/2)4 - 2.
Calculate the value of y: y = 6 - 2, which leads to y = 4.
The solution to the system of equations is x = 4 and y = 4.
A special deck of cards consists of 5 red cards, 20 blue cards, and 25 green cards. Samuel selects 1 card from the special deck 500 times. How many times can he expect to draw a red card?
Answer:
5
Step-by-step explanation:
Samuel can expect to draw a red card approximately 50 times.
To find out how many times Samuel can expect to draw a red card, we need to calculate the probability of drawing a red card and then multiply it by the number of times he selects a card.
Given:
- Number of red cards = 5
- Number of blue cards = 20
- Number of green cards = 25
- Total number of cards = 5 (red) + 20 (blue) + 25 (green) = 50
The probability of drawing a red card is the ratio of the number of red cards to the total number of cards:
[tex]\[ P(\text{Red}) = \frac{\text{Number of red cards}}{\text{Total number of cards}} = \frac{5}{50} = \frac{1}{10} \][/tex]
Now, to find the expected number of times Samuel will draw a red card, we multiply the probability of drawing a red card by the total number of times he selects a card:
[tex]\[ \text{Expected number of red cards} = P(\text{Red}) \times \text{Total number of selections} \][/tex]
Substituting the values:
[tex]\[ \text{Expected number of red cards} = \frac{1}{10} \times 500 = 50 \][/tex]
So, Samuel can expect to draw a red card approximately 50 times.
factorise
24p2 + pq - 23q²
24p² + pq - 23q² =
= 24p² + 24pq - 23pq - 23q²
= 24p(p + q) - 23q(p + q)
= (p + q)(24p - 23q)
The required factorization of the given expression is given as (24p - 23q)(p + q).
What are the factors?A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.
Given expression in the quesiton is 24p2 + pq - 23q², we have to factorize the given expression,
So,
24p² + pq - 23q²,
Substituting pq = 24 pq - 23pq
= 24p² + 24pq - 23pq - 23q²
= 24p(p + q)-23q(p + q)
= (24p - 23q)(p + q)
Thus, the required factorization of the given expression is given as (24p - 23q)(p + q).
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At a local fitness center, members pay a $12 membership fee and $3 for each aerobics class. Nonmembers pay $4 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same?
For 12 number of aerobics classes, cost for members and nonmembers is same
Solution:
Let "x" be the number of aerobic classes
At a local fitness center, members pay a $12 membership fee and $3 for each aerobics class
Therefore,
Members pay = 12 + 3(number of classes)
Members pay = 12 + 3x ------- eqn 1
Nonmembers pay $4 for each aerobics class
Nonmembers pay = 4x ------- eqn 2
For cost for members and nonmembers be the same, eqn 1 must be equal to eqn 2,
12 + 3x = 4x
4x - 3x = 12
x = 12
Thus for 12 number of aerobics classes, the cost for members and nonmembers will be same
Suppose that a code consists of 5 digits, none of which is repeated. ( A digit is one of the 10 numbers 0,1,2,3,4,5,6,7,8,9.) How many codes are possible?
Answer:
30240
Step-by-step explanation:
There are two primary ways to approach this problem - the logical and the mathematical.
The logical way is very simple:
Since you know that there are 5 digits and each must be different, start with the first digit and work your way up.
The first digit can be any of 10 digits (0–9).
However, the second digit can be any of only 9 digits as 1 digit has already been used and cannot be repeated.
Similarly, applying the same logic, there are only 8 options for the third digit, 7 for the fourth digit, and 6 for the fifth and final digit.
Now, multiply all these numbers together to get the total number of configurations like so:
10⋅9⋅8⋅7⋅6=30240
The more mathematically inclined way requires the use of a special formula. Since in this particular scenario, the order of the numbers matter, we can use the Permutation Formula:
P(n,r)=n!(n−r)!
where n is the number of numbers in the set and r
is the subset.
Since there are 10 digits to choose from, we can assume that n=10
.
Similarly, since there are 5 numbers that need to be chosen out of the ten, we can assume that r=5
.
Now, plug these values into the formula and solve:
=10!(10−5)!
=10!5!
=10⋅9⋅8⋅7⋅6
=30240
1. Suppose that AB and EF are corresponding sides of similar triangles. AB = 6 and the scale factor is 3, what is EF?
A. 3
B. 6
C. 9
D. 18
Answer:
d
Step-by-step explanation:
since since the scale factor is 3 angle ab abyou multiply 6 * 3 to get 18
The length of the Side EF is 18.
What is the scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object.
Given that corresponding sides are AB and EF, and EF is a side of the larger (second) triangle.
scale factor 3 means each length of the second is 3 times as long as the first.
Therefore, the length of the side EF when the length of side AB is 6 units is,
EF = 3 x AB
= 3 x 6 units
= 18 units.
Therefore, Side EF is 18.
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Describe the graph of the system of inequalities:
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}x>2\\y\leq4\end{array}\right[/tex]
x = 2
This is a vertical line passing through (2, 0) .
y = 4
This is a horizontal line passing through (0, 4).
<, > - dashed line
≤, ≥ - solid line
<, ≤ - shaded to the left (down) from the line
>, ≥ - shaded to the right (up) from the line
Answer:
Below.
Step-by-step explanation:
The shaded area will be to the right of the vertical dotted line x = 2, and below the horizontal continuous line y = 4.
Which of the following equations represents a line that is parallel to y = 3x +2
and passes through the point, (1, 6)?
O A. y = 3x +6
O B. y = 3x +9
O c. y=-3x+2
O D. y = 3x+3
The correct equation of the new line parallel to y = 3x + 2 and passing through (1, 6) is y = 3x + 3.
Explanation:To find the equation of the line that is parallel to the given line y = 3x + 2 and passes through the point (1, 6), we first need to acknowledge that parallel lines have the same slope.
Therefore, the slope of the new line will also be 3. We can use the point-slope form of the equation y - y1 = m(x - x1) to find the equation. Substituting the given point into the equation, we get y - 6 = 3(x - 1).
Simplifying the equation, we find y = 3x + 3. So, the equation of the line that is parallel to the original line and passes through the given point is y = 3x + 3.
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Lily had 16 tomatoes she give Brandy 1/8 of tomatoes,
sadie 1/2 of the tomatoes,
and Kiley 1/4 of the tomatoes.
how many tomatoes did lily give away?
how many tomatoes did sasha have left?
what fraction of the tomatoes did lily have left?
Answer:
she gave away 14 I think.
If you mean Lilly she had 2 left
1/8 tomatoes left
Step-by-step explanation:
1/8=2 1/2=8 1/4=4. 2+8+4=14
A hammer thrower is competing in a track and field meet. He rotates exactly 5 times in 2π seconds, and the motion of his hammer is represented by a sine function.
Which function rule could model this situation?
f(x)=5 sin x
f(x)= sin(5x)
f(x)=5π sin x
f(x)= sin(1/5x)
Answer:
Therefore the correct option is sin(5x).
Step-by-step explanation:
i) The hammer thrower rotates exactly 5 times in 2[tex]\pi[/tex] seconds.
Therefore one rotation is completed in [tex]\frac{2\pi }{5}[/tex] seconds.
ii) Since the motion of the hammer is represented by a sine function therefore
one rotation is considered to be one full cycle and the time period of that cycle
is given in equation i) and it is T = [tex]\frac{2\pi }{5}[/tex] seconds.
iii) the equation of a sine function is given by sin(2[tex]\pi[/tex][tex]\frac{1}{T}[/tex]) which in this case would
be sin(2[tex]\pi[/tex] × [tex]\frac{1}{\frac{2\pi }{5}}[/tex] × x) = sin(5x)
iv) Therefore the answer is sin(5x)
Avarie is cutting a 12 foot long piece of wood into 1/4 -foot sections. How many sections will result
1 foot would be four 1/4 foot pieces.
Multiply total feet by 4:
12 ft x 4 = 48 total pieces.
What’s the common denominator for 4 and 3
Will Mark as Brainliest whoever answers first
The common denominator in this problem
4 6/7 +7 3/14=
Step-by-step explanation:
We have,
[tex]4\dfrac{6}{7}+7\dfrac{3}{14}[/tex]
To find, the common denominator of [tex]4\dfrac{6}{7}+7\dfrac{3}{14}[/tex] = ?
∴ [tex]4\dfrac{6}{7}+7\dfrac{3}{14}[/tex]
= [tex]\dfrac{4\times 7 +6}{7} +\dfrac{7\times 14 +3}{7}[/tex]
[tex]=\dfrac{34}{7} +\dfrac{101}{7}[/tex]
Taking the common as [tex]\dfrac{1}{7}[/tex], we get
=[tex]\dfrac{1}{7}[/tex][tex](34+101)[/tex]
The denominator = 7
∴ The common denominator of [tex]4\dfrac{6}{7}+7\dfrac{3}{14}[/tex] = 7
Hence, the common denominator of [tex]4\dfrac{6}{7}+7\dfrac{3}{14}[/tex] = 7
A sphere has a radius of 16 in. Which statements about the sphere are true? Check all that apply.
The sphere has a diameter of 8 in.
The volume of the sphere is StartFraction 2,048 Over 3 EndFraction pi inches cubed.
The sphere has a diameter of 32 in.
The radius’s length is one-half the length of the diameter.
The volume of the sphere is StartFraction 16,384 Over 3 EndFraction pi inches cubed.
The diameter’s length is one-half the length of the radius.
Answer:
The sphere has a diameter of 32 in. CORRECT: the diameter of a sphere doubles its radio, so if the radio equals 16,the diameter measures the double, in this case, 32.The radius' lenght is one half the length of the diameter. CORRECT: , by definition, the diameter is the maximum distance between two opposite points on the surface of the sphere, and its lenght equals twice the radius because the radius is the distance between the center of the sphere and any point of the frontier of the sphere (then, one colud imagine that the distance between two opposite points in a sphere can be united by two radius, or a diameter).The volume (V) of a sphere can be calculated as [tex]\frac{4\pi r^3}{3}[/tex], where r is the radio. In this case, the volume of the sphere will be [tex]\frac{4\pi\times16^3}{3}=\frac{4\pi\times4096}{3}[/tex], which is also equal to [tex]\frac{16384\times\pi}{3}[/tex].Answer:
The True statements are:
The sphere has a diameter of 32 in.
The radius’s length is one-half the length of the diameter.
The volume of the sphere is StartFraction 16,384 Over 3 EndFraction pi inches cubed.
Step-by-step explanation:
The sphere has a diameter of 8 in. FalseThis is false because a radius is half of a diameter. Half of the given diameter of 8 in is 4 in whereas the radius in the question is 16 in.
The volume of the sphere is StartFraction 2,048 Over 3 EndFraction pi inches cubed. FalseThis is false because the volume of the sphere is 4πr³/3 = (16,384/3) π cubic inches.
The sphere has a diameter of 32 in. TrueThis is True because a radius is half of a diameter. Half of the given diameter of 32 in is 16 in and the radius in the question is also 16 in.
The radius’s length is one-half the length of the diameter. TrueThis is True because a radius is half of a diameter
The volume of the sphere is StartFraction 16,384 Over 3 EndFraction pi inches cubed. TrueThis is True because the volume of the sphere is 4πr³/3 = (16,384/3) π cubic inches.
The diameter’s length is one-half the length of the radius. FalseIt is the radius’s length that is one-half the length of the diameter
Please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
[tex]y=\sqrt[3]{x+3}+3[/tex]
Step-by-step explanation:
The S-shaped curve is that of the cube root function (choices C or D). The parent function has its critical point at the origin. Here, that has been moved 3 units left and 3 units up.
Replacing x with x-a will move a function's graph to the right by "a" units. Here, we have a=-3, so we expect to see ∛(x-(-3)) = ∛(x+3). The graph of that is moved up 3 units by adding 3 to the function value. This gives ...
y = ∛(x+3) +3 . . . . . matches choice D
Find PR
PR = 2x
RQ = 25
PQ = 6+3x (adding 2 lengths as seen on diagram)
Answer:
Therefore,
[tex]PR=10\ unit[/tex]
Step-by-step explanation:
Given:
PR = 2x
RQ = 25
Say M divide PQ such that
PM = 6
MQ = 3x
∠PRM ≅ ∠QRM
RM is the angle Bisector of angle PRQ
To Find:
PR = ?
Solution:
Angle Bisector Theorem:
The angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle.
It equates their relative lengths to the relative lengths of the other two sides of the triangle.
Here RM is the angle Bisector of angle PRQ
Therefore,
[tex]\dfrac{PR}{RQ}=\dfrac{PM}{MQ}[/tex] ...Angle Bisector Theorem.
Substituting the values we get
[tex]\dfrac{2x}{25}=\dfrac{6}{3x}\\\\x^{2}=25\\Square\ Rooting\\x=\pm\sqrt{25}\\x=5[/tex]
As x cannot be negative x =5
Substituting x value in PR we get
[tex]PR=2\times 5=10\ unit[/tex]
Therefore,
[tex]PR=10\ unit[/tex]
Convert 5/16 to a decimal using long division
Answer: 0.3125
Step-by-step explanation:
Convert the fraction to a decimal by dividing the numerator by the denominator.
A company that teaches self-improvement seminars is holding one of its seminars in Greenwood. The company pays a flat fee of $264 to rent a facility in which to hold each session. Additionally, for every attendee who registers, the company must spend $15 to purchase books and supplies. Each attendee will pay $16 for the seminar. Once a certain number of attendee register, the company will be breaking even. What will be the company's total expenses and revenues? How many attendees will that take?
Answer:
Step-by-step explanation:
expenses :
flat fee of 264 + 15 for every attendee (a)
264 + 15a
revenue :
16 per attendee
16a
break even point is when expenses = revenue
264 + 15a = 16a
264 = 16a - 15a
264 = a
total expenses: 264 + 15a......264 + 15(264) = $ 4224
total revenue : 16a......16(264) = $ 4224
attendees taken : 264
Which basic construction if shown here?
A) bisect an angle
B) bisect a like segment
C) construct a parallel line
D) copy a line segment
Answer:
A
Step-by-step explanation:
Consider triangle OAM and OBM. In these triangles,
OA is congruent to OB as radii of one circle;AM is congruent to BM as radii of two congruent circles;OM is congruent to OM by reflexive property (this side is common).Thus, triangles OAM and OBM are congruent by SSS postulate.
Congruent triangles have congruent corresponding parts, so
[tex]\angle AOM\cong \angle BOM[/tex]
Hence, OM is angle AOB bisector.
Answer:
a
Step-by-step explanation:
usatestprep
Can someone help me with this question please ?
Answer:
57.97 cm²
Step-by-step explanation:
The area (A) of a trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h( a + b)
where h is the perpendicular height between the parallel bases and a, b are the bases.
Here h = 6.2, a = 7.9 and b = 10.8, thus
A = 0.5 × 6.2 (7.9 + 10.8)
= 3.1 × 18.7 = 57.97 cm²
Answer:
Step-by-step explanation:
Area of trapezium = 1/2(a + b)h
a = 7.9cm, b = 10.8cm and h = 6.2cm
Area = 1/2(7.9 + 10.8)×6.2
Area = 1/2 × 18.7 × 6.2
Area = 57.97cm²
e^2x + 3e^x - 18 = 0
Solving e²ˣ + 3eˣ- 18 = 0 involves substituting y = ex to transform it into a quadratic equation. Solving this quadratic equation yields a valid solution, y = 3, leading to x = ln(3). Therefore, the solution is x = ln(3).
To solve the equation e²ˣ + 3eˣ- 18, we perform a substitution to convert it into a quadratic form.
Let y =eˣ. Then the equation becomes:
y² + 3y - 18 = 0.This quadratic equation can be solved using the quadratic formula:This gives us two solutions for y:
y = 3 and y = -6.Since y = eˣ, and eˣ must be positive:
y = -6 is not valid. Thus, y = 3.Finally, solve for x:
eˣ = 3 ⟹ x = ln(3).Therefore, the solution to the equation e²ˣ + 3eˣ- 18 = 0 is x = ln(3).
Chase purchased a sweatshirt from the clearance rack. The price of the sweatshirt after the discount is represented by the expression 0.75x, where x represents the original price of the sweatshirt.
Which expression also represents the discounted price of the sweatshirt?
A
(0.75 − 0.25)x
B
(0.75 + 0.25)x
C
x – 0.25x
D
x + 0.25x
Answer:B(0.75+0.25)x
Step-by-step explanation:
Is a discount of 0.75 was given the d real value of the sweatshirt would be a whole number
Which is 1-0.75=0.25
Can someone please help me with this question? :)
Answer:
Step-by-step explanation:
[tex]\frac{h*(a+b)}{2}=\frac{6.7*(7+10.4)}{2}\\\\=\frac{6.7*17.4}{2}=\frac{116.58}{2}=58.29[/tex] cm²
Is 3a a term for expressions
Answer:
yes
Step-by-step explanation
because it is an algebraic expression. 3a + a are called like terms because they both contain the same letter. To simplify an expression we collect together like terms. You can only add or subtract when the letters are the same.
In a video game,you score p game points and b triple bonus points. An expression for your score is p+3b. What is your score when you earn 245 games points and 20 triple bonus points
Your score in the game is 305 points.
Step-by-step explanation:
Given,
Expression used for score = p + 3b
p = game points
b = triple bonus points
Game points earned by you = p = 245 games point
Triple bonus points = b = 20
Putting these values in given expression
Total points = [tex]245+3*20[/tex]
Total points = [tex]245+60[/tex]
Total points = 305 points
Your score in the game is 305 points.
Keywords: addition, expression
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Jennifer is completing the square to solve the quadratic equation
X^2 - x - 3 = 0.
What should be her first step?
A- adding -x to both sides of the equation
B- Isolating the constant, -3
C- Isolating the first term, X^2
Isolate the variable by dividing each side by factors that don't contain the variable.
Hope it helps! :)
QuezoMartiinez <3
Answer:
The answer is B- Isolating the constant, -3
which of the following is an example of chemical property
a. boiling point
b. melting point
c. electric conductivity
d. decomposition caused by heat
Heat-induced decomposition is an illustration of chemical property.
Trying to break down is the phenomenon of decomposing. Whenever a substance is heated, it undergoes thermal breakdown, which is a chemical process.
At high temperatures, thermal breakdown processes occur. Before collapsing into the products, the reactions absorb a lot of energy.
So, Option "D" is the correct answer to the following question.
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Decomposition caused by heat is an example of a chemical property because it involves a substance changing into different substances through a chemical reaction.
Explanation:The question asks which of the following options is an example of a chemical property. Chemical properties are characteristics of a substance that indicate its ability to undergo a chemical change, resulting in the formation of new substances. Options like boiling point, melting point, and electric conductivity are considered physical properties because they describe aspects of a substance that can be observed or measured without changing the substance's chemical identity. In contrast, an option like decomposition caused by heat is a chemical property because it involves a chemical change where the original substance is transformed into different substances as a result of the chemical reaction induced by heat.
Therefore, the correct answer to the original question, "which of the following is an example of a chemical property?" is:
d. decomposition caused by heatSimilarly, from the reference exercises provided, flammability is also a chemical property. It specifies a substance's ability to burn or ignite, causing it to change chemically and form new substances as it reacts with oxygen in the air.
Does the graph represent a function? Yes or NO
You want to deliver a package to Japan. The FedEx delivery service charges a $15 flat fee plus $2 per additional kilogram. You can also use the USPS Priority Mail service which charges you $5 per kilogram. After how many kilograms will the total costs of the two options be the same?
Answer:
5kg
Step-by-step explanation:
Step 1.
Write in y=mx+c format
m= $/kg
c=flat fee
x=additional kilograms
FedEx:
y=2x+15
USPS:
y=5x
Step 2.
Keep Changing the x value (the no. of kilograms) in both equations until y is the same number
y=5×5
=25
y=2×5+15
=25
∴It would cost the same for both options at 5kg
Answer:
5kg
Step-by-step explanation:
Step 1.
Write in y=mx+c format
m= $/kg
c=flat fee
x=additional kilograms
FedEx:
y=2x+15
USPS:
y=5x
Step 2.
Keep Changing the x value (the no. of kilograms) in both equations until y is the same number
y=5×5
=25
y=2×5+15
=25
∴It would cost the same for both options at 5kg
A store advertises a 35% discount on a $951 computer system.
For this case we propose a rule of three:
$ 951 -------------> 100%
x -------------------> 35%
Where "x" is the variable that determines the amount of the discount equivalent to 35%.
[tex]x = \frac {35 * 951} {100}\\x = \frac {33285} {100}\\x = 332.85[/tex]
Thus, the discount is $332.85.
The new price of the computer system is:
$951- $332.85 = $617.5
Answer:
The new price of the computer system is: $617.5