Answer:
The system consists of parallel lines ⇒ 2nd answer
Both lines have the same slope ⇒ 3rd answer
Step-by-step explanation:
Lets revise the types of the solutions of the system of equations
Case 1:
→ If the two equations have the same coefficients of the two variables
and different numerical terms then the two equations represented
by two parallel lines
Ex: ax + by = c , ax + by = d
Case 2:
→ If the two equations have the same coefficients of the two variables
and same numerical term then the two equations represented
by the same line
Ex: ax + by = c , ax + by = c
Case 3:
→ If the two equations have different coefficients of one of the variables
or the two variables then they represented by two intersected lines
and the system has one solution
Ex: ax + by = c , dx + ey = f
The system of equation is
* y = [tex]\frac{1}{3}[/tex] x - 4
* 3 y - x = -7
Multiply the first equation by 3
∴ 3 y = x - 12
Subtract both sides by x
∴ 3 y - x = - 12 ⇒ (1)
∵ 3 y - x = - 7 ⇒ (2)
The system of equations has same x-coefficient and same y-coefficient
in both equations but the numerical terms are different, then they
represented by two parallel lines as first case above
and parallel lines have the same slope
The system consists of parallel lines
Both lines have the same slope
Answer:
BC
Step-by-step explanation:
What is the median of this list of numbers? 5, 10, 13, 7,5
Median: The middle number when all the numbers are listed in order.
To find the median of the data set shown here, we can first start by putting all the numbers in order from least to greatest.
Least to greatest - 5, 5, 7, 10, 13
Next, we locate the number that is exactly in the middle and if there is no number exactly in the middle, we find the two numbers and find halfway point between them.
The number that is exactly in the middle of the data set is 7 so our median is 7.
Evaluate 8a-1+0.5b8a−1+0.5b8, a, minus, 1, plus, 0, point, 5, b when a=\dfrac14a=
4
1
a, equals, start fraction, 1, divided by, 4, end fraction and b=10b=10b, equals, 10.
Answer: [tex]6[/tex]
Step-by-step explanation:
Given the following expression:
[tex]8a-1+0.5b[/tex]
You need to substitute the given values of "a" and "b" into the expression. Notice that these values are:
[tex]a=\frac{1}{4}\\\\b=10[/tex]
Then;
[tex]8a-1+0.5b=8(\frac{1}{4})-1+0.5(10)[/tex]
Now you must solve the multiplications:
[tex]=\frac{8}{4}-1+5=2-1+5[/tex]
The final step is to add the numbers. Therefore, you get the following answer:
[tex]=6[/tex]
The value of the expression 8a - 1 + 0.5b evaluates to 6 for a = 1/4 and b= 10.
To evaluate the expression 8a - 1 + 0.5b when a = 1/4 and b = 10, you can substitute these values into the expression and then perform the calculations:
1. Substitute the value of a:
8 * (1/4) - 1 + 0.5 * 10
2. Simplify each term:
- First term: 8 * (1/4) = 2
- Second term: -1
- Third term: 0.5 * 10 = 5
3. Add the simplified terms:
2 - 1 + 5 = 1 + 5 = 6
So, when a = 1/4 and b = 10, the expression 8a - 1 + 0.5b evaluates to 6.
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Find three consecutive integers whose sum is 441
Answer:
146, 147 and 148
Step-by-step explanation:
Let the three integers be x, x+1, and x+2.
(they are consecutive)
Now, we are given that their sum is 441.
So,
(x) + (x+1) + (x+2) = 441
3x + 3 = 441
3x = 438
x = 438/3
x = 146
Thus, the integers are:
x = 146
x+1 = 147
x+2 = 148
Please mark Brainliest if this helps!
Round 42395 to the nearest ten thousand
Answer:
40000
Step-by-step explanation:
4(2)395
if it smaller than 5 round down
if its lager than 5 round up
lim (x^3-8)/(x)
x-2
Can someone help me with this question it is so confusing
we know it takes 20lbs of Olive to make 3 liters of oil, we also know that the orchard for a whole year gets 3000 lbs, how much oil is there in those 3000 lbs for the year?
[tex]\bf \begin{array}{ccll} \stackrel{olive}{lbs}&\stackrel{olive~oil}{liters}\\ \cline{1-2} 20&3\\ 3000&x \end{array}\implies \cfrac{20}{3000}=\cfrac{3}{x}\implies \cfrac{1}{150}=\cfrac{3}{x}\implies x= 450[/tex]
Teresa’s age is 5 years more than twice Ben’s age. If Ben is x years old, the expression _____ gives the sum of Ben’s and Teresa’s ages. If Ben is 7 years old, the sum of Ben’s and Teresa’s ages is _____ years.
Using a system of equations, it is found that:
If Ben is x years old, the expression 3x + 5 gives the sum of Ben’s and Teresa’s ages. If Ben is 7 years old, the sum of Ben’s and Teresa’s ages is 26 years.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given by:
Variable x: Ben's age.Variable y: Teresa's age.Teresa’s age is 5 years more than twice Ben’s age, hence:
y = 2x + 5
The sum of their ages is:
x + y = x + 2x + 5 = 3x + 5.
Ben is 7 years old, hence the sum is given by:
3(7) + 5 = 26.
Then:
If Ben is x years old, the expression 3x + 5 gives the sum of Ben’s and Teresa’s ages. If Ben is 7 years old, the sum of Ben’s and Teresa’s ages is 26 years.
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The sum of Ben's and Teresa's ages is represented by the expression 3x + 5, and when Ben is 7 years old, their total age is 26 years.
Explanation:The expression to represent the sum of Ben's age and Teresa's age, given that Ben is x years old and Teresa's age is 5 years more than twice Ben's age, is 2x + 5 + x. This can also be simplified to 3x + 5.
When Ben is 7 years old, we plug in the value 7 for x in the simplified expression to calculate the sum of their ages: 3(7) + 5, which equals 21 + 5.
Therefore, the sum of Ben's and Teresa's ages when Ben is 7 years old is 26 years.
4. If DF = 9x - 39, find EF.
Help I’m so confused!!!!
Answer:
EF =58
Step-by-step explanation:
from the illustration,
EF =DF - DE
given that DF =9x-39 , DE =47 EF=3x +10
substitute them into the formula,
3x +10=9x-39 - 47
solving for x
3x +10 =9x -86
grouping like terms
3x - 9x =-86 -10
-6x=-96
dividing through by -6
[tex] \frac{ - 6x}{ - 6} = \frac{ - 96}{ - 6} [/tex]
[tex]x = \frac{96}{6} [/tex]
[tex]x = 16[/tex]
but EF=3x+10
substitute x=16 into it to get the EF
EF= 3(16)+10
EF=48+10
EF=58
[tex]\huge\boxed{58}[/tex]
First of all, we know that [tex]DE+EF=DF[/tex], because these are two segments that make up one larger segment.
Write this as an equation.
[tex]DE+EF=DF[/tex]
[tex]47+(3x+10)=9x-39[/tex]
Remove the parentheses. [tex]47+3x+10=9x-39[/tex]
Combine the like terms. [tex]3x+57=9x-39[/tex]
Subtract [tex]9x[/tex] from both sides. [tex]-6x+57=-39[/tex]
Subtract [tex]57[/tex] from both sides. [tex]-6x=-96[/tex]
Divide both sides by [tex]-6[/tex]. [tex]x=16[/tex]
Now, find [tex]EF[/tex].
[tex]3x+10[/tex]
[tex]3(16)+10[/tex]
Multiply. [tex]48+10[/tex]
Add. [tex]\boxed{58}[/tex]
A rectangle is 25 feet long.Its area is 375 square feet. What is the width of the rectangle?
Answer:
Width of rectangle is 15 ft !
Step-by-step explanation:
Given :-
• Area of rectangle = 375 ft²
• Length of rectangle = 25 ft
• Let width of the rectangle be b ft
Formula for area of rectangle
= ( lenght ) ( width )
Substituting the value ,
375 ft² = 25ft ( b ft )
[tex] \frac{375 {ft}^{2} }{25ft} = bft[/tex]
15 = b
So, the width of rectangle is 15 ft
The required width of the rectangle is 15 feet which is 25 feet long and the area is 375 square feet.
Given that,
A rectangle is 25 feet long. Its area is 375 square feet. What is the width of the rectangle is to be determined.
The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.
Here,
The area of the rectangle = length * width
25 = 375 * width
width = 375 / 25
width = 15
Thus the required width of the rectangle is 15 feet.
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Prove the inequality.
c+ 1/c ≥2 for c>0
The inequality c + 1/c ≥ 2 for c > 0 is proven by using the AM-GM inequality method. By applying this method, we find that the arithmetic mean of the variables is indeed greater or equal to 2, hence confirming the inequality.
Explanation:To solve the inequality c + 1/c ≥ 2 for c > 0, we can use the AM-GM (Arithmetic Mean - Geometric Mean) inequality method.
According to AM-GM inequality, for any positive numbers a, b, the arithmetic mean is always greater or equal to the geometric mean. In notation: (a + b)/2 ≥ sqrt(a * b). Applying this to our problem where a = c and b = 1/c, we get (c + 1/c) / 2 ≥ sqrt(c * 1/c). This simplifies to c + 1/c ≥ 2*1 = 2, therefore our inequality is confirmed.
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The inequality c + 1/c ≥ 2 for c > 0 is proven using the AM-GM inequality by setting a = c and b = 1/c, showing that their arithmetic mean is always greater or equal to their geometric mean.
To prove the inequality c + 1/c ≥ 2 for c > 0, we can apply the AM-GM inequality which stands for Arithmetic Mean - Geometric Mean inequality. The AM-GM inequality states that for any non-negative real numbers a and b, the arithmetic mean is always greater than or equal to the geometric mean. That is, (a + b)/2 ≥ √(ab).
In our case, we can let a = c and b = 1/c. Then, according to the AM-GM inequality, we get:
(c + 1/c)/2 ≥ √(c * 1/c)(c + 1/c)/2 ≥ √(1)(c + 1/c)/2 ≥ 1When we multiply both sides of the inequality by 2, we get:
c + 1/c ≥ 2This completes the proof for the inequality c + 1/c ≥ 2 when c > 0.
Find the sq root the sq root of 5 is 2.24
Answer: [tex]\bold{\dfrac{7-3\sqrt5}{2}}[/tex]
Step-by-step explanation:
You did great until you expanded (3 - √5)². You forgot the middle term
[tex]\dfrac{3-\sqrt5}{3+\sqrt5}\bigg(\dfrac{3-\sqrt5}{3-\sqrt5}\bigg)\\\\\\=\dfrac{(3-\sqrt5)(3-\sqrt5)}{(3+\sqrt5)(3-\sqrt5)}\\\\\\=\dfrac{9-3\sqrt5-3\sqrt5+5}{9-3\sqrt5+3\sqrt5-5}\\\\\\=\dfrac{14-6\sqrt5}{4}\\\\\\\text{Factor out a 2 from the numerator and denominator}\\=\dfrac{2(7-3\sqrt5)}{2(2)}\\\\\\=\large\boxed{\dfrac{7-3\sqrt5}{2}}[/tex]
Given: Can you use ASA postulate or the AAS Theorem to prove the triangles congruent?
Answer:
by ASA only
explanation:
They are reflective towards each other making them congruent
The coordinates of point A are (p, q) and coordinates of point B are (p+2q, q+2p). Provide your complete solutions and proofs in your paper homework and respond to questions or statements online. Show that the midpoint of AB is the same distance from the x-axis and y-axis
Answer:
The mid-point (p + q , q + p) of AB is the same distance from the x-axis and the y-axis
Step-by-step explanation:
* Lets explain how to solve the problem
- Any point will be equidistant from the x-axis and the y-axis must have
equal coordinates
- Ex: point (4 , 4) is the same distance from the x-axis and the y-axis
because the distance from the x-axis to the point is 4 (y-coordinate)
and the distance from the y-axis and the point is 4 (x-coordinate)
- If (x , y) is the mid-point of a segment its endpoints are
[tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex], then
[tex]x=\frac{x_{1}+x_{2}}{2}[/tex] and [tex]y=\frac{y_{1}+y_{2}}{2}[/tex]
* Lets solve the problem
∵ Point A has coordinates (p , q)
∵ Point B has coordinates (p + 2q , q + 2p)
- The mid-point of AB is (x , y)
∵ [tex]x=\frac{p+p+2q}{2}[/tex]
∴ [tex]x=\frac{2p+2q}{2}[/tex]
- Take 2 as a common factor from the terms of the numerator
∴ [tex]x=\frac{2(p+q)}{2}[/tex]
- Divide up and down by 2
∴ x = p + q
∵ [tex]y=\frac{q+q+2p}{2}[/tex]
∴ [tex]y=\frac{2q+2p}{2}[/tex]
- Take 2 as a common factor from the terms of the numerator
∴ [tex]y=\frac{2(q+p)}{2}[/tex]
- Divide up and down by 2
∴ y = q + p
∴ The mid point of AB is (p + q , q + p)
- p + q is the same with q + p
∵ The x-coordinate of the mid point of AB is p + q
∵ The y-coordinate of the mid point of AB is q + p
∵ p + q = q + p
∴ The coordinates of the mid-point of AB are equal
- According the explanation above
∴ The mid-point (p + q , q + p) of AB is the same distance from the
x-axis and the y-axis
Drag a statement or reason to each box to complete this proof.
this proof -2(x+1)=8, then x= -5
Step-by-step explanation:
distribute the -2 to (x+1) you end up with -2x-2=8 (multiplication property). Add 2 to both sides to get rid of the -2 of the left (addition property). 8+2=10. -2x=10 divide the -2 to both sides. x=-5 (division property).
Answer:
We have to prove that,
-2(x+1)=8, then x= -5
L.H.S.
[tex]-2(x+1)=8[/tex]
By distributive property,
[tex]-2x-2=8[/tex]
Adding 2 both sides ( Additive property of equality )
[tex]-2x-2+2=8+2[/tex]
[tex]-2x=10[/tex]
Divide both sides by -2 ( Division property of equality ),
[tex]\frac{-2x}{-2}=\frac{10}{-2}[/tex]
[tex]x=-5[/tex]
= R. H. S
Hence, proved....
Catherine is 4 centimeters taller than ally, while Katrina is 5 centimeters shorter than ally. Let t represent ally's height in centimeters.
Answer:
4 is right yur
Step-by-step explanation:
Solve v= 1/3 bh for h
Answer:
Step-by-step explanation:
v= 1/3 bh
multiply by : 3
3v = bh
dividid by b : h = 3v/b
To solve for h in the equation v = (1/3)bh, you need to isolate h on one side. Multiply both sides by 3 to eliminate the fraction, then divide both sides by b to solve for h.
Explanation:To solve the equation v = (1/3)bh for h, we need to isolate h on one side of the equation.
First, we can multiply both sides of the equation by 3 to get rid of the fraction: 3v = bh.
Next, to solve for h, we divide both sides of the equation by b. This gives us the final answer: h = 3v / b.
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What is the value of 128^3/7
Answer:
8
Step-by-step explanation:
kendra has 120 stickers . 10 stickers fill a page. how many pages can she fill?
Answer:
12 pages
Step-by-step explanation:
According to the question Kendra have 120 stickers
10 stickers fill a page
So, number of pages that can be filled be 120 stickers = [tex] \frac{120}{10} = 12[/tex]
Therefore, she can fill 12 pages by 120 stickers.
The total number of pages Kendra can fill with a total number of 120 stickers is 12 pages.
Kendra has 120 stickers, and 10 stickers fill a page.
To calculate how many pages she can fill, divide the total number of stickers by the stickers per page:
120 stickers ÷ 10 stickers/page = 12 pages.
How do I identify the rate of change on a linear function?
Answer:
Slope is the ratio of the vertical and horizontal changes between two points on a surface or a line. The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run.
Solve for x: 5 - (x + 5) > -2(x + 4)
The price of a house increased from $400,000 to $500,000 in one year. What is the percent increase?
Answer:
80%
Step-by-step explanation:
The percent increase in the price of the house is 25%. This is calculated using the formula for percent increase: (Final value - Initial value) / Initial value * 100.
Explanation:The question is asking for the percent increase in the price of a house. The formula for calculating percent increase is: (Final value - Initial value) / Initial value * 100. In this case, the initial value is the original house price of $400,000 and the final value is the new house price of $500,000.
So, the calculation will be: ($500,000 - $400,000) / $400,000 * 100 = 25%.
Therefore, the price of the house increased by 25% over the year.
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If a+b+c=7 and ab+bc+ca=20 find the value of a^2+b^2+c^2
Answer:
9
Step-by-step explanation:
Using the identity
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
Subtract 2(ab + bc + ca) from both sides, then
a² + b² + c² = (a + b + c)² - 2(ab + bc + ca) = 7² - 2(20) = 49 - 40 = 9
PLZ HELP ME I NEED THIS ASAP
Mean = 110
Sample size = 45
Standard deviation = 6
Z score for 90% is 1.645 ( from Z-table).
Lower Limit = Mean - Z(SD/√Sample size))
Lower limit = 110 - 1.645(6/√45)
Lower limit = 108.5
Upper Limit = Mean + Z(SD/√Sample size))
Lower limit = 110 +1.645(6/√45)
Lower limit = 111.5
The interval is (108.5, 111.5)
what is 1/3 to the 2ed power
Answer:
1/9
1/3 x 1/3 = 1/9 (because 3x3 = 9)
Hey!
---------------------------------------------------------------
Solution:
Take the numerator and denominator and solve it to the 2nd power.
1² = 1
3² = 9
Put it back as a fraction.
1/9
---------------------------------------------------------------
Answer:
1/9
---------------------------------------------------------------
Hope This Helped! Good Luck!
f(x) = 8x – 2
g(x) = 9x + 2
What is h(x) = f(x) – g(x)?
Options:
h(x) = 17x + 14
h(x) = x + 4
h(x) = –x – 4
h(x) = –x + 14
Answer:
-x-4
Step-by-step explanation:
8x-2-(9x+2)
8x-2-9x-2
-x-4
Function h(x) = f(x) – g(x) = -x - 4
What is a function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given functions
f(x) = 8x – 2
g(x) = 9x + 2
h(x) = f(x) – g(x)
h(x) = (8x – 2) - (9x + 2)
h(x) = 8x - 2 -9x - 2
h(x) = (8x - 9x) + (-2 - 2)
h(x) = -x - 4
Hence, h(x) = -x - 4
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can you guys help me out?
Answer:
5 inches
Step-by-step explanation:
V = (b² h) ÷ 3
Given that V = 25 and h = 3:
25 = (b² × 3) ÷ 3
25 = b²
b = 5
Therefore, the length of the base's sides is 5 inches.
is 15 a perfect square
Answer:
No.
Step-by-step explanation:
No.
16 is a perfect square because 4 times itself is 16.
9 is a perfect square because 3 times itself is 9.
So there are no whole numbers such that when yoy square it (times it by itself) gives you 15.
Whole numbers are numbers contained within the following set:
{0,1,2,3,4,5,...}
So here are the first few perfect squares:
0 because 0(0)=0
1 because 1(1)=1.
4 because 2(2)=4.
9 because 3(3)=9.
16 because 4(4)=16.
25 because 5(5)=25.
36 because 6(6)=36.
49 because 7(7)=49.
64 because 8(8)=64.
81 because 9(9)=81.
As you can see 15 isn't in that list.
Please select the word from the list that best fits the definition
Understands how formulas are used
Interpersonal
Musical
Body-Kinesthetic
Spatial
Linguistic
Intrapersonal
Logical-Mathematical
Answer:
Logical-Mathematical
Step-by-step explanation:
According to the theory of multiple intelligences, human intelligence has 8 different modalities (musical-rhythmic, visual-spatial, verbal-linguistic, logical-mathematical, bodily-kinesthetic, interpersonal, intrapersonal, naturalistic). In order to understand how formulas are used, logical-mathematical intelligence is used.
The term that corresponds to understanding how formulas are used is Logical-Mathematical. This refers to an individual's proficiency in carrying out mathematical operations and understanding complex mathematical problems, including the use of formulas.
Explanation:The word from the list that best fits the definition 'Understands how formulas are used' is Logical-Mathematical. This term is one of Howard Gardner's Multiple Intelligences and it refers to the ability to calculate, quantify, consider propositions and hypotheses, and carry out complete mathematical operations. In an educational setting, people who are strong in logical-mathematical intelligence can understand complex problems, detect patterns, and excel in mathematics, with skills such as understanding formulas playing a key role.
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what is the value of s(6)
Answer:
6s
Step-by-step explanation:
sx6 = 6s
What is the gcf of 42 and 10
Answer:
2
Step-by-step explanation:
Make a list
10: 1, 2, 5, 10
42: 1, 2, 3, 6, 7, 14, 21