[tex]4x - 2x = 7 + 3 \\ \\ 2x = 10 \\ \\ x = \frac{10}{2} \\ \\ x = 5.[/tex]
•••••••••••••••••••••••••••••••••••••••Correct Question : 2x + 6 = 7x - 14Solution : 2x + 6 = 7x - 14[tex]2x - 7x = - 14 - 6 \\ \\ - 5x = - 20 \\ \\ x = \frac{20}{5} \\ \\ x = 4.[/tex]
The point stope form of the equation of the line that passes through (-4,-3) and (12, 1) is y-1 = (x-12). What is
the standard form of the equation for this line?
Answer:
x-4y = 8
Step-by-step explanation:
The standard form for the equation of a line is Ax+By=C where A is a positive integer and B and C are integers
First we need to find the slope
m = ( y2-y1)/(x2-x1)
m = (-3-1) / (-4-12)
=-4/-16
= 1/4
The point slope form is
y-1 = 1/4(x-12)
Multiply each side by 4
4(y-1 )= 4*1/4(x-12)
4(y-1) = x-12
4y -4 = x-12
Subtract 4y from each side
4y-4-4y = x-4y -12
-4 = x-4y -12
Add 12 to each side
-4+12 = x-4y -12+12
8 = x-4y
x-4y = 8
The standard form is x-4y = 8
factorise:y(x+z)+z(x+y)+y^2+z^2
Answer: (x+z+y)(y+z)
Step-by-step explanation:
y(x+z)+z(x+y)+y^2+z^2
Factor out y and z from the expression
= y(x+z+y)+z(x+y+z)
Factor out x + z + y from the expression
= (x+z+y)(y+z)
Two towns that are 32 km apart are 8 cm on a map. What is the scale of the map?
This question is urgent, I have grade 8 final exams tomorrow and I'm struggling with this type of question.
If two towns that are 32 km apart are 8 cm on a map. Then the scale factor will be 1 cm = 4 km.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
Two towns that are 32 km apart are 8 cm on a map.
Then the scale factor will be
8 cm = 32 km
1 cm = 4 km
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Expand & simplify
3(t+5)+5(t−6)
Answer:
8t - 15
Explanation:
⇒ 3(t+5)+5(t−6)
distribute inside parenthesis
⇒ 3(t) + 3(5) + 5(t) + 5(-6)
multiply the variables
⇒ 3t + 15 + 5t - 30
collect like terms
⇒ 3t + 5t + 15 - 30
add/ subtract like terms
⇒ 8t - 15
Solution: 8t-15
Detailed explanation:
First the problem asks us to expand
[tex]\tt 3(t+5)=3\cdot t +3\cdot5=3t+15[/tex]
Similarly
[tex]\tt 5(t-6)=5\cdot t -5\cdot 6=5t-30[/tex]
Therefore
[tex]\tt 3t+15+5t-30[/tex]
Upon combining like terms
[tex]\tt 8t+15-30[/tex]
Upon doing this further
[tex]\tt 8t-15[/tex]
one gym membership charges $10 a month with a sign-up fee of $45. Another gym does not charge patrons a sign-up fee but costs $25 a month. at what month is the total cost of both memberships the same?
Answer:
3 months
Step-by-step explanation:
The quotient of a number p and 38
Answer:
[tex] \frac{p}{38} [/tex]
The required quotient of a number p and 38 is 38/p, as of the given condition
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
here,
In the quesiton, we have to determine the quotient of a number p and 38.
So, divide 38 by p to determine the quotient.
= 38/p
Thus, the required quotient of a number p and 38 is 38/p.
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Brainliest!
Which system is represented in the graph?
y>x²-2x-3
y > x + 3
Oy
y
Oy2x²-2x-3
y ≤ x + 3
Oy>x²-2x-3
y
Answer:
y ≥ x² -2x -3y ≤ x +3Step-by-step explanation:
When matching graph to inequality, the first things to look for are the nature of the boundary line (solid or dashed), and the direction of shading relative to the boundary line (above or below, left or right).
Boundary lineThe boundary line of the solution set of an inequality will be solid if the line is included in the solution. That is, the inequality will include the "or equal to" case. The corresponding inequality symbols are ≤ or ≥.
The boundary line of the solution set will be dashed if the line is not included in the solution. The corresponding inequality symbols are < or >.
ShadingThe shading will be above the boundary line if the solution set includes larger y-values than those on the boundary. This will be the case when the inequality is of the form y > ( ) or y ≥ ( ).
For inequalities of the form y < ( ) or y ≤ ( ), the shading will be below the boundary line.
Similarly, the shading for an inequality of the form x > ( ) will be right of the boundary line, where x-values are greater. For inequalities of the form x < ( ), the shading will be to the left of the boundary line.
ApplicationIn the given graph, both boundary lines are solid, so both inequalities will include the "or equal to" case. This eliminates choices A, B, D.
The shading is above the quadratic boundary line, and below the linear boundary line, so the inequalities can be expected to be of the forms ...
y ≥ x² +...y ≤ x +...These forms match choice C:
y ≥ x² -2x -3y ≤ x +3(6, -5) reflected aross the y axis
Answer:
Then the new point is (-6,-5)
Step-by-step explanation:
Trout Street and Salmon Street are the same distance from the boardwalk to the intersection of 1st Street, Trout Street, and Salmon Street as shown in the diagram. Abby walks down 1st Street and stops when she reaches the boardwalk.
How far of a walk does she have to get to Trout Street?
Abby's walk to Trout Street is _______ yards.
Answer:
800
Step-by-step explanation:
I did it on the test
Answer:
800
Step-by-step explanation:
I just fifnished test
Find the gradient of the line segment joining of
(1, 1) and (3, 5)
Answer:
2
Step-by-step explanation:
[tex]\text{First I'd recommend using this little equation:}\\\text{m}=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{Substitute the values::}\\\text{m}=\dfrac{5-1}{3-1} \\\text{m}=\dfrac{4}{3}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{The gradient is:: }\dfrac{4}{3}[/tex]
HELP PLEASE
which choice is equivalent to the quotient below? √15/3√3
A. √5/3
B. √5/9
C. √5/√3
D. √4
Answer:
A - [tex]\sqrt{5}[/tex]
Step-by-step explanation:
[tex]\sqrt{15} = \sqrt{5} *\sqrt{3} \\\frac{\sqrt{5} *\sqrt{3}}{3*\sqrt{3}} = \frac{\sqrt{5}}{3}[/tex]
Answer: √5/3
Step-by-step explanation:
4
Which equation represents a linear function that has a slope of 5 and a y-intercept of -6?
4
O y=-6x+²/
O y=x-6
Oy=x+6
Oy=6x+
k
Answer:
y = 5x - 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = 5 and c = - 6 , then
y = 5x - 6 ← equation of line
The equation represents a linear function with a slope of 5 and a y-intercept of -6 is y = 5x - 6.
The equation of a linear function is typically written in the form "y = mx + b," where "m" represents the slope and "b" represents the y-intercept.
Given that the slope is 5 and the y-intercept is -6, the equation becomes:
y = 5x - 6
Here's the calculation:
The slope (m) is 5, and the y-intercept (b) is -6. Therefore, the equation becomes:
y = 5x - 6
This equation represents a linear function with a slope of 5 and a y-intercept of -6.
Hence the equation represents a linear function with a slope of 5 and a y-intercept of -6 is y = 5x - 6.
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Solve x+ 2y = -2 I’m really confused
Answer:
y=−1/2x−1
Step-by-step explanation:
I put it in slope intercept form as I assume that is what the question is asking.
How do I solve an endless amount of numbers with a common ratio
..........
etc. 10+1+0.1+0.01+0.001....
Answer:
11 .21 add the number together
Notice that the given sum is equivalent to
[tex]10 + 1 + \dfrac1{10} + \dfrac1{10^2} + \dfrac1{10^3} + \cdots \\\\ ~~~~~~~~~~~~ = 10 \left(1 + \dfrac1{10} + \dfrac1{10^2} + \dfrac1{10^3} + \dfrac1{10^4} + \cdots\right)[/tex]
or 10 times the infinite geometric series with ratio 1/10.
To compute the infinite sum, consider the [tex]n[/tex]-th partial sum
[tex]S_n = 1 + \dfrac1{10} + \dfrac1{10^2} + \cdots + \dfrac1{10^{n-1}}[/tex]
Multiply both sides by the ratio.
[tex]\dfrac1{10} S_n = \dfrac1{10} + \dfrac1{10^2} + \dfrac1{10^3} + \cdots + \dfrac1{10^n}[/tex]
Subtract this from [tex]S_n[/tex] to eliminate all but the outermost terms,
[tex]S_n - \dfrac1{10} S_n = 1 - \dfrac1{10^n} \implies S_n = \dfrac{10}9 \left(1 - \dfrac1{10^n}\right)[/tex]
As [tex]n\to\infty[/tex], the exponential term will decay to 0, leaving us with
[tex]1 + \dfrac1{10} + \dfrac1{10^2} + \cdots = \dfrac{10}9[/tex]
Then the value of the sum we want is
[tex]10\times\dfrac{10}9 = \boxed{\dfrac{100}9}[/tex]
Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h.
A.
h(-3) = -1
B.
h(13) = 18
C.
h(2) = 16
D.
h(8) = 21
The true statement is h(2)=16.
What is domain and range?The domain of a function is the set of values that we are allowed to plug into our function. The range of a function is the set of values that the function assumes.
Given:
domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25,
Also, h(8) = 19 and h(-2) = 2,
Now,
2=h(-2)< h(2)<h(8) =19
h(8)=19≠21
h(13)> h(8) =19
h(-3)< h(-2) =2 [1 ≤ h(x) ≤ 25]
Hence, h(2)=16
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Study the table.
x
y
–2
8
–1
2
0
0
1
2
2
8
Which best describes the function represented by the data in the table?
linear with a common ratio of 4
linear with a common second difference of 4
quadratic with a common ratio of 4
quadratic with a common second difference of 4
Answer:
quadratic with a common second difference of 4
Step-by-step explanation:
quadratic equations: Quadratic equations are the polynomial equations of degree 2 example - a[tex]x^2\\[/tex]+ b[tex]x[/tex] + c = 0.
[tex]\begin{array}{cc}x&y\\-2&8\\-1&2\\0&0\\1&2\\2&8\end{array}\right][/tex]
from the table it is clear that,
function is y = 2[tex]x^2\\[/tex]
so the function is not linear as the equation specifies.
formula to find second difference of a quadratic equation:
f(x + 2) - 2f(x + 1) + f(x)
therefore;
[tex]2(x+2)^2[/tex] - [tex]4(x+1)^2[/tex] + [tex]2x^2[/tex]
[tex]2(x^2 + 4x + 4) - 4(x^2 + 2x+ 1 ) + 2x^2[/tex]
[tex]2x^2 + 8x + 8 - 4x^2 - 8x - 4 + 2x^2[/tex]
[tex]4x^2 - 4x^2 + 8x - 8x +8 - 4[/tex]
4
therefore, the answer is quadratic with a common second difference of 4
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What is the research hypothesis when using anova procedures?
When using ANOVA procedures, the research hypothesis is: there is no significance difference within the mean values of the groups.
What is a Research Hypothesis in ANOVA Procedure?ANOVA procedure compares the mean values of different groups that are administered with treatments. The research hypothesis, such as the null hypothesis would be stated as: no significance difference in the mean values within the groups.
Thus, we can conclude that the research hypothesis when using the ANOVA procedures can be stated as a null hypothesis, which states that: there is no significance difference within the mean values of the groups.
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I need help with this
Step-by-step explanation:
please mark me as brainlest
Which piecewise defined function is shown on the
graph?
f(x) =
f(x)
f(x)=
f(x) =
DONE
x+ 2, if 0 < x <4
x-3,if 4 < x <8
x+2, if 0≤x≤4
x-3,if 4 ≤x≤8
Intro
x+2, if 0 < x≤4
x-3, if 4 < x≤8
[x+2,if 0≤x <4
x-3, if 4 < x <8
10
8
20
2
9
8
x
10
Answer: (4)
Step-by-step explanation:
The first part has a closed hole at x=0 and an open hole at x=4, so it should be [tex]0 \leq x < 4[/tex].
This eliminates all the options except for (4).
The piecewise function that represents the graph will be f(x) = x + 2, 0 ≤ x < 4 and f(x) = x - 3, 4 ≤ x < 8. Then the correct option is D.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
A function that is based on a series of intervals is known as a specific goal. The absolute value serves as a frequent illustration. Other piecewise functions include the Boolean stepping, rectangle, and triangle functions.
The slope of the line is one. And the y-intercept is 2 and -3. Then the equation of the line is given as,
f(x) = x + 2, 0 ≤ x < 4
f(x) = x - 3, 4 ≤ x < 8
The piecewise function that represents the graph will be f(x) = x + 2, 0 ≤ x < 4 and f(x) = x - 3, 4 ≤ x < 8. Then the correct option is D.
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two consecutive odd integers such that 4 times the larger is 29 more than 3 times the smaller
Answer:
21
Step-by-step explanation:
a,a+2,..
4(a+2)=29+3a
4a+8=29+3a
4a-3a=29-8
a=21
Find the 12th term in the arithmetic sequence an = 3 − 6(n − 1)
Answer:
-63
Step-by-step explanation:
3 - 6(12 - 1) = 3 - 6(11) = 3 - 66 = -63
Ben, Tara and Liam are playing hide and seek. They start playing at quarter past 11. They play for 45 minutes, before stopping for a drink and a cookie. They continued to play for 45 minutes and head inside at 10 minutes past 1.
How long did they stop for a drink and a cookie. Explain your reasoning.
Answer:
25 minutes
Step-by-step explanation:
they started at a quarter past 11, which is 11:15
they then played for 45 minutes, which would be until 12:00
you also know that they stopped playing at 10 minutes past 1, at 1:10.
before 1:10, they had been playing for 45 minutes, which means they started playing for the second time at 12:25.
all that's left is the time between 12:00 and 12:25, which is 25 minutes, so they spent 25 minutes stopping for a drink and a cookie.
Find the values of a and b if 5+3√3/7+4√3 = a + √3b
The values of a and b are :
[tex]a = \sqrt{3} \\ \\ •\sqrt{3} b = - 1 \\ \\ b = \frac{ - 1}{ \sqrt{3} }. [/tex]
10 1/9 rounded to the whole or half
Answer:
Your answer is 68. Hope you got a big score!
Menna is traveling in a country that measures its temperature in degrees Celsius. If the high temperature for tomorrow will be 25
∘
C, what is the equivalent temperature in
∘
F?
a. 102.6∘
F
b. 57∘
F
c. 77∘
F
d. 45.9∘
F
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: Temp = 77° F[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: f = \bigg (c \sdot \cfrac{9}{5} \bigg) + 32[/tex]
[ convert 25° C to °F ]
[tex]\qquad \tt \rightarrow \: \bigg (25 \sdot \cfrac{9}{5} \bigg) + 32[/tex]
[tex]\qquad \tt \rightarrow \: (5 \sdot9) + 32[/tex]
[tex]\qquad \tt \rightarrow \: 45 + 32[/tex]
[tex]\qquad \tt \rightarrow \: 77 \degree \: \: f[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
77
Step-by-step explanation:
took the quiz
which one is it? I will give you twenty points, if you will answer
Answer:
A fraction equivalent to [tex]\frac{1}{2}[/tex] on the number line is [tex]\frac{3}{6}[/tex].
Drag the dot to [tex]\frac{3}{6}[/tex] on the number line.
Step-by-step explanation:
3 is half of 6. To check if this is correct multiply [tex]\frac{1}{2}[/tex] and 3.
[tex]\frac{1}{2}*3=\frac{3}{6}[/tex]
Hope this helps!
If not, I am sorry.
A plant was 8 in. tall last week, and grew x in. this week. 1. Which expression represents how tall, in inches, the plant is now? A. x + 8 B. 8x Explain your thinking. 2. For the expression not chosen, describe a scenario the expression might represent.
Answer:
Step-by-step explanation:
Solution
Total growth (2 weeks) = x + 8
Explanation
During the second week, the plant is already 8 inches tall. It adds x to its total growth. 8x is not the same thing.
Meaning of 8x
For plants, 8x could mean the amount of growth that took place in 8 weeks. x is the amount of growth that takes place in 1 week. You have to think that the growth (x) for each week is the same
Which of the following graphs represents the solution set
x>5?
Answer:
Graph A is correct.
Step-by-step explanation:
Graph A is the graph with the open circle and the arrow pointing to the right.
Someone please help with this !!!
Answer:
[tex]\dfrac 5{13}[/tex]
Step-by-step explanation:
[tex]\sin \theta =\dfrac{\text{Perpendicular}}{\text{Hypotenuse}} = \dfrac{5}{\sqrt{5^2 +12^2}} = \dfrac 5{\sqrt{169}} = \dfrac 5{13}[/tex]
Situation:
A 45 gram sample of a substance that's
used to preserve fruit and vegetables has
a k-value of 0.1109.
N-Noe-kt
No - initial mass (at time t - 0)
N = mass at time t
k - a positive constant that depends on
the substance itself and on the units
used to measure time
t-time, in days
Find the substance's half-life, in days.
Round your answer to the nearest tenth.
Enter the correct answer.
+00
DONE
A function assigns the values. The half life of the substance is 6.25 days.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given the function for the substance as [tex]N= N_o e^{-kt}[/tex], therefore, the half life of the substance can be written as,
[tex]N= N_o e^{-kt}\\\\\dfrac{N}{N_o}= e^{-kt}[/tex]
Since we need to find the half life, therefore, the ratio of the initial mass and the mass after half-life will be 1/2.
[tex]\dfrac12= e^{-kt}\\\\\ln (0.5) = -kt[/tex]
Given the value of k is 0.1109, therefore,
[tex]\ln (0.5) = -kt\\\\\ln (0.5) = -(0.1109)t\\\\t = 6.25[/tex]
Hence, the half life of the substance is 6.25 days.
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