The range of a function is the possible output values the function can have.
The range of the function is all real values except 0
The function is given as:
[tex]\mathbf{y = \frac{1}{4x + 1}}[/tex]
When the denominator of the function is 0, the function would not have a real value.
This means that:
[tex]\mathbf{y \ne 0}[/tex]
i.e. the value of y cannot be 0.
Hence, the range of the function is all real values except 0
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In the diagram below, \overline{ST} ST is parallel to \overline{PQ} PQ. If STST is 55 more than QTQT, RT=10RT=10, and PQ=15PQ=15, find the length of \overline{QT} QT. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.PQRTS
The length of the [tex]\overline{QT}[/tex] can be determined using the given information and
the relationship between corresponding sides of similar triangles.
[tex]\underline{\overline{QT} = 5}[/tex]Reasons:
The given parameters are;
[tex]\overline{ST} \parallel \overline{PQ}[/tex]
ST = QT + 5
RT = 10
PQ = 15
Required: The length of [tex]\overline{QT}[/tex]
Solution:
Using the relationship between corresponding sides of similar triangles, ΔRST and ΔRPQ, we have;
[tex]\displaystyle \frac{\overline{ST}}{\overline{RT}} = \mathbf{\frac{\overline{PQ}}{\overline{RQ}}}[/tex]RQ = QT + RT
Therefore;
[tex]\displaystyle \frac{\overline{ST}}{\overline{RT}} = \mathbf{\frac{\overline{PQ}}{\overline{QT} + \overline{RT}}}[/tex]Which gives;
[tex]\displaystyle \frac{\overline{QT} + 5}{\overline{RT}} = \frac{\overline{PQ}}{\overline{QT} + \overline{RT}}[/tex]
Plugging in the known values gives;
[tex]\displaystyle \frac{\overline{QT} + 5}{10} = \mathbf{\frac{15}{\overline{QT} + 10}}[/tex]
[tex](\overline{QT} + 5) \times (\overline{QT} + 10) = 10 \times 15[/tex]
[tex]\overline{QT}^2 + 10\cdot \overline{QT} + 5\cdot \overline{QT} + 50 = 10 \times 15[/tex]
[tex]\overline{QT}^2 + 15\cdot \overline{QT} + 50 - 150= 0[/tex]
[tex]\mathbf{\overline{QT}^2 + 15\cdot \overline{QT} -100} = 0[/tex]
Factorizing with a graphing calculator gives;
[tex](\overline{QT} -5) \cdot (\overline{QT} + 20)= 0[/tex]
[tex]\mathbf{\overline{QT} = 5} \ or \ \overline{QT} = -20[/tex]
Therefore, given that [tex]\overline{QT}[/tex] is a natural number, we have;
[tex]\underline{\overline{QT} = 5}[/tex]
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f(x)=x^4−4x^3−22x^2+4x+21
Select each correct answer.
−3
−1
0
1
3
7
Answer:
-1
1
7
-3
Step-by-step explanation:
Write x/2 - 2x + 4/ x + 1 as a single fraction, in its simplest form.
Answer:
x²-3x - 8 2(x + 1)
Explanation
Find common denominator and write the nu merators above common denominator:
x(x + 1) − (2x + 4) × 2
2(x + 1)
Apply Multiplicative Distribution Law :
x² + x - 4x = 8
2(x + 1)
Reorder and gather like terms:
x² + (x − 4x) — 8
2(x + 1)
Collect coefficients for the like terms:
x² + (1-4) × x-8
2(x + 1)
Calculate the sum or difference:x²-3x -8
2(x + 1)
Answer:
x²-3x - 8
2(x + 1)
5 4/6-4 2/3 ÷ 3 2/3?
Answer:
145/33
Step-by-step explanation:
Assuming what you wrote was mixed fractions, this is how to do the question.
Do the division first and then subtract that from 5 4/6/
x2-4x+6=0
Someone help with solve this
Answer:
0 is the answer..(•‿•)(. (•‿•)(•‿•)(•‿•)
whats the x and y-intercepts? y=5x−13,
Step-by-step explanation:
So in a linear function, it follows the form of y=mx+b where m is the slope of the graph (rise/run) and b is the y-intercept.
Since b is (-13) that is the y-intercept.
This can also be confirmed by making x=0 since that is where the y-intercept occurs.
y=5x-13
y=5(0)-13
y=-13
To find the x-intercept, we need to make y equal zero since that is where x-intercepts are found.
0=5x-13
(now solve using algebra to isolate x)
(add 13 to both sides)
13=5x
(divide 5 from both sides)
13/5 = x
2.6=x
Your y-intercept is -13 and the x-intercept is 13/5.
Hope this Helps :D
Answer:
x-intercept: (2.6, 0) or [tex](\frac{13}{5},0)[/tex]
y-intercept: (0, -13)
Step-by-step explanation:
Because the equation is written in slope-intercept form using the formula
[tex]y=mx+b[/tex]
b = y-intercept
y-intercept will be (0, -13)
To find x-intercept basically substitute 0 for y and solve for x
so x-intercept will be [tex](\frac{13}{5},0)[/tex] or simplified (2.6, 0)
Which properly illustrated in the statement (-2)(+5) = (+5)(-2)?
Answer: 7
Step-by-step explanation:
it is trust me.
What is the slope of this graph?
Answer:
-3
Step-by-step explanation:
1. To find the slope of this line, we can use the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] since we're given the two points from the line.
2. (Solving)
[tex]\frac{0-6}{3-1}[/tex] [tex]\frac{-6}{2}[/tex] [tex]-3[/tex]Therefore, the slope is -3.
(3 * 7) + (2 * 5)
[tex](3 \times 7) + (2 \times 5)[/tex]
Answer:
31
Step-by-step explanation:
Answer:
31
Step-by-step explanation:
3×7=21
2×5=10
21+10=31
It t takes a snail 10 seconds to move 1 centimeter.
How many centimeters does said snail move after 2 seconds?
2.5?
answer is 0.2 using cross multiplication.
Answer:
in 2 seconds, the snail will only move 0.2 centimeters or 2 millimeters. And after 2.5, 0.25 centimeters, or 2.5 millimeters.
Step-by-step explanation:
If a number is multiplied by 2/5, the product is (great than, less than, or equal to,) the number
Answer:
less than
Step-by-step explanation:
it's a fraction, so it will be a fraction of the original number.
4. In the diagram below, ZABD = (4x + 3)º and DBC = (7x-6)º.
a
Create an equation
AI
b. Solve for x.
D
B
c. Determine the measure of ZABD.
Answer:
Step-by-step explanation:
a) ∠ABD + ∠DBC = 90°
4x - 3 + 7x - 6 = 90
4x + 7x - 3 - 6 = 90
11x - 9 = 90
11x = 90 + 9
11x = 99
x = 99/11
x = 9
∠ABD = 4*9 - 3 = 36 - 3 = 33
Diya used modeling to find
2
.
82
÷
3
.
She regrouped 2 as 20 tenths and regrouped 0.8 as 7 tenths plus 10 hundredths. She divided all of the tenths and hundredths into three equal groups. Each group had 9 tenths and 4 hundredths. She decided that
2
.
82
÷
3
=
0
.
94
.
Which of the following is the correct conclusion about Diya's quotient of 0.94?
help mee
Answer:C
Step-by-step explanation: The quotient is correct because 27 tenths divided by 3 is 0.9 and 12 hundredths divided by 3 is 0.04
The quotient is correct because 27 tenths divided by 3 is 0.9 and 12 hundredths divided by 3 is 0.04.
Given that, Diya regrouped 2 as 20 tenths and regrouped 0.8 as 7 tenths plus 10 hundredths.
What are decimal numbers?Decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point. The dot present between the whole number and fractions part is called the decimal point.
According the given question, the numerical expression is
20/10 + 7/10+12/100
= 2+0.7+0.1
= 2.8
She divided all of the tenths and hundredths into three equal groups.
That is, 2.82/3
=0.94
Hence, the quotient is correct because 27 tenths divided by 3 is 0.9 and 12 hundredths divided by 3 is 0.04.
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through: (5, 4), slope = undefined
write the slope intercept
Answer:
Step-by-step explanation:
An "undefined slope" is a vertical line going through the x axis at 5. The slope is undefined since there is no change in x for all values of y. The means the slope, which is the change in y divided by the change in x, would be a fraction with a zero denominator. This makes it undefined.
One value of x, in this case x=5, will include all possible values of y. There is no y-intercept, but the line has an x-intercept of 5.
QUICK!!!! I NEED AN ANSWER!! Emily says that the negative sign means opposite of, so -(-45) means the opposite of negative 45, which is 45. Is Emily correct?
Answer:
Yes, Emily is correct.
Step-by-step explanation:
If you have a - sign in front of a number in parenthesis that is negative, then what you are doing is taking the opposite of that negative number. Remember that the opposite of a negative number is a positive number. In this case, we want the opposite of negative five. What is that? It is +45, or 45. So yes, Emily is correct.
Find m rs. sr 6x + 6 rq 2x + 14
Answer:
arc RS = 72°
Step-by-step explanation:
The measure of the inscribed angle SQR is half the measure of its intercepted arc RS , then
2x + 14 = [tex]\frac{1}{2}[/tex] (6x + 6) = 3x + 3 ( subtract 2x from both sides )
14 = x + 3 ( subtract 3 from both sides )
11 = x
Then
RS = 6x + 6 = 6(11) + 6 = 66 + 6 = 72°
The length of the base of an isosceles triangle is x. The length of a leg is 3x - 6. The perimeter of the triangle is 58. Find x.
Answer:
x = 10
Step-by-step explanation:
Perimeter of a triangle = the sum of the three sided of the triangle.
In an isosceles triangle, there are two equal sides and a base.
Perimeter = ( 3x - 6) + (3x - 6) + x
58 = 7x - 12
58 + 12 = 7x
70 = 7x
[tex]\frac{70}{7} = \frac{7x}{7}[/tex]
10 = x
I have no clue how to do any of this please help
Answer:
help with what there nothing there?
what do u need help with?
The cost to rent a moving truck is a flat fee of $25 plus $0. 60 per mile. The equation c = 25 0. 6m models the cost, c, in dollars for the number of miles, m, traveled in the truck. Identify the independent and dependent variables. The is the independent variable. The is the dependent variable.
Answer:
Independent variable = m
dependent variable = c
Step-by-step explanation:
c = 25 + 0.6m
where,
m = number of miles
c = total cost of rent
Find an equation of the vertical line through (4,-9)
Answer:
x = 4
Step-by-step explanation:
Whenever it asks for the equation of a vertical line all you have to do is look at the x point given to you which is 4 and make x = 4, doing this means that this certain vertical line covers all possible y values which includes -9 as well which is why the answer is x=4
What is the length of MN
PLZ HELP
help please i need help
Answer:
what do you need help on with this and maybe i can help....
Step-by-step explanation:
can we represent any number on number line
Answer:
Rational numbers can be depicted on the number line. The centre of the number line is called Origin (O). Positive rational numbers are illustrated on the right side of zero (called origin), and negative on left side of origin. The representation of rational numbers on the number line depends on the type of fraction.
Step-by-step explanation:
The numbers on the number line increase as one moves from left to right and decrease on moving from right to left. Here, fractions and decimals have been represented on the number line. A number line can also be used to represent both positive and negative integers as well.
For what value of x is line m parallel to line n?
x=?
Can someone help me with this question will mark brainliest.
Answer:
A:use SAS to show triangle PRQ is congruent to triangle SR.P
a string 27.2 meters long is cut into shorter pieces, each measuring 3.4 meters long. How many pieces were cut from the 27.2-metres string ?
Answer:
There are 8 pieces of string cut
Explanation:
27.2 ÷ 3.4 = 8
I need help :( I forgot how to do this
Answer:
[tex]A=\frac{1}{2}h(b_{1}+b_{2} ) | *2\\2A=h(b_{1}+b_{2} ) | : (b_{1}+b_{2} )\\\frac{2A}{(b_{1}+b_{2} )} = h[/tex]
I hope it's good.
Take care !
Write in index form
5 x 5 x 5
How to write in Simplified slope intercept form
Answer:
y = -5/3x + 8
Step-by-step explanation:
So the y - intercept is 8 and from that point the line goes down by 5 and right by 3.
System of equations pls help me
Answer:
(4,4)
Step-by-step explanation:
We can solve this system of equations using the elimination method.
In order to use the elimination method there must be two variables with the same coefficient. Note that the coefficients don't have to have the same sign ( eg. 6 and -6 would work ). If there are two similar variables with similar coefficients then you can add or subtract, depending on the signs of the coefficients, the two equations "eliminating" the variable. There would then be one variable left over in which you can solve for.
For this case, both equations have 7x, one negative 7 and one positive 7. When the signs are different you add the two equations. So our first step is to add the two equations
7x - 4y = -44
+ (-7x -3y = 16 )
-----------------------
Remove parenthesis
7x -4y = -44
-7x -3y = +16
------------------
0x - 7y = -28
We are left with -7y = -28.
Because there is now only one variable, we can solve for it.
-7y = -28
divide both sides by -7
y = 4
Now we want to find the value of x. We can do this by plugging in the value of y into one of the equations and then solving for x. Note that we can plug in 4 for y into either equation and solve for x and we would get the same answer.
7x - 3y = 16
y = 4
7x - 3(4) = 16
multiply 4 and -3
7x - 12 = 16
add 12 to both sides
7x = 28
divide both sides by 7
x = 4
So x = 4 and y = 4 so the solution to the system of equations is (4,4)