The vertex of the absolute value function is (-7,-2)
How to determine the vertex?The function is given as:
f(x) = 3|x + 7| - 2
The above function is an absolute value function.
An absolute value function is represented as:
f(x) = a|x - h| + k
Where:
Vertex = (h,k)
By comparison, we have:
(h,k) = (-7,-2)
Hence, the vertex of the absolute value function is (-7,-2)
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Your mother is out of toothpicks, and suggests you use cotton swabs instead. You measure them, and they are 7.5 cm tall. How many cotton swabs tall will your model be? If necessary, round your answer to the nearest whole number.
Answer:
6.3 *30= 189; so 4 cotton swabs
Solve 8x + c = k for x.
A. x=8(k-c)
OB. x=
_k+c
8
O C. x = 8(k+c)
O D. x=
k-c
8
Answer: [tex]x=\frac{c-k}{8}[/tex]
Step-by-step explanation:
[tex]1) \text { } 8x+c=k \text{ (given)}\\\\2) \text { }8x=c-k \text{ (subtract } k \text{ from both sides)}\\\\3) \text { } \boxed{x=\frac{c-k}{8}} \text{ (divide both sides by 8)}[/tex]
Construct the truth table and determine the truth value of the following compound statement.
a)p⟾¬(p ʌ r)
b) (q ʌ r) ⟾(p ⇔ q)
See the attached truth tables.
• A ∧ B is true only when both A and B are true
• A ⇒ B is true only when both A and B are true, or A is false. This logically equivalent to ¬A ∨ B
• ¬A is true only when A is false
• A ⇔ B is true only when both A ⇒ B and B ⇒ A are true. Equivalently, (¬A ∨ B) ∧ (¬B ∨ A)
Write a function rule for the table.
Days
1
2
3
4
Cost to Rent a Truck
29
47
65
83
Answer:
can you give upload the pictures
One positive number is 8 times another number. Their difference is 70.
Which of the following equations could be used to find the numbers?
Answer:
X equals 10.
8x - x = 70
Step-by-step explanation:
8 x 10 = 80
80 - 10 = 70
The assets (in billions of dollars) for a financial firm can be approximated by the function A(x)=318e^0.27x, where x=7 corresponds to the year 2007. Find the assets in each following years. A)2012 B) 2014 C) 2017
The value of the asset in 2012, 2014, and 2017 are 8119.72, 13933.55 and, 31321.23, respectively. A function assigns the values.
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 assets (in billions of dollars) for a financial firm can be approximated by the function [tex]A(x)=318e^{0.27x}[/tex], where x=7 corresponds to the year 2007. Therefore, the assets value in the following years will be,
A.) 2012 - [tex]A(12)=318e^{0.27\times 12} = 8,119.72[/tex]
B.) 2014 - [tex]A(14)=318e^{0.27\times 14} = 13,933.5[/tex]
C.) 2012 - [tex]A(17)=318e^{0.27\times 17} = 31,321.23[/tex]
Hence, the value of the asset in 2012, 2014, and 2017 are 8119.72, 13933.55 and, 31321.23, respectively.
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determine weather y varies directly with x. if so, find the constant variation and write the equation
Answer:
Yes, k = 1/3 and y = 1/3x
Step-by-step explanation:
[tex]\text{The given line passes through the origin, hence it has equation of the form:}\\y=kx[/tex]
[tex]\text{Therefore y varies directly as x.}The line passes through the point (3,1)}[/tex]
[tex]\text{This implies that,}[/tex]
[tex]1=k(3)\\k=\frac{1}{3}[/tex][tex]\text{Hence the constant of variation is}[/tex] ⇒ [tex]\frac{1}{3}[/tex]
The equation would be ⇒ [tex]y=\frac{1}{3} x[/tex]
Solve the equation x³ - 5x²+2x+8 = 0 given that - 1 is a zero of f(x)= x3 - 5x²+2x+8.
The solution set is? (Use a comma to separate answers as needed.)
Answer:
added in the picture
Step-by-step explanation:
added in the picture
need help with this question im stuck
Answer:
answer is B. 100°
Step-by-step explanation:
if correct please I need brainlist
Answer:
100°
Step-by-step explanation:
Opposite angles of a quadrilateral inscribed in a circle are supplementary, i.e., they add up to 180°.
The 80° angle and angle x are opposite each other, so:
x + 80° = 180°
x = 180° - 80°
x = 100°
Which sequences are geometric? Check all that apply.
5, 10, 20, 50,...
3, 12, 48, 192,...
3, 15, 75, 375,...
8, 15, 75,375,...
14, 21, 28, 35,...
17, 20, 23, 26,...
2, 10, 50, 250,...
Answer:
The first, third and last sequences
Complete the recursive formula of the geometric sequence 56, -28, 14, -7,....
Step-by-step explanation:
each term in the sequence is half of the value of the previous term, and in the opposite sign.
therfore, the quotient between terms is (-2)
so, to get one term from the previous term, we multiply by 1/(-2), so:
d(n) = d(n-1) × 1/(-2)
the first term is 56 so d(1)=56
Answer:
56 and -1/2
Step-by-step explanation:
khan
PLEASE HELP I WILL GIVE BRAINLEST!!!!!!
Below is the graph of a polynomial function with real comedic fangs. All local extreme of the function are shown in the graph.
Use the graph to answer the following questions.
(a) over which intervals is the function decreasing? Choose all that apply.
(-∞,-8) (-8,-4) (-4,0) (0,5) (-4,5) (9, ∞)
(b) At which x-values does the function have local minima? If there is more than one value seepage them with commas.
(C) what is the sign of the function’s leading coefficient?
Answers are positive, negative, not enough time
(D) which of the following is a possibility for the degree of the function? Choose all that apply
4 , 5 , 6 , 7 , 8 , 9
Part (a)
Decreasing means that as x increases, y decreases.
So the intervals are [tex](-8, -4), (0, 5), (9, \infty)[/tex]
Part (b)
A local minimum is where the function changes from decreasing to increasing.
So, the local minima are at [tex]x=-4, 5[/tex]
Part (c)
The function is approaching negative infinity as x approaches both positive and negative infinity, so the leading coefficient is negative
Part (d)
The degree is given by the number of roots (including multiplicity).
From the graph, we see there is a single root at x = -6, a single root at x = -1, a single root at x = 1, a single root between x=6 and x=8, and a single root at around x = 10.
Thus, there are a minimum of 5 roots for the graph (there could be more outside of the given section)
However, since the graph has the same end behavior in both directions, the degree must be even.
So, the possible answers are any even number that is at least 6
[tex]\frac{1}{28} + \frac{1}{70} + \frac{1}{130} + \frac{1}{208} + \frac{1}{304} = ?[/tex]
Evaluate this expression.
Considering the least common multiple of the denominators, it is found that the result of the expression is given by:
[tex]\frac{9100}{138320}[/tex]
How do we add fractions?We place all the terms of the addition in "equivalent" fractions, with the same denominator, found from the last common multiple of all the denominators.
In this problem, the denominators are as follows: 28, 70, 130, 208, 304. Using a calculator, their lcm is of 138,320.
Considering equivalent fractions(the numerators are the division of the lcm by the previous denominator), the expression is:
[tex]\frac{4940}{138320} + \frac{1976}{138320} + \frac{1064}{138320} + \frac{665}{138320} + \frac{455}{138320} = \frac{4940 + 1976 + 1064 + 665 + 455}{138320} = \frac{9100}{138320}[/tex]
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Alaric wants to determine if he can get a better grade in math by studying for longer periods of time.
He plans to experiment for 4 weeks.
Which statement is true of this experiment?
a.) The duration of Alaric's experiment is the explanatory variable.
b.) Alaric's math grade is the explanatory variable.
c.) The amount of time Alaric spends studying is the response variable.
d.) Alaric's math grade is the response variable.
The statement (d) Alaric's maths grade is the response variable is correct because maths grade is a dependent variable.
What is an explanatory variable?It is defined as the variable which is independent. They show the expected results and the result is known as the response variable which is dependent on the explanatory variable.
We have given:
Alaric wants to determine if he can get a better grade in maths by studying for longer periods of time.
The duration of the experiment is 4 weeks which is known or constant.
But the number of hours she studied is a variable, and it is independent.
The maths grade is the dependent variable which is on the number of hours Alaric study variable.
Thus, the statement (d) Alaric's maths grade is the response variable is correct because maths grade is a dependent variable.
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one interior angle of a polygon is a right angle and each of the other interior angles is 126°. Calculate the number of sides of the polygon
Answer:
There are 7 sides.
Step-by-step explanation:
Let's Use the formula that states that the sum of the angles of an n-sided polygon is given by.
S=(n−2)180
Since we are given that the two angles are right, the angles and each of the remaining angles is 144.
And Therefore, the sum is:
S=90
(n−2)144
(n−2)180
=90
+90
+(n−2)144
⇒(n−2)180
−(n−2)144
=180
⇒(n−2)(180
−144
)=180
⇒(n−2)(36
=180
⇒n−2=
36
180
⇒n−2=5
⇒n=5+2=7
Hence, the polygon has 7 sides.
The number of sides of the polygon such that one angle is the right angle will be 6.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
In any closed polygon, the number of sides is equal to the number of interior angles.
Suppose the number of sides is n in the given polygon.
Sum of angles = 90° + 126° × (n - 1)
The sum of angles is given as, 180(n - 2)
90° + 126° × (n - 1) = 180(n - 2)
90 + 126n - 126 = 180n - 360
180n - 126n = 90 - 126 + 360
54n = 324
n = 6
Hence "The number of sides of the polygon such that one angle is the right angle will be 6".
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Can y’all please help me with this ! Everybody have a good day!
Answer: A. She substituted incorrectly into the distance formula
She should be subtracting x from x and y from y but she is subtracting y from x.
X -6,-3,0,3,6 y 0 1 2 3 4 which equation contains the coordinate parts given in the table
The linear equation that contains the coordinate parts in the given table is: y = 1/3x + 2.
How to Find the Equation of a Linear Equation?To find the linear equation that contains the coordinate parts in the table given, find the slope (m) and y-intercept (b), then substitute the values into y = mx + b.
Slope (m) using two coordinate parts, (0, 2) and (3, 3):
Slope (m) = change in y / change in x = (3 - 2)/(3 - 0)
Slope (m) = 1/3
y-intercept (b) = 2 [this is the value of y when x = 0)
Substitute the values into y = mx + b
y = 1/3x + 2.
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Assume that the function f is a one-to-one function.
a. if f(3)=9, find ^-1 (9)
b. if f^-1(-8)=-9 , find f(-9)
Answer:
a. 3
b. -8
Step-by-step explanation:
let me know if you want an explanation
y=2x^2-4x-3
Solve quadratic questions
By applying the quadratic formula we conclude that the roots of the quadratic equation y = 2 · x² - 4 · x - 3 are 1 + 0.5√10 and 1 - 0.5√10, respectively.
How to find the roots of a quadratic equation
All quadratic equations of the form a · x² + b · x + c = 0 have two roots that can be found by using the quadratic formula:
[tex]x = \frac{-b \pm \sqrt{b^{2}-4\cdot a \cdot c}}{2\cdot a}[/tex] (1)
If we know that a = 2, b = - 4 and c = - 3, then the roots of the quadratic equations are:
[tex]x = \frac{4 \pm \sqrt{(-4)^{2}-4\cdot (2) \cdot (- 3)}}{2\cdot (2)}[/tex]
[tex]x = 1 \pm \frac{\sqrt{40}}{4}[/tex]
[tex]x = 1 \pm \frac{\sqrt{10}}{2}[/tex]
By applying the quadratic formula we conclude that the roots of the quadratic equation y = 2 · x² - 4 · x - 3 are 1 + 0.5√10 and 1 - 0.5√10, respectively.
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solve the following inequality, algebra 1.
will give brainliest answer !!
Answer:
See below
Step-by-step explanation:
r/6 <-6 multiply both sides by 6 to get
r < - 36
or 4r+2 > 18 subtract 2 from both sides of the equation
4r > 16 divide both sides by 4
r > 4
Step-by-step explanation:
[tex] \frac{r}{6} < - 6 \: \: \: \: \: \: \: \: \: \: ... 1[/tex]
[tex]4r + 2 > 18 \: \: \: \: \: \: \: \: \: \: ...2[/tex]
Solving for inequality 1:
[tex] \frac{r}{6} < - 6 \: \: \: \: \: \: \: \: \: \: ... 1[/tex]Multiplying both sides by 6:
6 * 1/6 r < -6*6r < -36Hence the solution is r < -36
Solving for inequality 2:
4r + 2 > 18Subtract 2 from both sides:
4r + 2 - 2 > 18 - 24r > 16Divide both sides by 4:
[tex] \cfrac{4r}{4} > \cfrac{16}{4} [/tex][tex]r > 4[/tex]Hence the answer is r > 4.
An electrical resistor is rated at 4500 ohms ± 3%. Express this tolerance in ohms and state the
actual range of resistance.
Answer:
Range = 4365-4635
Step-by-step explanation:
4500 * 3/100 = 135
4500 + 135 = 4635
4500 - 135 = 4365
Range = 4365-4635
The actual range of resistance is from 4365 ohms to 4635 ohms.
How to determine the tolerance in ohms and state the actual range of resistance.To express the tolerance in ohms, we need to calculate 3% of the rated resistance, which is 4500 ohms.
Tolerance in ohms = 3% of 4500 ohms
Tolerance in ohms = 0.03 * 4500
Tolerance in ohms = 135 ohms
The actual range of resistance can be found by adding and subtracting the tolerance from the rated resistance:
Lower limit = Rated resistance - Tolerance
Lower limit = 4500 ohms - 135 ohms
Lower limit = 4365 ohms
Upper limit = Rated resistance + Tolerance
Upper limit = 4500 ohms + 135 ohms
Upper limit = 4635 ohms
So, the actual range of resistance is from 4365 ohms to 4635 ohms.
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Two vertical angles are complementary. Statement is always, sometimes, or never true. Explain your reasoning
Answer:
depends upon the degree of the angle
Step-by-step explanation:
vertically opposite angles are always equal like
80 = 80 sum is equal to 160 degrees not equal to 90
45 = 45 , sums equal to 90 degrees ,equal to 90
30 = 30 sum is equal to 60 degrees, not equal to 90
so we can say it depends what is the no of degrees if it is 45 only we can say the vertically opposite angles are complementary angle
Select the correct answer.
A system of equations and its solution are given below.
System A
x + y = 8
4x - 6y = 2
Solution: (5,3)
Choose the correct option that explains what steps were followed to obtain the system of equations below.
System B
x + y = 8
10x = 50
Answer:
B will be the answer...
Step-by-step explanation:
The second equation in system B is only in terms of y, so we need to use elimination to eliminate the x term from the second equation in system A.
To do that, we need to multiply the first equation by 5.
5 (-x − 2y = 7)
-5x − 10y = 35
Add to the second equation. Notice the x terms cancel out.
(-5x − 10y) + (5x − 6y) = 35 + (-3)
-16y = 32
Combining this new equation with the first equation from system A will get us system B.
-x − 2y = 7
-16y = 32
Answer:
To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by 6. The solution to system B will be the same as the solution to system A.
Step-by-step explanation:
exact answer
Which function is represented by this graph? A line is graphed in an x y plane, where the x and the y axes range from negative 10 to 10 in increments of 2. The line falls through (negative 6, 10), (0, 4), (4, 0) to (7, negative 3), and then it rises through (10, 0). A. f(x) = |x + 7| − 3 B. f(x) = |x − 7| − 3 C. f(x) = |x + 3| − 7 D. f(x) = |x − 3| − 7
The line that represents the graph satisfying all condition is f(x) = |x − 7| − 3.
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
As, the points are given.
We have to find which equation satisfies all the points.
f(x) = |x − 7| − 3
put x= -6
y= 13-3 = 10
Similarly by putting all the values the only condition that satisfies is
f(x) = |x − 7| − 3
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Select the correct answer.
Choose the system of inequalities that best matches the graph below.
Answer:
Its A
Step-by-step explanation:
I said so
What is the solution to the following system?
4x+3y-z=-6
6x-y+3z=12
8x+2y+4z=6
x= 1, y = -3, z = -1
x= 1, y=-3, z = 1
x = 1, y = 3, z = 19
x = 1, y = 3, z = -2
The solutions are x = 1, y = -3, z = 1 after solving with substitution method option second x= 1, y=-3, z = 1 is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have three linear equations in three variable:
4x + 3y - z = -6 ..(1)
6x - y+ 3z = 12 ..(2)
8x + 2y + 4z = 6 ...(3)
From the equation (1)
[tex]\rm x=\dfrac{-6-3y+z}{4}[/tex]
Substitute the above value in the equation (2) and (3):
[tex]\rm 6\cdot \dfrac{-6-3y+z}{4}-y+3z=12\\\\ 8\cdot \dfrac{-6-3y+z}{4}+2y+4z=6[/tex]
After simplification:
[tex]\rm -11y+9z-18=24\\ -4y+6z-12=6[/tex]
After solving the above two equations by substitution method:
z = 1
y = -3
Plug the above two values in the equation (1), we get:
x = 1
Thus, the solutions are x = 1, y = -3, z = 1 after solving with substitution method option second x= 1, y=-3, z = 1 is correct.
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The exterior angles of a triangle are (2x+10),(3x+15)and (4x+20). What is the value of x and what is the largest interior angle of the triangle?
Answer:
x = 35 and 100°
Step-by-step explanation:
the sum of the exterior angles of a triangle = 360° , then
2x + 10 + 3x + 15 + 4x + 20 = 360 , that is
9x + 45 = 360 ( subtract 45 from both sides )
9x = 315 ( divide both sides by 9 )
x = 35
then each exterior angle is
2x + 10 = 2(35) + 10 = 70 + 10 = 80°
3x + 15 = 3(35) + 15 = 105 + 15 = 120°
4x + 20 = 4(35) + 20 = 140 + 20 = 160°
the sum of an exterior angle and corresponding interior angle = 180°
then
180° - 80° = 100°
180° - 120° = 60°
180° - 160° = 20°
the largest interior angle of the triangle is 100°
Answer:
x = 35
largest interior angle = 100°
Step-by-step explanation:
The exterior angles of a triangle sum to 360°
⇒ (2x + 10) + (3x + 15) + (4x + 20) = 360
⇒ 2x + 10 + 3x + 15 + 4x + 20 = 360
⇒ 9x + 45 = 360
⇒ 9x = 315
⇒ x = 35
Therefore, the three exterior angles are:
(2x + 10) = 2(35) + 10 = 80°(3x + 15) = 3(35) + 15 = 120°(4x + 20) = 4(35) + 20 = 160°If the side of a triangle is extended, the angle formed outside the triangle is the exterior angle. As angles on a straight line sum to 180°:
⇒ interior angle + exterior = 180°
So the largest interior angle will be the supplementary angle to the smallest exterior angle.
The smallest exterior angle is 80°, so:
⇒ largest interior angle + 80° = 180°
⇒ largest interior angle = 180° - 80°
⇒ largest interior angle = 100°
The formula M = 5/8 K gives the approximate distance in miles as a function of kilometers. Use the inverse to express 25 miles in kilometers.
look at the picture
Answer:
The x-intercept is 2.
Step-by-step explanation:
[tex]2 \sqrt[3]{x - 10} + 4 = 0[/tex]
[tex]2 \sqrt[3]{x - 10} = - 4[/tex]
[tex] \sqrt[3]{x - 10 } = - 2[/tex]
[tex]x - 10 = - 8[/tex]
[tex]x = 2[/tex]
There are 60 students studying Sciences (Biology, Chemistry or Physics). 7 students study Biology, Chemistry and Physics. 12 students study Biology and Chemistry. 15 students study Biology and Physics. 20 students study Chemistry and Physics. 35 students study Biology. 32 students study Physics. B Complete the Venn diagram. E P C There are 60 students studying Sciences ( Biology , Chemistry or Physics ) . 7 students study Biology , Chemistry and Physics . 12 students study Biology and Chemistry . 15 students study Biology and Physics . 20 students study Chemistry and Physics . 35 students study Biology . 32 students study Physics . B Complete the Venn diagram . E P C
Answer:
8 in the box.
Step-by-step explanation:
As, it is given that 35 students study Biology.
So, in Biology circle,
15+7+5+x=35
27+x=35
x=35-27
x=8
