[tex]15 \leq X \leq 25[/tex] is the equation represents the drivers allotted time (x) to receive a bonus.
What us the absolute value of inequality?An absolute value inequality is an expression with absolute functions as well as inequality signs.
According to the question:
Mathematically absolute value inequality is represented as :
|X -20|≤ 5
Solving the equation using
|z| ≤ a→ -a ≤ z ≤ a :
here, z = X- 20 and a = 5:
[tex]| X-20| \leq 5\\\\ - 5\leq X-20 \leq 5[/tex]
By Solving X adding 20 on the three sides of the inequality
[tex]-5 + 20 \leq X -20 +20 \leq 5 + 20[/tex]
By simplifying it:
[tex]15 \leq X \leq 25[/tex]
Therefore the equation or inequality which represents the drivers allotted time (x) to receive a bonus [tex]15 \leq X \leq 25[/tex]
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determine the scale factor for triangle abc to prime ^abc
The scale factor for triangle ABC to A'B'C' is 2
How to determine the scale factor?The complete question is in the attached image
From the attached image, we have the following corresponding sides
AC = 4 cm
A'C' = 8 cm
The scale factor is then calculated as:
Scale factor = A'C'/AC
This gives
Scale factor = 8cm/4cm
Evaluate the quotient
Scale factor = 2
Hence, the scale factor for triangle ABC to A'B'C' is 2
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pls help
Enter the equation for the graph.
Answer:
[tex]y=[1]cos([\frac{2\pi }{3}]x)[/tex]
Step-by-step explanation:
Looking at the graph, we can see the domain to be from (0 , 2π).
Now we have to find one period that corresponds to cos(x).
The half-period of cos(x) for this graph appears to be pi/3 and adding another pi/3 gets us 2pi/3 to be our cosine period.
b = 2pi/3
a is the same range as cos(x). Range: (0,0)
y = [a] * cos ([b]*x)
y = [1] * cos([2pi/3]x)
Andrea has 3 tiles. One is a regular octagon, one is a regular pentagon and one is a regular hexagon. Andrea thinks the 3 tiles will fit together perfectly, as shown in the diagram. Show calculations to prove that she is wrong.
From calculations, we can say that the given tiles will not fit together perfectly.
How to find the sum of interior angles of a Polygon?If the tiles join perfectly at a point, sum of all angles around the joining point should be 360°.
Expression for the measure of the interior angle of a polygon,
Interior angle of a polygon = [(n - 2) * 180]/n
Interior angle of a pentagon = [(5 - 2) * 180]/5 = 108°
Interior angle of a hexagon = [(6 - 2) * 180]/6 = 120°
Interior angle of an octagon = [(8 - 2) * 180]/8 = 135°
To prove that the given tiles fit together perfectly → Sum of all the angles around the common point should be 360°
Sum of all interior angles = 108° + 120° + 135° = 363°
Therefore, given tiles will not fit together perfectly.
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PLEASE HELP 15 POINTS
Answer:
B
Step-by-step explanation:
Used elimination method.
first plugged in (0,0)which remove A,D
than saw the line is not solid so chose B
What is the first step to solving the function below?
Answer:
option B, -(4x - 3)(x - 2)
Step-by-step explanation:
-4x^2 + 11x - 6
4x * x = 4x^2
x * -3x = -3x
-4x * -2 = -8x
-3 * -2 = -6
4
Find the measure of x.
X
12°
X = = [?]
Round to the nearest hundredth.
The measure of x will be 18.81 units.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
The given information are;
Perpendicular = 4
Base = x
Then, Tan ∅ = Perpendicular /Base
Tan 12 = 4/x
x = 4 /0.212
x = 18.818
Hence, the measure of x will be 18.81 units.
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Question 1 of 10
Solve 10x+16 ≥ 6x+ 20.
O A. x29
OB. x≤ 1
OC. x2 1
OD. x≤ 9
Find the slope of every line that is parallel to line on the graph (0,-3) (5,-4)
The slope of the line parallel to the line on the graph (0,-3) (5,-4) is - 1 / 5
How to find the slope of a parallel lines?Parallel lines have the same slope.
Therefore,
slope = m = y₂ - y₁ / x₂ - x₁
Therefore,
x₁ = 0
x₂ = 5
y₁ = -3
y₂ = -4
Therefore,
slope = -4 - (-3) / 5 - 0
slope = -4 + 3 / 5
slope = - 1 / 5
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Solve the System of Equations
-5x+4y=3
x=2y-15
Answer:
Point Form:
(9,12)
Equation Form:
x = 9
y = 12
Step-by-step explanation:
Answer:
[tex]\fbox{x = 9, y = 12}[/tex]
Step-by-step explanation:
[tex]\textsf {Let's solve by substitution.}[/tex]
[tex]\rightarrow \mathsf {-5x + 4y = 3}\\\rightarrow \mathsf {x = 2y - 15}[/tex]
[tex]\textsf {Substitute for x in the first equation of the system.}[/tex]
[tex]\implies \mathsf {-5(2y-15)+4y=3}[/tex]
[tex]\implies \mathsf {-10y+75+4y=3}[/tex]
[tex]\implies \mathsf {-6y=-72}[/tex]
[tex]\implies \textbf {y = 12}[/tex]
[tex]\implies \mathsf {x = 2(12) - 15}[/tex]
[tex]\implies \mathbf {x = 9}[/tex]
[tex]\textsf {The solution is : x = 9, y = 12}[/tex]
Select the statement below that correctly describes the relationship between the number of workers and the hours that they work.
Less workers = more hours
OR the answer might be worded as
More workers = less hours
What is the missing reason in the proof? (Reason 9)
Answer:
transitive property
Step-by-step explanation:
Generally proofs flow naturally from one step to the next. Consequently, each step usually follows from the previous step, and the Reason given justifies why that change is valid.
From statement 8, note that [tex]90^{o}=m\angle{ABD}[/tex]
For statement 9, the proof asserts that [tex]m\angle{ABC}=m\angle{ABD}[/tex]
What changed between line 8 and 9? The left side of the equation lost it's 90 degrees, and it became the measure of angle ABC.
So, what justifies changing the 90degrees into a measure of an angle (specifically, the measure of angle ABC)?
Recall from statement 3, that [tex]m\angle{ABC}=90^{o}[/tex].
The "substitution property" would be a valid reason for step 9, (but of the given options, that isn't one, so we must look for another valid reason).
Recall that the transitive property states:
[tex]\text{If }a=b\text{ and }b=c, \text{then }a=c[/tex]
There are three parts,
1. the first part needs a=b
2. the second part needs b=c
3. the third part produces a=c
Notice that in the second part, b=c, and then for the third part, on the left side, the "b" disappears, and the "a" sort of appears out of nowhere.
Statement 8 is like the second part, and statement 9 is like the third part.
Replacing "a" with [tex]m\angle{ABC}[/tex], replacing "b" with [tex]90^{o}[/tex], and replacing "c" with [tex]m\angle{ABD}[/tex], we can update the transitive property and see how it applies to our situation:
Original transitive property: [tex]\text{If }a=b\text{ and }b=c, \text{then }a=c[/tex]
Updated transitive property: [tex]\text{If }m\angle{ABC}=90^{o}\text{ and }90^{o}=m\angle{ABD}, \text{then }m\angle{ABC}=m\angle{ABD}[/tex]
In order to use the transitive property, we need the first part and the second part to be true, and then it will be a valid reason for the last part to be true. The first part was already proven back in statement 3, the second part was just proven in statement 8, so the conclusion (the third part) is valid and can be statement 9, because of the transitive property.
Please help!!! I will give u brainiest
Answer:
(2,3) ; (-2.11)
Step-by-step explanation:
Answer:
(2, 3); (-2, 11)
Step-by-step explanation:
f(x) = x² - 2x + 3
f(x) = -2x + 7
f(x) = f(x)
x² - 2x + 3 = -2x + 7
x² = 4
x = ±2
x = 2
f(2) = -2(2) + 7 = -4 + 7 = 3
x = -2
f(-2) = -2(-2) + 7 = 4 + 7 = 11
Answer: (2, 3); (-2, 11)
The nature of a graph, which has an even degree and a positive leading coefficient will be
The nature of a graph, which has an even degree and a positive leading coefficient will be up left, up right position
What is the nature of the graph of a quadratic equation?The nature of the graphical representation of a quadratic equation with an even degree and a positive leading coefficient will give a parabola curve.
Given that we have a function f(x) = an even degree and a positive leading coefficient. i.e.
y = f(x) = 2x²+ 4The domain of this function varies from -∞ < x < ∞ and the parabolic curve will be positioned on the upward left and upward right x-axis.
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The lowest point in the United States is the Death Valley in California. Its altitude is 282 feet below sea level. Identify the integer representing the lowest point (Death Valley).
Answer:
-282
Step-by-step explanation:
Any altitude below sea level would have a negative sign in front of it.
i do not now these questions
Using proportions, it is found that:
a) 5 people are needed.
b) Yes.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Item a:
Each person works for 32 hours, and 150 hours are needed, hence the number of people needed is given by:
150/32 = 4.6875.
However, an integer number is needed, hence 5 people are needed.
Item b:
With 30 hours, the number of people needed is given by:
150/30 = 5.
Which remains the same.
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its math help me out?
Its the first one
--------------------
Answer:
$24 = $0.40(60)
Step-by-step explanation:
Match the input value and its location in the equation.
__
$24 = $0.40(60)
_____
Additional comment
When input is liters and output is dollars, the constant of proportionality must have units of "dollars per liter." The dollar sign of these units is not shown in the left panel, but is shown on the answer choices. If you understand units conversion, this should not be a mystery. (The mystery is why the curriculum materials are inconsistent.)
Round 508.0219 to the nearest hundredth
Answer:
508.02
HOPE THIS HELPS
Todo <3
Step-by-step explanation:
Please help!!!!!!!! Asap, i need to finish
The solution to the given quadratic expression is x = -1 and x = 5
Factoring quadratic equationGiven the quadratic equation below
f(x) = x^2 - 4x - 5
Factorize
f(x) = x^2 - 5x + x - 5 = 0
f(x) = x(x - 5) + 1(x - 5) = 0
(x+1)(x-5) = 0
x = -1 and x = 5
Hence the solution to the given quadratic expression is x = -1 and x = 5
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Answer:
x = -1; x = 5
Step-by-step explanation:
Standard Form of a Quadratic Function: f(x) = ax² + bx + c, where a ≠ 0
Given function: f(x) = x² - 4x - 5
⇒ a = 1, b = -4, c = -5
We are asked to solve the following function by factoring. In order to do so, let's rewrite the middle term by finding the factors that give a product of the first and last terms (a • c = -5) and give us the sum of the middle term (b = -4).
Factors that give a product of a • c: 1 • -5 = -5
Factors that give a sum of b: 1 + (-5) = -4
Step 1: Substitute f(x) = 0.
⇒ 0 = x² - 4x - 5
Step 2: Rewrite the equation with the factors.
⇒ 0 = x² + x - 5x - 5
Step 3: Factor out x and -5.
⇒ 0 = (x² + x) + (-5x - 5)
⇒ 0 x(x + 1) - 5(x + 1) [ Factor out the common factor. ]
⇒ 0 = (x - 5)(x + 1)
Step 4: Apply the Zero-Product Property (if m•n = 0, then m = 0 or n = 0)
a) 0 = x - 5 ⇒ 0 + 5 = x - 5 + 5 ⇒ 5 = x
b) 0 = x + 1 ⇒ 0 - 1 = x + 1 - 1 ⇒ -1 = x
Therefore, the missing solution for this quadratic function is x = 5.
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8. Complete the table below by drawing an example of each shape.
Answer:
Please see attachment.
The first one is a quadrilateral that is not a parallelogram.
The second one is a triangle with a right angle.
Step-by-step explanation:
Hope this helps!
If not, I am sorry.
[tex]\{ \frac { ( \sqrt { 3 } ) \times 3 ^ { - 2 } } { ( \sqrt { 5 } ) ^ { 2 } } \} ^ { \frac { 1 } { 2 } }[/tex]solve this equation
Answer:
Step-by-step explanation:
Exponent law:
[tex]\sf \bf a^m * a^n = a^{m+n}\\\\ (a^m)^n = a^{m*n}[/tex]
[tex]\sf a^{-m}=\dfrac{1}{a^m}[/tex]
First convert radical form to exponent form and then apply exponent law.
[tex]\sf \sqrt{3}=3^{\frac{1}{2}}\\\\\sqrt{5}=5^{\frac{1}{2}}[/tex]
[tex]\sf \left(\dfrac{(\sqrt{3}*3^{-2}}{(\sqrt{5})^2}\right)^{\frac{1}{2}}= \left(\dfrac{3^{\frac{1}{2}}*3^{-2}}{(5^{\frac{1}{2}})^2} \right )^{\frac{1}{2}}[/tex]
[tex]= \left(\dfrac{3^{\frac{1}{2}-2}}{5^{\frac{1}{2}*2}}\right)^{\frac{1}{2}}\\\\=\left(\dfrac{3^{\frac{1-4}{2}}}{5}\right)^{\frac{1}{2}}\\\\=\left(\dfrac{3^{\frac{-3}{2}}}{5}\right)^{\frac{1}{2}}\\\\=\dfrac{3^{\frac{-3}{2}*{\frac{1}{2}}}}{5^{\frac{1}{2}}}\\\\ =\dfrac{3^{{\frac{-3}{4}}}}{5^{\frac{1}{2}}}[/tex]
Ms. Jerome wants to buy identical boxes of art supplies for her 25 students. If she can spend no more than $375 on art supplies, what inequality describes the price can she afford for each individual box of supplies,b?
The inequality 25b ≤ 375 describes the price she can afford for each individual box of supplies.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have:
Ms. Jerome wants to buy identical boxes of art supplies for her 25 students. If she can spend no more than $375 on art supplies
Let's suppose b is the price of each box of supplies.
Total cost for a 25 number of boxes = $25b
25b ≤ 375
Thus, the inequality 25b ≤ 375 describes the price she can afford for each individual box of supplies.
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A 2-column table with 3 rows. Column 1 is labeled x with entries 2, 4, 5. Column 2 is labeled y with entries 5, 10, 12.5.
Use the information in the table to find the constant of proportionality and write the equation.
The constant of proportionality is
.
The equation that represents this proportional relationship is
The equation will be a linear equation from (2, 5) to (4, 10) will be y = 2.5x.
What is a function?Mathematics is replete with functions, which are necessary for the construction of intricate connections.
A 2-column table with 3 rows. Column 1 is labeled x with entries 2, 4, 5. Column 2 is labeled y with entries 5, 10, 12.5.
Use the information in the table to find the constant of proportionality and write the equation.
The equation will be a linear equation from (2, 5) to (4, 10) will be
(y – 5) = [(10 – 5) / (4 – 2)] (x – 2)
y – 5 = 2.5x – 5
y = 2.5x
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Answer:
2.5 and y=2.5x
Step-by-step explanation: i got that question on an edguenity assignment
Gene has a gasoline budget of $300 per month. He uses an average of $6 of gasoline each day he drives. Which of the following equations represents how much money is left in his gasoline budget after x days of driving?
Answer:
300-6x
Step-by-step explanation:
Trust me
. If we start with one bacterium and it doubles in
number every 15 minutes, HOW LONG WILL IT
TAKE for one bacterium to become one million??
Answer:
298.97 minutes
Step-by-step explanation:
2^x = 1 000 000 where 'x' is the number of 15 minute periods
x = 19.931 15 minute periods = 298.97 minutes
What is the measure of AC?
Enter your answer in the box.
°
Image shows a circle with angle A B C inscribed in a circle. Angle B measures 4 x minus 5.5 degrees. Arc A C measures 3 x plus 9 degrees.
Answer:
In the circle, the measure of the arc AC is 21°.
Step-by-step explanation:
Concept: We can use the Inscribed Angle theorem to get the measure of AC.
Given that the inscribed angle ∠ABC is 3x-1.5 and the Intercepted arc AC is 3x+9.
Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of the intercepted arc.
So,
3x - 1.5 = 0.5(3x + 9)
6x - 3 = 3x + 9
3x = 12
x = 4
Since the intercepted arc AC is 3x + 9, putting the value of x = 4 we get,
intercepted arc AC is 21°.
Hence the intercepted arc AC is 21°.
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Which expression is equivalent to startfraction (4 p superscript negative 4 baseline q) superscript negative 2 baseline over 10 p q superscript negative 3 baseline endfraction? assume p not-equals 0, q not-equals 0.
The given expression is equivalent to [tex]\frac{p^{7}q}{160}[/tex]
What are indices?
An index is a small number that tells us how many times a term has been multiplied by itself.
The plural of index is indices.
Below is an example of a term written in index form :[tex]4^{3}[/tex]
4 is the base and 3 is the index.
We can read this as ‘4 to the power 3’
Another way of expressing [tex]4^{3}[/tex] is
4 x 4 x 4 = 64
Indices can be positive or negative numbers.
Given expression can be written as [tex]\frac{({4p^{-4}q})^{-2}}{10pq^{-3}}[/tex]
Now to simplify the given fractional expression :[tex]\frac{({4p^{-4}q})^{-2}}{10pq^{-3}}[/tex]
= [tex]\frac{4^{-2}p^{8}q^{-2}}{10pq^{-3}}[/tex] By using the property of exponents is given by:
[tex](a^{m})^{n}=a^{m n}[/tex]
=[tex]\frac{p^{7}q}{10 .16}[/tex] By using the property of exponents given by
[tex]a^{m}a^{n}=a^{m + n}[/tex] and [tex]a^{-m}= \frac{1}{a^{m}}[/tex]
= [tex]\frac{p^{7}q}{160}[/tex]
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answer?.............
Answer:
-21
Step-by-step explanation:
B, C and D are points on the circumference of a circle, centre O.
AB and AD are tangents to the circle.
Angle DAB = 50 degrees
Work out the size of angle BCD.
Construct OD and BD. Then, in quadrilateral ABOD, angles ODA and OBA are right angles and thus angle DOB is 130 degrees (since angles in a quadrilateral add to 360 degrees).
So, this means arc DB also measures 130 degrees. Hence, by the inscribed angle theorem, angle BCD is 65 degrees.
Given that h(-6)=0 for function h(x) = x^4 +8x³ +11x² - 8x - 12
which of the following statements are true?
A (x-3) is a factor of h(x)
B. (x+6) is a factor of h(x)
C. the remainder on division of h(x) by (x+6) is NOT 0
D. the remainder on division of h(x) by (x-3) is 0
Answer:
b
Step-by-step explanation:
when u plug in -6 u get the equation equal to 0 which means x+6 is a factor of that function.
If the triangles above are reflections of each other, then BC = to
Answer:
DF
Step-by-step explanation:
Paint a picture in your head reflecting the triangle. Just hold A and flip it so A = E , D = B
