Answer:
b = 3a
Step-by-step explanation:
a = < - 1, 3 >
b = < - 3, 9 >
Thus
b = 3a
Answer:
b = 3a
Step-by-step explanation:
how many times does the quadratic function below intersect the x-axis?
y=x^2+10x+25
Answer:
A. 1
Step-by-step explanation:
To find the x-intercept, substitute 0 for y and solve for x.
x-intercept(s): (-5,0)
Considering (-5,0) is the only intersection on the x-axis, 1 is your answer.
If you want a visual of this, I recommend you use the Desmos graphing calculator to input your equation. It will show you what the curved line looks like.
Which relation is a function?
{(-4,-7), (-9, 5), (4, -2), (-9, 0)}
{(-7, -7), (-2, 5), (−1, 6), (-2, −5)}
{(0, 1), (3, 2), (5, -3), (0, 2)}
{(-3, -2), (-1, 3), (0, -2), (3, 4)}
Answer:
Here's a little trick I learned in 8th grade. The first numbers don't matter all that matters are the 2nd numbers, and if you have 2 of the same kind of numbers then it's not a function so your answer would be B.
Dr. Smith and Dr. Jones want to study the effects on a patient's arthritis that curl in the patient believes that he was she use a new ointment the control group consists of the patient who chooses to visit Dr. Smith about arthritis and they receiving an appointment with no medical value the experimental group consists of the patients who chooses to visit Dr. Jones about the right s and they receive the new ointments is this study experimental or observational
Answer:I think observational
Step-by-step explanation:They want to study it so they trying it on people who are willing so they are looking closely to what happens.
A ship is stationary at sea.
A tugboat is 24km away at a bearing of 110°, and a yacht is 12km from the tugboat at a bearing of 085°.
Draw a scale diagram showing the positions of the three vessels.
Use a scale of 1 cm: 3 km.
Use your diagram to find the distance of the yacht from the ship to the nearest km.
The distance of the yacht from the ship is 35 km
How to determine the distance?See attachment for the diagram that represents the given parameters.
The distance of the yacht from the ship is then calculated using the following law of cosine.
YS^2 = ST^2 + YT^2 - 2 * ST * YT * cos(T)
This gives
YS^2 = 24^2 + 12^2 - 2 * 24 * 12 * cos(155)
Evaluate the exponents and the products
YS^2 = 576 + 144 + 522
Evaluate the sum
YS^2 = 1242
Take the square root of both sides
YS = 35
Hence, the distance of the yacht from the ship is 35 km
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Determine f(4) for A piecewise function f of x in three pieces. The function is defined by part 1, which is x cubed for x less than negative 3, part 2, which is 2 times x squared minus 9 for negative 3 is less than or equal to x which is less than or equal to 4, and part 3 which is 5 times x plus 4, for x greater than 4..
23
24
41
64
Answer:
23
Step-by-step explanation:
seen it before
What is the measure of the unknown angle?
straight angle divided into a one hundred thirty two degree angle and an unknown angle
48°
49°
51°
53°
Expand and simplify x(x + 2)(x + 4)
Answer:
Step-by-step explanation:
Comment
Expand the second and 3rd factors first. Then worry about the x.
Solution
x(x + 2)(x + 4)
first: x * x = x^2
Outside: 4*x = 4x
Inside: 2*x = 2x
Last: 2*4 = 8
Combine
x^2 + 4x + 2x + 8
x^2 + 6x + 8
Now is the time to worry about the extra x
x(x^2 + 6x + 8)
remove the brackets.
x*x^2 + x*6x + 8*x
Combine
Answer: x^3 + 6x^2 + 8x
Let f(x)=6/-2+2e^-0.3x. what is f(4)? enter your answer rounded to the nearest tenth
The value of the function f(x)=6/-2+2[tex]e^{-0.3x}[/tex] at x=4 after rounded to the nearest tenth is -2.4.
Given Function of x : f(x)=6/-2+2[tex]e^{-0.3x}[/tex]
The given function showing the relationship between x and f(x) is f(x)=6/-2+2[tex]e^{-0.3x}[/tex] where e is exponential and we have to find the value of f(4) by just putting the value of x=4 in the given function and round to the nearest tenth means replacing a number with an approximate value.
f(4)=6/-2+2[tex]e^{-0.3*4}[/tex] ( The value of e is 2.7812)
f(4)=-3+2[tex]e^{-1.2}[/tex]
f(4)=-3+2*0.30119 (The value of [tex]e^{-1.2}[/tex] is 0.30119)
f(4)=-3+0.60238
f(4)=-2.3972
Round -2.3972 to tenth is -2.4.
Hence the value of function of at x=4 is -2.4.
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The value of f(4) is -4.3.
The function is a relation between two different sets X and set Y which are in one-one or many-one relation. Here set X is called as the domain and set Y is called as the codomain.
For example: f(x)=3x+9
To get the value of the function at any point of x, we have to put the number in the function to get its function value.
For example the value of f(x) in above function at x=a will be f(a)=3a+9
Similarly given function in the question
[tex]f(x)=\frac{6}{-2+2e^{-0.3x}}[/tex]
to get the value of f(x) at x=4 put the value of x in the function,
[tex]f(x)=\frac{6}{-2+2e^{-0.3*4}}[/tex]
⇒[tex]f(x)=\frac{6}{-2+2e^{-1.2}}[/tex]
⇒f(x)=-4.3
Therefore the value of f(4) is -4.3.
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2. Given that 5-6 ÷ 5p = 125º, find the value of 1/2p
Answer: -50
Step-by-step explanation:
5 - 6 / 5p = 125 degrees
1/2p = ?
First, subtract 5 from both sides, that way, the 5 on the left side will cancel out.
-6/5p = 125-5 degrees
-6/5p = 120 degrees
now, multiply 5p on both sides.
-6 = 120 * 5p degrees
-6 = 600p degrees
divide 600 on both sides
-6/600 = p degrees
-0.01 = p degrees
p = -0.01
1/2p = 1 / -0.02 = -50
Hope I helped!
What are the solutions to the following system of equations?
y = x² + 7x-5
2x - y = -9
Answer:
Step-by-step explanation:
y = x² + 7x - 5 ............ (1)
2x - y = - 9 ................ (2)
(1) ------> (2)
2x - ( x² + 7x - 5 ) = - 9
- x² - 5x + 14 = 0 ........ (3)
- 1 × (3)
x² + 5x - 14 = 0
( x + 7 )( x - 2 ) = 0
[tex]x_{1}[/tex] = - 7 and [tex]x_{2}[/tex] = 2
2( - 7) - [tex]y_{1}[/tex] = - 9 ⇒ [tex]y_{1}[/tex] = - 5
2(2) - [tex]y_{2}[/tex] = - 9 ⇒ [tex]y_{2}[/tex] = 13
The solutions of system are
( - 7, - 5 ) and ( 2, 13 )
Kitchen chairs are purchased wholesale for $36 each by a discount furniture store. Then, the store marks up the chairs by 60 percent. The store has a special sale where all items are marked down by 20 percent. How much would two chairs cost during the sale?
$46.08
$57.60
$92.16
$115.20
The graph of a line goes up and to the right when:
When the coefficient of x is positive, the graph of a line rises and moves to the right. Option C is correct.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
The complete question is
"The graph of a line goes up and to the right when:
a) the coefficient of x is 0
b) the coefficient of x is negative
c) the coefficient of x is positive
d) there is no coefficient of x"
When the coefficient of x is positive, we know that the graph of a line will move upward and to the right.
Since we are aware that a line's upward and rightward movement indicates that the line is advancing, we will obtain a positive slope for the line, and we are also aware that the slope-intercept of a line is provided as:
y= mx+c
If m is a positive number, then positive is the coefficient of x.
The graph of a line goes up and to the right when the coefficient of x is positive.
Hence option C is correct.
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The circumference of a circle is 237 cm.
What is the area, in square centimeters?
Express your answer in terms of T.
Answer:
Circumference of a circle = 2 pie r
237 = 2 * pie * r
237 / 2 * Pie
118.5/ pie = r
118.5 = Pie*r
Area of circle = Pie *r²
= Pie r * r
= 118.5 * 118.5/ Pie
= 118.5 * 118.5 / pie
= 14042.25/ pie
taking value of pie = 3.14
= 4472.05 sq. cm
I need help please! What’s the answer?
Answer:
x = 17.32 units
Step-by-step explanation:
In a right triangle tan (angle) = opposite leg / adjacent leg...
for this triangle tan 27° = 34 / x
then x = 34 tan 27° = 17.32 units
Please help me answer question 8/11 asap
The value of a₄₁ mean the expression in 4th row and 1st column will be 2. Then the correct option is B.
The complete question is attached below.
What is the matrix?A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The [tex]\rm a_{ij}[/tex] element in a matrix, such as M, refers to the i-th row and j-th column element.
The matrix is given below.
[tex]\begin{bmatrix} 1&3&8&5&\\ 5&4&6&2\\6&7&1&8\\2&9&3&7&\\\end{bmatrix}[/tex]
Then the value of a₄₁ mean the expression in 4th row and 1st column will be 2.
Then the correct option is B.
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PLEASE HELP! SO CONFUSED! 25 POINTS!!
Answer:
D
Step-by-step explanation:
(f • g)(x)
= f(x) × g(x)
= (x + 4)(3x² - 7)
each term in the second factor is multiplied by each term in the first factor , that is
x(3x² - 7) + 4(3x² - 7) ← distribute both parenthesis
= 3x³ - 7x + 12x² - 28
= 3x³ + 12x² - 7x - 28 ← in standard form
On a coordinate plane, a right triangle has points A (negative 5, negative 6), B (negative 5, negative 2), C (negative 2, negative 2). Examine the right triangle ABC. Which rise and run would create a similar right triangle on the same line? a rise of 6 and a run of 8 a rise of 8 and a run of 6 a rise of 6 and a run of 5 a rise of 5 and a run of 6
A rise of 8 and a run of 6. Then the correct option is B.
What is a coordinate geometry?Coordinate geometry is the study of geometry using the points in space.
On a coordinate plane, a right triangle has points A (-5, -6), B (-5, -2), and C (-2, -2).
The distance between AB will be
AB² = (-5 + 5)² + (-2 + 4)²
AB² = 4²
AB = 4
The distance between BC will be
BC² = (-2 + 5)² + (-2 + 2)²
BC² = 3²
BC = 3
Then the rise and run will be
rise / run = 4 / 3
Then this can be written as
rise / run = 8 / 6
Then the correct option is B.
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1. Kelsey spent 55 hours over 2 weeks working on a ELA project. She worked 32 hours the
Answer:
23
Step-by-step explanation:
If Kelsey spent 32 hours in the first week. We subtract 32 from 55. 55-32=23. That means she worked 23 hours in the second week.
-16p+37=49-21p what is the answer
Answer:
p = 12/5Step-by-step explanation:
-16p+37=49-21p what is the answer?
-16p + 37 = 49 - 21p
-16p + 21p = 49 - 37
5p = 12p =
p = 12/5
Solve the equation.
3/4x+3-2= -1/4+1/2x+5
Answer:
15
Step-by-step explanation:
3x/4+1=19/4+1x/2
3x/4-x/2=19/4-1
x/4=15/4
collect like terms
x=15
Which of the following is equivalent to 5√12 - 2√27?
Answer:
A. 4 root 3
Step-by-step explanation:
Dixie lives in a $67,000 wood house in the country whose contents are valued at $12,000. She wants to know her monthly property insurance premium. Use the table above to calculate her monthly property insurance premium.
Without the table indicating the stated premium rates and applicable discounts, the monthly property insurance cannot be computed. Hence, on the assumption that the rate is 2.5% and the discount applicable is 7.5% the premium per month will come to $152.24
What is Property Insurance?
The simple definition of Property Insurance is, it is an insurance policy that covers a policyholder for the structure of a building and its contents against stated or agreed perils.
What is the calculation for the above?Given (based on assumption) that the applicable annual rate is 2.5%
and that:
Value of Wooden House = $67,000Value of the contents of the House = $12,000Applicable discount = 7.5% of premium/annumHence annual premium will be:
= (67,000 + 12000) * (2.5/100) * 0.925
Annual Premium Payable = $1,826.89.............A
Recall that we are asked to derive the monthly Insurance premium.
This is thus given as: Answer in A/12
→ 1,826.89/12
= $152.24
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Box y, box y, and box z each contain a pencil and a highlighter. An item is drawn randomly from each box. A) Draw a tree diagram to represent the possible outcomes.
B) Determine the probability that the items drawn are two pencils and one highlighter.
The probability that the items drawn are two pencils and one highlighter is 0.25
How to draw the tree diagramTo do this, we make use of the following representations:
P represents PencilsT represents HighlightersSince there are three boxes, the number of possible outcomes is:
Outcomes = 2³
Outcomes = 8
See attachment for the tree diagram.
How to determine the probability?From the tree diagram, we have:
Outcomes = 8Two pencils and one highlighter (PPT) = 2So, the probability is:
P = 2/8
Evaluate
P = 0.25
Hence, the probability that the items drawn are two pencils and one highlighter is 0.25
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Solve the simultaneous equations
2
x
+
3
y
=
5
5
x
−
2
y
=
−
16
Answer:
x = -2, y = 3
Step-by-step explanation:
2x + 3y = 5
5x - 2y = -16
In order to find the value of a variable, we must eliminate the other variable by multiplying the equations to get the same coefficient.
We can multiply the first equation by 5 and the second one by 2 to get the same coefficient for x, the equations then become:
10x + 15y = 25
10x - 4y = -32
Now we can subtract:
19y = 57
y = 3
Since we know the value of y, we can substitute it into one of the original equations:
2x + 3(3) = 5
2x + 9 = 5
2x = -4
x = -2
Pls help. !!!!!!!!!!!!!!!!!! (Give steps if you can)
Answer:
[tex]144 cm^{2}[/tex]
Step-by-step explanation:
Step 1: Find the true length of each side
We know that the perimeter is 56cm and the ratio of AD:AB:DC:BC is 5:12:6:5. It is safe to assume that this ratio is the simplified version, which means that if we multiply each of these numbers by a scale factor of [tex]x[/tex], then we get the true length of each side, so we would get [tex]5x, 12x, 6x, 5x[/tex] for the sides. We also know that when we add these numbers, we get the perimeter, which is 56. So, we can create the equation [tex]5x + 12x + 6x + 5x = 56[/tex]. Then, solve the equation for x, which would be 2, and go back and multiply each number with 2 to get the following:
AD = 5*2 = 10cm, AB = 12*2 = 24cm, DC = 6*2 = 12cm, BC = 5*2 = 10cm
Step 2: Calculate the Height
Now we know the lengths of each side, lets take a look at the formula for the area of a trapezium: [tex]\frac{base_{1} + base_2}{2}*height[/tex]. So, the next step would be to calculate the height. We can draw the height by drawing a line straight down from the vertex D and another straight down from the vertex C. These lines are both the height, and will be the exact same length. We can calculate that the height is 8 because AB is 24 cm, but the length from the height at vertex D to the height at vertex C is 12 cm, so that means that the base of each triangle is 12/2 = 6 cm. Then we can use Pythagorean theorem to figure out that the height is 8cm.
Step 3: Calculate the Area
Lastly, we can calculate the area. The formula is [tex]\frac{base_{1} + base_2}{2}*height[/tex]. In this case, the numbers would be [tex]\frac{12 + 24}{2} * 8 = 144cm^{2}[/tex]
I know this is a lot, so let me know if you have any questions!
What's the circumference of a circle with a diameter of 18 inches? Use 3.14 for I. T What's the circumference of a circle with a diameter of 18 inches ? Use 3.14 for I. T
Answer:
56.52 inches
Step-by-step explanation:
pi is the ratio of the circumference to the diameter so you can simply multiply the diameter by pi to get the circumference which is 3.14 * 18 = 56.52
What is the value of the expression below?
27−−√3
A
3
B
9
C
24
D
81
Answer:
I don't see a correct answer. See below.
Step-by-step explanation:
Thanks for clarifying the question. But if 27√3 is the correct expression, I don't see an answer option that fits.
√3 = 1.732
27*(1.732) = 46.77
But all the answer options are whole numbers. The presence of√3 makes it difficult to find an expression that would result in a whole number. Expressions such as:
27/√9 = 9, or
√27/√3 = 3
would be more consistent with producing a whole number result.
I hope this helps.
HELP MEE ,25 POINTS !!!!
Celina says that each of the following expressions is actually a binomial in disguise:
5abc-2a^2+6abc
5x^3∙2x^2-10x^4+3x^5+3x∙(-2) x^4
(t+2)^2-4t
5(a-1)-10(a-1)+100(a-1)
(2πr-πr^2 )r-(2πr-πr^2)∙2r
Based on the four expressions written above (image attached) one can say that She is right about the remaining four expressions as they all can shown or expressed as binomials.
What is Binomial Distribution?
Binomial distribution is known to be a kind of probability distribution whos models or show the probability of getting one of two outcomes in any said number of points or parameters.
Note that:
5abc -2a² + 6abc
Add like terms
= 11abc - 2a²
5x³∙ 2x² -10x⁴ +3x⁵+ 3x∙(-2) x⁴
Simply
=5 . 2x³⁺² - -10x⁴ +3x⁵+ 3x∙ 2x⁴
=10x³⁺² -10x⁴ +3x⁵+ 3∙ 2xx⁴
= 7x⁵ + 10x⁴
(t+2)²-4t
Simply
= (t² + 2t.2 + 2²) - 4t
= (t² + 2t.2 + 4) - 4t
= t² + 4
The same applies for the rest. Therefore, one can say that Based on the four expressions written above (image attached) one can say that She is right about the remaining four expressions as they all can shown or expressed as binomials.
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The sin (0) = - and lies in Quadrant III. Find the exact values of the sine
6'
and cosine of 20.
Answer:
Can you give exanation
I don't understand
FACTOR THE EXPRESSION GIVEN BELOW. WRITE EACH FACTOR AS A POLYNOMIAL IN DESCENDING ORDER. ENTER EXPONENTS USING THE CARET (^). FOR EXAMPLE, YOU WOULD ENTER x TO THE POWER OF 2 AS x^2.
343x^3 + 216y^3
Each given factor written as a polynomial in descending order is; (7x + 6y)(49x² - 42xy + 36y²)
How to factorize Polynomials?We are given the polynomial;
343x³ + 216y³
343x³ + 216y³ is a sum of cubes and factors in general as;
a³ + b³ = (a + b)(a² - ab + b²)
Thus;
343x³ + 216y³ = (7x)³ + (6y)³
= (7x + 6y)((7x)² - 7x(6y) + (6y)² )
= (7x + 6y)(49x² - 42xy + 36y²)
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