Answer:
x = 3
Pls, choose me as brainliest!
write the quadratic equation whose roots are 4 and -2, and whose leading coefficient is 4.
(use the letter x to represent the variable)
The quadratic equation with roots 4 and -2 and leading coefficient 4 is;
⇒ 4x² - 8x - 32
What is Quadratic equation?
A quadratic equation is an algebraic equation of the second degree of x.
Given that;
Roots of a quadratic equation = 4 and -2
Leading coefficient = 4
Now, The quadratic equation whose roots 4 and -2 with leading coefficient is calculated as;
⇒ 4 ( x - 4) (x + 2)
Solve as;
= 4 (x - 4) (x + 2)
= 4 (x² + 2x - 4x - 8)
= 4 (x² - 2x - 8)
= 4x² - 8x - 32
Thus, The quadratic equation with roots 4 and -2 and leading coefficient 4 is;
⇒ 4x² - 8x - 32
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Write an equation (y=mx+b) for the following word problem.
A cat weighs 30 pounds and is on a special diet to lose 2 pounds per month.
Please help this is due today
Answer:
Steps to find the equation of a line from two points:
Find the slope using the slope formula. ...
Use the slope and one of the points to solve for the y-intercept (b). ...
Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.
Step-by-step explanation:
Answer:
[tex]y=-2x+30[/tex]
where y is the weight of the cat (in pounds) and x is the number of months.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
The y-intercept is the y-value when x is zero, so the initial value.
If the cat initially weighs 30 pounds, the y-intercept is 30.
The slope is the rate of change.
If the cat lost 2 pounds per month, then the rate of change is -2.
Therefore, the equation the models the given word problem is:
[tex]\boxed{\begin{minipage}{7 cm}\phantom{ww}\\$y=-2x+30$\\\\where:\\ \phantom{ww}$\bullet$ $y$ is the weight of the cat (in pounds). \\ \phantom{ww}$\bullet$ $x$ is the number of months.\\\end{minipage}}[/tex]
Find the absolute maximum of f on [-10,7].
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
A. The absolute maximum of f is f(___) = ___.
(Type integers or fractions.)
B. There is no absolute maximum
A. The absolute maximum of the function f(x) is : f(-8) = 4.
We are given a graph of the function f(x).The domain of the function f(x) as seen from the graph is [-10, 7].The range of the function f(x) as seen from the graph is [-10, 4].We need to find the absolute maximum of the function f(x).From the graph, we can clearly figure out that the function has an absolute maximum value equal to 4.The function f(x) achieves a maximum y-value equal to 4 at an x-value of -8.Thus, the absolute maximum of the function f(x) is : f(-8) = 4.To learn more about similar functions, visit :
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3 times the sum of a number and 5
SHOW WORK
Answer:
3(n +5)
Step-by-step explanation:
You want the math expression that means "three times the sum of a number and five."
SumA sum is represented using a plus sign. "A number" is represented using a variable. "x" is a variable commonly used for an unknown value. "n" can also be used to represent "a number."
The sum of a number and 5 will be ...
n + 5
TimesWe want an expression that is 3 times that sum, so we multiply it by 3:
3(n +5) . . . . . . 3 times the sum of a number and 5
__
Additional comment
Note that the expression above is not the same as 3n+5, which would represent "the sum of 3 times a number and 5".
The table shows the temperature of an amount of water set on a stove to boil, recorded every half minute.According to the line of best fit, at what time will the temperature reach 100°C, the boiling point of water?55.566.5
This is a problem with a non-linear equation. The data is the temperature of water and the time. But we have to fit a line anyway.
We can the Least Squares Method, the best line fit is:
[tex]\begin{gathered} y=mx+b \\ m=\frac{n\sum ^{}_{}(x\cdot y)-\sum ^{}_{}x\cdot\sum ^{}_{}y}{n\sum ^{}_{}x^2-(\sum ^{}_{}x)^2} \\ b=\frac{\sum ^{}_{}y-m\sum ^{}_{}x}{n} \\ \text{where n is the number of points} \end{gathered}[/tex]Now, we apply the formula above:
[tex]m=\frac{10\cdot2072.5-22.5\cdot880}{10\cdot71.25-22.5^2}=\frac{20725-19800}{712.5-506.25}=\frac{925}{206.25}=4.48[/tex]David requires at least $250 to hold his birthday party. If David can save $43 a month, how many months will he need to save to be able to afford his birthday party?
a. Write an inequality that describes this situation.
b. Solve the inequality. Show all your work.
c. Write your answer in a complete sentence.
Answer:
Step-by-step explanation:
Let David will need m months to save to able to afford his birthday party.
Then 43m>=250 that is m>=5.814 .
But since months are whole numbers
So We take m>=6.
He will need at least 6 months to save to able to afford his birthday party.
The answer is 6 months .
Describe the location of the point having the following coordinates.
Negative abscissa, positive ordinate
• Quadrant 1
• Quadrant 2
• Quadrant 3
• Quadrant 4
The correct option for Negative abscissa, positive ordinate is -
• Quadrant 2
What is defined as the coordinate system?Graphing is done using a rectangular coordinate system with two axes. The horizontal axis is referred to as the x-axis, and the vertical axis is referred to as the y-axis. The x-axis is a straight line. The y-axis is a horizontal line. That is, we are combining two real numbers. We have the option of moving left-right or up-down.The coordinate plane is divided into quadrants that move counterclockwise.The origin is the point at which the two axes intersect. It has a value of 0 for x and a value of 0 for y.For the given question;
The other names for x and y axis are;
x -axis - abscissa
y- axis - ordinate
Thus, Negative abscissa means negative x axis.
And, positive ordinate means positive y axis.
This, lines in second quadrant.
Thus, Negative abscissa, positive ordinate will give the point is second quadrant.
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Find the roots and the vertex of the quadratic on a calculator. Round all values to 3
decimal places (if necessary).
y=-x² + 6x + 72
Which of the following methods would NOT be used to prove that two triangles are congruent?
Two triangles cannot be proven to be congruent using the method: A. Prove all sets of corresponding angles are congruent.
How to Prove that Two Triangles are Congruent?Two triangles are congruent to each other if they have the same shape and the same size, that is, all three sets of corresponding sides and all three sets of corresponding angles of the two triangles are congruent to each other.
Also, the following condition or criteria can be used to determine if two triangles are congruent to each other:
The HL congruence theorem: when two right triangles have corresponding equal hypotenuse and a pair of corresponding congruent legs, then they are congruent triangles by HL theorem.The SSS congruence theorem: two triangles having all three pairs of corresponding sides congruent are proven to be congruent by SSS congruence theorem.The SAS congruence theorem: Two triangles with two pairs of corresponding congruent sides and a pair of non-included congruent angle are congruent by the SAS.Thus, the method that cannot be used is: A. Prove all sets of corresponding angles are congruent.
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write a quadratic function
Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question.
Listed below are the jersey numbers of 11 players randomly selected from the roster of a championship sports team.
What do the results tell us?
55 64 45 77 88 51 41 54 35 67 18 D
a. Find the mean...
The mean is
(Type an integer or a decimal rounded to one decimal place as needed.)
Mean=54.1 Median=55 Mode=1 Midrange=53 are the correct values of mean, median, mode and midrange.
(a) Mean= sum of data/ number of data
=(55+64+45+77+88+51+41+54+35+67+18)/11
=595/11
=54.09 or 54.1
(b) Median is the middle value, which in this case is 51.
(c) Mode is the count of the number stating how many time it has been repeated in the data.
For instance in the given data :-
55 64 45 77 88 51 41 54 35 67 18
mode of 55 is 1, since it appears only one time.
No numbers in the given data repeats, i.e. all the values are unique. Thus the mode of the given data is 1.
(d) Mid-range is (highest value in the data + lowest value in the data)/2
in this case, the highest value is 88 and the lowest value is 18. Substituting these values in the formula:
(88+18)/2
=106/2
=53
What is mean median mode and midrange?
Mean is the sum of data divided by number of data, Median is the middle value of the data when arranged in ascending or descending order, Mode is the count of the number stating how many time it has been repeated in the data and Mid-range is highest value in the data plus lowest value in the data whole divided by 2.
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If a dragon can eat an entire cow weighing 500 kilograms in 12 seconds, how long will it take to eat a human weighing 90kilograms I need to know what the answer to that is and how I'd write it out mathematically
Dragon needs 2.16 seconds to eat 90 kilograms of human beings.
What is the ratio?
It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
It is given that,
If a dragon can eat an entire cow weighing 500 kilograms in 12 seconds,
500 kilograms = 12 seconds
By unitary method
1 kilogram = 12 / 500
1 kilogram = 0.024 second
For 90 kilograms
90 kilogram=90 × 0.024 second
90 kilogram = 2.16 second
Thus, a dragon needs 2.16 seconds to eat 90 kilograms of human beings.
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Harry downloads album A which has 11 tracks.
Each track on A costs the same.
The total cost of downloading A is £10.45
Harry also downloads album B and B has 14 tracks.
a) Work out the total cost of downloading B.
Assume each track costs the same as a track on A.
b) In fact, compared to the cost of each track on A the cost of 5 tracks on B is less by 5p each the cost of 9 tracks on B is more by 5p each.
Work out the actual total cost of downloading B.
Part a: Cost of downloading album B = 13.3 euros
Part b: Cost of downloading album B = 12.6 euros
Number of tracks in album A = 11 tracks
The total cost of downloading album A = 10.45 euro
Cost of each track on album A = Total cost of album/Number of tracks in the album
= 10.45/11
= 0.95 euro
Part a:
Number of tracks in album B = 14 tracks
Cost of album B = Number of tracks in album B * Cost of each track
= 0.95*14
= 13.3 euros
Part b:
The cost of 5 tracks on album B is 5p less therefore, the cost of 5 tracks will be 0.90*5 = 3.60 euros
The cost of 9 tracks on album B is 5p more therefore, the cost of 9 tracks will be = 1*9 = 9 euros
The total cost of downloading album B = 9+3.6 = 12.6 euros
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Marco has a piece of wood that measures 9x1/10+6x1/100+4x1/1000. How can this measurement b written as a decimal
The sum of the values is referred to as the operands, arguments, or inputs, while the result is referred to as the value, output, or result. Operations may require less than two inputs or more (including the case of zero input and infinitely many inputs). The answer will be 0.9+0.06+0.004= 0.964
What are mathematical operations?Not all possible values of the domain may be covered by an operation's definition. For instance, it is impossible to square the roots of negative integers or divide by zero in real numbers. An operation's domain of definition, also known as the active domain, is the set of values for which the operation is specified. The set that the values created are contained in is known as the codomain, while the set that the operation really produced is known as the codomain of definition, active codomain, image, or range. For instance, only non-negative numbers are produced by the squaring operation when applied to the real numbers; the set of real numbers is the codomain, but the non-negative numbers are the range.
A scalar can be multiplied by a vector to create another vector (a process known as scalar multiplication), and two vectors can be combined to make a scalar quantity in an inner product operation. An operation may or may not have specific characteristics, such as being idempotent, associative, commutative, or anticommutative.
The sum of the values is referred to as the operands, arguments, or inputs, while the result is referred to as the value, output, or result. Operations may require less than two inputs or more (including the case of zero input and infinitely many inputs).
9x1/10+6x1/100+4x1/1000
0.9+0.06+0.004= 0.964
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1. The amount of time 26 students spend on their phones on a given day (rounded to the nearest
hour) is recorded as follows.
0, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 12
Create a dot plot of the information. "Be sure to label all necessary parts!
PLEASE ANSWER Will mark brainliest
The total number of dots tells us the total number of observations of the values. the dot plot of the information are attached below.
How does the dot plot work?A Dot Plot is a graphical display of quantitative data consisting of dots plotted on a simple scale. Suppose we're measuring something whose values are numeric. For each value of that thing we observe, we plot a dot above that value in the number line.
If a value occurs more than once, then the dots are placed one above the other thus, that the height of the column of dots represents the frequency for that value.
Given data set:
{0, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 12}
First we need to Label the increments on the given line to include the range of data.
Then Label them order -2 to 16 increasing in 1 unit.
Now Label the dot plot with a suitable describing the dot plot.
Then Count the number of data points for each discrete category.
The dot plot of the information are attached below.
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hello, the question is in the picture :)
By cross multiplying the given equation, we have
[tex]6x=(x-2)(x+8)[/tex]By multiplying the right hand side, we get
[tex]6x=x^2+6x-16[/tex]Then, by subtracting 6x to both sides, we have
[tex]0=x^2-16[/tex]or equivalently,
[tex]x^2-16=0[/tex]Since the left hand side is a conjugate binomial, it can be expressed as
[tex]x^2-16=(x+4)(x-4)[/tex]Then, we have the equation
[tex](x+4)(x-4)=0[/tex]Therefore, the values of x that make the equation true are x= 4 and x= -4
Which of the following points would be on the graph of the linear equation? Select all that apply.
A. (-4,10)
B. (-2,8)
C. (5, -6)
Answer:
Outline 4 factors to the conside.
Please help me I’m miserable because I was sick.It’s 2:00AM and this is due at 8 somebody please help me
Answer:
see explanation
Step-by-step explanation:
(a)
the 2 angles are same- side interior angles and are supplementary.
(c)
since they are supplementary , they sum to 180° , that is
6x + 14 + 10x - 10 = 180
16x + 4 = 180 ( subtract 4 from both sides )
16x = 176 ( divide both sides by 16 )
x = 11
(d)
then
6x + 14 = 6(11) + 14 = 66 + 14 = 80
10x - 10 = 10(11) - 10 = 110 - 10 = 100
note 80 + 100 = 180 ( supplementary angles )
What is the answer to this question
Given that tanθ = 3.2603 where π < θ < 3π/2
[tex]\begin{gathered} \text{sin}\theta\approx0.9560 \\ \cos \theta\approx0.2932 \end{gathered}[/tex][tex]\begin{gathered} \sin ^2\theta+\cos ^2\theta=1 \\ \text{where} \\ \tan \theta=\frac{\sin \theta}{\cos \theta} \end{gathered}[/tex]From the calculation the value of θ = 72.95, hence the correct the error by adding 180
because it dint dnt fall in the range of
[tex]\pi<\theta<\frac{3\pi}{2}[/tex]And to correct the error add 180 to their answer,
Hence the value of θ = 180 + 72.95 = 252.95 degree
x+2y=7
1. What two things must be known to write the
equation of a line?
2. Identify the slope of the line and the point that the
line pass through to write your equation. Use the
point-slope formula to write an equation of the line in
standard form.
3. Identify the slope of the line and the point that the
line pass through to write your equation. Use the
slope y-intercept form to write the equation of the
line.
4. What did you notice about the slope and the point in which the line passed through for both parts 2 and 3
Step-by-step explanation:
Your slope and your x and y intercept.
x + 2y =7
Divide through by 2, we have:
x/2 + 2y/2 = 7/2
x/2 + y = 7/2
y = 7/2 - x/2
In the form y = mx + c gives.
Where m is the slope.
.: The slope = -1
pls help me with this
When solving an inequality, treat it like an equal sign while solving.
y - 4 ≤ -13
y - 4 + 4 ≤ -13 + 4
y ≤ -9
how do I find the answer to [2−∣∣−23−2(−15)∣∣]÷(−13)
The answer to the expression [2−||−23−2(−15)||]÷(−13) is 5/13.
In the question ,
the expression is given as
=[2−||−23−2(−15)||]÷(−13)
Solving the terms inside [ ] , we have
2*(-15) = -30
Substituting the value of 2*(-15) in the expression , we get
=[2-||-23-(-30)||]÷(−13)
=[2−||−23+30||]÷(−13) ....as -(-30) = 30
Solving the terms inside the modulus || || , we get
=[2−||+7||]÷(−13) ...as ||-23+30|| represents the modulus(norm) value ..
So ,Simplifying further , we get
=[2−7]÷(−13) ....as 2-7 = -5
=[-5]÷(−13) ...as a÷b can be written as a/b
= -5/-13
writing the answer in the simplified form .
= 5/13
Therefore , the answer to the expression [2−||−23−2(−15)||]÷(−13) is 5/13.
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a go-karts's top speed is 607,200 feer per hour. what is the speed in miles per hour?
First, we will start by converting 607,200 feet to miles
1 mile= 5280 foot
607, 200 feet can be changed to mile by dividing it by 5280
That is;
607,200 feet to mile = 607, 200 / 5280 = 115 miles
Hence; speed
= distance over t/
= 115 /1
=115 miles per hour
A shipping carton has the shape of right triangular prism. Thelength of the carton is 4 times the longer lag of the righttriangular base. The shorter leg of the base is 1/2 of the longerleg. If the volume is 5832 cubic inches what is the length of thecarton?
EXPLANATION
Let's see the facts:
Length = 4*longer leg
Shorter leg of the base= 1/2 longer leg
We know that Volume = 5832 = 1/2* length* longer leg* shorter leg
Let's call x to the longer leg, the variables are:
length= 4*longer leg= 4x --> x is the longer leg
Shorter leg= 1/2longer leg= 1/2x --> x is the longer leg
Substituting terms, the equation would be:
[tex]5832=\frac{1}{2}\cdot4x\cdot x\cdot\frac{1}{2}x[/tex]Multiplying like terms:
[tex]5832=\frac{4}{4}x^3[/tex]Simplifying:
[tex]5832=x^3[/tex]Switching sides:
[tex]x^3=5832[/tex]Isolating x:
[tex]x=\sqrt[3]{5832}[/tex]Solving the cubic root:
[tex]x=18[/tex]So, x is the value of the longer leg.
Now, we need to find the length, we know that length=4*longer leg
So, the length of the carton is 4*18= 72
The answer is 72
“use the converse of Pythagorean Theorem to tell whether the triangle is right, acute, or obtuse”
Answer: Using the pythaorean theoream we have to det
Dilate point S by a scale factor of 1/2
The location of the image of point S is the midpoint of the line segment RS. A representation of the geometric system and the rigid transformation is shown in the image attached below.
How to find the coordinates of the image of point S by using a transformation rule
Herein we know the center of dilation and the location of point S, which must be dilated by a rigid transformation, that is, a transformation applied on the point such that its Euclidean distance is conserved. The operation is defined by the following equation:
RS' = k · RS
S'(x) - R(x) = k · S(x) - k · R(x)
Where k is the scale factor.
If we know that R(x) = 0, S(x) = 6 and k = 1 / 2, then the location of the point S' is:
S'(x) - 0 = (1 / 2) · 6 - 0
S'(x) = 3
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The City of Amistad wants to fence in a portion of Amitie Park for an inclusive play space for children. Determine how much fencing they will need if the diameter of the section is 90 feet. Use 3.14 for π.
To fence in a portion of Amitie Park for an inclusive play space for children total fencing required of the section with diameter 90 feet is 282.6 feet.
As given in the question,
To fence in a portion of Amitie Park for an inclusive play space for children
Diameter of the section = 90 feet
Let r be the radius
r = diameter/2
⇒ r = 90 / 2
⇒r = 45 feet
Total fencing required to fence a play space
= 2πr
= 2 × 3.14 × 45
= 282.6 feet
Therefore, to fence in a portion of Amitie Park for an inclusive play space for children total fencing required of the section with diameter 90 feet is 282.6 feet.
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Norman buys a new car for $21,500. The simple interest rate is 4.2% and the amount of loan (plus simple interest) is repayable in 5 years. What is the total amount that must be repaid?
Round your answer to the nearest dollar and do not round until the final answer.
The total amount that must be repaid will be $26,015.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
A = P + (PRT)/100
Where P is the principal, R is the rate of interest, and T is the time.
For $21,500, Norman buys a brand-new vehicle. The loan amount (plus simple interest) must be repaid in full within five years, and the simple interest rate is 4.2%.
The total amount that must be repaid will be given as,
A = $21,500 + ($21,500 x 4.2 x 5)/100
A = $21,500 + $4,515
A = $26,015
The total amount that must be repaid will be $26,015.
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Give the equation of the circle centered at the origin and passing through the point (4, 0).
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: x² + y² = 16[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The distance between the centre and the point through which the circle is passing is equal to the radius of the circle.
so, let's use distance formula here :
[tex]\qquad \tt \rightarrow \: \sqrt{(y2 - y1) {}^{2} + (x2 - x1) {}^{2} } [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{(0 - 0) {}^{2} + (4 - 0) {}^{2} } [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{0 + (4) {}^{2} } [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{ {4}^{2} } [/tex]
[tex]\qquad \tt \rightarrow \: 4 \: \: units[/tex]
Now, let's write the equation of circle in standard form :
[tex]\qquad \tt \rightarrow \: (x - h) {}^{2} + (y - k) {}^{2} = r {}^{2} [/tex]
h = x - coordinate of circle k = y - coordinate of circle r = radius of circle[tex]\qquad \tt \rightarrow \: (x - 0) {}^{2} + (y - 0) {}^{2} = {4}^{2} [/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + {y}^{2} = 16 [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
the girl ran 5 miles * 2 + 60 + 54
Answer:
Equation = 1/4 x + 25 = 70
Solution = $180
Explanation:
Let the original amount she had before she went shopping be x
If she spent one-fourth on sloth, then the amount spent on cloth will be;
1/4 x
If she receives another $25 a week later totalling her money $70, then the equation that represents the situation will be;
1/4 x + 25 = 70
Find the solution
1/4 x + 25 = 70
1/4 x = 70 - 25
1/4 x = 45
x = 45 * 4
x = 180
Hence the amount she had before going for shoppind was $180