Suppose that the rule is of the form
[tex]y=mx+b[/tex]Where m is the slope and b is the intercept
The slope can be found using the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]You can take any two consecutive x and y values from the given table.
[tex]\frac{17-3}{3-1}=\frac{14}{2}=7[/tex]Similarly,
[tex]\frac{66-17}{10-3}=\frac{49}{7}=7[/tex]As you can see, you will end up with the same slope.
Now let us find the intercept b.
Take any x, y coordinates from the table
[tex](x,y)=(1,3)[/tex]Now substitute them in the slope-intercept equation.
[tex]\begin{gathered} y=7x+b \\ 3=7(1)+b \\ 3=7+b \\ b=-7+3 \\ b=-4 \end{gathered}[/tex]So the rule is
[tex]y=7x-4[/tex]Verification:
Let us verify whether we got the correct rule or not
Substitute the input x coordinates into the rule and check the outputs y coordinates.
[tex]\begin{gathered} y=7(1)-4=7-4=3 \\ y=7(3)-4=21-4=17 \\ y=7(10)-4=70-4=66 \\ y=7(6)-4=42-4=38 \end{gathered}[/tex]As you can see, we have got the same results therefore, the rule is correct.
A piece of wire 5/4 m long is to be cut into 20 pieces of the same length. What is the length of each piece?Each piece is ____ m long.(Simplify your answer. Type an integer or a fraction.)
When we divide a fraction by a number, that's equivalent to multiplying the first fraction by the inverse of that number.
In this problem, we need to divide the fraction 5/4 by 20. So we obtain:
[tex]\frac{5}{4}\colon20=\frac{5}{4}\cdot\frac{1}{20}[/tex]Now, we need to multiply the numerator of the first fraction by the numerator of the second one, and the denominator of the first fraction by the denominators of the second one:
[tex]\frac{5}{4}\cdot\frac{1}{20}=\frac{5\cdot1}{4\cdot20}=\frac{5}{80}[/tex]Now, we need to simplify the answer. To do so, we can divide both the numerator and the denominator by 5:
[tex]\frac{5\colon5}{80\colon5}=\frac{1}{16}[/tex]Therefore:
Each piece is 1/16 m long.
solve equation. -2(y-1)=9
y = -7/2
Explanation:-2(y-1)=9
expand the bracket:
-2 × y -2 × -1 = 9
-2y + 2 = 9
collect like terms:
-2y = 9 -2
-2y = 7
Divide both sides by -2:
-2y/-2 = 7/-2
y = -7/2
i forgot how i solved this, what im getting is 4x -24 which is wrong
Answer:
[tex](4x^2+22x-12)cm^2[/tex]Explanation:
From the given figure:
• The base of the triangle, b = (4x-2) cm
,• The perpendicular height, h = (2x+12) cm
The area of a triangle is calculated using the formula:
[tex]A=\frac{1}{2}bh[/tex]Substitute the given expressions:
[tex]\begin{gathered} A=\frac{1}{2}(4x-2)(2x+12) \\ Factor\text{ }4x-2\implies4x-2=2(2x-1) \\ A=\frac{1}{2}\times2(2x-1)(2x+12) \\ A=(2x-1)(2x+12) \end{gathered}[/tex]Next, open the brackets:
[tex]\begin{gathered} A=2x(2x+12)-1(2x+12) \\ =4x^2+24x-2x-12 \\ =(4x^2+22x-12)cm^2 \end{gathered}[/tex]The area of the triangle is:
[tex](4x^2+22x-12)cm^2[/tex]Classify the following triangle as acute, obtuse, or rightO A. AcuteO B. ObtuseOc. RightOD. None of theseSUBMIT
Given:
Triangle is given with the angles.
Given triangle is Acute
PLEASE HELP ME ASAP PLEASE PLEASE PLEASE
jaren is selling lampshades at a craft fair. for the price per lampshade in dollars is f (x) and it is a function of the
Number of lampshades bought as shown by the graph below. What is the total cost of buying 10 lampshades from Janet's stall
According to the graphic the total cost of buying 10 lampshades is 8 dollars
A total of $54,000 is invested at an annual interest rate of 5.25%. Find the balance after 6 years if it is compounded monthly.
Using the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
A = Amount
P = Principal = 54000
r = Interest rate = 5.25% = 0.0525
n = Number of times the interest is compounded per year = 12
t = Number of years = 6
So:
[tex]\begin{gathered} A=54000(1+\frac{0.0525}{12})^{12\cdot6} \\ A\approx73943.18 \end{gathered}[/tex]Answer:
The balance is $73943.18
A club that has 20 members is selecting a 5 representatives to send to a national conference. How many different groups of 5 can there be?
There can be a total of 15504 groups of selection
How to determine the groups of selection?From the question, we have
Total number of persons, n = 20
Numbers to selection, r = 5 i.e. the committee members
The number of ways of selection could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 20 and r = 5
Substitute the known values in the above equation
Total = ²⁰C₅
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 20!/15!5!
Evaluate
Total = 15504
Hence, the number of ways is 15504
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Answer:
There can be 4 groups of 5.
In circle C with m BCD= 48°, find the angle measure of minor arc BD.DB
Notice that angle BCD is a central angle, therefore, the measure of its arc will be the same as the measure of the angle, therefore, the measure of the minor arc BD is 48 degrees
hello can u help me please5.Admission to the Basketball Hall of Fame in Springfield is $5.00 per student. A group of students bought admission tickets. One student spent an extra $9.00 for a poster. The total amount they spent was $34.00. How many students were in the group?a.4b.5c.6d.7
Given:
The price per student for the admission, m=$5.
Extra amount spent by a student, c=$ 9.
Total amount spent, T=$34.
Let x be the number of students. Then, the expression for the total amount is,
[tex]T=mx+c[/tex]Substitute values and solve for x.
[tex]\begin{gathered} 34=5x+9 \\ 34-9=5x \\ 25=5x \\ x=\frac{25}{5} \\ x=5 \end{gathered}[/tex]Therefore, the number of students is 5.
Option (b) is correct.
5 lb of apples cost $8.20. How much is it for 1 lb?
2.) Your unusual boss decided to offer you a fourthoption to complicate your decision.Your payment would be described by the functionP(x) = 95,000x + 200,000, with x representingdays you work and P representing dollars you earn.Explain the meaning of the function based on thissituation and then decide if you would take this optionover the other three choices.On the next slide, you use a graph to support yourdecision.
P(x) = 95,000x + 200,000
The side walls of a regular quadrilateral pyramid are equilateral triangles with sides equal to 8 cm. Calculate the pyramid:1) the sum of the lengths of all the sides;2) the area of the base;3) the length of the height of the side wall;4) the area of the side wall.
a) 64cm
b) 64 square cm
c) 4√3 cm
d) 16√3 square cm
Explanations:A regular quadrilateral pyramid with equilateral triangles is as shown below;
1) The pyramid has 8 side lengths, hence the sum of the length of all the sides is given as:
[tex]\begin{gathered} Sum\text{ of side lengths}=8\times8cm \\ Sum\text{ of side lengths}=64cm \end{gathered}[/tex]2) Since the triangular sides are equilateral, the base of the pyramid will be a square with side length of 8cm. The area of the base is expressed as:
[tex]\begin{gathered} A=length\times length \\ A=8cm\times8cm \\ A=64cm^2 \end{gathered}[/tex]3) Since one side wall is an equilateral triangle, the height will be perpendicular to the base as shown:
In order to determine the height, we will use the Pythagorean theorem as shown:
[tex]\begin{gathered} 8^2=h^2+4^2 \\ h^2=8^2-4^2 \\ h^2=64-16 \\ h^2=48 \\ h=\sqrt{48}=4\sqrt{3}cm \\ \end{gathered}[/tex]4) The area of the side wall is equivalent to the area of the triangle expressed as:
[tex]\begin{gathered} Area\text{ of side wall}=\frac{1}{2}\times base\times height \\ Area\text{ of side wall}=\frac{1}{2}\times8cm\times4\sqrt{3} \\ Area\text{ of side wall}=16\sqrt{3}cm^2 \end{gathered}[/tex]4. The triangles below lie on the same line. Find thehorizontal distance of the smaller triangle.25DA10Distance:pe here to searchN
Thus the horizontal distance of the smaller triangle is 2.
Help !!!! Please asap
what is the slope of the line described by 5x+7y=19
Answer:
-5/7
Explanation:
Given the equation 5x+7y = 19
The standard form of an equation is y = mx+c
m is the slope
c is the intercept of a line
Make y the subject of the formula from the given equation
5x+7y = 19
7y = -5x + 19
Divide through by 7
7y/7 = -5x/7 + 19/7
y = -5/7 x + 19/7
Comparing with general formula;
mx = -5/7 x
m = -5/7
Hence the slope of the line is -5/7
A 33-ft ladder leans against a building so that the angle between the ground and the ladder is 85°.how high does the ladder reach on the building ?
We have the next situation:
Now, we need to label the sides:
- The largest side is always the hypotenuse
- The adjacent side is between the right angle and the given angle.
- The opposite side is opposite to the given angle.
Hence,
Hypotenuse = 33 ftt
Opposite side = h
Then, we need to find h:
We need to use a trigonometric function that involves the side that we know and the missing side:
So,
sinθ = opposite side / hypotenuse
Replacing:
Sin85 = 33ft / h
Solve for h:
h= 33ft¨*sin 85
h= 32.87
The answer is 32.87
What percentage of 371 is 120?
This question is about percentages.
To know which percentage of 371 is 120, we just have to divide
[tex]\frac{120}{371}=0.32[/tex]Then, we multiply by 100 to express it in percentage
[tex]\text{0}.32\cdot100=32[/tex]Therefore, 120 represents 32% of 370, approximately.In an octagon, five of the angles are equal and each of the other three angles is 24° greater than each of the five other ones. Determine the angles of the octagon anto
Given:
5 angles are equal: x
Each of the other angles is 24 greater than the other 5 angles: x+24
An octagon has 8 angles; the sum of the interior angles of an octaogn is 1080º
[tex]5x+3(x+24)=1080º[/tex]Use the equation above to solve x:
[tex]\begin{gathered} 5x+3x+72=1080 \\ 8x+72=1080 \\ 8x=1080-72 \\ 8x=1008 \\ x=\frac{1008}{8} \\ \\ x=126 \end{gathered}[/tex]The 5 angles that are equal measure 126º
The other 3 angles measure:
[tex]x+24=126+24=150º[/tex]Then, the angles of the octagon are: 126º,126º,126º,126º,126º,150º,150º,150ºInstructions: Write the function in slope-intercept form that represents the given. The roasting guide for a turkey suggests cooking for 100 minutes plus an additional 8 minutes per pound (x). Write the equation for total cooking time in terms of pounds of turkey.
Answer:
y = 8x + 100
Explanation:
Let us call the total cooking time y and the x the number of pounds of turkey, then we know that the roasing guid
I don’t understand the question its asking for the depth at 4 weeks and 9 weeks
Answer
Lake depth after 4 weeks: 343.6 ft
Lake depth after 9 weeks: 340.6 ft
Step-by-step explanation
The relation between time and lake depth is linear. Using the x-variable to represent time and the y-variable to represent the lake depth, we can use the next equation to relate these variables:
[tex]y=mx+b[/tex]where m is the slope and (0, b) is the y-intercept of the line.
The slope of the line that passes through the points (x₁, y₁) and (x₂, y₂) is calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]From the table, this line passes through (0, 346) and (2, 344.8), then its slope is:
[tex]m=\frac{344.8-346}{2-0}=\frac{-1.2}{2}=-0.6[/tex]From the table, this line passes through (0, 346), then parameter b is 346.
Substituting m = -0.6 and b = 346, the equation of the line is:
[tex]y=-0.6x+346[/tex]Evaluating this line at x = 4, that is, when time = 4 weeks, we get the next depth:
[tex]\begin{gathered} y=-0.6(4)+346 \\ y=-2.4+346 \\ y=343.6\text{ ft} \end{gathered}[/tex]Evaluating the equation of the line at x = 9, that is, when time = 9 weeks, we get the next depth:
[tex]\begin{gathered} y=-0.6(9)+346 \\ y=-5.4+346 \\ y=340.6\text{ ft} \end{gathered}[/tex]i inserted a picture of the question can you make it very shorta -4 b 8c 4d -8
a. -4
Explanation
the average rate of change is given by:
[tex]\begin{gathered} rateofch=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ where \\ P1(x_1,y_1)\text{ is the start point} \\ P2(x_2,y_2)\text{ is the end point} \end{gathered}[/tex]then
Let
[tex]\begin{gathered} x_1=1 \\ f(x_1)=0 \end{gathered}[/tex]and
[tex]\begin{gathered} x_2=3 \\ f(x_2)=-8 \end{gathered}[/tex]hence
P1(1,0)
P2(3,-8)
now, replace in the formula
[tex]\begin{gathered} rateofch=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{rate of change=}\frac{-8-0}{3-1}=\frac{-8}{2}=-4 \\ \text{rate of change=-}4 \end{gathered}[/tex]therefore, the answer is
a. -4
I hope th
S/14 = 14 a. -196 b. 196 C. 28 d. 0
In the given equation, the value of S is divided by 14, so to calculate the value of S you have to invert the operation, that is, multiply it by 14 so that both operations cancel each other.
And, for the equality to be valid, all operations made in one side of the = sign must be done on the other side as well. So, multiply both sides of the equation by 14:
[tex]\begin{gathered} \frac{14S}{14}=14\cdot14 \\ S=196 \end{gathered}[/tex]S=196 the correct choise is b.
Question 1 of 10 The graphs below have the same shape. What is the equation of the red graph? w GE? F%= 3 - 74 G(X)
The equation of the red graph (Parabola) is g(x) = 1 – x².
The given graph is the graph of the parabolas.
We are given;
The equation of the blue graph (Parabola) is f(x) = 4 – x².
We need to find the equation of the red graph g(x).
Let's observe the graph;
All of the lines in the blue graph pass through point 4 on the graph. The same is true for the red line, except that they all pass through 1. As a result, we should alter the 4 in the blue line equation to a 1 to represent the red line.
The equation of the blue graph is:
f(x) = 4 – x²
Substitute 4 by 1;
p(x) = 1 – x² = g(x)
This is our required equation.
Thus, the equation of the red graph (Parabola) is g(x) = 1 – x².
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what is the graph of x= 1 ?
The given equation x = 1 represents a horizontal lines that passes thourgh (1, 0).
Hence, the graph isThe answer is D.List the potential rational zeros of the polynomial function. Do not find the zeros.f(x) = -4x^4 + 2x^2 - 3x + 6A± , ± , ± , ± , ± 1, ± 2, ± 3, ± 4, ± 6B± , ± , ± , ± , ± 1, ± 2, ± 3, ± 6C± , ± , ± , ± , ± , ± 1, ± 2, ± 4D± , ± , ± , ± , ± , ± 1, ± 2, ± 3, ± 6
Answer:
±1,±2,±3 and ±6
Explanation:
We make use of the Rational Zero theorem below:
If a polynomial has integer coefficients, then every rational zero of f(x) has the form p/q where p is a factor of the constant term and q is a factor of the leading coefficient.
Given the function:
[tex]f\mleft(x\mright)=-4x^4+2x^2-3x+6[/tex]The steps to follow are given below.
Step 1: Determine all factors of the constant term and all factors of the leading coefficient.
The constant term is 6: Factors are ±1,±2,±3 and ±6
The leading coefficient is -4: Factors are ±1,±2, and ±4.
Step 2: Determine all possible values of p/q.
[tex]\begin{gathered} \frac{p}{q}=\pm\frac{1}{1},\pm\frac{2}{1},\pm\frac{2}{2},\pm\frac{3}{1},\pm\frac{6}{1},\pm\frac{6}{2} \\ =\pm1,\pm2,\pm1,\pm3,\pm6,\pm3 \\ =\pm1,\pm2,\pm3,\pm6 \end{gathered}[/tex]Therefore, the potential zeros are: ±1,±2,±3 and ±6.
Lucille wrote three numbers between 0.75 and 0.76 what numbers could she have written?
As an answer to this question, any decimal between 0.75 and 0.76 will do.
So let us choose the three numbers at random.
0.751 , 0.754, and 0.756 will do.
Find the equation of the line through the given points. (-8, 6) and (-8, 0)
The equation of a line is typically written as y=mx+b, where m is the slope and b the y-intercept.
The slope can be calculated like this:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case you have x1=-8, y1=6, x2=-8 and y2=0. Replace this values on the slope formula
[tex]m=\frac{0-6}{-8-(-8)}=\frac{-6}{-8+8}=\frac{-6}{0}\text{ the slope is undefined}[/tex]An undefined slope indicates that you have a vertical line parallel to the y-axis.
This line will pass through all points in the plane with an x-coordinate=constant (c). In this case this constant will be -8
The equation is written in the form x = c, then the equation of this line will be
[tex]x=-8[/tex]question will be in picture
given:
[tex]-7\le x[/tex]so, the line that represents the given inequality will be: b
Miranda has $100.00 in a saving account that earns 10 percent interest, compounded annually. what wull the balance be after 1 year round to the nearest cent
in pqr, what is the measurement of angle Q? 200 degrees871059010
In the triangle PQR we know that its angles have the following measures:
∠P=(6x+5)º
∠Q=(11x-5)º
∠R=xº
To determine the measures of ∠Q, you have to determine the value of x first. To do so you have to keep in mind that the measure of the inner angles of any triangle is 180º, so, for this triangle, the measure of the inner angles can be expressed as:
[tex]\begin{gathered} \angle P+\angle Q+\angle R=180º \\ (6x+5)+(11x-5)+x=180º \end{gathered}[/tex]From this expression, we can calculate the value of x.
-First, take the parentheses away, order the like terms together and simplify them:
[tex]\begin{gathered} 6x+11x+x+5-5=180º \\ 18x=180º \end{gathered}[/tex]-Second, divide both sides by 18 to determine the value of x:
[tex]\begin{gathered} \frac{18x}{18}=\frac{180}{18} \\ x=10 \end{gathered}[/tex]Now that we know that the value of x is 10º, we can determine the measure of ∠Q by replacing this value on the given expression for its measure:
[tex]\begin{gathered} \angle Q=11x-5 \\ \angle Q=11\cdot10-5 \\ \angle Q=110-5 \\ \angle Q=105º \end{gathered}[/tex]∠Q=105º, the correct option is the third one.