Answer:
[tex]y-7=-\dfrac{1}{3}(x-1)[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]
To find the equation of a line that passes through two given points, first find its slope by substituting the given points into the slope formula.
Define the points:
(x₁, y₁) = (1, 7)(x₂, y₂) = (7, 5)Substitute the points into the slope formula:
[tex]\implies m=\dfrac{5-7}{7-1}=\dfrac{-2}{6}=-\dfrac{1}{3}[/tex]
Therefore, the slope of the line is -¹/₃.
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
To find the equation in point-slope form, simply substitute the found slope and one of the given points into the point-slope formula:
[tex]\implies y-7=-\dfrac{1}{3}(x-1)[/tex]
Find the area of the circle. Use 3.14 or 227for π . thxQuestion 2
Step 1
State the area of a circle using the diameter
[tex]\frac{\pi d^2}{4}[/tex]Where d=diameter=28in
[tex]\pi=\frac{22}{7}[/tex]Step 2
Find the area
[tex]A=\frac{22}{7}\times\frac{28^2}{4}=616in^2[/tex]Answer;
[tex]Area\text{ = }616in^2\text{ when }\pi\text{ =}\frac{22}{7}[/tex]The composition of rigid motions T (-20,-6) •T (19,23 describes the route of a limousine in a city from its starting position. Describe the route in words. Assume that the positive y-axis points north. First the limousine drives (Type whole numbers.) block(s) east and block(s) north, and then it drives block(s) east and block(s) south.
You have the following rigid motion:
[tex]T_{<-20,-6>}T_{<19,23>}[/tex]The previous transformation means that the limousine was translated 20 units to the west and 6 units downward (south), next, the limousine was translated 19 units to the east and 23 units upward (north).
Hence, the limousine drives 20 blocks to the east and 6 blocks to south, and then it drives 19 block to the east and 23 blocks to north.
Write an equation of a line in slope-intercept form that has a slope of -3 and goes through the point (0, 3) O y = 3x - 1 O y = 3x + 2 O y = 3x O y = -3x + 3
ANSWER
y = -3x + 3
EXPLANATION
We want to write the equation in slope-intercept form, which is the form:
y = mx + c
where m = slope; c = intercept
To do that, we have to use the point-slope method:
y - y1 = m(x - x1)
where (x1, y1) = point the line goes through
From the question:
m = -3
(x1, y1) = (0, 3)
So, we have that:
y - 3 = -3(x - 0)
y - 3 = -3x
=> y = -3x + 3
That is the equation of the line in slope-intercept form.
Because of damage, a computer company had 5 tablets returned out of the 80 that were sold. Suppose the number of damaged tablets sold continue at this rate. How many tablets should the company expect to have returned if it sells 400 of them?
we are told that there 5 damaged tablets out of 80 that are sold. Therefore, the rate of damaged tablets per sold tablets is:
[tex]\frac{5\text{ damaged}}{80\text{ sold}}[/tex]Multiplying this rate by the 400 sold tablets we get:
[tex]\frac{5\text{ damaged}}{80\text{ sold}}\times40\text{0 sold}[/tex]Solving we get:
[tex]\frac{5\text{ damaged}}{80\text{ sold}}\times40\text{0 sold}=25\text{ damaged}[/tex]Therefore, if the rate continues, the company can expect to return 25 tablets.
determin wether true or false. (2 points) True False The functions f(x) = x – 5 and g(x) = -3x + 15 intersect at x = 5. The functions f (x) = 3 and g(x) = 11 – 2. intersect at x = 3. O The functions f (x) = x + 3 and g(x) = -x + 7 intersect at x = 2. The functions f (x) = {x – 3 and g(x) = -2x + 2 intersect at x = -2.
To find the intersection point between f(x) and g(x) we will equate their right sides
[tex]\begin{gathered} f(x)=x-5 \\ g(x)=-3x+15 \end{gathered}[/tex]Equate x - 5 by -3x + 15 to find x
[tex]x-5=-3x+15[/tex]add 3x to both sides
[tex]\begin{gathered} x+3x-5=-3x+3x+15 \\ 4x-5=15 \end{gathered}[/tex]Add 5 to both sides
[tex]\begin{gathered} 4x-5+5=15+5 \\ 4x=20 \end{gathered}[/tex]Divide both sides by 4 to get x
[tex]\begin{gathered} \frac{4x}{4}=\frac{20}{4} \\ x=5 \end{gathered}[/tex]Then the first one is TRUE
For the 2nd one
f(x) = 3, and g(x) = 11 - 2x
If x = 3, then substitute x by 3 in g(x)
[tex]\begin{gathered} g(3)=11-2(3) \\ g(3)=11-6 \\ g(3)=5 \end{gathered}[/tex]Since f(3) = 3 because it is a constant function and g(x) = 5 at x = 3
That means they do not intersect at x = 3 because f(3), not equal g(3)
[tex]f(3)\ne g(3)[/tex]Then the second one is FALSE
For the third one
f(x) = x + 3
at x = 2
[tex]\begin{gathered} f(2)=2+3 \\ f(2)=5 \end{gathered}[/tex]g(x) = -x + 7
at x = 2
[tex]\begin{gathered} g(2)=-2+7 \\ g(2)=5 \end{gathered}[/tex]Since f(2) = g(2), then
f(x) intersects g(x) at x = 2
The third one is TRUE
For the fourth one
[tex]f(x)=\frac{1}{2}x-3[/tex]At x = -2
[tex]\begin{gathered} f(-2)=\frac{1}{2}(-2)-3 \\ f(-2)=-1-3 \\ f(-2)=-4 \end{gathered}[/tex]g(x) = -2x + 2
At x = -2
[tex]\begin{gathered} g(-2)=-2(-2)+2 \\ g(-2)=4+2 \\ g(-2)=6 \end{gathered}[/tex]Hence f(-2) do not equal g(-2), then
[tex]f(-2)\ne g(-2)[/tex]f(x) does not intersect g(x) at x = -2
The fourth one is FALSE
Which representation does not show y as a function of x?1.II.€9> 10III.x 1 3 5 7y -6 -18 -30 -42IV. {(-2,3), (-1,4), (0,4), (3, 2)}a) I and IIb) I, II, and IIIc) I and IVd) All of the above are functions
We can say that I is not a function because inputs can only have one output.
II it's not a function since if you draw an horizontal line through the function intersect in two points, then it's not a function.
The answer is A.
PROGRESSIVEKayla ForshaeSupervisor: "Our goal is to make add-on sales during 85% of sales. If you make 35sales, how many add-on sales do you need to make to meet the goal?"
We are given that the total number of sales is 35.
According to the question, his goal is to make add-on sales during 85% of sales.
Therefore, the add-on sales would be:
[tex]\Rightarrow\frac{85}{100}\times35=29.75\approx30[/tex]Hence, we will need to make 30 add-on sales to meet the goal.
What is a quadrilateral that has reflection symmetry, but not rotation symmetry?
The quadrilaterals, parallelogram,square, rectangle has rotational symmetry but no reflectional symmetry
A trapezoid has neither a rotational symmetry nor a reflectional symmetry
But for an isosceles with only one pair of parallel sides has a reflectional symmetry but no rotational symmetry
Thus, the correct answer is
an isosceles with only one pair of parallel sides
Divide 8 1/8 by 7 1/12 simplify the answer and write as a mixed number
The division of 8 1/8 by 7 1/12 is 91/136.
What is division?Division simply has to do with reduction of a number into different parts. On the other hand, a mixed number is the number that's made up of whole number and fraction.
Dividing 8 1/8 by 7 1/12 will go thus:
8 1/8 ÷ 7 1/12
Change to improper fraction
65/8 ÷ 85/7
= 65/8 × 7/85
= 91/136
The division will give a value of 91/136.
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The National Oceanic and Atmospheric Administration tracks the amount of oysters harvested from the Chesapeake Bay each year.Years since 1900 2 28 53 67 78 89Oysters (metric tons) 54.2 22.5 7.38 5.28 3.52 2.38Find the exponential regression equation that models this data.Ay=-58(-0.964)OB. y = -58(0.964)Oc.y=58(0.964)*OD.y=58(-0.964)*Reset SelectionPreviouNext
Explanation
We are given the following table:
We are required to determine the exponential regression equation that models the data.
This is achieved thus:
We know that an exponential equation is given as:
[tex]y=ab^x[/tex]Using a graphing calculator, we have:
From the graph, we have:
[tex]\begin{gathered} a=58 \\ b=0.964 \end{gathered}[/tex]Hence, the answer is:
[tex]y=58(0.964)^x[/tex]Prove the Question according to the theorem of a Circle
Given -
P,Q,R and S are 4 points on the circle and PQRS is a cyclic quadrilateral
Prove -
[tex]\angle PQR\text{ + }\angle PSR\text{ = 180}[/tex]Explanation -
[tex]\angle1\text{ = }\angle6\text{ ------\lparen1\rparen \lparen Angles in same segment\rparen}[/tex][tex]\angle5\text{ = }\angle8\text{ ------\lparen2\rparen \lparen Angles in the same segment\rparen}[/tex][tex]\angle2\text{ = }\angle8\text{ ------\lparen3\rparen \lparen Angles in the same segment\rparen}[/tex][tex]\angle7\text{ = }\angle3\text{ -------\lparen4\rparen\lparen Angles in the same segment\rparen}[/tex]By using angle sum property of quadrilateral
[tex]\angle P\text{ + }\angle Q\text{ + }\angle R\text{ + }\angle S\text{ = 360}[/tex][tex]\angle1\text{ + }\angle2\text{ + }\angle3\text{ + }\angle4\text{ + }\angle5\text{ + }\angle6\text{ + }\angle7\text{ + }\angle8\text{ = 360}[/tex][tex](\angle1+\angle2+\angle7+\angle8)+(\angle3+\angle4+\angle5+\angle6)=360[/tex]By using equation 1,2,3 and 4
[tex]2(\angle3+\angle4+\angle5+\angle6)\text{ = 360}[/tex][tex]\angle3+\angle4+\angle5+\angle6\text{ = 180}[/tex][tex](\angle3+\angle4)+(\angle5+\angle6)\text{ = 180}[/tex][tex]\angle PQR\text{ + }\angle PSR\text{ = 180}[/tex]Hence Proved
Which of the following IS a function?
Answer:
The ans C hope it helps u
have a good day
O is the center of the regular hexagon below. Find its perimeter. Round to the nearest tenth if necessary.
To solve this problem, we have to find the side length and multiply it by the number of sides of the figure.
To find the length side we will use the following formula:
[tex]ap=\sqrt[]{I^2-(\frac{I^{}}{2})^2}\text{.}[/tex]Where ap is the length of the apothem, and I is the side length.
Substituting the given values, we get:
[tex]10=\sqrt[]{I^2-(\frac{I}{2})^2}.[/tex]Solving the equation for I, we get:
[tex]\begin{gathered} \\ I=\frac{2\times10}{\sqrt[]{3}}. \end{gathered}[/tex]Therefore, the perimeter of the hexagon is:
[tex]6I=6\times\frac{2\times10}{\sqrt[]{3}}\approx69.3\text{ units.}[/tex]Answer:
[tex]69.3\text{ units.}[/tex]simplify-6u^2 v-u^v^2-22u^2v^2
simplify-6u^2 v-u^v^2-22u^2v^2
we have
[tex]undefined[/tex]A toy rocket is shot vertically into the air from a launching pad 5 feet above the ground with an initial velocity of 32 feet
per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function
h(t)=1612 +32t+5. How long will it take the rocket to reach its maximum height? What is the maximum height?
A bourse named northern dancer won the Kentucky derby by running 1 1/4 miles in exactly 2 minutes. At this constant rate, how long does it take northern dancer to run the 1 1/2 mile Belmont stakes? Use unit rate
It is given that there are
[tex]1\frac{1}{4}=\frac{5}{4}\text{miles}[/tex]run in 2 minutes.
So, we have to determine time required to run
[tex]1\frac{1}{2}=\frac{3}{2}\text{miles}[/tex]Apply the unitary method,
For 5/4 miles required 2 minutes.
So , for 1 miles, time required
[tex]\frac{2}{\frac{5}{4}}=\frac{2\times4}{5}=\frac{8}{5}\min [/tex]Therefore,for 3/2 miles , time required is
[tex]\frac{3}{2}\times\frac{8}{5}=\frac{12}{5}\text{min}=2.4\min [/tex]Hence the time required is 2.4 minutes.
you get a student loan from the educational assistance Foundation to pay for your educational expenses as you earn your associate's degree you will be allowed 10 years to pay the loan back find the simple interest on the loan if you borrow $3,600 at 8 percent
Simple interest = PRT/100
where p = $3600
R=8
T=10
Substituting into the formula;
S.I = $3600 x 8 x 10 /100
=$36 x 8 x 10
=$2880
I need help with #1 of this problem. It has writings on it because I just looked up the answer because I’m confused but I want to know the answer and how to do it with work provided please
In the figure below
1) Using the theorem of similar triangles (ΔBXY and ΔBAC),
[tex]\frac{BX}{BA}=\frac{BY}{BC}=\frac{XY}{AC}[/tex]Where
[tex]\begin{gathered} BX=4 \\ BA=5 \\ BY=6 \\ BC\text{ = x} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \frac{4}{5}=\frac{6}{x} \\ \text{cross}-\text{multiply} \\ 4\times x=6\times5 \\ 4x=30 \\ \text{divide both sides by the coefficient of x, which is 4} \\ \text{thus,} \\ \frac{4x}{4}=\frac{30}{4} \\ x=7.5 \end{gathered}[/tex]thus, BC = 7.5
2) BX = 9, BA = 15, BY = 15, YC = y
In the above diagram,
[tex]\begin{gathered} BC=BY+YC \\ \Rightarrow BC=15\text{ + y} \end{gathered}[/tex]Thus, from the theorem of similar triangles,
[tex]\begin{gathered} \frac{BX}{BA}=\frac{BY}{BC}=\frac{XY}{AC} \\ \frac{9}{15}=\frac{15}{15+y} \end{gathered}[/tex]solving for y, we have
[tex]\begin{gathered} \frac{9}{15}=\frac{15}{15+y} \\ \text{cross}-\text{multiply} \\ 9(15+y)=15(15) \\ \text{open brackets} \\ 135+9y=225 \\ \text{collect like terms} \\ 9y\text{ = 225}-135 \\ 9y=90 \\ \text{divide both sides by the coefficient of y, which is 9} \\ \text{thus,} \\ \frac{9y}{9}=\frac{90}{9} \\ \Rightarrow y=10 \end{gathered}[/tex]thus, YC = 10.
个HS: Math II North Carolina High School Math II [M] (Prescripti8. Which statement is true?O OIf two figures are congruent, then they have the same shape but nOIf two figures are congruent, then they are similar.OIf two figures are similar, then they are congruent.OIf two figures are similar, then corresponding sides must be congru
For two triangles to be similar, it is enough if two angles of one triangle are equal to two angles of the other triangle.
If two figures are congruent, the corresponding sides must be equal and also the corresponding sides.
Therefore, the answer is:
If two figures are congruent, then they are similar
- 32 + 2Determine for each 2-value whether it is in the domain of f or not.In domainNot in domain203
f(x) = x-3 / x+2
To be in the domain, we have to avoid 0 on the bottom of the fraction.
So, the bottom of the fraction is x+2.
x=-2
(-2)+2= 0
-2 is not in the domain
x= 0
(0)+2= 2
0 is in the domain
x=2
(2)+2=4
simplest form , 7/6 ÷ 4
[tex]\text{ }\frac{7}{6}\text{ / 4 = }\frac{\frac{7}{6}}{\frac{4}{1}}\text{ = }\frac{7}{24}[/tex]
The answer is 7/24
Use the formula V=lwh and A=bg to complete the table below by evaluating the expression
we have that
the formula to calculate the area of a rectangle is equal to
A=L*W
we have
L=8.3 cm
W=4 cm
substitute
A=(8.3)*(4)
A=33.2 cm2
therefore
Formula A=L*W
Expression A=(8.3)*(4)
Solve A=33.2 cm2
Use dimensional analysis to determine which rate is greater. The pitcher for the Robins throws a baseball at 90.0 miles per hour. The pitcher on the Bluebirds throws a baseball 125.4 feet per second. Which pitcher throws a baseball faster? Complete the explanation:When I convert the Bluebirds pitcher's speed to the same units as the Robins pitcher's speed the speed is __ mi/h. Since the Bluebirds pitcher's speed is ____ the Robins pitcher's speed, the pitcher on the ____ throws a faster ball.
ANSWER and EXPLANATION
We want to solve the problem by using dimensional analysis.
To do this, let us convert the speed of the Bluebirds baseball to miles per hour.
We have that:
1 feet per second = 0.6818 miles per hour
125.4 feet per second = 85.50 miles per hour
As we can see the baseball of the Bluebirds is slower than the Robins (90 miles per hour)
Now, to complete the explanation:
When I convert the Bluebirds pitcher's speed to the same units as the Robins pitcher's speed, the speed is _85.50_ mi/h.
Since the Bluebirds pitcher's speed is _less than_ the Robins pitcher's speed, the pitcher on the __Robins_ throws a faster ball.
Write an equation that represents a vertical shrink by a factor of 1/4 of the graph of g(x)=|x|.
h(x)=?
an equation that represents a vertical shrink by a factor of 1/4 of the graph of g(x)=|x| is y = |x|/4
What is vertical stretch/vertical compression ?
• A vertical stretch is derived if the constant is greater than one while the vertical compression is derived if the constant is between 0 and 1.
• Vertical stretch means that the function is taller as a result of it being stretched while vertical compress is shorter due to it being compressed and is therefore the most appropriate answer.
The y-values are multiplied by a value between 0 and 1, which causes them to travel in the direction of the x-axis. This is known as a vertical shrink and tends to flatten the graph. A point (a,b) on the graph of y=f(x) y = f (x) shifts to a point (a,kb) (a, k b) on the graph of y=kf(x) y = k f (x) in both scenarios.
The function g(x) is defined as |x|.
To vertically shrink the graph of g(x) by a factor of 1/4, divide the function by 4.
g(x) = f(x)/3
f(x) is equal to (|x|)/4.
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1) What is the surface area of this Cylinder: height of 9cm and a radius of 7cm. 1) Use 3.14 and round your a 9 cm
EXPLANATION
This is a cylinder with a height of 9 cm and a radius of 7cm.
The Area of a cylinder is given by the following expression:
Area= 2xπxr ² + 2xπxrxh
As r=7cm and h=9cm, replacing terms:
Area = 2xπx(7) ² + 2xπx7x9
Multiplying numbers:
Area = 98xπ + 126xπ
Simplifying:
Area= 224xπ
Representing π as a number:
Area= 224 x 3.14= 703.36 cm^2
One of the legs of a right triangle measures 13 cm and the other leg measures
2 cm. Find the measure of the hypotenuse. If necessary, round to the nearest
tenth.
Answer:
13.2 cm
Step-by-step explanation:
Use Pythagorean Theorem
Hypotenuse^2 = (leg1)^2 + (leg2)^2
H^2 = 13^2 + 2^2
= 169 + 4
H^2 = 173
H = sqrt (173) = 13.2 cm
You are making a kite and need to figure out how much binding to buy. You need the binding for the perimeter of the kite. The binding comes
in packages of two yards. How many packages should you buy?
12 in.
15 in.
12 in.
20 in.
You should buy packages.
With the help of the Pythagorean theorem, we know that we should buy 3 packages.
What is the Pythagorean theorem?The Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.So, Pythagorean formula: c² = a² + b²
Each package contains 2 yards of binding.In the kite, there are right triangles, so use the Pythagorean theorem.(Refer to the image of the kite attached below)
△1:
a² + b² = c²15² + 12² = x₁²x₁ = √15² + 12²x₁ = 19.2 in△2:
x₂ = x₁ = 19.2 in
△3:
a² + b² = c²12² + 20² = x₃²x₃ = √12² + 20²x₁ = 23.3 in△4:
x₄ = x₃ = 23.3 inTotal: 19.2(2) + 15 + 2(12) + 20 + 2(23.3) = 144 in
Total (actual) > 144 inNow,
1 package = 2 yards = 6ft = 72 in2 yards × 3ft/1yrd × 12in/1ft = 72 in2 packages: 2(72) = 144 in3 packages: 3(72) > 144So, we should buy 3 packages.
Therefore, with the help of the Pythagorean theorem, we know that we should buy 3 packages.
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need help with excerise step by step been 20 year's
Given:
Standard deviation
[tex]\sigma=5.18[/tex]Mean
[tex]\mu=129[/tex]Required:
Find the longest braking distance one of these cars could have and still in the bottom.
Explanation:
The z-score formula is given as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Substitute the given values and find the value of z.
[tex]z=\frac{x-129}{5.18}[/tex]This is the first percentile which is X when Z has a p-value of 0.01, so z = -2.327.
[tex]\begin{gathered} -2.327=\frac{x-129}{5.18} \\ x-129=-2.327(5.18) \\ x-129=-12.054 \\ x=129+12.054 \\ x=116.946\text{ ft} \end{gathered}[/tex]Final answer:
The longest braking distance one of these cars could have and still in the bottom 1% is 116.946 ft.
so I've been using the formula for the volume of a cylinder but I'm still not getting anything even remotely close to my answer choices. the volume is 438.08π mL and the radius is 3.7 cm. I'm solving for the height
Answer:
H = 32 cm
Explanation:
The area of a cylinder is given by
[tex]V=\pi r^2h[/tex]Now solving for h gives
[tex]h=\frac{V}{\pi r^2}[/tex]Now V = 438.08 π and r = 3.7 cm. Putting these values in the above equations gives
[tex]h=\frac{438.08\pi\operatorname{cm}^3}{\pi(3.7cm)^2}[/tex][tex]\boxed{h=32\operatorname{cm}\text{.}}[/tex]which is our answer!
system: 3x+2y=6 x-y=-3 find the value for x. find the value for y.
Given a system of equations:
[tex]\begin{gathered} 3x+2y=6 \\ x-y=-3 \end{gathered}[/tex]We have to solve the system of equations.
We can solve this system of equations using the substitution method.
From the second equation, we have x - y = -3, which implies that x = y - 3. Substitute x = y - 3 in the first equation:
[tex]\begin{gathered} 3(y-3)+2y=6 \\ 3y-9+2y=6 \\ 5y=6+9 \\ 5y=15 \\ y=\frac{15}{5} \\ y=3 \end{gathered}[/tex]Now, we have y = 3, put in x = y - 3 to get,
[tex]\begin{gathered} x=3-3 \\ x=0 \end{gathered}[/tex]Thus, the solution of the system of equations is (0, 3).
