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]
A ladder that is 55 meters in length is resting on a branch of a tree, and the base of the ladder is 33 meters from the tree on the level ground. How high up is the branch on which the ladder is resting?
the diagram of situation is given as follows
so by using the right-angle property.
[tex]x^2+33^2=55^2[/tex][tex]\begin{gathered} x^2=3025-1089=1936 \\ x=\sqrt[]{1936} \end{gathered}[/tex][tex]x=44[/tex]so the height of the tree is 44
A satellite dish is the shape of a paraboloid. The dish is 42 inches wide, and 10 inches
deep. How many inches should the receiver be located from the vertex for optimal
reception? (round to the nearest thousandth)
The receiver is situated 44.24 inches from the vertex, is the correct response.
Define parabola.Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve. The topic of conic sections includes parabola, and all of its principles are discussed here. A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.
Observe the illustration below. It depicts the paraboloid's vertical cross-section through its axis of symmetry.
Make the origin of the parabola the vertex.
Then, it has the equation y = bx².
The parabola crosses via (21,10), therefore
10 = b(21²)
= 0.0226
because
Its equation is y =0.0226²
For best reception, the receiver should be positioned at the paraboloid's focus point.
The focus has a y-coordinate of
a = 1/(4b)
= 1/0.0226
= 44.24 in
The receiver is situated 44.24 inches from the vertex, is the correct response.
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Camden, a florist, is dividing 56 flowers equally into 8 bouquets. He uses division to find that he can put 7 flowers in each bouquet. Which subtraction equation could he use to check his answer?
The subtraction equation that Camden could use to check his answer is, x = 56 - 8 x 7.
What is a subtraction equation?A subtraction equation is an equation, which is a mathematical statement that two mathematical expressions share equality, which involves the use of the subtraction operation.
The result of a subtraction operation is known as the difference. The other parts of a subtraction operation are the minuend and the subtrahend.
The total number of flowers for the bouquets = 56
The number of bouquets = 8
The number of flowers for each bouquet = 7 (56/8)
Check:
x = 56 - 7 x 8
x = 56 - 56
x = 0
To check if the answer is correct, Camden should multiply 7 by 8 and then subtract the product from 56.
Thus, the difference in the subraction equation x = 56 - 8 x 7 that Camden used is zero, showing that his earlier division operation was correct.
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molly has 12 stickers 1/3 of her stickers are blue exactly how many stickers are not blue
Answer:
8 stickers
Step-by-step explanation:
beacuse 1/3 =4 4x3 =12 12-4=8 here you go:)
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-32-10A. 20-C?LBDIn the similaritytransformation of AABCEto AEDF, AABC was dilated bya scale factor of [?], reflectedacross the [ ], and movedthrough the translation [ ].B. 1/23 4F 5 Find the answer to all three missing boxes
To find the scale factor use the next formula:
[tex]sf=\frac{dimension\text{ }new\text{ }shape}{dimension\text{ }original\text{ }shape}[/tex]Use dimension of corresponding sides AB and ED:
[tex]sf=\frac{2}{4}=\frac{1}{2}[/tex]Then, the scale factor is 1/2___________After the dilation the figure is reflected across the y-axis_____________
Then, the triangle is translated one unit to the right and 3 units up [+1,+3] or [1,3]how many cheese pizzas can the girls buy if they pool all their money together? inequality form for each scenario. CHEESE PIZZA IS 7.25 DOLLARS.
Since we have 5 girls and their parents give each other $10, they have in total $50.
Now, let x be the number of pizzas they buy, since each pizza cost $7.25 the total cost for x pizzas is:
[tex]7.25x[/tex]this should be less or equal to $50 (otherwise the girls go over budget), then the inequality that represents this situation is:
[tex]7.25x\leq50[/tex]Now, solving the inequality we get:
[tex]\begin{gathered} 7.25x\leq50 \\ x\leq\frac{50}{7.25} \\ x\leq6.9 \end{gathered}[/tex]Therefore, they can buy a maximum of 6 pizzas without going over budget.
what is the domain of this exponential function y=2x-8+2
The given function is
[tex]y=2^{x-8}+2[/tex]The domain is all real numbers, but the range would be all the real numbers greater than 2 because the function approximates to y = 2.
Hence, the answer is the first option.can you help me with discount tax tip and markup
Answer:
Final Price = $24.5
Explanation:
To found the final price, we first need to find 30% of $35 as follows:
[tex]35\times30\text{ \% = 35}\times\frac{30}{100}=10.5[/tex]So, there will be a discount of $10.5
Then, the final price will be the original price less the 30% of $35, so the final price will be equal to:
Final Price = Original Price - Discount
Final Price = $35 - $10.5
Final Price = $24.5
So, the answer is $24.5
<1 and <2 are complementary angles. the measure of <1 is 55°. the measure of <2 is 5(x+1)°.find the value of x.
Answer:
Step-by-step explanation:
Answer 29
A library give every employee a $500 bonus. What effect, if any does it have on(a) mean (b) median (c) mode (d) Standard division
The mean is the
sum of salaries/number of employees
Assuming the salaries of 5 employees were
1000, 2000, 3000, 4000, 4000
Mean = (1000 + 2000 + 3000 + 4000, 4000)/5 = 2800
If we add a bonus of $500 to each, we have
1500, 2500, 3500, 4500, 4500
Mean = (1500 + 2500 + 3500 + 4500 + 4500)/5 = 3300
Thus, the mean increases
The median is the middle value
The middle value was 3000, the new median is 3500
The median increases
The mode is the value with the highest frequency. The former mode is 4000. The new mode is 4500
the mode increases
The standard deviation is how far the values are from the mean
Standard deviation = Square root of the square of (each value - mean)/ number of values. Thus, we have
[tex]undefined[/tex]
Find the degree of the polynomial.2x6 − 4x2 + 3x − 1
Given:
There are given the equation:
[tex]f(x)=2x^6-4x^2+3x-1[/tex]Explanation:
According to the question, we need to find the degree.
So,
From the concept of degrees:
The degree is the largest exponent of the variable.
Final answer:
Hence, the value of the degree is 6.
In the similaritytransformation of AABCto ADEF. ABC was dilatedby a scale factor of 1/2reflected across the !? 1,and moved through thetranslation [1.
Solution: C. Y-Axis
Analysis: In this case, the triangle is reflected across the Y-Axis. That's the reason why the triangle changes the orientation of the initial triangle.
Example: Point B reflects Point E. X=2 to X=-2. And the value of Y stands.
Vera cut a piece of fabric into 5 equal-length pieces. Then she cut another 3 centimeters off one piece, leaving 6 centimeters of fabric. How many centimeters long was her original piece of fabric? Write two equations with letters for the unknowns. Solve.
We have
fabric cut into 5 equal -length pieces
she cut 3 cm
l=length of one piece of the 5 equals pieces
l=6+3
l=9
the original piece of fabric is
o= length of the original fabric
o=5l
o=5(9)
o=45 cm
the original piece of fabric is 45 cm
in a 30 60 90° triangle giving the short leg equals 5 find a hypotenuse of the triangle
To answer this question we need to remember that the longest and shortest side in any triangle are always opposite to the largest and smallest angle, respectively.
With this in mind we can draw the triangle:
Now, we need to find the hypotenuse. To do this we can use the cosine function for the angle 60. Remember that the cosine function is given as:
[tex]\cos \theta=\frac{\text{adj}}{\text{hyp}}[/tex]In this case we have that:
[tex]\begin{gathered} \cos 60=\frac{5}{\text{hyp}} \\ \text{hyp}=\frac{5}{\cos 60} \\ \text{hyp}=10 \end{gathered}[/tex]Therefore the hypotenuse is 10.
Aaquib can buy 25 liters of regular gasoline for $58.98 or 25 liters of permimum gasoline for 69.73. How much greater is the cost for 1 liter of premimum gasolinz? Round your quotient to nearest hundredth. show your work :)
The amount by which the cost of 1 liter of permimum gasoline is greater is $0.43.
By how much is permimum gasoline greater?The first step is to determine the cost of 1 liter of each type of gasoline. In order to determine the cost of 1 liter, divide the total cost by the number of liters of gasoline bought.
Cost of 1 liter of gasoline = total cost / total liters bought
Cost of 1 liter of regular gasoline = $58.98 / 25 = $2.36
Cost of 1 liter of permimum gasoline = $69.73 / 25 = $2.79
Difference in price = $2.79 - $2.36 = $0.43
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How do I Graph the line with the given slope m and y-intercept b.
M=-4/3,b=2
I need help, I don’t know which one would have factors of 5x-8
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
factor:
5x - 8
Step 02:
difference of squares:
(5x - 8)(5x + 8) = 25x² - 64
The answer is:
25x² - 64
14 Tom can whitewash a fence alone in 4 hours, and Huck can whitewash the same fence in 5 hours working by himself. Tom whitewashes with Huck for 1 hour and then leaves. How long will it take Huck to finish whitewashing the fence?
Given:
Time it takes Tom = 4 hours
Time it takes Huck = 5 hours
Tom then whitewashes with Huck for 1 hour and then leaves.
Let's find how long it will take Huck to finish whitewashing the fence.
We have:
Tom's rate = 1/4
Huck's rate = 1/5
Total rate:
[tex]\frac{1}{4}+\frac{1}{5}=x[/tex]Now, let's find the time it will take them to whitewash together.
[tex]\begin{gathered} \frac{1}{T}=\frac{5+4}{20} \\ \\ \frac{1}{T}=\frac{9}{20} \\ \\ T=\frac{20}{9} \\ \\ T=2.22 \end{gathered}[/tex]It will take them 2.22 hours to whitewash together.
Now they both whitewash together for 1 hour before Huck leaves.
We have:
[tex]2.22-1=1.22[/tex]When Huck leaves after one hour, the time left for both of them to finish together is 1.22 hours.
Since only Huck will finish whitewashing the fence, the time it will take him will be:
[tex]5(1-\frac{1.22}{2.22})=2.25[/tex]Therefore, it will take Huck to finish whitewashing the fence is 2.25 hours.
ANSWER:
2.25 hours
In 2002, the population of Isosceles City was 200,000. If expected growth is 10% per year, what will the expected population be in 2010?
The expected population in [tex]2010[/tex] will be [tex]428,717.762[/tex].
In [tex]2002[/tex] the population of Icosceles city was [tex]200,000[/tex].
The expected growth per year [tex]=10%[/tex]%
We have to find the expected population in [tex]2010[/tex].
From [tex]2002[/tex] to [tex]2010[/tex] the total years are [tex]8[/tex].
Since the population is increased every year so the population of previous year added. So we can see that the population is increased compound. We can find the total population by multiplying the population in 2002 with the rate assembled by one. So we can use the formula
Total population in [tex]2010=[/tex]Population in [tex]2002(1+\frac{rate}{100})^{year}[/tex]
Total population in [tex]2010=[/tex] [tex]2010=200,000(1+\frac{10}{100})^{8}[/tex]
Total population in [tex]2010=200,000(1+\frac{1}{10})^{8}[/tex]
Total population in [tex]2010=200,000(\frac{11}{10})^{8}\\[/tex]
Total population in [tex]2010=200,000(\frac{214,358,881}{100000000} )[/tex]
Total population in [tex]2010=200,000(2.14,358,881)[/tex]
Total population in [tex]2010=428717.762[/tex]
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A) equation in center radius form B) equation in general form
The equation of a circle in center-radius form, is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]-Where the coordinates of the center of the circle are (h,k) and the radius of the circle is r.
From the given graph, we can see that the coordinates of the center are (-2,4) and the radius of the circle is 2.
a)
To determine the equation of the circle in center-radius form, replace h=-2, k=4 and r=2
[tex]\begin{gathered} \Rightarrow(x-(-2))^2+(y-(4))^2=2^2 \\ \Rightarrow(x+2)^2+(y-4)^2=4 \end{gathered}[/tex]Therefore, the equation of the circle in center-radius form is:
[tex](x+2)^2+(y-4)^2=4[/tex]b)
To find the equation of the circle in general form, expand the parentheses and take all the terms to the left member:
[tex]\begin{gathered} (x+2)^2+(y-4)^2=4 \\ \Rightarrow x^2+2(2)(x)+(2)^2+y^2-2(4)(y)+4^2=4 \\ \Rightarrow x^2+4x+4+y^2-8y+16=4 \\ \Rightarrow x^2+4x+y^2-8y+20=4 \\ \Rightarrow x^2+4x+y^2-8y+20-4=0 \\ \Rightarrow x^2+4x+y^2-8y+16=0 \end{gathered}[/tex]Write the quadratic terms first:
[tex]\Rightarrow x^2+y^2+4x-8y+16=0[/tex]Therefore, the equation of the circle in general form, is:
[tex]x^2+y^2+4x-8y+16=0[/tex]9. As a speed skater, Kyle cycles between sprinting and recovering on the 111.12-meter short track during practice every day for 50 minutes. Let t be the time in hours that Kyle sprints during a practice. A. Write the unsimplified expression to represent the total distance Kyle skates. It may help you to make a verbal model to represent the total distance Kyle skates. Be sure to use compatible units.
SOLUTIONS
As a speed skater, Kyle cycles between sprinting and recovering on the 111.12 meter short track during practice every day for 50 minutes.
Let t be the time in hours that Kyle sprints during practice.
Sprint Speed: 48 km/hr
Recovery: 18 km/hr
(a)
Write an unsimplified expression to represent the total distance Kyle skates.
[tex]speed=\frac{distance}{time}[/tex]If t= time sprinting then (50-t)= time recovering
Distance = rate x time= t(48) + (50-t)18
Distance = 111.2m
(c) Simplifying the expression
Hey there Mr or Ms could you help me out here with this problem? Just a head up this isn't a quiz, it's my homework assignment for today it's about Squares and Rhombi.
please see the attched figure o better understand the problem
Applying the Pythgorean Theorem
d^2=b^2+b^2
we have
b=10 units
substitute
d^2=10^2+10^2
d^2=100+100
d^2=200
[tex]d=\sqrt[]{200}[/tex]simplify
[tex]d=10\sqrt[\text{ }]{2\text{ }}\text{ units}[/tex]the diagonal is
[tex]d=10\sqrt[\text{ }]{2\text{ }}\text{ units}[/tex]1/4×3/2×8/9 whats the answer?
Multiply the given fractions to find the answer, use the given example:
Now, solve the given multiplication:
[tex]\frac{1}{4}\cdot\frac{3}{2}\cdot\frac{8}{9}=\frac{1\cdot3\cdot8}{4\cdot2\cdot9}=\frac{24}{72}=\frac{1}{3}[/tex]The answer is 1/3.
Adele opens an account with $140 and deposits $35 a month. Kent opens an account with $50 and also
deposits $35 a month. Will they have the same amount in their accounts at any point? If so, in how many
months and how much will be in each account? Complete the explanation.
have the same amount in their accounts at a certain point. Setting the expressions equal
which is (select)
and solving them gives 140=
They (select)
to each other gives 140 + 35x =
View Exampl
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Answer: No
Step-by-step explanation:
If Adele opens an account with more money than Kent, and they deposit the same amount each month, Adele will always have more money than Kent.
Find the average rate of change of the following function from t = 1 to t=2.5h(t) = 148 – 16t
The average rate of change of the function from t=1 to t=2.5 is given by:
[tex]\frac{h(2.5)-h(1)}{2.5-1}=\frac{h(2.5)-h(1)}{1.5}[/tex]It is given that:
[tex]\begin{gathered} h(t)=148-16t \\ h(2.5)=148-16\times2.5=108 \\ h(1)=148-6=142 \end{gathered}[/tex]Substitute the values to get:
[tex]\frac{h(2.5)-h(1)}{1.5}=\frac{108-142}{1.5}=\frac{-68}{3}\approx-22.6667[/tex]Hence the rate of change is -22.6667.
Choose all true inequalities from the list below.3 < 8-8 < -3-5 < -2118 > 4
ANSWER and EXPLANATION
We want to identify which of the inequalities are correct.
For the inequality to be correct, the left and right-hand sides of the inequality must agree with
Using the Distributive Property, which of the following expressions are equivalent to 7 x 6? Select all that apply. A. (6 x 7)+(6 x 7)
B. (5×6) + (2 × 6)
C. (7 x 6) + (1 x 6)
D. (7 x 6) + (2 x 6)
E. (2 x 6)+(5 x 6)
By using the Distributive Property, the equivalent expression to 6 x 7 is option (B) (5 x 6) + (2 x 6) and option (E) (2 x 6) + (5 x 6).
Distributive property:
The distributive Property defines that when a factor is multiplied by the addition of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition operation.
This property can be stated symbolically as:
A ( B+ C) = (A x B) + (A x C)
Where A, B and C are three different values.
Given,
Here we have the expression 7 x 6.
Now, we need to find the equivalent expression by using the distributive expression.
AS per the definition of distributive property,
First we have o identify in which term is got separated,
Here they separated the term 7.
So, there three way for dividing it,
They are,
6 + 1 = 7
2 + 5 = 7
3 + 4 = 7
Based on these, we have two way to write the expression,
one is,
(5 x 6) + (2 x 6)
Another way is,
(2 x 6) + (5 x 6)
So, the correct options are option (B) and (E).
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Can u guys simplify this?
(2x^-3y^5)^2*(x^7y^-11)
how much of each ingredient would you need to make an identical recipe that serves 8 people explain your reasoning
LITERS OF SODA
24 people calls for 4 liters of lemon soda
18 people calls for x liters of lemon soda
24 people = 4 liters
18 people = x
cross multiply
24x = 72
Divide both-side of the equation by 24
x = 3
18 peoples calls for 3 liters of soda
PINT OF SHERBET
24 people calls for 2 pint of sherbet
18 people calls for x pint of sherbet
24 people = 2 pint
18 people = x
cross-multiply
24x = 36
Divide both-side of the equation by 24
x =1.5
18 peoples calls for 1.5 pint of sherbet
CUPS OF RICE
24 peoples calls for 6 cups of rice
18 people calls for x cups of rice
24 people = 6 cups of rice
18 people = x
cross multiply
24x = 108
Divide both-side of the equation by 24
x=4.5
18 people calls for 4.5 cups of rice
Hence, 18 people calls for; 3 liters of soda, 1.5 pint of sherbet and 4.5 cups of rice