Answer:
y = -2x-13
1) plot the coordinate you have on a graph (starting at (0,0) move to the left until you hit -8 and then up until you are at +3)
2) Since your slope is negative the line will be higher on the left and lower on the right, so starting at the point you have plotted move down 2 units and to the right one unit.
3) Do this until you intersect with the y-axis (at -13), this is your value for 'b'
4) Plug your values for 'b' and 'm' into the slope-intercept equation
Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio
A(-3,2), B(5,-4); 2 to 6
QUICK I NEED IT BEFOR# MONDAY
The ordered pair P within the line segment AB is (- 1, 1 / 2).
What is the location of an ordered pair within a line segment?
In this question we have a segment whose endpoints are known: A(x, y) = (- 3, 2), B(x, y) = (5, - 4), and in which we need to determine the location of point P such that the following relationship is known:
k = AP / PB
[tex]\overrightarrow {AP} = k \cdot \overrightarrow {PB}[/tex]
P(x, y) - A(x, y) = k · [B(x, y) - P(x, y)]
(k + 1) · P(x, y) = A(x, y) + k · B(x, y)
P(x, y) = [1 / (k + 1)] · A(x, y) + [k / (k + 1)] · B(x, y)
Where:
A(x, y), B(x, y) - Endpoints of the line segment.P(x, y) - Ordered pair of a line segment.k - Segment ratio.If we know that A(x, y) = (- 3, 2), B(x, y) = (5, - 4) and k = 1 / 3, then the location of the ordered pair is:
P(x, y) = [1 / (4 / 3)] · (- 3, 2) + [(1 / 3) / (4 / 3)] · (5, - 4)
P(x, y) = (3 / 4) · (- 3, 2) + (1 / 4) · (5, - 4)
P(x, y) = (- 9 / 4, 6 / 4) + (5 / 4, - 1)
P(x, y) = (- 9 / 4, 3 / 2) + (5 / 4, - 1)
P(x, y) = (- 1, 1 / 2)
The ordered pair P is (- 1, 1 / 2).
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you were asked to find the value of z such that 0.05 of the area lies to the right of z. see below for graphical and symbolic representations of the problem.
The value of z such that 0.05 of the area lies to the right of z is 1.64.
Given:
0.05 = 5%
The z score is calculated:
z = x - μ / σ
from the t table the value of z is:
= 1.64
More details is in the image uploaded.
Therefore the value of z such that 0.05 of the area lies to the right of z is 1.64.
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Part A: The area of a square is (16x2 − 8x + 1) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points)
Part B: The area of a rectangle is (81x2 − 4y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)
The length of each side of the square is 4x - 1 while the area for the dimensions of the rectangle is (9x + 2y) by (9x - 2y) using the factorization methods of grouping and difference in two squares respectively.
Factorisation by grouping and difference in two squaresFactorization is the process of breaking down a number in which when multiplied together will arrive at the original number.
Part A: Given the area of square as 16x² - 8x + 1, applying factorization by grouping;
16x² - 8x + 1 = 16x² - 4x - 4x + 1 (group terms with common factors)
16x² - 8x + 1 = 4x(x - 1) - (4x - 1) (factor out the common factor in each group)
16x² - 8x + 1 = (4x - 1) × (4x - 1) (factor the common factor from the expression)
16x² - 8x + 1 = (4x - 1)²
Part B: For the area or rectangle given as 81x² - 4y², factorizing by the method of difference in two squares;
81x² - 4y² = 9²x² - 2²y² (express as squares)
81x² - 4y² = (9x)² - (2y)²
81x² - 4y² = (9x + 2y) × (9x - 2y)
Therefore, 4x - 1 is the length of one side of the square as all sides of a square are equal and (9x + 2y) by (9x - 2y) is the dimension of the rectangle using the factorization methods of grouping and difference in two squares.
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The perimeter of a park is 10 km . A wall is being constructed around it . If 4/5 of the wall has been constructed , how much part of the wall is incomplete
Perimeter of the park = 10km
Part of the wall's construction completed =
[tex] \frac{4}{5}th \: of \: perimeter [/tex]
=
[tex] \frac{4}{5} \times 10[/tex]
(cancel 5 and 10)
=
[tex] \frac{4}{1} \times 2[/tex]
= 8km
•.• Part of the wall left (to be constructed) = 10km - 8km = 2km
HOPE THIS HELPS YOU
Derek has $80 to spend on used books. Hardcover books cost $10 each, and paperbacks cost $20 each. Complete the equation which determines the number x of hardcover books and the number y of paperback books he can buy.
find the tension in each string and the acceleration of the 3-box system below if there is no friction
Tension in each string in the 3 - box system is T1 = m2 * f/m, T2 = m3 *f/m, a = f/m1+m2+m3.
In 3 - box system:
There are two tensions and two strings, let T1 and T2 be the tensions.
Let mass of boxes be m1,m2,m3
total mass m = m1+m2+m3
Acceleration a = force / m
a = f/m1+m2+m3
T1 = m2 * f/m
T2 = m3 * f/m.
Therefore Tension in each string in the 3 - box system is T1 = m2 * f/m, T2 = m3 *f/m, a = f/m1+m2+m3.
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Andrea earns $60 per day plus $4 for every sale she makes. On Wednesday, she wants to earn at least $128. Which best
describes the number of sales she needs to make to reach her goal?
at least 47 sales
at most 47 sales
at most 17 sales
at least 17 sales
Answer:
at least 17 sales
Step-by-step explanation:
On Wednesday she wants to earn 128.
Per day value = 60
128-60=68
She still needs to earn 68.
68 divided by 4=The number of sales needed to get 68 dollars=17
Thus she needs to make at least 17 sales, at most means maximum but she wants to earn AT LEAST 128 which means she wants more thus, answer is 4th option.
(1 point) a cylinder is inscribed in a right circular cone of height 2.5 and radius (at the base) equal to 7.5. what are the dimensions of such a cylinder which has maximum volume?
For the given data about about inscribed right circular cone of height 2.5 units and radius 7.5 units then the dimensions of the cylinder which has maximum volume is given by height = 0.83 units and radius 5 units.
As given in the question,
Height of the right circular cone = 2.5 units
And radius of right circular cone = 7.5 units
Let r be the radius of the cylinder and h be the height of the cylinder.
Volume of a cylinder 'V' = π r² h
Cylinder is inscribed in right circular cone
From origin edge cylinder is inscribed at x distance in right circular cone.
r = 7.5 - x
h = (2.5 /7.5) x
= x/3
V = π ( 7.5 - x )² ( x / 3)
⇒ V = π ( x² -15x + 56.25 ) (x/3)
⇒ V = (π /3)( x³ - 15x² + 56.25x)
For maximum volume ,
dV/dx = 0
dV/dx = (π/3)( 3x² -30x + 56.25)
(π/3) ≠ 0
⇒ 3x² -30x + 56.25 = 0
⇒ 3 ( x² -10x + 18.75) = 0
3 ≠ 0
⇒ x² -10x + 18.75 = 0
x = [ - (-10) ± √ (-10)² -4(1)(18.75)]/2(1)
⇒ x = [ 10 ± √ 100 -75]/2
⇒ x= ( 10 ± 5 ) / 2
⇒ x = 7.5 or 2.5
As r = 7.5 -x
Hence x ≠ 7.5
r = 7.5 -2.5
= 5 units
h = x/3
= 2.5/3
= 0.8333 units
Therefore, for the given data about about inscribed right circular cone of height 2.5 units and radius 7.5 units then the dimensions of the cylinder which has maximum volume is given by height = 0.83 units and radius 5 units.
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Helllppp 30 points pleases
Answer:
D
Step-by-step explanation:
Unit rates always compare quantities with different units
Ex. 10 km per 1 hour (10kph)
Two parallel lines are cut by a transversal as shown below. Suppose m4=83°. Find m5 and m7
The angles found by the given figure are:
m∠5 = 97°
m∠7 = 97°
From the graph given we can get that the two parallel lines are cut by a transversal and:
m ∠4 = m∠2
m∠2 = 83°
hence, m∠2 + m∠5 = 180°
so,:
m∠5 = 180° - m∠2
= 180 - 83
= 97°
hence m∠5 = 97°
now, m∠7 = m∠5
since the vertical angles of two increasing lines are equal
so, m∠7 = 97°
Hence we get the two angles respectively.
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When Richard turned 15, he deposited $1,500.00 in a savings account with an interest rate of 7% that is compounded daily. How much money will Richard have when he turns 27?
The amount of money that Richard will have when he turns 27 can be found to be $3, 474.26
How to find the amount compounded to?Convert the interest rate to a periodic rate which will be in days as the interest is compounded daily:
= 7% / 365 days a year
= 0.019178%
The number of periods is:
= (27 - 15) years x 365 days a year
= 4, 380 days
The money that Richard will have when he turns 27 is:
= 1, 500 x ( 1 + 0.019178%) ⁴³⁸⁰
= $3, 474.26
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a sample of 400 observations will be taken from an infinite population. the population proportion equals 0.8. find the probability that the sample proportion will be greater than 0.78.
The probability that the sample proportion will be greater than 0.78 is:
78% of 400 is 0.78× 400 = 312.
So this probability is 1 subtracted by the p value of Z when x = 312
Z = (X - μ)/σ
We are going to approximate the binomial distribution to the normal.
Binomial probability distribution-
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
E(X) = np
The standard deviation of the binomial distribution is:
√V(X) = √np(1 - p)
Normal probability distribution-
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation o, the zscore of a measure X is given by:
Z = (X-μ)/σ
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z- score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that-
μ = E (X), σ = √V√(X).
In this problem, we have that:
n=400, p=0.8
So = E(X)=np=400-0.8=320
σ = √V(X) = √np(1-p)=√400×√0.8×√0.2=8
Hence, the probability that the sample proportion will be greater than 0.78 is:
78% of 400 is 0.78× 400 = 312.
So this probability is 1 subtracted by the p value of Z when x = 312
Z = (X - μ)/σ
Z = (312- 320)/8.
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An appliance technician charges a fixed amount for a repair, plus an additional amount per hour. The equation below describes y, the total amount the technician charges, in dollars, for a repair that takes x hours. y = 20x + 50
What is the meaning of the y-intercept of the equation?
A. It means the technician charges a fixed amount of $20 for the repair. B. It means the technician charges $50 per hour for the repair.
C. It means the technician charges $20 per hour for the repair.
D. It means the technician charges a fixed amount of $50 for the repair.
The y-intercept of the equation means: D. It means the technician charges a fixed amount of $50 for the repair.
How to Interpret the Y-intercept of an Equation?The y-intercept of an equation that models a situation is the initial or starting value. The y-intercept is represented in an equation that is expressed in slope-intercept form, y = mx + b, as "b". The value of "b" is the y-intercept.
Therefore, we are given that y = 20x + 50 represents the total amount the technician charges, in dollars, for a repair that takes specific hours. This implies that:
x = hoursy = total amountm = 20, which is the additional amount per hour.b = 50 = y-intercept, which is the starting value that represents the fixed amount for a repair that the technician charges.Therefore, y-intercept, b = 50, means: D. It means the technician charges a fixed amount of $50 for the repair.
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1. Two families brought all their cats and dogs
into the vet this morning. The first family
brought in 2 cats and 3 dogs and paid $195.
The second family brought in 4 cats and
dog and paid $165. Wifite the two equations
and solve for the cost of a cat visit and a dog
visit at the vet.
Answer:
cat = $30
dog = $45
Step-by-step explanation:
write the equation, assume cat = c, dog = d1
2c + 3d = 195 -> eq 1
4c + d = 165 -> eq 2
rewrite eq 2 so that dog is in term of cat
d = 165 - 4c -> eq 3
replace eq 3 into eq 1
2c + 3(165-4c) = 195
2c + 495 - 12c = 195
2c - 12c = 195 - 495
-10c = -300
c = -300/-10 = 30
replace c in eq 3
d = 165 - 4(30) = 165 - 120 = 45
PLEASE HELP HURRY
Find the area of the figure below composed of a rectangle and a semicircle round to the nearest tenth place 8 10
The area of the composed rectangle and the semicircle is 92.56 square units.
Area of rectangle and semicircle
The formula for the Area of a Rectangle.
A = l × w.
where l refers length and w refers width of the rectangle
The area of a semicircle refers the half of the area of the circle. Therefore, the area of a semicircle is 1/2(πr²), where r is the radius.
Given,
Here we have the figure below composed of a rectangle and a semicircle And we need to find the area of this figure then round to the nearest tenth place.
Here we know the following values,
Length of the rectangle = 10
Width of the rectangle = 8
Diameter of the circle = 8
Through the given diameter we have identified the radius as 4.
Now, the area of the rectangle is calculated as,
A = 10 x 8
A = 80 square units.
Similarly, the area of the semicircle is
A = 1/2 (π x 4²)
A = 1/2 x π x 8
A = π x 4
We know the value of π = 3.14, then the area of the semicircle is,
A = 3.14 x 4
A = 12.56 square units.
Therefore, the are of the figure is,
Total area = area of rectangle + area of semicircle
Total area = 80 + 12.56
Therefore, the total area of the figure is 92.56 square units.
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Kenny has 2 red marbles and 4 black marbles which ration compares a part to a whole
The ratio which compares to be a whole is:
2/9
Given,
Kenny has 2 red marbles and 4 black marbles.
we are asked to determine the ratio which compares a part to whole.
Based on the given conditions, formulate:
2 ÷ (4+2+3)
Calculate the sum
2/6+3
calculate the sum:
2/9
hence ratio is:
2/9
Hence we get the ratio as 2/9.
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joy organised a large wedding guests had to choose there meals from beef chicken or vegetarian
1/3 of the guests chose beef
5/12 of the guests chose chicken
69 Of the guests chose vegetarian
How many guests were in the wedding?
There were total 276 guests in the wedding that Joy organised.
Given,
fraction of the guest that chose beef = 1/3
fraction of the guest that chose chicken = 5/12
fraction of the guest that chose vegetarian = 1 - 1/3 - 5/12 = 1/4
we are asked to find the total number of guests in the wedding:
guests that chose vegetarian = 1/4
guests that chose vegetarian = 69
1/4 of the guest = 69
4/4 of the guest = 69 x 4 = 276
Hence there are total 276 guests in the wedding.
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Which expression represents the total cost for mrs.Alvarez to rent skis for s days and poles for p days
At the ski shack, customers can rent,skis, snowboards, boots, and poles by the day Mrs.Alvarez is renting skis and poles she has a 18$ coupon off
which expression represents the total cost for Mrs.Alvarez to rent skis for s days and poles for p days
If the answer you asked is this:
48s+12p-18 the correct answer
The radius of the earth is approximately 6400 km. The equator is the circle around the earth dividing it into the northern and southern hemisphere. (The center of the earth is also the center of the equator.) What is the length of the equator? (numerical answer only; no units)
The length of the equator is 40192 km.
How to find the length of the equator?The radius of the earth is approximately 6400 km. The equator is the circle around the earth dividing it into the northern and southern hemisphere.
Let's find the length of the equator as follows:
The length of the equator is the circumference.
Therefore,
L = 2πr
where
r = radiusL = 2 × 3.14 × 6400
L = 6.28 × 6400
L = 40192 km
Therefore, the equator which is the circle around the earth has a length of 40192 km.
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given that sinx =3/5=x=90. evaluate (tan x+2cosx)
The value of (tanx+2cosx) = [tex]2\frac{7}{20}[/tex].
Given that
sinx = [tex]\frac{3}{5}[/tex]
sinx = [tex]\frac{opp}{hyp}[/tex]
Using the Pythagoras' theorem
[tex]hyp^{2} = opp^{2} + adj^{2} \\\\adj^{2} = 5^{2}- 3^{2} \\ \\= 25-9\\\\adj^{2} = 16\\ \\adj = \sqrt{16} \\[/tex]
adj = 4.
Now we have to find out tanx and cosx
[tex]tanx = \frac{opp}{adj}[/tex]
[tex]= \frac{3}{4}[/tex]
[tex]cosx = \frac{adj}{hyp}\\ \\= \frac{4}{5}[/tex]
Now we have to find out the given equation (tanx+2cox)
[tex]= \frac{3}{4} +2(\frac{4}{5})\\ \\= \frac{15+32}{20} \\\\= \frac{47}{20} \\\\or\\\\= 2\frac{7}{20}[/tex]
Hence the answer is the value of (tanx+2cosx) = [tex]2\frac{7}{20}[/tex].
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) a sector of a circle of radius 24 m has an area of 288 m2. find the central angle of the sector in radians.
The Central Angle of the sector in radians is 0.3184 π .
In the question ,
it is given that ,
the radius of the sector = 24 m
the area of the sector = 288 m²
we know that the Area of the sector of the circle is given by the formula
Area = πr²(θ/360)
Substituting the values , we get
288 = (3.14)*(24)²*(θ/360)
θ = (288*360)/((3.14)*(24)²)
θ = 1,03,680/1808.64
θ = 57.32°
converting the angle to radian ,
we get
θ = 57.32° × π/180 radian
= 0.3184 π
Therefore , The Central Angle of the sector in radians is 0.3184 π .
The given question is incomplete , the complete question is
A sector of a circle of radius 24 m has an area of 288 m² . find the central angle of the sector in radians .
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6 times a number is 7 less than the square of that number. Find the positive solution.
Answer: x = 7
Step-by-step explanation: 6x = x^2 - 7
x^2 - 6x -7 =0
(x-7) (x+1) = 0
x = 7
x = -1 ----> rejected
The positive solution of the required number is 7.
What is an expression?An expression is a grouping of one or more mathematical or logical operators, operands (values, variables, or other expressions), and brackets in mathematics and computer programming that denote a computation that can be evaluated to generate a value.
Let's start by translating the given sentence into an equation. Let "x" be the number we are trying to find. Then we can write:
6x = x² - 7
Now we need to solve for x. Let's rearrange the equation to get all the x terms on one side and all the constant terms on the other side:
x² - 6x - 7 = 0
We can solve this quadratic equation by factoring or using the quadratic formula, but let's use factoring for this problem. We need to find two numbers whose product is -7 and whose sum is -6. The two numbers are -7 and 1, so we can write:
(x - 7)(x + 1) = 0
This means that either x - 7 = 0 or x + 1 = 0. Solving for x, we get:
x = 7 or x = -1
Since we are looking for a positive solution, the answer is x = 7. Therefore, the positive solution is 7.
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A retaurant cutomer left $1. 65 a a tip. The tax wa 6% and the tip wa %15 of the cot including tax. What wa the total bill?
A retaurant cutomer left $1. 65 a tip. The tax was 6% and the tip was %15 of the cot including tax. Then the total bill is $13.31.
In the given question we have to find the total bill of the customer.
A retaurant cutomer left $1. 65 a a tip.
The tax was 6% and the tip was 15% of the cost including tax.
The tip was 15%(0.15) of the cost including tax.
Thus 0.15*X= 1.65
Divide both sides of the equation by 0.15.
x = 11
Now 6%(0.06) tax on meal at 11 is
11* 0.06 = 0.66
So the total bill cost = 6% tax on meal + 15% tip on meal+cost of meal
The total bill cost = $1.65 + $11+0.66
The total bill cost = 13.31
A retaurant cutomer left $1. 65 a tip. The tax was 6% and the tip was %15 of the cot including tax. Then the total bill is $13.31.
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a box of volume 252 m3 with a square bottom and no top is made of two different materials. the cost of the bottom is $40/m2 and the cost of the sides is $30/m2. find the dimensions of the box that minimize the total cost.
The dimensions of the box that minimizes the total cost is side of the square base is 7.23 m and height of the box is 4.82 m .
In the question ,
it is given that ,
the bottom of the box is = square ,
let the side of the square bottom be = "s" ,
so , the base area [tex]=[/tex] s²
let the height of the box [tex]=[/tex] h ,
Volume of the box = height × (base area)
So , the Volume of the box [tex]=[/tex] s²h
given that the volume of the box is 252 m³ , that means
s²h = 252
h = 252/s²
given that the Cost of bottom = $40 per m²
and the Cost of sides = $30 per m²
So , the total cost = 40s² + 30×(4sh)
substituting the value of h= 252/s² , we get
C = 40s² + 120s×252/s²
C = 40s² + 30240/s
to minimize the cost we differentiate with respect to s , and equating it to 0 ,
we get ,
80s - 30240/s² = 0
s³ = 30240/80
s³ = 378
s = 7.23
again differentiating C = 40s² + 30240/s with respect to s , and equating it to 0 ,
we get ,
d²C/ds² = 80 + (30240*2)/s³
at s=7.23 , d²C/ds² > 0
So , the minimum is at s = 7.23 ,
we have h = 252/(7.23)²
h = 4.82 .
Therefore , The dimensions of the box that minimizes the total cost is side of the square base is 7.23 m and height of the box is 4.82 m .
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9. If XYZ LMN, what is the length of XZ?
Answer:
XZ = 21 cm
Step-by-step explanation:
since the triangles are congruent then corresponding sides are congruent, so
LN = XZ , that is
5x - 19 = 2x + 5 ( subtract 2x from both sides )
3x - 19 = 5 ( add 19 to both sides )
3x = 24 ( divide both sides by 3 )\
x = 8
then
XZ = 2x + 5 = 2(8) + 5 = 16 + 5 = 21 cm
A child’s piggy bank has 3 times as many dimes as nickels. Altogether she has 3.85 how many dimes does she have
Step-by-step explanation:
d = number of dimes
n = number of nickels
one dime = $0.10
one nickel = $0.05
d = 3n
0.1×d + 0.05×n = 3.85
0.1×3n + 0.05×n = 3.85
0.3×n + 0.05×n = 3.85
0.35×n = 3.85
n = 3.85 / 0.35 = 11
d = 3n = 3×11 = 33
she has 33 dimes (and 11 nickels).
For a ride on a rental scooter, Boris paid a $2 fee to start the scooter plus 12 cents per minute of the ride. The total bill for Boris's ride was $10.52 . For how many minutes did Boris ride the scooter?
Answer: 119 minutes
Step-by-step explanation:
A system of three linear equations in three variables is consistent and dependent. How many solutions to the system
exist?
Onone
Oone
Othree
O infinitely many
As per the given system of linear equation, the number of solution is infinite.
Linear equations:
An algebraic equation of the form
y = mx + b
Involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept is known as linear equation.
Given,
A system of three linear equations in three variables is consistent and dependent.
Here we need to find the number of solution for this system.
Here we know that the given system of three linear equations in three variables which is consistent and dependent.
We know that, the system is said to be consistent if it has at least one solution. Which means that the system which has no solution is said to be inconsistent.
Similarly, the system is has consistent solution is said to be independent if it has only one solution whereas it is said to be dependent if it has an infinitely many solutions.
Therefore, here the given system of three linear equations in three variables which is consistent and dependent, the system has an infinitely many solutions.
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the sum of two-thirds of a number and twenty
(translating expressions)
Answer:
Step-by-step explanation:
(2/3)20
factorize:(sin alpha + cos alpha) ^ 2 - (sin alpha - cos alpha) ^ 2
After factorizing we get the value as:
4sinαcosα
Given,
we have the expression as:
(sinα + cosα)² - (sinα - cosα)²
open the brackets using the identity of:
(a+b)² = a²+b²+2ab
(a-b)² = a²+b²-2ab
now evaluate:
⇒ sin²α + cos²α + 2sinαcosα - (sin²α + cos²α - 2sinαcosα)
⇒ sin²α + cos²α + 2sinαcosα - sin²α - cos²α + 2sinαcosα
⇒ cancel the like terms
⇒ 2sinαcosα + 2sinαcosα
= 4sinαcosα
hence after factorization we get the value as 4sinαcosα
Learn more about Factorization here:
brainly.com/question/25829061
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