Answer:
43
Step-by-step explanation:
Find the equation of a line with each of the following characteristics. A) Parallel to the line y = 3x + 5 and has a y-intercept of -1 B) Perpendicular to the line y = 5x - 1 and passes through the point (10, 8) C) Perpendicular to the line y = 1⁄3x + 4 and has an x-intercept of 2.
Answer:
A) y = 3x - 1.
B) y = -1/5x + 10.
C) y = -3x + 6.
Step-by-step explanation:
A) It is parallel, so it will have the same slope of 3. The y-intercept is -1.
So, we have y = 3x - 1.
B) It is perpendicular, so it will have the negative reciprocal slope of -1/5.
To find the y-intercept, put the points into the equation.
8 = -1/5(10) + b
8 = -2 + b
b - 2 = 8
b = 10
So, we have y = -1/5x + 10.
C) It is perpendicular, so the slope will have a negative reciprocal of -3. The x-intercept is 2, so it has a point at (2, 0). We put that into the equation.
0 = -3 * 2 + b
0 = -6 + b
b - 6 = 0
b = 6
So, we have y = -3x + 6.
Hope this helps!
Answer:
Equation of a line is y = mx + c
where m is the slope
c is the y intercept
A).y = 3x + 5
Comparing with the above formula
Slope / m = 3
y intercept = - 1
Since the lines are parallel their slope are also the same
Substituting the values into the formula
We have the final answer as
y = 3x - 1B).y = 5x - 1
Slope / m = 5
Since the lines are perpendicular the slope of the line is the negative inverse of the original line
That's
m = - 1/5
Equation of the line using point (10, 8) is
y - 8 = -1/5( x - 10)
y - 8 = -1/5x + 2
The final answer is
y = -1/5x + 10C).y = ⅓x + 4
Slope / m = ⅓
Since the lines are perpendicular the slope of the line is the negative inverse of the original line
That's
m = - 3
Equation of the line using point (2,0) is
y - 0 = -3( x - 2)
We have the final answer as
y = - 3x + 6Hope this helps you
Can you translate a mathematical expression into a verbal expression?
Step-by-step explanation:
An example of a mathematical expression with a variable is 2x + 3. All variables must have a coefficient, a number that is multiplied by the variable. In the expression 2x + 3, the coefficient of x is the number 2, and it means 2 times x plus 3. ... For example, 2x + 3 could also be expressed as 2(x) + 3 or 2 * x + 3. are you talking about this
Which is the best description of the equivalency of the two expressions? Expression 1 Expression 2 5 x squared minus 2 x minus 4 + 6 x + 3 6 x squared minus 6 x + 6 minus x squared + 10 x minus 7 The two expressions are not equivalent because when x = 2, the two expressions do not have the same value. The two expressions are not equivalent because when they are simplified, they do not have the same coefficients for the x squared and x terms. They are equivalent because the sum of the constants is the same in both expressions. They are equivalent because when x = 2, the two expressions have the same value.
Answer:
The correct option is (D).
Step-by-step explanation:
The two expressions are:
[tex]\text{Exp}_{1}=5x^{2}-2x-4+6x+3\\\\\text{Exp}_{2}=6x^{2}-6x+6-x^{2}+10x-7[/tex]
On simplifying both the expressions we get:
[tex]\text{Exp}_{1}=5x^{2}+4x-1\\\\\text{Exp}_{2}=5x^{2}+4x-1[/tex]
Compute the value of both expressions for x = 2 as follows:
[tex]\text{Exp}_{1}=5(2)^{2}+4(2)-1=27\\\\\text{Exp}_{2}=5(2)^{2}+4(2)-1=27[/tex]
The value of both expressions are same for x = 2.
Thus, the correct option is:
"They are equivalent because when x = 2, the two expressions have the same value."
Answer:
d
Step-by-step explanation:
The speed at which a bike travels can be determined by the formula s=d/t, where S represents speed, D represents distance, and T represents time. Select yes or no to indicate if the measurement unit given is an appropriate measurement unit for the speed at which a bike travels
Answer:
Yes, No, Yes
Step-by-step explanation:
Yes for m/s which is meters per second.
No for min/ft which is reversed and should be feet per minute.
Yes for km/h which is kilometers per hour.
The correct unit for speed is distance per time.
Answer:
MPH
Step-by-step explanation:
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(2,−3) B(4,−3) C(4,5) D(2,5) What is the perimeter of rectangle ABCD? please answer URGENT! :)
Answer:
21 unit square
Step-by-step explanation:
First you want to find the length and width of the rectangle using the distance formula:
d=√(x2-x1)²+(y2-y1)²
AB=√(6-3)²+ (-2 - -2)²
AB=√3² + 0
AB=√9
AB=3
BC=√(6-6)²+ (5 - -2)²
BC=√0 + 7²
BC=√49
BC=7
We can find the area by multiplying these two distances together:
A=(3)(7)
A=21 units square.
Hope it helped...... And plz mark BRAINLIEST
Tysm
Which of the following sets contains all roots of the polynomial f(x)=2x^3+3x^2-3x-2?
Answer:
C
Step-by-step explanation:
Given
f(x) = 2x³ + 3x² - 3x - 2
Note that
f(1) = 2 + 3 - 3 - 2 = 0 , thus
(x - 1) is a factor
Dividing f(x) by (x - 1) gives
f(x) = (x - 1)(2x² + 5x + 2) = (x - 1)(x + 2)(2x + 1)
To find the roots equate f(x) to zero, that is
(x - 1)(x + 2)(2x + 1) = 0
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x + 2 = 0 ⇒ x = - 2
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]
The solution set is therefore
{ - 2, - [tex]\frac{1}{2}[/tex], 1 } → C
Plot the points A(−2, − 2), B(4, −2), ( 8, 3) and D(−3, 3 ) on the Cartesian plane. Join them in order and identify the figure so formed. Join AC and BD. Also write the coordinates of the points of intersection of both the diagonals with the X-axis as well as the Y-axis.
Answer:
The shape formed is trapezium
Step-by-step explanation:
Diagonal BD point of intersection with the y-axis = (0, 9) ,
Point of intersection of diagonal BD with the x-axis = (1.2, 0)
Diagonal AC point of intersection with the y-axis = (2, 0),
Point of intersection of diagonal AC with the x-axis = (0, 1)
Length of segment DC = 10.99 ≈ 11
Length of segment AB = 6.04
Length of segment DA = 5.13
Length of segment CA = 6.38
The perimeter of the formed trapezium = 11 + 5.13 + 6.38 + 6.04 = 28.55
The area of the trapezium = 1/2*(sum of parallel sides)*distance between the parallel sides
The parallel sides are DC and AB
The area of the trapezium = 1/2*(6.04+11)*5 = 42.6 unit.
Which of the following Functions is NOT Linear? A:f(x)=x+0.5 B:F(x)=-x+0.5 C: F(x)=x^2-0.5 D: f(x)=0.5x
Answer:
C: F(x)=x^2-0.5
Step-by-step explanation:
When the x is squared it's a parabola. A linear graph is shaped like a straight line, while a parabola is curved inward. I have included a graph of what that function would look like (tap/click on it to see the full graph.)
Answer:
C: f(x) = x² - 0.5Step-by-step explanation:
The grsaph of the linear function is a straight line.
The equation of a line in the slope-intercept fomr is:
y = mx + b
where
m - slope
b - y-intercept
We have:
A: f(x) = x + 0.5
it's a linear function: m = 1, b = 0.5
B: f(x) = -x + 0.5
it's a linear function: m = -1, b = 0.5
C: f(x) = x² - 0.5
it's not a linear function because in the equation is square of x (x²).
The graph of this function is a parabola.
D: f(x) = 0.5x
it's a linear function: m = 0.5, b = 0
why the system of si unit is developed
Step-by-step explanation:
Hi, there!!!!
The main purpose of developing si unit is to have standard unit of measurements and to bring uniformity in whole world in terms of measurements.
I hope it helps you...
Susan has 3 lists, each with 10 numbers. If there are 4 numbers on all three lists and 5 numbers on exactly 2 lists, how many numbers belong to just one list?
Answer:
Susan has 8 numbers belonging to just one list.
Step-by-step explanation:
Susan's 3 lists have 10 numbers each = 10 x 3 = 30 numbers
4 numbers appear on all three lists = 4 x 3 = 12 numbers
The remaining numbers after these 12 = 18 (30 -12)
Then, there are 5 numbers on 2 lists only = 5 x 2 = 10 numbers
The numbers on just one list = 18 - 10 = 8 numbers
Or
List 1 List 2 List 3 Total
Numbers on each list 10 10 10 30
Numbers on 3 lists -4 -4 -4 12
Numbers on 2 lists -5 -5 -0 10
Numbers on 1 list only 1 1 6 8
Please can someone help
Answer:
a) 0
b) 1
c) 0
Step-by-step explanation:
These are common values from the unit circle but you could also just check with your calculator. Just be sure to set it to degree mode and not radian mode.
A box contains 6 red, 3 white, 2 green, and 1 black (total 12) identical balls. What is the least number of balls necessary to take out randomly (without looking) to be sure of getting at least two white balls?
Answer:
10
Step-by-step explanation:
12 total and 3 whites
there is 10 11 and 12.
Frieda worked 26 hours 13 minutes last week. She earns $18.75 per hour. What is Frieda's pay for this work period? Round your answer to the nearest hundredth.
Answer:
$491.56
Step-by-step explanation:
Total number of hours worked by Frieda = 26 hours 13 minutes
lets convert 13 minutes to hour
60 minutes = 1 hour\
1 minutes = 1/60 hours
13 minutes = 13/60 hours
Thus,
Total number of hours worked by Frieda = (26 + 13/60) hours
In 1 hours Freida earns = $18.75
in (26 + 13/60) hours Frieda earns = $18.75((26 + 13/60)) = 487.5 + 4.06
in (26 + 13/60) hours Frieda earns = $491.56 (Answer)
I don't understand this question. Could someone please help me?
Answer:
its answer is a not b
As in Formula
A=3.14*r^2
A =144pift^2
Answer:
144π square feet
Step-by-step explanation:
The garden is shaped like a circle.
To find the area of it we can use the formula of area of a circle.
The formula for area of a circle is:
πr^2
Plug our values in.
π(12)^2
144π
The area of the garden is 144πft^2
Kelly is a waitress and her average tip rate is 18%. After taking a sample of her tips from a week, she thinks her tip rate is actually higher. The data below is the tip rate for 15 randomly chosen checks (the numbers represent percentage). Assume that tip rates are normally distributed.
18.5 18.2 20 21.3 17.9 17.9 18.1 17.5 20 18
a) Express the null and alternative hypotheses in symbolic form for this claim.
H0 : Select an answer
Ha: Select an answer
b) What is the test statistic. Round to 2 decimals.
c) What is the p-value. Round to 4 decimals p-value =
Answer:
Step-by-step explanation:
From the given information:
the null and alternative hypotheses in symbolic form for this claim can be computed as:
[tex]H_o:\mu = 18 \\ \\ H_a : \mu > 18[/tex]
Mean = [tex]\dfrac{18.5+18.2+20+21.3+17.9+17.9+18.1+17.5+20+18}{10}[/tex]
Mean = 18.74
Standard deviation [tex]\sigma = \sqrt{\dfrac{\sum(x_i - \mu)^2}{N}}[/tex]
Standard deviation [tex]\sigma = \sqrt{\dfrac{(18.5 - 18.74)^2+(18.2 - 18.74)^2+(20 - 18.74)^2+...+(18 - 18.74)^2}{10}}[/tex]
Standard deviation [tex]\sigma[/tex] = 1.18
The test statistics can be computed as follows:
[tex]Z= \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z= \dfrac{18.6- 18}{\dfrac{1.18}{\sqrt{10}}}[/tex]
[tex]Z= \dfrac{0.6}{\dfrac{1.18}{3.162}}[/tex]
Z = 1.6078
Z = 1.61
Degree of freedom = n -1
Degree of freedom = 10 -1
Degree of freedom = 9
Using t - calculator at Z = 1.6078 and df = 9
The P - value = 0.0712
In a certain group of students, the probability of a randomly-chosen student being male is 40%, the probability of the student studying Spanish is 18%, and the probability of the student being a male who studies Spanish is 5%. What’s the probability of the student being a male, if you know the student studies Spanish
Answer:
27.8%
Step-by-step explanation:
P(male | Spanish) = P(male and Spanish) / P(Spanish)
P(male | Spanish) = 0.05 / 0.18
P(male | Spanish) = 0.278
The probability of the student being a male is 27.8%
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of sample
Given that in a certain group of students, the probability of a randomly-chosen student being male is 40%, the probability of the student studying Spanish is 18%, and the probability of the student being a male who studies Spanish is 5%.
The probability of the student being a male will be calculated as below:-
P(male | Spanish) = P(male and Spanish) / P(Spanish)
P(male | Spanish) = 0.05 / 0.18
P(male | Spanish) = 0.278
Therefore, the probability of the student being a male is 27.8%
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If I mix 5 gallons of p% boric acid with 5 gallons of water, what is the concentration of the mixture?
Answer: The concentration of the mixture is 0.5 p % .
Step-by-step explanation:
Given: 5 gallons of p% boric acid is mixed with 5 gallons of water.
Amount of boric acid = p% of 5 gallons
[tex]=\dfrac{p}{100}\times5\text{ gallons}= 0.05p\text{ gallons}[/tex]
Total solution : 5 +5 = 10 gallons
then, the concentration of the mixture = [tex]\dfrac{\text{Amount of boric acid in solution}}{\text{Total solution}}\times100[/tex]
[tex]=\dfrac{0.05p}{10}\times100\\\\=0.5p[/tex]
Hence, the concentration of the mixture is 0.5 p % .
Answer:
0.5p% is the answer
how do i wright this as a expression? seven and the quotient of z and eight
8÷7=z and z is the answer you got when you divided,that's how I understand the question
Kate begins solving the equation (6x – 3) = (6x – 4). Her work is correct and is shown below. (6x – 3) = (6x – 4) 4x – 2 = 3x – 2 When she adds 2 to both sides, the equation 4x = 3x results. Which solution will best illustrate what happens to x ?
Answer:
x = 0.
Step-by-step explanation:
4x = 3x
4x - 3x = 0
x = 0
Hope this helps!
The best interpretation of the given equation is x = 0
What is the Equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Given that, Kate begins solving the (6x – 3) = (6x – 4). Her work is correct and is shown below. (6x – 3) = (6x – 4)
4x – 2 = 3x – 2 When she adds 2 to both sides, the equation becomes 4x = 3x
After performing the operations, we get,
4x = 3x
This is only possible when x = 0
Hence, the best interpretation of the given equation is x = 0
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A point H is 20m away from the foot of a tower on the same horizontal ground. From the point H, the angle of elevation of the point (P) on the tower and the top(T) of the tower are 30° and 50° respectively.
( a) draw a diagram to illustrate the information above.
(b) calculate correct to 3 s.f,
( I) /PT/
(ii) the distance between H and the too of the tower.
(III) the position of H if the angle of depression of H from the too of the tower is to be 40°
Answer:
a. See Attachment 1
b. [tex]PT = 12.3\ m[/tex]
c. [tex]HT = 31.1\ m[/tex]
d. [tex]OH = 28.4\ m[/tex]
Step-by-step explanation:
Calculating PT
To calculate PT, we need to get distance OT and OP
Calculating OT;
We have to consider angle 50, distance OH and distance OT
The relationship between these parameters is;
[tex]tan50 = \frac{OT}{20}[/tex]
Multiply both sides by 20
[tex]20 * tan50 = \frac{OT}{20} * 20[/tex]
[tex]20 * tan50 = OT[/tex]
[tex]20 * 1.1918 = OT[/tex]
[tex]23.836 = OT[/tex]
[tex]OT = 23.836[/tex]
Calculating OP;
We have to consider angle 30, distance OH and distance OP
The relationship between these parameters is;
[tex]tan30 = \frac{OP}{20}[/tex]
Multiply both sides by 20
[tex]20 * tan30 = \frac{OP}{20} * 20[/tex]
[tex]20 * tan30 = OP[/tex]
[tex]20 * 0.5774= OP[/tex]
[tex]11.548 = OP[/tex]
[tex]OP = 11.548[/tex]
[tex]PT = OT - OP[/tex]
[tex]PT = 23.836 - 11.548[/tex]
[tex]PT = 12.288[/tex]
[tex]PT = 12.3\ m[/tex] (Approximated)
--------------------------------------------------------
Calculating the distance between H and the top of the tower
This is represented by HT
HT can be calculated using Pythagoras theorem
[tex]HT^2 = OT^2 + OH^2[/tex]
Substitute 20 for OH and [tex]OT = 23.836[/tex]
[tex]HT^2 = 20^2 + 23.836^2[/tex]
[tex]HT^2 = 400 + 568.154896[/tex]
[tex]HT^2 = 968.154896[/tex]
Take Square Root of both sides
[tex]HT = \sqrt{968.154896}[/tex]
[tex]HT = 31.1\ m[/tex] (Approximated)
--------------------------------------------------------
Calculating the position of H
This is represented by OH
See Attachment 2
We have to consider angle 50, distance OH and distance OT
The relationship between these parameters is;
[tex]tan50 = \frac{OH}{OT}[/tex]
Multiply both sides by OT
[tex]OT * tan50 = \frac{OH}{OT} * OT[/tex]
[tex]OT * tan50 = {OH[/tex]
[tex]OT * 1.1918 = OH[/tex]
Substitute [tex]OT = 23.836[/tex]
[tex]23.836 * 1.1918 = OH[/tex]
[tex]28.4= OH[/tex]
[tex]OH = 28.4\ m[/tex] (Approximated)
Simplify the polynomial expressions by combining like terms, and then multiply the resulting
binomial expressions to find their product.
(6x - 9 - 2x)(8 + 5x - 5)
Answer:
The simplified expression is
20x^2 - 33x - 27
Step-by-step explanation:
(6x - 9 - 2x)(8 + 5x - 5)
We must first rewrite the expression as a product of two binomials.
This can be done by adding like terms
(6x - 9 - 2x)(8 + 5x - 5)
We have,
(4x-9)(5x+3)
Multiplying the resulting binomial expression
(4x-9)(5x+3)
(20x^2+12x-45x-27)
Add the like terms
20x^2-33x-27
The simplified expression is
20x^2 - 33x - 27
Twenty x squared minus thirty-three x minus twenty-seven
Answer:
20x^2 - 33x - 27
Step-by-step explanation:
Help it’s urgent please
Answer:
[tex] \frac{5 {x}^{2} + 20xy + 20 {y}^{2} }{x ^{2} - xy - {6y}^{2} } [/tex]
To simplify first factorize both the numerator and the denominator
For the numerator
5x² + 20xy + 20y²
Factor 5 out
5 ( x² + 4xy + 4y²)
Using a² + 2ab + b² = ( a + b)²
The numerator is
5( x + 2y)²
For the denominator
x² - xy - 6y²
Rewrite -xy as a difference
x² + 2xy - 3xy - 6y²
Factorize
We have the denominator as
( x + 2y)( x - 3y)
So we now have
[tex] \frac{5(x + 2y)(x + 2y)}{(x + 2y)(x - 3y)} [/tex]Simplify
[tex] \frac{5(x + 2y)}{x - 3y} [/tex]We have the final answer as
[tex] \frac{5x + 10y}{x - 3y} [/tex]Hope this helps you
find the center of the circle (x-2)^2+(y-8)^2=33
Answer:
The center is (2,8)
Step-by-step explanation:
The equation of a circle is written as
(x-h)^2+ (y-k)^2 = r^2
where ( h,k) is the center and r is the radius
(x-2)^2+(y-8)^2=33
The center is (2,8) and the radius is sqrt(33)
What type of linear system is shown below?
A inconsistent
B. consistent and independent
C. consistent and dependent
D. inconsistent and dependent
Graph is attached , please help
Answer:
The linear system shown on the graph is consistent and independent
Step-by-step explanation:
The linear system shown on the graph is consistent because it has at least one solution which satisfy both linear graphs. The solution is at the point of interception of the two line graphs.
The linear system shown on the graph is independent because the two line graphs are distinct and not parallel or dependent on one another.
Therefore, The linear system shown on the graph is consistent and independent
A lead ball weighs 326 grams. Find the radius of the ball to the nearest tenth of a
centimeter.
Answer:
1.9cm
Step-by-step explanation:
The density d of a material is related to its mass m and volume V as follows;
d = [tex]\frac{m}{V}[/tex] ------------------(i)
The material in question here is the lead ball.
Now, from known experiment;
the density of lead is 11.34g/cm³
From the question, the weight/mass of the lead ball is 326g
Substitute these values into equation (i) as follows;
11.34 = [tex]\frac{326}{V}[/tex]
V = [tex]\frac{326}{11.34}[/tex]
V = 28.75cm³
Now, since the ball is of course spherical, we can get the radius by using the following relation from the volume of a sphere;
V = [tex]\frac{4}{3} \pi r^3[/tex] [V = volume, r = radius]
V = 28.75cm³
=> 28.75 = [tex]\frac{4}{3} \pi r^3[/tex]
=> 3 x 28.75 = 4 π r³
=> 86.25 = 4 π r³
=> 21.5625 = π r³ [Take π = 3.142]
=> 21.5625 = (3.142) r³ [divide both sides by 3.142]
=> 6.86 = r³ [Take the cube root of both sides]
=> ∛6.86 = ∛r³
=> 1.90 = r
Therefore, the radius is 1.9cm to the nearest tenth
One liter of paint is needed to cover all 6 sides of a cubical block. How many liters will be needed to cover all 6 sides of a second cubical block whose edge is twice as long as an edge on the first block?
Will mark brainlist
Answer:
4 liters
Step-by-step explanation:
Let's assume that the side lengths of the cubical block are 2 inches.
This means that one of the sides area is 4 in².
Multiplying this by 6 (for there are 6 sides) gets us 24 in².
So one liter of paint covers 24 in².
Now if the side lengths (edge) of the second block is doubled, that means that the side lengths are [tex]2\cdot2 = 4[/tex] inches.
So the area of one side is 16 in².
Multiplying this by 6 (as there are 6 sides) gets us 96 in².
To find how many liters of paint this will take, we divide 96 by 24.
[tex]96\div24=4[/tex]
So 4 liters of paint will be needed for the second cubical block.
Hope this helped!
find the value of x and y if the distance of the point (x,y) from (-2,0) and (2,0) are both 14 units.
Answer:
[tex] (0, 8\sqrt{3}) [/tex] and [tex] (0, -8\sqrt{3}) [/tex] are both 14 units from points (-2, 0) and (2, 0).
Step-by-step explanation:
distance formula
[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
We want the distance, d, from points (-2, 0) and (2, 0) to be 14.
Point (-2, 0):
[tex] 14 = \sqrt{(x - (-2))^2 + (y - 0)^2} [/tex]
[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]
Point (2, 0):
[tex] 14 = \sqrt{(x - 2)^2 + (y - 0)^2} [/tex]
[tex] \sqrt{(x - 2)^2 + y^2} = 14 [/tex]
We have a system of equations:
[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]
[tex] \sqrt{(x - 2)^2 + y^2} = 14 [/tex]
Since the right sides of both equations are equal, we set the left sides equal.
[tex] \sqrt{(x + 2)^2 + y^2} = \sqrt{(x - 2)^2 + y^2} [/tex]
Square both sides:
[tex] (x + 2)^2 + y^2 = (x - 2)^2 + y^2 [/tex]
Square the binomials and combine like terms.
[tex] x^2 + 4x + 4 + y^2 = x^2 - 4x + 4 + y^2 [/tex]
[tex] 4x = -4x [/tex]
[tex] 8x = 0 [/tex]
[tex] x = 0 [/tex]
Now we substitute x = 0 in the first equation of the system of equations:
[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]
[tex] \sqrt{(0 + 2)^2 + y^2} = 14 [/tex]
[tex] \sqrt{4 + y^2} = 14 [/tex]
Square both sides.
[tex] y^2 + 4 = 196 [/tex]
[tex] y^2 = 192 [/tex]
[tex] y = \pm \sqrt{192} [/tex]
[tex] y = \pm \sqrt{64 \times 3} [/tex]
[tex] y = \pm 8\sqrt{3} [/tex]
The points are:
[tex] (0, 8\sqrt{3}) [/tex] and [tex] (0, -8\sqrt{3}) [/tex]
Find the midpoint of the segment between the points (−5,13) and (6,4)
Answer:
(0.5, 8.5)
Step-by-step explanation:
use this formula ((x1+x2/2), (y1+y2/2)) if you use desmos graphing calculator and you type this formula in, all you have to do it put in the correct numbers and you get your midpoint.
Hope this helped :)
The midpoint of the segment between the points (−5,13) and (6,4) are (0.5 and 8.5)
We have given that, the points (−5,13) and (6,4)
We have to determine the midpoints
What is the formula for the midpoint?((x1+x2/2), (y1+y2/2))
x1=-5,x2=6,y1=13 and y2=4
-5+6/2=1/2=0.5
and next is,
13+4/2=17/2=8.5
The midpoint of the segment between the points (−5,13) and (6,4) are (0.5 and 8.5)
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Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks
Dave and his cousin Emily are picking apples in their grandparents' orchard. Dave has filled 6
baskets with apples and is filling them at a rate of 5 baskets per hour. Emily has 9 full
baskets and will continue picking at 2 baskets per hour. Once the cousins get to the point
where they have filled the same number of baskets, they will carry them to the barn and then
eat lunch. How much fruit will they have picked by then? How long will that take?
Dave and Emily will each have filled
baskets in
hours.
Answer:
It will take 1 hour and they will have 11 baskets
Step-by-step explanation:
Dave
6 + 5h = b
Emily
9 + 2h=b
where h = hours and b = baskets
Setting the equations equal to each other
6+5h = 9+2h
Subtracting 2h from each side
6+3h = 9
Subtracting 6 from each side
3h = 3
Divide by 3
h =1
Then finding b
9+2h = b
9+2 =b
11=b
It will take 1 hour and they will have 11 baskets
4^6 • 4^-8 pls answer
Answer:
[tex]\boxed{4^{-2}}[/tex]
Step-by-step explanation:
[tex]4^6 \times 4^{-8}[/tex]
When bases are same for exponents and it is multiplication, then add the exponents.
[tex]4^{6+-8}[/tex]
[tex]4^{-2}[/tex]
Explanation: Since these two powers have the same base of 4, you can multiply them together by simply adding their exponents to get 4⁻².
When applying your exponent rules, the bases don't change!