An isosceles triangle’s altitude will bisect its base. Which expression could be used to find the area of the isosceles triangle above?
Answers
The expression could be used to find the area of the isosceles triangle above is [tex]\sqrt{40} \cdot \sqrt{40} /2[/tex]
The length of the base is the distance between the points 4+2i and 10+4i, so
Base= |10+ 4i (4+2i)| = |10+4i-4-2i|= |6 + 2i| = [tex]\sqrt{6^2 +2^2}[/tex] = [tex]\sqrt{36+4}[/tex]= √40
The middle point of the base is placed at point
4+2i+ 10 + 4i/2 = 6i +14/2 = 7+ 3i
The length of the height is the distance between the points 5+9i and 7+3i
Height = 5 +91 (7+3i)| =|5+ 9i −7 - 3i| = |−2+6i| = [tex]\sqrt{(-2)^2 + 6^2} = \sqrt {4+36}[/tex] = √40
So, the area of the triangle is
[tex]A= 1/2 \cdot Base \cdot Height= \sqrt{40} \cdot \sqrt{40} /2[/tex]
Therefore, The expression could be used to find the area of the isosceles triangle above is [tex]\sqrt{40} \cdot \sqrt{40} /2[/tex]
The probable question may be:
An isosceles triangle’s altitude will bisect its base. Which expression could be used to find the area of the isosceles triangle above?
Points on the graph of the triangle are (5+9i), (10+4i), and (4+2i).
A. \sqrt{40} \cdot \sqrt{40} /2
B. \sqrt{40} \cdot \sqrt{68} /2
C. \sqrt{232} \cdot \sqrt{288} /2
D. \sqrt{232} \cdot \sqrt{164} /2
Final answer:
To find the area of an isosceles triangle when given the length of the base and the altitude, you can use the formula A = ½ × base × height. The altitude of an isosceles triangle will bisect its base, so you can divide the base in half to find the length of the base above the altitude.
Explanation:
An isosceles triangle's altitude will bisect its base. To find the area of the isosceles triangle, we can use the formula A = ½ × base × height. Since the altitude bisects the base, we can divide the base in half to find the length of the base above the altitude. Let's say the length of the base is 2x and the length of the altitude is h. So, the expression to find the area of the isosceles triangle is A = ½ × (2x) × h = xh.
Related Questions
FOR 30 POINTS WILL MARK BRAINLIEST you have 500 sheets of notebook paper after one week you have 72% of the sheets left. you use the same number of sheets each week write an equation that represents the number y of pages remaining after 8 weeks
Answers
6.
The sum of two consecutive odd integers is 236. What is the smaller integer? (4 points)
a) 115
b) 117
c) 119
d) 113
Answers
Suppose the weights of farmer carl's potatoes are normally distributed with a mean of 8.0 ounces and a standard deviation of 1.1 ounces. suppose carl bags his potatoes in randomly selected groups of 6. what percentage of these bags should have a mean potato weight between 7.5 and 8.5 ounces?
Answers
The probability of a normally distributed data between two values (a, b) is given by:
[tex]P(a\ \textless \ X\ \textless \ b)=P\left(z\ \textless \ \frac{b-\mu}{\sigma/\sqrt{n}} \right)-P\left(z\ \textless \ \frac{a-\mu}{\sigma/\sqrt{n}} \right) \\ \\ =P(7.5\ \textless \ X\ \textless \ 8.5)=P\left(z\ \textless \ \frac{8.5-8.0}{1.1/\sqrt{6}} \right)-P\left(z\ \textless \ \frac{7.5-8.0}{1.1/\sqrt{6}} \right) \\ \\ =P(z\ \textless \ 1.113)-P(-1.113)=0.8672-0.1328=0.7344[/tex]
The greatest common factor of 4a(2) b and 6ab(3)
Answers
first, find the greatest common factor of ur coefficients 4 and 6.....and that is gonna be 2
as for ur variables and exponents....take the lowest ones
so both have an " a " and a " b " variable....the lowest a term is just " a "...and the lowest " b " term is b
so the GCF of these 2 terms are : 2ab
The greatest common factor of the expressions 4a^2b and 6ab^3 is 2ab.
The question seeks to determine the greatest common factor of the expressions 4a2b and 6ab3. To find this, one must look at the common factors of the numerical coefficients (4 and 6) and the variables raised to their respective powers (a2 and a, b and b3). The numerical common factor of 4 and 6 is 2. The lowest power of 'a' common to both terms is a1 and for 'b' is b1. On doing this we get 2ab.
Carla bought a shirt for $14 and a jacket for $69. She gave the cashier $100.
How much change should Carla get back?
Answers
Then you minus 83 from 100 and you get $17.00 Dollars to be exact.
BRAINLIEST!
Henry's rocket is designed to launch to a height of 100 feet in the air. The measurements so far have the launch height (h) varying no more than 4 feet. Which inequality below represents this scenario?
|h − 4| less than or equal to 100
|h + 4| greater than or equal to 100
|h − 100| less than or equal to 4
|h + 100| greater than or equal to 4
Answers
so answer is
|h − 100| less than or equal to 4
Answer:
|h − 100| less than or equal to 4
Step-by-step explanation:
We know the difference between h, the actual height, and the designed height, 100, is no more than 4.
This means that the actual height h could be up to 4 more than the designed height or up to 4 less than the designed height. This is why we use an absolute value inequality; this considers just the distance of 4 regardless of direction.
Since it can be "no more than" 4, we use less than or equal to; this gives us
|h − 100| less than or equal to 4
2. Pat is six years older than twice his Cousin Zach’s age. The sum of their ages is less than 36.
What is the greatest age that Zach could be?
Answers
C = Cousin Zach
2C + 6 = P
2C + 6 - 6= P - 6
2C = P - 6
2C/2 = P - 6/2
C = P - 3
C + 3 = P
so (C + 3) + P < 36
(C + 3 - 3) + P < 36 - 3
C + P < 33
Can you see what I am doing?
We know the following facts:
1.Pat is six years older than twice his Cousin Zach’s age. We can rewrite this statement as:
P=2*Z+6
2. The sum of their ages is less than 36.
P+Z<36
In order to find the greatest age that Zach could be we should find for which Z
P+Z=35 (the first whole number smaller than 36)
P=35-Z
35-Z=2*Z+6
35-6=3Z
29=3Z
Z=29/3
Z=9
Sheila is building a model for class. It's a tower that's designed to withstand high winds. She can use a maximum of 700 support beams and knows that each floor will require 22 beams. Sheila will track the number of beams that remain as she adds floors.
She can predict the number of beams that remain by using this function: remaining beams (y) is function of floor number (x).
How many beams will remain after she built 6 floors? Y=700-22(x)
Answers
then, after having 700 beams, she used 12, so: 700 - 132 = 568
So. 568 beams remain.
By graphing the system of constraints find the values of x and y that maximize the objective function, find the maximum value.
3x+y<=7
x+2y<=9
x>=0
y>=0
Maximum for P=2x+y
A. P=3
B. P=4
C. P=6
D. P=10
Answers
Answer:
x=1, y=4
P=6
Step-by-step explanation:
We are given that
[tex]3x+y\leq 7[/tex]
[tex]x+2y\leq 9[/tex]
[tex]x\geq 0[/tex]
[tex]y\geq 0[/tex]
Objective function
[tex]P=2x+y[/tex]
We have to values of x and y that maximize the P and maximum value of P .
First we change inequality equation into equality equation
[tex]3x+y=7[/tex] (I equation )
[tex]x+2y=9[/tex] (II equation)
Equation I multiply by 2 and then subtract from II equation
[tex]-5x=-5[/tex]
[tex]x=1[/tex]
Substitute x=1 in equation I
Then, we get
[tex]3(1)+y=7[/tex]
[tex]3+y=7[/tex]
[tex]y=7-3=4[/tex]
The two equation intersect at point (1,4).
Substitute x=0 in equation I
Then , we get y=7
Substitute y=0 then
[tex]3x=7[/tex]
[tex]x=\frac{7}{3}=2.3[/tex]
The equation I cut the x- axis at point (2.3,0)and y-axis at (0,7).
Substitute x=0 in equtaion II
[tex]2y=9[/tex]
[tex]y=\frac{9}{2}=4.5[/tex]
Substitute y=0
Then, we get
[tex]x=9[/tex]
Therefore, the equation II cut the x- axis at point (9,0) and y axis at point (0,4.5).
Substitute x=0 and y=0 in inequality Equation I
[tex]3(0)+0=0< 7[/tex]
It is true . Therefore, shaded region below the line.
Substitute x=0 and y=0 in inequality equation II
Then, [tex]0+2(0)=0 < 9[/tex]
It is true. Therefore, the shaded region below the line.
The feasible region is bounded.The feasible region bounded by (0,0),(0,4.5),(2.3,0) and (1,4).
At (0,4.5)
[tex]P=2(0)+4.5=4.5[/tex]
At (2.3,0)
[tex]P=2(2.3)+0=4.6[/tex]
At (1,4)
[tex]P=2(1)+4=6[/tex]
At (0,0)
[tex]P=2(0)+0=0[/tex]
Hence, maximum value of P is 6 at (1,4).
x=1 and y=4
Help me please its math under 10 minutes!!!
Answers
hope this helps
what is the constant rate of change of y=7-13x
Answers
The constant rate of change in the linear equation y=7-13x is -13, representing the slope of the line which remains constant for any value of x. This is different from nonlinear functions, where the rate can vary with x.
Explanation:The constant rate of change in the equation y=7-13x refers to the slope of the line represented by this linear equation. In this case, the constant rate of change, or the slope, is -13. This means for every one unit increase in x, y decreases by 13 units. Since the equation is linear, this rate does not change regardless of the value of x, unlike in nonlinear functions where the rate of change can vary with x.
To elaborate, if we have a nonlinear function, the rate of change depends on the interval of x we are looking at. For a linear function like this one, the slope is the same over any interval, so there's no need to compute it over smaller ranges of x to understand the rate of change.
Moreover, in calculus, the derivative represents the rate of change, and for a linear function, the derivative is simply the coefficient of x. Hence, the derivative of y with respect to x is -13. The derivative is zero for any constant term in a function, such as the 7 in the given equation.
Points d, e, and f are plotted on a number line. the coordinate of point f is 5. points d and e are the same distance from point f. what could be the coordinates of d and e?
a. d = –7, e = –1
b. d = –2, e = 12
c. d = 0, e = 5
d. d = 8, e = 11
Answers
hope i helped
The coordinates of d and e b. d = –2, e = 12.
To find the coordinates of points D and E, we need to remember that they are the same distance from point F, which has a coordinate of 5. This means D and E are equidistant from F on the number line. Let's check each option to see which one satisfies this condition:
Option a: d = -7, e = -1
The distance from -7 to 5 is 12.
The distance from -1 to 5 is 6.
Since the distances are not equal, this option is incorrect.
Option b: d = -2, e = 12
The distance from -2 to 5 is 7.
The distance from 12 to 5 is also 7.
Since the distances are equal, this option is correct.
Option c: d = 0, e = 5
The distance from 0 to 5 is 5.
The distance from 5 to 5 is 0.
Since the distances are not equal, this option is incorrect.
Option d: d = 8, e = 11
The distance from 8 to 5 is 3.
The distance from 11 to 5 is 6.
Since the distances are not equal, this option is incorrect.
Therefore, the correct answer is option b: d = -2, e = 12.
The solution to the equation 4(x – 7) = 64 is shown. Which step is a result of combining like terms?
A) Step 2
B) Step 3
C) Step 4
D) Step 5
Answers
Answer: C) step 4
Mrs. Noyes fills up a 5 gallon can of gas from the McIntosh’s local convenience store. They are selling gas at $2.099 a gallon. How much is she going to pay at the pump
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what is 230000 in standard form
Answers
It would be 2.3 x [tex] 10^{5} [/tex]
Standard form is a number between 1 and 10 times 10 to the nth power.
Hope This Helps You!
Good Luck :)
Final answer:
To write 230,000 in standard form, place the decimal point after the first non-zero digit. For 230,000, the standard form is 2.3 x 10⁵.
Explanation:
To express the number 230,000 in standard form, you simply write it as it is, moving the decimal point to the right until only one non-zero digit appears before the decimal. In this case, 230,000 in standard form is 2.3 x 10⁵.
What is the measure of an exterior angle in a regular dodecagon?
Answers
so each interior angle = [(12-2)180]÷12 = 1800÷12= 150°
so an exterior angle = 180 - interior angle
= 180-150 = 30°
Two parallel lines are crossed by a transversal. What is the value of g? g = 75 g = 80 g = 100 g = 105
Answers
I know this because look at the picture lol. You're welcome though.
The angle measure of g is ∠g = 105°.
The correct option is D.
What is an angle measure?When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
As per the information provided, it is given that the two parallel lines u and v are traversed by line g.
To find the angle measure of ∠g:
The angle measure of ∠g is equal to 105° by the alternate exterior angle theorem.
Therefore, ∠g = 105°.
To learn more about the angle measure;
brainly.com/question/14684647
#SPJ7
The complete question:
Two parallel lines are crossed by a transversal. What is the value of g? g = 75 g = 80 g = 100 g = 105
Solve for x: |2x + 12| = 18
Answers
18 - 12 = 6
2x = 6
x = 3
2x + 12 = 18 OR 2x + 12 = -18
subtract both sides by 12 for both equations
2x = 6 OR 2x = -30
divide both sides by 2 for both equations
x = 3 OR x = -15
i hope this helps!!
HELP PLZ!!
Solve for x: −3(x + 3) = −3(x + 1) − 5. (1 point)
6
−6
All real numbers
No solution
Answers
Multiply everything in the parenthesis by -3.
-3x - 9 = -3x - 3 - 5
Combine like terms.
-3x - 9 = -3x - 8
Add 9 to both sides.
-3x = -3x + 1
Add 3x to both sides.
0 = 1
This means that there is no solution.
Hope this helps!
3m + 7/2 = −2m + 5/2 the / means there fractions
Answers
3m +7/2 = -2m +5/2
subtract 5/2 from each side
3m +2/2 = -2m
2/2 = 1
3m+1 =-2m
subtract 3m from each side
1=-5m
divide both sides by -5
m = 1/-5 = -1/5
m = -1/5
Anyone wanna help me please?!
Allen has a photo that is 6 in by 8 in. What will the dimensions of the photo be if he scales it down by a factor of one-half ?
3 in by 4 in
6 in by 8 in
12 in by 16 in
1.5 in by 2 in
Answers
8:2=4
3 in by 4 in
A Chef buys 9 cucumbers, 18 peppers and 21 tomatos at the farmers market. Cucumbers ae 6 for $2, pEPPERS ARE 12 for $9 and tomatoes are 6 for $4
Answers
Cucumber: 2$/6 pieces= $0.33 /piece
Pepper: $9/12 pieces= $0.75/piece
Tomatoes: 4$/6 pieces= $0.66/piece
Then the total cost for the chef shopping item would be: 9 * $0.33 + 18 * $0.75 + 21* $0.66= $3 + $13.5+ $14= $30.5
Evaluate the determination for the following matrix [144] [522] [155]
Answers
1 4 4
5 2 2
1 5 5
=> Determinant =
1 * (2*5 - 2*5) - 4 * (5*5 - 1*2) + 4 * ( 5*5 - 2*1)
= 1*(10 - 10) - 4*(25 - 2) + 4*(25 -2) = 1*0 + 4* 23 + 4*(25 - 2) = 0 - 4*23 + 4*23 = 0
Answer: 0
Which amount is the best estimate for the cost of the vehicle to drive through the safari in 2009?
Answers
Replace x with 4 and use PEMDAS to simplify
y = 3.648*1.182^x
y = 3.648*1.182^4
y = 3.648*1.951955471376
y = 7.12073355957964
y = 7.12
The answer is choice A
At a point on the ground 24ft from the base of a tree, the distance to the top of the tree is 4ft more than 3times the height of the tree. find the height of the tree.
Answers
Francis has five more dollars than Julia. Together they have at most $45. Let x represent the amount of money Francis has. Which inequality can be used to find the possible amounts of money that Francis has?
Answers
Let x = Francis’s money
Francis has 5 more dollars than Julia
X = j+5
J(2)+5 less than or equal to 45
J(2) less than our equal to 40
J less than or equal to 20
X = j+5
So x = less than or equal to 25
I think this is right!!
Answer:
B) 2x - 5 ≤ 45
Step-by-step explanation:
The value of 110 coins, consisting of dimes and quarters, is $20.30. how many of each kind of coin are there?
Answers
0.10d + 0.25q = 20.30
0.10(110 - q) + 0.25q = 20.30
11 - 0.10q + 0.25q = 20.30
-0.10q + 0.25q = 20.30 - 11
0.15q = 9.30
q = 9.30/0.15
q = 62 <==== there are 62 quarters
d = 110 - q
d = 110 - 62
d = 48 <==== there are 48 dimes
Deon is saving money to buy a game. so far he has saved $20 , which is four-fifths of the total cost of the game. how much does the game cost?
Answers
(4/5)y=20
4y=100
y=25
Marc earned $1,650 per month as an assistant technician at a recording studio. His new job pays $9.80 per hour with time and a half for all hours over 36 hours per week. How many hours of overtime per week will he need to work to earn the same amount per week as his current job?
Answers
Marc will need to work just over 4 hours of overtime each week at his new job, which pays $9.80 per hour and $14.70 per hour for overtime, to earn the equivalent of his previous monthly income of $1,650.
To determine the number of overtime hours Marc needs to work at his new job to earn the same monthly income he did at his previous job, we'll first calculate his weekly income at his old job, then use the overtime pay rates at the new job to find the equivalent number of hours needed.
Marc previously earned $1,650 per month. Assuming a standard 4-week month, his weekly income was:
$1,650 per month / 4 weeks per month = $412.50 per week.
At his new job, Marc earns $9.80 per hour with time and a half for all hours over 36 hours a week. This means his overtime pay is 1.5 times his hourly rate, which is:
$9.80 per hour x 1.5 = $14.70 per hour for overtime.
Marc's income for the first 36 hours at his new job would be:
36 hours x $9.80 per hour = $352.80
To earn the equivalent of his old weekly salary, we must make up the difference with overtime pay:
$412.50 (old weekly income) - $352.80 (new regular pay) = $59.70 needed from overtime.
To determine the overtime hours needed to make $59.70: $59.70 / $14.70 per hour = approximately 4.06 hours.
Therefore, Marc will need to work just over 4 hours of overtime each week to earn the same amount he did at his previous job.
Which ordered pair (a,b) is a solution to the given system of linear equations.
Answers
Answer:
A. (-13,-3)
Step-by-step explanation:
Solve the system of two equations:
[tex]\left\{\begin{array}{l}-2a+3b=14\\a-4b=3\end{array}\right.[/tex]
From the second equation:
[tex]a=3+4b[/tex]
Substitute it into the first equation:
[tex]-2(3+4b)+3b=14\\ \\-6-8b+3b=14\\ \\-8b+3b=14+6\\ \\-5b=20\\ \\5b=-20\\ \\b=-4[/tex]
So,
[tex]a=3+4b=3+4\cdot (-4)=3-16=-13[/tex]
The solution is (-13,-4)
Answer:
A
Step-by-step explanation: