Answer:
AB = 5 units
Step-by-step explanation:
Given that:
A (1,-1) <=> x1=1 and y1=-1 B (1,4), <=> x2 = 1 and y2=4 C (8,4).So the the length in units of the line segment that connects vertex A and vertex B is the length of line AB. So we have the following formula:
AB = [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} }[/tex]
<=> AB = [tex]\sqrt{(1-1)^{2} +(4-(-1))^{2} }[/tex]
<=> AB = 5 units
Hope it will find you well.
The question relates to finding the distance between two points in a coordinate system. The length of the line segment connecting vertex A (1,-1) and vertex B (1,4) of the triangle ABC can be calculated using the distance formula, which yields a result of 5 units.
Explanation:The subject of your question is geometry, specifically the concept of distance between two points in a coordinate system. In finding the length of the line segment that connects vertex A (1,-1) and vertex B (1,4), you can use the distance formula based on Pythagorean theorem.
The distance formula is d = sqrt [(x2 - x1)² + (y2 - y1)²]. In this case, x1 = 1, x2 = 1, y1 = -1 and y2 = 4.
Substituting these values, we have d = sqrt [(1 - 1)² + (4 - (-1))²] = sqrt [0 + 25], hence d = sqrt [25] = 5 units.
Therefore, the length of the line segment connecting vertex A (1, -1) and vertex B (1, 4) is 5 units.
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evaluate 81/36 x^2 - y^2/25
Answer:
Step-by-step explanation:
Final answer:
To simplify the given expression involving fractions and variables, multiply, divide, and subtract accordingly to obtain the simplified form. Therefore, the simplified expression is [tex](9/4)x^2 - (1/25)y^2.[/tex]
Explanation:
The given expression is:
[tex]81/36 * x^2 - y^2/25[/tex]
To simplify this expression:
Multiply 81/36 which equals 9/4.
Then, divide [tex]x^2[/tex] by 4, and subtract [tex]y^2[/tex] divided by 25.
Therefore, the simplified expression is [tex](9/4)x^2 - (1/25)y^2.[/tex]
Solve the system of equations using any method.
6x + 4y = −8
4x − 2y = 2
A) (11/7, 2/7)
B) (2/7, 11/7)
C) (-2/7, 11/7)
D) (-2/7, -11/7)
PLEASE HELP!!!!
Answer:
My answer what I came up with is B And B
A student spends 2200 dollars during one semester of college. They spend 325 on books. What percentage was spent on books
Answer:
Step-by-step explanation:
percentage spent on books = (325/2200) * 100
= 325/22 = 14.77%
Karli and her friend can paint 6/7 of a picture in 3/14 of an hour. How many pictures can they paint in a full hour?
Write the quadratic equation whose roots are 3 and 4, and whose leading coefficient is 2.
(Use the letter x to represent the variable.)
Step-by-step explanation:
equation-
(x-3) (x-4) =
[tex] {x }^{2} - 3x - 4x + 12 = {x}^{2} - 7x + 12[/tex]
Given the roots 3 and 4 of a quadratic equation, and the leading coefficient 2, the quadratic equation can be derived as 2x^2 - 14x + 24.
Explanation:To find a quadratic equation given its roots and leading coefficient, you use the factored form of a quadratic equation, x = (x - root1)(x - root2).
Given that the roots are 3 and 4, the equation takes the form of x = (x - 3)(x - 4). When you multiply this out, you get x^2 - 7x + 12.
The problem also states that the leading coefficient is 2, so we multiply our obtained equation by 2 to get: 2x^2 - 14x + 24.
So, the requested quadratic equation is 2x^2 - 14x + 24.
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a concert venue can hold 200 people. student tickets are 50% less than adult tickets. Adult tickets at $50.00. The venue was sold out and made a revenue of $9125 for one event. How many adults vs. student tickets were sold?
The number of adult tickets sold is 165 and number of students tickets sold were 35
Solution:
Let "a" be the number of adult tickets sold
Let "s" be the number of student tickets sold
Cost of 1 adult ticket = $ 50.00
Student tickets are 50% less than adult tickets
Cost of 1 student ticket = Cost of 1 adult ticket - 50 % of Cost of 1 adult ticket
[tex]\rightarrow 50.00 - 50 \% \text{ of } 50.00\\\\\rightarrow 50 - \frac{50}{100} \times 50\\\\\rightarrow 50 - 25 = 25[/tex]
Thus Cost of 1 student ticket = $ 25
Given that a concert venue can hold 200 people
So we get,
number of adult tickets sold + number of student tickets sold = 200
a + s = 200 ----- eqn 1
The venue was sold out and made a revenue of $9125 for one event
So we can frame a equation as:
number of adult tickets sold x Cost of 1 adult ticket + number of student tickets sold x Cost of 1 student ticket = $ 9125
[tex]a \times 50.00 + s \times 25 = 9125[/tex]
50a + 25s = 9125 ---- eqn 2
Let us solve eqn 1 and eqn 2 to find values of "a" and "s"
From eqn 1,
a = 200 - s --- eqn 3
Substitute eqn 3 in eqn 2
50(200 - s) + 25s = 9125
10000 - 50s + 25s = 9125
-25s = 9125 - 10000
-25s = -875
s = 35Substitute s = 35 in eqn 3
a = 200 - 35
a = 165Thus the number of adult tickets sold is 165 and number of students tickets sold were 35
The probability of drawing 2 defective pieces one after the other on the first and second samples, without replacement, from a lot of 50 pieces containing 5 defective pieces is approximately
Answer: The required probability is 0.004.
Step-by-step explanation:
Since we have given that
Number of pieces = 50
Number of defective pieces = 5
So, we need to draw 2 defective pieces.
So, the probability of drawing 2 defective pieces one after the other on the first and second samples would be
[tex]\dfrac{5}{50}\times \dfrac{4}{49}\\\\=\dfrac{20}{2450}\\\\=0.004[/tex]
Hence, the required probability is 0.004.
Final answer:
Calculating the probability of drawing two defective pieces sequentially from a set of 50 pieces with 5 defectives.
Explanation:
The probability of drawing 2 defective pieces one after the other without replacement:
Find the probability of drawing the first defective piece: 5/50 = 1/10.
Since the pieces are drawn without replacement, the probability of drawing the second defective piece after the first is: 4/49.
Multiply the probabilities: (1/10) * (4/49) = 4/245.
what number is 10 times as great as 7962
To find a number that is 10 times greater than 7962, we can multiply.
7,962 * 10 = 79,620
79,620 is 10 times greater than 7,962.
Best of Luck!
Answer:
79,620
Step-by-step explanation:
7,962 (10) = 79,620
Evaluate f(1) using substitution:
f(x) =2x^3 -3x^2-18x+8
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Substitute 1 in everywhere you see 'x'
2(1)^3 - 3(1)^2 - 18(1) + 8
Solve:
f(1) = -11
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Final answer:
To evaluate the function f [tex](x) = 2x^3 - 3x^2 - 18x + 8[/tex] at x=1, substitute 1 for every instance of x in the function and simplify to get f(1) = -11.
Explanation:
The question appears to be a math problem where the student is asked to evaluate a function at a specific input. Specifically, the function given is [tex]f(x) = 2x^3 - 3x^2 - 18x + 8[/tex] and the student has been asked to evaluate this function when x is equal to 1. To find f(1), we replace every instance of x in the function with 1.
So, f(1) = [tex]2(1)^3 - 3(1)^2 - 18(1) + 8[/tex]= 2(1) - 3(1) - 18 + 8 = 2 - 3 - 18 + 8 = -11.
Thus, f(1) evaluates to -11.
Which equation has both -3 and 3 as possible values of y?
A
y^2=6
B
y^2=8
C
y^2=9
D
y^2=64
Answer:
C. [tex]y^2=9[/tex]
Step-by-step explanation:
1. [tex]y^2 = 9[/tex]
2. [tex]y = \frac{+}{}\sqrt{9}[/tex]
3. Equation solutions:
[tex]y_{1} = 3\\y_{2} = -3[/tex]
A movie theater sells out 7 times per month. How many times will it sell out in the next 2 years?
1 year = 12 months.
2 years = 12 x 2 = 24 months.
Multiply the number of times it sells out per month by the number of months:
7 x 24 months = 168 times.
what is the answer to the pic
Answer:
[tex]7[/tex]
Step-by-step explanation:
[tex]\frac{7^{-1}}{7^{-2}}[/tex]
[tex]7^{-1-(-2)}[/tex]
[tex]7^{-1+2}[/tex]
[tex]7^{1}[/tex]
[tex]7[/tex]
I used the following rules:
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]
[tex]a^1=a[/tex]
[tex]a \neq 0[/tex]
If James borrows $4,200 to pay his college tuition. He signs a 5 year simple interest loan. If monthly payments are $78.40, what is the interest rate on the loan?
Answer:
The rate of interest applied on the loan is 2.4%
Step-by-step explanation:
Given as :
The principal amount borrows as loan = p = $4200
The time period of loan = t = 5 years = 5 × 12 = 60 months
The monthly payment for loan = $78.40
So, The payment for 60 months = $78.40 × 60 = $4704
i.e Amount after 60 months = $4704
Let The rate of interest = r at simple interest
Now, From Simple Interest method
Simple interest = [tex]\dfrac{\textrm principal\times \textrm rate\times \textrm time}{100}[/tex]
Or, s.i = [tex]\dfrac{\textrm p\times \textrm r\times \textrm t}{100}[/tex]
Or, (Amount - principal) = [tex]\dfrac{\textrm p\times \textrm r\times \textrm t}{100}[/tex]
Or, $4704 - $4200 = [tex]\dfrac{\textrm 4200\times \textrm r\times \textrm 5}{100}[/tex]
Or,504 × 100 = 21,000 × r
∴, r = [tex]\dfrac{50400}{21000}[/tex]
i.e r = 2.4
So, The rate of interest = r = 2.4%
Hence, The rate of interest applied on the loan is 2.4% Answer
Which of the following shows the expression in factored form x2 + 2x - 8
A) (x-2)(x+4)
B) (x+2)(x+4)
C) (x-2)(x+8)
D) (x+1)(x-8)
Answer:
A) (x-2)(x+4)
Step-by-step explanation:
To the nearest tenth, what is the distance between the point (10, -11) and (-1, -5)
Answer:
≈ 12.5 units
Step-by-step explanation:
Calculate the distance d using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (10, - 11) and (x₂, y₂ ) = (- 1, - 5)
d = [tex]\sqrt{(-1-10)^2+(-5+11)^2}[/tex]
= [tex]\sqrt{(-11)^2+6^2}[/tex]
= [tex]\sqrt{121+36}[/tex]
= [tex]\sqrt{157}[/tex] ≈ 12.5 ( to the nearest tenth )
Tatiana wants to give friendship bracelets for 32 classmates. She already has 5 bracelets, and she can buy more bracelets in packages of 4. Will Tatiana have enough bracelets if she buy 5 packages? A. Yes, she will have enough for all 32 classmates if she orders 5 more packages of bracelets. Or b. No she will not have enough bracelets for all 32 classmates if she orders 5 more packages of bracelets
Answer:
b. No she will not have enough bracelets for all 32 classmates if she orders 5 more packages of bracelets
Step-by-step explanation:
write out the equation
p=the number of packages she needs to buy
32=5+4p
subtract five from both sides
32-5=5-5+4p
27=4p
dived both side by 4
27/4=4p/4
6.75=p round to 7
Check your answer:
4 x 7 = 28
add the number of bracelets she already has
28 + 5 = 33 bracelets
33>32
So 7 packages is the minimum number of packages she needs to buy
A gasoline generator provides the power to
light a construction project at night. The generator uses 5.5 gallons of gasoline for every 3 1/3 hours of operation.
Is of operation. How much
gasoline is used in 11 hours?
Answer:
The quantity of gasoline used for 11 hours is 18.37 gallons .
Step-by-step explanation:
Given as :
The quantity of gasoline use by generator = 5.5 gallons
The generator use 5.5 gallons of gasoline for duration = 3 [tex]\dfrac{1}{3}[/tex] hours
I.e The generator use 5.5 gallons of gasoline for duration = [tex]\dfrac{10}{3}[/tex] hours
Let The quantity of gasoline use by generator for 11 hours = x gallons
Now, According to question
Applying unitary method
∵For [tex]\dfrac{10}{3}[/tex] hours of power generate ,The quantity of gasoline use = 5.5 gallons
So For 1 hour of power generate ,The quantity of gasoline use = [tex]\frac{5.5}{\frac{10}{3}}[/tex] gallons
∴ For 11 hours of power generate ,The quantity of gasoline use = [tex]\frac{5.5}{\frac{10}{3}}[/tex] × 11 gallons
i.e For 11 hours of power generate ,The quantity of gasoline use = 1.67 × 11
Or, For 11 hours of power generate ,The quantity of gasoline use = 18.37 gallons
Hence,The quantity of gasoline used for 11 hours is 18.37 gallons . Answer
What did Tarzan like to play?
Answer:
Step-by-step explanation:
Write the equation of the line that passes through (-1, 8) and is parallel to the line that passes through (5, -1) and (2, -5).
Answer:
[tex]\large\boxed{y=-\dfrac{3}{4}x+\dfrac{29}{4}}[/tex]
Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\k\ ||\ l\iff m_1=m_2\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\=================================[/tex]
[tex]\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\text{Calculate the slops:}\\\\(5,\ -1),\ (2,\ -5)\\\\m_1=\dfrac{-5-(-1)}{2-5}=\dfrac{-5+1}{-3}=\dfrac{-4}{-3}=\dfrac{4}{3}\\\\\text{Therefore}\\\\m_2=-\dfrac{1}{\frac{4}{3}}=-1\left(\dfrac{3}{4}\right)=-\dfrac{3}{4}\\\\\text{Put the value of slope and coordinates of the given point (-1, 8) }\\\text{to the equation of a line:}\\\\8=-\dfrac{3}{4}(-1)+b\\\\8=\dfrac{3}{4}+b\qquad\text{subtract}\ \dfrac{3}{4}\ \text{from both sides}\\\\7\dfrac{1}{4}=b\to b=\dfrac{29}{4}\\\\\text{Finally:}\\\\y=-\dfrac{3}{4}x+\dfrac{29}{4}[/tex]
What is the General form of the parabola of (y-3)^2=6(x+8)
Answer:
x = 1.5[tex]t^{2}[/tex] , y = 3 + 2at.
Step-by-step explanation:
For the parabola [tex]Y^{2}[/tex] = 4aX ,
General form will be
(X = a[tex]t^{2}[/tex] , Y = 2at) ,
Thus , for the parabola [tex](y-3)^{2}[/tex] = 6(x +8)
Here , a = 1.5 and Y from the above equation should be substituted by y - 3 and X must be substituted by x + 8. After substitution of the same we can use the general equation formula for this parabola also.
Thus , general equation comes out to be :-
x + 8 = 1.5[tex]t^{2}[/tex] , y - 3 = 2at
x = 1.5[tex]t^{2}[/tex] , y = 3 + 2at.
The following proof shows an equivalent system of equations created from another system of equations. Fill in the missing reason in the proof.
Statements Reasons
2x + 2y = 14
−x + y = 5 Given
2x + 2y = 14
y = x + 5 ?
Answer:
As addition property of equality clearly states that if we add the same number to both sides of an equation, the sides remain equal.
Step-by-step explanation:
[tex]2x + 2y = 14[/tex]
[tex]-x + y = 5[/tex] Add x in both sides (Addition Property of Equality)
[tex]2x + 2y = 14[/tex]
[tex]y = x + 5[/tex] Multiply both sides by 2
[tex]2x + 2y = 14[/tex]
[tex]2y = 2x + 10[/tex] Subtract 2x in both sides
[tex]+\left \{ {{2x + 2y=14} \atop {-2x + 2y=10}} \right.[/tex] ∵adding both equation
[tex]4y = 24[/tex] divide both sides by 4
[tex]y = 6[/tex]
Put the value of y = 6 to the equation [tex]-x + y = 5[/tex]
[tex]-x + 6 = 5[/tex] Subtract 6 from both sides
[tex]-x = -1[/tex] Change the sign
[tex]x = 1[/tex]
Keywords: Addition property of equality, reason, proof
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The number of students enrolled at a college is 12,000 and grows 4% each year. Complete parts (a) through (e).
a) The initial amount a is
.
Answer:
48000
Step-by-step explanation:
12000 students
4%
1 =annually
12×4×1= 48000
Answer:12,000
Step-by-step explanation:can’t give you one cuz I’m doing this in mathxl :p
Simpliftly(-8.5)(-5)( -2)
how do i simplify it
Answer:
-85
Step-by-step explanation:
(-8.5)(-5)(-2)
Multiply
(42.5)(-2)
-85
Hope this helps :)
Each end of a glass prism is a triangle with a height that is 1 inch shorter than twice the base. If the area of the triangle is 60 square inches, how long are the base and height?
Answer:
Step-by-step explanation:
Let the base = x inches
So, h = 2x - 1
Area of triangle = 60 square inches
(1/2) * base *height = 60
(1/2) * x * (2x-1) = 60
x *(2x-1) = 60*2
2x² - x = 120
2x² - x - 120 = 0
2x² - 16x + 15x - 15*8 = 0
2x ( x - 8) + 15 (x -8) = 0
(x-8) (2x + 15 ) = 0
x- 8 = 0 {ignore 2x +1 as it will give negative value}
x = 8
Base = 8 inches
Height = 2*8 - 1 16 - 1 = 15 inches
how can you use functions to solve real world problems ??
Answer:ioj;i;
hStep-by-step explanation:
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Plz help me this isn’t that hard but I’m struggling so plz I don’t want another detention
Answer:
The length of the total 8 pieces in 0.8 meters = 6.4 meters
How many pieces there are in the remaining 0.4 meter = 6.5
Step-by-step explanation:
0.8 x 8 = 6.4
9 meters - 6.4 meters = the remaining 2.6 meters
2.6 x 0.4 = 6 1/2 pieces of ribbon in 0.4 meters.
Given the following diagram, if m ∠ COF = 150°, then m ∠ BOC = AD ⊥ BF
150 °
90 °
45 °
30 °
Answer:
[tex]m\angle BOC=30^o[/tex]
Step-by-step explanation:
step 1
Find the measure of angle COD
we know that
[tex]m\angle COF=m\angle COD+m\angle DOF[/tex] ---> by addition angle postulate
we have
[tex]m\angle COF=150^o[/tex] ----> given problem
[tex]m\angle DOF=90^o[/tex] ----> because AD is perpendicular to BF
substitute the given values
[tex]150^o=m\angle COD+90^o[/tex]
[tex]m\angle COD=150^o-90^o[/tex]
[tex]m\angle COD=60^o[/tex]
step 2
Find the measure of angle BOC
we know that
[tex]m\angle BOC+m\angle COD=90^o[/tex] ---> by complementary angles
we have
[tex]m\angle COD=60^o[/tex]
substitute
[tex]m\angle BOC+60^o=90^o[/tex]
[tex]m\angle BOC=90^o-60^o[/tex]
[tex]m\angle BOC=30^o[/tex]
short answer: 30 degrees :)
.The sum of the digits of a two-digit number is one-fifth the value of the
number. The tens digits is one less than the ones digit. What is the two-digit
number? (Hint: Assign a different variable to the value of each digit.)
Here's how I'm assigning a different variable to the value of each digit:
10x + y, where x is the first digit, and y is the second digit (you can test if this equation works)
The sum of the digits is 1/5 the value of the number. Using the information, we can form the equation:
x + y = (1/5)(10x + y)
Simplify
x + y = 2x + (1/5)y
The tens digit is one less than the ones digit. Using this information, we can form the equation:
x = y - 1
Adding both sides by 1 gives
x + 1 = y
Substituting this into the y's the first equation gives:
x + x + 1 = 2x + (1/5)(x + 1)
Distribute and simplify
2x + 1 = 2x + (1/5)x + 1/5
Subtract both sides by 2x
1 = (1/5)x + 1/5
Subtract 1/5 from both sides
4/5 = (1/5)x
Multiply both sides by 5
4 = x
x = 4
Use this to solve for y
x + 1 = y
4 + 1 = y
y = 5
Thus, x = 4 and y = 5. The 2 digit number is XY, which is 45.
Let me know if you need any clarifications; this was a very interesting math problem to solve!
Prove that ABCD is a square if a A(1,3) B(2,0) C(5,1) and D(4,4)
[tex]AB=BC=CD=AD = \sqrt{10}[/tex]
As all the sides have same length, ABCD is a square
Step-by-step explanation:
To prove ABCD a square we have to find the lengths of each side
So,
the distance formula will be used to find the lengths
The distance formula is:
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Now,
[tex]AB = \sqrt{(2-1)^2+(0-3)^2}\\= \sqrt{(1)^2+(-3)^2}\\=\sqrt{1+9}\\=\sqrt{10}[/tex]
[tex]BC = \sqrt{(5-2)^2+(1-0)^2}\\= \sqrt{(3)^2+(1)^2}\\=\sqrt{9+1}\\=\sqrt{10}[/tex]
[tex]CD = \sqrt{(4-5)^2+(4-1)^2}\\= \sqrt{(-1)^2+(3)^2}\\=\sqrt{1+9}\\=\sqrt{10}[/tex]
[tex]AD = \sqrt{(4-1)^2+(4-3)^2}\\= \sqrt{(3)^2+(1)^2}\\=\sqrt{9+1}\\=\sqrt{10}[/tex]
we can see that
[tex]AB=BC=CD=AD = \sqrt{10}[/tex]
As all the sides have same length, ABCD is a square
Keywords: Distance formula, square
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I need help with algebra 2a
Answer:
31
Step-by-step explanation:
[tex]\bf \displaystyle\sum\limits_{j=1}^{10}~2j+7\implies \displaystyle\sum\limits_{j=1}^{10}~2j+\displaystyle\sum\limits_{j=1}^{10}~7\implies 2\displaystyle\sum\limits_{j=1}^{10}~j+\displaystyle\sum\limits_{j=1}^{10}~7 \\\\\\ 2\cdot \cfrac{10(10+1)}{2}~~+~~(10)(7)\implies 2\cdot 55+70\implies 110+70\implies 180[/tex]