The area of triangle ABC with vertices is 22 square units
How to find the area of ABC with vertices?The vertices are given as:
A(4, -3) B(9,-3) , and C(10, −11)
The area of the triangle is calculated using
Area = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|
This gives
Area = 0.5 * |4 * (-3 + 11) + 9 * (-3 + 11) + 10 * (-3 - 3)|
Evaluate the sum of products
Area = 0.5 * |44|
Remove the absolute bracket
Area = 0.5 * 44
Evaluate
Area = 22
Hence, the area of ABC with vertices is 22 square units
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what is the slope of a line that passes through the points open parentheses 6 comma 1 close parentheses and open parentheses short dash 3 comma 4 close parentheses?
Answer:
-1/3
Step-by-step explanation:
So we need to find the slope of a line that passes through (6, 1) and (-3, 4).
We know that the line passes through 2 points, and using this information, we can find the slope of this line using our slope formula which is [tex]\frac{y1-y2}{x1-x2}[/tex].
So we can do [tex]\frac{4-1}{-3-6}=-\frac{1}{3}[/tex].
That's your answer.
Let me know if you have any questions
40 is 77% of what number?
Given y =
2x+1/4x-3
•Solve for x.
•evaluate x when y = 1
Answer:
Solve for x: [tex]x = \frac{3y+1}{4y-2}[/tex]
Evaluate x for y = 1: [tex]x = 2[/tex]
Step-by-step explanation:
[tex]Original:y=\frac{2x+1}{4x-3}\\Multiply\ out\ the\ denominator:(4x-3)*y = 2x+1\\Distribute: 4xy - 3y = 2x+1\\Group\ Like\ Terms:4xy-2x = 3y+1\\Factor\ Out\ x: x(4y-2) = 3y+1\\Divide\ to\ get\ x\ alone:x = \frac{3y+1}{4y-2}\\\\Plug\ in\ the\ value\ for\ y:x = \frac{3(1)+1}{4(1)-2}\\Multiply:x = \frac{3+1}{4-2}\\Add:x = \frac{4}{2}\\Simplify/Divide:x=2[/tex]
Find the product.
(−6)(−7)=
Answer:
The answer to your question is 42
the answer is 42 because the parentheses around the -6 and the -7 mean to multiply them and that two negatives make a positive so -6 * -7 equals 42
Hope this helps!
A chemist needs to mix a 2% acid solution and a 10% acid solution to make 600 mL of a 5% acid solution. write and solve a system of equations to find the volume of the 2% solution and the volume of the 10% solution that the chemist will need.
Points points points!!
By solving a system of equations, we can see that the chemist needs to use 375 mL of the 2% acid, and the other 225% of the 10% acid.
How to write and solve the system of equations?
Let's define the variables that we will need to write our system of equations:
x = mL of the 2% acid solution used.y = mL of the 10% acid solution used.We know that the chemist wants to make 600mL of a 5% acid solution, so we can write the system of equations:
x + y = 600
x*0.02 + y*0.10 = 600*0.05
If we isolate y on the first equation, then we get:
y = 600 - x
Now we can replace that on the other equation so we get:
x*0.02 + (600 - x)*0.10 = 30
With this, we can get the value of x.
x*0.02 + 60 - x*0.10 = 30
-x*0.08 = 30 - 60 = -30
x = 30/0.08 = 375
So the chemist needs to use 375 mL of the 2% acid, and the other 225% of the 10% acid.
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No, by rounding the conversion ratio, the Ruiz family will not be getting the most accurate answer. Using the more accurate conversion ratio will give an answer with more than 2 decimal places so the answer can accurately be rounded after the conversion.
Using proportions, it is found that the Ruiz family is not getting the most accurate ratio and are losing money, thus the rounding should be realized after the conversion.
What is the missing information?The Ruiz family is exchanging Euros for USD dollars, considering the following currency rate:
1 euro = 1.35261 USD.
Considering that the amounts in USD are rounded to the nearest hundredth, the use the following rule
1 euro - 1.35 USD.
It asks if the Ruiz family will be getting the most accurate answer.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For this problem, we suppose a 1000 euros amount, them:
1000 x 1.35261 = $1,352.61.1000 x 1.35 = $1,350.Hence the Ruiz family is not getting the most accurate ratio and are losing money, thus the rounding should be realized after the conversion.
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6c+5d-4c-3d+3c-6d; c=4 and d=-2
Evaluate the expression for the given values of the variables.
show all work please
We are to evaluate the expression:
[tex]6c + 5d - 4c - 3d + 3c - 6d[/tex]
Where:
[tex]c = 4[/tex], [tex]d = 2[/tex]
Here, we just have to replace the variables with their given values, as shown below:
[tex]6(4) + 5(2) - 4(4) - 3(2) + 3(4) - 6(2)[/tex]
Now, we calculate.
[tex]→24 + 10 - 16 - 6 + 12 - 12[/tex]
Final answer
[tex] = 12[/tex]
What´s 5/6 X 1/4 =? its fraction operations
Answer:
0.2083
Step-by-step explanation:
The perimeter of the triangle shown is 556 meters. Find
the length of each side.
x meters =
4x meters =
(8x - 3) meters =
(Type integers or decimals.)
4x meters
(8x - 3) meters
x meters
Answer X=43 ,4X=172, (8X-3)=101
Step-by-step explanation:
Perimeter = addition of all sides ie;
556=X+4X+8X-3
556=13X-3
556+3=13X
559/13=13X/13
X=43
replace x with 43 to get their
If the total price for two cars at a dealership is $98,000, where one car’s price is $13,000 less than twice the other, what is the price of the cheaper vehicle?
someone please help me with this question i really dont understand it
Answer:
d = 510 km
Step-by-step explanation:
She travelled the final 4 hours at a constant speed of 60 km/h.
distance = speed × time
distance = 60 km/h × 4 hours
distance = 240 km for the last 4 hours
She already had travelled 270 km in the first 3 hours.
d = total distance = 270 km + 240 km = 510 km
Answer: d = 510 km
Your goal in this section is to take a closer look at some aspects of the topic finding solutions of
quadratic equations. You are going to think deeper and test further your understanding about solving
quadratic equations using any of the four methods discussed.
1. Sheryl says that the solutions of the quadratic equations w² = 49 and
w² +49 = 0 are the same. Do you agree with Sheryl? Justify your answer.
2. Patricia says that it's more appropriate to use the method of factoring
than extracting square roots in solving the quadratic equation
4x² - 9 = 0. Do you agree with Patricia? Explain your answer.
3. If you are to choose between completing the square and factoring in
finding the solutions of each of the following equations, which would you
choose? Explain and solve the equation using your preferred method.
b. x² + 7x + 12 = 0
a. 4x² - 20x = 11
4. The values of a, b, and e of a quadratic equation written in standard form
are -2, 8, and 3, respectively. Another quadratic equation has 2, -8, and
-3 as the values of a, b, and c, respectively. Do you agree that the two
equations have the same solutions? Justify your answer.
"pa answer po please"..
1) Sheryl was wrong, the solution of w² = 49 and w² +49 = 0 are not same.
2) The solution of 4x² - 9 = 0 this quadratic equation is 3/2 and -3/2 through using factoring method.
3)
The solution of 4x² - 20x = 11 is 11/2 and -1/2, through using completing the square method.The solution of x² + 7x + 12 = 0 is -4 and -3, through using factoring method.4) The solution of both quadratic equations will give same results.
Explanation:
1) Sheryl says that the solutions of the quadratic equations w² = 49 and
w² +49 = 0 are the same. Do you agree with Sheryl? Justify your answer.
Solution:-
According to Sheryl says that the solutions w² = 49 and w² +49 = 0 are the same.
Let's find the solution of given quadratic equations
w² = 49w = √49 ( ∵√49 = 7 )
w = ±7
So the solution of this quadratic equation 7 and -7
w² + 49 = 0w² = -49
w = √(-49) ( ∵√49 = 7 )
w = ±7 √-1 ( ∵√-1 = i )
So the solution of this quadratic equation 7i and -7i
Both solutions are not same.2. Patricia says that it's more appropriate to use the method of factoring
than extracting square roots in solving the quadratic equation
4x² - 9 = 0. Do you agree with Patricia? Explain your answer.
Solution:-
Patricia says that it's more appropriate to use the method of factoring
than extracting square roots in solving the quadratic equation
4x² - 9 = 0.
We are agree with Patricia, the method of factoring is very easy to learn and best way to deliver the solution of this quadratic equation.Now, let's solve that quadratic equation through factoring method.
4x² - 9 = 0.(2x)² - (3)² = 0 {∵ a²-b²= (a-b)(a+b)
(2x-3)(2x+3) = 0
If (2x-3) = 0
2x-3 = 0
2x = 3
x = 3/2
And if (2x+3) = 0
2x+3 = 0
2x = -3
x = -3/2
The solution of 4x² - 9 = 0. is 3/2 and -3/2.3. If you are to choose between completing the square and factoring in
finding the solutions of each of the following equations, which would you
choose? Explain and solve the equation using your preferred method.
a. 4x² - 20x = 11
b. x² + 7x + 12 = 0.
Solution:-
a. 4x² - 20x = 11
For solve this quadratic equation, we can use completing the square method, because this equation is very hard to get it's factors.
So,
4x² - 20x = 11
[tex]x^2-5x+(\frac{5}{2})^2 = \frac{11}{4} +(\frac{5}{2})^2\\x^2-2\times \frac{5}{2} \times x+(\frac{5}{2})^2 = \frac{11}{4} +\frac{25}{4}\\(x-\frac{5}{2})^2 = \frac{11+25}{4}\\(x-\frac{5}{2})^2 = \frac{36}{4}\\(x-\frac{5}{2})^2 = 9\\(x-\frac{5}{2})^2 = (3)^2\\(x-\frac{5}{2}) = \pm (3)\\\\[/tex]
For taking + sign,
x - [tex]\frac{5}{2}[/tex] = 3
x = 3 + [tex]\frac{5}{2}[/tex]
x = [tex]\frac{6+5}{2}[/tex]
x = [tex]\frac{11}{2}[/tex]
For taking - sign,
x - [tex]\frac{5}{2}[/tex] = -3
x = [tex]\frac{5}{2}[/tex] - 3
x = [tex]\frac{5-6}{2}[/tex]
x = [tex]\frac{-1}{2}[/tex]
The solution of 4x² - 20x = 11 is 11/2 and -1/2, through using completing the square method.b. x² + 7x + 12 = 0.
For solve this quadratic equation, we can use factoring method, because that is very easy to get it's factors.
So,
x² + 7x + 12 = 0
x² + 4x +3x + 12 = 0
x(x+4) +3(x+4) = 0
(x+4)(x+3) = 0
If (x+4) = 0
x+4 = 0
x = -4
And if (x+3) = 0
x+3 = 0
x = -3
The solution of x² + 7x + 12 = 0 is -4 and -3, through using factoring method.4. The values of a, b, and e of a quadratic equation written in standard form are -2, 8, and 3, respectively. Another quadratic equation has 2, -8, and -3 as the values of a, b, and c, respectively. Do you agree that the two equations have the same solutions? Justify your answer.
Solution:-
We know that the standard form of quadratic equation is
ax²+bx+c = 0From question we have two values of a,b and c.
For 1st quadratic equation the value of a,b and c is -2, 8, and 3, respectively.
So, the quadratic equation is
-2x²+8x+3 = 0For 2nd quadratic equation the value of a,b and c is 2, -8, and -3, respectively.
So, the quadratic equation is
2x²-8x-3 = 0Now, we have to find the solution of both equations are same or not.
So, the solution of 1st quadratic equation
-2x²+8x+3 = 0
2x-8x-3 = 0 (multiplying - with both sides)
Now, this equation convert in the form of 2nd quadratic equation. So we can say that the solution of both quadratic equations will give same results.
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The formula for the volume V of a cylinder is V = r²h, where r is the radius of the base and his the height of the
cylinder. Solve the formula for h. Then find the height of a cylinder with a volume of 36 cm³ and a base with a
radius of 3 cm.
Answer: h=V/r²
h=4 cm
Step-by-step explanation:
V = r²h solve for h
V/r² = r²h/r² ==> divide the formula by r² to isolate h
h=V/r²
h=36/(3)²
h=36/9
h=4 cm
1. y=-4x+3
X
20
1
2
3
y
-5
-9
V
Answer:−4x+60X,1,2,3y−14
Step-by-step explanation:
1. simplify 3x x 20 to 60x
−4x+60X,1,2,3y−5−9
2. Simplify 3y- 5-9 to 3y - 14
−4x+60X,1,2,3y−14
show your work, and explain and write the final answer in a complete sentence. i will give brainlest to whoever answers! due right now please help this will impact my grade!
Answer: Simplify the expression.
Scientific Notation:
4 ⋅ 10^7
Expanded Form:
40000000
Step-by-step explanation:
by doing 2.7*10^(5) divided by 6.75*10^(3)
you get the answer or now saying its
4 ⋅ 10^7 miles away basically. hope this helped
I don’t understand the question 2 for this math equation.
Answer:
Step-by-step explanation:
Time/mph
the average lifetime of a certain new cell phone is three years. the manufacturer will replace any cell phone failing within two years of the date of purchase. the lifetime of these cell phones is known to follow an exponential distribution. the decay rate is:
The decay rate of a certain new cell phone is 0.333
For given question,
The average lifetime of a certain new cell phone is three years.
The manufacturer will replace any cell phone failing within two years of the date of purchase.
Also, the lifetime of these cell phones is known to follow an exponential distribution.
We need to find the decay rate.
We know that an exponential decay is the process of reducing an amount by a consistent percentage rate over a period of time.
since the average lifetime of a certain new cell phone is three years, the decay rate would be 1/3 = 0.333
Therefore, the decay rate of a certain new cell phone is 0.333
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4/7 x 1/7 what is the answer
Answer:
[tex]\frac{4}{49}[/tex]
Step-by-step explanation:
4/7 × 1/7
= 4 × 1/7 × 7
= 4/49
331 students went on a field trip. Six
buses were filled and 7 students
traveled in cars. How many students
were in each bus?
The number of students in each bus are 54 students .
Given that, 331 students went on a field trip. Six buses were filled and 7 students traveled in cars.
Now you may get that only 7 students out of 331 are travelled in cars whereas others travelled by bus.
number of total students travelled by bus are 331-7 = 324 students
Therefore 324 students travelled in 6 buses.
Number of students travelled in each bus = 324/6 = 54 students.
Therefore number of students travelled in each bus is 54 students .
verification:
number of buses = 6
number of students in each bus = 54
Therefore total number of students in 6 buses = 6*54 = 324 students.
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State the interval for which the following function is positive and its intercepts.
Answer:
see explanation
Step-by-step explanation:
the function is positive for values of y above the x- axis
the line goes on forever on the left side and terminates at x = 15 on the right side.
the interval where the function is positive is (- ∞, 15 ]
the x- intercept is where the line crosses the x- axis ( y = 0 )
x- intercept = 15
the y- intercept is where the line crosses the y- axis (x = 0 )
y- intercept = 3
Is 12/5 a integer number?
Answer:
Step-by-step explanation:
No. It has to be a whole number in order to be an integer, and 12/5 = 2.4, and therefore is not a whole number.
Last month, Juan and Mariana sold candy to raise money for their debate team. Mariana sold 1/10 as much candy as Juan did. If Juan sold 3 boxes of candy, how many boxes of candy did Mariana sell?
The number of boxes of candy that Mariana sells is 3/10.
How many boxes of candy did Mariana sell?A fraction is a non integer that is made up of a numerator and a denominator. An example of a fraction is 3/10. 3 is the numerator and 10 is the denominator.
In order to determine the boxes of candy that Mariana sold, multiply the fraction of boxes that Mariana sold by the number of boxes of candy that Juan sold.
Multiplication is the mathematical operation that is used to determine the product of two or more numbers. The sign used to represent multiplication is x.
Boxes that Mariana sells = fraction of boxes that Mariana sells x number of boxes that Juan sold
1/10 x 3 = 3/10
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Tyshawn bought 23 chicken wings for $23.00. If Tyshawn spent $3.00, how many
chicken wings did he buy?
3 chicken wings he buys after spending $3.00
What is multiplication?When you take a single number and multiply it by several, you are multiplying. There are a number of distinct indications of amplification that people utilize. The "x" sign represents the most typical, however, other symbols like the "*" sign are also occasionally used.
Tyshawn spent $23.00 on 23 chicken wings.
Therefore in $1 the chicken wings that can be brought will be
= 23 /23
= 1
As he spent $3.00 on the chicken wings then the quantity that he has brought will be
= $3 * 1
= 3
The number of chicken wings that were brought was 3.
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order of operation
2[(4+5)⋅3]
Answer: 54
Step-by-step explanation:
2[(4+5)⋅3]
⇒2[9⋅3]
⇒2[27]
⇒54
Find the measure of ∠b ?
Answer:
Below
Step-by-step explanation:
b = 180 - 81° (because of the Z angle law)
b = 99°
Answer:
Step-by-step explanation:
by inspection it is given that b and 81° are inside the parallel angles...they are sorted such that now we know they are co-inter.. anglesb+81°=180 since co-inter... angles are supplementaryb=180°-81°∴b=99°irections: Determine if the equations are parallel, perpendicular, or neither
1. x + y = 8 and y = -x - 1
Answer: They are parallel
Step-by-step explanation:
Turn them both into slope-intercept form:
y = -x + 8
y = -x - 1
Since the slope on both of them are the same (-1), they are parallel
The function f(x) = 5(1/5)* is reflected over the y-axis. Which equations represent the reflected function? Select two
options.
Of(x) = -(5)-x
f(x)=3*
f(x) = 5(-3)*
Of(x) = 5(5)*
f(x) = 5(5)*
The equations that will represent the reflected function are:
(c) [tex]f(x)=5(\frac{1}{5})^{-x}[/tex] and;
(d) [tex]f(x)=5(5)^{x}[/tex]
If two functions share the same domain and codomain and have values that are consistent across all domain elements, they are said to be equivalent.
Consider the function,
[tex]f(x)=5(\frac{1}{5})^{x}[/tex]
Now,
Positive x-values and negative x-values are switched by a reflection over the y-axis, which also swaps the values of x and x.
So,
[tex]f(-x)=f(x)[/tex]
The reflection of the function f(x) across the y axis will be:
[tex]f(x)=5(\frac{1}{5})^{-x}[/tex]
Therefore, the equivalent function will be:
[tex]f(x)=5(\frac{1}{5})^{(-1)(x)}[/tex]
[tex]f(x)=5 \times ((\frac{1}{5})^{-1})^{x} \\f(x)=5(5)^{x}[/tex]
Therefore, the equations which represent the function are:
[tex]f(x)=5(\frac{1}{5})^{-x}[/tex] and;
[tex]f(x)=5(5)^{x}[/tex].
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The complete question is mentioned below:
The function [tex]f(x)=5(\frac{1}{5})^{x}[/tex] is reflected over the y-axis. Which equations represent the reflected function? Select two options.
(a) [tex]f(x)=\frac{1}{5}(5)^{-x}[/tex]
(b) [tex]f(x)=\frac{1}{5} \frac{1}{5} [\frac{1}{5} ]^{x}[/tex]
(c) [tex]f(x)=5(\frac{1}{5})^{-x}[/tex]
(d) [tex]f(x)=5(5)^{x}[/tex]
(e) [tex]f(x)=5(5)^{-x}[/tex]
if h(t)=1/t divided by 1 what is h(1/2)
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Given the function [tex]h(t)=\frac{1}{t+1}[/tex], we can find [tex]h(\frac{1}{2} )[/tex] by substituting [tex]\bf{t=\frac{1}{2}}[/tex].
When t= [tex]\frac{1}{2}[/tex],
[tex]h(\frac{1}{2})[/tex]
[tex]=\frac{1}{\frac{1}{2}+1 }[/tex]
[tex]=\frac{1}{(\frac{3}{2} )}[/tex]
[tex]=\bf{\frac{2}{3}}[/tex]
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You and a friend are playing a board game. your final score $x$ is $12$ points less than your friend's final score. write and solve an equation to find your final score. round 9 round 10 final score your friend 22 12 195 you 9 25 ? equation: $=195$ your final score is points.
The equation formed using the given data is 195 = x + 12 and your final score is 183 points.
How to form an equation?
Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let's say your final score is x
Given that,
Your final score x is 12 points less than your friend's final score.
So,
x = friend final score - 12
Now,
Friend final score = 195
So,
x = 195 - 12
x + 12 = 195
195 = x + 12
Now,
x = 195 - 12 = 183
Hence "The equation formed using the given data is 195 = x + 12 and your final score is 183 points".
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HELP WITH THIS PROBLEM PLEASE