Answers
Answer: 10
Step-by-step explanation:
It appears that [tex]\overline{AC} \perp \overline{BC}[/tex], so to check if this is the case, we can use the slope formula.
[tex]m_{\overline{AC}}=\frac{3-1}{6-2}=\frac{1}{2}\\m_{\overline{BC}}=\frac{3-7}{6-4}=-2[/tex]
Since these slopes are negative reciprocals, we can see that this is the case. So, we can take [tex]\overline{AC}[/tex] as the base of the triangle and [tex]\overline{BC}[/tex] as the height of the triangle, and then use the formula [tex]A=\frac{1}{2}bh[/tex].
Using the distance formula,
[tex]AC=\sqrt{(6-2)^{2}+(3-1)^{2}}=\sqrt{16+4}=2\sqrt{5}\\BC=\sqrt{(4-6)^{2}+(7-3)^{2}}=\sqrt{4+16}=2\sqrt{5}[/tex]
So, the area is [tex]\frac{1}{2}(2\sqrt{5})(2\sqrt{5})=\boxed{10}[/tex]
Related Questions
Miguel Rodriguez borrowed $300 from his brother Julio to pay for books and tuition. He agreed to pay Julio in 6 months with simple annual interest at 6.9%
Answers
The amount of the interest with simple interest of 6.9% will be $ 10.35.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
Miguel Rodriguez borrowed $300 from his brother Julio to pay for books and tuition.
He agreed to pay Julio in 6 months with simple annual interest at 6.9%
Then the amount of the interest will be
Amount = P x R x T / 100
We have
P = $ 300
R = 6.9%
T = 6 months = 0.5 years
Then we have
P = (300 x 6.9 x 0.5) / 100
P = $ 10.35
More about the simple interest link is given below.
https://brainly.com/question/2793278
#SPJ1
Use triangle XYZ to answer questions 3-5.
1) Use special right triangles to help find the length of segment XY. What is the exact height of triangle XYZ?
Click the keyboard button to enter your answer.
2)What is the exact area of triangle XYZ? Leave your answer in radical terms.
Click the keyboard button to enter your answer. Show your work.
3)What is the area of triangle XYZ to the nearest tenth of a square in?
Answers
Answer:
Step-by-step explanation:
With a detailed explanation from the internet
1/(x-5)+3/(x+2)=4
Answers
Answer:
[tex]\boxed{ \sf x=\dfrac{4\pm\sqrt{43}}{2}}[/tex]
Explanation:
[tex]\rightarrow \sf \dfrac{1}{x-5}+\dfrac{3}{x+2}=4[/tex]
make the denominators same
[tex]\rightarrow \sf \dfrac{1(x+2)}{(x-5)(x+2)}+\dfrac{3(x-5)}{(x+2)(x-5)}=4[/tex]
join the fractions together
[tex]\rightarrow \sf \dfrac{x+2+3x-15}{(x-5)(x+2)}=4[/tex]
cross multiply
[tex]\rightarrow \sf x+2+3x-15=4(x-5)(x+2)[/tex]
simplify
[tex]\rightarrow \sf 4x-13=4x^2-12x-40[/tex]
group the variables
[tex]\rightarrow \sf 4x^2-16x-27 = 0[/tex]
use quadratic formula
[tex]\rightarrow \sf x = \dfrac{-\left(-16\right)\pm \sqrt{\left(-16\right)^2-4\cdot \:4\left(-27\right)}}{2\cdot \:4}[/tex]
simplify the following
[tex]\rightarrow \sf x=\dfrac{4\pm\sqrt{43}}{2}[/tex]
Answer:
[tex]x=\dfrac{4 \pm \sqrt{43}}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]\dfrac{1}{(x-5)}+\dfrac{3}{(x+2)}=4[/tex]
Make the denominators of the algebraic fractions the same, then combine them into one fraction:
[tex]\begin{aligned}\implies \dfrac{1}{(x-5)} \cdot \dfrac{(x+2)}{(x+2)}+\dfrac{3}{(x+2)}\cdot \dfrac{(x-5)}{(x-5)} & =4\\\\\implies \dfrac{x+2}{(x-5)(x+2)}+\dfrac{3(x-5)}{(x-5)(x+2)} & = 4\\\\ \implies \dfrac{x+2+3(x-5)}{(x-5)(x+2)} & = 4\\\\ \implies \dfrac{4x-13}{(x-5)(x+2)} & = 4 \end{aligned}[/tex]
Multiply both sides of the equation by [tex](x-5)(x+2)[/tex]:
[tex]\begin{aligned}\implies \dfrac{(4x-13)}{(x-5)(x+2)}\cdot (x-5)(x+2) & = 4(x-5)(x+2)\\\\\dfrac{(4x-13)(x-5)(x+2)}{(x-5)(x+2)} & = 4(x-5)(x+2)\\\\4x-13 & = 4(x-5)(x+2)\\\\4x-13 & =4x^2-12x-40\\\\4x^2-16x-27 & = 0\end{aligned}[/tex]
Solve using the Quadratic Formula:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\implies a=4\\\implies b=-16\\\implies c=-27[/tex]
Therefore:
[tex]\implies x=\dfrac{-(-16) \pm \sqrt{(-16)^2-4(4)(-27)} }{2(4)}[/tex]
[tex]\implies x=\dfrac{16 \pm \sqrt{688}}{8}[/tex]
[tex]\implies x=\dfrac{16 \pm 4 \sqrt{43}}{8}[/tex]
[tex]\implies x=\dfrac{4 \pm \sqrt{43}}{2}[/tex]
I need help please asap?!!!
Answers
Answer:
3660
Step-by-step explanation:
'milli..' in the metric system means 1000 th
there are 1000 milliliters in a liter
3.66 liters * 1000 ml/liter = 3660 ml
Please help! This is a math question and due soon I don’t understand the charting part please help , thank you
Answers
Answer:
it's 0 I think ok hope this helped stay safe
Someone please help
Answers
Answer:
Part (a)Given:
[tex]\displaystyle \int\limits_{1}^{3} x^2 \:dx[/tex]
Trapezium Rule
[tex]\displaystyle \int\limits_{a}^{b} y \:dx \approx \dfrac{1}{2}h\left[(y_0+y_n)+2(y_1+y_2+...+y_{n-1})\right] \quad \textsf{where }h=\dfrac{b-a}{n}[/tex]
Calculate the width of each strip (h).
Given:
a = 1b = 3n = 5[tex]\implies h=\dfrac{3-1}{5}=0.4[/tex]
Create a table with the x and y values:
[tex]\large\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} x & 1 & 1.4 & 1.8 & 2.2 & 2.6 & 3\\\cline{1-7} y & 1 & 1.96 & 3.24 & 4.84 & 6.76 & 9\\\cline{1-7}\end{array}[/tex]
Put all the values into the formula:
[tex]\begin{aligned}\displaystyle \int\limits_{1}^{3} x^2 \:dx & \approx \dfrac{1}{2}(0.4)\left[(1+9)+2(1.96+3.24+4.84+6.76)\right]\\& = 0.2\left[10+2(16.8)\right]\\\\& = 0.2\left[10+33.6\right]\\\\& = 0.2\left[43.6\right]\\\\& = 8.72 \end{aligned}[/tex]
Part (b)[tex]\begin{aligned}\displaystyle \int\limits_{1}^{3} x^2 \:dx &=\left[\dfrac{1}{3}x^3\right]^3_1\\& = \dfrac{1}{3}(3)^3-\dfrac{1}{3}(1)^3\\& = 9-\dfrac{1}{3}\\& = \dfrac{26}{3}\end{aligned}[/tex]
The exact area as a decimal is [tex]\sf 8.\dot{6}[/tex]. Therefore, the estimated answer of 8.72 is an overestimate.
Part (c)Answer to (a) = 8.72
To find the maximum possible error:
Identify the last non-zero digit to the right of the decimal point → 2The precision of the number is the place value: 0.01Divide the precision by 2Therefore, the maximum possible error for 8.72 is 0.005.
Part (d)Trapezoid Error formula
[tex]|E| \leq \dfrac{(b-a)^3}{12n^2}\left[\textsf{max}|f''(x)|\right],\quad a \leq x \leq b[/tex]
Calculate the second derivative:
[tex]f(x)=x^2[/tex]
[tex]f'(x)=2x[/tex]
[tex]f''(x)=2[/tex]
Input the values into the formula:
[tex]\implies |E| \leq \dfrac{(3-1)^3}{12n^2}(2) < 0.001[/tex]
[tex]\implies 16 \leq 0.012n^2[/tex]
[tex]\implies 36.5148...\leq n[/tex]
[tex]\implies 37\leq n[/tex]
Suppose that a sample is taken from a population whose mean value is 45. As the sample size increases, which value will the sample mean approach?
Answers
Suppose that a sample is taken from a population whose mean value is 45, the sample mean will approach
[tex]\mu=45[/tex]
Which value will the sample mean approaches?Generally, the equation for the standard deviation is mathematically given as
Standard deviation sample mean [tex]\mu = \frac{\sigma}{\sqrt{n}}[/tex]
Therefore, where a population whose mean value is 45 for any sample
size, Hence mean of the sample mean is
[tex]\mu = \=x[/tex]
[tex]\mu=45[/tex]
In conclusion, the value the sample mean approach is
[tex]\mu=45[/tex]
Read more about the sample mean
https://brainly.com/question/14127076
#SPJ1
4. What is the total cost of 400 square feet of land if it sells for
$110 per square foot?
Answers
The total cost of 400 square feet of land if it sells for $110 per square foot is $ 44,000.
what is Area?Area is the quantity that expresses the extent of a region on the plane or on a curved surface.
Here, Total area = 400 sq. units
Cost per square foot = $ 110
Total Cost = Total area X Cost per unit area
TC = 400 X 110
TC = 44,000
Thus, the total cost of 400 square feet of land if it sells for $110 per square foot is $ 44,000.
Learn more about Area from:
https://brainly.com/question/27683633
#SPJ1
Which of the following describes the best method of solving two-step equations? A. Apply the multiplication property of equality first, and then apply the addition property of equality to isolate the variable. B. Apply the addition property of equality first, and then apply the multiplication property of equality to isolate the variable. C. Apply only the multiplication property of equality to isolate the variable. D. Apply only the addition property of equality to isolate the variable.
Answers
The best method of solving two-step equation is "Apply the multiplication property of equality first, and then apply the addition property of equality to isolate the variable"
How to solve two step equationFor instance:
40 = 5(x) - 5
40 = 5x - 5
Add 5 to both sides40 + 5 = 5x
45 = 5x
x = 45/5
x = 9
Therefore, the correct answer is "Apply the multiplication property of equality first, and then apply the addition property of equality to isolate the variable".
Learn more about equation:
https://brainly.com/question/1214333
#SPJ1
Using only the markings given in the diagram, which triangle congruence criterion can be used to prove that PQR and STU are congruent?
Answers
Answer: HL
Step-by-step explanation:
If the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent. The correct option is D, HL.
What is the HL theorem?According to the HL theorem, If the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent. therefore, the hypotenuse will be congruent to each other, and the corresponding sides will be congruent to each other.
In the two of the given triangle, ΔPQR and ΔSTU, the following things can be seen,
PR ≅ SU (Leg of the triangle)
RQ ≅ TU (Hypotenuse)
Also, since the two of the triangles are right angle triangle, and the length of the one leg of the two triangles is equal, also, the hypotenuse of the two triangle is equal. Therefore, Using the HL postulate. The two triangles can be said to be congruent.
Hence, the triangle congruence criterion can be used to prove that PQR and STU are congruent is HL Congruency.
Learn more about HL theorem:
https://brainly.com/question/11804042
#SPJ5
Part A: Describe the solution(s) to 9x² - 36x + 36 = 0 by just determining the radicand. Show your work. (10 points) Part B: Describe the solution (s) to x²-x + 4 = 0 by just determining the radicand. Show your work. (10) points) Part C: Solve 4x² + 23 – 35 using an - appropriate method. Show the steps of your work and explain why you chose the method used. (15 points) (35 points)
Answers
The solution to the equations are:
9x² - 36x + 36 = 0 has two equal real solutionsx² - x + 4 = 0 has no real solutionsThe factored expression of 4x² + 23 – 35 is 4(x² -3)Part A: Describe the solutionThe equation is given as:
9x² - 36x + 36 = 0
The above equation is a quadratic equation which can be represented as:
ax² + bx + c = 0
The discriminant (d) is calculated as:
d = b² - 4ac
So, we have:
d = (-36)² - 4 * 9 * 36
d = 0
A discriminant of 0 means that the equation has two equal real solutions
Hence, 9x² - 36x + 36 = 0 has two equal real solutions
Part B: Describe the solution
The equation is given as:
x² - x + 4 = 0
The above equation can be represented as:
ax² + bx + c = 0
The discriminant (d) is calculated as:
d = b² - 4ac
So, we have:
d = (-1)² - 4 * 1 * 4
d = -15
A discriminant of -15 means that the equation has no real solutions
Hence, x² - x + 4 = 0 has no real solutions
Part C: The solution to the expression
We have:
4x² + 23 – 35
Evaluate the difference
4x² -12
Factor out 4
4(x² -3)
Hence, the factored expression of 4x² + 23 – 35 is 4(x² -3)
Read more about quadratic expressions at:
https://brainly.com/question/10449635
#SPJ1
Find the surface area of the cube shown below. units 2 2 squared
Answers
The surface area of the cube with a side length of 2 units is 24 units squared
How to determine the surface area?The side length of the cube is given as:
l = 2
The surface area is calculated as:
Surface area = 6l^2
This gives
Surface area = 6 *2^2
Evaluate
Surface area = 24
Hence, the surface area of the cube is 24 unit squared
Read more about surface area at:
https://brainly.com/question/13175744
#SPJ1
Maria’s suitcase has a mass of 14 kilograms. Her sister’s suitcase
has a mass of 1,600 grams. Which suitcase has a greater mass?
Explain.
Answers
prefix kilo means 1000
so 1 kilogram = 1000 grams
14 kilograms = 14000 grams
14000 g > 1600 g
Maria's suitcase has a greater mass because 14,000 grams is greater than 1,600 grams.
gal created a painting with an area of 56 square inches and a length if 7 inches. they create a second painting with an area of 40square inches. it has the same width as the first painting. What is the kength of the second painting?
Answers
Answer:
5 inches
Step-by-step explanation:
the length of painting is 56/7 = 8in. to find the length of the 2nd painting divide the area by the width: 40/8 = 5
A group of people were surveyed, and the data about their age and hemoglobin levels was recorded in a two-way table. Based on the data in the
table, match each probability with its correct value.
Age
Hemoglobin Level
Less than 25 Years 25-35 Years Above 35 Years Total
Less than 9
21
32
76
129
Between 9 and 11
49
52
46
147
Above 11
69
44
40
153
Total
139
128
162 429
the probability that a person older
than 35 years has a hemoglobin
level less than 9
the probability that a person
younger than 25 years has a
hemoglobin level above 11
the probability that a person in the
25-35 age group has a hemoglobin
level less than 9
the probability that a person older
than 35 years has a hemoglobin
level between 9 and 11
0.25
0.47
0.28
0.50
Answers
The probability that a person older than 35 years has a hemoglobin level less than 9 is 0.47.
The probability that a person younger than 25 years has a hemoglobin level above 11 is 0 .50
the probability that a person in the 25-35 age group has a hemoglobin
level less than 9 is 0.25.
The probability that a person older than 35 years has a hemoglobin level between 9 and 11 is 0.28.
What are the probabilities?The probability that a person older than 35 years has a hemoglobin level less than 9 = number of people order than 35 that have a hemoglobin level less than 9 / total number of people over 35
= 76 / 167 = 0.47
The probability that a person younger than 25 years has a haemoglobin level above 11 = people over 25 that have a haemoglobin level above 11 / total number of people above 25
69/139 = 0 .50
The probability that a person in the 25-35 age group has a hemoglobin
level less than 9 = people between 25 - 35 that have a haemoglobin level less than 9 / total number of people between 25 - 35
= 32/128 = 0.25
The probability that a person older than 35 years has a hemoglobin level between 9 and 11= number of people order than 35 that have a hemoglobin level 9 - 11 / total number of people over 35
46 / 162 = 0.28
To learn more about probability, please check: https://brainly.com/question/13234031
#SPJ1
Miriam reduced a square photo by cutting 3 inches away from the length and the width so it will fit in her photo album. The area of the reduced photo is 64 square inches. In the equation (x – 3)2 = 64, x represents the side measure of the original photo. What were the dimensions of the original photo?
Answers
The dimensions of the original photo is: X = 11
Meaning of dimension.A dimension can be defined as the parameters, measurement, scale or size of an object or figure.
A dimension is so important as is gives us a visual representation of an object.
Analysis(x-3[tex])^{2}[/tex] = 64
(x-3) = [tex]\sqrt{64}[/tex]
x = 8 + 3
x = 11
In conclusion, The dimensions of the original photo is: X = 11
Learn more about Dimensions : https://brainly.com/question/26740257
#SPJ1
Evaluate the following for the given values. 7xy - y + x - 1 for x = -2 and y = -1
Answers
The value of the expression 7xy-y+x-1, when x = -2 and y = -1 is 12.
What is evaluation?
To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.
To evaluate the given mathematical expression, we substitute the values of the unknown into the expression.
Expression = 7xy-y+x-1If, x = -2, y = -1Substitute these values into the expression
Therefore,
7(-2)(-1)-(-1)+(-2)-1Applying BODMAS,
14+1-2-112.Hence, the evaluation of 7xy-y+x-1 is 12
Learn more about evaluation here: https://brainly.com/question/4344214
#SPJ1
How do you find the length of an unknown leg in a right triange
Answers
By using the pythagoras theorum you can find an unknown leg of right angled triangle.
Hypotenuse side is in the front of the 90 degree angle and other two sides can be taken as base and perpendicular, so formula goes as :-
(Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2
H^2 = B^2 + P^2
Step-by-step explanation:
Hope it helps you!!Solve for (x): (14.5x − 5(x + 2) ≤ 4 + 4(4 − 1/8x)
Answers
Answer:x ≤ 3
Step-by-step explanation:
(14.5x − 5(x + 2) ≤ 4 + 4(4 − 1/8x)
14.5x - 5x-10 ≤ 4 + 16 - 1/2x Get rid of the parenthesis
9.5x-10 ≤ 20-1/2x Combine like terms
10x - 10 ≤ 20
10x/10 ≤ 30/10
x ≤ 3
Which expression is equal to
5(2x²-1) + 3(7x² + 1)?
11x² + 2
11x-2
31x² + 2
31x²-2
Answers
Answer:
d
Step-by-step explanation:
A closed rectangular box has volume 38 cm ^3. What are the lengths of the edges giving the minimum surface area
Answers
Answer:
3.361 3.361 3.361 cm
Step-by-step explanation:
Minimum surface are will be a cube
LWH = 38
L = cubrt (38) = 3.361 side length cm
If angles A and B are consecutive interior angles, what is the measure of
angle B if angle A measures 75°?
Answers
Answer:
105
Step-by-step explanation:
Consecutive interior angles need to add up to 180 degrees.
Therefore, 180 - 75 = 105
Answer:
105°
Consecutive interior angles are always supplementary, they add upto 180°
.
.
Angle A = 75°
Angle B = 180 - 75 = 105°
Step-by-step explanation:
I hope it helps u dear ^_^
please help with this math question.
Answers
The coordinate grid of the ordered pair is gotten from the combination of the y and X axis of the graph.
Finding of the ordered pairUsing the coordinates, an ordered pair for the given point is:
G = (4,3) because the 4 corresponds to the point in y axis and 3 on the X axis. H= (10,8) because the 10 corresponds to the point in y axis and 8 on the X axis. J= (6,4) because the 6 corresponds to the point in y axis and 4 on the X axis. K= ( 2,1) because the 2 corresponds to the point in y axis and 1 on the X axis.Learn more about coordinate grid here:
https://brainly.com/question/20362114
#SPJ1
Which number is an integer?
O
0 0
O
34
2.3
Answers
Answer:
I think 34.
Step-by-step explanation:
It's because, 34 can be a positive integer. Decimals can also be integers, but, this one looks a better option. While, the
O
0 0
O
don't seem to be integers.
¹T¹h¹a¹n¹k¹s¹
Triangel ABC has vertices A(-2,1) B(2,2), and C(2,y). The area of the triangle is 4 square units.
Y=
Answers
Answer:
i wish i knew
Step-by-step explanation:
Pls help me i need quick responses TwT
Answers
Answer:
56%
Step-by-step explanation:
i think your missing some info.
I got this question while practicing MAP, can someone lend a hand?
Answers
Answer:
see the attachment photo!
Evaluate log 8 base 5
Answers
The answer is 1.29029.
Given : [tex]log_{5}8[/tex]To evaluate the given equation.Solution:[tex]log_{5}8=log(8)/log(5)[/tex]
As we know, [tex]log8=0.9030899[/tex] and [tex]log(5)=0.69897000[/tex]
So equating is the above equation, we get;
[tex]log_{5}8=0.9030899/0.6989700[/tex]
[tex]log_{5}8=1.292029[/tex]
Hence, The answer of [tex]log_{5}8[/tex] is [tex]1.29029[/tex].
To learn more about the log, refer:
https://brainly.com/question/1695836
Find the equation (in terms of x ) of the line through the points ( − 2 , 4 ) and ( 5 , 2 )
Answers
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{(-2)}}} \implies \cfrac{-2}{5 +2} \implies \cfrac{ -2 }{ 7 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-\cfrac{2}{7}}(x-\stackrel{x_1}{(-2)}) \implies y-4=-\cfrac{2}{7}(x+2) \\\\\\ y-4=-\cfrac{2}{7}x-\cfrac{4}{7}\implies y=-\cfrac{2}{7}x-\cfrac{4}{7}+4\implies y=-\cfrac{2}{7}x+\cfrac{26}{7}[/tex]
HELPPP HELP MEH plane intersects a prism parallel to the base of the prism. The cross section is a polygon with eight sides. The base of the prism has__ sides.
Answers
The minimum number of sides that the polygon at the base of the prism must has 4 sides.
What is a Polygon?This refers to the plane figure in geometry that has three or more sides and angles in a finite straight line.
As we know the minimum number of sides a polygon does the base of the polygon have 4 side.
Now, as the plane intersect a prism parallel to base of the prism so the polygon of 5 sides will form then at least the base of the polygon will have 4 sides.
Learn more about polygons here:
brainly.com/question/1592456
#SPJ1