So to estimate, I would look at each set of numbers and determine which ones have higher numbers. For example in the first set the highest I see is 12x5=60
In the second set I see 14 AND 16 automatic telling me to estimate that Destiny has more using 14x4=56, but keeping in mind there is a 16 as well...
Lawrence's father gave him 200 baseball cards. Each week, Lawrence purchase 25 baseball cards to add to his collection. Which inequality can be used to find w, the number of weeks after starting his collection when Lawrence will have more than 750 baseball cards in his collection?
Answer:
it would take 22 weeks to get 750 baceball cards
Step-by-step explanation:
sence you already have 200 and you get 100 every 4 weeks, then thats 20 weeks to get to 700, then add 2 more weeks to get 750
What is SIN A?
Question 4 options:
3/4
4/3
3/5
4/5
Final answer:
The value of sin A cannot be determined without knowing the value of angle A.
Explanation:
The question is asking for the value of sin A. In mathematics, sin A represents the sine of angle A. The sine function is a mathematical function that relates the ratio of the length of the side opposite the angle to the length of the hypotenuse of a right triangle.
The correct answer to the question is 3/5. To find this value, you need to know the value of angle A. Without that information, we cannot determine the exact value of sin A.
Final answer:
The correct value of SIN A from the given options cannot be determined without additional context. SIN A refers to the ratio of the side opposite to angle 'A' to the hypotenuse in a right triangle or the y-coordinate on the unit circle at angle 'A'. Possible values are within the range of -1 to 1.
Explanation:
The question 'What is SIN A?' is seeking the trigonometric value of the sine function at a particular angle denoted by 'A'. When presented with options like 3/4, 4/3, 3/5, and 4/5, we need additional information regarding angle 'A' or the context of a right triangle or unit circle to determine the correct value. Without this information, we cannot definitively answer which option is correct.
Generally, in a right triangle, SIN A would represent the ratio of the length of the side opposite to angle 'A' to the length of the hypotenuse. Therefore, it is a value between -1 and 1. The options 3/4 and 3/5 could potentially be correct since they are within this range, but 4/3 cannot be because it exceeds this range. In a unit circle context, sin A would represent the y-coordinate of a point on the circle's circumference at an angle 'A' from the x-axis.
The function f shown in the graph is an even function. The graph has been hidden for x ≥ 0. Complete the following sentences.
Answer:
1. f is increasing over the interval 0 < x < 2.
2. f(2) = 3
3. f is decreasing over the interval 2 < x < 5.
Answer
increasing
3
decreasing
Step-by-step explanation:
Tom is the deli manager at a grocery store. He needs to schedule employees to staff the deli department at least 260260260 person-hours per week. Tom has one part-time employee who works 202020 hours per week. Each full-time employee works 404040 hours per week. Write an inequality to determine nnn, the number of full-time employees Tom must schedule, so that his employees will work at least 260260260 person-hours per week.
Answer:
6
Step-by-step explanation:
260=20+40n
subtract 20
240=40n
divide by 40
n=6
Match the following items by evaluating the expression for x = -6.
x^-2
x^-1
x^0
x^1
x^2
Choices:
1/36
-6
36
1
-1/6
x^-2 matches 1/36
x^-1 matches -1/6
x^0 matches 1
x^1 matches -6
x^2 matches 36
Explanation:When evaluating expressions with exponents for a specific value, we simply substitute that value for x and follow the order of operations (PEMDAS). Here's the breakdown for each expression:
x^-2: (-6)^-2 = 1/(-6)^2 = 1/36
x^-1: (-6)^-1 = 1/(-6) = -1/6
x^0: (-6)^0 = 1 (any non-zero number raised to the power 0 equals 1)
x^1: (-6)^1 = -6 (any non-zero number raised to the power 1 equals itself)
x^2: (-6)^2 = (-6) * (-6) = 36
Therefore, the matches are as listed above.
1.
Use technology or a z-score table to answer the question.
The expression P(z<1.45) represents the area under the standard normal curve below the given value of z.
What is P(z<1.45)?
0.0735
0.0749
0.9251
0.9265
2.Use technology or a z-score table to answer the question.
The scores on a standardized test are normally distributed with a mean of 500 and a standard deviation of 60. Jake scored 520 on the test.
What percent of students scored below Jake?
Round your answer to the nearest whole number.
33%
57%
63%
72%
3.Use technology or a z-score table to answer the question.
Lengths of newborn girls are normally distributed with a mean of 49.2 cm and a standard deviation of 1.8 cm. Consider a group of 2000 newborn girls.
Approximately how many girls will be 51 cm or shorter?
1683
1856
1928
1964
4.The number 0.9967 represents the area under the standard normal curve below a particular z-score.
What is the z-score?
Enter your answer, as a decimal to the nearest hundredth, in the box.
5.Use technology or a z-distribution table to find the indicated area.
Suppose ages of cars driven by company employees are normally distributed with a mean of 8 years and a standard deviation of 3.2 years.
Approximately 75% of cars driven by company employees are older than what age?
2.1
4.8
5.9
10.2
Answer:
1.) 0.9265
2.) 63%
3.) 1683
4.) 5.9
I hope this helped and give me brainiest please
Answer:
Step-by-step explanation:
1) From standard distribution table we find that
P(Z<1.45) = 0.5+0.4265
=0.9265 Option d
2) Given that X, The scores on a standardized test is N(500,60)
percent of students who scored below Jake
[tex]=100*P(X<520)\\=100*P(Z<\frac{20}{60} )\\=100(0.5+0.1293)\\=62.93%\\=63%[/tex]
3) X, lengths of new born girls is N(49.2, 1.8)
n = 2000
P(X<51) = P(Z<1) =0.84
No of girls =2000(0.84) =1683
4) P(Z<2.72) is the answer
5)X, ages of cars driven is N(8,3.2)
75% correspond to z=0.675
X = 8+0.675(3.2) =10.16=10.2
Angle 3 and angle 4 are supplementary angles. Angle 3 is 88°. What is the measure of angle 4?
1. You do 180-88 because supplementary angles add up to 180°.
2. 180-88=92°. Angle 4 is 92°
Answer:
92 degrees
Step-by-step explanation:
YOUR WELCOME
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The scale on a map is 1: 25 000. How many kilometers on the ground is represented by 9 cm on the map?X
1 cm : 25000 cm
Convert 25000cm to km = 1cm : 0.25 km9cm = 9 x 0.25 km9cm = 2.25 kmOn a map with a scale of 1:25,000, 9 cm represents 225,000 km on the ground.
Explanation:To find how many kilometers on the ground is represented by 9 cm on the map, we can use the scale given. The scale is 1:25,000, which means that 1 cm on the map represents 25,000 cm on the ground. Since we want to find the number of kilometers, we need to convert the units. 1 km is equal to 100,000 cm. So we can set up the proportion: 1 cm (on the map) / 25,000 cm (on the ground) = 9 cm (on the map) / x km (on the ground). Cross multiplying, we get 1 * x km = 25,000 * 9 cm. Solving for x, we find that x = 225,000 km.
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the library is 5miles from the post office how many is the yards is the library from the post office
1 mile =1760 yd so 5 miles to the library=8800 yd yards hope this helps
The monthly payment for a home loan is given by a function f(p,r,n)f(p,r,n) where pp is the principal (the initial size of the loan), rr the interest rate, and nn the length of the loan in months. interest rates are expressed as a decimal: a % interest rate is denoted by r=0.06r=0.06. if p=400000,r=0.06p=400000,r=0.06, and n=192n=192(a 16-year loan), then the monthly payment is f(400000,0.06,192)=1195f(400000,0.06,192)=1195. furthermore, with these values we have
a) The monthly payment increases by approximately $6.60 for a $1000 increase in the principal. b) The monthly payment increases by approximately $39.25 for an increase in the interest rate from 0.075 to 0.08. c) The monthly payment increases by approximately $32.81 for a decrease in the loan term from 26 years to 24 years.
To solve these problems, we'll use the partial derivatives of the monthly payment function with respect to the principal P, interest rate r, and the length of the loan in months N.
Given values:
- Principal P = 450,000
- Interest rate r = 0.075
- Loan term N = 312 (26 years)
- Monthly payment [tex]\( f(450000, 0.075, 312) = 1962 \)[/tex]
Partial derivatives:
- [tex]\(\frac{\partial f}{\partial P} = 0.0066 \)[/tex]
- [tex]\(\frac{\partial f}{\partial r} = 7849 \)[/tex]
- [tex]\(\frac{\partial f}{\partial N} = -1.3672 \)[/tex]
a) The change in monthly payment per 1000 increase in loan principal
The partial derivative [tex]\(\frac{\partial f}{\partial P}\)[/tex] tells us the rate of change of the monthly payment with respect to the principal. To find the change in the monthly payment for a $1000 increase in the principal:
[tex]\[\Delta f \approx \frac{\partial f}{\partial P} \cdot \Delta P\][/tex]
Here, [tex]\(\Delta P = 1000\):[/tex]
[tex]\[\Delta f \approx 0.0066 \cdot 1000 = 6.6\][/tex]
So, the monthly payment increases by approximately $6.60 for a $1000 increase in the principal.
b) The change in monthly payment if the interest rate changes from [tex]\( r = 0.075 \) to \( r = 0.08 \)[/tex]
The partial derivative [tex]\(\frac{\partial f}{\partial r}\)[/tex] tells us the rate of change of the monthly payment with respect to the interest rate. To find the change in the monthly payment for a change in the interest rate from 0.075 to 0.08, we calculate the difference in the rates:
[tex]\[\Delta r = 0.08 - 0.075 = 0.005\][/tex]
Then, using the partial derivative:
[tex]\[\Delta f \approx \frac{\partial f}{\partial r} \cdot \Delta r\][/tex]
[tex]\[\Delta f \approx 7849 \cdot 0.005 = 39.245\][/tex]
So, the monthly payment increases by approximately $39.25 for an increase in the interest rate from 0.075 to 0.08.
c) The change in monthly payment if the length of the loan changes from 26 to 24 years
The partial derivative [tex]\(\frac{\partial f}{\partial N}\)[/tex] tells us the rate of change of the monthly payment with respect to the length of the loan in months. To find the change in the monthly payment for a change in the loan term from 26 years (312 months) to 24 years (288 months), we calculate the difference in months:
[tex]\[\Delta N = 288 - 312 = -24\][/tex]
Then, using the partial derivative:
[tex]\[\Delta f \approx \frac{\partial f}{\partial N} \cdot \Delta N\][/tex]
[tex]\[\Delta f \approx -1.3672 \cdot (-24) = 32.8128\][/tex]
So, the monthly payment increases by approximately $32.81 for a decrease in the loan term from 26 years to 24 years.
The complete question is
The monthly payment for a home loan is given by a function f(P, r, N) where P is the principal (the initial size of the loan), r the interest rate, and N is the length of the loan in months. Interest rates are expressed as a decimal: A% interest rate is denoted by r = 0.075. If P = 450000, r = 0.075 and N = 312 (a 26-year loan), then the monthly payment is f(450000, 0.075, 312) = 1962. Furthermore, with these values we have
[tex]\frac{\partial f}{\partial P}=0.0066, \quad \frac{\partial f}{\partial r}=7849, \quad \frac{\partial f}{\partial N}=-1.3672[/tex]
Estimate
a) The change in monthly payment per 1000 increase in loan principal.
b) The change in monthly payment if the interest rate changes from r = 0.075 to r = 0.08
c) The change in monthly payment if the length of the loan changes from 26 to 24 years.
Find the length of '' c '' using the pythagorean theorem. A triangle has a height of 5, and length of 12
Answer: 13
Step-by-step explanation:
[tex]5^{2} + 12^{2} = c^{2} \\25 +144= c^{2} \\\sqrt169= \sqrt c^{2} \\13=c[/tex]
Find the circumference of a cercle with the radious of 5.5 in. Use 3.14 for n round the nerest tenth
Answer:
34.54 in
Step-by-step explanation:
c = 2π r
c = 2 (3.14)(5.5)
c = 34.54 in
WHAT ARE THE ELEMENTS NEEDED TO PROVE SIMILARITY BETWEEN TWO FIGURES? EXPLAIN.
Answer:
AAA (Angle Angle Angle) Proving that the angles are the same (Or of the same ratio if diluted), if this is true, the two figures are similar.
SSS (Side Side Side) Proving all the sides are the same size (Or again of the same ratio) also proves similarity.
SAS (Side Angle Side) If two sides and the angle in between are the same, then the triangles are similar.
Step-by-step explanation:
EX)
Triangle A has sides 10, 5, and 12
Triangle B has sides 20, 10, and 24
The relationship is the same between both triangles, just that the sides are multiplied by 2. This is SSS
If Triangle A has two sides 5 and 10 with an angle of 25 degrees, then Triangle B must have that same angle alongside those two sides, or at least a consistent ratio if diluted. Proof SAS
If Triangle A and B have the same angles, they are similar.
V^2-8v=0 solving quadratic equation
Answer:
v = 0, or v = 8
Step-by-step explanation:
The quadratic can be factored, then the zero product rule applied.
v^2 -8v = 0
v(v -8) = 0
A product will be zero when any of the factors is zero. So, the solutions are values of v that make the factors be zero.
v = 0
v -8 = 0 . . . ⇒ . . . v = 8
3x − 2y = 6
3x + 10y = −12
Find the common x and y.
x = 1
y = -3/2
Solution: (1, -3/2)
//Hope it helps.
Answer:
(x, y) = (1, -1.5)
Step-by-step explanation:
Subtract the first equation from the second to eliminate the x-variable.
(3x +10y) -(3x -2y) = (-12) -(6)
12y = -18
y = -18/12 = -1.5
Substituting into the second equation, you get ...
3x +10(-1.5) = -12
3x -15 = -12 . . . . . . .simplify
3x = 3 . . . . . . . . . . . add 15
x = 1 . . . . . . . . . . . . . divide by 3
The values of x and y that satisfy both equations are (x, y) = (1, -1.5).
At a school 141 students play at least one sport. This is 30% of students at that school. How many students are at the school
Answer:
There are 470 students at the school.
Step-by-step explanation:
141 / x = 3 / 10 since 3/10 is equal to 30% you're looking for a denominator that corresponds equally to 141 and when simplified, 141 / x equals 3 / 10.
Use algebra to solve: 141 * 10 = 3x → 1410 = 3x → 470 = x.
Final answer:
There are 470 students at the school.
Explanation:
In the given question, we are dealing with a basic percentage problem. We are told that 141 students, which is 30% of all students at the school, are playing at least one sport. To find the total number of students in the school, we need to solve for the whole when a part and its percentage are known.
Let x represent the total number of students at the school. According to the question:
30% of x = 141 students
We can set up the equation:
0.30 * x = 141
To find x, we'll divide both sides of the equation by 0.30:
x = 141 / 0.30
Performing the division gives us:
x = 470
Therefore, there are 470 students at the school.
The points A, B, C, and D are taken in order on the circumference of a circle. Chords AC and BD intersect at point E. mABarc = 76° and mCDarc = 80°. Draw chord AD. Find m∠AEB.
Answer:
∠AEB = 78°see attached for a drawingStep-by-step explanation:
The angle where the chords cross is the average of the two intercepted arcs:
∠AEB = (∠AOB +∠COD)/2 = (76° +80°)/2 = 78°
___
Chord AD connects points A and D.
Which is the most appropriate to describe a quantity decreasing at a steady rate
Which is the most appropriate to describe a quantity decreasing at a steady rate?
With a linear equation.
Select the correct answer from each drop-down menu. ∆ABC has A(-3, 6), B(2, 1), and C(9, 5) as its vertices. The length of side AB is units. The length of side BC is units. The length of side AC is units. ∠ABC ≈ °.
Answer:
√50
√65
√145
105 °
Step-by-step explanation:
Given the coordinates
A(-3, 6)
B(2, 1)
C(9, 5)
To find the length of AB ,AC and BC, we will use distance formula
√((x2-x1)² + (y2-y1)²)AB:
√(2+3)² + (1-6)²
√5²+5²
√50
BC:
√(9-2)² + (5-1)²
√7² + 4²
√49+16
√65
AC:
√(9+3)² + (5-6)²
√12²+1²
√145
To find ∠ABC
cos(B) = c² + a² − b² / 2ca
= 65 + 50 - 145 / 2(√65)(√50)
cosB = -0.26311
B = cos^-1(-0.26311)
= 105 °
Answer:
√50
√65
√145
105 °
Step-by-step explanation:
Find the value of X. Round to the nearest 10th. diagram not to scale. (Image attached)
Will give BRAINLIEST to the first to answer correctly and please show your work :)
Answer: [tex]x=10.2[/tex]
Step-by-step explanation:
The triangle shown in the image attached is a right triangle.
Therefore, you can calculate the value of x as you can see below:
[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]
In this case, you have that:
adjacent=x
hypotenuse=11
[tex]\alpha=22\°[/tex]
Therefore, when you substitute values and solve for x, you obtain the following result:
[tex]cos(22\°)=\frac{x}{11}\\\\x=11*cos(22\°)\\x=10.2[/tex]
Answer:
The value of x = 10.2
Step-by-step explanation:
From the figure we can see a right angled triangle. One side and one angle are given.We have to find one side of triangle.
Points to remember
Cos θ = Adjacent side/Hypotenuse
To find the value of x
Here θ = 22°, Hypotenuse = 11, Adjacent side =?
Cos 22 = Adjacent side/Hypotenuse = x/11
x = 11 * Cos 22 = 11 * 0.9271 = 10.2 units
Express the following rate as a unit rate.
answering 36 questions in 3 minutes
18 questions per minute
12 questions per minute
15 questions per minute
36 questions per minute
The answer is 12 questions per minute as you divide 36 by 3
Answer=12 questions per minute
Answer:
12
Step-by-step explanation:
rewrite the following equation in exponential form. log^5 25=2
logb(x) = y is equivalent to b^y =x
y = 2
b = 5
x = 25
Substitute the values to get 5^2 = 25
A grocery store has 12 cartons of yogurt for sale, of which 3 are raspberry what is the probability that a randomly selected carton of yogurt will be raspberry?
a) 1/2,
b) 1/4,
c) 1/3
d) 4/5
Answer:
Your answer would be 1/4
Step-by-step explanation:
The probability that a randomly selected carton of yoghurt will be raspberry is 1/4. The correct option is b.
What is probability?Probability is defined as the ratio of the number of favourable 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 favourable outcomes / Number of sample
Given that a grocery store has 12 cartons of yoghurt for sale, of which 3 are raspberry.
The probability that a randomly selected carton of yogurt will be,
Probability = Number of favourable outcomes / Number of sample
Probability = 3 / 12
Probability = 1 / 4
Therefore, the probability that a randomly selected carton of yoghurt will be raspberry is 1/4. The correct option is b.
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A cylinder has a height of 10 cm and a radius of 4 cm. A cone has a height of 5 cm and a radius of 4 cm. How does the volume of the cylinder compare to the volume of the cone? A) It is 2 times larger. B) It is 3 times larger. C) It is 6 times larger. D) It is 9 times larger.
Plz help me
When graphed, which function has a horizontal asymptote at 4?
A.f(x)=2x-4
B.f(x)=2(3^x)+4
C.f(x)=-3x+4
D.f(x)=3(2^x)-4
Answer:
It is B.
Step-by-step explanation:
f(x) = 2(3^x) + 4
As x approaches negative infinity 2(3^x) approaches zero and f(x) approaches 4.
Answer:
B.[tex]f(x)=2(3^x)+4[/tex]
Step-by-step explanation:
We have to find that which graph has horizontal asymptote at 4
We know that to find the horizontal asymptote , we simply evaluate the limit of the function as it approaches to infinity or it approaches to negative infinity.
A.[tex]f(x)=2x-4[/tex]
[tex]\lim_{x\rightarrow \infty}(2x-4)=\infty[/tex]
[tex]\lim_{x\rightarrow -\infty}(2x-4)=-\infty[/tex]
Limit of function does not exits, so function have not horizontal asymptote.
B.[tex]f(x)=2(3^x)+4[/tex]
[tex]\lim_{x\rightarrow \infty}(2(3^x)+4)=\infty[/tex]
[tex]3^{\infty}=\infty [/tex]
[tex]\lim_{x\rightarrow -\infty}(2(3^x)+4)=4[/tex]
Because [tex]3^{-\infty}=0[/tex]
Hence, function have horizontal asymptote at 4.
C.[tex]f(x)=-3x+4[/tex]
[tex]\lim_{x\rightarrow \infty}(-3x+4)=\infty[/tex]
[tex]\lim_{x\rightarrow -\infty}(-3x+4)=-\infty[/tex]
Hence, function have not horizontal asymptote.
D.[tex]f(x)=3(2^x)-4[/tex]
[tex]\lim_{x\rightarrow \infty}(3(2^x)-4)=\infty[/tex]
Because [tex]2^{\infty}=\infty[/tex]
[tex]\lim_{x\rightarrow -\infty}(3(2^x)-4)=-4[/tex]
[tex]2^{-\infty}=0[/tex]
Hence, function have horizontal asymptote at -4.
Therefore, option B is true.
The cost of three tickets to a movie is at least $20. Select an inequality that represents the cost x (in dollars) of each ticket. Then solve the inequality. Write your solution in decimal form rounded to the nearest cent.
Answer:
[tex]x\geq \$6.67[/tex]
Step-by-step explanation:
Let
x------> the cost of each ticket
we know that
[tex]3x\geq 20[/tex] ----> inequality that represent the situation
solve for x
Divide by 3 both sides
[tex]x\geq 20/3[/tex]
[tex]x\geq \$6.67[/tex]
The cost of each movie ticket, represented by x, can be determined by solving the inequality 3x ≥ 20 which gives the result x ≥ $6.67.
Explanation:The subject problem can be formulated as an inequality problem based on the given information. The cost of three tickets is at least $20. Therefore, we can express it as 3x ≥ 20, with x representing the cost of each ticket.
To solve for x, we would simply divide each side of the inequality by 3. Thus we get x ≥ 20/3.
Converted into decimal form and rounded to the nearest cent, this gives us that x ≥ $6.67. Hence, by solving this inequality, we established that the cost of each movie ticket is at least $6.67.
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Which statement about function F and Function G is true?
Answer:
C. Both functions have a y-intercept of -2
Step-by-step explanation:
A. Function F in decreasing then increasing, therefore it's incorrect
B. Function F is symmetrical about the y-axis, but Function G is not
C. Both functions intercept the y-axis at (0,-2) so it's correct
D. Only function G shows a linear relationship.
To look at a picture of what Function G looks like. Press y= on your Ti-84 calculator (top left) put the function in, and then press graph (top right)
This is 100% correct. I took algebra 1 last year.
a thermometer read -17° f at 1:00 am. by 2:30 am the temperature has dropped 9.1 degree f. what was the temperature at 2:30 am?
Answer:
The temperature was -26.1° f at 2:30 am.
Step-by-step explanation:
* In this type of problems, we must think about
- What is the meaning of wards;
above and below or
raised and dropped or
increased and decreased
- For above , raised , increase
we will add the value of them to the initial value
- For below , dropped , decreased
we will subtract the value of them from the initial value
* In our problem:
- The reading of thermometer is -17° f at 1:00 am.
- The temperature has dropped 9.1° f when the time was 2:30 am.
* Lets use the explanation above
- We will subtract 9.1 from -17
∴ -17 - 9.1 = -26.1° f
* The temperature was -26.1° f at 2:30 am.
Final answer:
To find the temperature at 2:30 am, you subtract the temperature drop of 9.1°F from the initial temperature of -17°F, resulting in a new temperature of -26.1°F.
Explanation:
If a thermometer read -17°F at 1:00 am and by 2:30 am the temperature has dropped by 9.1 degrees Fahrenheit, we calculate the new temperature by simply subtracting the temperature drop from the initial temperature. Subtracting a negative change from the current temperature results in an even lower temperature because you are going further down the scale.
Here's the calculation:
Initial temperature at 1:00 am: -17°F
Temperature drop by 2:30 am: 9.1°F
New temperature at 2:30 am: -17°F - 9.1°F = -26.1°F
What is the are of a triangle (picture provided)
Answer:
Area Δ = 102.3 units² ⇒ The answer is (d)
Step-by-step explanation:
* Use the formula of the area:
∵ Area of the triangle = 1/2 (a)(b) sin(C)
∵ We have the length of the 3 sides
∴ Use cos Rule to find the angle C
∵ cos(C) = (a² + b² - c²)/2ab
∵ a = 25 , b = 13 , c = 17
∴ cos(C) = (25² + 13² - 17²)/2(25)(13) = 625 + 169 - 289/650 = 505/650
∴ m∠C = 39°
∴ Area Δ = (1/2)(25)(13)sin(39) = 102.3 units²
∴ The answer is (d)
Answer:
Area Δ = 102.3 units² ⇒ The answer is (d)
Step-by-step explanation:
Use the formula of the area:
∵ Area of the triangle = 1/2 (a)(b) sin(C)
∵ We have the length of the 3 sides
∴ Use cos Rule to find the angle C
∵ cos(C) = (a² + b² - c²)/2ab
∵ a = 25 , b = 13 , c = 17
∴ cos(C) = (25² + 13² - 17²)/2(25)(13) = 625 + 169 - 289/650 = 505/650
∴ m∠C = 39°
∴ Area Δ = (1/2)(25)(13)sin(39) = 102.3 units²
∴ The answer is (d)
lines DE and AB intersect at point C. What is the value of x? A) 12 B) 25 C) 38 D) 52
Answer:
B
Step-by-step explanation:
∠ACE and ∠ECB form a straight angle whose sum = 180°, hence
2x + 2 + 5x + 3 = 180
7x + 5 = 180 ( subtract 5 from both sides )
7x = 175 ( divide both sides by 7 )
x = 25 → C
The value of x if lines DE and AB intersect is 25
How to determine the value of xTo calculate the value of x, we make use of the following supplementary angle formula.
So, we have:
2x + 2 + 5x + 3 = 180
Collect like terms
2x + 5x+ 2 + 3 = 180
Evaluate the like terms
7x + 5 = 180
Subtract 5 from both sides
7x = 175
Divide both sides by 7
x = 25
Hence, the value of x is 25
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