The length of the side CA is 29.84. Therefore, option C is the correct answer.
We need to calculate the length b to two decimal places.
AB=14, BC=22 and ∠B=110°.
What is the cosine rule to find the length of the side of the triangle?The cosine rule to find the length of the side of the triangle is a²=b²+c²-2bc cos A.
b²=14²+22²-2×14×22×cos110°
⇒b²=680-616×(-0.342)
⇒b²=680+210.672
⇒b=29.84
The length of the side CA is 29.84. Therefore, option C is the correct answer.
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For which of the following intervals is the graph decreasing?
O A. -2
OB.-4
C. -8 < X <-5
OD. 6
If x+y=3 and xy=2 find the value of x^2+y^2
Answer:
yes but something like that
Answer:
5
Step-by-step explanation:
We know that
[tex]x + y = 3[/tex]
and
[tex]xy = 2[/tex]
Solve for x in first variable
[tex]x = 3 - y[/tex]
Substitute this into second equation
[tex](3 - y)y = 2[/tex]
[tex] - {y}^{2} + 3y - 2[/tex]
Simplify
[tex] {y}^{2} - 3y + 2[/tex]
[tex](y - 1)(y - 2)[/tex]
[tex]y = 1[/tex]
[tex]y = 2[/tex]
So x or y can be
[tex]x = 1 \: \: y = 2[/tex]
or
[tex]x = 2 \: \: \: y = 1[/tex]
So we need to find x^2 and y^2.
[tex] {2}^{2} + {1}^{2} = 5[/tex]
the set is points indicated by 10. is the ___of the angle
Answer:
the points indicats exterior of the angle
If the cost of white tiles is $240, what is the unit cost of white tiles?
I need help with C and G and are A,B,E, and F right?? Plz help ASAP
Answer:
$15 and 3600ft^2
Step-by-step explanation:
C) There are 16 white tiles used. The unit cost of a white tile=240/16=$15
E) The cafeteria area consists of 36 tiles of dimensions 10 ft x 10 ft, so the area of the floor is 3600ft^2
If you know the answer can you please walk me through how you got it.
Answer: Choice B
1 & 3/4
=============================================
Explanation:
Rewrite 1/2 into 4/8 so that it has the same denominator as 7/8.
Now that the denominators are the same, we focus on the numerators. This is because the equal denominators cancel out when we divide the fractions later on.
We'll divide the numerators 7 and 4 to get
7/4 = (4+3)/4
7/4 = (4/4) + (3/4)
7/4 = 1 + (3/4)
7/4 = 1 & 3/4
Meg can get 1 & 3/4 servings from the jug.
Please help! Solve each equation with its indicated method. Please show your work and upload a picture. Thank you!
1. Solve using substitution
2x + 3y = 24
-3x - 5y = 15
2. Solve using elimination
x - y = 3
2x + 4y = 9
Refer to the attachment
help me please it easy.
Answer: there is no picture attached or equation? what's the question?
Step-by-step explanation:
ok, what do you need help with?
Is the rate of change of the function 5? help pls :')
Answer: B
No, because y does not change by 5 every time x changes by 1
Step-by-step explanation:
rate of change is basically slope
if the rate of change of the function of 5, then the slope will be 5/1
The x changes by 1 every time y changes by 4
so the slope of the function is 4
If necessary, write in simplest radical form
Answer:
2*sqrt(5)
Step-by-step explanation:
By using Pythagoras theorem, we have
4^2+2^2=(the third side)^2
16+4=(the third side)^2
Third side=sqrt(20)=2*sqrt(5)
In the game of Twister, a spinner randomly selects either an arm or a leg, and also selects one of four colors, one of which is red, each with equal probability, and players have to move the appropriate body part to the appropriately colored spot on the ground. There are four players. Each player spins once, and makes the move the spinner selects. What is the probability that in these four spins, there will be exactly two moves to a red spot, and the body part selected to move will be an arm exactly $3$ times
Answer:
In agreement to your twister question, a spinner can randomly select whether they want to put an arm or a leg, meaning this choice is entirely upon them. The color choice is also independent, so spinners are allowed to choose freely, whichever color as well as limb they want to move in the game of twister.
See the attached image for step by step explanation of the final probability
When a projector is placed 10 meters from a screen as shown, it produces an image 3 meters high. If the tallest image that the projector can produce without distortion is 4.5 meters high, what's the maximum distance the projector can be placed form the screen
Answer:
Step-by-step explanation: 10 meters/3 meters =x/4.5 meters
Where x = the maximum distance the projector can be placed that can produce an image 4.5 meters high
3x = 10 (4.5)
3x = 45
X= 45/3
X= 15 meters
So, the maximum distance that the projector can be placed from the screen which produces an image 4.5 meters high is 15 meters.
Select all sets in which the number - 12 is an element.
A. real numbers
B. whole numbers
C. integers
D. irrational numbers
E. natural numbers
F. rational numbers
Help plz
real numbers, integers, rational numbers
=========================================================
Explanation:
So far in your studies, every number is a real number. This is assuming your teacher hasn't introduced complex or imaginary numbers yet.
So that's why -12 is a real number.
Choice A is one of the answers
---------------
The set of whole numbers is {0,1,2,3,4,...} so we aren't including negative values here, which rules out choice B. However, the set of integers does include negative values
{..., -3, -2, -1, 0, 1, 2, 3, ...}
That makes -12 an integer
Choice C is one of the answers
----------------
The value -12 is not irrational because we can write it as a fraction of two integers. Eg: -12 = -12/1
This shows that -12 is rational and why choice F is one of the answers and allows us to rule out choice D.
------------------
We can rule out choice E because the set of natural numbers is {1,2,3,4,...} basically the set of whole numbers but we kicked out 0.
The requried, -12 is an element of sets of real numbers, integers, and rational numbers. Options A, C, and F are correct.
What is a number system?A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.
What is set?Sets are an orderly collection of items in mathematics that can be expressed in set-builder or roster form.
Here,
Only sets that consist of negative values are, real numbers, integers, and rational numbers.
So - 12 is a negative number that belongs to the set of real numbers, integers, and rational numbers.
Thus, the requried, -12 is an element of sets of real numbers, integers, and rational numbers. Options A, C, and F are correct.
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PLS HELP WILL GIVE BRAINLY!!
What is the weight (in grams) of a liquid that exactly fills a 182.8 milliliter container if the density of the liquid is 0.135grams over milliliter? Round to the nearest hundredth when necessary, and only enter numerical values, which can include a decimal point
Answer:
24.68 gram
Step-by-step explanation:
Given that :
Volume = 182.8 ml
Density of liquid = 0.135 gram/ml
Recall :
Density = mass (g/ml) / volume (ml)
Substitute the value into the equation :
0.135 = mass / 182.8
Mass = 0.135 * 182.8
Mass = 24.678 gram
Hence, weight = 24.678 grams
What is the equation of a line that passes through the point (5,3) and has a slope of -2?
Answer:
y = -2x +13
Step-by-step explanation:
you know the point is (5,3) and slope is -2
sub into the linear equation y=mx+b
3 = -2(5) +b
rearrange and solve for b
b= 3 + 10
b = 13
find x.
can someone work it out for me so i can try and figure out how to do problems like this on my own? please and thank you
Answer:
x = 7/2
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj side / hypotenuse
cos 45 = x / 7 sqrt(2) /2
7 sqrt(2)/2 cos 45 = x
7 sqrt(2)/2 (1/ sqrt(2))= x
7/2 = x
Which two repeating decimals are equivalent to 10/11 A b c or D
Answer:
I think it is 0.909090909090. Hope this helped.
Step-by-step explanation:
PLS PLS help me create a new polynomial identity ASAP!!!!!
(y+x) + (ax+b)
Square the expression on the left, then add the expression on the right.
Answer:
ax + b + y^2 + 2yx + x^2
Step-by-step explanation:
(y+x)^2
= (y+x)(y+x)
= y^2 + 2yx + x^2
y^2 + 2yx + x^2 + (ax+b)
= ax + b + y^2 + 2yx + x^2
Please hurry I will mark you brainliest
What is the slope of the line with an x-intercept of 4 and a y-intercept of -3?
the answer to this question is the slope is 43
Answer:
Therefore, the slope is 3/4
Step-by-step explanation:
An x -intercept is the value of x when y=0 , so an x-intercept of 4 can be written as a coordinate on the graph as (4,0)
Likewise, an
y -intercept is the value of y when x=0 , so an y -intercept of −3can be written as a coordinate on the graph as (0,-3)
Now we have two points(4,0) (0,-3)
To find the slope given two points, we use the formula
rise÷run , or y2−y1÷x2−x1 .
Plug in the given points into the formula
-3-0/0-4
-3/-4
3/4
Therefore, the slope is 3/4
Hope this helps!
Please help quick pleaseeeeeeeeeeee
Answer:
think this one
Step-by-step explanation:
the answers there
i think
Convert 7.5 gallons to quarts using a unit multiplier.
Answer:
7.5 Imperial Gallons = 30 Imperial Quarts
Hi there!
»»————- ★ ————-««
I believe your answer is:
30 qt.
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
There are 4 quarts in a gallon.7.5 * 4 = 30
7.5 gal. = 30 qt.
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Joanna bakes a cake in the shape of a
cylinder. The cake is 10 inches in
diameter and 4.5 inches tall. She
wants to put frosting on the entire
cake that is not resting on the tray.
How many square inches of frosting
will she need? im confused on how to do the work. please answer quickly
Answer:
total surface area = 298.45105 m2
lateral surface area = 141.37155 m2
top surface area = 78.53975 m2
bottom surface area = 78.53975 m2
Step-by-step explanation:
Joanna will need approximately 298.3 square inches of frosting to cover the entire cake.
To calculate the amount of frosting Joanna will need for the entire cake, we first need to find the surface area of the cylindrical cake.
The formula for the surface area of a cylinder is given by:
Surface Area = 2πr² + 2πrh
Where r is the radius of the base and h is the height of the cylinder.
Given that the diameter of the cake is 10 inches, we can find the radius by dividing it by 2: r = 10/2 = 5 inches.
Plugging in the values, we have:
Surface Area = 2π(5)² + 2π(5)(4.5)
Simplifying the equation:
Surface Area = 2π(25) + 2π(22.5)
Surface Area = 50π + 45π
Surface Area = 95π
To find the actual numerical value, we can approximate π as 3.14:
Surface Area ≈ 95 * 3.14
Surface Area ≈ 298.3 square inches
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Prove hat the ditance between any two points inside triangle ABC is not greater than half the perimeter of ABC
Answer:
It is not because the half the perimeter is not only one side but another half side of the triangle, and the distence between two points in a triangle can never become longer then the length of one side.
Step-by-step explanation:
The math part I am unsure of because you did say prove but let me know if this helps. Thanks!
Find the value of ( 1+cosA) (1-cosA)
Answer:
sin^2 A
Step-by-step explanation:
first expand the trigonometry
1(1-cosA)+cosA(1-cosA)
=1-cosA+cosA-cos^2 A
= 1-cos^2 A
from trigonometric identity sin^2 A + cos^2 A= 1
sin^2 A= 1- cos^2 A
=sin^2 A
Phil’s age is 7 years more than times Peter’s age. Also, 4 times Phil’s age is 2 years less than twice Peter’s age. If x is Peter’s age in years, identify the equation that represents this situation and identify the solution to the equation
Answer:
simultaneous equations
Step-by-step explanation:
phils age =7x
Peter age=x
scenario 2
phils age = 4(7x)
Peter age= 2x-2
[tex]7x + x = 4(7x) + 2x - 2[/tex]
The Lewis family and the Martin family each used their sprinklers last summer. The water output rate for the Lewis family's sprinkler was 30L per hour. The water output rate for the Martin family's sprinkler was 15L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total water output of 1350L. How long was each sprinkler used
Answer:
Martin family: 20 hours
Lewis family: 35 hours
Step-by-step explanation:
Let's say that the Lewis family sprinklers were out for L hours and the Martin family's sprinklers were out for M hours. We know that for each hour that the Lewis family sprinkler was on, 30L of water was put out. We can thus write the Lewis family sprinkler water output as 30L per each hour of L = 30 * L. Similarly, the Martin family sprinkler water output = 15 * M .
We know that the total hours for the sprinklers is 55, so L + M = 55. The total water output for the sprinklers is the sum of the sprinkler outputs, so 30 * L + 15 * M = 1350
L + M = 55
30 * L + 15 * M = 1350
One way to solve this would be to solve for L in the first equation and substitute that into the second
subtract M from both sides in the second equation
55 - M = L
30 * (55-M) + 15 * M = 1350
30 * 55 - 30 * M + 15 * M = 1350
1650 - 15M = 1350
subtract 1650 from both sides to isolate the M and its coefficient
-15M = -300
divide both sides by -15 to isolate M
M = 20
L = 55-20 = 35
NEED HELP ASAP!
Slove for x.
A.4
B.10
C.8
D.7
i think it 10 because the angle your looking at is x is 7
Find the slope and the y-intercept of the line.
- 3x - 4y= -20
Write your answers in simplest form.
Answer:
The slope is -3/4 and the y intercept is 5
Step-by-step explanation:
- 3x - 4y= -20
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
Solve for y
Add 3x to each side
- 3x - 4y+3x=3x -20
-4y = 3x-20
Divide by -4
-4y/-4 = 3x/-4 -20/-4
y = -3/4 x+5
The slope is -3/4 and the y intercept is 5
Answer:
Slope: [tex]\displaystyle-\frac{3}{4}[/tex]
Y-intercept: 5
Step-by-step explanation:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex], where m is the slope and b is the y-intercept.
[tex]-3x-4y=-20[/tex]
To find the slope and y-intercept of the given line, rearrange the equation into slope-intercept form. We can do this by isolating y.
Add 3x to both sides:
[tex]-3x-4y+3x=-20+3x\\-4y=3x-20[/tex]
Divide both sides by -4:
[tex]y=\displaystyle -\frac{3}{4} x+5[/tex]
Now, we can identify [tex]\displaystyle-\frac{3}{4}[/tex] to be in place of m, the slope, and 5 to be in place of b, the y-intercept. Here is a comparison:
[tex]y=\displaystyle -\frac{3}{4} x+5[/tex]
[tex]y=mx+b[/tex]
I hope this helps!
Tommy started a business in the year 1991. He got $44,000 profit in the first year. Each year his
profit decreased by 3%. Identify an exponential decay model to represent his decreasing annual
profit in the business?
Answer= decreasing annual profit in the business
are $13200.
Answer:
[tex]P = 44,000(.97)^{t}[/tex]
P=Profit
t=years
Step-by-step explanation:
[tex]P = 44,000(.97)^{t}[/tex]
P=Profit
t=years
Pls answer my question ty ;)
Answer:
x=11
Step-by-step explanation:
5x+7=62
5x=62-7
5x=55
x=11
Answer:
Step by step explanation:
Answer:
Step-by-step explanation:
a) [tex]t_{n}[/tex] = 2n - 3
[tex]t_{1}=2*1-3 = 2-3=-1\\\\t_{2}=2*2-3=4-3=1\\\\t_{3}=2*3-3=6-3=3\\\\t_{4}=2*4-3=8-3=5\\\\S_{4}=t_{1}+t_{2}+t_{3}+t_{4}\\\\= -1 + 1 + 3 + 5 \\\\= 8[/tex]
d)
[tex]t_{n}=\frac{2n-1}{2n+1}\\\\\\t_{1}=\frac{2-1}{2+1}=\frac{1}{3}\\\\t_{2}=\frac{4-1}{4+1}=\frac{3}{5}\\\\t_{3}=\frac{6-1}{6+1}=\frac{5}{7}\\\\t_{4}=\frac{8-1}{8+1}=\frac{7}{9}\\\\[/tex]
[tex]S_{n}=\frac{n}{2}(a+l)\\\\S_{4}=\frac{4}{2}(\frac{1}{3}+\frac{7}{9})\\\\=2*(\frac{1*3}{3*3}+\frac{7}{9})\\\\=2*(\frac{3}{9}+\frac{7}{9})\\\\=2*\frac{10}{9}\\\\=\frac{20}{9}[/tex]
