Answer:
40 feet
Step-by-step explanation:
The perimeter of a triangle is the distance around the triangle. It can be found by adding all the sides together. First, find the amount each side is by substituting x = 4 and simplifying.
3x - 4 = 3(4) - 4 = 12 - 4 = 8
x² -1 = (4)² - 1 = 16 - 1 = 15
2x² - 15 = 2(4)² - 15 = 32 - 15 = 17
Add the sides together, 8 + 15 + 17 = 40 feet
The figures below are similar. the area of the larger trapezoid is 121m^2. Find the area of the smaller trapezoid to the nearest square meter. Please help!
Answer:
54 square meters
Step-by-step explanation:
Similar figures have corresponding lengths as equal ratios.
Smaller trapezoid's base is given 12 and larger trapezoids base is given 18, so the scale factor is [tex]12k=18\\k=\frac{18}{12}\\k=1.5[/tex]
this means the lengths of larger is 1.5 times lengths of smaller.
In terms of area, the scale factor is squared. Hence the scale factor for area is [tex]k^2=(1.5)^2=2.25[/tex]
this means the area of larger is 2.25 times the area of smaller.
Now, Let area of smaller trapezoid be x so we can say: [tex]x(2.25)=121\\x=\frac{121}{2.25}\\x=53.78[/tex]
to nearest square meter, x = 54 meters squared
△ABC is a right triangle with right angle at ∠B . AB=34 cm AC=55 cm What is the measure of ∠C , to the nearest degree? Enter your answer in the box.
Answer:
38°
Step-by-step explanation:
One side length is 34cm and the hypotenuse is 55cm. Used SOH-CAH-TOA to find what trig function to use. You have the opposite side and the hypotenuse, so use sine. SinC = 34/55. You can input this into a calculator as 34/55 and press sin^-1 to get the angle value, which is approximately 38°.
Answer:
△ABC is a right triangle with right angle at ∠B.
AB=34 cm
AC=55 cm
What is the measure of ∠C, to the nearest degree?
Enter your answer in the box.
38°
Step-by-step explanation:
There are red and blue balls in a bag. The number of blue balls is 27 and the red balls are 4/ 7 of all balls. What is the total number of balls in the bag?
➷ We know this:
3/7 = 27
You need to find the value of 1/7
To do this, divide by 3
27/3 = 9
1/7 = 9
Multiply this by 7 to get the total number of balls:
9 x 7 = 63
There are 63 balls.
✽➶ Hope This Helps You!
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➶ Have A Great Day ^-^
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If Logan's family can drive 23 1/8 miles on 1 gallon of gas,how far can they drive on 17 gallons
[tex]\bf \begin{array}{ccll} miles&\stackrel{gas}{gallons}\\ \cline{1-2}\\ 23\frac{1}{8}&1\\\\ x&17 \end{array}\implies \cfrac{23\frac{1}{8}}{x}=\cfrac{1}{17}\implies \cfrac{\frac{23\cdot 8+1}{8}}{x}=\cfrac{1}{17}\implies \cfrac{\frac{185}{8}}{x}=\cfrac{1}{17} \\\\\\ \cfrac{\frac{185}{8}}{\frac{x}{1}}=\cfrac{1}{17}\implies \cfrac{185}{8}\cdot \cfrac{1}{x}=\cfrac{1}{17}\implies \cfrac{185}{8x}=\cfrac{1}{17} \\\\\\ 3145=8x\implies \cfrac{3145}{8}=x\implies 393\frac{1}{8}=x[/tex]
Given a triangle with angles of 23, 90, 67, what type of triangle is it: acute, equiangular, obtuse, or right?
Answer:
It is a right triangle because if it contains a 90 degree angle (a right angle), it's a right triangle.
Step-by-step explanation:
It would be a right angled triangle because all triangles with a 90 degree angle are right angle triangles : 90 degrees is a right angle
What is the 101st term in the sequence 997, 989, 981, ...?
197
189
1805
1797
Answer: first option.
Step-by-step explanation:
Find the common difference d of the arithmetic sequence:
[tex]d=a_n-a_{(n-1)}\\d=989-997\\d=-8[/tex]
Then the formula for the 101st term is the shown below:
[tex]a_n=a_1+(n-1)d[/tex]
Where:
[tex]a_1=997\\d=-8\\n=101[/tex]
Substitute values into the formula. Therefore, you obtain:
[tex]a_n=997+(101-1)(-8)=197[/tex]
Answer:
[tex]a_{101}=197[/tex]
Step-by-step explanation:
The first term of the sequence is
[tex]a_1=997[/tex]
The given sequence is 997, 989, 981, ...
The common difference is
[tex]d=989-997=-8[/tex]
The nth ter of the sequence is
[tex]a_n=a_1+d(n-1)[/tex]
We plug in the first term and the common ratio to obtain;
[tex]a_n=997-8(n-1)[/tex]
[tex]a_n=997-8n+8[/tex]
[tex]a_n=1005-8n[/tex]
We substitute n=101 to get;
[tex]a_{101}=1005-8(101)[/tex]
[tex]a_{101}=197[/tex]
graph this Function 1: f(x) = −3x2 + 2
I guess that's f(x) = -3x^2+2
Well :
-3x^2+2=0
-3x^2=-2 / : (-3)
x^2= -2/-3
x^2= 2/3 / sqrt
x= +/ - sqrt(2)/sqrt(3)
We got the zero points.
x ~ +/- 0.81
f(0)= -3(0)^2 + 2
f(0)= 2
Mark three points:
(0.81;0)
(-0.81;0)
(0;2)
Connect with parabolic line and ya got a your graph
A campus radio station surveyed 500 students to determine the types of music they like. The survey revealed that 206 like rock, 161 like country, and 118 like jazz. Moreover, 30 like rock and country, 27 like rock and jazz, 22 like country and jazz, and 11 like all three types of music. What is the probability that a randomly selected student likes neither rock nor country? Note: A Venn diagram may be useful here.
Answer:
163/500 = 0.326
Step-by-step Explanation:
Drawing a Venn diagram for this, we will have 3 circles. One will represent rock, one will represent country, and one will represent jazz.
There are 11 students that like all 3 types of music. This means the number 11 goes in the intersection of all 3 circles.
There are a total of 30 students that like rock and country; taking out the 11 that like all 3, this leaves 30-11 = 19 students in the intersection of just rock and country.
There are a total of 27 students that like rock and jazz; taking out the 11 that like all 3, this leaves 27-11 = 16 students in the intersection of just rock and jazz.
There are a total of 22 students that like country and jazz; taking out the 11 that like all 3, this leaves 22-11 = 11 students in the intersection of just country and jazz.
There are 206 students that like rock; taking out the 11 that like all 3, the 19 that like rock and country, and the 16 that like rock and jazz, we have
206-(11+19+16) = 206-(46) = 160 in just rock.
There are 161 students that like country; taking out the 11 that like all 3, the 19 that like rock and country, and the 11 that like country and jazz, we have
161-(11+19+11) = 161-(41) = 120 in just country.
There are 118 students that like jazz; taking out the 11 that like all 3, the 16 that like rock and jazz, and the 11 that like country and jazz, we have
118-(11+16+11) = 118-38 = 80 in just jazz.
This leaves
500-(80+120+160+11+11+19+16) = 500-417 = 83 students that like none of the 3 types of music.
This means for the probability that a student likes neither rock nor country, they either like just jazz or none of the 3; this is (83+80)/500 = 163/500 = 0.326.
The probability that a randomly selected student likes neither rock nor country is;
P(R' ∩ C') = 0.326
Let us denote them as follows;
Number that like rock music be R
Number that like Country music be C
Number that like Jazz music be J
Thus, as we are given we have;
R = 206
C = 161
J = 118
R ∩ C = 30 - 11 = 19
R ∩ J = 27 - 11 = 16
C ∩ J = 22 - 11 = 11
R ∩ C ∩ J = 11
Thus, number that liked only jazz music is;n(only jazz) = J - [(R ∩ J) + (C ∩ J) + (R ∩ C ∩ J)]
n(only jazz) = 118 - (16 + 11 + 11)
n(only J) = 80
Number of students that liked only Rock music;n(only Rock) = R - [(R ∩ C) + (R ∩ J) + (R ∩ C ∩ J)]
n(only Rock) = 206 - (19 + 16 + 11)
n(only R) = 160
Number of students that liked only country music;n(only country) = C - [(R ∩ C) + (C ∩ J) + (R ∩ C ∩ J)]
n(only country) = 161 - (19 + 11 + 11)
n(only C) = 120
Now, the number of students that like neither of the 3 music is;
A' ∩ B' ∩ C' = 500 - [(R ∩ C) + (R ∩ J) + (C ∩ J) + (R ∩ C ∩ J) + n(only J) + n(only R) + n(only C)]
⇒ 500 - (80 + 120 + 160 + 19 + 16 + 11 + 11)
⇒ A' ∩ B' ∩ C' = 83
Thus, number of students that likes neither rock nor country is;
n(A' ∩ B') = (A' ∩ B' ∩ C') + n(only C)
n(A' ∩ B') = 83 + 80
n(A' ∩ B') = 163
Thus, probability that a randomly selected student likes neither rock nor country = 163/500 = 0.326
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Find the value of y. m angle 1 = 4y+22
I believe y = 41
Hope this helped!
The answer would be -21/4
Here’s how you solve it!
First move the variable to the left side which makes it change the sign to a negative
-4y➕1=22
Then you move the constant to the other side and change the sign
-4y=22-1
Now you subtract
22-1=21
-4y=21
Then divide both sides by -4
Then you are left with your answer
Y=-21/4
Hope this helps! :3
Identify the area of the rhombus. HELP PLEASE!!
Answer:
A = (x^2 - 2x - 8) m^2
Second option
Step-by-step explanation:
Area of rhombus = 1/2 d1 * d2
= 1/2(2x+4)(x-4)
= 1/2 (2x^2 -8x + 4x - 16)
= 1/2 (2x^2 - 4x - 16)
= x^2 - 2x - 8
This is the manipulated variable in an experiment or study whose presence or degree determines the change in the dependent variable. When graphed this is graphed usually on the horizontal axis.
Answer:
This is called the independent variable.
Step-by-step explanation:
We know this because it is independent of all outside factors. Additionally, the horizontal axis (also known as the x axis), is the axis known for the independent variable.
What is the solution to the system of equations? Use the substitution method. Y=?3x+12x+5y=18
The answer is
[tex]y = - 3x + \frac{18}{5} [/tex]
Will give brainliest!!! Landry took out a cash advance of $ 240 on his credit card. If the bank charges him a $ 3.20 fee and his credit card company charges 3.4 percent of the advance, how much did the advance cost him?
Answer:
$ 11.36
Step-by-step explanation:
The advance cost him;
3.20 + 3.4% of 240
3.20 + (3.4/100)*240
3.20 + 8.16 = $ 11.36
can someone PLEASE HELP ME ASAP!!!!!
Answer:
Last choice: 14 = (1/2)x(x - 12)
Step-by-step explanation:
base = x
height = x - 12
area = (1/2)bh
14 = (1/2)x(x - 12)
The answer is C. Thank Me Later ?
Bob started mowing his lawn at 9:55. It took 70 minutes. At what time did bob finish mowing?
60 minutes = 1 hour
55 + 5 = 60 70 - 5 = 65 10:00
10:00 + 60 min = 11:00 65 - 60 = 5
11:00 + 5 min = 11:05
Bob finished mowing at 11:05
The following system has a solution: x=10, y=-3, z=14
In this problem, we have the following System of Three Equations in Three Variables, so our goal is to determine whether [tex]x=10, \ y=-3, \ z=14[/tex] is the solution to this system, that is, the ordered triple [tex]P(x,y,z)[/tex] where three planes intersect.
The easier way to find the answer is to plug in the x, y and z values in the equations and figure out whether the equations satisfy the solutions. Then:
[tex]First \ Equation: \\ \\ 3(10)+7(-3)-14=-5 \\ \\ It \ satisfies \ the \ first \ equation \\ \\ \\ Second \ Equation: \\ \\ 9(10)-(-3)-4(14)=37 \neq 17 \\ \\ It \ doesn't \ satisfy \ the \ second \ equation[/tex]
STOP HERE! Since the x, y an z values doesn't satisfy the second equation, the [tex]x=10, \ y=-3, \ z=14[/tex] is not the solution to the system of equations.
A quantity x varies directly with y and inversely with z. Which expression represents the constant of variation, k?
A) xz/y
B) xy/z
C) z/xy
D) y/xz
There are x boys playing in the park. The number of girls playing in the park is equal to the square root of the number of boys. If the total number of boys and girls playing in the park is 42, find the number of boys. A. 36 B. 6 C. 49 D. 7
Answer:
Option A. 36
Step-by-step explanation:
Let
x-------> the number of boys
y------> the number of girls
we know that
[tex]x+y=42[/tex] -----> equation A
[tex]y=\sqrt{x}[/tex] -----> equation B
using a graphing tool to solve the system of equations
Remember that the solution is the intersection point both graphs
The solution is the point (36,6)
see the attached figure
therefore
The number of boys is 36
A yield sign measures 30 inches on all three sides. what is the area of the sign
Answer:
450
Step-by-step explanation:
To find an area of the triangle, you must first multiply the base and the height.
Which is NOT a major expense category?A) housingb) transportationc) electricityd) food???
Answer: the one that is not a magor epense catgortuy is c : transportation
Step-by-step explanation:
the answer is: C) transportation
What is the sum of the given polynomials in standard from? (x^2 -3x) + (-2x^2+5x-3)
The pic will help you
Good luck:))
a car insurance company paid 1758.90 to repair a car that has been rear ended. this was 75% towards the total cost of the repair. what was the total cost
Answer:
Step-by-step explanation:
$2345.20
The total cost price of the car is $2,345.2.
Given that, a car insurance company paid 1758.90 to repair a car that has been rear-ended. This was 75% of the total cost of the repair.
We need to find what was the total cost price of the car.
What is the cost price?The amount paid to purchase an article or the price at which an article is made is known as its cost price. The cost price is abbreviated as C.P. Selling Price: The price at which an article is sold is known as its selling price. The selling price is abbreviated as S.P.
Let the total cost price be x.
Now, 75% of x=1758.90
⇒0.75×x=1758.90
⇒x=$2,345.2
Therefore, the total cost price of the car is $2,345.2.
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https://brainly.com/question/11027396.
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Problem Eight days ago, I put 50 sheets of paper in my binder. I used the same number of sheets each day. Now I only have 2 sheets left. How many sheets of paper did I use each day?
As given,
Number of sheets of paper put in the binder 8 days ago = 50 sheets
Current number of sheets left after 8 days = 2 sheets
So, number of sheets used in 8 days = [tex]50-2=48[/tex] sheets
As it is stated that the same number of sheets are used each day, so number of sheets used per day = [tex]\frac{48}{8}=6[/tex] sheets.
Hence, 6 sheets of paper were used each day.
Answer:
6
Step-by-step explanation:
A company advertises that there are an average of 25 grams of potato chips in each bag of chips. A consumer group has collected a sample and wants to perform a test to see if the company is providing less than it advertises. H0: μ = 25 Ha: μ < 25 Which type of significance test should be used for this situation?
Answer:
one sample t-test will be appropriate in this case
Step-by-step explanation:
We are carrying out a hypothesis test of the mean with the population standard deviation being unknown. We shall estimate the population standard deviation with the sample equivalent, s in determining the value of the test-statistic.
Answer:
A left-tailed test
Step-by-step explanation:
If A=[tex]\left[\begin{array}{ccc}-4&-3&5\\-5&-4&-2\\-1&-2&-4\end{array}\right][/tex] and B=[tex]\left[\begin{array}{ccc}3&-4&-1\\-5&-5&1\\-1&-3&2\end{array}\right][/tex], find AB.
It's not C because
[tex](AB)_{1,1}=A_{1,c}B_{r,1}=\begin{bmatrix}-4&-3&5\end{bmatrix}\begin{bmatrix}3\\-5\\-1\end{bmatrix}=-2[/tex]
where [tex](AB)_{1,1}[/tex] denotes the element of [tex]AB[/tex] in row 1, column 1, [tex]A_{1,c}[/tex] denotes the first row of [tex]A[/tex], and [tex]B_{r,1}[/tex] denotes the first column of [tex]B[/tex].
It's not A because
[tex](AB)_{1,2}=A_{1,c}B_{r,2}=\begin{bmatrix}-4&-3&5\end{bmatrix}\begin{bmatrix}-4\\-5\\-3\end{bmatrix}=16[/tex]
It's not D because
[tex](AB)_{2,2}=A_{2,c}B_{r,2}=\begin{bmatrix}-5&-4&-2\end{bmatrix}\begin{bmatrix}-4\\-5\\-3\end{bmatrix}=46[/tex]
So B must be the correct answer (and it is).
(8CQ) Determine whether the series -5+25-125+... is convergent or divergent.
Answer:
The answer is divergent ⇒ answer (b)
Step-by-step explanation:
* The series is -5 + 25 + -125 + ........
- It is a geometric series with:
- first term a = -5 and common ratio r = 25/-5 = -5
* The difference between the convergent and divergent
in the geometric series is :
- If the geometric series is given by sum = a + a r + a r² + a r³ + ...
* Where a is the first term and r is the common ratio
* If |r| < 1 then the following geometric series converges to a / (1 - r).
- Where a/1 - r is the sum to infinity
* The proof is:
∵ S = a(1 - r^n)/(1 - r) ⇒ when IrI < 1 and n very large number
∴ r^n approach to zero
∴ S = a(1 - 0)/(1 - r) = a/(1 - r)
∴ S∞ = a/1 - r
* If |r| ≥ 1 then the above geometric series diverges
∵ r = -5
∴ IrI = 5
∴ IrI > 1
∴ The series is divergent
Examine the right triangle. What is the length of the hypotenuse, c?
Answers are in the pic
a^2+b^2=c^2 <----- the equation to find out sides for a right triangle
Every right triangle follows the pythagorean theorem: given the legs [tex]a[/tex] and [tex]b[/tex] and the hypothenuse [tex]c[/tex] we have
[tex]a^2+b^2=c^2 \implies c=\sqrt{a^2+b^2}[/tex]
In your case, a=3 and b=5, so we have
[tex]c=\sqrt{3^2+5^2}=\sqrt{9+25}=\sqrt{34}[/tex]
The area of rectangle bathroom floor is 53 5/8 feet. If the bathroom is 6 1/2 feet wide, what is the length
Answer:
The length is [tex]8\frac{1}{4}\ ft[/tex]
Step-by-step explanation:
we know that
The area of a rectangle is equal to
[tex]A=LW[/tex]
In this problem we have
[tex]A=53\frac{5}{8}\ ft^{2}[/tex]
[tex]W=6\frac{1}{2}\ ft[/tex]
convert to an improper fraction
[tex]A=53\frac{5}{8}=\frac{53*8+5}{8}=\frac{429}{8}\ ft^{2}[/tex]
[tex]W=6\frac{1}{2}=\frac{6*2+1}{2}=\frac{13}{2}\ ft[/tex]
substitute in the formula and solve for L
[tex]\frac{429}{8}=L\frac{13}{2}[/tex]
[tex]L=\frac{429*2}{8*13}=\frac{858}{104}\ ft[/tex]
Convert to mixed number
[tex]L=\frac{858}{104}=\frac{832}{104}+\frac{26}{104}=8\frac{1}{4}\ ft[/tex]
The length of the bathroom floor in this case is 8 1/4 feet.
The area of a rectangle is calculated by multiplying its length by its width. In this case, with the bathroom floor having an area of 53 5/8 square feet and a width of 6 1/2 feet, we can find the length as follows:
Area = Length x Width
53 5/8 = Length x 6 1/2
Length = 53 5/8 / 6 1/2
Length = 8 1/4 feet
Therefore, the length of the bathroom floor is 8 1/4 feet.
A 2012 Gallup survey of a random sample of 1014 American adults indicates that American families spend on average $151 per week on food. The report further states that, with 95% confidence, this estimate has a margin of error of ±$7 . (a) This confidence interval is expressed in the form: “estimate ± margin of error.” What is the range of values (lower bound, upper bound) that corresponds to this confidence interval? (Enter your answers as a whole number.) lower bound: upper bound: (b) What is the parameter captured by this confidence interval? What does it mean to say that we have " 95% confidence" in this interval? The parameter captured by this interval is the population mean weekly spending on food ???? for all American adults. " 95% confidence" means that this interval was found using a procedure that produces correct results 95% of the time. The parameter captured by this interval is the populations weekly spending on food ???? for all American adults. " 95% confidence" means that this interval is correct 95% of the time. The parameter captured by this interval is the population mean weekly spending on food ???? for all American adults. " 95% confidence" means that this interval represents 95% of the population of American adults. The parameter captured by this interval is the populations weekly spending on food ???? for all American adults. " 95% confidence" means that this interval was found using a procedure that produces correct results 95% of the time.
Answer:135.9
Step-by-step explanation:you just have to multiply
What are the zeros of the function? f(x)=x(x−2)(x+6)
Select each correct answer.
−6
−2
0
2
6
Answer:
-6,0,2
Step-by-step explanation:
f(x)=x(x−2)(x+6)
To find the zeros of the function, set the function equal to zero
0 =x(x−2)(x+6)
Using the zero product property
x=0 x-2 =0 x+6=0
Solve each equation
x=0 x=2 x=-6
There are three zero's
-6,0,2