Answers
x =14
Answer:
[tex] m\angle ABC = 51°[/tex]
Step-by-step explanation:
11. By inscribed angle theorem:
[tex] 83°=\frac{1}{2} \times (9x+40)°\\\\
83°\times 2 = (9x+40)°\\
166°= (9x+40)°\\
166 = 9x + 40\\
166 - 40 = 9x\\
126 = 9x\\\\
x = \frac{126}{9}\\\\
\huge \red {\boxed {x = 14}} [/tex]
12. Again by inscribed angle theorem:
[tex] (5x+11)°=\frac{1}{2} \times (16x-26)°\\\\
2\times (5x+11)°= (16x-26)°\\
(10x+22)°= (16x-26)°\\
10x + 22 = 16x - 26\\
22+26 = 16x - 10x\\
48= 6x\\\\
x = \frac{48}{6}\\\\
\huge \purple{\boxed {x = 8}}\\
m\angle ABC = (5x+11)°\\
m\angle ABC = (5\times 8+11)°\\
m\angle ABC = (40+11)°\\
\huge \orange{\boxed {m\angle ABC = 51°}} \\
[/tex]
Related Questions
The numbers $1,$ $2,$ $\dots,$ $10$ are to be entered into the 10 boxes shown below, so that each number is used exactly once: \[P = (\square + \square + \square + \square + \square)(\square + \square + \square + \square + \square).\]What is the maximum value of $P$? What is the minimum value of $P$?
Answers
Hint
If we define x to be the value of one of the factors, since 1 + 2 + 3 + 4 + 5 ... + 10 = 11(5) = 55, the value of the other factor has to be 55-x.
To maximize P, you'd like to make x as close as possible to the vertex you found. What if you want to minimize P? Remember x must be an integer.
I hope this helps :)
it was found that out of 45 girls,10 joined singing but not dancing and 24 joined dancing . how many joined but not singing ? how many joined both
Answers
45-10 singing= 35 not singing
45-24 dancing = 21 not dancing
24+10= 34 in singing OR dancing,
Subtract the 34 from 45
which leaves 11 in both singing AND dancing.
21 girls joined but not singing and 14 girls joined both singing and dancing.
What are Arithmetic operations?Arithmetic operations can also be specified by the, subtract, divide, and multiply built-in functions.
Total no. of girls = 45
No. of girls are dancing = 24
No. of girls are singing but not dancing = 10
No. of girl are both singing and dancing = 24-10 = 14
No. of girls are dancing but not singing = 45-24=21
Hence, 21 girls joined but not singing and 14 girls joined both singing and dancing.
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The function f(x) = (x - 4)(x-2) is shown.
What is the range of the function?
1:01
all real numbers less than or equal to 3
all real numbers less than or equal to - 1
all real numbers greater than or equal to 3
all real numbers greater than or equal to -1
6+
4
2
10.-
-6
-4
8
10
X
-2
-2
-4
-6
-10
Save and Exit
Next
Submit
Mark this and return
Answers
Answer:
the range for f(x) = (x-4) (x-2) is [-1,∞)
Step-by-step explanation:
all real numbers greater than or equal to -1
The range of the function is all real numbers greater than or equal to -1
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
Let the function be represented as A
Now , the value of A is
f ( x ) = ( x - 4 ) ( x - 2 ) be equation (1)
On simplifying , we get
f ( x ) = x ( x - 2 ) - 4 ( x - 2 )
f ( x ) = x² - 2x - 4x + 8
f ( x ) = x² - 6x + 8
Now , the range of the function is set of possible y values
The vertex of the parabola is at ( 3 , -1 )
So , the range of the function is f ( x ) ≥ -1 and the interval is [ -1 , ∝ ]
Hence , the range of the function is f ( x ) ≥ -1
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PLEASE HELP ASAP A group of 8th and 9th graders were surveyed about whether they use social media to communicate with their friends. The results are shown below in the conditional relative frequency table by row. A 4-column table with 3 rows. The first column has no label with entries 8th grade, 9th grade, total. The second column is labeled do not use with entries 0.06, 0.19, 0.38. The third column is labeled use with entries 0.84, 0.81, 0.62. The fourth column is labeled total with entries 1.00, 1.00, 1.00. Which conclusions can be drawn from the results of the survey? Check all that apply. There is no association between using social media and grade level. The probability a student uses social media, given that he or she is in 9th grade, is 81%. A student who is more likely to not use social media is in 8th grade. An 8th grader is more likely to use social media than not. Knowing a student’s grade level does not help determine if he or she uses social media.
Answers
Options A, B, D, and E are correct answers such that the probability of the usage of social media by 8th and 9th-grade students is given.
A. There is no association between using social media and grade level.
B. The probability a student uses social media, given that he or she is in 9th grade, is 81%.
D. An 8th grader is more likely to use social media than not.
E. Knowing a student’s grade level does not help determine if he or she uses social media.
What is Probability?Probability is the ratio of the favorable outcomes to the total outcomes.
Given that, a group of 8th and 9th graders were surveyed about whether they use social media to communicate with their friends.
We can see that, there is no relationship between the usage of social media and grade level so, we can say that there is no association between using social media and grade level.
Probability of using social media by a 9th grader is-
P(9) = 0.81 / 1 x 100 = 81%
Probability of using social media by a 8th grader is-
P(8) = 0.84 / 1 x 100 = 84%
We cannot define the usage of social media depending on the grade level.
Thus, Options A, B, D, and E are correct answers.
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The table is attached
-2x2-x-1=0
our answer...
Answers
Answer:
_______________________________________
→ x = - 1 ± i√7 ;
4
_______________________________________
Or: Write as:
_______________________________________
→ x = -1 + i√7 ; -1 − i√7 ;
4 4
_______________________________________
Step-by-step explanation:
_______________________________________
Given:
-2x² − x − 1 = 0 ;
Solve for " x " .
________________
First, let us multiply BOTH sides of the equation by "-1" ;
to get rid of that "negative sign" in the coefficient: " -2" ;
→ as follows:
________________
-1 * {-2x² − x − 1 } = 0 *{-1} ;
_________________
Rewrite the value: "x" on the "left-hand side" of the question; as: "1x" ;
since "any value" ; multipled by "1" ; results in that same individual value:
_________________
-1 * {-2x² − 1x − 1 } = 0 *{-1} ;
________________
Note the "distributive property" of multiplication:
________________
a(b + c) = ab + ac ;
________________
Likewise, from the "left-hand side" of the equation:
-1 * {-2x² − 1x − 1 } = {-1 * -2x²} + {-1 * -1x} + {-1* -1 } ;
= 2x² + 1x + 1 ;
_______________________________________
Rewrite the "left-hand side" of the equation:
2x² + 1x + 1 ;
Now, the "right-hand side of the equation:
" { 0 * -1 } = 0 " .
Now, rewrite the entire equation:
2x² + 1x + 1 = 0 ;
________________
Note: This equation is written in "quadratic format" ;
that is: " ax² + bx + c " ; [a ≠ 0] ;
→ in which:
a = 2 ; b = 1 ; c = 1 ;
________________
→ which means we can solve for the value(s) for "x" ; by using the
"quadratic equation formula" ;
→ that is:
________________
→ x = -b ± √(b² − 4ac) ;
2a
________________
So; to solve for the values for "x" ; we substitute our known values for:
"a" ; "b" ; and "c" ; and solve:
________________
→ x = -1 ± √(1² − 4*2 *1) ;
4
_________________________
→ x = -1 ± √(1 − 8) ;
4
_________________________
→ x = -1 ± √(-7) ;
4
_________________________
Note: "√(-7)" ; is the square root of a negative number.
Note that we use the lower case letter, " i " ;
as a symbol to represent the imaginary number: " √(-1) " .
This is an "imaginary number" ; since one cannot take the "square root" of a "number lower than zero."
So, we write: √-7 ; as: " i * 7 " ; or, just: " i √7 " ; since:
"i = √-1" ; and since: " √-7" would "factor out" to: "√7 * √-1 " .
_________________________
Note: In the mainstream U.S.A. , the concept of " i " as the "imaginary number" — " √-1 " ; is usually introduced in the second year college-prep algebra class (after "first year high school algebra" in 9th grade; and after "geometry" in 10th grade).
_________________________
So; we have:
→ x = -1 ± √(-7) ;
4
___________
We can rewrite this as:
____________
→ x = -1 ± i√7 ;
4
_____________
We can leave our answer written like that.
We have two (2) solutions—so we can also write out both solutions for the value of x:
_____________
→ x = -1 + i√7 ; -1 + i√7 ;
4 4
_____________________________________________
Hope this explanation is helpful to you!
Best of luck— and best wishes!
_____________________________________________
Find the height of a rectangular prism if the surface are is 288 square centimetres and the base has a length of 4 centimetres and a width of 9 centimetres.
Answers
The area of one of the faces is lxh or lh, and the area of the face opposite to it is also equal, so the area of those two equal faces is 2lh.
The area of the base of the prism is lxw, and the area of its opposite face is equal, so the area of those two equal faces is 2lw.
The area of the face in the left side of the prism is wxh, and the area of the face opposite to it is also equal, so their combined area is 2wh.
So, to find the total surface area of a rectangular prism, we’d add the sum of all the rectangular faces, so the formula of finding the surface area of a rectangular prism=
2lh+2lw+2wh
=2(lh+lw+wh)
Given,
Surface area of the rectangular prism=288 cm^2
2(lh+lw+wh)=288
2[4h+(4x9)+9h)]=288
4h+(4x9)+9h=288/2
4h+(4x9)+9h=144
13h+36=144
13h=144-36
13h=108
h=108/13
h=8.308 cm
Hope this helps!
The height of a rectangular prism is 8.3 cm.
What is Surface Area?The area is the space occupied by a two-dimensional flat surface. It is expressed in square units. The surface area of a three-dimensional object is the area occupied by its outer surface.
We have,
Surface Area = 288 square cm
Base length = 4 cm and width = 9 cm
So, SA of rectangular prism
288 = 2(lw+ wh + lh)
144 = (36 + 9h + 4h)
13h = 144- 36
13h = 108
h = 8.30 cm
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what is 5 + 5 /2 - 4 x 10
Answers
Step-by-step explanation:
use bodmas
start with multiplication
-4*10 = -40
5+5/2 - 40
addition next
5 + 5/2 = 7.5
7.5 - 40 = -32.5
I NEED HELP PLZ I FORGOT HOW TO DO THIS PLZ EXPLAIN HOW U GOT UR ANSWER HELPP
Answers
Answer:
5
Step-by-step explanation:
Using the formula of a trapezoid, we can solve this!
Formula is A=1/2(b1+b2)h.
A=1/2(2+8)1
A=1/2(10)1
A=1/2(10)
The area would be 5 cubic in2.
Please tell me if im wrong! im just a student .m.
Answer:
5 units²
Step-by-step explanation:
a for a trapezoid = [tex]\frac{a+b}{2} *h[/tex]
[tex]\frac{8+2}{2} *1[/tex] = [tex]\frac{10}{2} * 1[/tex] = 5*1 = 5
The area is 5 units²
Timmy has 6 pennies. Sara steals 3 pennies from Timmy. How many pennies does Timmy have now ?
Answers
Answer:
Timmy has 3 pennies.
Step-by-step explanation:
If Timmy has 6 pennies at first, and Sarra takes away 3
then 6-3=3, so timmy has three left.
3 because she stole 3. 6-3=3
Which table represents a linear function?
Answers
Answer: C
Step-by-step explanation:
when x increases by 1 y increases by 2 and is consistent
hope this helps :3
What is 0.83¯¯¯¯ expressed as a fraction in simplest form?
Enter your answer in the box.
Answers
Answer: 5/6
Step-by-step explanation:
Answer:
the answer is
100÷83
Step-by-step explanation:
hope this helps
Kate recorded the length of her last six workouts. Workout Length (minutes) 1 49 2 29 3 32 4 55 5 42 6 29 What is the median of the lengths of Kate's workouts? (Round, if necessary.) A. 6 minutes B. 29 minutes C. 39.33 minutes D. 37 minutes Reset
Answers
Answer:
1, 2, 3, 4, 5, 6, 29, 29, 32, 42, 29, 55
median = 29
Step-by-step explanation:
median is the middle number in a list of numbers from least to greatest.
Can anyone help me fix the mistakes i made? I will give you brainiest if you do and the teacher tells me its correct.
Answers
Answers:
#1: infinite solutions; #2: no solutions
Step-by-step explanations:
Steps for #1
3(2x+7)=13+4(x+2)+2x
6x+21=13+4x+8+2x
6x+21=21+6x
6x=6x
x=x
After completing the steps to find the value of x using Order of Operations, we see that in the end, the answer we have is x=x. We can easily conclude that x is equal to any number because the final answer in this exercise is always whatever the value of x is. For example, if x=4, our final answer would be 4.
Steps for #2
5(6x+8)=9x-10+21x
30x+40=30x-10
40=-10
Here, we see that once we've completed the steps using the Order of Operations, we come out with the answer 40=-10, which is not true on any terms. Therefore we can simply conclude that the answer for #2 is "no solutions."
If you have any trouble figuring out how I got my answers, please refer back to the steps I used to get the answers.
Thank you!
Solve for 2.
Write the smaller solution first, and the larger solution second.
(3x – 6)(-x + 3) = 0
smaller x =
larger x =
Answers
Answer:
(3x – 6)(-x + 3) = 0
=> 3x - 6 = 0 => x = 6/3 = 2
and
=> -x + 3 = 0 => x = 3
Hope this helps!
:)
can you please help me fill this out thanks
Answers
Answer: [tex]\sqrt{2}[/tex]
Step-by-step explanation:
In a 45 45 90 triangle the two sides are 1 wile the hypothenuse is [tex]\sqrt{2}[/tex]
What is the answer to this
Answers
Answer:
im pretty sure it's c
Step-by-step explanation:
Answer:
its C
Step-by-step explanation:
Jen has a newer car than Amelie, and it has One-third the miles of Amelie’s car. Amelie’s car has 45,000 miles. Which of the following equations model this situation? Select all that apply.
3(m) = 45,000
1/3 + m = 45,000
m = (1/3) (45,000)
m = 3(45,000)
m = 1/3 = 45,000
Answers
Answer:
Its 1rst and 3rd
Step-by-step explanation:
I took the assignment. Its correct.
Answer:
1 and 3
Step-by-step explanation:
on edge just got it right :)
how to make a dot plot
Answers
Answer:
draw a a big L and put your numbers
Right triangle RST is shown below with the dimensions given in feet
(ft)
Which is closest to the measure of ZR?
Select one
15.1
15.7
74.3
74.9
Answers
Answer:
As the triangle is right angled ,
sinR = 17/63
Angle R = 15.7⁰
The closest value of the measure of ∠R is,
⇒ ∠R = 15.7°
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
Given that;
Right triangle RST is shown below with the dimensions given in feet.
Now, By trigonometric formula;
tan x = Opposite / Adjacent
Here, Opposite side of angle R = 17 ft
And, Adjacent side = 63 ft
Hence, We get;
tan x = Opposite / Adjacent
tan R = 17 / 63
tan R = 1/9
R = 15.7°
Thus, The closest value of the measure of ∠R is,
⇒ ∠R = 15.7°
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The area of a swimming pool is 120 sq meters. The width of the pool is 8 meters. what is the length of the pool in centimeters ?
Answers
15m = 150cm
Answer 150cm
find the surface area of the prism
Answers
Answer: C
Step-by-step explanation:
Length: 6in
Width: 8in
Height: 9in
[tex]A=2(wl+hl+hw)\\A=2[(8in)(6in)+(9in)(6in)+(9in)(8in)]\\A=2(48in^2+54in^2+72in^2)\\A=2(174in^2)\\A=348in^2[/tex]
Find the perimeter of the following quadrilateral.
Write your answer as a mixed number in simplest form.
Be sure to include the correct unit in your answer.
Answers
Answer:
Plus all the fractions together .
Which equals to 35/4 cm
Step-by-step explanation:
hope it helps you !!
The perimeter of the quadrilateral is P = 8 3/4 cm
Given data:
The perimeter of a quadrilateral is the sum of the lengths of all its sides. A quadrilateral is a polygon with four sides. The formula for finding the perimeter of a quadrilateral depends on the specific type of quadrilateral.
So, the sides of the quadrilateral is represented as:
AB = 3 1/2 cm
BC = 2 cm
CD = 1 4/5 cm
DA = 1 9/20 cm
So, the perimeter is P = 3 1/2 cm + 2 cm + 1 4/5 cm + 1 9/20 cm
On simplifying ,
P = 3.5 cm + 2 cm + 1.8 cm + 1.45 cm
P = 8.75 cm
Hence , the perimeter is P = 8 4/3 cm
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distance between two points: what is the distance between 2, -3 and 8, -9?
Answers
Answer:
6sqrt(2) units
Step-by-step explanation:
Distance² = (-9 - -3)² + (8 - 2)²
Distance² = (-6)² + 6²
Distance² = 36 + 36
Distance² = 72
Distance = 6sqrt(2)
sqrt: square root
If Nick used 56 feet of fence to enclose a square garden.How long,in feet was each side of Nicks garden?
Answers
Answer:
Each side is 14 ft.
Step-by-step explanation:
If there are 4 equal sides, you divide 56 by 4. That equals 14.
Please can people help??!!
Photo below
Answers
i think this is the method for solving it
Expand. Your answer should be a polynomial in standard form. (x - 7)(x - 3)
Answers
Answer:
x^2-10x+21
Step-by-step explanation:
Answer:
The answer is x^2-10x21
f(x) = (x-6)(x + 5)
What are the zeros of the quadratic?
Answers
Answer:
x=6 x=-5
Step-by-step explanation:
f(x) = (x-6)(x + 5)
To find the zeros, set the function equal to zero
0 = (x-6)(x + 5)
Using the zero product of property
0 = x-6 0=x+5
x=6 x=-5
Ben and Tom each take their driving test. The probability that ben and tom will pass is 0.8 and 0.7, respectively. Work out the probability that only one of them will pass their driving test.
Answers
Answer:
Pr(only one of them will pass the driving test) = 0.38
Step-by-step explanation:
The probability that Ben will pass = 0.8
Let Pr = pribability
Pr(Ben pass) = 0.8
Pr(Ben fail) = 1 - Pr(Ben pass) = 1-0.8
Pr(Ben fail) = 0.2
The probability that Tom will pass = 0.7
Pr (Tom pass) = 0.7
Pr (Tom fail) = 1 - Pr (Tom pass) = 1-0.7
Pr (Tom fail) = 0.3
Pr(only one pass) = Pr(Ben pass and Tom fail) + Pr (Tom pass and Ben fail)
Pr(only one pass) = (0.8 × 0.3) + (0.7 × 0.2)
Pr(only one pass) = 0.24 + 0.14
Pr(only one pass) = 0.38
Answer:0.38
Step-by-step explanation:
Write the equation of a line that passes through the point (4, 2) and is parallel to the line graphed below.
Answers
Answer:
Step-by-step explanation:
(-2, 2) (2, -3)
(-3 - 2)/(2 + 2)
-5/4 the slope
y - 2 = -5/4(x + 2)
y - 2 = -5/4x - 5/2
y- 4/2 = -5/4x - 5/2
y = -5/4x - 1/2
.
A person invests 10000 dollars in a bank. The bank pays 5.5% interest compounded
monthly. To the nearest tenth of a year, how long must the
person leave the
in the bank until it reaches 27400 dollars?
leave the money
r
A = P(1 + -)nt
n
Answers
Answer:
The answer is 18.4 months.
