What is the length of side AC of the triangle?
Enter your answers in the boxes.
Answers
Answer:
[tex]AC=25[/tex]
Step-by-step explanation:
From the given figure, it can be seen that [tex]{\angle}A={\angle}C[/tex], thus ΔABC is an isosceles triangle.
Therefore,[tex]AB=BC[/tex]
⇒[tex]5x+5=7x-1[/tex]
Solving the above equation, we get
⇒[tex]5x-7x=-1-5[/tex]
⇒[tex]-2x=-6[/tex]
⇒[tex]x=3[/tex]
Now, substituting the value of x in AC, we have
⇒[tex]AC=6x+7[/tex]
⇒[tex]AC=6(3)+7[/tex]
⇒[tex]AC=18+7[/tex]
⇒[tex]AC=25[/tex]
Thus, the length of the side AC of the given triangle is 25 units.
Related Questions
if right triangle LMN, L and M are complementary angles and sin (L) is 19/20 what is cos (M)
Answers
Answer: Value of cos(M) is
[tex]\cos M=\frac{19}{20}[/tex]
Step-by-step explanation:
Since we have given that
LMN is a right angled triangle where L and M are complementary angles ,
And,
[tex]\sin L=\frac{19}{20}=\frac{Perpendicular}{Hypotenuse}[/tex]
so, we will find base now by using "Pythagorus theorem":
[tex]H^2=B^2+P^2\\\\20^2=B^2+19^2\\\\400=B^2+361\\\\400-361=B^2\\\\39=B^2\\\\\sqrt{39}=B[/tex]
As we know that side opposite to mentioned theta is considered as perpendicular as shown in the figure ,
For M as [tex]\theta[/tex]
NL will be its perpendicular and MN will be its base and to find the cos(M) we use Base and Hypotenuse.
So, now we will find cos(M) i.e.
[tex]\cos M=\frac{Base}{Hypotenuse}=\frac{19}{20}[/tex]
Hence,
[tex]\cos M=\frac{19}{20}[/tex]
The box plots show male and females grades in mathematics class: Which of the following best describes the information about the interquartile ranges?
Answers
Answer:
The interquartile ranges are quite close in value.
Step-by-step explanation:
We have been given two box-plots and we are asked to choose the correct statement about the interquartile ranges.
Since we know that interquartile range is difference between upper and lower quartile.
[tex]IQR=Q_3-Q_1[/tex]
Let us find IQR for the female grades in math.
We can see from box-plot representing female grades that upper quartile is about 90 and lower quartile is about 75.
[tex]\text{IQR of female grades}=90-75[/tex]
[tex]\text{IQR of female grades}=15[/tex]
Now let us find IQR for the male grades in math.
[tex]\text{IQR of male grades}=85-70[/tex]
[tex]\text{IQR of male grades}=15[/tex]
We can see IQR values for males and females are same, therefore, last statement is true.
Find the Least Common Multiple of these two monomials:
16jk^8m^5 and 20j^9k^4m^6
36j^9k^8m^6
80j^9k^8m^6
4jk^4m^5
80j^10k^12m^11
Answers
lcm 16 & 10 = 80
lcm j^8 & j^9 = j^9
lcm k^8 & k^4 = k^8
lcm m^5 & m^6 = m^6
answer is: 80j^9k^8m^6
1. use the zero product property to solve the equation. (x-9)(x-8)=0
Answers
x=9
x-8=0
x=8
Thus the answer is x=9, x=8
Answer:
X= 8 or 9
Step-by-step explanation:
For a field trip, a bus company charges a flat fee plus an additional fee per student. for 25 students, the total cost is 132.50. if there are 30 students, the total cost is 145. which equation represents the total cost y of the field trip for x students?
Answers
Answer:
[tex]y=2.5x+70[/tex]
Step-by-step explanation:
First of all, this problem is modelled by a linear equation, where the ratio of change is the slope of the line.
Now, we know that [tex]x[/tex] represents students and [tex]y[/tex] represents the total cost.
The problem states that for 25 students, the total cost is $132.50. And for 30 students, the total cost is $145. This information represents two points
[tex](25,132.50)[/tex] and [tex](30,145)[/tex].
So, to find the equation, we first have to find the slope using these two point and the following formula
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} } =\frac{145-132.50}{30-25}=\frac{12.5}{5}=2.5[/tex]
This means the slope is 2.5
Now we use the point-slope formula to find the linear equation
[tex]y-y_{1} =m(x-x_{1} )\\y-145=2.5(x-30)\\y=2.5x-75+145\\y=2.5x+70[/tex]
Therefore, the equation that models this problem is
[tex]y=2.5x+70[/tex]
Where the flat fee is $70, and the fee per student is $2.5.
A basketball team played 14 games. the team's mean score was 66 points. how many total points did they score in the 14 games?
Answers
Donald baked 77 cookies in the morning and 83 cookies in the afternoon for 14 days how many total cookies did he bake
Answers
The sum of the squares of two consecutive even integers is 452. find the integers.
Answers
Trina employer purchased a health insurance plan that's costs $550 per month. Trina pays $85 toward the plan each month. What is the annual value of the employer contribution?
Answers
subtract the amount Trina pays from the total:
550 - 85 = 465 per month employer pays
12 months per year
465 * 12 = $5,580 per year is what the employer pays
Answer: $5580.00
Step-by-step explanation:
There is an average of 3.5×10−2 kilograms of dissolved salt in each liter of seawater.
The Pacific Ocean contains approximately 6.6×1020 liters of seawater.
About how many kilograms of dissolved salt are in the Pacific Ocean?
Enter your answer, in scientific notation, in the boxes.
(blank) x 10(blank) kg
Answers
IT IS 2.31, I AM TELLING YOU THIS IS 2.31
How do transformations in m and b effect the graph of y=mx+b
Answers
It is called so because if all the solutions (x, y) of this equation are plotted, they form a line with slope m and y-intercept b.
If m is positive, the line is increasing. So if m is positive, the greater the m, the more steeper the line, in increasing direction.
If m is negative, the line is decreasing. The smaller the m, the steeper the line, in decreasing direction.
b represents the y-intercept. If b is 0, the line passes through the origin. The larger the value of b, the higher the y-intercept. The smaller the value of b, the lower the y-intercept.
Find the value of x so that f || g. The diagram is not to scale.
Answers
Lines f and g are parallel with a transversal forming same side interior angles with measures 3x and 5x + 36.
Theorem: If parallel lines are cut by a transversal, then same side interior angles are supplementary.
The angles measuring 3x and 5x + 36 are supplementary, so their measures add up to 180 degrees
3x + 5x + 36 = 180
8x + 36 = 180
8x = 144
x = 18
The answer is x = 18.
Answer:
18
The answer is 18
Step-by-step explanation:
Thomas has $6.35 in dimes and quarters the number of dimes is three more than three times the number of quarters how many quarters does he have?
let q represent the number of quarters then which of the following expressions represents the value of number of dimes in cents?
a)3q+3
b)6.35-q
c) 10(3q+3)
Answers
T = +3 * 3q
or 3q + 3
The answer is A
The answer is
c) 10(3q + 3)
because it is asking for the VALUE of the number of dimes, not the number of dimes. To get the value of the number of dimes, you have to take the equation 3q+3 and multiply it by 10.
Please rate and thank :)
Please mark as brainliest
Decide whether the function is an exponential growth or exponential decay function, and find the constant percentage rate of growth or decay.
f(x) = 2479 ⋅ 0.9948x
Answers
The distributive property to express 48+72
Answers
Answer:
24(2+3)=24.2+24.3=48+72
Step-by-step explanation:
Given form of number is 48+72.
we have to apply the distributive property to express the above number.
The distributive property is
a(b+c)=ab+ac
Multiply the common term with the term inside the parentheses
So to express 48+72 we have to take the highest factor outside
Let us take 24 outside, we get
24(2+3)=24.2+24.3=48+72
Hence applied
The required expression is [tex]24(2+3)[/tex] by using the distributive property.
Given:
The given expression is [tex]48+72[/tex].
To find:
The equivalent expression by using the distributive property.
Explanation:
According to the distributive property:
[tex]a(b+c)=ab+ac[/tex]
We have,
[tex]48+72[/tex]
It can be rewritten as:
[tex]48+72=24\times 2+24\times 3[/tex]
Using the distributive property, we get
[tex]48+72=24(2+3)[/tex]
Therefore, the required expression is [tex]24(2+3)[/tex].
Learn more:
https://brainly.com/question/19652806
Select the table that represents the following graph.
The stuff is on the links/screenshots
Answers
Answer:
The first image in your answer choices
Explanation:
To find the table of solutions for the given graph, we observe points on the graph that are intersected by the line.
The easiest starting point is often where the line intercepts (or crosses) the vertical y-axis. This occurs one unit above the origin (0,0), so we would say list this point as ordered pair (0, 1). This eliminates the third and fourth tables as answer choices.
Now we use the horizontal x-axis to find other points that the line crosses through. Starting at x = 1, we can see the line goes through the point 4 units above the x-axis here; therefore, its ordered pair is (1, 4). This eliminates the second table as an answer choice.
Let's use one more point to confirm we have the right choice. Starting at x = -1, we can see the line goes through the point 2 units below the x-axis here; therefore its ordered pair is (-1, -2).
The first table contains all of these ordered pairs (0, 1), (1, 4), and (-1, -2), making it your answer choice.
Mr. Greenjeans planted 6 different crops on 2 acres of land. If half of it was planted with green beans, how many acres were planted with green beans?
Answers
To determine how many acres were planted with green beans, we simply take half of the total acreage. Mr. Greenjeans planted a total of 2 acres, so half of this is 1 acre; therefore, 1 acre was planted with green beans.
The question is asking how many acres were planted with green beans, given that Mr. Greenjeans planted crops on 2 acres of land and half of it was with green beans. To find the answer, we need to calculate half of the total land area.
Here is the step-by-step explanation:
Start with the total number of acres: 2 acres.Since half of the land was planted with green beans, we divide the total acres by 2.2 acres / 2 = 1 acre.Therefore, Mr. Greenjeans planted 1 acre of land with green beans.
How many 12ths are equivalent to 1/3?
Answers
4/12 is the answer
What is the diameter of a dime in inches?
Answers
Which graph is represented by the following table?
The pictures show the table and graphs. The graphs are what can show which one is the answer.
Answers
x and y represents the coordinates of points on the line
The scale on a map shows that 2 inches represents 15 miles. Which proportion can be used to find the actual distance, x, represented by 30 inches on the map?
Answers
could also be :
15 /2 = x/30...15 miles to 2 inches = x miles to 30 inches
either way, u will get the same answer
Answer:
I think it's 2/15 = 30/x
Step-by-step explanation:
sorry if it's wrong
A quantity x varies directly with y and inversely with z. Which expression represents the constant of variation,k?
Answers
the answer is xz/y.
Answer:
The expression represents the constant of variation k is [tex]\frac{xz}{y}[/tex].
Step-by-step explanation:
As given
A quantity x varies directly with y and inversely with z.
[tex]x \propto y[/tex]
and
[tex]x \propto \frac{1}{z}[/tex]
Than combined the above equation.
[tex]x \propto \frac{y}{z}[/tex]
[tex]x = k\frac{y}{z}[/tex]
Where k is the constant of variation.
Than
[tex]k = \frac{xz}{y}[/tex]
Therefore the expression represents the constant of variation k is [tex]\frac{xz}{y}[/tex].
Determine the type and number of solutions of −4x^2 − 4x − 1 = 0
Help me please, I'm extremely behind in math
Answers
so
if
b^2-4ac=0 then there is one real soultion
if
b^2-4ac<0 then there are two imaginary soultions that differ in the sign between them
if
b^2-4ac>0 then there are two real soultions
so a polynomial is written in the form
ax^2+bx+c=0
so a=-4
b=-4
c=-1
so b^2-4ac=16-16=0
so one real soultion is the answer you are looking
type:real
number:1
PLEASE HELP!!!!
What is the distance between points M and N?
___ meters.
Answers
Answer:
The distance between points M and N is 9.8m.
Step-by-step explanation:
It is given that JKL is a triangle and M and N are the mid points of the KL and JL respectively.
Now, if we join the mid points together that is MN, then we can see that the basic proportionality holds that is:
[tex]\frac{LM}{MK}=\frac{LN}{NJ}[/tex]
[tex]\frac{10.7}{10.7}=\frac{7.4}{7.4}=\frac{1}{1}[/tex] which holds.
And which also proves that MN is parallel to JK.
Now, if MN is parallel to JK, then the measure of MN will be half the measure of JK, that is:
[tex]MN=\frac{1}{2}JK[/tex]
[tex]MN=\frac{1}{2}(19.6)[/tex]
[tex]MN=9.8 m[/tex]
Thus, the measure of MN is 9.8 meters.
Answer:
yah its 9.8 meters bro
Step-by-step explanation:
best of luck to yall on assignment and happy new year!!!
On Wednesday night in St. Petersburg, Russia, the temperature is -11°C. On the same night in Bombay, India, the temperature is 17°C. What is the difference in temperature? Show your work.
Answers
A toy manufacturer makes a toy truck, a toy car, and a toy boat. The production spreadsheet is:Toy Time to Produce Cost to Produce Profit for Each Truck 10 minutes $1.00 $1.00 Car 12 minutes $0.75 $1.50 Boat 8 minutes $0.80 $0.60 After accounting for breaks, a worker actually works 400 minutes each day. The manufacturer needs each worker to generate a potential profit of $35 each day. Write a system of inequalities that expresses these constraints
Answers
truck 10 min 1.00dollar t
car 12min 1.50 dollar c
boat 8min 0.60 dollar b
let the worker produce t trucks, c cars, and b boats.
10t+12c+8b=400
t+1.5c+0.6b is more than or equal to 35
t is more than or equal to 0
c is more than or equal to zero
b is more than or equal to zero
(this question is kinda wierd. i do not know if i am correct, because mine is not exactly a system of inequalities, but if you really need an answer, you can try this one.)
If 8 ounces of a sports drink contain 110 milligrams of sodium what is the total number of milligrams of sodium in 20 ounces of the sports drink
Answers
Work:
I divided 110 by 8 which gave me 13.75
13.75 is the milligrams of sodium in each ounce.
I then divided it by 20 and got 275 the number of milligrams in a 20 ounce drink.
Twice the sum of a number and 2 is equal to three times the difference of the number and 8. find the number please help
Answers
Answer:
28
Step-by-step explanation:
Let n represent the number.
Twice the sum of the number and 2 is ...
2(n +2)
Three times the difference of the number and 8 is ...
3(n -8)
The problem statement tells us these quantities are equal, so ...
2(n +2) = 3(n -8) . . . . the given quantities are equal
2n +4 = 3n -24 . . . . . use the distributive property to eliminate parentheses
2n +28 = 3n . . . . . . . add 24
28 = n . . . . . . . . . . . . subtract 2n
The number is 28.
_____
Check
The sum of the number and 2 is 30; twice that is 60.
The difference of the number and 8 is 20; three times that is 60--the same number.
What is the missing term in the factorization? 18x2−32=2(3x+?)(3x−4)
Answers
Answer:
4.
Step-by-step explanation:
[tex]18x^{2} -32 = 2(9x^{2} -16)[/tex]
we apply difference of squares
2(3x-4)(3x+4)
So, the missing term is 4.
The missing term in the factorization 18x² − 32 = 2(3x + ?)(3x − 4) is 4.
What is Factorization ?Factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form. Factorization is expressing a mathematical quantity in terms of multiples of smaller units of similar quantities.
For an integer, Factorization is decomposition of that integer in terms of smaller integers; when multiplied with each other give back that considered number. Those composing integers are called factors of that considered integers.
WE have given an expression as;
18x² − 32 = 2(3x + ?)(3x − 4)
Now we apply difference of squares;
2(9x² - 16)
2(3x + 4)(3x - 4)
OR
2(3x-4)(3x+4)
Therefore, the missing term is 4.
Learn more about factorization here:
https://brainly.com/question/10454590
#SPJ2
What is the exact value of tan (-pi/3)?
Answers
Answer:
[tex]-\sqrt{3}[/tex]
Step-by-step explanation:
we know that
[tex]tan(-\frac{\pi}{3})=-tan(\frac{\pi}{3})[/tex]
and
[tex]tan(\frac{\pi}{3})=\frac{sin(\frac{\pi}{3})}{cos(\frac{\pi}{3})}[/tex]
remember that
[tex]cos(\frac{\pi}{3})=\frac{1}{2}[/tex]
[tex]sin(\frac{\pi}{3})=\frac{\sqrt{3}}{2}[/tex]
substitute the values
[tex]-tan(\frac{\pi}{3})=-\frac{(\sqrt{3}/2)}{(1/2)}\\ \\=-\sqrt{3}[/tex]