The value of the unknown variable x in the equation x² + 5² = 13² is 12.
The use of numbers and words in the same mathematical equation is considered as an algebraic expression.
We can calculate the square of a number by multiplying the number by itself.
Therefore, the square of 5 is equal to 5 multiplied by 5 which is equal to 25.
While the square of 13 is equal to 13 multiplied by 13 which is equal to 169.
So to find the value of x, we can rearrange the given equation as:
x² = 13² - 5 ²
x² = 169 - 25
x² = 144
As x² is equal to 144, we can calculate the value of x by taking the square root of the value of 144.
Therefore,
x= √144
x= 12
Hence, the value of the unknown variable x in this equation is 12.
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What is 22 1/2 divided by 1/2?
(Twenty-two wholes & one-half DIVIDED BY one-half?)
In this problem, you will investigate the location of the points of concurrency for any equilateral triangle.
a. Concrete Construct three different equilateral triangles on tracing paper and cut them out. Fold each triangle to locate the circumcenter, incenter, centroid, and orthocenter.
Fold the triangles to find their circumcenter (by making perpendicular bisectors), incenter (by making angle bisectors), centroid (by constructing medians), and orthocenter (using a different piece of patty paper for each equilateral triangle) (by making the altitudes of each side).
What points of concurrency are always inside the triangle?A triangle's three angle bisectors are concurrent in a point equidistant from its sides. The incenter of a triangle is the point where the angle bisectors of a triangle intersect. The incenter is always found within the triangle.
The circumcenter of a triangle is the point where the three perpendicular bisectors meet. It is the circumcenter of the circle circumscribed around the triangle, which is equidistant from the triangle's three vertices.
Fold the triangles to find their circumcenter (by making perpendicular bisectors), incenter (by making angle bisectors), centroid (by constructing medians), and orthocenter (using a different piece of patty paper for each equilateral triangle) (by making the altitudes of each side).
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the rectangle shown has an area of 84 square inches. find the dimensions of the rectangle
Answer:
x(x+8)=84
x² + 8x = 84
x² + 8x - 84 = 0
(x+14) (x-6) = 0
x= -14 or 6
Perimeter = 40 in.
Please help! Due in 5 mins!
Answer:
It's the first option, if you simplify 6 by 4, its 1 1/2 and first option is also 1 1/2 the last option is also equivalent
Step-by-step explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)
-2 2/3 * (-4 3/7) help me please. thanks
:)
Answer:
11.8
Step-by-step explanation:
I simply just did multiplication
I multiplied the whole numbers alone and did the same with the fraction
Example: -2*-4=8
2/3*3/7
then you add the two products and get your answer
The measure of one angle is 3 degrees more than 1/2 the measure of its supplement. Identify and solve an algebraic equation.
Answer: x+(x/2 + 3)=180 ==> 1st option
62 degrees ==> smaller angle
118 degrees ==> Larger angle
Step-by-step explanation:
x=one angle
y=1/2 x + 3
x+y=180 ==> supplementary angles add up to 180 degrees.
x+(1/2 x + 3)=180
x+(x/2 + 3)=180 ==> 1st option
x+x/2 + 3=180
2x/2 + x/2 + 3=180
(2x+x)/2 + 3=180
3x/2 + 3=180
3x/2=177
3x=354
x=118 degrees ==> Larger angle
x/2 + 3=
118/2 + 3=
59+3=62 degrees ==> smaller angle
The diagram shows a triangle. What is the value of b?
Answer:
b=95
Step-by-step explanation:
180=34+(b-30)+(b-14)
190=2b
b=95
34+(95-30)+(95-14) = 180
Answer:
b-30+b-14+34=180
2b+4-14=180
Step-by-step explanation:
2b=190 ,b=95
A studio engineer charges a flat fee of 450 for equipment rental and 42 an hour for recording and mixing time. Write the equation that shows the cost to hire the studio engineer as a function of time. How much would it cost to hire the studio engineer for 17 hours?
Slope-intercept form, y = mx + b, of linear equations, emphasizes the slope and the y-intercept of the line.
The cost to hire the studio engineer for 17 hours is $ 1164.
What is slope-intercept form?Let x be the time measured in hours and y be the total cost in dollars if two different costs are provided. This problem has been solved with the help of slope-intercept form, y = mx + b.
The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given exists even the y-intercept (0, b). In the formula, b represents the y value of the y-intercept point.
Slope-intercept form, y = mx + b, of linear equations, emphasizes the slope and the y-intercept of the line.
From the given information, we get
W = 450 + 42 [tex]*[/tex] 17
= $ 1164
The cost to hire the studio engineer for 17 hours is $ 1164.
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Find the exact circumference of circle by using the given polygon.
a. inscribed right triangle with legs 7 meters and 3 meters long
The distance round a polygon, which include a rectangular or a rectangle, is referred to as the perimeter (P). On the alternative hand, the space round a circle is called the circumference (C). Therefore, the circumference of a circle is the linear distance of an fringe of the circle.
What is the formula here we use to calculate the equation:
[tex]c^{2} =a^{2} +b^{2}[/tex]
Find the solution:
[tex]c^{2} =a^{2} +b^{2}[/tex]
[tex]x^{2} =7^{2} +3^{2}[/tex]
[tex]\sqrt{x} ^{2} =49+9[/tex]
[tex]x=\sqrt58[/tex]
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Write each arithmetic series in summation notation. 105+97+89+ . . . . . . +(-71)
The algebraic expression or sigma (summation) notation is given by:
∑ = 22(105 - 71)/2
And its value is ∑ = 374
What is sigma notation?The sigma notation is a mathematical operation used to determine the final value of the sum of "n" terms consecutively, when dealing only with numbers without variables this is known as an arithmetic series.
The equation for this type of problem is:
∑ = n(a1 + an)/2
n : number of termsa1 : first terman : last termOur values are:
105+97+89+ . . . . . . +(-71)
a1 =105an = -71n = 22∑ = 22(105 - 71)/2
∑ = 22(34)/2 = 11(34)
∑ = 374
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It took Brooke 14 hours to paint
5 rooms. At that rate. how many
Minutes did it take her to paint
one room?
Under unitary method - 168Minutes did it take her to paint one room
If it took 14 hours to paint 5 rooms and we need to find how many
Minutes did it take her to paint one room, we need to know how much time taken to paint a room
this can be obtained using unitary method
so time taken to paint one room is time taken to paint 5 rooms divided by number of rooms
= 14 hours /5
=2.8 hours
As we need answer in unitary method minutes we are required to convert hours into minutes which can be done by multiplying with the number of minutes in an hour that is 60
Minutes did it take her to paint one room = 2.8 hours × 60
=168 minutes
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Given j(x) = -3√3x, find j(3)
Step-by-step explanation:
You only need to change the x for a 3
Can yall help me with this
Answer:
3
Step-by-step explanation:
anyone please help me this
Hot dogs come in packs of 10, while buns come in packs of eight. What are the least numbers of packs you should buy in order to have the same numbers of hot dogs and buns?.
Solving for the least common multiple (LCM), the least numbers of packs you should buy in order to have the same numbers of hot dogs and buns is 4 packs of hotdogs and 5 packs of buns.
A common multiple is defined as a whole number, that is a shared multiple of each set of numbers. The least common multiple (LCM) of two integers is the smallest positive integer that is divisible by both numbers.
If hot dogs come in packs of 10, while buns come in packs of eight, solving for their LCM,
10 : 10, 20, 30, 40, 50, . . .
8 : 8, 16, 24, 32, 40, 48, . . .
LCM = 40
Considering 40 hotdogs and 40 buns, dividing each by 10 and 8, the number of packs of each will be:
packs of hotdogs = 40/10
packs of hotdogs = 4
packs of buns = 40/8
packs of buns = 5
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Determine whether y varies directly with x . If so, find the constant of variation.
y-6 x=0
The required value of constant of variation, k for which x and y vary directly is 6.
What is the constant of proportion?
A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.
Solving for the value of constant of variation
When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion —-- 1
Given relation is y - 6x = 0
y = 6x
On comparing it with equation 1, we get,
k = 6
Hence, the required value of constant of variation is 6.
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i need help solving this angle problem
Answer:
Step-by-step explanation:
42=8x+10
42+10=8x
52=8x
x=52/8
x=6.5
the measure of a supplement of an angle exceeds 10 times the measure of its complement by 9. Find the measure of the angle
Answer:
81°
Step-by-step explanation:
Let the angle be x. Then,
complementary angle = 90 - xsupplementary angle = 180 - xAccording to question,
=> 180 - x - 10(90 - x) = 9
=> 180 - x - 900 + 10x = 9
=> 9x - 720 = 9
=> 9x = 729
=> x = 81
The measure of the angle is 81° (ans)
Answer:
81°
Step-by-step explanation:
Definitions
Complementary angles: Two angles whose measures sum to 90°.
Supplementary angles: Two angles whose measures sum to 180°.
Define the unknown angle
Let x be the unknown angle.Therefore:
Complement of x = 90° - x°Supplement of x = 180° - x°If the measure of the supplement exceeds 10 times the measure of its complement by 9:
⇒ supplement = 10 × complement + 9
⇒ (180 - x) = 10(90 - x) + 9
⇒ 180 - x = 900 - 10x + 9
⇒ 180 - x = 909 - 10x
⇒ 180 - x + 10x = 909 - 10x + 10x
⇒ 180 + 9x = 909
⇒ 180 + 9x - 180 = 909 - 180
⇒ 9x = 729
⇒ 9x ÷ 9 = 729 ÷ 9
⇒ x = 81
Therefore, the measure of the angle is 81°.
Use a two-dimensional model and the dimensions provided to calculate the circumference and area of the flower. Round to the nearest tenth,
if necessary.
circumference:
area:
in2
in.
5 in-
The circumference and area of the flower are 15.7 and 19.6 respectively
How to calculate the circumference and area of the flower?The image that completes the question is added an attachment
From the image, we have
Diameter = 5 inches
The circumference is calculated as
C = π * Diameter (d)
So, we have
C = πd
This gives
C = 3.14 * 5
Evaluate
C = 15.7
The area is calculated as
A = π(d/2)^2
This gives
A = 3.14 * (5/2)^2
Evaluate
A = 19.6
Hence, the circumference and area of the flower are 15.7 and 19.6 respectively
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A die is rolled. Find the probability of the outcome. P(1 or 6 )
The required probability is 1/3
Rolling a die is an equally likely event which means that probability of getting any number on rolling a die is same. When a die is rolled, there are total six outcomes in sample space which are 1, 2, 3, 4, 5, and 6 .
If a die is rolled once, then the probability of getting 1 is 1/6, and the probability of getting 6 is also 1/6.
These two events are mutually exclusive.
Thus, the probability of getting either 1 or 6 in a single throw is,
P(A or B) = P(A) + P(B)
P(A or B) = 1/6 + 1/6 = 2/6
P(A or B) = 1/3
The required probability is 1/3
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find L in the cone
please hurry
Answer:
12
Step-by-step explanation:
Answer:
can you maybe explain it a little more?
Step-by-step explanation:
Which lines are parallel to the graph of 4x – y = 6? Check all that apply.
x – 4y = –12
y – 2 = –4(x + 1)
y + 1 = 4(x – 2)
y = 4x + 11
y = x – 3
8x – 2y = 6
Answer: Options 3, 4, 6
Step-by-step explanation:
[tex]4x-y=6 \\\\-4x+y=-6\\\\y=4x-6[/tex]
This means are looking for lines with a slope of 4 (since parallel lines have the same slope).
x – 4y = –12: This rearranges to y=0.25x+3, so the slope is 1/4.y – 2 = –4(x + 1): This has a slope of -4.y + 1 = 4(x – 2): This has a slope of 4.y = 4x + 11: This has a slope of 4.y = x – 3: This has a slope of 1.8x – 2y = 6: This rearranges to y=4x-3, so the slope is 4.Find the value of each variable
The Value of 3-5c is 1 less than the value of 1-c.
Answer:
½ < C
Step-by-step explanation:
that is the answer above
CCSS ARGUMENTS Determine whether each statement is true or false. If false, give a counterexample. If true, explain your reasoning.
Two triangles with two pairs of congruent corresponding angles and three pairs of congruent corresponding sides are congruent.
Two triangles with two pairs of congruent corresponding angles and three pairs of congruent corresponding sides are congruent: Always TRUE
What exactly does the term "triangle congruency" mean?Two triangles are said to be congruent if their three corresponding sides are equal and their three corresponding angles are equal in size.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are repositioned, they will coincide.Two triangles are congruent if they satisfy all five congruence conditions.They are the side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).The statement states that:
Two triangles with two pairs of congruent corresponding angles and three pairs of congruent corresponding sides are congruent.So, the statement is always true as it satisfies two conditions of congruency which are the SSS condition and AA condition.Therefore, the statement "two triangles with two pairs of congruent corresponding angles and three pairs of congruent corresponding sides are congruent" is Always TRUE.
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Find the value of x to the nearest tenth. 336.4/x = π
x = 107.1 is the value of x.
What do we mean by a value?In mathematics, a value is a number that represents the outcome of a calculation or function. So, in the preceding example, you could tell your teacher that the value of 5 x 6 is 30 or that the value of x + y is 9 if x = 6 and y = 3. A variable or constant can also be referred to as a value.To find the value of x:
Given: 336.4/x = πTo find the value of x, we will simplify the given equation after we have entered the value of π.So,
336.4/x = π336.4/x = 3.14159336.4/3.14159 = xx = 107.07953Then rounding to the nearest tenths gives x = 107.1.
Therefore, x = 107.1 is the value of x.
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Explain whether the Federal Reserve reducing interest rates helps to expand economic growth. (1 point) Responses
1. Reducing interest rates does not help the economy expand because prices of goods and services decrease from reduced demand.
2. Reducing interest rates does not help the economy expand because businesses save instead of spend with low-interest rates, slowing economic growth.
3. Reducing interest rates helps the economy expand because it lowers the cost of borrowing for business to expand, leading to more jobs and economic growth.
4. Reducing interest rates helps the economy expand because businesses earn a greater return on their savings, leading to additional spending and economic growth.
Answer:Lowering rates makes borrowing money cheaper. This encourages consumer and business spending and investment and can boost asset prices. Lowering rates, however, can also lead to problems such as inflation and liquidity traps, which undermine the effectiveness of low rates.
Step-by-step explanation:
Answer:
1. A sole proprietorship is distinguished by the fact that it has
Answer - only one owner.
2. James would like to create a sole proprietorship operating under the name Super Lawn Care. Which of the following is true?
Answer - James will need to register the business with his local state as the name of his business differs from his own.
3. A recent high school graduate would like to establish an online tutoring service as a sole proprietorship operating under her own name. Having never worked before and having no current income, which of the following hurdles is she likely to face?
Answer - It will be difficult to cover start-up costs since banks will be unlikely to loan her money.
4. What is a subsidy?
Answer - a government payment to a business to generate employment and economic growth
5. Explain whether the Federal Reserve reducing interest rates helps to expand economic growth.
Answer - Reducing interest rates helps the economy expand because it lowers the cost of borrowing for business to expand, leading to more jobs and economic growth.
Step-by-step explanation: I just took the test and got it right
Do the following side lengths form a right triangle?
15, 15, 35
Answer:No
Step-by-step explanation:
It does not
Answer:
No
Step-by-step explanation:
given 3 sides of a triangle
using the converse of Pythagoras' identity
if the square of the longest side is equal to the sum of the squares of the other 2 sides, then the triangle is right.
longest side = 35 and 35² = 1225 , then
15² + 15² = 225 + 225 = 450
since 1225 ≠ 450 then the 3 sides do not form a right triangle.
Given two terms of each arithmetic sequence, find a₁ and d . a₃ =5 and a₅ =11
The two terms of each arithmetic sequence an=a1+(n-1)d are 2,7,12,17,..., 52.
What is sequence?an=a1+(n-1)d
a1=2
a2=2+5=7
a3=7+5=12
a4=12+5=17
a11=2+(11-1)*5=2+10*5=2+50=52
so terms are 2,7,12,17,..., 52
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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Lauren is saving up. she alright has $40 and can save an additional $5 per week using money from her after school job. How much money would Lauren have after 9 weeks of saving?
Answer:
$85
Step-by-step explanation:
y=5x+40
x=weeks
y=total money
y=5(9)+40
y=45+40
y= 85
Zoe and Mackenzie are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Zoe is 249 miles away from the stadium and Mackenzie is 237 miles away from the stadium. Zoe is driving along the highway at a speed of 58 miles per hour and Mackenzie is driving at speed of 55 miles per hour. Let ZZ represent Zoe's distance, in miles, away from the stadium tt hours after noon. Let MM represent Mackenzie's distance, in miles, away from the stadium tt hours after noon. Write an equation for each situation, in terms of t,t, and determine whether Zoe or Mackenzie is closer to the stadium 2 hours after noon.
According to the question, the given data are as follows:
Zoe’s distance = ZZ(miles); Stadium time = tt (hours); Mackenzie’s distance = MM(miles)
Distance between Zoe and stadium = 249 miles
Distance between Mackenzie and stadium = 237 miles
Zoe speed = 58 miles per hour
Mackenzie speed = 55 miles per hour
Time = 2 hours
Using standard distance formula:
Distance = (speed)(time)
As per relative speed, distance gets added and speed gets subtracted when objects are away or parallel from each other.
ZZ = 249 -58tt
MM = 237 -55tt
When both are at the same distance, the time will be t = 4 hours
249 -58tt = 237 -55tt
tt = 4 hours
What is distance?
Distance can be defined as the resultant displacement between two points. It can be calculated in different units like kilometers, meters, miles etc. Based on direction, the distance formulas change.
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