Answers
Answer:
1. 14
2. 25
3. 22
4. 25
5. 8
Step-by-step explanation:
These are actually simple linear equations disguised as geometry.
Image 1.
the triangle is an isosceles triangle, so 2x = 50
sum in triangle is 180, so
5y+10 = 180 - 2*50
5y = 70
y = 14
Image 2.
the triangle is an isosceles triangle, so AB=BC
5x+5 = 7x-1
5 = 2x-1
2x = 6
x = 3
AC = 6x+7 = 18+7 = 25
Image 3.
the triangle is an isosceles triangle, so AC=AB
2x-24 = x-2
x-24=-2
x = 22
BC = x = 22
Image 4.
The triangle is an equilateral triangle, so AB=BC=AC
3x-5=2x+20
x-5=20
x=25
Image 5.
The triangle is an equilateral triangle, so every angle is 60 degrees
7x+4 = 60
7x = 56
x = 8
Related Questions
line that has passes through the point (4, 6) and has a slope of 3. Which linear equation models this line?
Answers
(1)What are the two equations to set up to solve the equation
|3x -2| =19
3x -2=
(2) Solve.
-2|2x+3| + 14≥ - 16
Answers
The two equations to set up to solve the absolute value equation given are; 3x - 2 = 19 and 3x - 2 = -19.
The solution of the inequality given; -2|2x+3| + 14 ≥ - 16 is; x ≥ 6 OR x ≤ -9.
What are the two equations to set up in order to solve the absolute value equation?It follows from absolute value equations that;
| x | = ±x
Hence, | x | = x OR | x | = -x
Ultimately, the two equations to set up are; 3x - 2 = 19 and 3x - 2 = -19.
2. Also, the equation given; -2|2x+3| + 14≥ - 16 can be solved as follows;
-2|2x+3| ≥ - 16 - 14
-2|2x+3| ≥ - 30
|2x+3| ≥ 15
Hence, the equation can be solved as;
2x + 3 ≥ 15 OR 2x + 3 ≤ -15
2x ≥ 12 OR 2x ≤ -18
x ≥ 6 OR x ≤ -9.
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Trevon invests $1650.00 into an account that earns 2% annual interest rate compounded continuously. Assuming no other withdrawals or
deposits, how much will be in the account in 8 years? (Numeric answer only, do not type a $ sign. Round to the nearest cent).
Answers
Answer:
1914
Step-by-step explanation:
interest for one year = 33
interest of 8 years = 264
1650+264 will be in the account in 8 years.
at lone star middle school 2 out of 5 randomly selected students participate in the school science fair if there are 800 students at the middle school how many students will be expected to participate in the science fair.
Answers
The number of students that are expected to participate in the science fair is 320.
How many students are expected to participate in the science fair?The ratio of student that participate to the total number of student is 2 : 5. Ratio is used in mathematics to compare two or more numbers together. In this question, for every 5 students, 2 would be chosen to participate in the fair.
In order to determine the number of students that would participate in the fair, multiply the ratio by the total number of students. Multiplication is the process of determining the product of two or more numbers.
Number of students that would participate in the fair = (ratio of students that would participate / total ratio of students) x number of students in middle school
(2 / 5) x 800 = 320 students
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Which of the following inequalities is represented by the number line?
A) x > 4.5
B) x ≤ 4.5
C) x ≥ 4.5
D) x < 4.5
Answers
Answer:
A
Step-by-step explanation:
i took this test
Answer: B) x ≤ 4.5
Step-by-step explanation:
Closed circles either mean “less than or equal to” or “greater than or equal to,” which would be marked as either
≤ or ≥. Since the number line includes values that are less than 4.5, the ≤ symbol would have to be used.
Order the following numbers from least to greatest: 6.5, -26, -1.3, 0, 2.6, 12
Answers
Answer: least to greatest:
-26, -1.3, 0, 2.6, 6.5, 12
Step-by-step explanation:
We can start by putting the negative numbers last (-26, -1.3) the greater a negative number is the smaller it actually is! so -26 would be the least followed by -1.3
0 would be after because well it's zero. then we can go least to greatest, 2.6, 6.5, 12.
Trigonometry question
Given the following function, choose the graph with the two possible angles with the domain 0[tex]\leq[/tex]0[tex]\leq[/tex]360 degrees.
1. sin0 = -2/3
2. sec0 = 2/1
3. tan0 = 4/5
4. csc0 = -3/2
5. cos0 = -3/5
Answers
The graphs that give the possible solution to the trigonometric functions are as follows
[tex]1. \ sin(\theta) = \dfrac{-2}{3};\ graphs \ 2\ and \ 3[/tex]
[tex]2. \ sec(\theta) = \dfrac{2}{1};\ graph \ 3[/tex]
[tex]3. \ tan(\theta) = \dfrac{4}{5};\ graph \ 3[/tex]
[tex]4. \ csc(\theta) = \dfrac{-3}{2};\ graph \ 2\ and \ 3[/tex]
[tex]5. \ csc(\theta) = \dfrac{-3}{5}\ graph \ 1[/tex]
What is a trigonometric function?A trigonometric function specifies the relation between two side lengths and an interior angle of a right triangle.
1. The given function is sinθ = -2/3
The definition of sin(θ) is [tex]sin(\theta) = \dfrac{Opposite\ side \ length}{Length \ of \ the \ hypotenuse\ side}[/tex]
From the equation, [tex]sin(\theta) = \dfrac{-2}{3}[/tex], which can be taken as the form, [tex]sin(\theta) = \dfrac{-y}{\sqrt{x^2+y^2} }[/tex], therefore, the opposite side leg, y, will be in the third or fourth quadrant, where the y-value is negative.
The possible graphs are therefore, Graph 2, and Graph 3
2. [tex]sec(\theta) = \dfrac{2}{1}[/tex]
Therefore, [tex]cos(\theta) = \dfrac{1}{2}[/tex]
The definition of cos is [tex]cos(\theta) = \dfrac{Adjacent\ side \ length}{Length \ of \ the \ hypotenuse\ side}[/tex]
Therefore, for the angle in standard position, [tex]cos(\theta) = \dfrac{x}{\sqrt{x^2+y^2} }[/tex]
The adjacent side of the angle is in the positive x-axis, which gives an angle in the Quadrant I or Quadrant IV
The only possible option is graph 3
3. [tex]tan(\theta) = \dfrac{4}{5}[/tex]
The definition of the tangent of an angle is: [tex]tan(\theta) = \dfrac{Opposite\ side \ length}{Length\ of\ the \ Adjacent\ side}=\dfrac{y}{x}[/tex]
Which gives a point at (x, y) or (-x, -y), which are points in Quadrant I and Quadrant III respectively.
The possible solution is therefore graph 3
4. [tex]csc(\theta) = \dfrac{-3}{2}[/tex]
Which gives, [tex]sin(\theta) = \dfrac{-2}{3}[/tex]
Given that the y-value is negative, the possible angle is in Quadrant 3 or 4.
The possible solution is, therefore, graph 2 or 3
5. [tex]cos(\theta) = \dfrac{-3}{5}[/tex]
The x-value is negative; therefore, the angle is in either Quadrant II or Quadrant III
The solution is the graph 1
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Please help you got ten min
DO IT STEP BY STEP
Answers
Step-by-step explanation:
the scatter plot shows the results of a survey in which 10 people were asked how many e-mail accounts and how many credit cards they have. how many credit cards does the person with 3 e-mail accounts have?
Answers
In the scatter plot, the person with 3 e-mail accounts have 1 credit card.
Define scatter plot.Typically, the relationship between variables is observed and visually displayed using a scatter plot, a type of chart. Dots are used to indicate the variable values. Scatter plots employ Cartesian coordinates to show the values of the variables in a data set because the placement of the dots on the vertical and horizontal axes will reveal the value of each individual data point. Other names for scatter plots are scattergram, scatter graphs, and scatter charts.
The association between two numerical variables measured for the same individuals is displayed in a scatterplot. The values of one variable are plotted on the horizontal axis, and the values of the other variable are plotted on the vertical axis. On the graph, each individual in the data is represented by a point.
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A graph with the point 6,-5 with a slope of -2/3
Answers
The graph of the line y=-2/3x-1 can be given as follows,
What is a equation of ?
The general equation of straight line is y=mx+c where m is the slope and c is the y-intercept.
every point on the line satisfies its equation.
We are given a point (6,-5) and slope -2/3.
we first need to find the equation of the line
y=mx+c
[tex]y=\frac{-2}{3}x+c[/tex]
The point (6,-5) satisfies the equation.
[tex]-5=\frac{-2}{3}(6)+c[/tex]
[tex]-5=-4+c\\c=-1[/tex]
Substituting the value of c in the equation
we get,
[tex]y=\frac{-2}{3}x-1[/tex]
Now we plot the graph of the equation,
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Suppose corn chips cost 33.5 cents per ounce. if a bag costs $4.35, how many ounces are in the bag of chips? Round your answer to the nearest hundredth, if necessary.
Answers
Answer:
13
Step-by-step explanation:
0 what number is the dividend in the division problem below? 54 divided by 6 equals 9 A. 9 B.6 C. 54 submit
Answers
The dividend in the division problem is 54
How to determine the dividend?The mathematical statement is given as
54 divided by 6 equals 9
The above statement is a quotient expression or quotient statement
A quotient statement is represented as
Dividend divided by Divisor equals Quotient
By comparing the quotient statement with the given mathematical statement, we have the following
Dividend = 54Divisor = 9Quotient= 9This implies that the dividend is 54
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Trigonometry question
Given the following function, choose the graph with the two possible angles with the domain 0[tex]\leq[/tex]0[tex]\leq[/tex]360 degrees.
1. sin0 = -2/3
2. sec0 = 2/1
3. tan0 = 4/5
4. csc0 = -3/2
5. cos0 = -3/5
Answers
The trigonometric functions sin θ = - 2 / 3 and csc θ = - 3 / 2 are related to each other in accordance with the trigonometric formula: sin θ · csc θ = 1. (Correct choices: 1, 4)
What two trigonometric functions have the same angle?
In this question we must look for two trigonometric functions that are associated to one and same angle. This can be done by relations between fundamental and derivate trigonometric functions. There are two fundamental trigonometric functions (sine, cosine) and four derivate trigonometric functions (tangent, cotangent, secant, cosecant).
After a quick inspection, sin θ = - 2 / 3 is related to csc θ = - 3 / 2 as it fulfill the following trigonometric formula: sin θ · csc θ = 1
RemarkThe graph is missing and cannot be found, so we decided to change the intend of the question to find two trigonometric functions associated with the same angle.
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8 Select the correct answer. Which inequality represents all the solutions of 10(3x + 2) > 7(2x - 4)? ОА. X> 4 OB. X
Answers
The given inequality is expressed as
10(3x + 2) > 7(2x - 4)
The first step is to open the brackets on each side of the inequality by multiplying the terms outside the bracket by the terms inside. Thus, we have
10 * 3x + 10 * 2 > 7 * 2x - 7 * 4
30x + 20 > 14x - 28
Collecting like terms, we have
30x - 14x > - 28 - 20
16x > - 48
Dividing both sides by 16, it becomes
16x/16 > - 48/16
x > - 3
Which functions have a maximum and are transformed to the left and down of the parent function, f(x)=x2? Check a
that apply.
O p(x)=14(x + 7)²+1
O g(x) = -5(x+10)²-1
D s(x) = −(x−1)2 +0.5
O g(x)=2x² +10x-35
Ot(x)=-2x² - 4x-3
Answers
The results for the given function are as follows:
1. p(x) = 14(x + 7)² + 1, The direction is upward by 1 unit.
2. q(x) = –5(x + 10)² – 1, The direction is downward by 1 unit.
3. s(x) = –(x – 1)² + 0.5, The direction is upward by 0.5 unit.
4. g(x) = 2x² + 10x – 35 = (x+5/2)² - 23.75, The direction is downward by 23.75 unit.
5. t(x) = –2x² – 4x – 3 = -(x + 1)² - 0.5, The direction is downward by 0.5 unit.
What is the function?
In mathematics, the function is an expression or rule, or law which defines the relationship between dependent and independent variable. Functions are ubiquitous and are essential for designing physical relationships.
According to the question, the given function expression as well as transformation results are as follows:
p(x) = 14(x + 7)² + 1, The direction is upward by 1 unit.
q(x) = –5(x + 10)² – 1, The direction is downward by 1 unit.
s(x) = –(x – 1)² + 0.5, The direction is upward by 0.5 unit.
g(x) = 2x² + 10x – 35 = (x+5/2)² - 23.75, The direction is downward by 23.75 unit.
t(x) = –2x² – 4x – 3 = -(x + 1)² - 0.5, The direction is downward by 0.5 unit.
By using property of the function which states that if a constant value is added to the function it will go upward, similarly, If we subtract a constant then it will go downward.
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12x-4=5x+17 please help me solve this equation other conculaters wont help
Answers
Add 4 to both sides
Simplify by adding the numbers
Subtract 5x from each side
Simplify by combining alike terms
Divide both sides by the same factor
Simplify by cancelling terms both in the numerator and denominator and then divide the numbers
Solution:
x=3
7
Return
Previous
Ne
10 points
A cylindrical can holds 28 in³ of soup. If the can is 4 in. tall, what is the radius of the can to the nearest tenth of an inch?
Round your answer to the nearest hundredth. Only numbers in your answer.
(Hint: V = πr²h)
V =
type your answer...
h =
type your answer...
r =
type your answer...
Answers
The radius of the cylinder is 1.49.
What is a cylinder?
A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance.
These bases are normally circular in shape (like a circle) and the center of the two bases are joined by a line segment, which is called the axis. The perpendicular distance between the bases is the height, “h” and the distance from the axis to the outer surface is the radius “r” of the cylinder.
Volume of the cylinder can be found with the help of the formula
V = πr²h, where V is the volume of the cylinder, r is the radius and h is the height.
Given,
volume of cylinder = 28
Height of the cylinder = 8
Formula of volume of cylinder is
π[tex]r^{2} h[/tex]= 28
Substitute the values
3.14([tex]r^{2}[/tex])(4)= 28
[tex]r^{2}[/tex] = 28/12.56
[tex]r^{2}[/tex] = 2.22
r = [tex]\sqrt{2.22}[/tex]
r = 1.49
Hence, the radius is given by 1.49 in.
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what is three hundred thousand twelve in standard form?
Answers
Sound it out
I NEED THESE IN 7 MINS PLEASE SOMEONE ANSWER THIS ILL GIVE U EXTRA POINTS!!! ANSWER THEM ALL PLEASE!!!
Answers
The circumference of the circle is 62.8 feet.
In geometry, the circumference of a circle or ellipse is referred to as its perimeter (from the Latin circumference, meaning "carrying around").
In other words, the circumference would match the length of the circle's arc if the circle were spread out and straightened into a line segment. The perimeter of any closed figure is more frequently used terminology for the length of the curve around. The exact location of the circle, which corresponds to the edge of a disc, can also be referred to as the "circumference." Any one of the great circles has a length equal to the circumference of a sphere.The diameter of the circle = 20 ft
radius (r) = 20 ÷ 2 = 10 ft
Circumference = 2πr = 2 × 3.14 × 10 = 62.8 feet.
For the second problem
The circumference is 17 feet
∴2πr=17
or, 2r = 17 ÷ 3.14 = 5.414... ≈5.41 feet
Hence the diameter is 5.41
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4 = -(x + 3) implemented as a real life problem
Answers
a boat travels 30 miles up the river in the same amount of time it takes to travel 42 miles down the same river. if the current is 3 miles per hour, what is the speed of the boat in still water? in still water, the boat travels at miles per hour.
Answers
The boat travels at 18 miles per hour.
What is speed?
Speed is calculated as follows: speed = distance / time. Knowing the units for distance and time is necessary to calculate the units for speed.
The rate at which an object travels a certain distance can be described using the speed formula. The distance that a body travels in a certain amount of time is a common way to measure speed.
Given: A boat travels 30 miles up the river in the same amount of time it takes to travel 42 miles down the same river. The current is 3 miles per hour.
From the above information we can write,
Let, u is the boat speed in still water, then
[tex]\frac{30}{u-3} = \frac{42}{u+3}[/tex]
Taking cross multiplication,
30(u + 3) = 42(u - 3)
Solving,
30u + 90 = 42u - 126
42u - 30u -126 -90 = 0
12u = 216
u = 18
Therefore, the speed of boat in still water is, 18 miles per hour.
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Select the equivilent expression(4 ^ 3 / 5 to the negative power of two) ^ 5
Answers
A rule that we need to know in order to solve this is:
[tex](a^b)^c=a^{bc}[/tex]The extended rule would be:
[tex](\frac{a^b}{c^d})^x=\frac{a^{bx}}{c^{dx}}[/tex]Also, remember another rule:
[tex]\frac{1}{a^{-x}}=a^x[/tex]Keeping all these rules in mind, we can simplify:
[tex](\frac{4^3}{5^{-2}})^5=\frac{4^{15}}{5^{-10}}=4^{15}\cdot5^{10}[/tex]THis is the final form.
A concert hall is having a special. If a group of five pays $6.75 each for tickets, each person can get a snack for $4.25. Use the expression 5(6.75+4.25) to find the total cost for 5 friends?
Answer: The total cost is $55
Answers
The total cost of 5 friends is $55.
What is multiplication?
Multiplication is a basic arithmetic function in which occurs when we add a number a particular number of times.
We are given that if group of five pays $6.75 each they get the snack for $4.25.
To find the total cost we first find the cost of one
The cost of one can be given as [tex]6.75+4.25=11[/tex]
To find the cost of 5 we multiply this amount by 5
We get,
[tex]5[/tex]·[tex]11=55[/tex]
Hence the total cost is $55.
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How does the graph of the function g(x)=2|x+7| differ from the graph of the parent function f(x)=|x| ?
a. The graph is translated 7 units to the left. The graph is narrower than the graph of the parent function.
b. The graph is translated 7 units to the left. The graph is wider than the graph of the parent function.
c. The graph is translated up 7 units. The graph is narrower than the graph of the parent function.
d. The graph is translated 7 units to the right. The graph is narrower than the graph of the parent function.
Answers
Answer:
Step-by-step explanation:
A
The odometer in a car measures the number of miles driven by the car since it was made. During the trip, the odometer in Anita‘s car is modeled by the function Y=9500+55X where X represents the number of hours driven during the trip and y represents the odometer reading in miles. What is the meaning of the rate change in this function?
Answers
The given function is y=9500+55x, where x is in hours driven and y is in miles.
Therefore, the slope of the function is
[tex]\frac{miles}{number\text{ of hours driven}}[/tex]The answer is the number of miles driven each hour during the trip, the first option.A basketball player made 74 out of 100 attempted free throws. What percent of free throws was made
Answers
Answer:
74%
Step-by-step explanation:
74 divided by 100 is 0.74, and 0.74 =
74%
Which of the following is the area between a z-score of -0.3 and 0.6?
Answers
Answer:
0.34366
Step-by-step explanation:
I'm not 100% sure but that's what I found. also, it says which of the following, so I don't know the answer choices so don't blame me if it's not on the answer choices
please help 100 points urgent algebra 2
write without using rational exponents
(m^3n^5)^1/4
write out the steps and the answer and please do it right
Answers
The expression (m³n⁵)¹/⁴ can be wriiten as ⁴√m³ . ⁴√n⁵.
To solve the expression (m³n⁵)¹/⁴ without using rational exponents
(m)ᵃ/ᵇ = ᵇ√mᵃ
The given algebric expression is (m³n⁵)¹/⁴
As per the Power distribution Formula :
(mᵃnᵃ)ᵇ = mᵃᵇ nᵃᵇ
(m³n⁵)¹/⁴ = m³ ˣ ¹/⁴ x n⁵ ˣ ¹/⁴
We know that
fraction formula : a¹/ⁿ = ⁿ√a
(m)ᵃ/ᵇ = ᵇ√mᵃ
(m³n⁵)¹/⁴ = m³ ˣ ¹/⁴ x n⁵ ˣ ¹/⁴
⁴√m³ x ⁴√n⁵
⁴√m³ . ⁴√n⁵
The expression (m³n⁵)¹/⁴ can be wriiten as ⁴√m³ . ⁴√n⁵.
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pls help will mark brainliest
Answers
Answer:
I think your answer is A.
Step-by-step explanation:
10=x 15=y
The amount spent is $220
so
10x +15y = 220
Bekah has a rectangular garden. The length and width are different odd number
measures, and the perimeter is 12 feet. What is the area of her garden?
Answers
Answer:
Step-by-step explanation:
Equationi
2x+1 + 2y+1 = 12 The +1 guarantees that the number is odd. 2x makes any integer even.
Givens
L = 2x + 1
W = 2y + 1
The problem is that you do not have a second equation. So you can just choose.
2x + 1 + 2y + 1 = 12 Combine the left
2x + 2y + 2 = 12 Subtract 2 from both sides
2x + 2y + 2 - 2 = 12 - 2
2x + 2y = 10
x = 3
y = 2
======
x = 2
y = 3
======
L= 3*2 + 1
w = 2*2 + 1
L = 7
w = 5
I don't think there is another solution. The negatives cannot be used because a length or width cannot be (say)
x = - 5
y = 11
Can you measure something that is - 5 units long? Not in this lifetime.
