Answers
Answer:
x = 9
Step-by-step explanation:
given a line parallel to a side of the triangle and intersecting the other 2 sides, then it divides those sides proportionally.
[tex]\frac{x-1}{3x+1}[/tex] = [tex]\frac{6}{21}[/tex] = [tex]\frac{2}{7}[/tex] ( cross- multiply )
7(x - 1) = 2(3x + 1) ← distribute parenthesis on both sides
7x - 7 = 6x + 2 ( subtract 6x from both sides )
x - 7 = 2 ( add 7 to both sides )
x = 9
Related Questions
Is the volume of the resulting sugar mixture equal, more than or less than the sum (20 mL sugar +50mL water ) of the volumes of the unmixed sugar and water?
Answers
The volume of the resulting sugar mixture is less than the sum (20 mL sugar + 50 mL water) of the volumes of the unmixed sugar and water.
About water moleculesWhen sugar is dissolved in water, the sugar molecules fit into the spaces between the water molecules, resulting in a decrease in volume. To explain this further, let's use the following steps:
1. Start with 20 mL of sugar and 50 mL of water in separate containers. 2. Pour the sugar into the water.
3. Stir the mixture until the sugar is completely dissolved.
4. Measure the volume of the resulting sugar mixture. You will notice that the volume of the sugar mixture is less than the sum of the volumes of the unmixed sugar and water (70 mL).
This is because the sugar molecules are now occupying the spaces between the water molecules, resulting in a decrease in volume.
In conclusion, the volume of the resulting sugar mixture is less than the sum (20 mL sugar + 50 mL water) of the volumes of the unmixed sugar and water.
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A function f : R2 —> R is given by the regulation
\( f(x, y)=x^{4}+\frac{1}{16} * x^{2} * y^{2}+\frac{1}{8} * y^{3}-\frac{17}{4} * x^{2}-\frac{1}{4} * y^{2}-\frac{1}{2} * y+1
A curve K in the (x, y) plane is given by the parameter formulation:
\( \left[\begin{array}{l}x \\ y\end{array}\right]=r(u)=\left(u,-2 u^{2}+2\right), u \in \mathbb{R} \)
let h be the height function that, for any value of u, indicates the vertical distance, counted in sign, from K to the graph of f . Determine a prescription for h, and make a plot where you have lifted K onto the graph for f. Determine the values of u in which the differential quotient of h is respectively 0, negative and positive
a) state the value of the height function h(-2) =
----------------------------------------------------------------------------------------------------------
It is stated that f has two stationary points. In the first, which we call Q, f actually has
local extremum. In the second, which we call R , the Hessian matrix has the eigenvalue 0.
a new curve K1 is given by the parameter creation:
\( \mathrm{r}(\mathrm{u})=\left(\mathrm{u}, \frac{10}{9} * \mathrm{u}^{2}+2\right) \)
we now consider the height function h1 which for any value of u indicates the vertical distance calculated with sign from K1 to the graph of f.
b) determine a prescription for h and determine whether h1 has: local maximum, local minimum or no local extrema in u=0
Answers
The value of the height function h(-2) is 0.
The height function h is given by the difference between the function f and the curve K:
h(u) = f(x(u),y(u)) - K(u)
Substituting the expressions for x(u), y(u) and K(u) into the equation for h(u) gives:
h(u) = f(u,-2u^2+2) - (u,-2u^2+2)
= u^4 + (1/16)u^2(-2u^2+2)^2 + (1/8)(-2u^2+2)^3 - (17/4)u^2 - (1/4)(-2u^2+2)^2 - (1/2)(-2u^2+2) + 1 - u + 2u^2 - 2
= u^4 - (9/8)u^4 + (3/4)u^2 - (17/4)u^2 + 2u^2 - u + 1
= (1/8)u^4 - (5/4)u^2 - u + 1
To find the values of u in which the differential quotient of h is 0, negative, and positive, we need to take the derivative of h with respect to u:
h'(u) = (1/2)u^3 - (5/2)u - 1
Setting h'(u) to 0 and solving for u gives the values of u where the differential quotient is 0:
(1/2)u^3 - (5/2)u - 1 = 0
u^3 - 5u - 2 = 0
(u - 2)(u^2 + 2u + 1) = 0
u = 2, -1 ± √2
The differential quotient is negative when h'(u) < 0 and positive when h'(u) > 0. Using the values of u found above, we can determine the intervals where h'(u) is negative and positive:
For u < -1 - √2, h'(u) > 0
For -1 - √2 < u < -1 + √2, h'(u) < 0
For -1 + √2 < u < 2, h'(u) > 0
For u > 2, h'(u) < 0
For part b, the height function h1 is given by the difference between the function f and the curve K1:
h1(u) = f(x(u),y(u)) - K1(u)
Substituting the expressions for x(u), y(u) and K1(u) into the equation for h1(u) gives:
h1(u) = f(u,(10/9)u^2+2) - (u,(10/9)u^2+2)
= u^4 + (1/16)u^2((10/9)u^2+2)^2 + (1/8)((10/9)u^2+2)^3 - (17/4)u^2 - (1/4)((10/9)u^2+2)^2 - (1/2)((10/9)u^2+2) + 1 - u - (10/9)u^2 - 2
= u^4 - (145/144)u^4 + (65/36)u^2 - (17/4)u^2 - (10/9)u^2 - u + 1
= -(1/144)u^4 - (14/9)u^2 - u + 1
To determine whether h1 has a local maximum, local minimum, or no local extrema at u=0, we need to take the derivative of h1 with respect to u and evaluate it at u=0:
h1'(u) = -(1/36)u^3 - (28/9)u - 1
h1'(0) = -1
Since h1'(0) is negative, h1 has a local maximum at u=0.
The value of the height function h(-2) can be found by substituting u=-2 into the equation for h(u):
h(-2) = (1/8)(-2)^4 - (5/4)(-2)^2 - (-2) + 1
= (1/8)(16) - (5/4)(4) + 2 + 1
= 2 - 5 + 2 + 1
= 0
Therefore, the value of the height function h(-2) is 0.
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F. Find the domain and the range of the following functions. Write your answers in set builder form. 1) \( f(x)=4 x^{2}-2 x+1 \) 2) \( g(x)=2 x-1 \), where \( x \neq 2 \) 3) \( h(x)=2 x-\sqrt{x+1} \)
Answers
The domain and range of the functions in set builder form are:
1) Domain: \(\{x|x\in\mathbb{R}\}\), Range: \(\{y|y\in\mathbb{R}\}\)
2) Domain: \(\{x|x\in\mathbb{R}, x\neq2\}\), Range: \(\{y|y\in\mathbb{R}\}\)
3) Domain: \(\{x|x\in\mathbb{R}, x\geq-1\}\), Range: \(\{y|y\in\mathbb{R}\}\)
The domain and range of a function are the possible values of x and y, respectively, for which the function is defined. We can find the domain and range of the given functions using set builder form, which is a way of describing a set of numbers using an expression.
The function \(f(x)=4x^{2}-2x+1\) is a polynomial function, and the domain of a polynomial function is all real numbers. Therefore, the domain of this function is \(x\in\mathbb{R}\), or in set builder form, \(\{x|x\in\mathbb{R}\}\). The range of this function is also all real numbers, so the range is \(y\in\mathbb{R}\), or in set builder form, \(\{y|y\in\mathbb{R}\}\).
The function \(g(x)=2x-1\) is also a polynomial function, so the domain is all real numbers except for x=2, since the function is undefined at that point. Therefore, the domain of this function is \(x\in\mathbb{R}, x\neq2\), or in set builder form, \(\{x|x\in\mathbb{R}, x\neq2\}\). The range of this function is also all real numbers, so the range is \(y\in\mathbb{R}\), or in set builder form, \(\{y|y\in\mathbb{R}\}\).
The function \(h(x)=2x-\sqrt{x+1}\) is a radical function, and the domain of a radical function is the set of values for which the expression under the radical is greater than or equal to zero. Therefore, the domain of this function is \(x\in\mathbb{R}, x\geq-1\), or in set builder form, \(\{x|x\in\mathbb{R}, x\geq-1\}\). The range of this function is also all real numbers, so the range is \(y\in\mathbb{R}\), or in set builder form, \(\{y|y\in\mathbb{R}\}\).
In conclusion, the domain and range of the functions in set builder form are:
1) Domain: \(\{x|x\in\mathbb{R}\}\), Range: \(\{y|y\in\mathbb{R}\}\)
2) Domain: \(\{x|x\in\mathbb{R}, x\neq2\}\), Range: \(\{y|y\in\mathbb{R}\}\)
3) Domain: \(\{x|x\in\mathbb{R}, x\geq-1\}\), Range: \(\{y|y\in\mathbb{R}\}\)
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The simple interest charged on a 4-month loan of \( \$ 12,000 \) is \( \$ 496 \). Find the simple interest rate. (Round your answer to one decimal place.) \( \% \)
Answers
The simple interest rate for this loan is 12.4%.
To find the simple interest rate, we can use the formula for simple interest, which is:
Simple Interest = Principal x Rate x Time
In this case, we are given the simple interest (\$496), the principal (\$12,000), and the time (4 months). We can plug these values into the formula and solve for the rate.
\$496 = \$12,000 x Rate x (4/12)
Simplifying the equation, we get:
\$496 = \$4,000 x Rate
Dividing both sides by \$4,000, we get:
Rate = 0.124
To convert this to a percentage and round to one decimal place, we multiply by 100 and round:
Rate = 0.124 x 100 = 12.4%
Therefore, the simple interest rate for this loan is 12.4%.
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Central School has 758 students. There are 2 lunch periods at Central School. Three hundred seventy-one students eat during the first lunch period. Which lunch period has more students? Conjecture: More students eat during the second lunch period. 1. Construct an argument to justify the conjecture. 2. Explain another way you could justify the conjecture
Answers
The lunch period that has more students is the second lunch period.
Which period has more students?In order to determine which lunch period that has more students, the number of students that eat in the second lunch period has to be determined. In order to determine this value, the mathematical operation that would be used is subtraction.
Subtraction is the process of determining the difference between two or more numbers. The sign that is used to represent subtraction is -.
Number of students that ear in the second lunch period = total number of students - students that eat in the first lunch period
758 - 371 = 387
387 > 371
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(a)Let Q be the quotient of the ring R=Z*Z by the ideal I= 2Z*2Z.
What is Q four elements?
(b) Use the Fundamental Homomorphism Theorem to show Q is
equivalent to Z2*Z2?
Answers
By the Fundamental Homomorphism Theorem, Q is isomorphic to Z2*Z2.
a) Q is the quotient ring R/I, which has four elements: [0]_I, [1]_I, [2]_I, and [3]_I. Here, [x]_I is the equivalence class of x in R/I.
b) Using the Fundamental Homomorphism Theorem, we can show that Q is equivalent to Z2*Z2. Since I is a normal subring of R, the quotient ring Q can be written as Q = R/I. Then the homomorphism defined by φ: R → Z2*Z2, where φ(r) = (r mod 2, r mod 2) is onto and I is the kernel of φ. Thus, by the Fundamental Homomorphism Theorem, Q is isomorphic to Z2*Z2.
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35 points So umm can you guys help me figure out what type of histogram this is?
Answers
Answer:
Okay this is the bi-modal distribution histogram
sarah plants 760 vines in rows containing either 20 vines or 25 vines. there are 3 times as many rows containing 25 vines as there are rows containing 20 vines. how many rows contain 25 vines?
Answers
Answer:
Let's start by using variables to represent the number of rows containing 20 vines and 25 vines. Let:
x be the number of rows containing 20 vines
3x be the number of rows containing 25 vines (since there are 3 times as many rows containing 25 vines as there are rows containing 20 vines)
We know that Sarah plants a total of 760 vines, and that each row contains either 20 vines or 25 vines. Therefore, we can write an equation based on the total number of vines:
20x + 25(3x) = 760
Simplifying and solving for x:
20x + 75x = 760
95x = 760
x = 8
So there are 8 rows containing 20 vines, and 3 times as many rows containing 25 vines, or 3(8) = 24 rows containing 25 vines.
Therefore, Sarah planted 8 rows with 20 vines and 24 rows with 25 vines.
Adina is starting a band and wants to buy a guitar and amplifier. The cost of the guitar is g(m) = 680 + 10m where m is time in months. The amplifier cost is represented by the function a(m) = 450 - 5m. Adina hopes to have
enough money saved up to buy both items in 4 months. How much will she need?
A. $1,070
B. $290
C. $1,190
D. $1,150
Answers
Answer:
b
Step-by-step explanation:
its really easy when u read it multiple of times
option D.
Step by step solved:
Adina needs to find the total cost of the guitar and amplifier after 4 months.
The cost of the guitar after 4 months is given by g(4) = 680 + 10(4) = 720.
The cost of the amplifier after 4 months is given by a(4) = 450 - 5(4) = 430.
The total cost after 4 months is the sum of the cost of the guitar and the cost of the amplifier:
Total cost = 720 + 430 = 1150.
Therefore, Adina will need $1,150 to buy both items in 4 months.
Hence, the correct answer is option D.
What are the solutions to the following equation (c+5)^2=36
Answers
The quadratic equation (c+5)²=36 will give c = 1,-11.
What exactly is a quadratic equation?A quadratic equation is a type of equation in algebra that involves a variable (usually denoted as "x") raised to the power of 2, or squared. The standard form of a quadratic equation is:
ax² + bx + c = 0
where a, b, and c are constants, with a≠0. The goal is to solve for the variable x, which may have one or two possible solutions depending on the coefficients of the equation.
Now,
To solve the equation (c + 5)² = 36:
Taking the square root of both sides of the equation
√(c + 5)² = ±√36
Simplify the left-hand side using the rule that √a² = |a|:
|c + 5| = ±6
Solve for c in each case by subtracting 5 from both sides of the equation:
c + 5 = 6 or c + 5 = -6
Solve for c in each equation:
c = 1 or c = -11
Therefore, the solutions to the equation (c + 5)² = 36 are c = 1 and c = -11.
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A shed is 12 feet long, 8 feet wide, and 10 feet tall. The rental cost is $3 per cubic foot. How much does it cost to rent one shed?
Answers
The cost to rent one shed is $ 2880 where rental cost is $3 per cubic foot.
The length of the shed is 12 feet , that is l= 12 feet
The width of the shed is 8 feet, that is b=8 feet
The height of the shed ( tallness of the shed) is 10 feet , that is h=10 feet
The volume of the shed can be calculated by the formula
= length*breadth*height (cubic units)
= l*b*h (cubic foot)
= 12*10*8 cubic foot
= 960 cubic foot
The rental cost of per cubic foot is $3.
Thus the rental cost of 960 cubic foot will be = $ (960*3 )
= $ 2880
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x^(2)+(144)/(1369)(144)/(1369)=1 3 isolate the variable term and simplify the right
Answers
We have that, given the equation x^(2)+(144)/(1369)(144)/(1369)=13 , we will have as a solution x = 485/1369
To isolate the variable term and simplify the right, we need to follow the steps below:
Step 1: Subtract the fraction term from both sides of the equation.
[tex]x^2+(144/1369)(144/1369) - (144/1369)(144/1369) = 13 - (144/1369)(144/1369)[/tex]
Step 2: Simplify the right side of the equation by multiplying the fractions and then subtracting from 13.
[tex]x^2 = 13 - (20736/1874161)[/tex]
Step 3: Combine the terms on the right side of the equation by finding a common denominator and subtracting.
[tex]x^2 = (24320661/1874161) - (20736/1874161)[/tex]
Step 4: Simplify the right side of the equation by subtracting the numerators and keeping the common denominator.
[tex]x^2 = (24320661 - 20736)/1874161[/tex]
Step 5: Simplify the fraction on the right side of the equation by reducing to lowest terms.
[tex]x^2 = (24300025/1874161)[/tex]
Step 6: Take the square root of both sides of the equation to isolate the variable term.
[tex]x = \sqrt{(24300025/1874161)}[/tex]
Step 7: Simplify the square root by factoring out any perfect squares.
[tex]x = \sqrt{(485^2)/(1369)}[/tex]
Step 8: Simplify the square root by taking the square root of the perfect squares.
[tex]x = 485/1369[/tex]
Therefore, the solution to the equation is [tex]x = 485/1369[/tex].
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"a. For what values of x is f(x) > 0?
b. What is the domain of f?
c. What is the range of f?
d.What are the x-intercept(s)?
e.What are the y-intercept(s)?
f.How often does the line"
Answers
I can provide general information about how to find the values, domain, range, x-intercepts, and y-intercepts of a function.
To answer these questions, we need to have a function f(x) to work with. Without knowing the specific function, it is impossible to accurately answer the questions. However, I can provide general information about how to find the values, domain, range, x-intercepts, and y-intercepts of a function.
a. To find the values of x for which f(x) > 0, we need to set f(x) > 0 and solve for x. The solution will give us the values of x that make the function greater than zero.
b. The domain of a function is the set of all possible x-values that can be plugged into the function. To find the domain of f, we need to look for any restrictions on the x-values, such as values that would make the denominator of a fraction equal to zero or values that would make the argument of a square root negative.
c. The range of a function is the set of all possible y-values that can be obtained from the function. To find the range of f, we need to look for any restrictions on the y-values, such as values that cannot be obtained from the function.
d. The x-intercepts of a function are the points where the function crosses the x-axis. To find the x-intercepts of f, we need to set f(x) = 0 and solve for x.
e. The y-intercepts of a function are the points where the function crosses the y-axis. To find the y-intercepts of f, we need to set x = 0 and solve for f(x).
f. The question "How often does the line" and cannot be answered without further information.
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Find the final amount for an investment of $5,000 over 5 years at an annual interest rate of 6% if the interest is compounded quarterly.
Answers
The final amount for the investment of $5,000 over 5 years at an annual interest rate of 6% compounded quarterly is $ 6,749.29.
Compound interest:To find the final amount for an investment P over t years at an annual interest rate of r compounded quarterly, we can use the formula for compound interest:
[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]
Where:
A = Final amount
P = Principal (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Time period in years
Here we have
P = $5,000,
r = 6% = 0.06,
n = 4 (since the interest is compounded quarterly), and
t = 5 years.
Using the above formula
[tex]A = 5000(1 + 0.06/4)^{(4*5)[/tex]
[tex]A = 5000(1.015)^{20}[/tex]
[tex]A = 5000(1.34985711)[/tex]
[tex]A = $6,749.29[/tex]
Therefore,
The final amount for the investment of $5,000 over 5 years at an annual interest rate of 6% compounded quarterly is $ 6,749.29.
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Use Euclid's first book to prove what specific quadrilaterals are produced by perpendicular, unequal, bisecting diagonals.
Answers
By using Euclid's first book, we can prove that the quadrilateral produced by perpendicular, unequal, bisecting diagonals is a kite. A kite is a quadrilateral with two pairs of adjacent sides that are equal in length. In this case, the two pairs of adjacent sides are formed by the diagonals bisecting the quadrilateral into four smaller triangles with equal areas.
According to Euclid's first book, when two lines intersect at a right angle (perpendicular), they form four right angles. In the case of a quadrilateral with perpendicular, unequal, bisecting diagonals, the diagonals intersect at a right angle and divide the quadrilateral into four smaller triangles with equal areas.
1. Draw a quadrilateral with perpendicular, unequal, bisecting diagonals.
2. Label the points where the diagonals intersect as A, B, C, and D.
3. Label the point where the diagonals intersect as E.
4. Use Euclid's first book to prove that the angles at E are all right angles.
5. Use Euclid's first book to prove that the four triangles formed by the diagonals are congruent (equal in area).
6. Use the definition of a kite to prove that the quadrilateral is a kite (two pairs of adjacent sides are equal in length).
7. Therefore, the quadrilateral produced by perpendicular, unequal, bisecting diagonals is a kite.
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Brenda's school is due west of her house and due south of her friend Trevor's house. The distance between the school and Trevor's house is 4 miles and the straight-line distance between Brenda's house and Trevor's house is 6 miles. How far is Brenda's house from school? If necessary, round to the nearest tenth.
Answers
In response to the supplied query, we may state that Hence, Brenda's Pythagorean theorem home is around 7.2 kilometers away from the school.
what is Pythagorean theorem?The fundamental Euclidean geometry relationship between the three sides of a right triangle is the Pythagorean Theorem, sometimes referred to as the Pythagorean Theorem. This rule states that the areas of squares with the other two sides added together equal the area of the square with the hypotenuse side. According to the Pythagorean Theorem, the square that spans the hypotenuse (the side that is opposite the right angle) of a right triangle equals the sum of the squares that span its sides. It may also be expressed using the standard algebraic notation, a2 + b2 = c2.
Points A, B, and C can be used to create a right triangle in this situation. The hypotenuse of the line segment between points A and C is its length, while the other two sides are the lengths of the segments connecting A and B and B and C.
We'll refer to the separation between positions A and C as "x". Next, we have:
[tex]x2 = 6 + 4, x2 = 36 + 16, x2 = 52, x = \sqrt(52) = 7.2.[/tex]
Hence, Brenda's home is around 7.2 kilometers away from the school.
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3 + 10x+ 4x as an algebradic expression
Answers
Answer: 10x² + 3x + 4
Step-by-step explanation: I hate math.
Ramon is filling cups with juice. Each cup is shaped like a cylinder and has a diameter of 4.4 inches and a height of 7 inches. How much juice can Ramon pour into 6 cups? Round to the nearest hundredth and approximate using π = 3.14.
A) 2,553.20 cubic inches
B)638.30 cubic inches
C)425.53 cubic inches
D)106.38 cubic inches
Answers
Answer:
D) 106.38 cubic inchesStep-by-step explanation:
Info:Diameter is the width of the cup and 7 is the height.
Process of elimination rules out A as it is too big.
The base of the cup is a circle.
Finding the base:Formula for area of a circle is Pi (3.14) times the radius squared.
1. Find radius
Diameter is 2x the radius, so if we have a 4.4 diameter, the radius will be 2.2.
2. Square radius
2.2x2.2=
4.84
3. Times Pi
Multiply 4.84 by 3.14 (Pi) to get
15.1976
Finding area:15.1976 is the area of the base. Now we multiply that by 7!
15.1976 x 7=
106.3832This is our answer, but we need to round it to the nearest hundredth, the question tells us.
106.38 is the final answer.
help please, im not sure what im doing anymore
Answers
The length of arcs MH and TY in terms of π are 18π cm and 22π cm respectively.
How to determine the lengths of arc MH and TYArc length = (central angle / 360) x (2 x π x radius)
Arc length of sector of circle = (θ/360º) × 2πr
For the sector MRH:
θ = 180° - 72° = 108°
r = 30 cm
Arc length MH = (108°/360º) × 2π × 30 cm
Arc length MH = 9 × 2π cm
Arc length MH = 18π cm.
For the sector MRH:
θ = 72°
r = (25 + 30) cm = 55 cm
Arc length TY = (72°/360º) × 2π × 55 cm
Arc length TY = 1 × 2π × 11 cm
Arc length TY = 22π cm
Therefore, the length of arcs MH and TY in terms of π are 18π cm and 22π cm respectively.
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A tent is shaped like a triangular prism with the dimensions shown. If the volume of the tent is 12.6 cubic meters, what is the center height of the tent? The dimensions are 2.8m for the base and 4.5 for the height that connects the bases.
Answers
Answer:
2 m
Step-by-step explanation:
You want the height of the triangular base of a triangular prism that has a volume of 12.6 m³. The base of the triangle is 2.8 m, and the height of the prism is 4.5 m.
VolumeThe volume formula for the triangular prism is ...
V = Bh . . . . the product of the triangle area and the base–base distance
12.6 = B·4.5
2.8 = B . . . . . . . area of the triangular base
AreaThe area of the triangular base is given by ...
A = 1/2bh
The area is shown above to be 2.8 m², and the base of the triangle is given as 2.8 m, so we have ...
2.8 = 1/2(2.8)h
2 = h . . . . . . . . . . . . divide by 1.4, the coefficient of h
The center height of the tent is 2 meters.
__
Additional comment
If you combine the formulas, you see that a triangular prism has half the volume of a rectangular prism with the same overall dimensions.
V = 1/2LWH
12.6 = 1/2(4.5)(2.8)h = 6.3h
2 = h . . . . meters
Fin the perimeter of the triangle circumscribed about the circle below
Answers
According to the information the perimeter of the triangle is 69.19cm
How to find the perimeter of the triangle?To find the perimeter of a triangle, it is necessary to add the length of its sides. However, we do not know the length of its height, so it is necessary to apply the Pythagorean theorem to find the length of the height. In this case we must apply the following variant:
a = [tex]\sqrt{c^{2} - b^{2} }[/tex]
So we just have to replace the values and get the result.
Then we can infer that the base measures 16cm and the hypotenuse measures 29cm; the formula would be like this:
[tex]a = \sqrt{29^{2} - 16^{2} } \\a = \sqrt{841 - 256}\\a = \sqrt{585} \\a = 24.18[/tex]
According to the above, we can infer that the height of this triangle is 24.18cm. Now to find the perimeter of the figure we must add the length of its sides:
24.18cm + 16cm + 29cm = 69.19cmLearn more about perimeter at: https://brainly.com/question/6465134
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Using a scale of 1 inch : 16 feet, what are the blueprint dimensions of a building that is 70 feet × 90 feet?
0.27 inches X 0.2 inches
4.375 inches X 5.625 inches
1,120 inches X 1,440 inches
4 inches X 5 inches
Answers
The blueprint dimensions of a building that is 70 feet × 90 feet is: 4.375 inches X 5.625 inches.
What is scale ?Scale refers to the ratio or proportion between the dimensions of an object or a system in the real world and its representation in a model, drawing, or map. A scale is typically expressed as a ratio or a fraction, such as 1:100 or 1/4, which indicates the relationship between the size of the object in the real world and the size of its representation in the model or drawing.
According to given information :Using a scale of 1 inch : 16 feet means that every inch on the blueprint represents 16 feet in the actual building. To find the blueprint dimensions of a building that is 70 feet x 90 feet, we need to divide each dimension by 16.
The blueprint dimensions are:
70 feet ÷ 16 = 4.375 inches
90 feet ÷ 16 = 5.625 inches
Therefore, the blueprint dimensions of the building are approximately 4.375 inches by 5.625 inches.
The answer is: 4.375 inches X 5.625 inches.
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The line 8-2y=x is dilated by a scale factor of 1/4 about the center. What is the equation of the image
Answers
The equation of the image is x = 32 - 2y which is dilated by a scale factor of 1/4 about the center.
What is dilation?Dilation is a process for creating similar figures by modifying the dimensions.
To dilate a line by a scale factor of 1/4 about the center, we can first find the coordinates of the center of dilation.
Since no center is given in the problem, we can assume that the center is the origin (0,0).
To find the equation of the image, we need to apply the dilation to the original line. The dilation multiplies all distances by the scale factor, so the image of the point (x, y) is (1/4)x, (1/4)y).
So, the image of line 8 - 2y = x under this dilation is:
8 - 2(1/4)y = (1/4)x
8 - (1/2)y = (1/4)x
32 - 2y = x
Therefore, the equation of the image is x = 32 - 2y.
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blake collects stamps. He collected a total of 250 . If 84% of the stamps he collected were foreign, how many other stamps did he collect?
Answers
Answer: 40
Step-by-step explanation: 100% - 84% = 16% and 16% of 250 is 40
Answer:
40
Step-by-step explanation:
jordan cut strips of border for a design for a triangular sign to put on a bulletin board. two of the strips were 15 inches long and the third was 30 inches long. determine if the design can be made.justify your response.
Answers
Given that Jordan cut strips of border for a design for a triangular sign to put on a bulletin board. Two of the strips were 15 inches long and the third was 30 inches long. We need to determine if the design can be made.
To determine whether the design can be made or not, we will check whether the sum of the lengths of any two sides of the triangle is greater than the length of the third side or not. Let a, b and c be the three sides of the triangle such that c is the longest side. According to the Triangle Inequality Theorem, For a triangle to be formed, the sum of the lengths of any two sides of the triangle should be greater than the length of the third side.Thus, a + b > cIf the above condition is satisfied, then the design can be made. If not, then the design cannot be made.
Let's check for the given design:
a + b > ca + b = 15 + 15 = 30 (Since two of the strips were 15 inches long)
Therefore, 30 > 30 (Since the third strip was 30 inches long)The given design satisfies the Triangle Inequality Theorem. Hence, the design can be made.
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t Marie's Beading Boutique, 32 out of the 32 beads on clearance are plastic. What percentage of beads on clearance are plastic?
Write your answer using a percent sign (%).
Answers
Answer:
100%
Step-by-step explanation:
If all 32 the beads were plastic it would be 100%
Given f (x) = |x| - 3; x ≥
0, write an equation for f -1(x).
(Hint: Sketch f (x) and note the domain
and range.)
Select one:
a. f -1(x) = |x + 3|;
x ≥ 0
b. f -1(x) = |x | + 3;
x ≥ -3
c. f -1(x)
Answers
The correct answer is option b. f -1(x) = |x| + 3; x ≥ -3.
To find the inverse of a function, we can switch the x and y values and solve for y. In this case, we can start with the original equation:
f(x) = |x| - 3
Switch the x and y values:
x = |y| - 3
Solve for y:
|x| = y + 3
|y| = x + 3
Since the original function has a domain of x ≥ 0, the inverse function will have a range of y ≥ 0. This means that the absolute value of y will always be positive, so we can drop the absolute value bars:
y = x + 3
So the inverse function is:
f -1(x) = x + 3
And since the original function has a domain of x ≥ 0, the inverse function will have a domain of x ≥ -3. So the final equation for the inverse function is: f -1(x) = x + 3; x ≥ -3
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On a certain day, the temperature of the pool was 76°F at 10 A.M. and 91°F at 1 P.M. If the temperature rose at a constant rate from 10 A.M. to 1P.M. on that day, what was the temperature at 11 A.M.? a. 79°F d. 89°F b. 81°F e. 90°F c. 86°F
Answers
The correct answer is b. 81°F.
On a certain day, the temperature of the pool rose at a constant rate from 76°F at 10 A.M. to 91°F at 1 P.M. To find the temperature at 11 A.M., we need to find the rate of change in temperature and then use it to calculate the temperature at 11 A.M.
The rate of change in temperature can be found by dividing the difference in temperature by the difference in time:
Rate of change = (91°F - 76°F) / (1 P.M. - 10 A.M.) = 15°F / 3 hours = 5°F per hour
Now, we can use this rate of change to find the temperature at 11 A.M.:
Temperature at 11 A.M. = 76°F + (5°F per hour)(1 hour) = 81°F
Therefore, the correct answer is b. 81°F.
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100 points and mark brainly please hurry
Answers
Answer:
12 of them
Step-by-step explanation:
5x5 cube so
25*48%
Answer:
its 12 squares
Step-by-step explanation:
First you take all the squqres as 100 percent then you divide both sides by 100 to find how much squares is 1 percent, then multiply the 1 percent answers by the percentage you need which is 48 to get the squares
Find x to the nearest degree
Answers
The nearest value of x is 56°. We solve this question using Pythagoras theorem for that we also find one of its side which is not given.
What is Pythagoras theorem?The square on the hypotenuse of a right-angled triangle has the same area as the sum of the squares on the other two sides, according to a Pythagorean theorem.
Given AB = 5 and AC = 9
By Using Pythagoras theorem,
AB² + BC² = AC²
5² + BC² = 9²
BC² = 9² - 5²
BC² = 81 - 25
BC = 7.48 (Approx.)
Now, we will find the value of x°
[tex]So, tan\ x^{\circ} = \frac{BC}{AB}[/tex]
[tex]tan \ x^{\circ} = \frac{7.48}{5}[/tex]
[tex]tan\ x^{\circ} = 1.496[/tex]
[tex]x^{\circ} =tan^{-1} 1.496[/tex]
[tex]x^{\circ} = 56.24^{\circ}[/tex] , which is close to 56°
So the nearest value of x is 56°.
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