Which set of measurements would prove that ΔABC and ΔDEF are similar?

A. DE = 15, EF = 20 and m∠D = 35
B. DE = 16, DF = 21 and m∠D = 35
C. DE = 12, DF = 16 and m∠D = 35
D. DE = 18, EF = 24 and m∠D = 70

The measure of each angle and side is given above.

Given is that the red triangle is a dilation of the blue triangle, with a scale factor of {k} = 1.5.

We can write -

57/RT = 1.5

RT = 57/1.5

RT = 38

LM/20 = 1.5

LM = 20 x 1.5

LM = 30

MN/26 = 1.5
MN = 26 x 1.5
MN = 39

∠2 = 15°

∠1 = 121°

Therefore, the measure of each angle and side is given above.

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Answer:

Base: 8. Height: 3.

Step-by-step explanation:

Let the height be x. Then the base would be 2x+2. The formula for the area of a triangle is 1/2*base*height. We know the area, and we know the base and height in terms of x. Now you just solve for x. 1/2*x*(2x+2) = 12. x(2x+2) = 24. You could plug in factors of 24, but I used the quadratic formula to solve this equation. 2x^2 +2x -24 = 0. Plugging in these values into the quadratic formula, we get that x = 3. This means that the height is 3. Since the base is 2x+2 and x is 3, then the base is 8.

Reginald used 2 square tiles to make the mosaic

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

The area is the product of the length and width. Hence:

Area = length * width

Reginald created a mosaic from 6" square tiles. Therefore:

Area of tiles = 6 in * 6 in = 36 in²

If the completed mosaic was 2 feet by 3 feet, Hence:

Area of mosaic = 2 feet * 3 feet = 6 feet

1 feet = 12 in

6 feet = 6 feet * 12 in per feet = 72 in²

Number of tiles = Area of mosaic / area of tiles = 72 in² / 36 in² = 2

Reginald used 2 tiles

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Answer:

Step-by-step explanation:

38.06

The slant height of the square base pyramid is calculated as l = 17 using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

we can observe the right triangle with hypotenuse l, height = 15, and base = 8 {half the pyramid base of 16}

the slant height is calculated as follows:

l² = 15² + 8²

l² = 225 + 64

l² = 289

l = √289 {take square root of both sides}

l = 17.

Therefore, the slant height of the square base pyramid is calculated as l = 17 using the Pythagoras rule.

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Answer:

17.6 feet.

Step-by-step explanation:

The length of the I-beam can be calculated as follows:

Weight = Length * Weight per Foot

Rearranging this equation:

Length = Weight / Weight per Foot

Substituting the given values:

Length = 444.5 lb / 25.4 lb/ft = 17.6 ft

So, the length of the I-beam is 17.6 feet.

The graph of the system of the equation y > -1, y≥ x²+ 1, and (x-1)²+(y-1)² ≤ 16 is attached with the feasible region of each part shaded

The equation y > -1 is a horizontal line drawn at point y = -1 and shaded above the line because the sign is greater than. the line is dashed line line since the equation is not "greater than or equal to".

The equation y ≥ x²+ 1 is a parabolic equation

The equality sign attached to the greater than makes the line a solid line and because it is greater than the shading is inside the curve.

The equation (x - 1)² + (y - 1)² ≤ 16 is a equation of a circle

The equality sign attached to the greater than ("greater than or equal to") makes the line a solid line and because it is greater than the shading is inside the circle

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Answer:the answer is -69/8

Step-by-step explanation:

first you plug -9 into 3/8 and it gives you -72/8+3/8 if you add those together you get -69/8

The solution is, the required cost of the used game X= 19.

An equation which can be expressed as a mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

So he bought the $120 game with $82

and 2 equally priced game.

This can be changed to an equation: 120= 82+2X.

The X represents the cost of the used game.

120= 82+2X

-82 -82

——————-

38= 2X

38= 2X

Divide by 2 on both sides

X= 19

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To sketch the angle θ in standard position, you can start by plotting the point ( -3, 4 ) on the coordinate plane. Next, you draw a line from the origin ( 0, 0 ) to the point ( -3, 4 ), which represents the terminal side of the angle.

Now, you can use the six trigonometric functions to find the exact values for θ:

Cosine ( cos θ ) = x / r = -3 / 5

Sine ( sin θ ) = y / r = 4 / 5

Tangent ( tan θ ) = y / x = 4 / -3

Secant ( sec θ ) = 1 / cos θ = -5 / 3

Cosecant ( csc θ ) = 1 / sin θ = -5 / 4

Cotangent ( cot θ ) = 1 / tan θ = -3 / 4

Here, r represents the distance from the origin to the point ( -3, 4 ), which is 5 units. Note that these values are for the least positive measure of the angle, which is in the second quadrant.

The requried complete system of equation is given as -2x + y = -5 and y = -x + 10.

A system of simultaneous equations, also known as a system of equations, is a set of two or more equations that must be solved at the same time. In a system of two equations, for example, the solution is the set of values of the variables that satisfy both equations simultaneously.

Here,
Given equation are
_x + y = −5 - -- - - -(1)

y = −x + _ - - - - - (2)

Now,
Let the coefficient of x in equation 1 is m and the intercept of equation 2 be y,

In equation 1,
Put the given points (5, 5)
m(5) + 5 = - 5
5m = -10
m = -2

Now,
Put the same point equation 2 with C
5 = -5 + C
C = 10

Thus, the requried complete system of equation is given as -2x + y = -5 and y = -x + 10.

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Answer: 87.96m

Step-by-step explanation:

Circumference of a circle = 2[tex]\pi[/tex][tex]r^{2}[/tex] --> 2[tex]\pi[/tex]14² = 87.96m

Given that there are 26 red cards in the deck of 52 cards, the probability of obtaining a red card on any given draw is 26/52 = 1/2.

The probability of the complimentary event—the probability that no red cards are drawn in the first three draws—can be used to determine the likelihood that a red card will be pulled at least once by the third draw.

Particular that there are 26 non-red (black) cards in the 52-card deck, there is a 50% chance that no red cards will be drawn on any given draw.

As a result, the likelihood that none of the three draws will result in a red card is:

(1/2) x (1/2) x (1/2) = 1/8

The likelihood of drawing a red card at least once by the third draw is the counterpart of this probability.

1 - 1/8 = 7/8

Therefore, by the third draw, there is a 7/8 chance of drawing a red card at least once, or 0.88 rounded to two decimal places.

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The height of tree is 9.9372.

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

ΔABC ~  ΔDEF  only if ratio of two sides of ΔABC and corresponding two sides of ΔDEF is equal and the angle included in both sides are congruent.

Given;

Juanita is 1.82 meters tall

From the tree's base, she walks 12.20 meters along the tree's shadow to a position where the end of her shadow.

She is now 6.10 meters from the end of the shadows.

Now,

Let, h be the height of the tree;

Here, ΔABC ~ ΔADE,

So, DE/BC = AD/AB

h/1.82 = (6.10 + 12.20)/6.10

h/1.82= 18.30/6.10

h=33.306/6.10

h=5.46

h = 1.82*5.46

= 9.9372

Therefore, by congruency of triangle the answer will be 9.9372.

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The substraction of 50 3/5 ft and 48 1/3 can be expressed as34/15.

The concept that will be used here is substraction. One of the four operations used in mathematics, along with addition, multiplication, and division, is substraction. Removal of items from a collection is represented by the operation of subtraction. For instance, the adjacent image shows 5 2 peaches, which are 5 peaches with 2 peaches subtracted, for a total of 3 peaches.

50 3/5 ft - 48 1/3 =

this mixed numbers can be converted to fractions as

253/5 - 145/3

= 34/15

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[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hfill \begin{array}{llll} \textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{6x^{-1}y^{-1}}{\sqrt[4]{xy^4}}\implies \cfrac{6}{x^1 y^1 \left( xy^4 \right)^{\frac{1}{4}}}\implies \cfrac{6}{x^1 y^1 \left( x^{\frac{1}{4}}y^1 \right)}\implies \cfrac{6}{x^1x^{\frac{1}{4}} y^1 y^1} \\\\\\ \cfrac{6}{x^{1+\frac{1}{4}} y^{1+1}}\implies \cfrac{6}{x^{\frac{5}{4}} y^2}\implies {\Large \begin{array}{llll} \stackrel{a\quad b \quad ~~ c}{6x^{-\frac{5}{4}}y^{-2}} \end{array}}[/tex]

The expression that represents the area of each section is 14z-9

The expression to denote the area of each section would be: 14z -9

Given that,

The expression for the area of plot  area 84z -54

The number of equal sections in which it is divided 6

To find,

The expression for each section = ?

The area of each section = (total area of the garden(/number of equal sections

= (84x-54)/6

= 6(14z-9)/6

=14z - 9

Thus,  is the expression that would represent every section's area.

The inverse of the radical equation x = [√(a + 2) + √(a - 2)] / [√(a + 2) - √(a - 2)] is the equation a = x + 1 / x. (Correct choice: A)

In this problem we find the case of a radical equation in explicit form, that is, a variable x only in terms of a variable a, and we need to obtain the inverse of the function, that is, an expression in terms of a variable x. This problem can be solved by algebra properties.

First, write the original equation:

x = [√(a + 2) + √(a - 2)] / [√(a + 2) - √(a - 2)]

Second, rationalize the expression:

x = [[√(a + 2) + √(a - 2)] · [√(a + 2) + √(a - 2)]] / [[√(a + 2) - √(a - 2)] · [√(a + 2) + √(a - 2)]]

x = [√(a + 2) + √(a - 2)]² / [(a + 2) - (a - 2)]

x = [a + 2 - 2 ·√(a² - 4) + a - 2] / 4

x = [a - √(a² - 4)] / 2

2 · x = a - √(a² - 4)

Third, eliminate the square root operator by algebra properties:

√(a² - 4) = a - 2 · x

a² - 4 = (a - 2 · x)²

Fourth, find the solution to the expression:

a² - 4 = a² - 4 · x · a + 4 · x²

- 4 = - 4 · x · a + 4 · x²

1 = x · a - x²

1 + x² = x · a

a = (1 + x²) / x

a = 1 / x + x

a = x + 1 / x

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Answer: To determine the point where Leila should stop for her break, we need to find the midpoint of the line segment connecting points P and R, since the midpoint will represent equal distances from both points.

Let the distance between points P and R be d, and let's call the point where Leila stops for her break point B.

Since the ratio of the distance travelled to the distance remaining is 3:5, we know that the distance from B to P is 3/8 of the total distance d, and the distance from B to R is 5/8 of the total distance d.

Therefore, point B is the midpoint of line segment PR, and can be found by dividing the distance between P and R by 2.

Step-by-step explanation:

The linear inequality to represent given situation will be 127+18x≥390 where x=no. of weeks and he will take 14.6 weeks to reach his goal.

What is a linear inequality, exactly?

In mathematics, an inequality is a mathematical statement that does not have equal sides. In mathematics, an inequality occurs when a connection results in a non-equal comparison of two expressions or two numbers. In the statement, any of the inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠), can be used to replace the equal sign "=". Inequalities are grouped into three forms in mathematics: polynomial inequalities, rational inequalities, and absolute value inequalities.

The symbols " <and >" represent severe disparities, whereas " ≤ and ≥ " represent slack inequalities. A linear inequality resembles a linear equation, but the formula is different.

Now,

Total miles to run=390 mile

He already ran=127 mile

Distance left to run=390-127

=263 mile

Rate of running=18 miles/ week

weeks taken to complete 263 miles=263/18

=14.6 weeks

and given situation can be represented by inequality 127+18x≥390 where x=no. of weeks.

Hence,

          The linear inequality to represent given situation will be 127+18x≥390 and he will take 14.6 weeks to reach his goal.

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The volume of the solid with a semicircular base of radius 4 whose cross sections perpendicular to the base and parallel to the diameter are squares is 512/3 cubic units

The radius of the base = 4 units

The length of the side of the square = 2x

The area of the square = a^2

Where a is side of the square

The area of the square = (2x)^2

= 4x^2

The equation of the circle is

x^2 + y^2 = 16

x^2 = 16 - y^2

The area = 4(16 - y^2 )

= 64 - 4y^2

The volume of the square

V = [tex]\int\limits^a_b {A(y)} \, dy[/tex]

= [tex]\int\limits^4_0 {64-4y^{2} } \, dy[/tex]

= 64×4 - 4×(4^3/3)

= 256 - 256/3

= 512/3 cubic units

Therefore, the volume of the solid is 512/3 cubic units

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Answer: 35

Step-by-step explanation: 52-13-4

Answer:

Step-by-step explanation:

The meaning of the function notations are

G(Jada) = 4 means that the first name Jada has four letters

C(11-15)= chemistry means that the Monday class for 11-15 is chemistry

How to interpret the function notations?

The meaning of the function G

From the question, we have the following parameters that can be used in our computation:

Function G gives the number of letters in the first name for its output.

Next, we have

G(Jada) = 4

Using the meaning of the function, we have

G(Jada) = 4 means that the first name Jada has four letters

The meaning of the function C

From the question, we have the following parameters that can be used in our computation:

Function C gives a student's Monday class for its output.

Next, we have

C(11-15)= chemistry

Using the meaning of the function, we have

C(11-15)= chemistry means that the Monday class for 11-15 is chemistry

Answer: If the lady sells each brouse for 1500 KSH and makes a profit of 150 KSH for each brouse, then the cost price of the brouse is 1500 KSH - 150 KSH = 1350 KSH.

So, the lady pays 1350 KSH for each brouse.

Step-by-step explanation:

The equation that describes this situation is, 3 + 15n = 153

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

Given that,

Three more than product of 15,

And a number n is 153.

More than = + (addition)

Product = x (multiplication)

Product of 15 and n = 15 x n = 15n

Therefore, the equation is 3 + 15n = 153.

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Answer: B) 56

Step-by-step explanation:

[tex]x:y=7:18[/tex]

[tex]x=49[/tex]

find the value of [tex]y[/tex]

let, [tex]x^2[/tex] [tex]7a[/tex]

and let, [tex]y^2[/tex] [tex]8a[/tex]

A/Q

[tex]x=49[/tex]

[tex]7a=49[/tex], divide both sides by 7 to let the [tex]a[/tex] alone,

[tex]a=7[/tex]

///

[tex]y=8a[/tex], so that we now that [tex]a=7[/tex]

so, [tex]y=8*7[/tex]

[tex]y=56[/tex]

hope you've understanded...

To find the x-intercept of the equation 3x + 5y = 9, we set y = 0 and solve for x.When y = 0, the equation becomes 3x + 5(0) = 9, which simplifies to 3x = 9.Solving for x, we get x = 3.The x-intercept of the equation 3x + 5y = 9 is (3, 0).

What is x-intercept ?

An x-intercept is a point where a graph or a line crosses the x-axis. It is the value of the independent variable (x) when the dependent variable (y) is equal to zero. In other words, it is the point at which a function or equation intersects the x-axis, and its coordinates are of the form (x, 0). To find the x-intercept of a graph or equation, you can set y=0 and solve for x.

To find the x-intercept of the equation 3x + 5y = 9, we need to set y = 0 and solve for x.

So, we have:

3x + 5(0) = 9

3x = 9

x = 3

Therefore, the x-intercept of the equation 3x + 5y = 9 is (3,0), which means the point where the line intersects the x-axis is (3,0).

To verify, we can graph the equation and see that the point (3,0) is indeed on the x-axis.

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Answer: $169.15

Step-by-step explanation: 15 percent of 199 is 29.85, and 199-29.85 is 169.15