I need help with problem 7.Use the figure to find the values of x, y, and z that makes triangle DEF similar to triangle GHF.
Answers
ANSWER
• x = 12
,• y = 16
,• z = 7
EXPLANATION
Because the triangles are similar, we have that:
• The ratio between corresponding sides is constant:
[tex]\frac{DE}{GH}=\frac{EF}{GF}=\frac{DF}{HF}[/tex]• Corresponding angles are congruent:
[tex]\begin{gathered} \angle D\cong\angle H \\ \angle E\cong\angle G \\ \angle F\cong\angle F \end{gathered}[/tex]We know that the measure of angle E is 16°, so the measure of angle G must be the same because they are congruent,
[tex]16\degree=2(x-4)\degree[/tex]With this equation, we can find x. First, divide both sides by 2,
[tex]\begin{gathered} \frac{16}{2}=\frac{2(x-4)}{2} \\ \\ 8=x-4 \end{gathered}[/tex]And then, add 4 to both sides,
[tex]\begin{gathered} 8+4=x-4+4 \\ \\ 12=x \end{gathered}[/tex]Hence, x = 12.
Now we know that the length of side EF is,
[tex]EF=x-5=12-5=7[/tex]To find y and z, we will use the proportions we got at the top of this explanation,
[tex]\frac{DE}{GH}=\frac{EF}{GF}=\frac{DF}{HF}[/tex]Replace with the known values and the expressions with y and z,
[tex]\frac{25}{6z+8}=\frac{7}{14}=\frac{24}{3y}[/tex]With the first two, we can find z,
[tex]\frac{25}{6z+8}=\frac{7}{14}[/tex]Simplify the right side,
[tex]\frac{25}{6z+8}=\frac{1}{2}[/tex]Rise both sides to the exponent -1 - i.e. flip both sides of the equation,
[tex]\frac{6z+8}{25}=2[/tex]Multiply both sides by 25,
[tex]\begin{gathered} 25\cdot\frac{(6z+8)}{25}=2\cdot25 \\ \\ 6z+8=50 \end{gathered}[/tex]Subtract 8 from both sides,
[tex]\begin{gathered} 6z+8-8=50-8 \\ 6z=42 \end{gathered}[/tex]And divide both sides by 6,
[tex]\begin{gathered} \frac{6z}{6}=\frac{42}{6} \\ \\ z=7 \end{gathered}[/tex]Hence, z = 7.
Finally, with the last two proportions, we can find y,
[tex]\frac{7}{14}=\frac{24}{3y}[/tex]The first two steps are the same we did to find z: simplify the left side and flip both sides,
[tex]2=\frac{3y}{24}[/tex]Multiply both sides by 24,
[tex]\begin{gathered} 24\cdot2=24\cdot\frac{3y}{24} \\ \\ 48=3y \end{gathered}[/tex]And divide both sides by 3,
[tex]\begin{gathered} \frac{48}{3}=\frac{3y}{3} \\ \\ 16=y \end{gathered}[/tex]Hence, y = 16.
Related Questions
I need whit math thats all(x-2) +(x+6)
Answers
To simplify the expression (x-2) +(x+6), you have to follow these steps:
1.Get rid of the parentheses:
(x-2) +(x+6)
x -2 + x + 6
2. Combine like terms:
x + x - 2 + 6
2x + 4
So the answer is 2x + 4
The cost of a Turkish cloth varies jointly as the length and width of the cloth. If the cost is TL3848 for an 8 ft by 13 ft cloth, then what is the cost of a 17 ft by 23 ft cloth?
Answers
The cost of the the 17 feet by 23 feet Turkish cloth given the constant of variation is TL14,467.
What is the cost?A variable varies jointly if the value of one variable depends on the value of two or more variables. In this question, if the length and width of the cloth increases, the cost of the cloth increases. Also, if the length and width of the cloth decreases, the cost of the cloth decreases.
The equation that represents joint variation is:
y = kab
Where:
y = dependent variable = cost of the Turkish cloth k = constant of variation a = dependent variable = length of the cloth b = dependent variable = widthTL3848 = k(13 x 8)
k = TL3848 / (13 x 8)
k = $37
The cost of 17 feet by 23 feet cloth :
37 x 17 x 23 = TL14,467
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the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths
negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
Simplify the expression.
the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths
negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
Which expression is equivalent to 3(−4.5b − 2.1) − (6b + 0.6)?
19.5b + 1.5
−19.5b − 1.5
−19.5b − 6.9
19.5b − 6.9
Answers
A) Simplification of the given Algebraic Expression is; [-⁴³/₂₄j + (-1)]/12
B) The equivalent expression to 3(−4.5b − 2.1) − (6b + 0.6) is - 19.5b - 6.9
How to simplify Algebraic Expressions?A) We want to simplify negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths. This would be expressed as;
-1/8j + 2/3 - (5/3j + 9/12)
= -1/8j + 2/3 - 5/3j - 9/12
= -1/8j - 5/3j + (2/3 - 9/12)
= (-3j-40j / 24 + (8-9) / 12
= [-⁴³/₂₄j + (-1)]/12
B) The expression equivalent to 3(−4.5b − 2.1) − (6b + 0.6)
Expand the brackets to get;
-13.5b - 6.3 - 6b - 0.6
= -13.5b - 6b - 6.3 - 0.6
= - 19.5b - 6.9
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7=1/4ax, solve for a
Answers
The given expression is
[tex]7=\frac{1}{4}ax[/tex]Solving for a means that we need to isolate that variable.
First, we need to multiply the equation by 4
[tex]7\cdot4=4\cdot\frac{1}{4}ax\rightarrow28=ax[/tex]Second, we divide the equation by x
[tex]\frac{28}{x}=\frac{ax}{x}[/tex]Therefore, the answer is
[tex]a=\frac{28}{x}[/tex]Of the 120 families, approximately___pay more than $5710 annually for day car per child.
Answers
1) Considering a Normal Distribution, then we can write out the following:
[tex]P(X>5710)=P(X-\mu>5710-6000)=P(\frac{X-\mu}{\sigma}>\frac{5710-6000}{1000})[/tex]Note that we're dealing with probabilities.
2) Let's find out the Z-score resorting to a table, we get:
[tex]Z=\frac{x-\mu}{\sigma}=\frac{5710-6000}{1000}=-0.29[/tex]2.2) So we can infer from 1 and 2:
[tex]P(X>5710)=P(Z>-0.29)=0.6141[/tex]Notice that this distribution refers to 120 families
SpongeBob spins the spinner to the left. What is the probability that the spinner lands on a number greater than 6?
Answers
SpongeBob spins the spinner to the left. What is the probability that the spinner lands on a number greater than 6?
we know that
The total numbers in the spinner are 10
The numbers that are greater than 6 are (7,8,9 and 10)------> 4 numbers
so
To find out the probability, divide the total numbers that are greater than 6 by the total number
therefore
P=4/10
Percent
P=4/10(100)
the answer is
P=40% o P=4/10 or P=0.414. PR is the diameter of the circle with centre O. If mZPRQ = 65°. What will be the measure of
mZPOQ?
A. 65⁰
B. 90⁰
C. 130⁰
D. 150⁰
Answers
Here PQ chord subtends 65 on the circumference=> it will subtend 130 on the center
Hence answer is (c)
I need help with this question but no one is helping me! Can someone please help me
Answers
Step-by-step explanation:
Chance to roll even number on one dice is 1/2 so
[tex] \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} [/tex]
which of the following is a function. then graph the function.
Answers
A relationship is a function if and only if for each input, there exists only one output i.e an input cannot have two or more outputs.
We can determine which of the relationship is a function by plotting a graph of the relationship.
The only correct option is the relationship:
[tex]y=x^2[/tex]The graph of the function is shown below:
Could you please set it up in the form of "systems of equations" meaning, set to different equations with "x" and "y" ??
That is what they want me to do in class.
Answers
There are various types of equation systems, including linear, non-linear, and multiple or single-variable systems.
Explain the System of equations?A set of two linear equations with two variables is a system of linear equations.
ax + by = C
A set of two or more equations in two or more variables that includes at least one nonlinear equation is referred to as a system of nonlinear equations. A nonlinear equation can be written as ax+by+C≠0 or ax + b y + C ≠0.
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution.
Ex: ax+b = 0
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i need helpppp plsssssss
Answers
At the local food stand, the vendor sells small drinks for $1.25 each and large drinks for $2.50 each. They sold 155 drinks today and made $265. How many small drinks and how many large drinks did they sell?
Answers
Answer:
98 small drinks and 57 large drinks.
Explanation:
Let's call x the number of small drinks and y the number of large drinks.
If they sold 155 drinks, we can write the following equation:
x + y = 155
In the same way, they made $265, so
1.25x + 2.50y = 265
Because each small drink cost $1.25 and each large drink cost $2.50.
Now, we can have the following system of equations
x + y = 155
1.25x + 2.50y = 265
Solving the firs equation for y, we get:
x + y - x = 155 - x
y = 155 - x
Replacing this on the second equation:
1.25x + 2.50y = 265
1.25x + 2.50(155 - x) = 265
Then, solving for x, we ge:
1.25x + 2.50(155) - 2.50(x) = 265
1.25x + 387.5 - 2.50x = 265
-1.25x + 387.5 = 265
-1.25x + 387.5 - 387.5 = 265 - 387.5
-1.25x = -122.5
-1.25x/(-1.25) = -122.5/(-1.25)
x = 98
Finally, we can find the value of y replacing x = 98
y = 155 - x
y = 155 - 98
y = 57
Therefore, they sell 98 small drinks and 57 large drinks.
Suppose that IQ scores have a bell-shaped distribution with a mean of 101 and a standard deviation of 14. Using the empirical rule, what percentage of IQ scores are at least 73? Please do not round your answer.
Answers
Answer:
Explanation:
From the information given,
mean = 101
standard deviations = 14
We need to find the number of standard deviations between 73 and the mean.
Number of standard deviations = (73 - 101)/14 = - 28/14 = - 2
It is 2 standard deviations from the mean. According to the empirical rule, 95% of the population lies between 2 standard deviations of the mean. The required area is to the right of 2 standard deviations since we want to find the least score. Thus, the probability of having IQ scores are at least 73 is
We would convert to percentage by multiplying by 100
5/8p−3/4=4
A) p=95/32
B) p=26/5
C) p=38/5
Answers
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p-\frac{3}{4}=4 } \end{gathered}$}}[/tex]
Add 3/4 to both sides.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=4+\frac{3}{4} } \end{gathered}$}}[/tex]
Convert 4 to the fraction 16/4.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{16}{4} +\frac{3}{4} } \end{gathered}$}}[/tex]
Since 16/4 and 3/4 have the same denominator, add their numerators to add them together.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{16+3}{4} \longmapsto \ \ Add } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{19}{4} } \end{gathered}$}}[/tex]
Multiply both sides by 8/5, the reciprocal of 5/8.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{19}{4}\times\left(\frac{5}{8}\right) } \end{gathered}$} }[/tex]
Multiply 19/4 by 8/5 (to do this, multiply the numerator by the numerator and the denominator by the denominator).
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{19\times8}{4\times5 }\longmapsto \ Multiply } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{152}{20} } \end{gathered}$}}[/tex]
We reduce the fraction 152/20 to its minimum expression by extracting and canceling 4.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{152}{20} \ \ \longmapsto \ p=\frac{152\div4}{20\div4}=\frac{38}{5} } \end{gathered}$}}[/tex]
Therefore, the answer is option C.5/8 p= 19/4
P= 19/4 / 5/8
P= 19/4 x 8/5
P= 38/5
The answer is C
A diagram of the side of Robert's barn is shown. If he decides to paint one side of the barn, how many square feet will Robert paint?
1. 254.5 ft^2
2. 310.5 ft^2
3. 391 ft^2
4. 805 ft^2
Answers
Robert will paint 310.5 square ft
The side of Robert's barn contains a triangle and a rectangle of which the dimensions are given in the diagram.
If Robert paint one side of the barn, then he needs to paint the triangle as well as the rectangle. So we need to find the area of the triangle and rectangle first.
For the triangle, base = 23 ft
height = 7 ft
Area of the triangle = 1/2 bh
= 1/2 x 7 x 23
= 80.5 square ft.
For the rectangle, length = 23 ft
width = 10 ft
Area of the rectangle = length x width
= 23 x 10
= 230 square ft.
Area Robert needs to paint = Area of the triangle + Area of the rectangel
= 80.5 + 230
= 310.5 square ft.
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I need help with this question I not sure but my answer was number 3 i for sure
Answers
To solve this problem, we have to compute the circumference of a circle of diameter:
[tex]d=840ft.[/tex]Recall that the circumference of a circle is given by the following formula:
[tex]C=d\pi,[/tex]where d is the diameter.
Therefore, the circumference of the reservoir is:
[tex]C=\frac{22}{7}*840ft=2640ft.[/tex]Answer:[tex]2640ft.[/tex]the graph shows the mass of the bucket containing liquid depends on the volume of liquid in the bucket. Use the graph to find the domain of the function.
Answers
The domain of the function for the volume of the liquid = 0 ≤ V ≤ 7.5 liters.
What is domain of a function?The domain of a function is the complete set of possible values of the independent variable.
Also a domain of a function refers to "all the values" that go into a function.
From the graph the domain of the function of the volume of the of liquid in the bucket is calculated as follows;
The minimum value of the volume of liquid in the bucket = 0
The maximum value of the volume of liquid in the bucket = 7.5 liters
The domain of the function for the volume (V) of the liquid = {0, 1, 2, 3, 4, 5, 6, 7.5 liters}
0 ≤ V ≤ 7.5 liters
Thus, the domain of the function or independent variables that satisfies the function include natural numbers between 0 to 7.5 liters. That is the domain of the function is {0, 1, 2, 3, 4, 5, 6, 7.5 liters}.
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What is the sum of the first five terms in this series? 6 - 6/3+6/9-6/27+•••
A 61/81
B 16
C 122/27
D 20/3
Answers
The sum of the first five terms in this series is 4 14/27.
What are fractions?Fractions are used to depict the components of a whole or group of items. Two components make up a fraction. The numerator is the number that appears at the top of the line. It specifies how many identically sized pieces of the entire event or collection were collected. The denominator is the quantity listed below the line. The total number of identical objects in a collection or the total number of equal sections that the whole is divided into are both displayed. A fraction can be expressed in one of three different ways: as a fraction, a percentage, or a decimal. The first and most popular way to express a fraction is in the form of the letter ab. Here, a and b are referred to as the numerator and denominator, respectively.
The first five terms
6
-6/3
6/9
-6/27
+6/81
The first thing to do is change all the fractions denominators to 81.
Sum = 6*81/81 - 6(27)/81 + 6 × 9/81 - 6 × 3/81 + 6/81
Now add
Sum = 366/81
Sum = 4 14/27
Sum = 4.5185
Recall the first term. It was increased by 6 × 81/81. Nothing is affected by the 81 over 81 in terms of value. 6 × 81/81 remains 6. It merely makes combining it with the other members of the series simpler.
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mario's school is also planning a smaller rectangular are as a sitting spot. A scale drawing of the sitting sot is shown. redraw the sitting spot on the grid at a scale of i grid unit/4 feet.
write and simplify the ratio of the new scale
Answers
The ratio of the new scale that we are to be having is going to be 1/2
How to simplify the new scale of the gridwe have the ratio to be 1 grid unit / 2 ft
the new scale ratio is given as 1 grid unit / 4 ft
We have to divide the ratio of the original scale to the new scale that we have here
This would be ( 1 grid unit / 4 ft ) / ( 1 grid unit / 2 ft)
This can be written as
1/4 * 2/1
when we rewrite it we would have 2/4
= 1/2
This is 1 unit 2 feet
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4. Describe the transformation from the parent graph of y - 4 = – 2(x – 3)?. Graphboth the parent graph and the transformed graph on the grid provided. Plot at leastthree distinct points for each.
Answers
Describe the transformation from the parent graph of y - 4 = – 2(x – 3)^2. Graph
both the parent graph and the transformed graph on the grid provided. Plot at least
three distinct points for each.
we have that
the parent function is
y=x^2
Is a vertical parabola open upward with the vertex at (0,0)
the transformed function
is
y-4=-2(x-3)^2
y=-2(x-3)^2+4
Is a vertical parabola open downward with vertex at (3,4)
so
The transformations are
1) Reflection over x-axis
Rule is
(x,y) ------> (x,-y)
y=x^2 ------------------> y=-x^2
2) Vertical Dilation with a scale factor of 2
Rule
(x,y) --------> (x,2y)
y=-x^2 ----------> y=-2x^2
3) Translation 3 units at right and 4 units up
Rule is
(x,y) --------> (x+3,y+4)
y=-2x^2 --------> y=-2(x-3)^2+4
see the graph to better understand the problem
I need help on this question please?
Answers
parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone.
What is a parabola in math?
Drawing a parabola for the quadratic function f(x) = ax2 + bx + c results in a U-shaped curve.When an is smaller than zero, the parabola's graph is downward (or opens downward).When the value of an is greater than 0, the parabola's graph ascends (or opens up). The locus of points in that plane that are equally spaced apart from the direct x and the focus is known as the parabola.A right circular conical surface and a plane parallel to another plane that is tangential to the conical surface intersect to form a parabola, which is also known as a conic section.A parabola's general equation is written as y = a(x - h)2 + k or x = a(y - k)2 + h.Vertex here is indicated by (h, k).The typical form is y = a(x - h)2 + k.-9(x_6)²_1
= -9(x-6)1
=-9x+54
Differentiate x
-9
-9(x-6)²
Subtract
d/dx(-9(x-6)
Calculate x-6
d/dx (-9x+54)
-9x1-1
-9x
=-9
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Solve this system of equations usingthe substitution method.y = x + 9y = -4x – 612] [UN
Answers
The given system of equations is
[tex]\begin{gathered} y=x+9\rightarrow(1) \\ y=-4x-6\rightarrow(2) \end{gathered}[/tex]We will substitute y in equation (2) by equation (1)
[tex]x+9=-4x-6[/tex]Now, add 4x to both sides
[tex]\begin{gathered} x+4x+9=-4x+4x-6 \\ 5x+9=-6 \end{gathered}[/tex]Subtract 9 from both sides
[tex]\begin{gathered} 5x+9-9=-6-9 \\ 5x=-15 \end{gathered}[/tex]Divide both sides by 5
[tex]\begin{gathered} \frac{5x}{5}=\frac{-15}{5} \\ x=-3 \end{gathered}[/tex]Substitute x by -3 in equation (1) to find y
[tex]\begin{gathered} y=-3+9 \\ y=6 \end{gathered}[/tex]The solution of the system is (-3, 6)
a girl (who liked riddles) was asked how old she was, she responded "in 2 years I will be twice as old as I was 5 years ago". how old is she now?
Answers
Given data:
The expression for the age of the girl after two year is,
x+2
The age of girl 5 year ago is,
x-5
According to the given statement of the question.
x+2=2(x-5)
x+2=2x-10
x=12
Thus, the present age of the girls is 12 years old.
calculate the area of this trapiziuem
Answers
Answer:
............where is it?
Identify the vertex: y = (x+10)2+ 2 a. (10,2) b. (-10, -2) c. (-10,2) ) d. (10, -2)
Answers
Given a quadratic equation in vertex form
[tex]y=a(x-h)^2+k[/tex][tex]\begin{gathered} \text{ wh}ere\text{ a, h, and k are constants, } \\ \text{then the point (h, k) is the vertex of the function} \end{gathered}[/tex]In our case,
[tex]y=(x+10)^2+2[/tex]h = -10, and k= 2
Therefore the vertex is (-10, 2)
Solve for r.
r - 15 / -1 = -4
Answers
Answer:
r=19
Step-by-step explanation:
15-r=-4
r=19
:]
What is the distance from Point B (-1, 11) to line y = -1/3x - 6?
Answer in simplest radical form
Answers
The distance from Point B (-1, 11) to line y = (-1 ÷ 3x) - 6 is 15.811.
The distance from the point B(-1 , 11) to the line y= (-1 ÷ 3x) - 6 is given by the distance formula d = (|Ax1 + By1 + C|) ÷ (√(A² + B²)).
Comparing the equation y= (-1 ÷ 3x) - 6 with the standard forms Ax + By+ C = 0.
It is clear that the coefficient of x, A = -1 ÷ 3.
The coefficient of y, B = -1. The constant C = -6 and the points x1 = -1 and y1 = 11.
Substituting these data in the equation the distance d = (|(-1÷3)×(-1)+ (-1)×11 + (-6)|) ÷ √((-1 ÷ 3)² + (-1)² ) solving the equation the distance d becomes,
d = 15.811.
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Rewrite the polynomial .22 – 52 + 6 as 2? + m2 + n2 +6, where m. n = 6 and m +n=-5. What are the values of m and n?
Answers
Answer:
m = -2 and n = -3
Explanation
Given the polynomial
x^2 - 5x + 6
Rewrite as x^2 +mx + nx + 6
x^2 - 2x - 3x + 6
Compare
mx = -2x
m = -2
Similarly;
nx = -3x
n = -3
Hence m = -2 and n = -3
Rewrite the expression (17x3 – 12x2 + 6x - 4)/(x – 1) in the form q(x) + r(x)/b(x) where q(x) = quotient, r(x) = remainder, and b(x) = divisor, using the synthetic division method.
Answers
Given that
The equation is
[tex]\frac{17x^3-12x^2+6x-4}{x-1}[/tex]and we have to convert it into the form of
[tex]\begin{gathered} q(x)+\frac{r(x)}{b(x)} \\ where\text{ q\lparen x\rparen is quotient, r\lparen x\rparen is remainder, and b\lparen x\rparen is divisor.} \end{gathered}[/tex]a box is filled with 3 red cards, 6 Blue cards, and 6 green cards. A card is chosen at random from the box. what is the probability that it is a red or a green card? write your answer as a fraction in simplest form
Answers
Probability of red or green card = 3/5
Explanation:Number of red cards = 3
Number of blue cards = 6
Number of green cards = 6
Total number of cards = 6 + 6 + 3 = 15
Probability of red or green card = Probability of red card + Probability of green card
Probability of red card = number of red cards/total number of cards
Probability of red card = 3/15
Probability of green card = number of green cards/total number of cards
Probability of green card = 6/15
Probability of red or green card = 3/15 + 6/15
Probability of red or green card = 9/15
In simplest term:
Probability of red or green card = 3/5
Answer:
85% but in a fraction 17/20
Step-by-step explanation: