Answers
1) We have to solve for x.
We have a right triangle, so we can apply the Pythagorean theorem to relate the side lengths.
As x is the hypotenuse, we can write:
[tex]\begin{gathered} x^2=9^2+15^2 \\ x^2=81+225 \\ x^2=306 \\ x=\sqrt{306} \\ x\approx17.5 \end{gathered}[/tex]Answer: x = 17.5
Related Questions
The figures to the right are similar. Compare the first figure to the second. Give the ratio of the perimetersand the ratio of the areas.
Answers
SOLUTION
Since the rectangles are similar,
The ratio of their perimeter is thus
[tex]\begin{gathered} \frac{P1}{P2}=\frac{l1}{l2} \\ \\ \frac{P1}{P2}=\frac{10}{25} \\ \\ P1\colon P2=\frac{2}{5} \\ \\ P1\colon P2=2\colon5 \end{gathered}[/tex]Ratio of their areas become
[tex]\begin{gathered} \frac{A1}{A2}=\lbrack\frac{l1}{l2}\rbrack^2 \\ \\ \frac{A1}{A2}=\lbrack\frac{10}{25}\rbrack^2 \\ \\ \frac{A1}{A2}=\frac{100}{625} \\ \\ \frac{A1}{A2}=\frac{4}{25} \\ \\ A1\colon A2=4\colon25 \end{gathered}[/tex]If they had 15 oranges,9 peaches and 18 pears to distribute into the baskets.How many baskets can they make with the SAME number of pieces of fruit in each one?? How many pieces of each type of fruit will be in each basket?
Answers
Which of the following is the correct representation of (-5,6) as a linear combination of unit vectors?05i - 6j0 -5i + 6jO 6i - 5j0 -6i + 5j
Answers
The correct combination of vectors is:
[tex]-5i+6j[/tex]This comes from the fact that we need to multiply the x component by i and the y component by j.
answer this |
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90 times by x = 9,000
Answers
The value of x based on the multiplication in 90 × x = 9000 is 100.
What is multiplication?Multiplication simply means the product of numbers given. This is illustrated with the sign given as ×.
In this case, 90 × x = 9000
Multiply 90 by x which equates to 9000
90x = 9000
Divide by 90
90x / 90 = 9000 / 90
x = 100
The value of x is 100.
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I need help with this practice problem.It’s from my trig prep guide. It asks to answer (a) & (b).
Answers
The general binomial theorem can be expressed as:
[tex](a+b)^n=\sum ^n_{k\mathop=0}C^n_k\cdot a^{n-k}\cdot b^k[/tex]Now, for this problem we identify:
[tex]\begin{gathered} a=3x^5 \\ b=-\frac{1}{9}y^3 \\ n=4 \end{gathered}[/tex](a)
Then, using the general form:
[tex](3x^5-\frac{1}{9}y^3)^4=\sum ^4_{k\mathop{=}0}C^4_k\cdot(3x^5)^{4-k}\cdot(-\frac{1}{9}y^3)^k[/tex](b)
The combination operator for this sum:
[tex]\begin{gathered} C^4_0=C^4_4=1 \\ C^4_1=C^4_3=4 \\ C^4_2=6 \end{gathered}[/tex]Then, the simplified terms of the expansion are:
[tex]\begin{gathered} C^4_0\cdot(3x^5)^4\cdot(-\frac{1}{9}y^3)^0=81x^{20} \\ C^4_1\cdot(3x^5)^3\cdot(-\frac{1}{9}y^3)^1=4\cdot(27x^{15})\cdot(-\frac{1}{9}y^3)=-12x^{15}y^3 \\ C^4_2\cdot(3x^5)^2\cdot(-\frac{1}{9}y^3)^2=6\cdot(9x^{10})\cdot(\frac{1}{81}y^6)=\frac{2}{3}x^{10}y^6 \\ C^4_3\cdot(3x^5)^1\cdot(-\frac{1}{9}y^3)^3=4\cdot(3x^5)\cdot(-\frac{1}{729}y^9)=-\frac{4}{243}x^5y^9 \\ C^4_4\cdot(3x^5)^0\cdot(-\frac{1}{9}y^3)^4=\frac{1}{6561}y^{12} \end{gathered}[/tex]Please help!!
Solve for angle FGD
Answers
Answer:
m∠FGD = 132°
Step-by-step explanation:
Corresponding Angles Postulate
When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.
Therefore, as AB is parallel to CD, and line EH intersects them:
⇒ m∠EFB = m∠FGD
Substitute the given expressions for the angles and solve for x:
⇒ (3x - 120)° = (x + 48)°
⇒ 3x - 120 = x + 48
⇒ 3x - 120 - x = x + 48 - x
⇒ 2x - 120 = 48
⇒ 2x - 120 + 120 = 48 + 120
⇒ 2x = 168
⇒ 2x ÷ 2 = 168 ÷ 2
⇒ x = 84
Substitute the found value of x into the expression for m∠FGD:
⇒ m∠FGD = (84 + 48)°
⇒ m∠FGD = 132°
A 6-foot hiker casts a 11-foot shadow, and a nearby tree casts a 34-foot shadow. Find the height of the tree
(round to the nearest tenth).
feet
Answers
Answer: 62.33
The ratio of the real length to the shadow is 6:11. to make the first ratio 34 then I could multiply both sides by 34/6 which would make 34:374/6. When 374 is divided by 6 it equals 62 1/3 which also equals 62.33333... Then I would round it to 62.33.
what is the value of 5(y+3)-3x^2 when x=4 and y=2?
A .–23
B. –10
C. 10
D. 23
Answers
[tex]{ \orange{ \tt{ - 23}}}[/tex]
Step-by-step explanation:
Given:-
x = 4 and y = 2.
Substitute the value of x and y in this below equation.
[tex]{ \red{ \tt{5(y + 3) - {3x}^{2}}}}[/tex]
[tex]{ \red{ \tt{5(2 + 3) - {3(4)}^{2}}}}[/tex]
[tex]{ \red{ \tt{5(5) - 3(16)}}}[/tex]
[tex]{ \red{ \tt{25 - 48}}}[/tex]
[tex] = { \red{ \tt{ - 23}}}[/tex]
Answer:
A: -23
Step-by-step explanation:
The difference between nine times a number and one more than six times the number.
the algebraic expression?
Answers
The required algebraic expression is: 9n - (6n +1)
What is an algebraic expression and how is it formed?
Variables and constants are used to create algebraic expressions using a variety of techniques. It is a mathematical expression made up of terms and includes variables, constants, and algebraic operations like addition, subtraction, etc. When operations like addition, subtraction, multiplication, division, etc. are performed on any variable, the resulting equations are called algebraic expressions. An algebraic expression (or variable expression) is a grouping of terms that have undergone operations like addition, subtraction, multiplication, division, etc.
Let the given number be = n
Therefore, nine times the number = 9n
Also, six times the number = 6n
Again, one more than six times the number = 6n + 1
Given, difference between nine times a number and one more than six times the number.
Using all of the expressions derived above, we curate the algebraic expression as:
Algebraic expression: 9n - (6n +1)
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The x-intercept of 2x – y = 6 is -6.
True
False
Answers
Answer:
False
Step-by-step explanation:
The [tex]x[/tex] intercept is when [tex]y=0[/tex].
Substituting [tex]y=0[/tex], we get [tex]2x=6[/tex], meaning that [tex]x=3[/tex].
So, the [tex]x[/tex] intercept is 3, not -6.
What is the sum of + 5 16 000 ? 9 B 13. 32 o c. 9 16 D. 13 16
Answers
Answer:
The sum of the fractions is;
[tex]\frac{13}{16}[/tex]Explanation:
We want to find the sum of the fraction;
[tex]\frac{1}{8}+\frac{5}{16}+\frac{3}{8}[/tex]The least common multiple is 16;
[tex]\begin{gathered} \frac{1}{8}+\frac{5}{16}+\frac{3}{8} \\ =\frac{2+5+6}{16} \\ =\frac{13}{16} \end{gathered}[/tex]The sum of the fractions is;
[tex]\frac{13}{16}[/tex]2 a+6 divided by 2a²-18
Answers
[tex] \frac{2a + 6}{ 2{a}^{2} - 18} \\ = \frac{2(a + 3)}{2( {a}^{2} - 9)} \\ = \frac{a + 3}{(a + 3)(a - 3)} \\ = \frac{1}{a + 3} [/tex]
ATTACHED IS THE SOLUTION
Given a line with slope of -1 and y-intercept of 8, which of the ordered pairs given below would NOT be on the line?
Answers
We have a line with slope -1 and y-intercept of 8.
We can write the equation of this line as:
[tex]\begin{gathered} y=mx+b \\ y=-x+8 \end{gathered}[/tex]Then, we can test the values for each x-coordinate and see if it matches the y-coordinate indicated by the point:
Point (3,5)
[tex]y(3)=-3+8=5\longrightarrow\text{ is on the line}[/tex]Point (2,10)
[tex]y(2)=-2+8=6\ne10\longrightarrow\text{ is NOT on the line}[/tex]Answer: the point (2,10) is not on the line.
A carpenter spend his 40-hour workweek as follows: 1/4 of his ordering materials; 1/2 of his time doing the wooodwork; and 1/8 of his time talking to customers. The rest of his time devoted to cleanup. What is the approximately percentage of time the carpenter spend doing cleanup?
Answers
The forty hours of the workweek of the carpenter are distributed as follows:
Then, the time that the carpenter spends cleaning up is (what remains from the 40 hours after subtracting the time he spends in the other activities):
[tex]40h-10h-20h-5h=5h\text{.}[/tex]The question now is, what percentage does 5h represent in 40h? We need to use the percentage formula:
[tex]\begin{gathered} 5=\frac{\%}{100}\cdot40.\leftarrow\begin{cases}\%=\text{ Percentage that 5 represents in 40}\end{cases} \\ \\ \end{gathered}[/tex]Solving this equation, we get
[tex]\begin{gathered} 5=\frac{\%}{100}\cdot40, \\ \\ 5=\frac{\%\cdot40}{100}, \\ \\ 100\cdot5=\%\cdot40, \\ \\ 500=\%\cdot40, \\ \\ \frac{500}{40}=\%, \\ \\ \%=\frac{500}{40}, \\ \\ \%=12.5. \end{gathered}[/tex]AnswerThe percentage of time that the carpenter spends cleaning up is 12.5%.
Which equation represents the ordered pairs in the table? Х у 6 2 12 4 18 6
Answers
From the table, we have the following:
[tex]\frac{y}{x}=\frac{2}{6}=\frac{4}{12}=\frac{6}{18}=\frac{1}{3}[/tex]Thus, we have that:
[tex]\frac{y}{x}=\frac{1}{3}\Rightarrow y=\frac{x}{3}\Rightarrow y=\frac{1}{3}x[/tex]We obtain this result if we multiply both sides of the equation by x.
Therefore, the result is:
[tex]y=\frac{1}{3}x[/tex]The answer is the third option.
Select the three equations that pass through the points (–4, –16) and (5, 2):
y + 4 = 2(x – 16)
y – 2 = 2(x – 5)
y = 2x – 8
y + 16 = 2(x + 4)
Answers
The equations of the line are:
y – 2 = 2(x – 5)
y + 16 = 2(x + 4)
y = 2x – 8
How to Find the Equation of a Line that Passes through two Points?The equation of a line, in point-slope form, that passes through two points can be expressed as y - b = m(x - a).
To find the equation, first, we will need to find the slope of the line. Next, we will use a point and the slope to write the equation by simply substitute their values in y - b = m(x - a), where the slope is m and a point is (a, b).
Given the points:
(–4, –16) (5, 2)Find the slope of the line (m):
Slope of the line (m) = change in y / change in x = (-16 - 2)/(-4 - 5)
Slope of the line (m) = -18/-9
Slope of the line (m) = 2
Substitute m = 2 and (a, b) = (5, 2) into y - b = m(x - a):
y - 2 = 2(x - 5)
Or, substitute m = 2 and (a, b) = (-4, -16) into y - b = m(x - a):
y + 16 = 2(x + 4)
Any of the above equations can be rewritten in slope-intercept form as:
y = 2x - 8.
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Looking for help on this problem. Help is appreciated a lot!
/
Answers
[tex]t^3=-\cfrac{27}{343}\implies t^3=-\cfrac{3^3}{7^3}\implies t^3=-\left( \cfrac{3}{7} \right)^3\implies t^3=-\left( \cfrac{3}{7} \right)\left( \cfrac{3}{7} \right)\left( \cfrac{3}{7} \right) \\\\\\ t^3=+\left( -\cfrac{3}{7} \right)\left( -\cfrac{3}{7} \right)\left( -\cfrac{3}{7} \right) \implies t^3=+\left( -\cfrac{3}{7} \right)^3 \\\\\\ t^3=\left( -\cfrac{3}{7} \right)^3\implies t=-\cfrac{3}{7}[/tex]
Question 6 of 14
A researcher creates two random samples, each with a sample size of
10. He
does not find a statistically significant difference between the two groups.
Which of the following statements is correct? Select all that apply.
Answers
Correct option is D. Since sample size is 10, the sample size is not adequate, the conclusion is likely to be untrue.
What is meant by sample size?The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component.
The quantity of completed survey replies is known as the sample size. Because it merely reflects a portion of the target population (or set of people whose ideas or behavior you are interested in), it is known as a sample.
How is the sample size determined?The equation reads Sample Size = N / (1 + N*e2), where N is the population size.
Be aware that this is the least desirable and least precise formula.
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Complete Question -
A researcher creates two random samples, each with a sample size of . He does not find a statistically significant difference between the two groups. Which of the following statements is correct? Select all that apply.
A. Since the sample size is adequate, the conclusion is likely to be true.
B. Since random samples were used, the conclusion is likely to be true.
C. Sample size does not affect the outcome of statistical significance.
D. Since the sample size is not adequate, the conclusion is likely to be untrue.
The weight of 8 eggs is 496 grams. Identify the constant of proportionality of total weight to number of eggs.
Group of answer choices
60
56
62
58
Answers
The constant of proportionality of total weight to number of eggs having the weight of 8 eggs as 496 grams is 62.
How can the constant of proportionality of total weight to number of eggs be determined?The weight of 8 eggs is given as 496 grams
The equation can be written as :
w=n
where n= number of the eggs
we= weight of the eggs
then the equation can be written as
w∝n
Then we can introduce the proportionality constant sign as ;
then w=kn
where k is the proportionality constant
then we can substitute the given figures as ;
496=k *8
then k=496/8 = 62.
Therefore third option is correct.
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eight Row in the table below gives you a number x a number Y and either a third number Z or the average pay of the three numbers that have which of the three numbers is given by a equals x + y + z / 3 fill in the missing numbers
Answers
Given three numbers x, y and z
The average of the numbers = A
[tex]A=\frac{x+y+z}{3}[/tex]We will complete the given table
When : x = 7 , y = 12 , z = 8
[tex]A=\frac{7+12+8}{3}=\frac{27}{3}=9[/tex]When x = 23 , y = 17 , z = 2
[tex]A=\frac{23+17+2}{3}=\frac{42}{3}=14[/tex]For the last case,
x = 4 , y = 11 , A = 6
[tex]6=\frac{4+11+z}{3}[/tex]Solve for z, multiply both sides by 3
[tex]\begin{gathered} 6\cdot3=\frac{4+11+z}{3}\cdot3 \\ 18=4+11+z \\ 18=15+z \\ \\ z=18-15=3 \end{gathered}[/tex]How many employees did it have a title and round your answer to the nearest whole number
Answers
From the given question,
The employees in the one country is, 12900 and it is the 24.2% of the total employee.
So,
Suppose x is the total number of the employees in the company.
Then,
[tex]24.2\text{\% of x=12900}[/tex]then,
[tex]\begin{gathered} 24.2\text{\% of x=12900} \\ x=\frac{12900}{24.2\text{ \%}} \\ x=\frac{12900}{0.242} \\ x=53,306 \end{gathered}[/tex]Hence, the value of total employess is 53,306.
4x-3 x=2 4(2)-3 the blank property is used here
Answers
From the information given above, The substitution property is used here. See further explanation below.
What is substitution property?The substituted property of equality states that one value may be substituted for another in an expression or equation and the result will be the same.
If the values of x and y are equivalent, then x and y may be substituted for one another. The property's opposite is likewise true.
For exmaple,
If x=y for any real integer x and y, then y may be replaced for x in any statement.
In the above instance, x = 2 and hence can be substituted for x in the first expression given as:
4x -3.
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Full Question:
4x-3
x=2
4(2)-3
The _____ property is used here.
Simplify: x + (7 + 14x)Options:15 x + 721 x22 x21 x + 1
Answers
Step 1
Given;
[tex]x+(7+14x)[/tex]Required; To simplify the question.
Step 2
[tex]\begin{gathered} Bring\text{ like terms together} \\ x+14x+7 \\ Simplify \\ 15x+7 \end{gathered}[/tex]Answer;
[tex]15x+7[/tex]On a camping trip, Nina kept a log of the types of snakes she saw. She noted their colors and approximate lengths. Red Bright orange 1 foot long 3 3 2 feet long 3 1 3 feet long 2 2 What is the probability that a randomly selected snake is 3 feet long or bright orange? Simplify any fractions. S
Answers
we make a ratio between the number of the selected snakes and the total of snakes
selected snakes
are 3 feet long or bright orange
4 are 3 feet long and 6 are orange, but 2 oranges are 3feet long too, then we count
The volume of a cube is 64 feet, and hat is the length of the cube?
Answers
So the volume of a cube is given by:
[tex]r^3=64[/tex]Where r is the length of its sides. By finding r we can find the length of the cube:
[tex]\begin{gathered} r^3=64 \\ r=\sqrt[3]{64}=4 \end{gathered}[/tex]So the cube is 4 feet long.
Answer:
B,C,D:)
Step-by-step explanation:
i got 100%
Find the period in degrees of F(x)= –2 sin(4x)
Answers
Answer:
Explanation:
We were given that:
help meeeeeeeeeeeeeeeeeeeeeee
thank you
Answers
The height of the object based on the information is 1963 feet.
How to calculate the height?It should be noted that a function is important to show the relationship between the variables given in the data.
In this case, the function given for the height of the object is given as:
h = 16t² + 1899
where t = time
When the time is 2 seconds, the height will be:
h = 16t² + 1899
h = 16(2)² + 1899
h = 64 + 1899
h = 1963
The height is 1963 feet.
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Answer the question in the picture below please someone help me
Answers
Answer:
here is the Answer The population will be 799,500 people
Step-by-step explanation:
11/12 divided by 4/5
Answers
Given the general rule for the division of fractions:
[tex]\begin{gathered} \frac{a}{b}\frac{\cdot}{\cdot}\frac{c}{d}=\frac{a\cdot d}{b\cdot c} \\ b,d\ne0 \end{gathered}[/tex]in this case, we can use the formula in the following way:
[tex]\frac{11}{12}\frac{\cdot}{\cdot}\frac{4}{5}=\frac{11\cdot5}{12\cdot4}=\frac{55}{48}[/tex]therefore, the answer is 55/48
Sheila is making a model of a stadium using a scale where 3 centimeters equal 20 feet. If the model is 30.5 centimeters wide, what is the actual width of the stadium, in feet?
Answers
Answer:
answer is in the explanation
Step-by-step explanation:
first w have to get from 3cm to 30.5cm
to do that we can multiply by 10 1/6
3*10=30
1*3=3
30 3/6
the scale factor, like I said is 10 1/6.
20*10 1/6=20*10+20*1/6=200+20/6=203 2/6, or 203 1/3, or 203.3333333, or 610/3
