We need to check each of the options to determine which equation is true
x = -2
equation1: 2.4x + 2.6 = 17
2.4(-2) + 2.6 = 17
-4.8 + 2.6 = 17
-2.2 = 17
equation2: 16 = -8(-6 - 2x)
16 = -8(-6 -2(-2))
16 = -8(-6+4)
16 = -8(-2)
16 = 16
equation 3: 3
Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree. a. 87 ft b. 74 ft c. 65 ft d. 63 ft
Given the information on the picture, we have the following right triangle:
we can use the tangent trigonometric function to find the height of the tree:
[tex]\begin{gathered} tan(44)=\frac{\text{opposite side}}{adjacent\text{ side}}=\frac{h}{90} \\ \Rightarrow\tan (44)=\frac{h}{90} \end{gathered}[/tex]solving for h, we get:
[tex]\begin{gathered} \frac{h}{90}=\tan (44) \\ \Rightarrow h=90\cdot\tan (44)=86.9\approx87 \\ h=87ft \end{gathered}[/tex]therefore, the height of the tree is 87 ft
Solve the system using the elimination method. State your final answer as an ordered pair. DO NOT include any spaces in your answers.
Given:-
let
5x-4y=1 be the equation 1
-5x-10y=-15 be the equation 2
step 1-
add equation 1 and 2
we get=
-14y=-14
y=1
this is required value of y
we are going to put this value of y in equation 1
we get
5x-4(1)=1
5x-4=1
5x=1+4
5x=5
x=1
this is required value of x
hence value of x and y are(1,1)
pets : | bird | cat | dog | snake |frequency: | 3 | 5 | 11 | 1 |which of the following statments does NOT reflect the distribution of the data?a. one-fourth of the pets are catsb. snakes represent 10% of the pets on the farmc. the number of biirds and snakes on the farm make up 20% d. more than half of the pets on the farm are dogs
SOLUTION:
Case: Interpreting from tables
The total number of pets is 20
Checking the options
Option A.
One-fourth of the pets are cats
[tex]\frac{1}{4}\times20=5\text{ }pets[/tex]This is TRUE from the table
Option B
Snakes represent 10% of the pets on the farm
[tex]\begin{gathered} 10\%\times20 \\ \frac{10}{100}\times20=2\text{ }pets \end{gathered}[/tex]This is FALSE from tables as there is only 1 snake
Option C
The number of biirds and snakes on the farm make up 20%
[tex]\begin{gathered} 20\%\times20 \\ \frac{20}{100}\times20=4\text{ }pets \end{gathered}[/tex]This is TRUE from the table
Option D
More than half of the pets on the farm are dogs
[tex]\frac{1}{2}\times20=10\text{ }pets[/tex]This is TRUE from the table
Suppose the mean income of firms in the industry for a year is 95 million dollars with a standard deviation of 17 million dollars. If incomes for the industry are distributed normally, what is the probability that a randomly selected firm will earn less than 112 million dollars? Round your answer to four decimal places.
0.8413 is the probability that a random selected firm will earn less than 112 million dollar
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.
Let X be a random variable represents the income of the firm in the industry
Hence
X~ N (mean =u= 95 , standard deviation= d = 17 )
We must determine the likelihood that a randomly chosen company will make fewer than 112 million dollars in earnings ie.
P(X<112) = P(X-u/d < 112-95/17)
Z=X-u/d = 112 - 95/17 = 1
P(X<112) = P(Z-1)=0.8413
Using the standard normal probability table.
P(X<112) = 0.8413
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A linear function has a slope of 11. Interpret this slope with a complete sentence using the words“inputs” and “outputs”. (1 point)As the inputs________,_______
Answer
the inputs increase by 1 and the outputs increase by 11
Step-by-step explanation:
The standard form of a linear function is written as
y = mx + c
where m = slope
Since the slope is 11
y = 11x + c
This implies that the inputs increase by 1 and the outputs increase by 11
Find the slope of the line that passes through (4,2) and (2,1) which set up in the formula is correct? Select all that apply.
The formula for calculating the slope of a line passing through the points (x1, y1) and (x2, y2) is expressed as:
[tex]slope=\frac{y_2-y_1}{x_2-x_1}\text{ }or\text{ }\frac{y_1-y_2}{x_1-x_2}[/tex]Given the coordinate points (4,2) and (2,1), the possible set up formulas are:
[tex]\begin{gathered} x_1=4 \\ y_1=2 \\ x_2=2 \\ y_2=1 \end{gathered}[/tex][tex]\begin{gathered} slope=\frac{1-2}{2-4} \\ slope=\frac{2-1}{4-2} \end{gathered}[/tex]This are the slopes of the line formula
PLEASE HELP!!
Write an equation of a quadratic function with the given properties: f(3)=f(-5)=0; f(-6)=-36
The equation for a quadratic function with given properties is, f(x) = -201.5 (x² +2x - 15)
Given,
f(3) = f(-5) = 0;
f(-6) = -36
Here,
The x intercepts of the quadratic equation are;
x₁ = 3 , x₂ = -5
The quadratic equation in factored form is equal to
f(x) = a(x - x₁) (x - x₂)
Substitute x₁ = 3 , x₂ = -5 in f(x)
Then,
f(x) = a(x - 3) (x - -5)
f(x) = a(x - 3) (x + 5)
We have;
f(-6) = -36
That is, if x = -6 then f(x) = -36
So,
f(x) = a(x - 3) (x + 5)
-6 = a(-36 - 3) (-36 + 5)
-6 = a x - 39 x - 31
-6 = 1029a
a = -1029/6
a = -201.5
Here,
f(x) = -201.5(x - 3) (x + 5)
Apply distributive property;
f(x) = -201.5(x² +5x - 3x - 15)
f(x) = -201.5 (x² +2x - 15)
That is,
The equation for a quadratic function with given properties is, f(x) = -201.5 (x² +2x - 15)
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I need help with the question I post as a photo.
We will have the following:
*First:
[tex]3x+\frac{1}{4}-x+1\frac{1}{2}=2x+\frac{1}{4}+\frac{3}{2}[/tex][tex]=2x+\frac{7}{4}=2x+1\frac{3}{4}[/tex]So, the first one is not equivalent to the other expression.
*Second:
[tex]2(3x+1)=6x+2[/tex]So, the second one is equivalent to the other expression.
*Third:
[tex]3(x+1)-(1+x)=3x+3-1-x[/tex][tex]=2x+2[/tex]So, the third one is not equivalent to the other expression.
*Fourth:
[tex]4(x+1)-x-4=4x+4-x-4[/tex][tex]=3x[/tex]So, the fourth one is equivalente to the other expression.
*Fifth:
[tex]5.5+2.1x+3.8x-4.1=5.9x+1.4[/tex]So, the fifth one is equivalent to the other expression.
0 Rick has been losing weight at a constant rate since he began his new fitness plan. The table below shows Rick's weight for the first four weeks, 2 3 I 220.2 218.6 221.8 223.4 Weight (lbs) a) Write an equation to represent this sequence. b) Find Rick's weight after 16 weeks. ter your answer(s) here
To make the equation lets us find the rate of change of the weight
The form of the equation is y = m x + b
where:
m is the rate of change (slope)
b is the y-intercept (value y when x = 0)
To find m use two-point from the table
(1, 223.4) , (2, 221.8)
[tex]m=\frac{221.8-223.4}{2-1}=-\frac{8}{5}=-1.6[/tex]Substitute it in the form of the equation
[tex]y=-1.6x+b[/tex]To find b use any point in the table
(1, 223.4)
x = 1 , y = 223.4
[tex]\begin{gathered} 223.4=-1.6(1)+b \\ 223.4=-1.6+b \end{gathered}[/tex]Add 1.6 for both sides to find b
[tex]\begin{gathered} 223.4+1.6=-1.6+1.6+b \\ 225=b \end{gathered}[/tex]Substitute value b in the equation
[tex]y=-1.6x+225[/tex]The equation of the sequence is y = -1.6 x + 225
to find his weight after 16 weeks substitute x by 16
[tex]\begin{gathered} y=-1.6(16)+225 \\ y=-25.6+225 \\ y=199.4 \end{gathered}[/tex]His weight after 16 weeks is 199.4 Ibs
Match each expression on the left with its sum on the right. Some answer options on the right will not be used.
To match the expression with the sum, what you have to do is solve each sum.
Remember that to sum/subtract two fractions, both of them should be expressed using the same denominator,
1)
[tex]-\frac{2}{3}+\frac{5}{6}[/tex]The denominators of these fractions are "3" and "6", the least common denominator between both values is 6. To express the first fraction as its equivalent with denominator 6, you have to multiply it by 2:
[tex]-\frac{2\cdot2}{3\cdot2}+\frac{5}{6}=-\frac{4}{6}+\frac{5}{6}[/tex]Now you can proceed to add both fractions:
[tex]-\frac{4}{6}+\frac{5}{6}=\frac{-4+5}{6}=\frac{1}{6}[/tex]The result for this sum is 1/6
2)
[tex]\frac{7}{12}+(-\frac{3}{4})[/tex]First, simplify both symbols, when a plus symbol and a minus symbol and next to each other, the plus sign gets canceled:
[tex]\frac{7}{12}+(-\frac{3}{4})=\frac{7}{12}-\frac{3}{4}[/tex]To subtract both fractions the first step is to express them using the same denominator. The least common denominator between 12 and 4 is 12, to express -3/4 as its equivalent with denominator 12, you have to multiply the fraction by 3:
[tex]\frac{7}{12}-\frac{3\cdot3}{4\cdot3}=\frac{7}{12}-\frac{9}{12}[/tex]Next, subtract both fractions:
[tex]\frac{7}{12}-\frac{9}{12}=\frac{7-9}{12}=-\frac{2}{12}[/tex]The result is no in its simplest form, 2 and 12 are divisible by 2, so to simplify the fraction you have to divide the numerator and denominator by 2:
[tex]-\frac{2\div2}{12\div2}=-\frac{1}{6}[/tex]The result for this expression is -1/6
3)
[tex]-\frac{1}{4}+\frac{3}{8}[/tex]Same as before, the first step is to express both fractions with the same denominator. the least common denominator for both fractions is 8. To express -1/4 as its equivalent with denominator 8, you have to multiply the fraction by 2
[tex]-\frac{1\cdot2}{4\cdot2}+\frac{3}{8}=-\frac{2}{8}+\frac{3}{8}[/tex]Next, add both fractions:
[tex]-\frac{2}{8}+\frac{3}{8}=\frac{-2+3}{8}=\frac{1}{8}[/tex]The result for this sum is 1/8
So the corresponding matches are:
[tex]\begin{gathered} 1)-\frac{2}{3}+\frac{5}{6}=\frac{1}{6} \\ 2)\frac{7}{12}+(-\frac{3}{4})=-\frac{1}{6} \\ 3)-\frac{1}{4}+\frac{3}{8}=\frac{1}{8} \end{gathered}[/tex]numbers in order from greatest to least 1/5 0.12 0.17
1/5 = 0.2
the order is:
1/5
0.17
0.12
Solve 5x² + 25 = 0Ox= -5x = -5 and x = 5Ox=5No Real Solutions
Solve for x:
Subtract 25 from both sides:
[tex]\begin{gathered} 5x^2+25-25=-25 \\ 5x^2=-25 \end{gathered}[/tex]Divide both sides by 5:
[tex]\begin{gathered} \frac{5x^2}{5}=-\frac{25}{5} \\ x^2=-5 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} x=\pm\sqrt{-5} \\ x=\pm\sqrt{5}i \end{gathered}[/tex]Therefore, there are no real solutions
Answer:
No Real Solutions
what is 40+56 in GCF
The GCF stands for greatest common factor. To represent a sum by its GCF we need to use the distributive property and we need to first find the GCF of the numbers. Let's break each number by its factors:
[tex]\begin{gathered} 40=2\cdot2\cdot2\cdot5 \\ 56=2\cdot2\cdot2\cdot7 \end{gathered}[/tex]We now multiply the numbers that appear on both.
[tex]\text{GCF}=2\cdot2\cdot2=8[/tex]We now apply the distributive property:
[tex]8\cdot(5+7)[/tex]Which is 56,900,000 in scientific notation?o 5.69 x 10⁷o 56.9 x 10⁷o 5.69 X 10⁶o 56.9 X 10⁶
Answer:
5.69 x 10⁷
Explanation:
A number is said to be in the scientific notation when it is written as a product of a number between 1 and 10 and a power of 10.
The number 56,900,000 in scientific notation is 5.69 x 10⁷.
The correct choice is A.
f(x) = -5x -4 and g(x) = x^2 + 3 find (g+f)(x)
f(x) = -5x -4
g(x) = x^2+3
To find (g+f)(x) , simply add both equations:
(g+f)(x)= x^2+3 + (-5x -4 )
(g+f)(x)= x^2+3 -5x -4
Combine like terms
(g+f)(x)= x^2-5x+3-4
(g+f)(x)= x^2-5x-1
-Exponential and Logarithmic Functions- Solve the following, round the answer to the nearest hundredth.
Answer:
x = 1.70
Explanation:
We were given that:
[tex]\begin{gathered} 5^x=15.4 \\ \text{Take the natural logarithm of both sides, we have:} \\ \ln 5^x=\ln 15.4 \\ x\cdot\ln 5=\ln 15.4 \\ \text{Divide both sides by ''ln5'', we have:} \\ x=\frac{\ln 15.4}{\ln 5}=1.699 \\ x=1.699\approx1.70 \\ x=1.70 \\ \\ \therefore x=1.70 \end{gathered}[/tex]Therefore, x = 1.70
Which choice is equivalent to the expression below?V-81A. 91B. AiC.D. -29E. -9SUBMIT
Given the expression:
[tex]\sqrt[]{-81}[/tex]As we know, there is no square root for the negative numbers
But, using the complex numbers:
[tex]i=\sqrt[]{-1}[/tex]So, the given expression can be written as:
[tex]\sqrt[]{-81}=\sqrt[]{-1}\cdot\sqrt[]{81}=i\cdot9=9i[/tex]So, the answer will be option A) 9i
how many 3×3 cm squares would fit in a 4×6 inch rectangle
Answer:2
Step-by-step explanation:
6 divided by 2 would be 3, which is the length size of the square. The height does not allow to stack, which means you can fit two squares.
Gina left home, riding her bicycle at a rate of 25 miles per hour. Sean left 1 hour later, riding at a rate of 30 miles per hour. How long will it take Sean to catch up to Gina?
As per the distance formula, it take 1 hour of time for Sean to catch up to Gina.
Distance formula:
The equation that relates the distance, rate, and time is
d = rt
Where d represents the distance traveled, r represents the rate, and t represents the time.
Given,
Gina left home, riding her bicycle at a rate of 25 miles per hour. Sean left 1 hour later, riding at a rate of 30 miles per hour.
Here we need to find the time take by Sean to catch up Gina.
Let us consider x be the time when Gina left the home.
Then, Sean left 1 hour later from her time.
So, it can be written as,
=> x + 1
As the Distance traveled is the same, the ratio of Speed in case 1 to the Speed in case 2 will be the inverse of the Time taken in both cases.
Therefore, the ratio of Speed in both cases
=> 25 : 30
=> 25/30
=> 5/6
Therefore, it can be written as,
x/x+1 = 5/6
When we cross multiply them, then we get,
5x + 5 = 6x
x = 5.
If Gina left at the time of 5, then Sean left at the time of 6.
So, it take 1 hour for Sean to catch up to Gina.
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Which graph represents 2x + 3y < 6?Choose 1 answer:
Given: An inequality
[tex]2x+3y<6[/tex]Required: To determine the graph of the inequality.
Explanation: The inequality represent an area either inside or outside a line determined by repl
Mari pushed a cube- shaped box to explore force. She examined the attributes of the box. Does a face of her box have a right angle? Explain
The face of a cuboid box have 4 right angles.
What is mean by Cuboid?
A cuboid is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six rectangular faces with eight vertices and twelve edges is called cuboid.
Given that;
Mari pushed a cube- shaped box to explore force.
And, She examined the attributes of the box.
Now,
In the cube shape, faces are all squares.
And, A square is a quadrilateral in which all angles are 90 degree.
Thus, The face of a cuboid box have 4 right angles.
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A park meadow is planted with wildflowers. The Parks Department plans to extend the length of the rectangular meadow by x meters. Which expressions represent the total area, in square meters, after the meadow's length is increased? Select all that apply. 15. A 310 + x B 15.5(20x) C 20x + 15.5 D 15.5x + 310 E 15.5(20 + x) F 35.5 + x Ilse the distributi
We have the following:
The area would be the length by the width, but since x amount was added to the length, it would be like this
[tex]\begin{gathered} A=w\cdot l \\ w=15.5 \\ l=20+x \end{gathered}[/tex]replacing
[tex]A=15.5\cdot(20+x)=310+15.5x[/tex]Therefore, the answer is E and D
Alberto is saving money to buy a pair of shoes that cost $50 he has already saved $32 he still needs to save D dollars explain how to solve your equation to find how much money Alberto needs to save how much more does he need to save
This is the formula that represents how much money needs Alberto to buy a pair of shoes.
To solve this equation, first, subtract 32 to both sides of the equation:
[tex]32\text{ - 32 + x = 50 - 32}[/tex][tex]x\text{ = 50 - 32}[/tex][tex]x\text{ = 18}[/tex]Thus, he still needs to save $18 to buy the shoes.
simplify the rational expression. 18x3y5 45x5y9
Multiplying and Dividing Integers 10-16 Name: 1. As a cold front passed through Temple, the temperature changed steadily over 6 hours. Altogether it change -18 degrees. What was the change in temperature each hour for the 6 hours? a.-18 - 6 = -3 degrees b. 18 - 6 = 3 degrees c. 18 + 6 = 24 degrees d. 18 - 6 = 12 degrees 2. Q. Four college roommates rented an apartment together. When they moved out, they were charged $1500 for damages to the carpet and walls. The roommates agreed to equally share the cost. What integer represents how much each person will have to pay?
Given the total change in temperature in 6 hours, it is necessary to divide it by the number of hours
[tex]-\frac{18}{6}=-3[/tex]The change in temperature each hour is -3 degrees
231231312312312312311
Answer: 3456765432345
Step-by-step explanation:
2345676543456
describe and state a situation where you can apply the concepts of point, line, and plane in real-life situation
Point
A point is an exact position or location on a plane surface.
Real life situation: The end of a knife used for cutting meat in preparation for a meal.
Description: The end of knife is a point whose location is precise. It has ability to pass through surfaces easily due to this fact.
Line
A line is a one-dimensional figure, which has length but no width.
Real-life situation : The edge of a wall or rectangular table.
Description: The edge of a table represent a distance from one end to another end.
Plane:
A plane is a flat, two-dimensional surface that extends indefinitely.
Real-life situation: The surface of the floor or table.
Description: The surface of a floor is such that it can accommodate things on it showing that it is 2-dimensional.
Explain if the triangles are similar using SAS-. If they are similar, which angles are congruent and how do you know? (Explain your reasoning using evidence like a paragraph proof NOT a rigid motion proof!)
We have two triangles GBL and XYL.
From the picture we notice that the GL=39 and BL=34. We also notice that XL=30 and YL=27.
The SAS theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.
This means that we need that:
[tex]\frac{GL}{XL}=\frac{BL}{YL}[/tex]and that the angle between them is the same.
It is clear that the angle L is the same for both triangles, hence we only need to proof tha the sides are congruent, but in this case:
[tex]\frac{39}{30}\ne\frac{34}{27}[/tex]since the sides are not proportional, we conclude that triangles are not congruent.
urgently need help with question 30, it’s Venn diagram, is it valid or not valid & is the argument sound or not?
For statement 30:
Premise: All fruits are foods with sugar;
Premise: Chocolate bars contain sugar;
Conclusion: Chocolate bars are fruit.
Since the conclusion does not necessarily follow from the premises, this is an invalid argument, regardless of whether chocolate is fruit.
M/4 + q ; m=2/3 , and q= 1/4
Given the expression:
[tex]\frac{m}{4}+q[/tex]We will find the value of the expression when m=2/3, and q= 1/4
So,
[tex]\begin{gathered} (\frac{2}{3}\div4)+\frac{1}{4} \\ \\ =(\frac{2}{3}\times\frac{1}{4})+\frac{1}{4} \\ \\ =\frac{1}{6}+\frac{1}{4}=\frac{2}{12}+\frac{3}{12}=\frac{5}{12} \end{gathered}[/tex]So, the answer will be: 5/12